Answer:
120 pi
Step-by-step explanation:
a. 1/3pi(6)^2(10)
just plug them into the calculator using pi.
b. pi is more accurate because you aren't round to 3.14. If you use 3.14 your answer will be rounded and not an exact number.
The volume of the cone is 120π.
Because 3.14 is an approximation to π which is accurate to about one twentieth of a percent.
What is the volume of the cone?The volume of the cone is;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\Where \ r= radius , \ h = height[/tex]
A trap to catch fruit flies uses a cone in a jar.
The cone is shown with a height of 10 centimeters (cm) and a radius of 6 centimeters (cm.)
1. The volume of the cone is;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\ Volume \ of \ cone=\dfrac{1}{3}\times \pi \times 6^2\times 10\\\\ Volume \ of \ cone=\dfrac{1}{3}\times \pi \times 36\times 10\\\\ Volume \ of \ cone=120\pi \\\\[/tex]
The volume of the cone is 120π.
2. Because 3.14 is an approximation to π which is accurate to about one twentieth of a percent.
If you are dealing with everyday physical measurements, this accuracy for π will likely exceed the accuracy of your measurement (such as your height to within a millimetre or four hundredths of an inch!). Hence a calculated answer would not be more accurate than if you simply used 3.14 or, just to be sure, 3.142.
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Suppose that a researcher studying public opinion on raising taxes to pay for road repairs finds that in a simple random sample of 541 adult residents of the state, that 345 of the residents agree that taxes should be raised for road repairs. When testing the claim that the proportion of adults who favor raising taxes is greater than 0.60, the P-Value of 0.0367 is obtained.
Interpret this result for someone who doesn't know statistics.
They ask: "what can we know for certain?" Broadly answer their question.
The interpretation of the p-value itself does not provide certainty about the truth or falsehood of the claim being tested.
Instead, it helps assess the strength of the evidence against the null hypothesis the assumption that the proportion is not greater than 0.60.
Based on the provided information and the obtained p-value of 0.0367, there are a few conclusions draw for certain,
The researcher conducted a survey among 541 adult residents of the state regarding their opinion on raising taxes for road repairs.
In the sample, 345 residents out of the 541 agreed that taxes should be raised for road repairs.
The researcher tested a claim or hypothesis that the proportion of adults favoring raising taxes is greater than 0.60 (60%).
The p-value of 0.0367 was obtained as a result of the statistical test.
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Beth filled 48 jars with paint. If each jar holds 1 pint of paint, how many gallons of paint did Beth use?
The gallons of paint that Beth used is 6 gallons.
How many gallons did Beth use?The first step is to convert pint to gallon:
1 pint = 0.125 gallon
The second step is to multiply 0.125 by 48 : 0.125 x 48 = 6 gallons
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The width of a rectangle is 4 feet and the diagonal length of he rectangle is 13 feet what is the measurement is the closest to the length of the rectangle in feet
Answer:
The length is APPROXIMATELY equal to 12.4.
Step-by-step explanation:
Use the converse of the Pythagorean Theorem ([tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex] [where "c" is both the longest side and the hypotenuse]) since a rectangle's diagonals will always cut it into two right triangles:
[tex]13^{2} = 169[/tex]
[tex]4^{2} =16[/tex]
169-16=153.
[tex]\sqrt{153}[/tex] ≈ 12
or
[tex]\sqrt{153}=12.36931688[/tex]
or if the problem has to be exact (using radicals)
3*[tex]\sqrt{17}[/tex]
I hope this helps ;)
The price p (in dollars) and the demand x for a particular clock radio are related by the equation x=4000-40p. (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 2700 clock radios. (D) Interpret R'(3200) = -60.00.
A) The price-demand relationship for a clock radio is given by x=4000-40p. B) The revenue function R(x) is found to be R(x) = x * [(4000 - x) / 40]. C) The marginal revenue at a production level of 2700 clock radios is calculated using the derivative R'(x) = (4000 - 3x) / 40, and D) R'(3200) = -60.00 indicates a decrease in revenue of $60.00 per unit at a production level of 3200 clock radios.
(A) To express the price p in terms of the demand x, we can rearrange the equation x=4000-40p to solve for p. Subtracting x from both sides and dividing by -40, we get p = (4000 - x) / 40. The domain of this function represents the possible values for x, which should be non-negative since it doesn't make sense to have negative demand. Therefore, the domain is x ≥ 0.
(B) The revenue R(x) from selling x clock radios can be calculated by multiplying the price p by the quantity x. Since p = (4000 - x) / 40, we have R(x) = x * p = x * [(4000 - x) / 40]. The domain of the revenue function depends on the domain of x, which we determined in part (A) as x ≥ 0.
(C) The marginal revenue represents the change in revenue resulting from producing one additional unit. To find the marginal revenue at a production level of 2700 clock radios, we need to find R'(x) (the derivative of the revenue function) and evaluate it at x = 2700. Differentiating R(x) = x * [(4000 - x) / 40] with respect to x, we find R'(x) = (4000 - 3x) / 40. Substituting x = 2700 into the derivative, we get R'(2700) = (4000 - 3 * 2700) / 40.
(D) The interpretation of R'(3200) = -60.00 is that the marginal revenue at a production level of 3200 clock radios is -60.00 dollars per unit. This means that producing an additional unit at this level would result in a decrease in revenue by $60.00. The negative value indicates a diminishing marginal revenue, which suggests that the market might be becoming saturated or that there are competitive factors affecting the demand for the clock radios.
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find the length of the arc on a circle of radius 14 inches intercepted by a central angle 140.
The length of the arc intercepted by a central angle of 140° on a circle with a radius of 14 inches is approximately 34.1557 inches.
To find the length of the arc intercepted by a central angle on a circle, we can use the formula:
Arc Length = (Central Angle / 360°) * Circumference
In this case, the radius of the circle is 14 inches, and the central angle is 140°.
First, we need to calculate the circumference of the circle:
Circumference = 2 * π * radius
Circumference = 2 * π * 14 inches
Now, we can calculate the length of the arc:
Arc Length = (140° / 360°) * Circumference
Arc Length = (140/360) * (2 * π * 14 inches)
Arc Length ≈ (0.3889) * (2 * 3.1416 * 14 inches)
Arc Length ≈ 0.3889 * 87.9648 inches
Arc Length ≈ 34.1557 inches
Therefore, the length of the arc intercepted by a central angle of 140° on a circle with a radius of 14 inches is approximately 34.1557 inches.
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In a recent election 65% of people supported reelecting the incumbent. Suppose a poll is done of 1390 people. If we used the normal as an approximation to the binomial, what would the mean and standard deviation be?
A standard deviation of 23.16.
In a recent election, where 65% of people supported reelecting the incumbent, a poll was conducted with a sample size of 1390 people.
To approximate the binomial distribution with a normal distribution, we can calculate the mean and standard deviation.
The mean is determined by multiplying the sample size (1390) by the proportion of support (0.65), resulting in a mean of 898.5.
The standard deviation is calculated by taking the square root of the product of the proportion of support (0.65) with the proportion of opposition (0.35), divided by the sample size, and then multiplied by the square root of the sample size.
This yields a standard deviation of approximately 23.16.
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Which of the following would indicate the possible presence of multicollinearity in a regression analysis?
a. a significant p-value for a test of overall significance
b. a high correlation between two or more independent variables.
c. a small value for the coefficient of determination
d. All of these choices would be indicators of possible multicollinearity.
B) A high correlation between two or more independent variables would indicate the possible presence of multicollinearity in a regression analysis.
Multicollinearity occurs when two or more independent variables in a regression model have a strong correlation with one another, making it difficult to distinguish the individual influence of each independent variable on the dependent variable.
Poorly constructed experiments, heavily observational data, introducing new variables that are dependent on other factors, including identical variables in the dataset, incorrect use of dummy variables, or inadequate data can all lead to multicollinearity.
Calculating the variance inflation factor (VIF) for each independent variable is one way for detecting multicollinearity; a VIF value more than 1.5 shows multicollinearity.
To correct multicollinearity, one of the highly correlated variables can be removed, combined into a single variable, or a dimensionality reduction approach such as principal component analysis can be used.
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Please help !!!!!! Thanks
Step-by-step explanation:
[tex]2 \times 14 \times 13 +12 \times 10 + 14 \times 10 = \\ = 624[/tex]
Find the missing side length and round it to the nearest tenth please :)
Answer:
171
Step-by-step explanation:
This is a Right triangle,
So this means that all the sides should add up to 180,
So far we have 9
So we will have to Subtract 9 from 180 which leaves us with 171,
I hope this is correct!!
pls help how do i solve log(5x+2)=1
like what rule do I use and how do I do it step by step
Answer:
x = -0.2
Step-by-step explanation:
(5x + 2) = 1
- 2 -2
--------------------
5x = -1
Divide each side by 5
-1/5
= -0.2
Check:
(5x + 2) = 1
replace x with -0.2
(-1 + 2) = 1
1 = 1
The equation is true.
Hope this helped :)
A local fast food chain had revenue represented by the polynomial 6x ^ 2 + 5x - 8 for one fiscal year and expenses for that same fiscal year represented by the polynomial 4x ^ 2 - 3x + 7 7. What was the company's profit for the fiscal year?
Answer:
2x^2+8x - 16
Step-by-step explanation:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
Given
R(x) = 6x ^ 2 + 5x - 8
C(x) = 4x ^ 2 - 3x + 7
P(x) = 6x ^ 2 + 5x - 8-(4x ^ 2 - 3x + 7)
P(x) = 6x ^ 2 + 5x - 8 - 4x ^ 2 + 3x - 8
Collect the like terms;
P(x) = 6x^2-4x^2+5x+3x-8-8
P(x) = 2x^2+8x - 16
Hence the company's profit for the fiscal year is 2x^2+8x - 16
f
) Solve by Gaussian-Jordan algorithm (reducing to rref). Show all the row operations you applied! -2x + 3y + z -3x + y + 3z = -2 = -4 2y - z = = 0
By applying the Gaussian-Jordan algorithm to the given system of equations, we can find the reduced row-echelon form (rref) of the system. The resulting rref shows that the system is consistent, and the solution is x = 1, y = -28/17, and z = -28/17.
We start by writing the augmented matrix of the system:
[ -2 3 1 -2 ]
[ -3 1 3 -4 ]
[ 0 2 -1 0 ]
To obtain the rref, we perform row operations to eliminate the coefficients below and above the pivots. Our goal is to transform the matrix into the following form:
[ 1 0 0 a ]
[ 0 1 0 b ]
[ 0 0 1 c ]
First, we divide the first row by -2 to make the pivot in the first column 1:
[ 1 -3/2 -1/2 1 ]
[ -3 1 3 -4 ]
[ 0 2 -1 0 ]
Next, we perform row operations to eliminate the coefficient -3 in the second row:
[ 1 -3/2 -1/2 1 ]
[ 0 2/2 9/2 -7 ]
[ 0 2 -1 0 ]
Then, we divide the second row by 2 to make the pivot in the second column 1:
[ 1 -3/2 -1/2 1 ]
[ 0 1 9/4 -7/2 ]
[ 0 2 -1 0 ]
Now, we perform row operations to eliminate the coefficient 2 in the third row:
[ 1 -3/2 -1/2 1 ]
[ 0 1 9/4 -7/2 ]
[ 0 0 -17/4 7 ]
Finally, we divide the third row by -17/4 to make the pivot in the third column 1:
[ 1 -3/2 -1/2 1 ]
[ 0 1 9/4 -7/2 ]
[ 0 0 1 -28/17 ]
The resulting rref shows that the system is consistent, and the solution is x = 1, y = -28/17, and z = -28/17.
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Find the area of a circle with radius 14 mm. Round your answer to the nearest tenth.
Step-by-step explanation:
1cantimeter=10mm
14mm=1.4cm
Area of circle pi r²=pi*1.4²=1.96pi
math help please now
Answer:
1. Yes
2. Yes
3. No
4. Yes
Step-by-step explanation:
Complementary angles are angles that add up to 90 degrees.
For 1, 76+14 = 90.
Etc., you can do the math, I believe you are smarter than addition.
There were two times as many pepperoni pizzas as cheese pizzas, plus one pizza they ordered 13 pizzas altogether how many pepperoni pizzas were there? How many cheese pizzas were there
Answer:
pepperoni pizzas = 8
cheese pizzas = 4
Step-by-step explanation:
let x = cheese pizza
2x + x + 1 = 13
3x = 13 -1
3x = 12
x = 4
pepperoni = 2x4 = 8
You earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour. You need to earn at least $120 per week, but you do not want to work more than 20 hours per week. a. Write a system of linear inequalities that represents the situation. Use x for hours worked at the grocery store and y for hours teaching music lessons. i need the inequility for total work. please fast
Answer:
without numbers= 10x + 15y = 120
Step-by-step explanation:
grocery store= 10x (x=8 in this case)
music lessons= 15y
48 - 5 + 7 · 3² ÷ (7-10)²
Answer:
the answer is 50
Answer:
50
Step-by-step explanation:
BODMAS/BIDMAS
48 - 5 + 7 x [tex]3^{2}[/tex] ÷ (7-10)²
= 48 - 5 + 7 x [tex]3^{2}[/tex] ÷ (-3)²
= 48 - 5 + 7 x [tex]3^{2}[/tex] ÷ 9
= 48 - 5 + 7 x 9 ÷ 9
= 48 - 5 + 63 ÷ 9
= 48 - 5 + 7
= 43 + 7
= 50
on a certain hot summer day 688 people used the public swimming pool. the daily prices are 1.75 for children and 2.00 for sdults the receipt for admission totaled 1293.50. how many children and how many adults swam at the public pool that day
Answer:
Number of children = x = 330
Number of adults = y = 358
Step-by-step explanation:
Let
Number of children = x
Number of adults = y
x + y = 688 (1)
1.75x + 2.00y = 1293.50 (2)
From (1)
x = 688 - y
Substitute x = 688 - y into (2)
1.75x + 2.00y = 1293.50
1.75(688 - y) + 2.00y = 1293.50
1,204 - 1.75y + 2.00y = 1293.50
- 1.75y + 2.00y = 1293.50 - 1,204
0.25y = 89.50
y = 358
Substitute y = 358 into (1)
x + y = 688
x + 358 = 688
x = 688 - 358
x = 330
Number of children = x = 330
Number of adults = y = 358
If the length of a rectangle is 10 feet and the width is 3 inches, what is the area of the rectangle in units of
square feet?
Answer:
30 ft
Step-by-step explanation:
10 feet = 120 inches
120 in x 3 in = 360 in
360 in ÷ 12 in = 30 ft
Please Help!!!! What is the final step to prove....
Answer:
D
Step-by-step explanation:
Step 1(Base step) − It proves that a statement is true for the initial value.
Step 2(Inductive step) − It proves that if the statement is true for n=k, then it is also true for n=k+1.
In the diagram, point K is a point of tangency, MK = 720, and MN = 648. What is the radius of J
A. 76
B. 70
C. 72
D. 64
The radius of J is 76. so option A is correct.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
By applying Pythagoras theorem In right triangle,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
(720 + J)² = (648)² + J²
518400+ J² + 1440J = 419904 + J²
1440J = 518400- 419904
J = 76
Therefore, J = 76 units is the answer.
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3u = 72 simplified math problem
Answer:
Simplifying
3u = 72
Solving
3u = 72
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Divide each side by '3'.
u = 24
Simplifying
u = 24
3u= 72
three will go to the other side so it will divide
and it well be
u= 24
or each of the following functions, find the constant c such that f(x)is a pdf; find the cdf, f(x)= p(x ≤ x); graph the pdf and cdf; and find μ and σ2: (a) f(x)= 4xc for 0 ≤ x ≤ 1
c = 1/2 ,the mean is μ = 1/2, the CDF of f(x) is 2x^2 and the variance is σ² = 1/6.
The given pdf is f(x) = 4xc for 0 ≤ x ≤ 1.
To find the constant c such that f(x) is a pdf: We know that, For f(x) to be a pdf, it must satisfy the following two conditions:
The integral of f(x) over its support should be equal to 1. f(x) must be greater than or equal to 0 for all values of x. So,
Let us find the value of c first integral of f(x) from 0 to 1 should be equal to 1, therefore∫f(x)dx = ∫(4xc)dx for 0 ≤ x ≤ 1∫f(x)dx = 4∫xc dx for 0 ≤ x ≤ 1∫f(x)dx = 4[c(x^2/2)]_0^1∫f(x)dx = 2c
Therefore,∫f(x)dx = 1 implies 2c = 1 or c = 1/2.
Now we know the value of c. Let us find the CDF of f(x): CDF of f(x) = P(x ≤ X) = ∫f(t)dt from -∞ to x= ∫f(t)dt from 0 to x= ∫(4xt)dt from 0 to x= 2x^2 from 0 to x= 2x^2Therefore, the CDF of f(x) is 2x^2.
Graph of the PDF of f(x)For graphing the PDF of f(x), we need to know the values of x for which f(x) is defined as well as its shape and maximum value.f(x) = 4xc for 0 ≤ x ≤ 1The given function is a straight line with a slope of 4c and intersects the x-axis at 0 and the y-axis at 0.
We know that c = 1/2, thus (x) = 2x for 0 ≤ x ≤ 1The graph of f(x) will look as follows: Graph of the CDF of f(x)The graph of the CDF of f(x) will look as follows:
We can find the mean and variance of the PDF of f(x) using the following formulae: Mean, μ = ∫xf(x)dx from -∞ to ∞.Variance, σ² = ∫(x - μ)²f(x)dx from -∞ to ∞.
Substituting f(x) and its limits in the above formulae, we get: Mean, μ = ∫xf(x)dx from 0 to 1= ∫(2x^2)x dx from 0 to 12(1^4 - 0^4)/4= 1/2.
Variance, σ² = ∫(x - μ)²f(x)dx from 0 to 1= ∫(x - 1/2)²(2x)dx from 0 to 1= 1/6.
Therefore, the mean is μ = 1/2, and the variance is σ² = 1/6.
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A researcher was interested in how students' college major affected their opinions on environmental safety. To investigate this a researcher gave a environmental safety questionnaire to 20 random business majors and 20 random neuroscience majors. Their responses to the questionnaire were not normally distributed. What is the most appropriate statistical test for these data from the list below? Wilcoxon Signed Rank test Student's t-test O Wilcoxon Ranked Sum test Paired t-test
The most appropriate statistical test for these data from the list below would be: the Wilcoxon Ranked Sum test.
Why is the Wilcoxon Ranked Sum test best?The Wilcoxon Ranked Sum test is the best for the analysis because it does not assume a normal distribution. The Wilcoxon ranked sum test compares two independent populations to determine if there is a statistical significance between them.
In the example given there is no normal distribution, so the Wilcoxon Ranked Sum test will analyze the responses differently to confirm if there is a relationship.
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Round to the nearest tenth
8.94427191
Answer:
8.9
Step-by-step explanation:
8.94427191
Answer:
8.9
Step-by-step explanation:
8.94427191 the number 1 spot to the right of the decimal point is tenths. the number is 9 the number to the right of that is 4. unless that number 2 digits to the right of the decimal point is 5 or over the 9 stays the same
Help pleaseeeeeeeeeee
Answer:
5 is c 6 is b
Step-by-step explanation:
Answer:
5) C 6) B
Step-by-step explanation:
Yw
solve the equation, then check s + 10.5 = 17.
Answer:
s=6.5
Step-by-step explanation:
to check, just substitute s for its value
6.5+10.5+17
so the correct answer is, s=6.5
») What is the circumference of the rim of a basketball hoop with a radius of 9 inches? First, multiply the radius by__ to get the diameter__ inches. Then, multiply the diameter by 3.14 (an approximation for 1) to get a circumference of
about__ inches. ») Convince Me! If the diameter is doubled, what happens to the circumference? Explain.
Answer:
First, multiply the radius by 2 to get the diameter 18 inches. Then, multiply the diameter by 3.14 (an approximation for 1) to get a circumference of about 56.52 inches. If the diameter doubles the circumference doubles.
Step-by-step explanation:
18π = 56.52
36π = 113.04
56.52*2 = 113.04
How many solutions does the nonlinear system of equations graphed below
have?
The curves are intersecting at (-1.75, 2.5) and (1.75, 2)
Nonlinear functions include all functions that are not linear. The following are some instances of nonlinear functions: f(x) = x2 - 2x + 2, ln (x), ex, etc.
In the above question, a graphical representation of non-linear system of equations is given
We need to find the solution of this non-linear system of equations based on the graphical representation
We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations
We can clearly see that, the curves are intersecting at
(-1.75, 2.5) and (1.75, 2)
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i dont have a question for this. look at the photo
Answer:
first is no second is yes third is no fourth is yes
Step-by-step explanation:
I'm not sure btw