A garden hose can fill a swimming pool in 7 days, and a larger hose can fill the pool in 4 days. How long will it take to fill the pool if both hoses are used?

Answer:360 minutes

Step-by-step explanation: 15 x 26 = 360

360 minutes = to 6 HOURS

Answer: 390 minutes

Step-by-step explanation:

Answer: 137000 cm³

Step-by-step explanation:

formula to find the volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³

formula to find the volume of a cylinder= πr²×h

both the shapes will have the same radius therefore to get the radius you should divide the diameter by two *you probably already know abt it*

so 46/2= 23 (the radius of both the shapes)

In order to get the height of the cylinder you should subtract the radius of the hemisphere from the total height given as the radius is the same all around the hemisphere **but remember not to mistake the diameter as the radius when subtracting a hemisphere's height from a total height**

height of the cylinder= 90cm- 23cm= 67

Therefore now substitute the values into the formulas and find the volumes of the two shapes separately...

volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³

                                         = [tex]\frac{2}{3}[/tex]× π × 23³

                                         = 25482.5 cm³

volume of a cylinder= πr²×h

                                  = π × 23² × 67 (including the height calculated above)

                                 = 111347.5 cm³

Now add the volumes you found which will give you the volume of water that the tank holds when it if full.

volume of a cylinder + volume of a Hemisphere

111347.5 + 25482.5

136830

137000 cm³ (make sure to estimate the final answer to 3s.f or else you'll                     lose your accuracy mark)

Answer:

44.57

Step-by-step explanation:

area of two semicircles = πr²

3.142×2×2= 12.568

area of rectangle=L×W2

4×8=32

32+12.568

44.568

=44.57

The simplified form of the given expression is 1073741824x¹⁵.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given expression is ((4x)³)⁵

= (4x)¹⁵

= 1073741824x¹⁵

Therefore, the simplified form of the given expression is 1073741824x¹⁵.

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If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.

E. 0.17

The approximate slope between points C and D can be calculated by taking the difference in the y-values (9-15) and dividing it by the difference in the x-values (4-2). This yields a slope of -0.17.

The approximate slope between points C and D can be determined by first calculating the change in y-values (9-15) and the change in x-values (4-2). Then, the change in y-values is divided by the change in x-values to calculate the slope. In this case, the slope is -0.17. This means that for every unit of increase in x-values, the corresponding y-values decrease by 0.17. If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.

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Answer:

Step-by-step explanation:

Let's call the number we're trying to find "x".

We know that:
25% of x is 60 (0.25x = 60)
90% of x is 216 (0.9x = 216)

We can use the first equation to solve for x:
x = 60 / 0.25 = 240

Now we can use this value of x to find 65% of it:
65% of x = 0.65 * 240 = 156

So, 65% of that number is 156.

The value of k is -1 in the given matrix.

In mathematics, a matrix is a rectangular array or table of digits, characters, or expressions that is used to represent a mathematical object or a characteristic of one.

Matrixes represent linear maps and allow for explicit linear algebraic calculations in the absence of additional information.

Due to the fact that matrices can be used to express the majority of abstract linear algebra's properties and operations, a significant portion of linear algebra is devoted to their study. Matrix multiplication, for instance, can be used to represent how linear maps are put together.

the det(Y)=|Y| value is 0. Expanding through third column we get

[tex]0 - 7 \times \left[\begin{array}{ccc}2&-1\\k&2\\\end{array}\right] + 3 \times \left[\begin{array}{ccc}2&-1\\-1&4\\\end{array}\right][/tex]

0 - 7(4 -(-k)) + 3(8 -(1)) = 0

- 7(4 +k) + 3(8 -1) = 0

-28 - 7k + 24 -3 = 0

-7k -7 = 0

-7k = 7

k = -7/7

k = -1

Thus, The value of k is -1 in given matrix.

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Based on the functions, the statements that are true about these functions include the following: C. I, II, and III.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

x = 3y³ + 2

3y³ = x - 2

y³ = (x - 2)/3

y = ∛[(x - 2)/3]

Therefore, the function f(g(x)) is given by:

Function, f(g(x)) = 3[∛((x - 2)/3)]³ + 2

Function, f(g(x)) = 3[(x - 2)/3] + 2

Function, f(g(x)) = x

For the function g(f(x)), we have:

Function, g(f(x)) = ∛[(3x³ + 2 - 2)/3]

Function, g(f(x)) = ∛x³

g(f(x)) = x

In conclusion, the input value (x-value) and output value (y-value) of these functions are interchangeable.

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This doesn’t represent a function because the x value 2 repeats

Hope this helped =)

Answer: 156, 56, 336

Answer:

85,510 and 185.

Step-by-step explanation:

let the first number be "a"

let the second number be "b"

let the third number be "c"

we know that

b=6a

c=100+a and

a+b+c=780

If we substitute the first 2 equations on the third one we get:

a+6a+100+a=780

8a+100=780

8a=780-100

8a=680

8 8

a=85

b=6a

b=6×85

b=510

c=100+a

c=100+85

c=185

Answer:

6(45 + 25)

Step-by-step explanation:

Based on the information given in the bar chart, it should be noted that the most popular last names are Smith, Johnson, and Williams.

The complete question is,

Most Popular Last Names. In alphabetical order, the six most common last names in the United States in 2018 are Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). Assume that a sample of 50 individuals with one of these last names provided the following data:

Brown Williams Williams Williams Brown

Smith Johnson Williams Smith Miller

Johnson Williams William Johnson Jones

Miller Jones Jones Smith Smith

Miller Johnson Smith Jones Jones

Johnson Smith Brown Smith Johnson

Jones Smith Smith Williams Brown

Johnson Johnson William Smith Brown

Smith Miller Johnson Brown Johnson

Brown Jones Miller Smith Miller

Summarize the data by constructing the following:

A. Relative and percent frequency distributions

B. A bar chart

C. A pie chart

D. Based on these data, what are the three most common last names?

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Answer:

Solution in attached photo.

Step-by-step explanation:

Steps are in the attached photo, do note for this question, the units for vectors are called 'units'. Also do note that square roots and squared will cancel out each other (Power 2 x Power Half = Power 1).

Edit: I have included solutions for both scenarios for reference.

Yes, the conditions to calculate a confidence interval for a proportion are satisfied.

n = 738

p = 170/738 = 0.2297

np ≥ 10 and n(1-p) ≥ 10

np = 0.2297*738 = 169.686 ≥ 10

n(1-p) = 738(1-0.2297) = 568.314 ≥ 10

Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.

Yes, the conditions for calculating a confidence interval for a proportion are satisfied. The sample size of the poll was 738 randomly selected customers of a major U.S. cell-phone carrier. Out of these 738 customers, 170 had walked into something or someone while talking on a cell phone. This gives us a population proportion of 170/738 or 0.2297. We need to ensure that np ≥ 10 and n(1-p) ≥ 10. Calculating these values, np = 0.2297*738 = 169.686 which is greater than 10 and n(1-p) = 738(1-0.2297) = 568.314 which is also greater than 10. Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.

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The parameterization equation for (0,0,0) and (5,3,7/2) is[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]. Equation of parameterization is what it is.

mathematical formulas

[tex]$$\begin{aligned}& x=0+5 t \\& y=0+3 t \\& z=0+3.5 t\end{aligned}$$[/tex]

Equations with symmetry

[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]

A straight line is the most straightforward curve to parametrize. It is possible to parametrize a line that passes through the origin along the vectors a, b. X is equal to AT and Y is BT. Two vectors parallel to the plane and a point on the plane must be located in order to find a parametrization. On the plane, finding a location is simple. We may use any number for x and y to determine z using the plane's equation. In the event when x and y are both 0, equation (1) states that

z= 18 x + 2 y 3 = 180 + 2 (0) 3= 6.

The process of locating parametric equations of a curve, a surface, or, more generally, a manifold or a variety, described by an implicit equation, is known as in mathematics, and is most commonly used in geometry.

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In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).

a) The probability that a married adult has three children is 0.30.

b) The expected value in this example represents the average number of children married adults in the country have.

c) The expected value is 1.90 children.

d) It is more likely that a married adult will have two to three children, with p = 0.55. This is because the probability of having two to three children (0.30 + 0.25 = 0.55) is greater than the probability of having four to six children (0.10 + 0.05 = 0.15).

In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).

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The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.

The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.

The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.

The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.

The complete question is :

Which of the following are magnitudes for rotational symmetry of the isosceles trapezoid below about the marked point?

a) 2

b) 4

c) 6

d) 8

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Answer:

A) y = 3/2 x - 1

Step-by-step explanation:

y + 4 = 3/2 (x + 2)  This is the point slope form of a line.

y + 4 = 3/2 x + 3    Subtract 4 from both sides

y = 3/2 x -1

The surface area of the cylinder is 125.66

The surface area of a cylinder is the area occupied by its surface in a three-dimensional space. A cylinder is a three-dimensional structure having circular bases which are parallel to each other. It does not have any vertices. Generally, the area of the three-dimensional shapes refers to the surface area.

The surface area of a cylinder is calculated with the formula:

= 2π × r × h + 2πr2= 2πr (h + r) Square units

A=2πrh+2πr2

With the following parameters from the question:

r = 2

h = 8

Substituting the parameters into the formula

A = 2πrh+2πr2=

A = 2·π·2·8+2·π·22

A = 125.66371

Hence, the surface area of the cylinder is  125.66371

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The answer of the given question based on the compound interest is     (a)  Noah will have £4995.45 in the account after 9 years. (b)  Noah will have earned £995.45 in interest from this account after 9 years.

Compound interest is  type of the interest that is calculated on the both principal (initial amount) and any accumulated interest from the previous periods. In other words, interest is earned not only on the initial investment, but also on the interest earned in previous periods.

a) The formula for compound interest is given by:

A = P(1 + r/n)^(n*t)

In this case, P = £4000, r = 0.025 (2.5% as a decimal), n = 1 (since the interest is compounded annually), and t = 9. Substituting the values into  formula, we will get:

A = £4000(1 + 0.025/1)⁽¹*⁹⁾ = £4995.45

Therefore, Noah will have £4995.45 in the account after 9 years.

b) The amount of interest earned is simply the difference between the amount at the end of the time period and the initial deposit, i.e.,

Interest = A - P = £4995.45 - £4000 = £995.45

Therefore, Noah will have earned £995.45 in interest from this account after 9 years.

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The total number of coins in the jar is 10.

The total number of coins in the jar can be determined using the following formula:

Number of Coins = (1-cent coins) + (5-cent coins) + (10-cent coins) + (25-cent coins) + (50-cent coins)

Since the jar contains a total of 100 cents, we can calculate the number of coins in the jar by solving the following equation:

1x + 5x + 10x + 25x + 50x = 100

The solution to this equation is x = 2. This means that the jar contains 2 coins of each denomination, for a total of 10 coins in the jar. Therefore, the total number of coins in the jar is 10.

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The multiplication equation and division equation can

help Raelyn determine how many key chains she can make is 9

When solving multiplication equations, these equations may have the form ax = c, bx = d, or cx = f

The question says that Raelyn has 33 red beads and 21 blue beads. She mixes the

beads together and uses 6 beads for each key chain she

makes.

Based on the given conditions, formulate:: (33+21) /6

Calculate the sum or difference: 54/6

Cross out the common factor: 9

Therefore, the multiplication equation and division equation gives 9

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Step-by-step explanation:

The area of a rectangular room is given by the formula A = l * w, where l is the length and w is the width. In this case, we know that A = 750 square feet and w = l - 5 feet. We can use this information to create equations to solve for the length of the room.

Three options that can be used to solve for y are:

y(y + 5) = 750

This equation can be obtained by substituting the given information into the formula for the area of a rectangular room.

y(l - 5) = 750

y(l) - 5y = 750

y2 – 5y = 750

This equation can be obtained by expanding the first equation and moving all the terms to one side of the equation.

y(l) - 5y = 750

y2 - 5y = 750

(y + 25)(y - 30) = 0

This equation can be obtained by factoring the second equation, in which you get two solutions, y = -25 and y = 30. The first solution is not a valid solution because the length of a room can not be negative but the second one is a valid solution.

Note that 750 - y(y - 5) = 0 and y(y - 5) + 750 = 0 are not valid options as they are not equation that can be used to solve for y.

Given the following histogram (image now attached), for a set of data, the number of values in the data set that are greater than 6.5 and less than 9.5 is: 14 (Option D)

A histogram is a rough depiction of the numerical data distribution. Karl Pearson was the first to coin the phrase.

A histogram is a graph that depicts the frequency distribution of a few data points from a single variable. Histograms frequently divide data into "bins" or "range groups" and count the number of data points that belong to each of those bins.

Between 6.5 and 9.5 there are 3 bars. Their heights are:

3, 6, 5, 4, and 3. Adding the values, we have:

3 + 6 + 5 = 14

Thus, the values in the data set are greater than 6.5 and less than 9.5 are 14.

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Full Question:

See attached image.

The value of x that makes the given pair of ratios equivalent is: A. 32.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;

x/16 = 50/25

Cross-multiplying, we have the following:

25x = 16 × 50

25x = 800

x = 800/25

x = 32.

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The Line chart should be used by the data analyst.

Option (A) is correct.

What is a line chart?

A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

Line chart

This type of chart is called a line chart. A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

It uses a horizontal x-axis and a vertical y-axis, with the data points connected by a line. It is great for visualizing trends and changes in data over a period of time, and it can be used to compare multiple variables at once.

Hence, the Line chart should be used by the data analyst.

Option (A) is correct.

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Answer:

19

Step-by-step explanation:

First we need to add all these numbers together

20+25+7+27+18+17=114

Next, we have to divide all these numbers by the number of values there are.

If we count, there are 6 values that we added together.

After that, we divide 114 by 6 to get the answer

114/6=19.

Step-by-step explanation:

this is a college question ???

and you don't know how to do this ?

remember middle school and high school ? besides math classes themselves, did you never track your class scores and such ?

the average or mean value is always the sum of all data points divided by the number of data points.

here we have 6 data points.

the average is

(20+25+7+27+18+17)/6 = 114/6 = 19

There is no real nth root. Option C

You should understand that a square root of a number is a number that when multiplied by itself yields the original number.

Also, to indicate that we want both the positive and the negative square root of a radicand we put the symbol ± (read as plus minus) in front of the root. ... Zero has one square root which is 0. ... Negative numbers doesn't have real square roots since a square is either positive or 0.

The formula is

nth root of x

Where x ≥0

-729≥0

In conclusion there is no real root for the figure -729

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When the value of p is - 1, then p- 1 ≤ 0.5 is the required inequality.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

We have the inequalities;

(A). p- 1 ≤ 0.5

When p = -1,

-2  ≤ 0.5.

(B). -p - 1 ≤ -0.5

When p = -1,

0  ≤ -0.5.

This is contradiction.

(C).  p - 1 ≥ 0.5

When p = -1,

-2  ≥ 0.5.

This is contradiction.

(D). -p -1 ≥ 0.5

When p = -1,

0  ≥ 0.5.

This is contradiction.

Therefore, p- 1 ≤ 0.5 is the required inequality.

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The complete question:

Which inequality is true when the value of p is -1?

(A). p- 1 ≤ 0.5

(B). -p - 1 ≤ -0.5

(C).  p - 1 ≥ 0.5

(D). -p -1 ≥ 0.5