Therefore ,the radius of the given cylinder is 10 inches
What is volume ?A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.
Here,
The volume of the cylinder is 1570 cubic inches
Volume of the cylinder = 1570 cubic inches
Volume of cylinder = π[tex]r^{2}[/tex]h
Where r is the radius of cylinder
h is the height of cylinder
So,
Volume of the cylinder = 1570 cubic inches
=> 1570 = π[tex]r^{2}[/tex]h
=> 1570 = 3.14*[tex]r^{2}[/tex]*5
=> 1570/3.14 = [tex]r^{2}[/tex]*5
=> 500=[tex]r^{2}[/tex] *5
=> 500/5 =[tex]r^{2}[/tex]
=>100 =[tex]r^{2}[/tex]
=>r=10 inches
Therefore the radius of the given cylinder is 10 inches.
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Find The value of my coins. If i have p pennies, n nickels and twice as many quarters as pennies.
Translate into an algebraic expression and simplify if possible.
The value of p pennies, n nickels and twice as many quarters as pennies is (51p + 5n) cents or $(51p + 5n)/100.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).
Given that you have p number of coins of pennies, n number of coins of nickels and twice as many quarters as pennies.
Thus the number of coins of quarters is 2p.
The value of penny, nickel, and quarter are
1 penny = 1 cent
1 nickel = 5 cents
1 quarter = 25 cents
The value of p number of pennies is p cents.
The value of n number of nickels is (n×5) =5n cents.
The value of 2p number of quarter is (2p × 25) = 50p cent.
The total value is p + 5n + 50p = (51p + 5n) cents
Divide 51p + 5n by 100 to convert it into dollar:
(51p + 5n) cents = $(51p + 5n)/100
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Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using first two then four rectangles.f(x)=x^3 between x=0 and x=1
The area under the graph using the first two and then four rectangles = 0.221 unit square
According to the graphs given in the below figure,
Given in the question,
f(x) = [tex]x^{3}[/tex] when x = 0 and x = 1
The first rectangle of the first graph goes from 0 to 0 .6,
Width = 0.6
Height measured from the middle point = 0.3
f( 0.3) = [tex]( 0.3)^{3}[/tex]
f(0.3) = 0.027 units.
Area of first rectangle = 0.6 x 0.027 = 0.0162 unit square
Now taking the second rectangle of the first part,
It is going from 0.6 to 1.0,
Width = 0.4 units
height = 0.8 units
Height measured from the middle-
f(0.8) = [tex](0.8)^{3}[/tex] = 0.512
Area of the second part of the rectangle = 0.512 x 0.4
= 0.2048 unit square
Final area = 0.2048 + 0.0162 = 0.221 square units
Therefore, the same could be done with the second part rectangle of 4
For the given first part of four rectangles = width = 0.6 units and height = 0.1 unit
so f(0.1) = [tex]0.1^{3}[/tex]
= 0.001 units
Therefore, the area under the graph using the first two and then four rectangles = 0.221 unit square
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Line p passes through points (8, 7) and (4, 4). Line q is parallel to line p. What is the slope of line q?
Answer:
slope of line q = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
calculate the slope of line p using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )
m = [tex]\frac{4-7}{4-8}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes
then slope of line q = [tex]\frac{3}{4}[/tex]
Suppose 41% of the registered voters in a country are Republican. If a sample of 488 voters is selected, what is the probability that the sample proportion of Republicans will be greater than 44%?
The probability that the sample's Republican percentage will be higher than 44% is 0.089.
What is probability?Probability is a metric used to express the possibility or chance that a particular event will occur.
Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
To determine the probability of a sample proportion, the normal probability is used as the z-test statistic of one sample proportion.
When the sample size is big, the z-test statistic, a normal test statistic, is employed.
So, the probability will be:
We know that the sample size is n = 488 and the proportion is p = 0.41.
Now, obtain P(p > 0.44) as follows:
[tex]\begin{aligned}& P(\hat{p} > 0.44)=1-P\left(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} \leq \frac{0.44-p}{\sqrt{\frac{p(1-p)}{n}}}\right) \\& P(\hat{p} > 0.44)=1-P\left(Z \leq \frac{0.44-0.41}{\sqrt{\frac{0.41(1-0.41)}{488}}}\right) \\& P(\hat{p} > 0.44)=1-P(Z \leq 1.347)\end{aligned}[/tex]
Excel function for the p-value:
P(p > 0.44) = 1 - 0.911
P(p > 0.44) = 0.089
Therefore, the probability that the sample's Republican percentage will be higher than 44% is 0.089.
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Put the following values in order from greatest to least.
Justify your answer.
0.388
3/8
38.38%
0.39
Answer:
0.39, 0.388, 38.38%, 3/8
Step-by-step explanation:
The owner of a landscaping business wants to know how much time, on average, his workers spend mowing one lawn. Which is the most appropriate rate with which to calculate an answer to his question?
lawns per employee
hours per lawn
employee per lawn
lawns per day
The mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1. It can be solved by rate of work.
The rate lawns per employee gives the lawns mowed by one employee.
The rate hours per lawn gives the number of hours required to mow one lawn.
The rate employee per lawn gives how many employees are required to mow one lawn.
The rate lawns per day gives the number of lawn mow in one day.
Since the mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1.
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Select the correct location on the expression.
Mateo uses this exponential expression to determine the balance of his savings account. Which value in the expression represents the
annual interest rate for his savings account?
100(1+0,02)
12t
Answer:
0,02
Step-by-step explanation:
i got it correct
Simplify by combining like terms.
3a +15-2a²+5a²-7+5a
Answer:
8a + 3a^2 + 8
Pls help what this is
Stem-and-leaf plots
Answer:
C is the answer
Step-by-step explanation:
Stem and leaf plots were also confusing to me at first, but once you understand they are actually easy!
Look at the first column where it says 2,3,4,5 and 6. Those are the tens place. The columns next to it with 2,3,8,9,etc are the ones place. For example, the first column has two, so we know that the number has a two in the tens place.
2_
Look at the numbers next to it, there's 2,3, and 8.
Since there's 3 numbers, that means that there are three numbers that have a two in the ones place. 2,3 and 8 are the numbers that go in the ones place.
So in the graph there is 22,23 and 28.
If you look at your choices, you can find all of them except 38, since on the row with the 3, next to it is the number 9 and not the number 8.
Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modeled by the function y=3.5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary.
The rate of change of the modelled equation is 3.5 and the initial value is 5.
How to find the rate of change in a slope intercept equation?Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.
Equation in slope intercept form is as follows:
y = mx + b
where
m = slope = rate of changeb = y-intercept = initial valueTherefore, Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modelled by the function y = 3.5x + 5 where y is the total miles jogged and x is the number of hours.
The equation is modelled in slope intercept form.
Therefore,
rate of change = 3.5
initial value = 5
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Factor a²+4 b² completely.
a²+4b²=_____
Answer: The expression a²+4b² can be factored in the following way:
a²+4b² = (a² + 2ab + 2ab + 4b²)
= (a+b)²
In general, the square of a binomial (a+b) can be written as (a+b)² = a² + 2ab + b². This is known as the "square of a sum" formula. In this case, we can apply this formula to the binomial a+b to obtain a² + 2ab + b² = (a+b)². We can then use the fact that the square of a binomial can be written as the square of each term plus twice the product of the two terms. This allows us to write the expression as (a+b)² = a² + 2ab + b² = a² + 2ab + 2ab + 4b² = (a² + 2ab + 2ab + 4b²) = (a²+4b²). Therefore, the fully factored form of a²+4b² is (a+b)².
The ratio of top dogs to fat cats was 24 to 19. if they were 152 fat cats, how many top dogs were there?
The ratio shows how many times one value is contained in another value.
The number of top dogs is 192.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of top dogs to fat cats was 24 to 19.
if they were 152 fat cats.
This means,
Number of top dogs = 24x
Number of fat cats = 19x
Now,
Number of fat cats = 152
This means,
152 = 19x
x = 8
Now,
Number of top dogs = 24x
= 24x
= 24 x 8
= 192
Thus,
The number of top dogs is 192.
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6. Mrs. Ramirez' groceries cost $50 before tax, and the total including sales tax was $55. What is
the sales tax rate that Mrs. Ramirez paid?
Answer:sales tax rate would be 0.1
using the formula
Sales tax rate = Sales tax percent / 100
Rahim is saving for a new bike which will cost $1600. Rahim earns $3000 per month. Rahim spends his money on bills, food and extras in the ratio 6:4:2. Of the money he spends on extras, and puts 20% into his savings account to buy his bike. How long will it take rahim to save for his new bike
Answer:
it will take rahim 16 months
Step-by-step explanation:
6:4:2
3000÷12=250
1500:1000:500
20% 100
100×16=1600
A mason is a person who builds structures with bricks, stone, cement block, or wee. A mason usually uses, mortar to hold the bricks together. A general rule of thumb in masonry is that 2 1/2 bags of mortar are needed for every 100 cement blocks. Use a double number line to determine each answer.
By using the concept of unitary method, it can be calculated that
a) For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required
b) For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, unitary method will be used
The double number line has been shown below-
a) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required
For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required
For 350 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 350[/tex] bags of mortar are required
For 350 blocks of cement, [tex]\frac{35}{4}[/tex] bags of mortar are required
For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required
b) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required
For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required
For 50 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 50[/tex] bags of mortar are required
For 50 blocks of cement, [tex]\frac{5}{4}[/tex] bags of mortar are required
For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required
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Use the following table to find the rate of change. Remember the below equation rise/ run
X 2 4 6 8 10
Y 4 8 12 16 20
pls help :)
The rate of change of the function that is defined by the table:
X: 2 4 6 8 10
Y: 4 8 12 16 20
is r = 2
How to find the rate of change?For a function with two known points (x₁, y₁) and (x₂, y₂), the rate of change between these two points is written as:
r = ( y₂ - y₁)/(x₂ - x₁)
Here we have the table that defines a function:
X: 2 4 6 8 10
Y: 4 8 12 16 20
Here we can use any pair of two points on the table, for example, if we use the first pair and last pair:
(2, 4) and (10, 20)
The rate is:
r = (20 - 4)/(10 - 2) = 16/8 = 2
If we use the first two pairs (2, 4) and (4, 8) we get:
r = (8 - 4)/(4 - 2) = 4/2 = 2
So the rate of change of the function is r = 2.
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Which scale factors produce a contraction under a dilation of the original image? Select each correct answer. Responses −6 , negative 6, −0.5 , negative 0.5, 0.5 0.5 6
The set of scale factors that would produce a contraction under a dilation of the original image are:
B. -0.5
C. 0.5
What is scale factor?A scale factor can be defined as the ratio of two corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, quadrilaterals, and other types of polygons.
In Mathematics, the following rules are applied to interpret and understand the dilation of a geometric figure:
A geometric figure is enlarged when the scale factor is greater than 1 (k > 1).A geometric figure is reduced or contracted when the scale factor is less than 1 (k < 1).A geometric figure will remain the same when the scale factor is equal to 1 (k = 1).For a contraction under a dilation of the original image, the scale factor (k) must either be negative or less than one (1). Therefore, the required values are -0.5 and 0.5 respectively.
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URGENT!!!!!!!!!!
identify the conic section represented by the equation x+2=-2(y-3)^2
circle
ellipse
hyperbola
parabola
Step-by-step explanation:
[tex] - \frac{x}{2} - 1 = (y - 3) {}^{2} [/tex]
[tex] - 0.5(x + 2) = (y - 3) {}^{2} [/tex]
A parabola with a vertex (-2,3)
PLEASEEEEE HELP MEEEEEE!
Find the missing number so that the equation has infinitely many solutions.
–2x + 8= __x + 8
a
3
b
-4
c
8
d
-2
Answer:
-2
Step-by-step explanation:
If both sides are identical, there will be infinitely many solutions.
The arts & crafts club is selling candles to raise money. It costs $100 to rent a booth to sell the candles in. Materials to decorate the booth cost $32.50. The candles cost $2.50 each to make and the club sells them for $5 each. How many candles must be sold to break even?
We know that we need to sell out 53 candles to break even using mathematical operations.
What are mathematical operations?
The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, the total expense of the shop:
$100 + $32.50 = $132.50
No, the candle costs $2.50.
The selling price of a candle is $5.
Profit in each candle is: 5 - 2.50 = $2.50
A number of candles that we need to sell to break even are:
132.50/2.50
53
Therefore, we know that we need to sell out 53 candles to break even using mathematical operations.
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A water tank initially contained 111 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
How many minutes have passed, m, when the tank contains 194 liters? Round to the nearest hundredth.
Answer:
9.22 minutes
Step-by-step explanation:
You could use the form y=mx + b to find this equation
y will represent the total liters
x will represent the total number of minutes
b will represent the initial number of liters in the beginning
1. Plug 194 in for y, plug 9 in for m, put 111 in place of b
The equation should look be: [tex]194 = 9x + 111[/tex]
2. Solve the equation
3. Subtract 111 on both sides. The equation would now be: [tex]83 = 9x[/tex]
4. Divide both sides by 9 (to get x by itself). [tex]\frac{83}{9} = 9.22222222[/tex]
5. Round to the nearest hundredth place to get 9. 22 minutes
Mark and Aly were selling slices of pizza for a school event. Mark had 2 1/3
of a pizza pie left over. Aly had 1 5/9 left.
Together, how much pizza did Mark and Aly have left?
Answer:
11/9
Step-by-step explanation:
If this is an addition question then this is your answer.
Jason drops a tennis ball outside of his hotel balcony. He is standing 52 feet above the street. If the ball hits the hotel canopy 12 feet above street-level, how long after Jason releases the ball will it hit the canopy. Use the function h(t) = -16t2 + 52. Round your answer to the nearest tenth.
Jason drops a tennis ball outside of his hotel balcony. He is standing 52 feet above the street. If the ball hits the hotel canopy 12 feet above street-level, how long after Jason releases the ball will it hit the canopy. Use the function h(t) = -16t2 + 52. Round your answer to the nearest tenth.
1.6 seconds
2.0 seconds
0.4 seconds
4.0 seconds
1.6 seconds. The ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.
How to find time ?To find the time it takes for the ball to hit the canopy, we need to solve the equation h(t) = 12 for t.
The given equation for h(t) is h(t) = -16t^2 + 52, so we can substitute this into the equation h(t) = 12 to get:
12 = -16t^2 + 52
To solve this equation, we can move all the terms to one side of the equation to get:
-16t^2 + 40 = 0
We can then divide both sides of the equation by -16 to get:
t^2 - 2.5 = 0
We can then use the quadratic formula to solve for t:
t = +/- sqrt(2.5)
t = +/- 1.58
Thus, the ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.
Rounding this answer to the nearest tenth gives us 1.6 seconds, so the correct answer is 1.6 seconds.
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For the functions f(x)=2x3 and g(x)=3x3−2, find (f∘g)(1) and (g∘f)(1).
Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
What is composite function?
Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x
Main body:
according to question;
f(x) = 2x³
g(x) = 3x³ -2
we need to find composite function:
f o g (x) = 2(3x³-2)
{to find composite function , we replace one function as value of x in another}
f o g(x) = 6x³ -4
= 6x³ -4
f o g(1) = 6*1 -
= 2
g o f(x) = 3(2x³)-2
g o f(x) = 6x³ -2
= 6x -2
g o f(1) = 6*1 -2
= 5
Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
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Find the area of the circle with a diameter of 6.1
What is the rate of change of the function y=-5x+3
Answer:
-5
Step-by-step explanation:
The rate of change, also known as slope, would be -5.
Slope can be found with two points and the formula y minus y divided by x minus x or the change of y divided by the change in x.
To identify the slope on the equation is easy since this is slope-intercept form.
y=mx+b
where m is the slope
m in this case is -5, so -5 is your answer
A phone company offers two monthly plans plan a cost $19 plus an additional $0.11 for each minute of calls plan b has no initial fee but costs $0.15 for each minute of costs For what amount of calling do the two plans cost the same? What is the cost when the two plans cost the same?
When the costs of the two plans are equal, plan A will cost $37.81, whereas plan B will cost $25.65.
To find the number of calls at which the two plans cost the same, we need to set the costs equal to each other and solve for the number of minutes. The cost of plan A is $19 + $0.11 per minute, and the cost of plan B is $0.15 per minute. Setting these equal to each other, we get:
$19 + $0.11 per minute = $0.15 per minute
We can then solve for the number of minutes by dividing both sides by the per-minute cost:
$19 / $0.11 per minute = $0.15 per minute / $0.11 per minute
This simplifies to:
171 minutes = 135 minutes
Therefore, the two plans cost the same at 171 minutes of calling.
To find the cost at this point, we can substitute 171 minutes back into either of the original cost equations:
Plan A: $19 + $0.11 per minute × 171 minutes = $19 + $18.81 = $37.81
Plan B: $0.15 per minute × 171 minutes = $25.65
Thus, the cost when the two plans cost the same is $37.81 for plan A and $25.65 for plan B.
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Assume that females have pulse rates that are normally distributed with a mean of 76.0 beats per minute and a standard deviation of 12.5 beats per minute. A) If 4 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute.
The probability that their mean pulse rate is less than 80 beats per minute is of:
0.7389 = 73.89%.
How to obtain a probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 76, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]
The probability that their mean pulse rate is less than 80 beats per minute is the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (80 - 76)/6.25
Z = 0.64
Z = 0.64 has a p-value of 0.7389.
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59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible)
The probability that a resident own a cat or a dog is 48%
How to determine the probability a resident own a cat or a dogFrom the question, we have the following parameters that can be used in our computation:
P(Own a cat) = 70%
P(Own a dog) = 59%
P(Own a cat and a dog) = 42%
The probability a resident own a cat or a dog is then calculated as
Probability a resident own a cat or a dog = P(Own a cat) + P(Own a dog) - P(Own a cat and a dog)
Substitute the known values in the above equation, so, we have the following representation
Probability a resident own a cat or a dog = 70% + 59% - 42%
Evaluate the sum and the difference
Probability a resident own a cat or a dog = 48%
Hence, the probability is 48%
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Complete question
59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find:
the probability a resident own a cat or a dog
(round to 4 decimal places where possible)