Answer:
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
The diameter of the base is 20in, so the radius is half of that, or 10in.
Plugging in the given values, we get:
V = π(10in)^2(16in)
V = 1600π cubic inches
V ≈ 5026.55 cubic inches (rounded to the nearest tenths place)
Therefore, the volume of the cylinder is approximately 5026.55 cubic inches.
Answer: The cylinder's volume is roughly 5026.55 cubic inches.
explanation: The volume of a cylinder is calculated using the formula V = r2h, where r is the radius of the base and h is the cylinder's height.
The radius of the base is half the diameter of the base, or 10in.
With the provided values, we get: V = (10in)2(16in).
1600 cubic inches = V
V 5026.55 cubic inches (rounded to the nearest tenths of a millimeter)
As a result, the cylinder's volume is roughly 5026.55 cubic inches.
Solve the following problems using the Charged Chip model. Please draw pictures and explain your thinking for each
problem:
1.9+(-4)
2.9-(-4)
3.-9+4
4.-9-(-4)
5. Make up your own problem and then solve it!
The values with Charged Chip model are
9 + (-4) = 5.
9-(-4)=13
-9+4=-5
-9-(-4)=-5
To solve 9 + (-4), we start with 9 positive chips and take away 4 negative chips. We can represent this as:
[+][+][+][+][+][+][+][+][+]
[-][-][-][-]
When we combine the chips, we end up with 5 positive chips remaining:
[+][+][+][+][+]
Therefore, 9 + (-4) = 5.
To solve 9 - (-4), we start with 9 positive chips and add 4 negative chips. We can represent this as:
[+][+][+][+][+][+][+][+][+]
[-][-][-][-]
When we combine the chips, we end up with 13 positive chips remaining:
[+][+][+][+][+][+][+][+][+][+][+][+][+]
Therefore, 9 - (-4) = 13.
Similarly -9+4 value is -5
-9-(-4) value is -5
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I need help with the answer
Answer:
Correct equation:
x + 22 + x + 22 + 10 = 48
Please help me and show work
Step-by-step explanation:
'Find the product...' just means multiply the two numbers together:
(use your calculator) 5602 x 17 = 95,234
Product means multiply them together. Please see image showing multiplication. You could also break this up into (5602 x 7) + (5602 x 10), which is basically what I did vertically.
Help xangle, x and
∠
y
∠yangle, y are supplementary angles.
∠
y
∠yangle, y measures
14
2
∘
142
∘
142, degrees.
What is the measure of
∠
x
∠xangle
Answer:
∠x = 38°
Step-by-step explanation:
∠x + ∠y = 180°
∠x + 142° = 180°
∠x = 180° - 142
∠x = 38°
#CMIIWIn a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.7 hours.
A button hyperlink to the SALT program that reads: Use SALT.
(a)
The sample standard deviation was not reported, but suppose that it was 5 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.5 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.)
According to the given sample data, and assuming a sample standard deviation of 5 hours, the results of the hypothesis test suggest that there is substantial evidence to support the assertion that the average time spent using the internet by Canadians exceeds 12.5 hours.
To conduct the hypothesis test, we first set the null and alternative hypotheses. The null hypothesis (H0) states that the mean time spent by Canadians on the internet is equal to or less than 12.5 hours. The alternative hypothesis (Ha) states that the mean time spent by Canadians on the internet is greater than 12.5 hours.
Using the given sample data, and assuming a sample standard deviation of 5 hours, we calculate the test statistic and the p-value. To calculate the test statistic, we use the formula t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
We find that the test statistic is 1.78 (rounded to two decimal places). If the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is strong evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.
If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean time spent using the internet by Canadians is greater than 12.5 hours.
In this case, assuming a significance level of 0.05, we calculate the p-value to be 0.0397 (rounded to four decimal places). Since the p-value is less than the significance level, we reject the null hypothesis and conclude that there is substantial evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.
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Calculate the volume of air in cubic centimeters of a sphere with diameter = 9 centimeters. Use your calculator’s pi button and round answers to two decimal places. V=______ cm3
The volume of air of a sphere with diameter 9 centimeters is 381.51 cubic centimeters
The formula for the volume of a sphere is:
V = (4/3)πr³
where r is the radius of the sphere.
The diameter of the sphere is 9 cm, which means the radius is half of that:
r = 9/2 = 4.5 cm
Substituting this value into the formula, we get:
Volume = (4/3)π(4.5)³
Volume = (4/3)×3.14 × 91.125
Volume = 381.51 cubic centimeters
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Drag one number to each box (?) to make three true statements.
1
2
3
4
5
7
6
7
8
9
3/8 x ?/? > 1
3/8 x ?/? = 1
3/8 x ?/? < 1
Answer: 638
Step-by-step explanation:1
2
3
4
5
7
6
7
8
9
3/8 x ?/? > 1
3/8 x ?/? = 1
Polygon ABCD with vertices at A(-4, 6), B(-2, 2), C(4,-2), D(4, 4) is dilated using a scale factor of to create polygon A'B'C'D'. Determine the vertices of polygon
4
A'B'C'D'.
OA(-3, 4.5), B(-1.5, 1.5), C(3, -1.5), D'(3, 3)
OA(-12, 18), B(-6, 6), C(12,-6), D'(12, 12)
OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3)
OA (4.5, -3), B(1.5, -1.5), C(-1.5, 3), D'(3, 3)
Answer:
The correct answer is: OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3).
To dilate a point using a scale factor of 4, we multiply each coordinate of the original point by 4.
Thus, the coordinates of A' are (-4 * 4, 6 * 4) = (-16, 24)
The coordinates of B' are (-2 * 4, 2 * 4) = (-8, 8)
The coordinates of C' are (4 * 4, -2 * 4) = (16, -8)
The coordinates of D' are (4 * 4, 4 * 4) = (16, 16)
To check our work, we can plot these points on a graph and compare with the original polygon:
Original Polygon:
A(-4, 6) B(-2, 2)
* *
\ /
\ /
\ /
\ /
\ /
* *
C(4,-2) D(4,4)
Dilated Polygon:
A'(-16, 24) B'(-8, 8)
* *
\ /
\ /
\ /
*
C'(16,-8) D'(16,16)
If we divide the coordinates of the dilated polygon by 4, we get the answer:
A'(-16/4, 24/4) = (-4, 6)
B'(-8/4, 8/4) = (-2, 2)
C'(16/4, -8/4) = (4, -2)
D'(16/4, 16/4) = (4, 4)
So the vertices of polygon A'B'C'D' are OA (3, -4.5), B(1.5, -1.5), C(-3, 1.5), and D'(-3,-3).
DATE 5 Sasha has 47 Popsicle sticks (4 bundles of 10 and 7 sticks), and Jose has 62 (6 bundles of 10 and 2 sticks). a Sketch Sasha's sticks in the first box and Jose's in the second box. (Hint: Use rectangle for each bundle and a line for each stick.)
There are 10 bundles and 1 sticks in the Popsicle sticks
Given that Sasha has 47 Popsicle sticks (4 bundles of 10 and 7 sticks)
4B+7S=47
Jose has 62 (6 bundles of 10 and 2 sticks).
6B+2S=62
We have to find B and S values
12B+21S=141
12B+4S=124
Subtract both the equations
21S-4S=141-124
17S=17
Divide both sides by 17
S=1
Now let us plug in the value of S
4B+7=47
4B=40
B=10
Hence, there are 10 bundles and 1 sticks in the Popsicle sticks
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If g(x) is the inverse of f(x), what is the value of f(g(2))?
Answer:
The answer is C) 2.
Step-by-step explanation:
Since g(x) is the inverse of f(x), we know that f(g(x)) = x for all x in the domain of g.
Therefore, f(g(2)) = 2.
The answer is C) 2.
A school is constructing a rectangular play area against an exterior wall of school building. It uses 120 feet of fencing material to enclose three sides of the play area. a Complete the table by giving the length and area for each build. b write an equation to represent l, the length of the play area in feet, as a function of w, the width in feet. c write an equation to represent A, the area in square feet, as a function of w, the width in feet.
An equation to represent A, the area in square feet, as a function of w, the width in feet will be; A = 120W -2W²
Here, the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
To maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have,
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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ASAP PLEASE ANSWER
AND IF U COULD PLEASE ANSWER MY OTHER QUESTIONS THAT ARE FOR COLLEGE, I ACCIDENTALLY PRESSED COLLEGE INSTEAD OF MIDDLE SCHOOL
The statement "Each additional serving will require 1 additional can of beans" is not correct.
How to explain the informationIt should be noted that to make more than 3 servings, Robert will need to increase the amount of both beans and ground turkey used in the recipe.
Assuming that the recipe calls for one 18-ounce can of beans for 3 servings, Robert will need to use 6 cans of beans for 12 servings.
This is because each serving requires 6 ounces of beans (18 ounces ÷ 3 servings), and 12 servings would require a total of 72 ounces of beans (12 servings × 6 ounces per serving).
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A vending machines coin box contains nickels dimes and quarters the total number of coins in the box is 312 the number of dimes is three times the number of nickels and quarters together and the box contains $31.30 find the number of nickels dimes and quarters that it contains
Answer:
58 nickels; 234 dimes; 20 quarters
Step-by-step explanation:
number of dimes = d
number of nickels = n
number of quarters = q
n + d + q = 312
d = 3(n + q)
0.05n + 0.1d + 0.25q = 31.3
n + d + q = 312
d = 3n + 3q
5n + 10d + 25q = 3130
n + 3n + 3q + q = 312
5n + 30n + 30q + 25q = 3130
4n + 4q = 312
35n + 55q = 3130
n + q = 78
7n + 11q = 626
n = 78 - q
7(78 - q) + 11q = 626
546 - 7q + 11q = 626
4q = 80
q = 20
n = 78 - 20 = 58
d = 3(58 + 20) = 3(78) = 234
Answer: 58 nickels; 234 dimes; 20 quarters
i need help pls will give brainlist
Answer:
the answer is C!
A population has a mean = 76 and a standard deviation o = 24. Find the mean and standard deviation of a sampling distribution of sample means with sample
size n = 64.
The mean and standard deviation is x ~ N(76,3).
Given that a population has a mean = 76 and a standard deviation o = 24
We need to find the standard deviation of a sampling distribution of sample means with sample, n = 64.
The mean of the sampling distribution of sample means is =
x = μ
x = 76
Now,
SD = σ/√n
= 24/√64
= 24/8
= 3
Hence, x ~ N(76,3).
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Adrian made a cone from construction paper. the equation for the surface area of a cone is a=pi r^(2)+pi rs, where r is the radius of the base and s is slant height of the cone. dimensions of the cone are h=,8 ; r=,3
what is the total of paper needed?
The total amount of paper required is 3π(3+√71)unit²
The equation for the surface area of a cone is given as follows:
A = πr²+πrs.
Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)
Substituting the values of r & h to determine s
s = √(8²+3²)
s = √71
Substituting the values to get Area,
A=π*3²+π*3*√71.
A=3π(3+√71)
Hence, the required paper will be A=3π(3+√71)unit²
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Factor the following expressions completely. Show and check all work on your own paper.
4x4+8x3+4x2
The complete factorization of the original expression is:
4x² (x + 1)²
We have,
First, we can factor out 4x².
4x² (x² + 2x + 1)
Next, we can see that the expression inside the parentheses is a perfect square trinomial, which means it can be factored as:
4x² (x + 1)²
Thus,
The complete factorization of the original expression is:
4x² (x + 1)²
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A fair coin is tossed 8 times. Find the probability it comes up heads at least TWICE. Will give brainliest!!
Step-by-step explanation:
At least twice means it could be 2 3 4 5 6 7 or 8 heads
there is 8 chances of having only one TAIL
there are 2^8 outcomes = 256 outcomes possible
take away the EIGHT with one tail
248 out of 256 have at least 2 heads
248/256 = 31/32
( Let me know if this is incorrect and I will re-evaluate !)
Answer:
[tex]\frac{247}{256}[/tex]
Pre-requisite Knowledge:
Permutations and Combinations
Elementary Probability
Step-by-step explanation:
Total number of outcomes (Cardinality of the sample space) = [tex]2^{8}[/tex]
P(at least 2 heads show up) = 1 - [ P(no Head) + P(exactly 1 Head) ]
[tex]= 1-\frac{C(8,0)+C(8,1)}{2^8}\\\\=1-\frac{1+8}{256}\\\\ =1-\frac{9}{256}\\\\= \frac{247}{256}[/tex]
In a class of students, the following data table summarizes how many students have a
cat or a dog. What is the probability that a student chosen randomly from the class
does not have a cat?
The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
The class has a cat and a dog = 9
Has a dog and does not have a cat = 2
Does not have a dog and has a cat = 4
Does not have dog and cat = 5
The total strength of the class is 20
The probability that a student is chosen randomly from the class has a cat or a dog = Number of favorable outcomes / total number of outcomes
P(E) = 15 /20
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Answer:
Step-by-step explanation:
its 11/28
using the Pythagorean Identity to find the exact value (i.e. Radicals and fractions, not rounded decimals) of sin θ if cosθ=1/2 and θ terminates in Quadrant IV
1) 〖 sin〗^2 θ+〖cos〗^2 θ=1
Step 1: Pythagorean Identity
2) 〖sin〗^2 θ+〖(1/2)〗^2=1 Step 2: Substitute 1/2 for cos θ
The exact value of sin θ, given that cosθ = 1/2 and θ terminates in Quadrant IV, is -√(3)/2.
The Pythagorean Identity states that sin²θ + cos²θ = 1. This identity can be used to find the value of sinθ, given the value of cosθ, and vice versa.
In Quadrant IV, the cosine function is positive, and the sine function is negative. This is because in Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative.
Given that cosθ=1/2, we can use the Pythagorean Identity to find the value of sin²θ.
sin²θ + cos²θ = 1
sin²θ + (1/2)² = 1
sin²θ + 1/4 = 1
sin²θ = 1 - 1/4
sin²θ = 3/4
To find the value of sinθ, we take the square root of both sides of the equation:
sinθ = ±√(3/4)
However, since θ terminates in Quadrant IV, sinθ is negative. Therefore, we take the negative square root of 3/4:
sinθ = -√(3/4)
We can simplify this expression by writing 3/4 as a fraction in terms of its square roots:
sinθ = -√(3/4)
sinθ = -√(3)/√(4)
sinθ = -√(3)/2
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Line, line segment, angle,ray
PLEASE HELP!!!!!! I WILL MARK BRAINIEST!!!!!
g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.
Option C is the correct answer.
We have,
To find the transformation that maps f(x) to g(x), we need to determine how the points of g(x) relate to the points of f(x).
First, we can see that the two functions have the same x-coordinates (1 and 4). This means that the transformation only affects the y-coordinates of the points.
At x = 1,
f(x) has a y-value of 4, and g(x) has a y-value of 2.
This means that g(x) is f(x) after vertical compression by a factor of 1/2.
At x = 4, f(x) has a y-value of 8, and g(x) has a y-value of 4.
This means that g(x) is f(x) after vertical compression by a factor of 1/2.
Therefore,
g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.
i.e
g(x) = (1/2) f(x)
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find the value of 6!.
Answer:
the absolute value of 6 is just 6
Explain why or why not the given divisions of integers will be rational
A) 0/3. B) 3/0. C) -3/8
The rational numbers are solved and the incorrect number is A = 3/0
Given data ,
Let the rational number be represented as A
Now , the value of A is
A)
The division 0/3 will be a rational number because any number divided by 0 is undefined, but in this case, the division is defined and the result is 0, which is a rational number.
B)
The division 3/0 will not be a rational number because any number divided by 0 is undefined, and therefore, the division is not defined.
C)
The division -3/8 will be a rational number because it can be expressed as a ratio of two integers (-3 and 8) and can be written in the form of a fraction -3/8
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please helppp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Using Pythagorean trigonometric identity, the value of cosθ is √2/2
What is the value of cosθTo find the value of cosθ, we can use Pythagorean identity to do this. However, we are also told that θ terminates in the the first quadrant.
sinθ = √2/2
sin²θ + cos²θ = 1
Substituting the value of sin θ into the formula above
cos²θ + (√2/2)² = 1
cos²θ + 1/2 = 1
collect like terms
cos²θ = 1 - 1/2
cos²θ = 1/2
cosθ = √(1/2)
cosθ = √2/2
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When spinning a penny, Claire believes the proportion of times the penny lands on heads is not 0.5. She spins a penny 50 times and it lands on heads 30 times. Which hypotheses would test Claire’s claim?
The hypothesis are
Null Hypothesis: The proportion of time the penny lands on heads 0.5
Alternative Hypothesis: The proportion of times the penny lands on heads in not 0.5.
We can denote the proportion of times the penny lands on heads as p.
If the null hypothesis is true, then p = 0.5. If the alternative hypothesis is true, then p is not equal to 0.5.
We can use a hypothesis test to determine if the sample data provides evidence to reject the null hypothesis in favor of the alternative hypothesis. One possible hypothesis test is the two-tailed z-test for proportions.
To perform this test, we would calculate the test statistic :
z = (p' - p) / √(p x (1-p) / n)
where p' is the sample proportion, p is the null hypothesis proportion (0.5), and n is the sample size.
In this case, we have a sample size of n = 50 and a sample proportion of p' = 30/50 = 0.6. We can calculate the test statistic:
z = (0.6 - 0.5) / √(0.5 x 0.5 / 50)
z ≈ 2.24
To determine if this test statistic is significant at the 5% level, we would compare it to the critical values from the standard normal distribution. For a two-tailed test at α = 0.05, the critical values are -1.96 and 1.96.
Since 2.24 falls outside of this range, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the proportion of times the penny lands on heads is not 0.5.
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Ahmed placed salt water in a beaker and left it on his desk for a week. After a week, there was only salt. Which best explains the missing water from the beaker?
A. The water became a new substance.
B. The water evaporated.
C. The water disappeared forever.
D. The water condensed.
The water evaporated.
Option B is the correct answer.
We have,
When a liquid is left open in a container, it can undergo a phase change to become a gas or vapor, which is known as evaporation.
In this case,
The water in the beaker would have evaporated, leaving behind the salt. The water did not disappear forever but instead changed state to become a gas in the air.
Thus,
The water evaporated.
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need help will give brainlist
The expressions that shows a correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is (-4-6) / (-7 - 3) (option c).
To find the slope of a line that passes through two points, we can use the slope formula, which is:
slope = (change in y) / (change in x)
This formula tells us how much the y-coordinate changes (rise) for every one unit of change in the x-coordinate (run).
Now let's use the given points (3,6) and (-7,-4) to set up the slope formula. We'll call the first point (x₁, y₁) and the second point (x₂, y₂). Then we can plug these values into the slope formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Plugging in the coordinates of the two given points, we get:
slope = (-4 - 6) / (-7 - 3)
We simplify this expression to get:
slope = (-10) / (-10)
Which simplifies further to:
slope = 1
So the correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is:
slope = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 6) / (-7 - 3)
= 1
Therefore, the slope of the line passing through these two points is 1.
Hence the correct option is (c).
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5 1/2 feet =what to inches
Answer:
66 inches
Step-by-step explanation:
Every foot is twelve inches
Answer: 66 inch is in 5 1/2 feet
Step-by-step explanation: there is 12 inches in 1 foot so you do 12 x 5= 60 then there is 6 inches in a half of a foot so you add 60 and 6 and you get 66 inches
In the function above, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function
The equation of the new line will be y = -9x + 4. Then the correct option is B.
Given that:
Linear equation, y = x + 2
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The y-value of the y-intercept will be raised by 2 units, and the slope will be multiplied by -9.
Then the slope of the equation will be given as,
m = -9 x 1
m = - 9
The y-intercept of the equation is given as,
c = 2 + 2
c = 4
The equation of the new line will be y = -9x + 4. Then the correct option is B.
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In the function y = x + 2, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function
