Answers
Note that the line plot or number line for the data above is given as attached.
What is the explanation for the above response?1) To create an inequality for a line plot using the given data set, we can use the minimum and maximum distances as the endpoints of the inequality.
The minimum distance is 1 3/8, which is equivalent to 1.375 miles. The maximum distance is 3 1/4, which is equivalent to 3.25 miles.
Therefore, the inequality can be written as:
1.375 ≤ x ≤ 3.25
where x represents the distance of a ski trail in miles.
This inequality states that any value of x (distance of a ski trail) that is between 1.375 and 3.25, inclusive, is a valid value for the data set.
2. The total number of ski trails is 12.
3. The difference in length between the longest ski trail (3 1/4) and the shortest ski trail (1 3/8) is: 3 1/4 - 1 3/8 = 1 7/8
4. The total length of the ski trails that are 2 7/8 is:
2 7/8 + 2 7/8 + 2 7/8 = 8 1/4
5. The sum of the lengths of the shortest (1 3/8) and the longest (3 1/4) ski trails is:
1 3/8 + 3 1/4 = 4 5/8
6. Sam is correct. The longest ski trail is 3 1/4 miles and the shortest ski trail is 1 3/8 miles, so:
3 1/4 > 3 * 1 3/8
10 1/4 > 4 1/8
2.5 > 1
Therefore, the longest ski trail is indeed more than three times the length of the shortest ski trail.
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Related Questions
Determine any data values that are missing from the table, assuming that the data represent a linear function. x y -9 3 -6 2 -3 0 a. Missing x:-2 Missing y:0 c. Missing x:-2 Missing y:2 b. Missing x:0 Missing y:1 d. Missing x:-1 Missing y:1 Please select the best answer from the choices provided
Answers
We can use the formula for the equation of a line to determine any missing values. The formula is:
�
=
�
�
+
�
y=mx+b
where $m$ is the slope of the line and $b$ is the y-intercept.
We can use the given data points to calculate the slope of the line:
�
=
change in y
change in x
=
�
2
−
�
1
�
2
−
�
1
m=
change in x
change in y
=
x
2
−x
1
y
2
−y
1
where $(x_1, y_1)$ and $(x_2, y_2)$ are any two points on the line. Let's use the points $(-9, 3)$ and $(-6, 2)$:
\begin{align*}
m &= \frac{y_2 - y_1}{x_2 - x_1} \
&= \frac{2 - 3}{-6 - (-9)} \
&= \frac{-1}{3}
\end{align*}
Now we can use the slope-intercept form of the equation of a line to determine any missing values. Let's go through each option:
a. Missing $x:-2$, Missing $y:0$
We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:
\begin{align*}
y &= mx + b \
&= -\frac{1}{3} \cdot (-2) + 3 \
&= \frac{7}{3}
\end{align*}
So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7}{3}}$.
b. Missing $x:0$, Missing $y:1$
We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-intercept:
\begin{align*}
y &= mx + b \
3 &= -\frac{1}{3} \cdot (-9) + b \
3 &= 3 + b \
b &= 0
\end{align*}
So the y-intercept is $0$. Now we can substitute $b = 0$ and $m = -\frac{1}{3}$ into the formula $y = mx + b$ to find the y-value when $x = 0$:
\begin{align*}
y &= mx + b \
&= -\frac{1}{3} \cdot 0 + 0 \
&= 0
\end{align*}
So the missing value of $y$ when $x = 0$ is $\boxed{0}$.
c. Missing $x:-2$, Missing $y:2$
We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:
\begin{align*}
y &= mx + b \
&= -\frac{1}{3} \cdot (-2) + 3 \
&= \frac{7}{3}
\end{align*}
So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7
use identities to find indicated value for each angle measure
cos theta = -5/13 , pi/12 < theta < pi find cos (2theta)
Answers
Answer:
Step-by-step explanation:
I'm a little confused where the angle is, because I don't understand English units of measurement well, but the answers must be correct!
i use formula [tex]sin^{2} \alpha + cos^{2} \alpha =1[/tex]
A survey reports that the probability a person has blue eyes is 0.10. Assume that 4 people are randomly selected at Miramar College and asked if they have blue eyes. Use the Binomial distribution.
a) Find the probability that exactly 3 of them have blue eyes. Round to 3 decimal places.
b) Find the probability that exactly 2 of them have blue eyes. Round to 3 decimal places.
c) Find the probability that at least 1 of them has blue eyes. Round to 3 decimal places.
0.344
Correct
d) Find the probability that more than 2 have blue eyes. Round to 3 decimal places.
e) Find the expected number of students out of the 4 with blue eyes. Round to 1 decimal place.
0.291
Incorrect
f) Find the variance. Round to 2 decimal places.
g) Find the standard deviation. Round to 2 decimal places.
Answers
The probability that more than 2 students have blue eyes is 0.149, the expected number of students out of the 4 with blue eyes is 0.4, the variance is 0.36, and the standard deviation is 0.6.
a) P(X = 3) = (4 choose 3) * [tex](0.10)^3 * (0.90)^1[/tex] = 0.0036
So the probability that exactly 3 of them have blue eyes is 0.0036.
b) P(X = 2) = (4 choose 2) * [tex](0.10)^2 * (0.90)^2[/tex] = 0.0386
So the probability that exactly 2 of them have blue eyes is 0.0386.
c) P(at least 1) = 1 - P(none) = 1 - [tex](0.90)^4[/tex] = 0.3439
So the probability that at least 1 of them has blue eyes is 0.344.
d) P(X > 2) = P(X = 3) + P(X = 4) = (4 choose 3) * [tex](0.10)^3 * (0.90)^1[/tex] + (4 choose 4) * [tex](0.10)^4 * (0.90)^0[/tex] = 0.0001
So the probability that more than 2 have blue eyes is 0.0001.
e) E(X) = n * p = 4 * 0.10 = 0.4
So the expected number of students out of the 4 with blue eyes is 0.4, not 0.291 as provided.
f)Var(X) = n * p * (1 - p) = 4 * 0.10 * 0.90 = 0.36
So the variance is 0.36.
g) SD(X) = sqrt(Var(X)) = sqrt(0.36) = 0.6
Standard deviation is 0.6.
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Will give thanks
trig
Answers
The distance between the two cruise ships after 2 hours is approximately 4.201 miles.
How to find distance?
To solve this problem, we need to use trigonometry to find the distance between the two cruise ships after 2 hours.
In the diagram, A and B are the two cruise ships, and D is the distance between them after 2 hours. The angle between their paths is 35 degrees.
We can use the formula: distance = speed x time
to find how far each cruise ship travels in 2 hours. For Cruise A, the distance it travels is
[tex]distance_A = 18 \times 2 = 36 \: miles[/tex]
For Cruise B, the distance it travels is
[tex]distance_B = 15 \times 2 = 30 \: miles
[/tex]
Now we can use trigonometry to find the distance between the two cruise ships. We can use the tangent function, since we know the angle and the opposite and adjacent sides of the triangle formed by the two cruise ships and the distance between them:
tan(35°) = D / (36 - 30)
Simplifying this equation, we getting,
D = (36 - 30) x tan(35°)
D = 6 x 0.7002
D ≈ 4.201 miles
Therefore, the distance between the two cruise ships after 2 hours is approximately 4.201 miles.
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A couple of two way radios were purchased from different stores. Two way radio A can reach 8 miles in any direction. Two way radio B can reach 11.27 kilometers in any direction.
Part A: How many square miles does two way radio A cover? Use 3.14 for TT and round to the nearest whole number.
B. Part A: How many square miles does two way radio B cover? Use 3.14 for TT and round to the nearest whole number.
C. If 1 mile= 1.61 kilometers, which two way radio covers the larger area?
D. Using the radius of each circle, determine the scale factor relationship between the radio coverages.
Answers
Answer:
Step-by-step explanation:
A) To find the area covered by two-way radio A, we need to calculate the area of a circle with a radius of 8 miles:
Area = πr² = 3.14 x 8² = 200.96 square miles
Rounding to the nearest whole number, two-way radio A covers 201 square miles.
B) To find the area covered by two-way radio B, we need to convert the radius from kilometers to miles and then calculate the area of a circle with that radius:
Radius in miles = 11.27 / 1.61 = 6.9988 miles (rounded to 4 decimal places)
Area = πr² = 3.14 x (6.9988)² = 153.94 square miles
Rounding to the nearest whole number, two-way radio B covers 154 square miles.
C) Two-way radio A covers a larger area than two-way radio B (201 square miles vs 154 square miles).
D) The scale factor relationship between the radio coverages can be found by dividing the radius of radio A by the radius of radio B:
Scale factor = radius of A / radius of B = 8 miles / (11.27 km / 1.61 km/mile) = 4.97
This means that the coverage of two-way radio A is almost 5 times larger than that of two-way radio B.
Less strict regulation results in many more companies obtaining the right to mine coal in Mpumalanga. At the same time, alternative energy solutions result in a decrease in the demand for coal-generated electricity. Explain how the market for coal will be affected by these changes. Clearly indicate how the equilibrium price and equilibrium quantity of coal will be affected by these changes. Make use of a combination of diagrams and verbal explanations to explain your answer.
Answers
What similarities is being shown in the figure given?
1) a a similarity
2)sss similarity
3)sas simulator
4)none
Answers
In the given figure the similarity is angle-angle property.
What are angles?An angle is the result of the intersection of two lines.
An "angle" is the length of the "opening" between these two beams.
Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.
In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.
The two primary components of an angle are the limbs and the vertex.
The joint vertex is the common terminal of the two beams.
Hence, In the given figure the similarity is angle-angle property.
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How do I do part 2 and 3?? Please show all steps of working. I have no clue how to do this!
Answers
The vector b is [10, 5, 10] and the general solution for [A|b] is [1, 5, -3] + [-3, 2, -1]s
Calculating the vector bTo find the vector b, we need to multiply the matrix A by the vector x and solve for b in the equation Ax = b.
So, we have:
[tex]\left[\begin{array}{ccc}1&3&-3&0&1&-2&3&5&-1\end{array}\right]\left[\begin{array}{c}1&1&-2\end{array}\right] &= \left[\begin{array}{c}10&5&10\end{array}\right][/tex]
Therefore, the vector b is [10, 5, 10].
Calculating the general solution for [A|b]To find the general solution of [A | b], we need to perform row reduction on the augmented matrix [A | b] and express the pivot variables in terms of the free variables.
[tex]\left[\begin{array}{ccc|c}1&3&-3&10&0&1&-2&5&3&5&-1&10\end{array}\right] &\rightarrow \left[\begin{array}{ccc|c}1&0&3&1&0&1&-2&5&0&0&0&0\end{array}\right][/tex]
The third column does not have a pivot variable, so we can express x3 in terms of the free variables.
Let s be the free variable, then we have:
x3 = -s - 3
We can now express the pivot variables in terms of s:
x1 = 1 - 3s
x2 = 5 + 2s
Thus, the general solution of [A | b] is:
[tex]\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] &= \left[\begin{array}{c}1 - 3s&5 + 2s&-s - 3\end{array}\right] \&= \left[\begin{array}{c}1&5&-3\end{array}\right] + s\left[\begin{array}{c}-3&2&-1\end{array}\right][/tex]
Therefore, the general solution of [A | b] is [1, 5, -3] + [-3, 2, -1]s
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It would have cost the family an
additional $22.70 a month to purchase
disability insurance for Camila. The
family opted out of this expense.
Assuming that you had no knowledge of
Camila's impending accident, would you
have made the same decision to not
purchase disability insurance? Explain.
Answers
Yes,I would have made the same decision to purchase disability insurance .
What is disability insurance?
Disability insurance provides financial protection in the event that you become unable to work due to an illness or injury. It can help you pay for living expenses, medical bills, and other costs while you are unable to work.
When deciding whether or not to purchase disability insurance, it's important to consider your financial situation and your ability to manage expenses if you were to become disabled. If you have a good amount of savings or other sources of income, you may be able to manage without disability insurance. However, if you rely heavily on your income to pay for living expenses and do not have significant savings, disability insurance may be a wise investment.
It's also important to consider the cost of disability insurance and whether it fits within your budget. While the additional $22.70 a month may not seem like a lot, it can add up over time. You should evaluate whether the cost of the insurance is worth the potential benefits it provides.
Ultimately, the decision to purchase disability insurance is a personal one that depends on individual circumstances and priorities. While it's impossible to predict the future, having disability insurance can provide peace of mind and financial protection in case the unexpected happens.
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Write the slope-intercept form of the equation of each line given the slope and y-
intercept.
Slope = -7, y - intercept = - 3
Answers
Answer:
y = -7x - 3
Step-by-step explanation:
The slope-intercept form of the equation of a line is:
y = mx + b where m is the slope and b is the y-intercept.
Given the slope m = -7 and the y-intercept b = -3, we can write the equation of the line in slope-intercept form as:
y = -7x - 3
Therefore, the equation of the line with slope -7 and y-intercept -3 in slope-intercept form is y = -7x - 3.
please loo at the follwng picture
Answers
Answer: I am pretty sure 7
Step-by-step explanation: I think this because 20 is the most and 13 is the leased so 20 -13 =7 but i just got done like a month or 2 ago so i just learned this so dont quote me sorry if it isn't right
large rectangle below is divided into two
smaller regions; shaded and unshaded. The area of
the whole rectangle is: 5x² + 4x - 8. The area of
the shaded region is: 2x² + 7x. What is the area of
the unshaded region?
Answers
The area of the unshaded region is 3x²-3x-8
What is area of rectangle?
A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.
The area of a rectangle is expressed as;
A = l× w
Area of the unshaded part = Area of the whole rectangle - area of shaded part
Therefore area of the unshaded part =
5x²+4x-8 -(2x²+7x)
= 5x²+4x-8 -2x²-7x
collect like terms
5x²-2x²+4x-7x-8
= 3x²-3x-8
therefore the area of the unshaded part is 3x²-3x-8
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A gardener makes a new circular flower bed. The bed is twelve feet in diameter. Calculate the circumference and the area of the circular flower bed
circumference = 6
feet, area = 36 square feet
circumference = 12
feet, area = 12 square feet
circumference = 12
feet, area = 144 square feet
circumference = 12
feet, area = 36 square feet
Answers
Answer:D=12, R=6
A=πr², C=2πr
A=36π, C=12π
A=113.04 ft²
C=37.68 ft
Y= 5x*4 tan X
Find dy/dx
Answers
[tex] \:\:\:\:\:\:\star\longrightarrow \sf \underline{y = 5\:x^4\:tanx}\\[/tex]
Differentiating with respect to x-
[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{d}{dx}\:y = \dfrac{d}{dx}\: 5\:x^4\:tanx\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}\:= 5\:\dfrac{d}{dx}\: \:x^4\:tanx\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{d}{dx}\:y =5\:\bigg[tanx\times \dfrac{d}{dx}\: \:x^4\:+x^4\times \dfrac{d}{dx} tanx\bigg]\\[/tex]
[tex]\pink{\star}\:\boxed{\sf\sf\dfrac{d}{dx}\bigg[f(x)\:g(x)\bigg] = f(x) \dfrac{d}{dx} g(x) + g(x) \dfrac{d}{dx} f(x)}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}= 5\:\bigg[tanx\times 4\:x^3+ x^4 \times sec^2x \bigg]\\[/tex]
[tex] \qquad\pink{\star}\:\:\:\:\boxed{\sf \dfrac{d}{dx}x^n=nx^{n-1}}\\[/tex]
[tex] \qquad\pink{\star}\:\:\:\:\boxed{\sf \dfrac{d}{dx}tanx=sec^2x}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}= 5\:x^3\:\bigg[4tanx+ x sec^2x \bigg]\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{\dfrac{dy}{dx}= \boxed{\sf5\:x^3\:\bigg[4tanx+ x sec^2x \bigg]}}\\[/tex]
hello!please help!then done!:)
Answers
The answer should be 2.The lower quartile of the number of absence is 2
0 is the lowest number and then 2 would be lower quartile, The 4 would be the Median or the middle of all the data 7 is the upper quartile and 10 would be the highest number of absences.
The lower quartile, also known as the first quartile, is a measure of central tendency that divides a dataset into four equal parts. It represents the point at which 25% of the data values fall below and 75% of the data values fall above. In other words, the lower quartile marks the boundary between the lowest 25% and the upper 75% of the data. It is often used in statistics to help summarize and analyze datasets, and can be helpful in identifying outliers or unusual values in the lower end of a dataset.
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Let m ∈ Real numbers[x] be a polynomial with deg m ≥ 1. Define a relation Sm on R[x] by the rule that ( f , g) ∈ S if and only if m is a factor of g − f .
(a) Prove that Sm is an equivalence relation on Real numbers[x]
(b)The division rule for polynomials implies that every equivalence class of Sm con-
tains one polynomial with a special property. What is this property?
(c) Write down a polynomial m ∈ Real numbers[x] such that the set {f ∈ Real numbers[x] : f(2) = 3} is an equivalence class of Sm. Give a brief justification
Answers
a. Sm satisfies all three properties of an equivalence relation, it is indeed an equivalence relation on Real numbers[x].
b. The equivalence class of Sm containing f is the set of all polynomials g that satisfy the condition m | (g - f).
c. The equivalence class of Sm containing the polynomial f(x) = x + 1 is the set {g ∈ Real numbers[x] : g(2) = 3}.
What is real number?Real numbers are those that can be used to calculate constant values like temperature, time, or distance. They are equivalent to countless decimal increases. They are the sum of all positive and negative integers, fractions, decimals, transcendental numbers, and irrational numbers.
(a) To prove that Sm is an equivalence relation on Real numbers[x], we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.
Reflexivity: For any polynomial f ∈ Real numbers[x], we have f − f = 0, which is clearly a multiple of any polynomial m. Therefore, (f, f) ∈ Sm for all f ∈ Real numbers[x], and Sm is reflexive.
Symmetry: If (f, g) ∈ Sm, then m is a factor of g − f. This means that there exists a polynomial q ∈ Real numbers[x] such that g − f = mq. It follows that f − g = −mq, which is a multiple of m. Therefore, (g, f) ∈ Sm, and Sm is symmetric.
Transitivity: If (f, g) ∈ Sm and (g, h) ∈ Sm, then m is a factor of g − f and m is a factor of h − g. This means that there exist polynomials q1 and q2 ∈ Real numbers[x] such that g − f = mq1 and h − g = mq2. It follows that h − f = (h − g) + (g − f) = mq2 + mq1 = m(q2 + q1). Therefore, m is a factor of h − f, and (f, h) ∈ Sm. Thus, Sm is transitive.
Since Sm satisfies all three properties of an equivalence relation, it is indeed an equivalence relation on Real numbers[x].
(b) The division rule for polynomials states that for any polynomials f and g with g ≠ 0, there exist unique polynomials q and r such that f = qg + r and deg r < deg g. The equivalence class of Sm containing f is the set of all polynomials g that satisfy the condition m | (g - f).
Applying the division rule for polynomials to the polynomial g - f, we can write it as g - f = mq + r, where deg r < deg m. This means that g - r = f + mq, and therefore, any polynomial in the equivalence class of Sm containing f can be written as g = r + f + mq, where deg r < deg m. In other words, every equivalence class of Sm contains a polynomial of the form r + f + mq, where r is a polynomial of degree less than deg m.
(c) Let m(x) = x - 2. Then for any polynomial f(x) ∈ Real numbers[x], we have (f, g) ∈ Sm if and only if g(x) - f(x) is a multiple of x - 2. This means that g(2) - f(2) = 0, or in other words, f(2) = g(2). Therefore, the equivalence class of Sm containing the polynomial f(x) = x + 1 is the set {g ∈ Real numbers[x] : g(2) = 3}.
Justification: Let g(x) = (x - 2) + 3. Then g(2) = 3, and g(x) - f(x) = (x - 2) + 3 - (x + 1) = x - 2, which is a multiple of x - 2. Therefore, (f, g) ∈ Sm, and the set {g ∈ Real numbers[x] : g(2) = 3} is an equivalence class of Sm.
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When do we write in2 in or in3
Answers
Answer:
Use in² for area; use in³ for volume.
Explanation:
When you calculate the area of a rectangle, you multiply length times width. Both units are in inches so:
inches × inches = (inches)² or in²
When you calculate the volume of a box (rectangular prism), you multiply length by width by height. All three units are in inches so:
inches × inches × inches = (inches)³ or in³
Graph the following inequality on the sketchpad below. Be sure to shade in the correct
area on the graph.
x<-3
Answers
According to the information to graph the inequality we have to show a number line with an open circle at -3 and an arrow pointing to the left, with the shaded region to the left of -3 labeled as x < -3.
How to graph the inequality?To graph the inequality x < -3, we need to draw a number line and mark the point -3 on it. Since the inequality is "less than," we want to shade the region to the left of -3 on the number line.
We start by drawing a horizontal line with a labeled point for -3. Then we draw an arrow to the left of -3, to indicate that all the values to the left of -3 satisfy the inequality.
Here are the steps to graph the inequality on the sketchpad:
Open the sketchpad or a graphing tool that can plot a number line.Draw a horizontal line and mark the point -3 on it.Draw an arrow to the left of -3 to indicate that all the values to the left of -3 satisfy the inequality.Shade in the region to the left of -3 to indicate the solution set of the inequality.Label the shaded region with the inequality x < -3.The resulting graph should show a number line with an open circle at -3 and an arrow pointing to the left, with the shaded region to the left of -3 labeled as x < -3.
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julie asked her friends how many hours per week they read for fun. she got the following answers: 1/2, 1/2, 2 1/2, 4 1/2, 7, and 12. what is the median amount of time julies friend spend reacding each week?
Answers
The median amount of time Julie's friends spend reading each week is 3 1/2 hours, which is the average of the two middle values when the given values are arranged in order.
To find the median value, we first need to put the given values in order from smallest to largest. The given values are: 1/2, 1/2, 2 1/2, 4 1/2, 7, and 12. When we arrange them in order, we get:
1/2, 1/2, 2 1/2, 4 1/2, 7, 12
The median is the middle value of the ordered list. If there is an odd number of values, the median is simply the middle value. However, in this case, we have an even number of values. Therefore, we take the average of the two middle values to find the median. The two middle values are 2 1/2 and 4 1/2. So, the median is:
(2 1/2 + 4 1/2)/2 = 3 1/2
This means that half of Julie's friends read for more than 3 1/2 hours per week and half of them read for less than 3 1/2 hours per week.
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Can someone please help with this ?!!! 30 points
Answers
The total surface area of a cube is given by the formula:
SA = 6s^2
where s is the side length of the cube. In this case, s = 3 centimeters.
To find the surface area of each face of the cube, we need to calculate the surface area of a single dot and then multiply by the number of dots on each face. The surface area of a single dot is the surface area of a hemisphere, which is given by:
SA = 2πr^2
where r is the radius of the hemisphere. In this case, r = 0.1 centimeters.
So the surface area of a single dot is:
SA = 2π(0.1)^2 = 0.0628 square centimeters
Each face of the cube has one dot, so the total surface area contributed by the dots on each face is 0.0628 square centimeters.
Now we can calculate the total surface area of the cube:
SA = 6s^2 = 6(3)^2 = 54 square centimeters
Therefore, the surface area of the cube is 54 square centimeters.
Please help me with this
Answers
The area of the square is equal to 64 square units.
How to determine the area of the square related to a circle
In this problem we find the representation of a geometric system formed by a circle and a square and we must compute the area of the latter figure. First, find the side length of the square by Pythagorean theorem:
10² = (2 · x)² + (1.5 · x)²
100 = 4 · x² + 2.25 · x²
100 = 6.25 · x²
x² = 16
x = 4
Second, compute the area of the square:
A = (2 · 4)²
A = 64
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Find the value of each variable and round to the nearest tenth. Can anyone help me pls????
Answers
Answer:
9) x = 12 cm
10) x = 10.4 ft (Rounded)
11) y = 39.7 in (Rounded)
Step-by-step explanation:
Just use Pythagorean theorem
Answer and Explanation:
We can solve for x in these questions using the Pythagorean Theorem:
a² + b² = c²,
where a and b are the legs (shorter sides) of a right triangle, and c is its hypotenuse (longest side).
Applying this theorem to the problems at hand:
9. We are using (10 / 2) as one of the legs.
(10 / 2)² + x² = 13²
↓ simplifying division
5² + x² = 13²
↓ subtracting 5² from both sides
x² = 13² - 5²
↓ simplifying the right side
x² = 169 - 25
x² = 144
↓ taking the square root of both sides
x = 12
10.
6² + x² = 12²
↓ subtracting 6² from both sides
x² = 12² - 6²
↓ simplifying the right side
x² = 144 - 36
x² = 108
↓ taking the square root of both sides
x = [tex]\sqrt{108}[/tex]
↓ simplifying the square root
[tex]\sqrt{108} = \sqrt{3 \cdot 3 \cdot 3 \cdot 2 \cdot 2} = (3\cdot 2)\sqrt{3} = 6\sqrt3[/tex]
x = 6[tex]\sqrt3[/tex]
11.
24² + 33² = y²
↓ simplifying the right side
576 + 1089 = y²
1665 = y²
↓ taking the square root of both sides
y = [tex]\sqrt{1665}[/tex]
↓ simplifying the square root
[tex]\sqrt{1665} = \sqrt{3 \cdot 3 \cdot 5 \cdot 37} = 3\sqrt{5 \cdot 37} = 3\sqrt{185}[/tex]
y = 3[tex]\sqrt{185}[/tex]
Test the equation for symmetry. Need 3 tests for symmetry or else it’s incorrect.
Answers
the equation [tex]r = 3 - 3cos(\theta)[/tex] is symmetric with respect to the vertical line but not with respect to the origin or the pole .
What is the trigonometric functions ?Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides.
The equation r = 3 - 3cos(θ) represents a polar curve, where r is the distance from the origin to a point on the curve, and θ is the angle between the positive x-axis and the line connecting the origin to the point.
1. Symmetry with respect to the origin: A curve is symmetric with respect to the origin if replacing (r, θ) with (-r, θ + π) gives the same curve. Substituting -r for r and θ + π for θ in the equation, we get:
[tex]-r = 3 - 3cos(\theta + \pi)[/tex]
[tex]-r = -3 - 3cos(\theta)[/tex]
[tex]r = 3 + 3cos(\theta)[/tex]
This is not the same as the original equation, so the curve is not symmetric with respect to the origin.
2.Symmetry with respect to the pole (x-axis): A curve is symmetric with respect to the pole if replacing (r, θ) with (r, -θ) gives the same curve. Substituting -θ for θ in the equation, we get:
[tex]r = 3 - 3cos(-\theta)[/tex]
[tex]r = 3 + 3cos(\theta)[/tex]
This is not the same as the original equation, so the curve is not symmetric with respect to the pole.
3.Symmetry with respect to the vertical line (y-axis): A curve is symmetric with respect to the vertical line if replacing (r, θ) with (-r, π - θ) gives the same curve. Substituting -r for r and π - θ for θ in the equation, we get:
[tex]-r = 3 - 3cos(π - \theta)[/tex]
[tex]-r = -3 + 3cos(\theta)[/tex]
[tex]r = 3 - 3cos(\theta)[/tex]
This is the same as the original equation, so the curve is symmetric with respect to the vertical line (y-axis).
Therefore, the equation [tex]r = 3 - 3cos(\theta)[/tex] is symmetric with respect to the vertical line (y-axis) but not with respect to the origin or the pole (x-axis).
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The graph of r = 3 - 3cos(theta) is symmetric about the x-axis but not about the origin or about the y-axis.
What is the symmetry of the equation?Symmetry is described in geometry as a balanced and proportionate likeness seen in two sides of an object. It signifies that one side is a mirror image of the other. The line of symmetry is the imaginary line or axis along which you can fold a figure to obtain the symmetrical halves.
The symmetry equation is r = 3 -3 cosФ depicts a cardioid-shaped polar graph. We can use the following tests to determine symmetry:
1) We can test for symmetry with regard to the origin by seeing if the equation remains the same after substituting r with -r and Ф with Ф + pi.
r = 3 - 3cosФ - r = 3 - 3cos(Ф + pi)
3 - 3(-cos(Ф)) = r
-r = 3 + 3cos(Ф)
Because this is not equal to the original equation, the graph is not symmetric about the origin.
2) Symmetry with respect to the x-axis: We may test for symmetry with respect to the x-axis by seeing if the equation stays unchanged when theta is replaced with -theta.
r = 3 - 3cos(Ф)
r = 3 - 3cos(-Ф)
r = 3 - 3cos(Ф)
This is the same as the original equation, hence the graph is symmetric about the x-axis.
3) Symmetry with respect to the y-axis: We may test for symmetry with respect to the y-axis by seeing if the equation stays unchanged when theta is replaced with pi - theta.
r = 3 - 3cos(Ф)
r = 3 - 3cos(pi - Ф)
r = 3 + 3cos(Ф)
Because this is not equal to the original equation, the graph is not symmetric about the y-axis.
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A store is having a sale with 45% off every item. Which numbers are equivalent to 45%? Select TWO correct answers. 1 45 9 20 2²/²3 5 45 100 20 4/1/2
Answers
Answer:
45/100, 0.45, 9/20
Step-by-step explanation:
Answer 1: A percentage is part of a number is written in hundredths. Thus, 45% is the same as 45/100
Answer 2: To convert 45% to a decimal, you can rewrite 45% as 45.0%. Then, you can move the decimal two places to the left, which is the same as dividing by 100. You can also do standard division and you'll find the 45 divided by 100 = 0.45
Answer 3: 45/100 is not the simplest form of this fraction. To simplify, we must find the greatest common factor of the numerator (45) and the denominator (100). Both of these numbers can be divided evenly by 5 so 5 is the GCF of the two numbers.
Now, we divide both numbers by 5 to simplify the fraction:
45 / 5 = 9 and 100 / 5 = 20. Thus, 45/100 reduces down to 9/20
Select any of the two answers available on your worksheet (if I'm reading what you wrote correctly, it seems like the two answer choices they provided were 9/20 and 45/100
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Match the description table or graph or equation with the correct type of function
A. Linear function table
B. Non linear function graph
C. Linear function equation
D. Non linear function equation
E. Linear function graph
F. Non linear function table
Answers
The description table or graph or equation with the correct type of function:
Linear function table: A
Non-linear function graph: B
Linear function equation: C
Non-linear function equation: D
Linear function graph: E
Non-linear function table: F
What is function?A function is a mathematical concept that describes a relationship between two sets of values, where each input value (independent variable) corresponds to exactly one output value (dependent variable). In other words, a function is a rule or a formula that takes an input value and produces a unique output value.
Here,
The table of values shows a constant rate of change, which indicates a linear function. We can verify this by calculating the slope between any two points, which should be the same. For example, the slope between (-2, -8) and (2, 0) is (0 - (-8))/(2 - (-2)) = 8/4 = 2. So the function is of the form y = mx + b, where m = 2 and b = -4. This gives us the equation y = 2x - 4, which is a linear function. Therefore, the correct match is A.
The graph shows a curve, which indicates a non-linear function. It does not resemble a straight line, so we can eliminate linear functions. The shape of the graph suggests that it might be a quadratic function, which has a U-shaped curve. Quadratic functions can be represented by an equation of the form y = ax² + bx + c. We can't determine the equation of the function from the graph alone, but we can conclude that it is a non-linear function. Therefore, the correct match is B.
The equation 3x - 4y = 27 can be rearranged to solve for y in terms of x: y = (3/4)x - (27/4). This equation is of the form y = mx + b, where m = 3/4 and b = -27/4, which indicates a linear function. Therefore, the correct match is C.
The equation 3x² - 2x = 4y is a quadratic equation, which has a variable raised to the second power. Quadratic functions are non-linear, so the correct match is D.
The graph shows a straight line, which indicates a linear function. We can determine the equation of the line by finding the slope and y-intercept. The slope is (5 - (-1))/(2 - (-2)) = 6/4 = 3/2, and the y-intercept is -1. So the equation of the line is y = (3/2)x - 1, which is a linear function. Therefore, the correct match is E.
The table of values does not show a constant rate of change, which indicates a non-linear function. For example, between x = -2 and x = -1, y changes by 5, but between x = 0 and x = 1, y changes by only 1. This suggests that the function is not linear. We can't determine the exact form of the function from the table alone, but we can conclude that it is a non-linear function. Therefore, the correct match is F.
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You are setting up a home saloon for which you have Rs.53000. Out of your budget, you can spend 15% on furniture. You are planning to order all skin care products and cosmetics from an online store “Makeup4uonline.” Your cosmetics bill accounts for 15% of total bill which is 25% of the budget. Appliances purchased are 15% of your budget at 20% discount. For electric works, vendor charges are 5% of your total budget which is 12% of your wall décor and lights. You are required to calculate all amounts for following heads: •1. Skin care products •2. Wall décor and lights •3. Rate of Discount to total budget •4. Any leftover amount for covid-19 safety measures. •5. Rate of leftover amount to total budget
Answers
Answer: Let's break down the budget into different categories:
Furniture: 15% of the budget
15% of Rs. 53000 = Rs. 7950
So you can spend Rs. 7950 on furniture.
Cosmetics: 25% of the budget
25% of Rs. 53000 = Rs. 13250
So your cosmetics bill from Makeup4uonline is Rs. 13250.
Appliances: 15% of the budget at 20% discount
15% of Rs. 53000 = Rs. 7950
The appliances are at a 20% discount, so you only need to pay 80% of the price:
80% of Rs. 7950 = Rs. 6360
So you can spend Rs. 6360 on appliances.
Electric works: 5% of the total budget which is 12% of wall décor and lights
12% of the budget = 12/100 x Rs. 53000 = Rs. 6360
5% of the budget = 5/100 x Rs. 53000 = Rs. 2650
So you can spend Rs. 6360 on wall décor and lights, and Rs. 2650 on electric works.
Leftover amount for COVID-19 safety measures
The total amount spent so far is:
Rs. 7950 + Rs. 13250 + Rs. 6360 + Rs. 2650 = Rs. 30110
So the leftover amount for COVID-19 safety measures is:
Rs. 53000 - Rs. 30110 = Rs. 22890
Rate of leftover amount to total budget
The rate of leftover amount to total budget is:
(Rs. 22890 / Rs. 53000) x 100% = 43.2%
So 43.2% of the total budget is leftover for COVID-19 safety measures.
Step-by-step explanation:
A patient reports taking three teaspoons of a liquid medication every four hours at home. How should the total daily amount of this medication be documented using the metric system?
Answers
To document the total daily amount of liquid medication using the metric system, we need to convert teaspoons to milliliters, which is the standard unit of volume in the metric system.
One teaspoon is equal to approximately 5 milliliters, so three teaspoons would be equal to 15 milliliters.
If the patient is taking 15 milliliters every four hours, then they would be taking the medication 6 times a day (24 hours divided by 4 hours per dose).
Therefore, the total daily amount of the medication would be:
15 milliliters per dose x 6 doses per day = 90 milliliters per day
So, the total daily amount of the liquid medication should be documented as 90 milliliters per day in the patient's medical records using the metric system.
write a rule that relates the number of months to the cost of a gym membership. What is the cost of a 1 year membership?
Sign up fee: $25
Then pay just $15 each month!
Answers
Answer:
Step-by-step explanation:
The rule that relates the number of months (m) to the cost (c) of a gym membership is:
c = 15m + 25
To find the cost of a 1 year (12 months) membership, we substitute m = 12 into the equation:
c = 15(12) + 25 = 205
Therefore, the cost of a 1 year membership is $205 (which includes the $25 sign up fee).
The coordinates at the end of
the diameter of a circle are
(-2,1) and (4,3). Find the
equation of the circle.
Answers
Answer:
Step-by-step explanation:
Center of circle will be at the midpoint of (-2,1) and (4,3):
[tex]M=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
[tex]=(\frac{-2+4}{2} ,\frac{1+3}{2} )[/tex]
[tex]=(1,2)[/tex]
Radius will be distance from circle center (1,2) to edge (4,3):
[tex]r=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2 }[/tex]
[tex]=\sqrt{(4-1)^2+(3-2)^2 }[/tex]
[tex]=\sqrt{3^2+1^2 }[/tex]
[tex]=\sqrt{10}[/tex]
Equation of circle with center (1,2) and radius [tex]\sqrt{10}[/tex]:
[tex](x-h)^2+(y-k)^2=r^2[/tex] center (h,k) radius r
[tex](x-1)^2+(y-2)^2=\sqrt{10}^2[/tex]
[tex](x-1)^2+(y-2)^2=10[/tex]
SOLUTION: [tex](x-1)^2+(y-2)^2=10[/tex]
solve the equation for exact solution in interval [0 degree , 360 degree)
(cot theta-1)(2sin theta +square root 3)=0
Answers
Answer: We can start by using the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.
So, we can set each factor equal to zero and solve for theta:
Factor 1: cot(theta) - 1 = 0
Using the identity cot(theta) = cos(theta) / sin(theta), we can rewrite this as:
cos(theta) / sin(theta) - 1 = 0
cos(theta) - sin(theta) = 0
cos(theta) = sin(theta)
Dividing both sides by cos(theta), we get:
tan(theta) = 1
The solutions to this equation are theta = 45 degrees and theta = 225 degrees (since tangent is positive in the first and third quadrants).
Factor 2: 2sin(theta) + sqrt(3) = 0
Subtracting sqrt(3) from both sides and dividing by 2, we get:
sin(theta) = -sqrt(3)/2
The solutions to this equation are theta = 240 degrees and theta = 300 degrees (since sine is negative in the third and fourth quadrants, and sin(240) = sin(300) = -sqrt(3)/2).
Therefore, the exact solutions in the interval [0 degrees, 360 degrees) are:
theta = 45 degrees, 225 degrees, 240 degrees, 300 degrees.
Step-by-step explanation: