The area of the regular pentagon is about 9 square units.
To find the area of a regular polygon, we need to know the length of the apothem and the perimeter of the polygon. The apothem is the distance from the center of the polygon to the midpoint of one of its sides, and the perimeter is the sum of the lengths of all the sides.
Since the polygon is regular, all of its sides have the same length. Let's call that length "s". We also know that the polygon has 5 sides, so it is a pentagon. To find the perimeter, we can simply multiply the length of one side by the number of sides:
Perimeter = 5s
Now, to find the apothem, we can use the formula:
Apothem = (s/2) x tan(180/n)
Where "n" is the number of sides. For our pentagon, n = 5, so we have:
Apothem = (s/2) x tan(36)
We can simplify this a bit by noting that tan(36) is equal to approximately 0.7265. So we have:
Apothem = (s/2) x 0.7265
Now we have everything we need to find the area. The formula for the area of a regular polygon is:
Area = (1/2) x Perimeter x Apothem
Substituting in the values we found earlier, we have:
Area = (1/2) x 5s x (s/2) x 0.7265
Simplifying this expression, we get:
Area = (s^2 x 1.8176)
Rounding to the nearest whole number of square units, we have:
Area = 9
So the area of the regular pentagon is about 9 square units.
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to
Mrs. James, a sixth grade teacher, recorded how many minutes
each student reported reading over winter break.
Time spent reading (min.)
0
H
200.
What was the upper quartile of the time spent reading?
minutes
Submit
100
H
300.
400
+
500
The upper quartile of the time spent reading is 300.
We have,
The upper quartile, also known as the third quartile, is a measure of central tendency that divides a data set into four equal parts.
It represents the data point that separates the top 25% of the data from the bottom 75%.
Now,
From the box pot.
Median = 250
Lower quartile = 100
Upper quartile = 300
Thus,
The upper quartile is 300.
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If R is the unbounded region between the graph of [tex]y=\frac{1}{x(ln(x))^2}[/tex] and the x-axis for [tex]x\geq 3[/tex] then what is the area of R?
will give brainliest to answer with good explanation please i'm desperate
The area of the unbounded region R between the graph of y=1/(xln(x))² and the x-axis for x≥3 is 1/ln(3) square units. The integral was found by substitution and evaluated at the interval limits.
To find the area of the region R, we need to integrate the function y = 1/(x ln(x))² with respect to x over the interval x≥3.
Let's first find the indefinite integral
∫ 1/(x ln(x))₂ dx = ∫ u₂ du [where u = ln(x)]
= - u⁻¹ + C
= - ln(x)⁻¹ + C
Now, to find the definite integral, we need to evaluate this expression at the upper and lower bounds of the interval x≥3
[tex]\int\limits^ \infty} _3[/tex]1/(x ln(x))² dx = [- ln(x)⁻¹[tex]]^ \infty} _3[/tex]
= [- ln(∞)⁻¹] - [- ln(3)⁻¹]
= 0 - (-1/ln(3))
= 1/ln(3)
Therefore, the area of the region R is 1/ln(3) square units.
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The school budget for e-readers was $40,000 in 2014. The budget for 2015 was 20% less than the budget for 2014. What was the school budget for e-readers in 2015?
Answer: 32000
Step-by-step explanation: 40000 x 80% because you still have 80 percent of that budget so you minus 20 for 100.
Aaden is driving to a concert and needs to pay for parking. There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Aaden have to pay for parking if he left his car in the lot for 3 hours? How much would Aaden have to pay if he left his car in the lot for
�
t hours?
Answer:
$15.
Step-by-step explanation:
9 + 3*2
= $15.
Imagine that the price per gallon of gas with a $7 car wash is $3. 19 and the price without the car wash is $3. 39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?
If we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.
The car wash costs $7, and the price per gallon of gas with the car wash is $3.19, while the price per gallon of gas without the car wash is $3.39. Let's assume that we buy x gallons of gas, then the total cost of buying gas with the car wash would be:
Total cost with car wash = 7 + 3.19x
The total cost of buying gas without the car wash would be:
Total cost without car wash = 3.39x
To determine when it is worth it to buy the car wash, we need to find when the total cost with the car wash is less than the total cost without the car wash:
7 + 3.19x < 3.39x
Solving for x:
7 < 0.2x
x > 35
This means that if we plan to buy more than 35 gallons of gas, it is worth it to buy the car wash.
Now, let's consider the scenario where the car wash costs $2. The total cost of buying gas with the car wash would be:
Total cost with car wash = 2 + 3.19x
To determine when it is worth it to buy the car wash in this scenario, we need to find when the total cost with the car wash is less than the total cost without the car wash:
2 + 3.19x < 3.39x
Solving for x:
2 < 0.2x
x > 10
This means that if we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.
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1. Mrs. Zimmerman is interested in learning about how much time seventh grade students at our school spend outdoors on a typical school day.
Select all the samples that are a part of the population. Justify your reasoning.
. The 20 students in a seventh grade math class.
B. The first 20 students to arrive at school on a particular day.
C. The seventh grade students participating in a science fair put on by the four middle schools in a school district.
D. The 10 seventh graders on the school soccer team.
E. The students on the school debate team.
A, c, D
Step-by-step explanation:
A) we can sample these 7th graders as we are looking to study 7th graders.
b) The first 20 students could be from any grade and so this option wouldn't work.
c) Involves 7th graders.
d) involves 7th graders
E) The students could be any grade level on the debate team so, this option wouldn't work.
Let the function f be defined by
f(x) = x² + 28. If f(3y) = 2f(y), what is the one possible
value of y?
A) -1
B) 1
C) 2
D) -3
The one possible value of y, will be 2. Option C is correct.
We have f(x) = x² + 28, and f(3y) = 2f(y). Substituting 3y for x in the definition of f, we get;
f(3y) = (3y)² + 28 = 9y² + 28
Substituting y for x in the definition of f, we get;
f(y) = y² + 28
Using the given equation, we have;
2(y² + 28) = 9y² + 28
Expanding and simplifying, we get;
0 = 7y² - 56
Dividing by 7, we get:
y² - 8 = 0
Factoring, we get;
(y + 2)(y - 2) = 0
So y = -2 or y = 2. Since we are looking for only one possible value of y is 2.
Hence, C. is the correct option.
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Emilio draws an example of an obtuse triangle. Which triangle could be Emilio's drawing?
A.
Triangle with three angles less than 90 degrees.
B.
Triangle with one 90 degree angle and two angles less than 90 degrees.
C.
Triangle with two angles less than 90 degrees and one angle greater than 90 degrees.
D.
Triangle with three angles less than 90 degrees.
Answer:
C. An obtuse triangle has two angles less than 90 degrees and one angle greater than 90 degrees.
The point (7,8) in the coordinate plane represents a ratio. adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point. is adela correct? explain.
For the point (7,8) in the coordinate plane which represents a ratio, Adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point is incorrect.
Adela claim is not correct. To find an equivalent ratio, you should multiply (or divide) both coordinates by the same nonzero number instead of adding the same number.
1. The point (7,8) represents the ratio 7:8.
2. If we add the same number to both coordinates, let's say 2, we get the point (9,10), which represents the ratio 9:10.
3. We can check if 7:8 and 9:10 are equivalent ratios by cross-multiplying:
7 * 10 = 70 and 8 * 9 = 72. Since 70 ≠ 72, these ratios are not equivalent.
Therefore, Adela's claim is incorrect because adding the same number to both coordinates of the point does not result in an equivalent ratio. To find equivalent ratios, you should multiply (or divide) both coordinates by the same nonzero number.
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A school’s art teacher designs a circular flower bed inside a rectangular sandbox. The sandbox is 6 feet wide and 10 feet long. How many square feet will there be for sand after the flower bed is installed? Use 3.14 for pi. ROUND the answer to the NEAREST SQUARE FOOT.
A. 22 square feet
B. 28 square feet
C. 32 square feet
D. 41 square feet
whats the answer!???????
Which expression is equivalent to 3x – (2x + 4) + 5?
Responses
The expression that is equivalent to 3x – (2x + 4) + 5 is x+1 ( optionB)
What is equivalent of expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.
For example , 2a+6a is equivalent to 2a( 1+3) and they will surely have the same value when a value is replaced with a
3x – (2x + 4) + 5 = 3x-2x-4+5
= x-4+5
= x +1
therefore the equivalent of 3x – (2x + 4) + 5 is x+1
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Find x in the equation. 2 times x plus one fourth equals one fourth times x plus 2
HELP PLEASE!
I WILL MAKE YOU GENIUS!
x = 1
Step-by-Step Explanation[tex]2x + \dfrac{1}{4} = \dfrac{1}{4}x + 2[/tex]
1. subtract (1/4)x from both sides
[tex]\dfrac{7}{4}x + \dfrac{1}{4} = 2[/tex]
2. subtract 1/4 from both sides
[tex]\dfrac{7}{4}x = \dfrac{7}{4}[/tex]
3. multiply both sides by the reciprocal of x's coefficient
The reciprocal of [tex]\frac{\bold{7}}{\bold{4}}[/tex] is [tex]\frac{\bold{4}}{\bold{7}}[/tex].
[tex]\left(\dfrac{\not4}{\not7}\right)\left(\dfrac{\not7}{\not4}x\right) = \left(\dfrac{\not7}{\not4}\right)\left(\dfrac{\not4}{\not7}\right)[/tex]
[tex]\boxed{x = 1}[/tex]
A particle moves along the x-axis so that its position at time t>0 is given by
X(t) = (t^2 - 9)/(3t^2 + 8)
A) show that the velocity of the particle at time this given by v(t) = 70t/(3t^2 + 8)^2
B) is the particle moving toward the origin or away from the originator time t = 2? Give a reason for your answer.
C) The acceleration of the particle is given by £(t). Write an expression for £(t), and find the value of £(2).
D) What position does the particle approach as t approaches infinity?
The velocity of the particle at time t is given by [tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
The expression for the acceleration of the particle is a(t) [tex]= (210t^2 + 1120)/(3t^2+8)^3.[/tex]
A) To find the velocity of the particle, we need to take the derivative of its position with respect to time:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
[tex]v(t) = dX/dt = [(2t)(3t^2+8) - (t^2-9)(6t)]/(3t^2+8)^2[/tex]
[tex]v(t) = (6t^3 + 16t - 6t^3 + 54t)/(3t^2 + 8)^2[/tex]
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
Therefore, the velocity of the particle at time t is given by[tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
B) To determine whether the particle is moving toward or away from the origin at time t = 2, we need to examine the sign of the velocity v(2). Plugging t = 2 into the expression for v(t), we get:
[tex]v(2) = 70(2)/((3(2)^2 + 8)^2) = 280/169[/tex]
Since v(2) is positive, the particle is moving away from the origin at time t = 2.
C) The acceleration of the particle is given by the derivative of its velocity with respect to time:
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
[tex]a(t) = dv/dt = (70(3t^2+8)^2 - 2(70t)(2t)(3t^2+8))/(3t^2+8)^4[/tex]
[tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]
Therefore, the expression for the acceleration of the particle is [tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]. To find the value of a(2), we plug in [tex]t = 2:a(2) = (210(2)^2 + 1120)/(3(2)^2+8)^3 = 175/677[/tex]
D) To find the position that the particle approaches as t approaches infinity, we examine the behavior of X(t) as t gets very large. We can do this by looking at the leading term of the numerator and denominator of X(t) as t approaches infinity:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
As t approaches infinity, the numerator is dominated by the t^2 term, and the denominator is dominated by the 3t^2 term. Therefore, as t approaches infinity, X(t) approaches:
[tex]X(infinity) = t^2/3t^2 = 1/3[/tex]
So the particle approaches the point x = 1/3 as t approaches infinity.
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A zebra crossing has alternating white and black stripes, each 50 cm wide. The first stripe is white and the last one is white. The zebra crossing in front of our school has 8 white stripes. How wide is the road? A) A 7m 7,5m © 8m 8m 0 8,5m E 9m
The road with alternating white and black stripes and each 50 cm wide is 7.5 m wide.
The road consists of alternating white and black stripes
No. of white stripes = 8
As the first and last stripe is white so in between the black stripes will be 7
No. of black stripes = 7
Total no. of stripes = 15
Width of black stripe = 50 cm
Width of white stripe = 50 cm
Width of whole road = total no. of stripes × width of each stripe
Width of whole road = 15 × 50
Width of whole road = 750 cm
To convert m into cm
Now, 1 m = 100 cm
1 cm = 1/100 m
750 cm = 750/100 m
750 cm = 7.5 m
Hence the width of the road is 7.5 m
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Let f(2)= 1 / x² + root x, is it converge or diverge?
To determine whether the function f(2) converges or diverges, we need to evaluate the limit of the function as x approaches 2. We can rewrite the function as:
f(2) = 1 / (x² + √x) = 1 / (x² + x^(1/2))
As x approaches 2, both x² and x^(1/2) approach 2, so we can substitute 2 for both of these terms:
f(2) = 1 / (2² + 2^(1/2)) = 1 / (4 + 1.414) ≈ 0.176
Therefore, f(2) converges to a finite value of approximately 0.176, and does not diverge.
Based on the given information, let's analyze the function f(x) = 1 / (x² + √x). To determine if the function converges or diverges, we can examine its behavior as x approaches infinity.
As x gets larger, both x² and √x increase, but x² increases at a much faster rate. Therefore, the denominator (x² + √x) will become larger and larger as x approaches infinity. Consequently, the value of the function f(x) = 1 / (x² + √x) will approach 0.
Since the function approaches 0 as x goes to infinity, we can conclude that the function f(x) = 1 / (x² + √x) converges.
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I’m confused math has never really been my strong suit
Thus, 25.13 cubic inches is the closest estimate for the ice cream's overall volume.
what is volume ?Volume is a mathematical concept that describes how much space a three-dimensional object occupies. It is frequently expressed in terms of cubic units like cubic metres (m3), cubic feet (ft3), or cubic centimetres (cm3). Depending on the shape of the object, different formulas can be used to determine its volume. Consider this: The formula V = l w h, where l has been the length, w is the broad, and h corresponds to the height of the rectangular prism (box), gives the volume of the object. A sphere's volume can be calculated using the method V = (4/3)r3, where r is the sphere's radius.
given
The formula for a cone's volume is as follows, assuming that the ice cream has the correct circular cone shape with radius r = 2 in and height h = 6 in:
[tex]V = (1/3) * \pi * r^2 * h[/tex]
Inputting the values provided yields:
[tex]V = (1/3) * \pi * (2 in) * (2 in) * (6 in)[/tex] = 25.13 cubic inches
Thus, 25.13 cubic inches is the closest estimate for the ice cream's overall volume.
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The complete question is:-
r = 2 in.
h = 6 in.
Which is closest to the total volume of the ice
cream?
please hurry A 4-column table with 3 rows. Column 1 has entries boys, girls, total. Column 2 is labeled less than 8 pounds with entries a, c, e. Column 3 is labeled greater-than-or-equal-to 8 pounds with entries 50, d, 70. Column 4 is labeled Total with entries b, 96, 160.
Last July, 160 babies were born in a hospital in Maine; 3
5
of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more.
a = 64, b = 14, c = 76, d = 20, e = 90
a = 14, b = 64, c = 90 d = 20, e = 76
a = 14, b = 76, c = 64, d = 90, e = 20
a = 14, b = 64, c = 76, d = 20, e = 90
Answer: the correct answer is:
a = 14, b = 64, c = 76, d = 20, e = 90
Step-by-step explanation: can i get brainliest :D
how many times can 2 go into 1742? please its for my homework due tomorrow
Solve the system of equations.
6x – y = 6
6x2 – y = 6
A (0, 6) and (0, –6)
B (1, 0) and (0, –6)
C (2, 6) and (1, –11)
D (3, 12) and (2, 19)
Can anyone help? i need to solve these using the completing the square method
Using the completing the square method, the quadratic equation x²-5x=9 can be simplified to (x-2.5)²=15.25, and the solutions are x=2.5+√15.25 and x=2.5-√15.25.
To solve this quadratic equation using the completing the square method. Here are the steps
Move the constant term (in this case, 9) to the right-hand side of the equation
x² - 5x = 9 becomes x² - 5x - 9 = 0
To complete the square, we need to add and subtract a constant term inside the parentheses. The constant term we add is half of the coefficient of the x-term, squared. In this case, the coefficient of the x-term is -5, so we need to add and subtract (5/2)² = 6.25.
x² - 5x - 9 + 6.25 - 6.25 = 0
Rearrange the terms inside the parentheses to group the perfect square with the x-term
(x² - 5x + 6.25) - 15.25 = 0
Factor the perfect square trinomial inside the parentheses
(x - 2.5)² - 15.25 = 0
Add 15.25 to both sides of the equation
(x - 2.5)² = 15.25
Take the square root of both sides
x - 2.5 = ±√15.25
Add 2.5 to both sides
x = 2.5 ±√15.25
So the solutions to the equation x² - 5x = 9, using the completing the square method, are x = 2.5 + √15.25 and x = 2.5 - √15.25.
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--The given question is incomplete, the complete question is given
"Can anyone help? i need to solve these using the completing the square method
x²-5x = 9"--
in KLMO, OM-25. What are the coordinates of M and K?
L(2b+4c4d)
ㅁ
M
The value of coordinate M and K are,
M = (25, 0)
K = (2b + 4c - 25, 2d)
Given that;
In KLMO,
OM = 25
L = (2b + 4c , 4d)
Hence, We can formulate;
The value of coordinate of M is,
M = (25, 0)
Since, M lies on x - axis.
Let the coordinate of K is,
K = (x, y)
Hence, Midpoint of LO is same as midpoint of KM.
Midpoint of LO is,
(0 + 2b + 4c / 2, 4d/2)
(b + 2c, 2d)
Midpoint of KM is
(x + 25/2, y + 0/2)
(x + 25/2 , y/2)
By comparing,
x + 25/2 = b + 2c
x + 25 = 2b + 4c
x = 2b + 4c - 25
y/2 = 2d
y = 2d
Thus, the coordinate of K is,
K = (2b + 4c - 25, 2d)
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Let a be a number. Find the n-vector b for which,bc =p/(a).This means that the derivative of the polynomial at a given point is a linear functionof its coefficients.
We have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn. Let's start by writing out the polynomial:
[tex]c0 + c1x + c2x^2 + ... + cnx^n[/tex]
The derivative of this polynomial with respect to x is:
[tex]c1 + 2c2x + 3c3x^2 + ... + ncnx^(n-1)[/tex]
At the point x=a, the derivative becomes:
[tex]c1 + 2c2a + 3c3a^2 + ... + ncn*a^(n-1)[/tex]
We want this to be a linear function of the coefficients c0, c1, ..., cn. That means we need to find a vector b such that:
[tex]c1 + 2c2a + 3c3a^2 + ... + ncna^(n-1) = b0c0 + b1c1 + ... + bncn[/tex]
Let's compare coefficients of c0, c1, ..., cn on both sides:
c1 = b1c1
2c2a = b2c2
[tex]3c3a^2 = b3c3[/tex]
...
[tex]ncna^(n-1) = bn*cn[/tex]
We can simplify these equations by dividing both sides by ci (assuming ci is not zero):
b1 = 1
b2 = 2a/c2
[tex]b3 = 3a^2/c3[/tex]
...
[tex]bn = n*a^(n-1)/cn[/tex]
So the vector b we're looking for is:
b = [1, 2a/c2, [tex]3a^2[/tex]/c3, ...,[tex]n*a^(n-1)/cn][/tex]
And if we multiply b by the coefficient vector c, we get:
bc = c1 + 2c2a + [tex]3c3a^2[/tex] + ...[tex]+ ncn*a^(n-1)[/tex] = the derivative of the polynomial at x=a
Therefore, we have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn.
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Write 23.4571 correct to
b) the nearest 10
Answer:
20
Step-by-step explanation:
Answer:
23.50
Step-by-step explanation:
23.4571 rounded of to the nearest tenth 23.4+1
Jack plus 1/3 pound of birdseed into his birthday. Every time he sells it how many times can jack sell his bird feeder with 4 lb of birdseed
Jack can sell 12 bird feeders with 4 lb of birdseed. We can use Proportion method to calculate this :
Assuming that Jack mixes 1/3 pound of birdseed for each bird feeder, we can find out how many bird feeders he can sell with 4 pounds of birdseed by using a proportion.
Let x be the number of bird feeders Jack can make with 4 pounds of birdseed. We can set up the proportion:
1/3 pounds of birdseed per bird feeder = 4 pounds of birdseed / x bird feeders.
Simplifying this equation, we get:
1/3 = 4/x
To solve for x, we can cross-multiply:
1x = 12
x = 12
Therefore, Jack can make and sell 12 bird feeders with 4 pounds of birdseed.
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3. The table below shows the relationship between the amount of electricity used by a customer in different months and the cost shown on the customer's electric bill. Month 1 2 3 4 Monthly Electric Bills for a Customer Amount of Electricity Used (kilowatt-hours) A 0.095x < 65.00 B. 0.095x> 65.00 C. 0.92x < 65.00 D. 0.92x> 65.00 290 350 460 500 Cost of Electricity Used ($) 27.55 33.25 43.70 47.50 Based on the information shown in the table, which inequality could be used to determine all the numbers of kilowatt-hours (x) of electricity a customer could use in a month for the cost to be less than $65.00?
The correct inequality is:
A. 0.095x < 65.00.
To determine the inequality that represents the numbers of kilowatt-hours a customer could use in a month for the cost to be less than $65.00, we need to look for the rate at which the cost of electricity changes with the amount of electricity used.
From the table, we can see that the cost of electricity increases as the amount of electricity used increases.
We can also see that the cost per kilowatt-hour (the rate) is not constant. For example, the cost per kilowatt-hour for the first month is:
27.55 / 290 ≈ 0.095
But for the fourth month, it is:
47.50 / 500 ≈ 0.095
This means that the rate is not constant, and we cannot simply use a proportion to determine the numbers of kilowatt-hours that will result in a cost of less than $65.00.
However, we can use the data to create an inequality that represents the numbers of kilowatt-hours that will result in a cost less than $65.00. We can start by finding the highest cost per kilowatt-hour:
43.70 / 460 ≈ 0.095
This means that the cost per kilowatt-hour is always less than or equal to 0.095.
Next, we can set up the inequality:
0.095x < 65.00
This inequality represents the numbers of kilowatt-hours that will result in a cost less than $65.00, because if the cost per kilowatt-hour is always less than or equal to 0.095, then the total cost will be less than $65.00 if and only if the number of kilowatt-hours used is less than 684.21 (which is the result of dividing $65.00 by 0.095).
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sin^2(x) + sin(x) = 0
After simplifying, which expressions are equivalent? select three options. (3.4a – 1.7b) (2.5a – 3.9b) (2.5a 1.6b) (3.4a 4b) (–3.9b a) (–1.7b 4.9a) –0.4b (6b – 5.9a) 5.9a – 5.6b
(3.4a – 1.7b) and (–1.7b 4.9a) and (5.9a – 5.6b) are equivalent expressions.
Which expressions are equivalent after simplification?
The question presents a list of six expressions. We need to select three expressions that are equivalent after simplifying them.
One of the expressions is (3.4a - 1.7b), and another is (-1.7b + 4.9a). These two expressions can be simplified to 2.4a - 1.7b.
Another expression is (2.5a - 3.9b), and another is (-3.9b + a). These two expressions can be simplified to 3.5a - 3.9b.
The third expression is 5.9a - 5.6b, which cannot be simplified further.
The three expressions that are equivalent after simplifying are (3.4a - 1.7b) and (-1.7b + 4.9a), (2.5a - 3.9b) and (-3.9b + a), and 5.9a - 5.6b.
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Scores at a local high school on the Algebra 1 Midterm are extremely skewed left with a mean of 65 and a standard deviation of 8. A guidance counselor takes a random sample of 10 students and calculates the mean score, x¯¯¯.
(a) Calculate the mean and standard deviation of the sampling distribution of x¯¯¯
(b) Would it be appropriate to use a normal distribution to model the sampling distribution? Justify your answer
The standard deviation of the sampling distribution is 2.53. It would not be appropriate to use a normal distribution to model the sampling distribution.
(a) When dealing with a sampling distribution, the mean of the sampling distribution (μ_x) is equal to the mean of the population (μ). In this case, the mean of the population is 65. Therefore, the mean of the sampling distribution is also 65.
To calculate the standard deviation of the sampling distribution (σ_x), you will use the following formula: σ_x = σ / √n, where σ is the standard deviation of the population and n is the sample size. In this case, the standard deviation of the population is 8 and the sample size is 10. So the standard deviation of the sampling distribution is:
σ_x = 8 / √10 ≈ 2.53
(b) The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution, provided that the population is not heavily skewed or has extreme outliers. Since the scores are extremely skewed left and the sample size is only 10, it would not be appropriate to use a normal distribution to model the sampling distribution. A larger sample size would be needed to use a normal distribution model.
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Sara collects beads in a jar she weighs the jar every week to see how many grams of beads she has. she as 2.5 grams if blue beads. 4.9 grams of pink beads, 7.1 grams of yellow beads and the rest are white beads
if sara weighs her jar this week and finds out that she has 1.8 grams of beads, how many grams of white beads does she have?
Therefore, Sara has 3.5 grams of white beads in her jar.
Based on the information provided, Sara has 2.5 grams of blue beads, 4.9 grams of pink beads, and 7.1 grams of yellow beads. If she weighs her jar this week and finds out she has a total of 18 grams of beads, we can determine the number of grams of white beads she has by following these steps:
Step 1: Add the weights of the blue, pink, and yellow beads together.
2.5 grams (blue) + 4.9 grams (pink) + 7.1 grams (yellow) = 14.5 grams
Step 2: Subtract the total weight of the blue, pink, and yellow beads from the total weight of the jar (18 grams).
18 grams (total weight) - 14.5 grams (blue, pink, and yellow beads) = 3.5 grams
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