Answer: We can use the fact that the sine function is an odd function, which means that:
sin(-x) = -sin(x)
So, we have:
sin(-15 degrees) = -sin(15 degrees)
We can use the sum and difference identity for sine, which states that:
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
Letting a = 45 degrees and b = 30 degrees, we get:
sin(45 degrees - 30 degrees) = sin(45 degrees)cos(30 degrees) - cos(45 degrees)sin(30 degrees)
We can use the fact that cos(45 degrees) = sin(45 degrees) = √2 / 2 and cos(30 degrees) = √3 / 2 and sin(30 degrees) = 1 / 2 to simplify:
sin(15 degrees) = (√2 / 2)(√3 / 2) - (√2 / 2)(1 / 2)
sin(15 degrees) = (√6 - √2) / 4
Therefore, we have:
sin(-15 degrees) = -sin(15 degrees) = -[(√6 - √2) / 4] = (-√6 + √2) / 4
So the exact value of sin(-15 degrees) is (-√6 + √2) / 4.
Step-by-step explanation:
Solve the simultaneous equations
X-Y=-1
2X-Y=0
Answer: X = 1, Y = 2
Step-by-step explanation:
X - Y = -1
X = Y - 1
2(Y - 1) - Y = 0
2Y - 2 - Y = 0
Y - 2 = 0
Y = 2
X - (2) = -1
X - 2 = -1
X = 2 - 1
X = 1
If the sin 90° = 1, then which statement is true?
cos 0° = 1, because the angles are complements
cos 90° = 1, because the angles are supplements
cos 0° = 0, because the angles are complements
cos 90° = 0, because the angles are supplements
The statement "cos 0° = 1, because the angles are complements" is true.
A portfolio has a value P(E, S), so that the value P is a function of E, the price of a Euro in Canadian dollars, and S, the level of the TSX stock index. Presently the portfolio is worth $207,000, while a Euro is $1.50 Canadian, and the index is S = 18,000. If the partial derivatives of P have values ∂P ∂E = 80,000, and ∂P ∂S = −20, what approximately will the portfolio value be if the price of a Euro goes down by 0.07 and the stock index goes down by 629?
Answer:
The new value of the portfolio would be $207,000 - $18,180 = $188,820
Step-by-step explanation:
Using the first-order partial derivatives, we can calculate the approximate change in the portfolio value due to changes in E and S using the formula:
ΔP ≈ ∂P/∂E * ΔE + ∂P/∂S * ΔS
where ΔE is the change in the price of a Euro and ΔS is the change in the TSX stock index.
Given that ∂P/∂E = 80,000 and ∂P/∂S = -20, and the changes ΔE = -0.07 and ΔS = -629, we can plug in the values and get:
ΔP ≈ 80,000 * (-0.07) + (-20) * (-629)
≈ -5,600 - 12,580
≈ -18,180
Therefore, the portfolio value is expected to decrease by approximately $18,180 if the price of a Euro goes down by $0.07 and the TSX stock index goes down by 629 points. The new value of the portfolio would be $207,000 - $18,180 = $188,820.
HELP PLS I GIVE BRAINLIEST
Step-by-step explanation:
The density of gold is given as 5×2^2 grams/cm³, which means that one cubic centimeter of gold has a mass of 5×2^2 grams.
To find the mass of 8 × 25 cm³ of gold, we need to first find the total volume of gold:
Total volume = 8 × 25 cm³ = 200 cm³
Now we can use the density of gold to find the mass:
Mass = Density × Volume
Mass = (5×2^2 grams/cm³) × 200 cm³
Mass = 5 × 4 × 200 grams
Mass = 4000 grams
Therefore, the mass of 8 × 25 cm³ of gold is 4000 grams.
Dylan and Eric were the lead scorers in a basketball game. Dylan scored p points in the second period of the game. Eric scored as many points as Dylan in the same period of the game. a) Write an expression for Eric's score in terms of p. points b) If Dylan scored 18 points in the second period, how many points did Eric score?
I think the answers 3048_&8_9_)_)_
PLEASE HELPP!!! MIDDLE SCHOOL MATH!!!!!!!
In the figure shown, m∠2 is 16 more than 3 times m∠1. Find the measure of each angle.
PLEASE LOOK AT PICTURE BELOW!!!!!! SHOW WORK PLEASEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
m∠1 = 41°
m∠2 = 139°
Step-by-step explanation:
Set variables:
1. ∠1 = x
2. ∠2 = y
Make first equation:
It says "m∠2 is 16 more than 3 times m∠1."
So let's convert that into an equation:
y = 16° + 3x
Now, by looking at the photo, we can tell that its a straight line, which is equal to 180°
Derived from that, we can get m∠1 + m∠2 = 180°, which in other "words" is x + y = 180°.
Great, now we have our 2 equations, and we just have to solve.
Equations:
1. y = 16° + 3x
2. x + y = 180°
Let's substitute what we have for y into the second equation:
x + (16° + 3x) = 180°
Solve:
(We can take out parentheses because it's a "+" sign)
Combine like terms:
4x + 16° = 180°
Subtract 16° from both sides
4x = 164°
Isolate x by dividing both sides by 4
x = 41°
Substitute:
Now that we have x = 41°, we can substitute that in for the equation - "y = 16° + 3x"
New Equation:
y = 16° + 3(41°)
Solve:
Multiply 3 and 41°, which is 123°
y = 16° + 123°
Simplify:
y = 139°
Reminder:
m∠1 = x
m∠2 = y
Therefore,
m∠1 = 41°
&
m∠2 = 139°
Hopefully this helps!
(If you want, please mark me brainliest tomorrow)
Answer:
Basically, a straight line is equal to 180 degrees. If angle 2 is 16 more than 3 times angle 1, we get the equation of y = 16 + 3x. Put them together and you get x + 16 + 3x = 180. Then you just solve, and get x = 41. Then you put x in for the other equation and get y = 139.
The mean weight of an adult is 79 kilograms with a standard deviation of 10 kilograms. If 188 adults are randomly selected, what is the probability that the sample mean would be greater than 80.5 kilograms? Round your answer to four decimal places.
The average adult weight is 79 kilοgrammes, with a standard deviatiοn οf 10 kilοgrammes.
We want tο find the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams.
An n-sample sample mean is given by: x = xi / n
where xi is the tοtal οf the sample's individual weights.
The sample mean distributiοn is apprοximately nοrmal, with mean = 79 and standard deviatiοn [tex]= 10 /\sqrt{(n)} = 10 / \sqrt{(188)0.727.}[/tex]
We can standardise the sample mean tο find the prοbability that it is greater than 80.5 kilοgrammes using the fοrmula: [tex]z = (x - ) / ( / \sqrt{(n)})[/tex]
where z is the standard nοrmal variable.
Substituting the values, we get:
[tex]z = (80.5 - 79) / (10 / \sqrt{(188)}) \approx2.14[/tex]
Using a standard nοrmal table οr calculatοr, we can find the prοbability that z is greater than 2.14:
P(z > 2.14) ≈ 0.0161
Therefοre, the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams is apprοximately 0.0161, rοunded tο fοur decimal places.
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The average annual cost (in dollars) of tuition and fees at a 2 -year college for selected years is shown in the given table, where year 0 represents 2004. The data can be approximated by the equation y=83.66x+3915 . Predict the average annual cost in 2014 to the nearest dollar.
The average annual cοst in 2014 is $4751.6.
What is equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equatiοn that represent the annual cοst in dοllars.
=> y = 83.66x+3915
Where x= number οf years
In 2004 , t = 0 years
Sο , In 2014 , t = 2014-2004 = 10 years.
Then average annual cοst in 2014 is,
=> y=83.66(10)+3915
=> y=836.6+3915
=> y = $4751.6.
Hence the average annual cοst in 2014 is $4751.6.
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The probability that a Caucasian person in the U.S. has AB- blood is 1%. Four unrelated Caucasian people in the U.S. are selected at random. Find the probability that none of the 4 have AB- blood.
The probability that none of the four unrelated Caucasian people in the U.S. have AB- blood is approximately 0.9606 or 96.06%.
The problem states that the probability that a Caucasian person in the U.S. has AB- blood is 1%. This means that the probability of a Caucasian person not having AB- blood is 1 - 0.01 = 0.99.
The problem asks to find the probability that none of the four unrelated Caucasian people have AB- blood. Since we are assuming that the blood types of the four people are independent, we can multiply the probabilities of each person not having AB- blood to find the probability that none of them have AB- blood.
Using the multiplication rule of probability, we can calculate the probability of no AB- blood as:
P(No AB- in 4) = P(Not AB-) * P(Not AB-) * P(Not AB-) * P(Not AB-)
P(No AB- in 4) = 0.99 * 0.99 * 0.99 * 0.99
P(No AB- in 4) = 0.9606
Therefore, the probability that none of the four unrelated Caucasian people in the U.S. have AB- blood is approximately 0.9606 or 96.06%. This means that there is a high likelihood that none of the four people have AB- blood.
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Vary the plane of intersection, and note all the types of cross sections you observe. In the table, describe the shape of the cross section formed when a particular plane passes through the pyramid.
Answer:
Cross Sections
In this task, you will use cross section flyer, an online tool, to investigate the cross sections of cones, cylinders, pyramids, and prisms by passing different planes through such objects.
For each part of this task, you will select a three-dimensional object from the list of shapes in the bottom-left corner of the screen. A three-dimensional view of the object appears on the left, and the two-dimensional cross section formed by the intersection of the object with the chosen plane appears on the right. The bottom-right controls allow you to rotate and move the plane of intersection. By varying the intersecting plane, you can change the resulting cross section.
You can also adjust the view of the three-dimensional object by clicking and dragging anywhere inside the object window. Use the coordinate X-Y-Z axes to guide you through the views. You can verify the name of a cross section by using the Click to show identification of cross section checkbox.
(3- 2x + 2x²) - (4x -5 +3x²)
Answer:
−x2−6x+8
Step-by-step explanation:
1,Rearrange terms
2.Distribute
3.Add the numbers
4.combine like terms
hope this helps i lfet some steps for you!!!<3333
A circle with equation (x + 2 )^2 + (y – 3 )^2 = 16 is graphed on the coordinate plane. Which represents the line of tangency at the point (–6, 3)?
The line of tangency at the point (–6, 3) is x = -6. So, the correct option is (b).
What is tangent?
In geometry, the tangent is a trigonometric function that relates to the angles and sides of a right triangle. Specifically, the tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side.
To find the line of tangency to a circle at a given point, we need to first find the slope of the radius that passes through that point, and then take the negative reciprocal of that slope to get the slope of the tangent line.
Given the circle equation: (x + 2)² + (y - 3)² = 16, we can see that its center is at the point (-2, 3) and its radius is 4.
To find the slope of the radius passing through the point (-6, 3), we can use the point-slope formula:
(y - y1) = m(x - x1)
where m is the slope of the radius, and (x1, y1) is the center of the circle (-2, 3). Plugging in the values, we get:
(y - 3) = m(x + 2)
Substituting the point (-6, 3) into the equation, we get:
(3 - 3) = m((-6) + 2)
0 = -4m
m = 0
So the slope of the radius is 0. To find the slope of the tangent line, we take the negative reciprocal of the slope of the radius:
slope of tangent line = -1/0 = undefined
Since the slope of the tangent line is undefined, it must be a vertical line passing through the point (-6, 3). Thus, the line of tangency at the point (-6, 3) is the vertical line x = -6.
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(2x-3)+[2(2x^2-3x+1)]
Answer:4x^2-4x-1
Step-by-step explanation:
Part B What is the recursive formula for the sequence 8, 10, 12.5, 15.625
Answer:
Step-by-step explanation:
The given sequence can be written as:
a_1 = 8
a_2 = 10
a_3 = 12.5
a_4 = 15.625
To find the recursive formula, we need to find the common ratio (r) between consecutive terms:
r = a_2 / a_1 = 10 / 8 = 1.25
r = a_3 / a_2 = 12.5 / 10 = 1.25
r = a_4 / a_3 = 15.625 / 12.5 = 1.25
Since the common ratio is constant, we can use the formula for a geometric sequence to find the recursive formula:
a_n = r * a_{n-1}
Substituting r = 1.25 and a_1 = 8, we get:
a_n = 1.25 * a_{n-1}
Therefore, the recursive formula for the given sequence is:
a_n = 1.25 * a_{n-1}, with a_1 = 8.
Find the area and the circumference of a circle with a radius of 2km. Write your answers in terms of pi, and be sure to include the correct units in your answers.
The area and the circumference of the circle would be 4π square kilometers and 4π kilometers respectively.
Area and circumference of a circleThe area of a circle with a radius r is given by:
A = πr^2The circumference of a circle with a radius r is given by:
C = 2πr.Given that the radius of the circle is 2km, we can substitute r = 2 into these formulas to find the area and circumference:
Area = πr^2 = π(2km)^2 = 4π km^2Circumference = 2πr = 2π(2km) = 4π kmIn other words, the area and the circumference of the circle are 4π square kilometers and 4π kilometers respectively.
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models the
A 25% orange juice drink is mixed with a 100% orange juice drink. The function f(x) (4)(1.0)+z(0.25)
=
concentration of orange juice in the drink after a gallons of the 25% drink are added to 4 gallons of pure juice.
4+z
What will be the concentration of orange juice in the drink if 2 gallons of 25% drink are added? Give the answer as a percent
but do not include the percent sign (%).
The amount of citrus juice in the combination is therefore 0.75, or 75%.
A volume basic meaning is what?The area filled within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's potential.
If 2 gallons of 25% orange juice drink are added to 4 gallons of pure orange juice, then the total volume of the mixture will be 2 + 4 = 6 gallons.
Let's use the given function f(x) to calculate the concentration of orange juice in the mixture:
f(2) = (4 × 1.0 + 2 × 0.25) / (4 + 2)
= (4 + 0.5) / 6
= 4.5 / 6
= 0.75
Therefore, the concentration of orange juice in the mixture is 0.75 or 75%.
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16. Find the difference 4/9 - ⅖
17. Find the quotient 2/9 / ⅚
18. Write each terminating decimal as a quotient of integers. (a) 0.437 (b) 8.2
19. Use the method below to decide whether each rational number would yield a repeating or a terminating decimal.
(Hint: Write in lowest terms before trying to decide.)
Terminating decimal - if the only prime factor of the denominator is 2 or 5 or both.
Repeating decimal - if a prime other than 2 or 5 appears in the prime factorization of the denominator.
Example: 24/75 can be simplified to 8/25 by dividing 3 into both the numerator and the denominator. Next, factor the denominator 25 using prime factors: 25 = 5x5, the only prime factor of the denominator is 5 in this case, so the original fraction is a Terminating decimal
(a) 8/15
Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)
(b) 8/35 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)
(c) 13/125 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)
(d) 3/24 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)
(e) 22/55 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)
(f)) 24/75 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)
1 ) Finding the difference 4/9 - ⅖:
We require a common denominator to subtract fractions. The least frequent multiple of 9 and 5 in this example is 45. So we'll recast both fractions with 45 as the denominator:
[tex]\frac{4}{9} = \frac{20}{45} \\\frac{2}{5} = \frac{18}{45}[/tex]
Now we can subtract:
[tex]\frac{20}{45} - \frac{18}{45} = \frac{2}{45}[/tex]
Therefore, the difference between 4/9 and ⅖ is 2/45.
How will you find if the fraction is terminating or repeating?Examine the prime factors of the denominator when the fraction is in its simplest elementary form to determine if it will have a terminating or repeating decimal. The decimal will end if they are made up of 2s and/or 5s.
2) calculating the quotient 2/9 / ⅚:
Fractions are divided by multiplying the first fraction by the reciprocal of the second fraction. So:
2/9 ÷ ⅚ = 2/9 x 6/5
Before multiplying, we can simplify:
2/9 x 6/5 = 12/45
And here's another example:
12/45 = 4/15
As a result, the quotient of 2/9 56 is 4/15.
3) Writing each terminating decimal as an integer quotient:
(a) 0.437 = 437/1000
(b) 8.2 = 82/10 = 41/5
4) Choosing whether each rational number will result in a repeated or terminating decimal:
(a) 8/15
Yes, the fraction is simplified.
The simplified denominator contains factors 2 0r 5.
It is a terminating decimal.
(b) 13/125
Yes, the fraction is simplified.
The simplified denominator contains factors other than 2 or 5.
It is a repeating decimal.
(c) 8/35
Yes, the fraction is simplified.
The simplified denominator contains factors other than 2 or 5.
It is a repeating decimal.
(d) 3/24
Yes, the fraction is simplified.
The simplified denominator contains factors other than 2 or 5.
It is a repeating decimal.
(e) 22/55
Yes, the fraction is simplified.
The simplified denominator contains factors other than 2 or 5.
It is a repeating decimal.
(f) 24/75
No, the fraction is not simplified.
The simplified fraction is = 8/25
The simplified denominator contains factors 2 or 5.
It is a terminating decimal.
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A 5 m ladder reaches 4.7 m up a wall. What angle does the ladder make with the wall?
The ladder makes an angle of approximately 19.94 degrees with the wall.
Calculating the angle of the ladder up on the wallWe can use trigonometry to solve for the angle between the ladder and the wall.
Let's call the angle we're looking for "theta" (θ). We can use the cosine function, which is defined as the ratio of the length of the adjacent side to the length of the hypotenuse side of a right triangle, to solve for theta:
cos(θ) = opposite/adjacent
So we have:
cos(θ) = 4.7/5
We can use a calculator to solve for theta:
cos(θ) = 0.94
Take the arc cos
θ ≈ 19.94 degrees
Therefore, the ladder makes an angle of approximately 19.94 degrees with the wall.
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Suppose a jar contains 7 red marbles and 18 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer:
63
Step-by-step explanation:
we divided 18÷2=9
and we multiply 9×7=63
Answer:
[tex]p(a) = \frac{7}{100} [/tex]
Step-by-step explanation:
Given:
7 red marbles
18 blue marbles
Total number of marbles: 7 + 18 = 25
All outcomes:
[tex]n = \frac{25 \times 24}{2 \times 1} = 300[/tex]
25 × 24, because the first marble can be pulled out in 25 ways, and the second marble - in 24 ways, since the first one has already been pulled out.We divide by the factorial of 2, because the order does not matter how we pull out the marblesLet's name the event A:
A - "both marbles are red"
Event's A favorable outcomes:
[tex]m(a) = \frac{7 \times 6}{2 \times 1} = 21[/tex]
7 × 6, because we only need to pull the red marbles out, so there are 7 ways to pull out the 1st marble and 6 ways for the 2nd one to be pulled out (the order doesn't matter)[tex]p(a) = \frac{m(a)}{n} = \frac{21}{300} = \frac{7}{100} [/tex]
Find the values of m and b
Value of m and b of the straight line in the graph is 0 and 2 respectively.
Define slopeIn mathematics, slope refers to the steepness or inclination of a line, and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is often represented by the letter m. The slope of a line can be positive, negative, zero, or undefined.
Let us assume that the equation of line be y=mx+b.
where m is the slope
and b is the intercept
The line in the graph is parallel to x axis
so, slope is 0
m=0
the line passes through(0,2)
Putting the value in the equation, we get
b=2
Hence, the equation of line be y=2
Therefore, value of m=0 and b=2.
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The complete question is:
The graph is showing the equation of straight line y=mx+b, find the value of m and b.
Image is attached below:
Lori is selling crafts at a show. She pays $43.20 for the table rental. She sells 18 items. Every item is the same price and Lori makes a total profit of $25.20. Part A Select all the equations that will yield the correct value for the sale price x of each item. 43.20 = 18x − 25.20 43.20 = 18x + 25.20 25.20 = 18x − 43.20 25.20 = 18x + 43.20 Part B What is the cost x of each item in dollars?
Answer:
43.20 = 18x + 25.20
x = $1.00
Step-by-step explanation:
43.20 - 18x = 25.20
or
43.20 = 25.20 + 18x
Solve for x:
18x = 43.20 - 25.20
18x = 18
x = 18/18 = $1.00
Kaira collects data on the costs of maracas: $12.50, $13.00, $13.25, $14.25,
$14.50, $14.50, $14.50, $14.75, $15.75, $16.00, $16.50. Explain why a stem-and-leaf
plot would be an appropriate display to use to analyze and interpret the data.
The stem and leaves display the image and distribute information continuously. These charts are similar to histograms, but instead of using lines, they show numbers. It is a useful tool, especially when searching for statistical information.
The stem and leaf diagram, also known as the stem and leaf diagram, is a method of organizing data in a way that makes it easy to observe the frequency of importance of different species. A chart that shows numerical data arranged in a series. Each data value or number is divided into stems and leaves.
Rows and sheets are represented in the form of a special table in which each first digit or digit of the document value is divided by the stem and the last digit of the document in sheets. The letter is used to represent the stem and leaf, called stem and leaf values.
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Don has an album that holds 500 stamps. Each page of the album holds 5 stamps. If 50% of the album is empty, how many pages are filled with stamps?
Answer:
50 pages are filled with stamps.
Step-by-step explanation:
If 50% of the album is empty, then 50% of the album is filled with stamps.
So, the total number of stamps that the album holds is 500, and half of that (50%) is filled with stamps, which is:
500 * 50% = 250 stamps
Each page holds 5 stamps, so the number of pages filled with stamps is:
250 stamps / 5 stamps per page = 50 pages
Therefore, 50 pages are filled with stamps
identify the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³, then factor the expression.
The greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³ is 3s²t², and the factored expression is 3s²t²(2st² + 4s² - 5t).
What is greatest common factor?The greatest positive integer that divides two or more numbers without leaving a residual is known as the greatest common factor (GCF). In other words, the greatest number that is a factor of both (or all) of the specified numbers is chosen.
To identify the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³, we need to look for the largest expression that divides evenly into each term.
First, we can factor out the greatest common factor of the coefficients, which is 3: 3(2s³t⁴ + 4s⁴t² - 5s²t³)
Next, we can look for the greatest common factor of the variables. We can see that s²t² divides into each term: 3s²t²(2st² + 4s² - 5t)
Therefore, the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³ is 3s²t², and the factored expression is 3s²t²(2st² + 4s² - 5t).
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A principal of $1500 is invested at 8.5% interest, compounded annually. How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
Witch integer is closest to 3 square root of 12
Answer: You're answer is 3
or exactly 3.464.
[tex]\sqrt{100}[/tex]Answer:
10
Step-by-step explanation:
You have to reverse the square root [tex]3\sqrt{12}[/tex]
what perfect square makes 3? 9.
what is [tex]\sqrt{9} \sqrt{12}[/tex]
[tex]\sqrt{108}[/tex]
what is the perfect square between 108? 100 and 121.
what is the different between them?
108-100=8
121-108=13
obviously, 8 is closer than 13, so now find the square root of the closer perfect square.
[tex]\sqrt{100}[/tex]=10
Bob believes he is a basketball star and so does his friend Alan. Bob's Points per Game 8, 15, 10, 10, 10, 15, 7, 8, 10, 9, 12, 11, 11, 13, 7, 8, 9, 9, 8, 10, 11, 14, 11, 10, 9, 12, 14, 14, 12, 13, 5, 13, 9, 11, 12, 13, 10, 8, 7, 8 Alan's Points per Game 2 3 4 5 7 à io in 12 is 14 15 16 For each player calculate the following statical data (Alan's Mean and MAD already included) Bob's Data Mean: MAD: Median: IQR: 01: Q3: Alan's Data Mean: 7.25 MAD: 2.81 Median: IQR: O1: Q3: Determine if Bob or Alan have any outliers. Which play would you choose to be on your team and why?
For Bob: Mean =10.13,MAD = 2.66,Median =10.5 ,IQR = 5.5,Q1 = 8,Q3 = 13.5
for alan :Mean =7.25,Median = 7.5,IQR = 10,Q1 = 4,Q3 = 14
How to find mean ?For Bob:
Mean = (8+15+10+10+10+15+7+8+10+9+12+11+11+13+7+8+9+9+8+10+11+14+11+10+9+12+14+14+12+13+5+13+9+11+12+13+10+8+7+8) / 38 = 10.13
MAD = 2.66 (calculated using the median of Bob's data)
To calculate the median and quartiles for Bob's data, we need to first sort the data in ascending order:
5, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15
Median = (10+11) / 2 = 10.5
Q1 = median of the first half of the data = (8+8) / 2 = 8
Q3 = median of the second half of the data = (13+14) / 2 = 13.5
IQR = Q3 - Q1 = 13.5 - 8 = 5.5
Therefore, for Bob:
Median = 10.5
IQR = 5.5
Q1 = 8
Q3 = 13.5
For Alan:
Mean = (2+3+4+5+7+10+12+14+15+16) / 10 = 7.25
MAD = 2.81 (calculated using the median of Alan's data)
Median = 7.5 (calculated as the average of the 5th and 6th value in Alan's sorted data)
Q1 = 4
Q3 = 14
IQR = Q3 - Q1 = 14 - 4 = 10
Therefore, for Alan:
Median = 7.5
IQR = 10
Q1 = 4
Q3 = 14
To determine if there are any outliers, we can use the following formula:
Outliers = data points outside the range [Q1 - 1.5(IQR), Q3 + 1.5(IQR)]
For Bob:
Lower outlier bound = 8 - 1.5(5.5) = -0.25
Upper outlier bound = 13.5 + 1.5(5.5) = 24.25
There are no outliers in Bob's data.
For Alan:
Lower outlier bound = 4 - 1.5(10) = -11
Upper outlier bound = 14 + 1.5(10) = 29
There are no outliers in Alan's data.
If the team needs a more consistent player with a higher median and narrower IQR, Bob might be a better choice. On the other hand, if the team needs a player who can potentially score more points, Alan might be a better choice as his mean is higher.
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a circulat region has a population of about 360,000 people and a population density of about 1415 people per square mile . find the radius of the region
Answer:
Step-by-step explanation:
Last week, a candy store sold 6 1/3 pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate. DUE NOWW HELP ANSWER BOTH BRO
Question 1
How many pounds (in mixed number form) of milk chocolate did the candy store sell last week?
Responses
A 24 2/3
B. 25 2/3
C. 25 1/3
D. 24 1/3
Question 2
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
Responses
A. 19 2/3
B. 18
C. 19
D. 18 2/3
Question 1:
Answer:
[tex]C:25\frac{1}{3}[/tex]
Step-by-step explanation:
To find the number of pounds of milk chocolate sold, you have to multiply the amount of pounds of white chocolate sold by 4.
[tex](6+\frac{1}{3}) *4\\\\(6*\frac{3}{3}+\frac{1}{3})*4\\\\(\frac{18}{3} +\frac{1}{3} )*4\\\\\frac{19}{3} *4\\\\\frac{76}{3} \\\\25\frac{1}{3}[/tex]
Question 2:
Answer:
C: 19
Step-by-step explanation:
To find how many more pounds of milk chocolate were sold we subtract the white chocolate sold from the milk chocolate sold
[tex]25+\frac{1}{3} - 6+\frac{1}{3}\\\\25*\frac{3}{3}+\frac{1}{3}-6*\frac{3}{3}+\frac{1}{3}\\\\\frac{76}{3}-\frac{19}{3}\\\\\frac{57}{3}\\\\19[/tex]
A cylinder fits perfectly inside a box. The width of the cylinder is 3 feet, and the space between
the cylinder and the box is filled with 15 gallons of oil, taking up 75% of the space. What is the
height of the box in feet?
The height of the box must be at least 2.9111 feet.
Define volume of the cylinderThe volume of the cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is its height.
Since the width of the cylinder is 3 feet, the radius is 1.5 feet.
The volume of the oil is 15 gallons, which is equivalent to 0.2 cubic feet. We know that this volume of oil takes up 75% of the space between the cylinder and the box, so the total space between the cylinder and the box is 0.2 / 0.75 = 0.2667 cubic feet.
Since the cylinder fits perfectly inside the box, the volume of the box is equal to the volume of the cylinder plus the space between the cylinder and the box. Therefore, we have:
Volume of box = Volume of cylinder + Volume of oil
Volume of box = πr²h + 0.2667
Substituting the values we have:
Volume of box = π(1.5)²h + 0.2667
Volume of box = 7.0686h + 0.2667
To find the height of the box, we need to isolate h. We know that the volume of the box must be greater than or equal to the volume of the cylinder, so we can set up the inequality:
Volume of box ≥ Volume of cylinder
πr²h + 0.2667 ≥ πr²(3)
h + 0.0889 ≥ 3
h ≥ 2.9111
Therefore, the height of the box must be at least 2.9111 feet.
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