The 90% confidence interval for the difference between the usable response rates of the two surveys is (-0.0124, 0.0912).
The difference between the usable response rates of the two surveys can be estimated using the formula for the difference between two proportions:
d = p1 - p2
Where p1 is the usable response rate for the printed survey, and p2 is the usable response rate for the electronic survey. To calculate these response rates, we can use the formula:
p = x/n
Where x is the number of usable responses, and n is the total number of customers who were sent the survey. For the printed survey, we have:
p1 = 261/631 = 0.4138
And for the electronic survey, we have:
p2 = 155/414 = 0.3744
So the difference between the two response rates is:
d = 0.4138 - 0.3744 = 0.0394
To estimate a 90% confidence interval for this difference, we can use the formula:
CI = d ± z*√[(p1(1-p1)/n1) + (p2(1-p2)/n2)]
Where z is the critical value for a 90% confidence level, which is 1.645. Plugging in the values we have:
CI = 0.0394 ± 1.645*√[(0.4138(1-0.4138)/631) + (0.3744(1-0.3744)/414)]
CI = 0.0394 ± 1.645*√[0.000407 + 0.000581]
CI = 0.0394 ± 1.645*0.0315
CI = 0.0394 ± 0.0518
CI = (-0.0124, 0.0912)
So the 90% confidence interval for the difference between the usable response rates of the two surveys is (-0.0124, 0.0912). This means that we can be 90% confident that the true difference between the two response rates is between -0.0124 and 0.0912.
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what is the slope intercept for
(5,1) and (2,16)
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
What distinguishes a linear equation?If an equation is expressed in the form y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line passing through the two given points (5,1) and (2,16), we can use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (5,1) and (x2, y2) = (2,16)
m = (16 - 1)/(2 - 5) = -5
So the slope of the line is -5.
To find the y-intercept b, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (5,1) and the slope m = -5, we get:
y - 1 = -5(x - 5)
Simplifying this equation, we get:
y = -5x + 26
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
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The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 21 HCF of water is
$35.39, and the cost for using 57 HCF is $83.99. What is the cost for using 56 HCF of water?
Monthly cost
(in dollars)
Water usage
(In HCF)
E
If the cost for using 21 HCF of water is $35.39. the cost for using 56 HCF of water is $82.64.
How to find cost for using 56 HCF of water?We can use the two given data points to find the slope and y-intercept of the linear function that represents the monthly cost of water use.
Let's use (21, 35.39) and (57, 83.99) as our two data points.
First, let's find the slope of the line:
slope = (y2 - y1) / (x2 - x1)
slope = (83.99 - 35.39) / (57 - 21)
slope = 48.6 / 36
slope = 1.35
Now that we have the slope, we can use either of the two data points to find the y-intercept. Let's use (21, 35.39):
y = mx + b
35.39 = 1.35 * 21 + b
35.39 = 28.35 + b
b = 35.39 - 28.35
b = 7.04
So the linear function that represents the monthly cost of water use is:
y = 1.35x + 7.04
where y is the cost (in dollars) and x is the amount of water used (in HCF).
Now we can use this function to find the cost for using 56 HCF of water:
y = 1.35x + 7.04
y = 1.35 * 56 + 7.04
y = 82.64
So the cost for using 56 HCF of water is $82.64.
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Much of Ann's investments are in Cilla Shipping. Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626. Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share. Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share. Which of Ann's investments has increased in value more, and by how much?
Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41
What is purchase price?
The complete cost of purchasing an asset is known as the original cost. The whole costs associated with purchasing and using an asset are taken into account when calculating its initial cost.
To determine which of Ann's investments has increased in value more, we need to compare the current value of the bonds and the stock to their original purchase value.
First, let's calculate the purchase price of the bonds:
7 bonds x $500 par value x 0.95626 market rate = $3,349.82
So, Ann initially invested $3,349.82 in the Cilla Shipping bonds.
Next, let's calculate the purchase price of the stock:
125 shares x $28.00 per share = $3,500.00
So, Ann initially invested $3,500.00 in the Cilla Shipping stock.
Now, let's calculate the current value of the bonds:
7 bonds x $500 par value x 1.06384 market rate = $37,286.48
So, the current value of the bonds is $37,286.48.
Let's also calculate the current value of the stock:
125 shares x $30.65 per share = $3,831.25
So, the current value of the stock is $3,831.25.
To determine which investment has increased in value more, we can calculate the percentage increase for each investment:
Percentage increase in bonds = [(current value - purchase price) / purchase price] x 100%
= [(37,286.48 - 3,349.82) / 3,349.82] x 100%
= 1010.46%
Percentage increase in stock = [(current value - purchase price) / purchase price] x 100%
= [(3,831.25 - 3,500.00) / 3,500.00] x 100%
= 9.48%
So, we can see that the bonds have increased in value more than the stock, by a significant amount.
The bonds have increased in value by 1,010.46%, while the stock has increased in value by only 9.48%. The bonds have increased in value by a total of $33,936.66 ($37,286.48 - $3,349.82), while the stock has increased in value by a total of $331.25 ($3,831.25 - $3,500.00).
Therefore, Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41 ($33,936.66 - $331.25).
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Marshall purchases a duffel bag priced at $20. With sales tax, the total comes out to $20. 95. What is the sales tax percentage?
well, the tax is cleary just 20.95 - 20 = 0.95, so 95 cents, now, if we take 20(origin amount) to be the 100%, what is 0.95 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 0.95& x \end{array} \implies \cfrac{20}{0.95}~~=~~\cfrac{100}{x} \\\\\\ 20x=95\implies x=\cfrac{95}{20}\implies x=4.75[/tex]
Determine the slope and intersection with the y-axis of each graph
y=-2x-1
[tex] \mathbb{ANSWER:}[/tex]
The slope is -2 while the y-intercept is -1.
[tex] \mathbb{EXPLANATION:}[/tex]
The slope and the intersection with the y-axis of the graph or the y-intercept is already given if you will just simply look at the equation. An equation written in y = mx + b is in slope-intercept form, where m is the slope and b is the y-intercept. So, the number being multiplied to x or the coefficient of x is the slope while the constant is the y-intercept.
Shaun goes to a fast food restaurant and orders some tacos and burritos. He sees on the nutrition menu that tacos are 160160 calories and burritos are 320320 calories. If he ordered 1515 items and consumed a total of 36803680 calories, how many tacos and how many burritos did Shaun order and eat?
Tacos eaten:
Burritos eaten:
Shaun ordered 7 tacos and 8 burritos, for a total of 160160 calories from tacos and 320320 calories from burritos.
To solve this problem, we need to use a system of equations. Let's call the number of tacos Shaun ordered x and the number of burritos he ordered y. We can then write the following equations:
160x + 320y = 3680 (the total number of calories consumed)
x + y = 15 (the total number of items ordered)
We can rearrange the second equation to get y = 15 - x and then substitute that into the first equation to solve for x:
160x + 320(15 - x) = 3680
160x + 4800 - 320x = 3680
-160x = -1120
x = 7
Now that we know x, we can plug it back into the second equation to solve for y:
7 + y = 15
y = 8
So, Shaun ordered and ate 7 tacos and 8 burritos.
Tacos eaten (x) : 7
Burritos eaten (y) : 8
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D. Elementary Applications of the Fundamental Homomorphism Theorem In each of the following letAbe a commutative ring. Ifa∈Aandnis a positive integer, the notationnawill stand fora+a+…+a(n terms )1 Suppose2x=0for everyx∈A. Prove that(x+y)2=x2+y2for allxandyinA. Conclude that the functionh(x)=x2is a homomorphism fromAtoA. IfJ={x∈A:x2=0}andB={x2;x∈A), explain whyJis an ideal ofA,Bis a subring ofA, andA/J≅B
A/J≅B
The Fundamental Homomorphism Theorem states that for any homomorphism f from a ring A to a ring B, the kernel of f (the set of elements of A mapped to the identity of B) is an ideal of A. Applying this to the given problem, let A be a commutative ring and f:A→A be the homomorphism f(x)=x2. The kernel of f is J = {x∈A:x2=0}. Then J is an ideal of A.
To prove that (x+y)2=x2+y2 for all x,y∈A, consider (x+y)2 = (x+y)(x+y) = x2 + xy + yx + y2. Since A is commutative, xy=yx and so (x+y)2=x2+2xy+y2. Since 2xy=2yx, then (x+y)2=x2+y2, as desired.
Now, we can conclude that f is a homomorphism from A to A. In addition, B={x2;x∈A} is a subring of A, since for all x,y∈A, (x+y)2=x2+y2 and so x2+y2∈B. Moreover, since J is an ideal of A, A/J≅B.
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how can jamie rewrite the expression 1/1-sin theta so that the fraction has cos^2 theta in the denominator
0 she can multiply the numerator and denominator by cos theta
0 she can mulitply the numerator and denominator by tan theta
0 she can mulitply the numerator and denominator by 1- cos theta
0 she can multiply the numerator and denominator by 1+ sin theta
As a result, Jamie could rewrite the equation as (1+sin theta)/cos² theta by multiplying both the denominator and the numerator by (1+sin theta), and then replacing 1-sin² theta with cos² theta.
What exactly is a fraction in mathematics?A ²is part of a whole. The number is expressed mathematically as a quotient, which divides the denominator and the numerator. Both are integers in a simple fraction. A complicated fraction contains a fraction in the numerator or denominator. The denominator of a correct fraction is greater than the numerator
Jamie can double the numerator and write 1/(1-sin theta) to ensure that the fraction's denominator is cos² theta. Neither 1-cos theta nor any other option, but the numerator by (1+sin theta):
1/(1-sin theta) × (1+sin theta)/(1+sin theta) = (1+sin theta)/(1-sin² theta)
We may replace cos² theta for 1-sin² theta using the identity sin² theta + cos² theta = 1:
(1+sin theta)/cos² theta
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Imagine two cars that are traveling down the highway. The distance (in miles) each car has traveled can be represented using the following polynomials where t is the number of hours that has passed.
Car A: 7t²+50t+150
Car B: 7t²+45t
Part 1)Write a polynomial for the number of miles between the two cars
Part 2)What is the distance between the two cars after 3 hours of traveling on the highway?
Part 3) After how many hours will the distance between the two cars be 200 miles?
The polynomial for the number of miles between the two cars is d(t) = 5t + 150
The distance between the two cars after 3 hours is 165 milesThe time after traveling 200 miles apart is 10 hoursThe polynomial for the number of miles between the two carsGiven that
Car A: 7t²+50t+150
Car B: 7t²+45t
The distance function is represented as
d(t) = 7t²+50t+150 - 7t² - 45t
So, we have
d(t) = 5t + 150
The distance after 3 hoursThis means that t =3
So, we have
d(3) = 5 * 3 + 150
d(3) = 165
The time the distance after is 200 milesThis means that d(t) = 200
So, we have
5t + 150 = 200
Evaluate the difference
5t = 50
So, we have
t = 10
Hence, the time is 10 hours
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A regular hexagon is shown below. Find the value of x. (11x + 21)° X =
The given angle measures 120 degrees, which is indeed an interior angle of a regular hexagon
What is hexagon ?
A hexagon is a six-sided polygon, which is a two-dimensional geometric shape with straight sides. The word hexagon comes from the Greek words "hexa" meaning "six" and "gonia" meaning "angle."
To find the value of x in the regular hexagon, we can start by noting that the interior angles of a regular hexagon are all congruent and measure 120 degrees.
Next, we can see that the given angle (11x + 21)° is an interior angle of the hexagon. Therefore, we can set this angle equal to 120 degrees and solve for x:
11x + 21 = 120
11x = 99
x = 9
Therefore, the value of x is 9.
Note that we can check our answer by substituting x = 9 into the original equation:
11x + 21 = 11(9) + 21 = 120
Therefore, the given angle measures 120 degrees, which is indeed an interior angle of a regular hexagon
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The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 3 3/4 inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 5 1/4 inches apart on the map. The scale on the map is 12 inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville?
the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.
What is the distance in math?
As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.
Smithville to Jonesville distance in map = 3(3/4) inches = (15/4) inches .
given that,
(1/2) inch = 4 miles .
1 inch = 8 miles .
Distance from Smithville to Jonesville = (15/4) * 8 = 30 miles .
similarly,
Jonesville to Clarksville distance in map = 5(1/4) = (21/4) inches .
Distance from Jonesville to Clarksville = (21/4) * 8 = 42 miles .
The actual distance the Patel family will travel by the time they reach Clarksville = 30 + 42 = 72 miles
Hence, the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.
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You wish to test the following claim (H_a) at a significance level of alpha = 0.05. H_0: p = 0.14 H_a: p ≠ 0.14 You obtain a sample of size n = 585 in which there are 55 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... a. less than (or equal to) alpha b. greater than alpha This test statistic leads to a decision to... a. reject the null b. accept the null c. fail to reject the null As such, the final conclusion is that.. a. There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.14. b. There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.14. c. The sample data support the claim that the population proportion is not equal to 0.14. d. There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.14.
a)1.597
b)0.1101
c)The population proportion is not equal to 0.14
The test statistic for this sample is 1.597. The corresponding p-value is 0.1101. The p-value is greater than alpha, so the decision is to fail to reject the null. As such, the final conclusion is that there is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.14. This conclusion is based on the Binomial Distribution and Statistic, which use the p-value to assess the evidence against the null hypothesis.
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what is the decimal multiplier to decrease by 68%?
Answer:
I think it is 0.68. Try that. If not sorry.
HELP PLS BRAINLIEST AND FIVE STAR IF ALL OF THESE ARE CORRECT
a)√(x^2-14x+49)=x-7
b)√(4x^2-20x+25)=5-2x
C)√(y^4+2y^2+1)=y^2+1
d)√(x^2+2x+1)=x+1
e)√(y^2-20y+100)=y-10
f)√(y^6-2y^3+1)=y^3-1
pls answer all pls pls pls
(also the answer is most likely NOT all real numbers or no solutions)
The solution to the all given equations is that they have infinite many real solutions
How to determine the solution to the equationsEquation (a)
From the question, we have the following parameters that can be used in our computation:
√(x^2-14x+49)=x-7
When both sides of the equations are squared, we have:
x^2 - 14x + 49 = x^2 - 14x + 49
Evaluate the like terms
0 = 0
This represents infinite many solutions
Equation (b)
Here, we have:
√(4x^2-20x+25)=5-2x
When both sides of the equations are squared, we have:
4x^2-20x+25 = 25 - 20x + 4x^2
Evaluate the like terms
0 = 0
This represents infinite many solutions
For the remaining expressions, we have the following (using the above steps)
Equation (c)
√(y^4+2y^2+1) = y^2 + 1
y^4 + 2y^2 + 1 = y^4 + 2y^2 + 1
0 = 0
Equation (d)
√(x^2+2x+1)=x+1
x^2 + 2x + 1 = x^2 + 2x + 1
0 = 0
Equation (e)
√(y^2-20y+100)=y-10
y^2 - 20y + 100 = y^2 - 20y + 100
0 = 0
Equation (f)
√(y^6-2y^3+1)=y^3-1
y^6-2y^3+1 = y^6-2y^3+1
0 = 0
Hence, the equations have infinite solutions
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Use the LCD of the fractions to make your polynomial contain only whole numbers
Polynomial without fractions
x^4+1/2 x^3+7/2 x^2+2x-2
The polynomial without fractions is 2x^4 + x^3 + 7x^2 + 4x - 4.
To make the polynomial contain only whole numbers, we need to find the least common denominator (LCD) of the fractions and multiply each term by the LCD.
The LCD of the fractions 1/2 and 7/2 is 2.
So, we multiply each term by 2 to get rid of the fractions:
2(x^4) + 2(1/2 x^3) + 2(7/2 x^2) + 2(2x) + 2(-2)
Simplifying the terms gives us:
2x^4 + x^3 + 7x^2 + 4x - 4
Therefore, the polynomial without fractions is 2x^4 + x^3 + 7x^2 + 4x - 4.
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7. You have a 8-kilogram bag of dog food. You give your dog 100 grams of food
oqeach day. How many days does the bag of food last?
teris fiel even uoy ob enjur to equo
pje ever vo
We can start by converting the mass of the bag of dog food from kilograms to grams:
8 kilograms = 8,000 grams
Then, we can divide the total mass of the bag of food by the daily amount given to the dog:
8,000 grams ÷ 100 grams/day = 80 days
Therefore, the bag of dog food will last for 80 days.
a park is 70 meters wide and 110 meters long, give the length and width of another park that has the same perimeter but a larger area
Answer: 80 meters wide and 100 meters long.
Step-by-step explanation:
Well, if the park has to have a larger area, but the same perimeter, all you need to do in this case is turn 70 to 80 and 110 to 100.
80 + 80 + 100 + 100 = 360 meters in perimeter
70 x 110 = 7700
80 x 100 = 8000 ← This has greater area than the park above
Create a multi-dimensional visualization of (a+b)5 in
the style of this post. Remember, (a+b)5 = a5
+ 5a4b +10a3b2 +
10a2b3 + 5ab4 +
b5
To create a multi-dimensional visualization of (a+b)^5, we can use a Pascal's Triangle, which shows the coefficients of each term in the expansion. Each row of the triangle corresponds to a power of (a+b), and the numbers in each row are the coefficients of the terms in the expansion. Here is a visualization of the first six rows of Pascal's Triangle:
```
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
```
The sixth row corresponds to the expansion of (a+b)^5, and the numbers in this row are the coefficients of the terms in the expansion: 1, 5, 10, 10, 5, 1. We can use these coefficients to create a multi-dimensional visualization of (a+b)^5:
```
a^5
5a^4b
10a^3b^2
10a^2b^3
5ab^4
b^5
```
Each term in the expansion is represented by a different level in the visualization, with the coefficient of each term shown at the beginning of the level. This multi-dimensional visualization allows us to see the relationship between the coefficients and the terms in the expansion of (a+b)^5.
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A grain silo has a cylindrical shape. Its diameter is 17 ft , and its height is 42 ft . What is the volume of the silo?
The volume of the silo is approximately 9,685.73 cubic feet.
What is volume of a cylinder?
The volume of a cylinder can be calculated using the formula:
[tex]V = \pi r^2h[/tex] where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
We are given that the diameter of the silo is 17 feet. The radius, which is half the diameter, is therefore:
r = 17/2 = 8.5 feet
We are also given that the height of the silo is 42 feet.
Using the formula for the volume of a cylinder, we can calculate the volume of the silo:
[tex]V = \pi r^2h[/tex]
[tex]= \pi(8.5)^2(42)[/tex]
≈ 9,685.73 cubic feet
Therefore, the volume of the silo is approximately 9,685.73 cubic feet.
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Find \( A \). \[ (4 A)^{-1}=\left[\begin{array}{ll} 5 & 2 \\ 4 & 2 \end{array}\right] \]
Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1.
To find \( A \), start by multiplying both sides by \( (4A) \). Then, you will have \( (4A)^{-1}(4A)=\left[\begin{array}{ll} 5 & 2 \\ 4 & 2 \end{array}\right] \). This simplifies to \( \left[\begin{array}{ll} 5A & 2A \\ 4A & 2A \end{array}\right] \). Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1. This means that \( 5A=1 \) and \( 2A=1 \). Solving these two equations yields \( A=\frac{1}{5} \).
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find the median of 3,5,6,8,8,9,10
Answer:
the meadian is 8
Step-by-step explanation:
The value of the middle-most observation is called the median of the data.
The diameter of a cylindrical construction pipe is 3ft. If the pipe is 17ft long, what is its volume?
Use the value 3.14 for /pi, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
First, we need to find the radius of the pipe by dividing the diameter by 2:
radius = 3ft / 2 = 1.5ft
Next, we can use the formula for the volume of a cylinder:
V = πr²h
where V is volume, π (pi) is approximately 3.14, r is the radius, and h is the height (or length) of the cylinder.
Plugging in the values we have:
V = 3.14 x (1.5ft)² x 17ft
V = 3.14 x 2.25ft² x 17ft
V = 3.14 x 38.25ft³
V ≈ 120ft³
Rounding to the nearest whole number and including the unit:
The volume of the pipe is about 120 cubic feet.
[tex]\bold{Work \ Shown:}[/tex]
[tex]d = 3 = diameter[/tex]
[tex]r = d\div2 = 3\div2 = 1.5 = radius[/tex]
[tex]h = 17 = height \ or\ length \ of \ the\ pipe[/tex]
[tex]\pi = 3.14\ approximately[/tex]
[tex]V = volume \ of \ the \ cylinder \ pipe[/tex]
[tex]V = \pi \times r^2 \times h[/tex]
[tex]V = 3.14 \times (1.5)^2\times 17[/tex]
[tex]V = 120.105[/tex]
[tex]V=120[/tex]
The cylindrical pipe's volume is about 120 cubic feet.
At the store, oranges are 5 for $3.00. How much would it cost to buy 8 oranges?
Answer:
$4.8
Step-by-step explanation:
5 for $3
So $3 ÷ 5 to get the price of one
Answer is 60c or $0.6
Then you multiply $0.6 with 8 to get the price of 8 oranges
So $0.6 x 8 = $4.8
Answer:
the cost of 8 oranges is 4.8$
step by step explanation
using ratio amd proportion
let x be the unknown amount
[tex]5 = 3 \\ 8 = x \\ cross \: multiply \\ 5x = 24 \\ divide \: \: both \: sides \: by \: 5 \\ \frac{5x}{5} = \frac{24}{5} \\ x = \frac{24}{5} \\ x = 4.8[/tex]
therefore the answer is 4.8 dollars will buy 8 oranges
thank you
The cost of eight tickets to a Houston texans game is $498.40. What is the constant of proportionally, k, that relates the cost in dollars, y, to the number of tickets, x? ________
A recipe says to use 3 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made,y, to the number of cups of flor used, x?____
A circle has a diameter of 7.6 feet. What measurement is closet to the circumference of the circle in feet?
The constant of proportionality, k, that relates the cost in dollars, y, to the number of tickets, x, is $62.30. The constant of proportionality that relates the number of cookies made, y, to the number of cups of flour used, x, is 16. The circumference of the circle is approximately 23.876 feet.
1. To find the constant of proportionality, k, we need to divide the cost of the tickets by the number of tickets.
k = y/x = $498.40/8 = $62.30
Therefore, the constant of proportionality, k, is $62.30.
2. To find the constant of proportionality, k, we need to divide the number of cookies made by the number of cups of flour used.
k = y/x = 48/3 = 16
Therefore, the constant of proportionality is 16.
3. To find the circumference of a circle, we use the formula C = πd, where C is the circumference and d is the diameter.
C = π(7.6) = 23.876 feet
The measurement closest to the circumference of the circle in feet is 23.876 feet.
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a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
The solution is: population in 2015 will be 40,115,896
What is exponential?The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents.
But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
calculate the average percent change in population in California from 2000-2009.
Add all the percentage than divide by 9 since there is 9 year
1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9 = 1.3567%
The number of periods from 2009 to 2015 is 6:
Future: 37,000,000•(1+0.013567)^6 = 40,115,896.06
Hence, the solution is: population in 2015 will be 40,115,896
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For parallelogram ABCD, Find m∠1.
The measure of angle 1 would be equal to 59 degrees.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
We have been given the angles as 31 degrees and 90 degree
We know that the sum of angle of triangle is 180 then the angle 1 will be;
31 + 90 + m∠1 = 180
m∠1 = 180 - 90 - 31
m∠1 = 59
Hence, m∠1 = 59
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The sum of four times a number x and another number y is 65. The difference of five times the number x and three times y is 94. What is the value of y?
The value of y is -3. The equation formed from the question is 4x + y = 65 and 5x -3y = 94.
First, we will solve for x
Multiplying the 4x + y = 65 equation by 3 we get
12x +3y =195
Now solving both the equation
The variable y gets cancelled because of having the same value
∴ 17x = 289
x= 17
Now putting the value of x in equation 4x + y = 65 to get the value of y
4*17 +y =65
68 +y = 65
y= -3
Now putting the value of x in equation 5x -3y = 94 to get the value of y
5*17 -3y =94
85 -3y =94
-3y = 94-85
y= -3
Therefore, the value of y is -3
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in Chicago, the temperature was 3 degrees. By 5am, it had dropped 15 degrees. What was the temperature at 5am?
Factorise : 9x^{2} +4x^{2} +16z^{2} +12xy-16yz-24xz[/tex]
Anyone help wit this
The lengths in the left side are proportional to the ones in the right side, with that we know that x = 10.
How to find the value of x?The lengths in the left side and the ones in the right side are proportional, such that the scale is k.
Then we can write:
21*k = 27
(x - 3)*k = (x - 1)
With the first equation, we can find the value of k, then we will get.
k = 27/21
Replacing that in the second equation we will get:
(x - 3)*27/21 = (x - 1)
Now we can solve this.
(x - 3)*27 = 21*(x - 1)
Now we can solve this for x.
27x - 81 = 21x - 21
27x - 21x = 81 - 21
6x = 60
x = 60/6 = 10
x = 10
That is the value of x.
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