So, there is approximately an 85.02% probability that the sample mean will be between 50 and 54.
How to solve
We'll use the Central Limit Theorem which states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is large enough (n ≥ 30).
In this case, the sample size is 42, so we can apply the Central Limit Theorem.
First, we'll calculate the standard deviation of the sampling distribution (also known as the standard error) using the formula:
Standard error (SE) = population standard deviation / √sample size
SE = 9 / √42 ≈ 1.387
Next, we'll calculate the Z-scores for the lower and upper bounds of the range (50 and 54) using the following formula:
Z = (sample mean - population mean) / standard error
For the lower bound (50):
Z1 = (50 - 52) / 1.387 ≈ -1.44
For the upper bound (54):
Z2 = (54 - 52) / 1.387 ≈ 1.44
Now, we'll use a Z-table or calculator to find the probability that the sample mean lies between these Z-scores. We need to find the area between Z1 and Z2.
P(-1.44 < Z < 1.44) = P(Z < 1.44) - P(Z < -1.44)
Using a Z-table or calculator:
P(Z < 1.44) ≈ 0.9251
P(Z < -1.44) ≈ 0.0749
Now subtract:
P(-1.44 < Z < 1.44) = 0.9251 - 0.0749 = 0.8502
So, there is approximately an 85.02% probability that the sample mean will be between 50 and 54.
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Given a sample of size 42 drawn from a population with a mean of 52 and a standard deviation of 9, what is the probability that the sample mean is between 50 and 54?
Tammy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tammy $9.95 per pound, and type B coffee costs $4.40 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $560.50. How many pounds of type A coffee were used?
Answer:
Step 1 : we will name the number of pounds of type A coffee were used is letter x then
We also do the same name the number of pounds of type B coffee were used in letter y.
Step 2: we will find the hints to find x and y
Hint 1 : We have total cost of two type A and type B is $560.5.
Price per pound of Type A : $9.95
Price per pound of Type B : $4.40
Cost = price per pound * (multipe) number per pound .So we have an expression 1:
9.95 * x + 4.4*y = 560.5
Hint 2: This month's blend used twice as many pounds of type B coffee as type A . That means the number of pounds of type B is double than the the number of pounds of type A so we have a another expression 2:
y = 2*x (2)
Step 3: we have enough hints so we could find x (number of pounds of type A coffee)
We will pass the value of y = 2*x into the expression 1 so we get:
9.95 *x + 2*x*4.4 = 560.5
9.95x + 8.8x = 560.5
18.75x =560.5
x = 560.5 / 18.75
x = 29.89
The anwser is number of pounds of type A coffee is 29.89
Graph the feasible region for the given system of inequalities
x+3y≤9
3x+y≤9
x≥0
y≥0
The feasible region is the area below the line x+3y=9, below the line 3x+y=9, and to the right of the y-axis and the bottom of the x-axis.
What are the steps to make the graph for the feasible region?
To graph the feasible region, we first graph the boundary lines of the inequalities.
To graph the line x + 3y = 9, we can first find its intercepts by setting x = 0 and y = 0:
When x = 0,
3y = 9, so y = 3
When y = 0, x = 9
So the line passes through the points (0, 3) and (9, 0).
To graph the line 3x + y = 9, we can again find its intercepts:
When x = 0, y = 9
When y = 0,
3x = 9, so x = 3
So the line passes through the points (0, 9) and (3, 0).
Now we can shade the region that satisfies all the inequalities, which is the region below the line x + 3y = 9, below the line 3x + y = 9, and to the right of the y-axis and the bottom of the x-axis (since x and y must both be greater than or equal to 0).
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a bag has red, green, blue, black, and white marbles. There are 8 of each color in the bag. What fraction of marbles, in simplest form, are not black or white
Answer:
2/3
Have a wonderful day!!!
What is the value of the expression below when x = 3 x=3? 7 x 2 − 2 x + 2 7x 2 −2x+2
As a result, By substitute for "x = 3," the expression's value is **59**.
what is the substitution method?The substituting method is an easy way to use algebra to discover the solutions to the variables in a system of linear equations. It includes, as the name implies, determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation
The phrase is given to us:
``` 7x² - 2x + 2 ```
It entails, as the name suggests, finding the value of the x-variable from the first equation in terms of the y-variable and then substituting or replacing
We need to figure out what this equation's answer is when "x = 3."
Therefore, in the following phrase, we substitute every instance of "x" with "3":
``` 7(3)² - 2(3) + 2
= 7(9) - 6 + 2
= 63 - 6 + 2
= 59
```
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Use the correct sign (< or >) to make the inequality true.
3/4 2/3
Answer:
>
Step-by-step explanation:
This is because when we look at the numbers the may look equal at first glance but when we evaluate it we see that the denominator of 3/4 is bigger than the denominator of 2/3 so they correct answer would be
3/4>2/3
HOPE THIS HELPS
PPLLSS GIVE BRAINLIST AND HAVE A NICE DAY
Which equation represents the graph? a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 4 y equals negative one third times x minus 1 y = −3x − 1 y equals negative one third times x plus one third y equals negative 3 times x plus one third
The equation with the given coordinate points is y=-3x-1.
The given coordinate points are (0, -1) and (1, -4).
Here, slope (m) = (-4-(-1))/(1-0)
= (-4+1)/1
= -3
Substitute m=-3 and (x, y)=(0, -1) in y=mx+c, we get
-1=-3(0)+c
c=-1
Substitute m=-3 and c=-1 in y=mx+c, we get
y=-3x-1
So, the equation is y-3x-1
Therefore, the equation with the given coordinate points is y=-3x-1.
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A bakery is 10 yards wide and 14 yards long. The baker wants to put a wooden shelf around the inside of the bakery. The wooden shelving costs $7.00 per yard. How much will the baker's shelf cost?
The baker's shelf will cost $336.00.
What is the perimeter?
The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.
To calculate the cost of the wooden shelf, we first need to find the perimeter of the bakery:
Perimeter = 2 × (length + width)
Perimeter = 2 × (14 yards + 10 yards)
Perimeter = 48 yards
So the baker needs 48 yards of wooden shelf.
The cost of the wooden shelf is $7.00 per yard, so we can find the total cost by multiplying the number of yards by the cost per yard:
Total cost = 48 yards × $7.00 per yard
Total cost = $336.00
Therefore, the baker's shelf will cost $336.00.
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What is the volume of the tent in feet cubed (ft^3)? Type only a whole number.
HINTs: Find the area of the front of the tent. Then multiply it by the "stretch" height.
V = Bh = (1/2bh)h. The Hieght is 6 The front is 6 And the side is 8
The Volume of the given tent is calculated as: 144 cubic.units
What is the volume of the tent?The tent being described here is basically a triangular prism.
A triangular prism is simply referred to as a three-sided polyhedron with two parallel triangular bases and also three rectangular faces. This should not be mistaken with a pyramid. Now, to calculate the particular volume of a triangular prism, we have to first of all calculate the area of one of the triangular bases and then multiply that area by the height of the shape.
The formula used in expression for the Volume of the tent is:
V = Bh
= (¹/₂bh)h
where:
B is called base area
b is called base length
h is called height
We are given:
b = 8
h = 6
Thus:
V = (¹/₂ * 8 * 6) * 6
V = 144 cubic.units
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Use the figure shown on the right.
11. What is the classification of the figure?
A. rectangular pyramid
B. pentagonal prism
my
C. rectangular prism
D. pentagonal pyramid
B
A
Ej.
C
D
H
11.
ONLY NUMBER 11 don’t mind the top
Answer:
Rectangular prism
Step-by-step explanation:
It's not a pyramid because it has 2 bases, so you can eliminate the choices with pyramid. The base of the figure is a rectangle, so it's a rectangular prism
Answer:
C. Rectangular prism.
Step-by-step explanation:
Answer all questions please
Answer:
a) f(1) = 3
b) f(-1) = -0.25
c) x = 0, 3
d) x = -0.75
e) domain [-2, 4]
range [-1, 3]
Step-by-step explanation:
In this graph, f(x) is represented by the y-axis.
a) We can see that f(1) (the y-value when x = 1) is 3.
b) Looking at the graph, we can estimate f(-1) as about -0.25.
c) We need to find the x-values when the y-axis is at 1. We can see that there are two points at x = 0, 3.
d) Looking at the graph, we can estimate that f(x) = 0 around when x = -0.75.
e) The domain of a function is its set of x-values. We can see that f(x) spans from x = -2 to x = 4. That range in interval notation is: [-2, 4]
The range of a function is its set of y-values. We can see that f(x) spans from y = -1 to y = 3. That range in interval notation is: [-1, 3].
Relative intensity of 9 decibels is how many times higher than that of 8 decibels
Answer:
what do you mean by land ?
The intensity of sound is proportional to the square of its amplitude.
Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:
I9/I8 = (10^(9/10))/(10^(8/10))
I9/I8 = 10^(0.1)
I9/I8 = 1.2589
Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.
May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
find the volume of a sphere with a surface area of 900 pi in squared
The volume of the given sphere is 14130 cubic inches.
Given that, the surface area of a sphere is 900π square inches.
We know that, the surface area of a sphere is 4πr².
Here, 4πr²=900π
r²=900/4
r²=225
r=15 inches
The volume of the sphere is given by: Volume of Sphere, V = (4/3)πr³
Here, volume of a sphere = 4/3 ×3.14×15³
= 14130 cubic inches
Therefore, the volume of the given sphere is 14130 cubic inches.
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Find the equation of the line passing through the point
(−2, 3)
that is perpendicular to the line
5x + 4y = 9.
y = −
5
4
x +
3
4
y = −
5
4
x −
3
4
y =
4
5
x +
23
5
y =
4
5
x −
14
5
y =
4
5
x −
23
5
By answering the presented question, we may conclude that As a result, slope the correct answer is y = (4/5)x + 23/5.
what is slope?The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7)
To determine the equation of the line perpendicular to the line 5x + 4y = 9, travel via the point (-2, 3).
5x + 4y = 9 4y = (-5/4)x + 9/4
As a result, the slope of the supplied line is -5/4.
4/5 is the negative counterpart of -5/4.
As a result, the new line's slope will be 4/5.
y - y1 = m(x - x1), where (x1, y1) is the provided point and m is the newly discovered slope.
y - 3 = (4/5)(x + 2)
y = (4/5)x + (8/5) + 3
y = (4/5)x + 23/5
Hence the equation of the perpendicular to the line 5x + 4y = 9 line going through the point (-2, 3) is y = (4/5)x + 23/5.
As a result, the correct answer is y = (4/5)x + 23/5.
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What is the measure of angle?
Here's a way to help you find the measure of an angle
An angle is the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.
PLS HELP ME !!! The volume of a rectangular pyramid is 1824 units^3.
If the length of the rectangular base measures 12 units and the width of the rectangular base measures 19 units, find the height of the pyramid.
The answer of the given question based on the rectangular pyramid is , the height of the pyramid is 24 units.
What is Volume?Volume is the amount of space occupied by an object or a substance. It is a three-dimensional measurement that is expressed in units like cubic meters, cubic centimeters, liters, or gallons.
The volume of rectangular pyramid is given by formula:
V = (1/3) * B * h
where V is the volume, B is the area of the rectangular base, and h is the height of the pyramid.
In this problem, we are given that the volume of the pyramid is 1824 units^3, and the length and width of the rectangular base are 12 units and 19 units, respectively. We can use this information to find the area of the rectangular base:
B = length * width = 12 * 19 = 228 units²
Substituting this value and the formula for the volume into the equation above, we get:
1824 = (1/3) * 228 * h
Multiplying both sides by 3, we get:
3 * 1824 = 228 * h
Simplifying, we get:
5472 = 228 * h
Dividing both sides by 228, we get:
h = 5472 / 228
Simplifying, we get:
h = 24
Therefore, the height of the pyramid is 24 units.
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Experimental probablity
Outcome. 1, 2, 3, 4, 5, 6
Frequency. 17, 20, 14, 18, 16, 15
What is the probably the the number rolled was even, after 100 rolls?
Answer:
Step-by-step explanation:I think 3
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
Only one choice is True: the graph is a parabola.
Step-by-step explanation:
f(x) = x^2 - 5x + 12
f(-10) = (-10)^2 - 5(-10) + 12
= 100 + 50 + 12
= 162 so f(-10) = 82 is FALSE.
The graph is a parabola:
TRUE
The graph opens up ( as coefficient of x^2 is positive. FALSE
Plug in (20, -8):
(-8) = 20^2 - 5(20) + 12
= 400 - 100 + 12 = 312 FALSE.
The graph contains (0,0) : FALSE
( as (0)^2 - 5(0) + 12 = 12..
Imagine that the Sun, Earth, and Jupiter were perfectly aligned. As a reminder, Earth is
the third planet from the Sun and Jupiter is the fifth planet from the Sun. To find the
distance, you need to add the distances from the Sun to Earth and the Earth to Jupiter
together. The average distance from the Sun to the Earth is 1.5 x 108 km. The distance
from the Earth to Jupiter at their closest point is 5.88 x 108
km.
What is the distance from the Sun to Jupiter?
solve the equation
log(x+9)-logx=3
a. 0.0090
b. 0.3103
c. 3.2222
d. 111
The logarithmic equation log(x+9)-logx=3 has a solution of x = 0.0090
Solving the logarithmic equationFrom the question, we have the following parameters that can be used in our computation:
log(x+9)-logx=3
Apply the quotient rule
So, we have
log((x + 9/x) = 3
Remove the logarithmic expression
So, we ave
(x + 9)/x = 10^3
Evaluate
(x + 9)/x = 1000
So, we have
1000x = x + 9
Subtract
999x = 9
So, we have
x = 0.0090
Hence, the solution is x = 0.0090
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A first-year teacher wants to retire in 40 years. The teacher plans to invest in an account with a 5.67% annual interest rate compounded continuously. If the teacher wants to retire with at least $100,000 in the account, how much money must be initially invested? Round your answer to the nearest dollar.
$10,352
$10,512
$34,703
$35,905
Using compound interest, we can find that the principal investment required to get a total amount of $100,000.00 from compound interest at a rate of 5.67% per year compounded 1 time per year over 40 years is $11,013.66.
Define compound interest?Interest that is accrued on both principal and previous interest is known as compound interest. As a result, it is often referred to as "interest over the interest". Here, the principal is increased by the interest that has already accrued, and the resulting sum serves as the new principal for the subsequent period. i.e., compound interest is equal to interest on the principal plus interest on interest already paid.
First, convert R as a percent to r as a decimal.
r = R/100
r = 5.67/100
r = 0.0567 per year,
Then, solve the equation for P:
P = A / [tex](1 + r/n)^{nt}[/tex]
P = 100,000.00 / [tex](1 + 0.0567/1)^{40}[/tex]
P = 100,000.00 / [tex](1 + 0.0567) ^{40}[/tex]
P = $11,013.66
The principal investment required to get a total amount of $100,000.00 from compound interest at a rate of 5.67% per year compounded 1 time per year over 40 years is $11,013.66.
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Which expression should you simplify to find the 90% confidence interval for a sample of 64 with a mean of 6 and a standard deviation of 3
The 90% confidence interval for the sample mean is approximately [tex](5.26, 6.74)[/tex].
How to find the confidence interval?To find the 90% confidence interval for a sample of 64 with a mean of 6 and a standard deviation of 3, you can use the formula:
[tex]CI = \bar x\ _-^+\ Z_{\alpha/2} * (\sigma/ \sqrt n)[/tex]
where,
CI is the confidence interval
[tex]\bar X[/tex] is the sample mean =6
[tex]Z_{\alpha/2} = 1.645[/tex] i.e. 90% confidence.
σ is the population standard deviation =3
n is the sample size = 64
So the expression to simplify would be:
[tex]6\ _-^+ \ 1.645 * (3/\sqrt{64})[/tex]
Simplifying this expression gives:
[tex]= 6\ _-^+\ 0.7378125\\[/tex]
So, The 90% confidence interval for the sample mean is approximately [tex](5.26, 6.74)[/tex].
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What is the length of three carts stacked together?
The length of the three carts that are stacked together would be = 35.5 in
How to calculate the length of the given number of carts?To calculate the length of the three cart stacked together, the following steps should be taken.
The length of a cart that is unstacked = 36 in.
The length of 6 carts that are stacked together = 71 in.
That is;
If 6 carts = 71 in
3 carts = X in
Make X in the subject of formula;
X in = 3×71/6
= 213/6
= 35.5 in
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please answer fast i need to submit this!!!!
Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation
As per the given polygon, the direction and angle of rotation is a 90° clockwise rotation.
The image shows that polygon ABC is in quadrant 4, while its rotated image A' B' C' is in quadrant 3. This means that the rotation is clockwise.
To determine the angle of rotation, we can see that the vertices A and A' are located 6 units apart on the x-axis. Similarly, B and B' are located 4 units apart on the y-axis. This means that the rotation is a combination of a translation and a rotation.
To find the angle of rotation, we need to determine the angle between the line segments of polygon AA' and BB'. We can use the tangent function to find this angle:
tanθ = 4/6 = 2/3
θ ≈ 33.69°
Therefore, the direction and angle of rotation is a 90° clockwise rotation.
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What meaning of the statement this?
The given passage is a proof that a certain set H is a subgroup of a group X.
What is the explanation for the above response?
The given passage is a proof that a certain set H is a subgroup of a group X. It first defines H as the set of all products of elements of X and inverses of elements of X.
Then, it shows that H satisfies the three conditions necessary for it to be considered a subgroup: H contains the identity element I, it is closed under products (i.e., if h and k are in H, then hk is also in H), and it is closed under inverses (i.e., if h is in H, then h^-1 is also in H).
Finally, it concludes that since H contains all elements of X and is closed under products and inverses, it must be the smallest subgroup of X that contains X itself. Therefore, H is a subgroup of X.
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The equation A equals P quantity 1 plus 0.06 over 4 end quantity all raised to the power of 4 times t represents the amount of money earned on a compound interest savings account with an annual interest rate of 6% compounded quarterly. If after 15 years the amount in the account is $16,497.06, what is the value of the principal investment? Round the answer to the nearest hundredths place.
$13,195.22
$9,744.88
$6,752.18
$4,384.00
The value of the principal investment is approximately $6,752.18 rounded to the nearest hundredths place.
What is called simple interest?Simple interest is a technique used to calculate the proportion of interest paid on a sum over a set time period at a set rate. The principal amount remains constant in simple interest. Simple interest is a straightforward and easy technique for calculating interest in money.
The given equation is:
A = [tex]P(1 + 0.06/4)^4t[/tex]
where A is the amount in the account after t years, P is the principal investment, and 0.06 is the annual interest rate.
We are given that after 15 years, the amount in the account is $16,497.06. So we can substitute A = $16,497.06 and t = 15 into the equation above and solve for P:
$16,497.06 = [tex]P(1 + 0.06/4)^{4 *15}[/tex]
$16,497.06 = [tex]P(1.015)^{60}[/tex]
P = [tex]$16,497.06 / (1.015)^{60}[/tex]
Using a calculator, we get:
P ≈ $6,752.18
Therefore, the value of the principal investment is approximately $6,752.18 rounded to the nearest hundredths place.
Hence, the answer is $6,752.18.
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the radius of a circle is 4, what is the diameter and circumference
The diameter of the circle is 8, because the diameter is twice the radius. The circumference of the circle is 25.1327, because the circumference is calculated using the formula C = 2πr, where r is the radius and π is approximately equal to 3.14.
Ivania's curtain company is making curtains for a local hotel. She wants each curtain to be 36 inches long. At the fabric store, fabric is sold by the foot. If Ivania's curtain company wants to make 64 curtains, how many feet of fabric will she need?
(pls helppp is it A,B or C??)
Answer:
192 feet of fabric
Step-by-step explanation:
Since each curtain needs to be 36 inches long, or 3 feet long, the total length of fabric needed for one curtain is 3 feet. To make 64 curtains, Ivania's curtain company will need a total of:
3 feet/curtain x 64 curtains = 192 feet of fabric
The number of feet of fabric that Ivania needs to make the curtains is 192 feet.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
Ivania's curtain company is making curtains for a local hotel.
Length of each curtain needed = 36 inches
= 36/12 feet
= 3 feet
At the fabric store, fabric is sold by the foot.
Number of curtains needed to make = 64
We have to multiply the length of each curtain with the total number of curtains to find the total length of the curtain needed.
Feet needed = 64 × 3 feet = 192 feet
Hence the feet of curtains needed is 192 feet.
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Enter a formula in cell C8 that divides the product of cells C5 through C7 by cell C4.
Answer: The formula in cell C8 that divides the product of cells C5 through C7 by cell C4 is:
=(C5C6C7)/C4
Step-by-step explanation:
To divide the product of cells C5 through C7 by cell C4, use the formula =PRODUCT(C5:C7)/C4.
Explanation:To divide the product of cells C5 through C7 by cell C4 in cell C8, you can use the formula =PRODUCT(C5:C7)/C4.
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This question is really hard for me
The calculated length of the segment RP has a value of 150 units
Calculating the length RPFrom the question, we have the following parameters that can be used in our computation:
QW = 11
VP = 50
TU = 90
The length RP is
RP = RQ + QP
Where
QP^2 = (50 + 11)^2 - 11^2 --- Pythagoras theorem
So, we have
QP^2 = 3600
This gives
QP = 60
Recal that
RP = RQ + QP
Where
RQ = TU = 90
So, we have
RP = 90 + 60
Evaluate
RP = 150
Hence, the length RP is 150 units
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Hove
Find the average rate of change indicated below.
y = 4x+1
[-1, 1)
A.15
B.3.75
C.1.875
D.7.5
The average rate of change of the function over the interval is 4
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
y = 4x + 1
The interval is given as
[-1, 1)
The function is a linear function
This means that it has a constant average rate of change
From y = 4x + 1, we have
Rate = 4
Hence, the rate is 4
Read more about average rate of change at
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