An artist is building a pedestal out of wood that will be used to display a piece of sculpture. She plans to cover the pedestal with tile. How much tile will it take to cover the pedestal, including the bottom?





224 square feet

192 square feet

144 square feet

288 square feet

Answer:

1130.4

Step-by-step explanation:

2x100pi + 160pi

Answer:

42/11

Step-by-step explanation:

11/7 = 6/v

cross multiply:

11v = 6x7 = 42.

v = 42/11 ≈ 3.81

The calculated value Z = 11.792 >1.96 at a 0.05 level of significance.

The null hypothesis is rejected

The alternative hypothesis is accepted at a 0.05 level of significance.

The mean weight is less than 16 ounces.

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

Step:-1

Given that the mean of the Population = 16

Given that the standard deviation of the process

σ = 0.03 ounce

Given that the mean of the sample = 16.05 ounces

Null hypothesis: H₀:μ > 16 ounces

Alternative Hypothesis H₁: μ <16 ounces

Step:-2

Test statistic

Z = x-mean/SD√n

Z = 11.792

Level of significance = 0.05

Z₀.₀₅ = 1.96

Final answer:-

The calculated value Z = 11.792 >1.96 at a 0.05 level of significance.

The null hypothesis is rejected

The alternative hypothesis is accepted at a 0.05 level of significance.

The mean weight is less than 16 ounces

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Answer:

4/12 and 3/12

the simplified version is 1/3 and 1/4

Step-by-step explanation:

Answer:

[-0.2  0.4]

[0.8   -0.6]

Answer:157.35

Step-by-step explanation: multiply then add the tax

D. The function  {(4,1), (-7,0), (-12,2), (0,0), (-12,1)} has the given domain  {-12, -7, 0, 4, 12} and range  { 0, 1, 2}.

The domain is the set of all inputs which has an output or range.The range of a function is the set of all outputs form which the domain is defied.

According to the given question domain and range of a function are given they are { -12, -7, 0, 4, 12 } and { 0, 1, 2 }.

This can be written an an ordered pair as { (-12,0), (-12,1), (-12,2), (-7,0), (-7,1), (-7,2), (0,0), (0,1), (0,2), (4,0), (4,1), (4,2), (12,0), (12,1), (12,2) }.

From the given options we can observe that in option D. which has ordered pairs { (4,1), (-7,0), (-12,2), (0,0), (-12,1) }.

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Answer:

The recursive formula for an=1/8(2)n-1 is:

a1=1/8 an+1=1/8(2)(n)

This formula defines a sequence where each term is equal to 1/8 of the previous term multiplied by 2.

Step-by-step explanation:

Simplifying the given equation:

Thus, the simplified form is

Answer:

hi, see mate the third angle is not in the photo, please upload another one

Answer:

A vertical Iine (x = a ) has an undefined slope.

Step-by-step explanation:

A vertical line has undefined slope because all points the line have the same x-coordinate.  

Since any two points on a vertical line have the same x-coordinate, the slope cannot be calculated as a finite number.  If you try to solve for the slope using the slope formula, m = (y2 - y1)/(x2 - x1), it will result in an undefined quotient because division by zero is an undefined operation.

Vertical lines are symbolically represented by the equation, x = a where a is the x-intercept. More importantly, vertical lines are not functions; they do not pass the vertical line test because the same input value (or x-coordinate) corresponds to more than one output (y-coordinates).

Answer:

249798.8

Hope this helps! <3

Answer:

14v-2

Step-by-step explanation:

1. distribute

2. combine like terms

see photo for more information

Answer:

$3.77 is the tax. Total is $57.62 is you buy it.

Step-by-step explanation:

Answer:

3.77

Step-by-step explanation:

Sales price x sales tax rate = sales tax

53.85 x .07 (7%) =  3.77

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).

Answer:  \(b^2\)

You can write this as b^2

===================================================

Work Shown:

\(c = \frac{(ab^5)^{1/2}}{(ab)^{1/2}}\\\\c = \left(\frac{ab^5}{ab}\right)^{1/2}\\\\c = \left(b^4\right)^{1/2}\\\\c = b^{4*1/2}\\\\c = b^{2}\\\\\)

Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

Answer:

f(8) = 216

Step-by-step explanation:

f(x) = (2x −10)³

f(8) = (2(8) −10)³

     = (16 - 10) ^3

     =  6^3

     = 216

f(8) = 216

The value of the equation f ( 8 ) when f ( x ) = ( 2x - 10 )³ is f ( 8 ) = 216

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( 2x - 10 )³

To calculate the value of f ( 8 ) , substitute the value of x as x = 8 in the equation , we get

f ( x ) = ( 2x - 10 )³

On simplifying the equation , we get

f ( x ) = ( 2x )³ - ( 10 )³ - 3 ( 2x )²( 10 ) + 3 ( 2x ) ( 10 )²

So , the equation is

f ( x ) = 8x³ - 1000 - 120x² + 600x  

So , the equation is

f ( x ) = 8x³ - 120x² + 600x - 1000

Now ,  substituting x = 8 ,

f ( 8 ) = 8 ( 8 )³ - 120 ( 8 )² + 600 ( 8 ) - 1000

f ( 8 ) =  4096 - 7680 + 4800 - 1000

On simplifying the equation , we get

f ( 8 ) = 216

Therefore , the value of f ( 8 ) = 216

Hence ,

The value of the equation f ( 8 ) when f ( x ) = ( 2x - 10 )³ is f ( 8 ) = 216

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Answer:

∫ cosec²(7-5x) dx =[-cot(7-5x)]/-5 +c

=(1/5)cot(7-5x)+c

note: d/dx(cotx)=- cosecx

3a. An equation in slope-point for this line is y + 2 = 1/2(x - 0).

3b. The equation in slope-intercept form is y = 1/2(x) - 2.

4a. An equation in slope-point form to represent this function is y - 3875 = -1/695(x - 19375).

4b. The cost of operating a car that has been driven 31250 km is $3892.086.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part 3.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(4 - 0)

Slope (m) = 1/2

At data point (0, -2) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1/2(x - 0)

y = 1/2(x) - 2

Part 4a.

Based on the information provided about Jay's business, we would determine the slope of the line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3900 - 3875)/(2000 - 19375)

Slope (m) = 25/-17375

Slope (m) = -1/695

At data point (19375, 3875) and a slope of -1/695, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3875 = -1/695(x - 19375)

Part 4b.

For the cost when x = 31250 km, we have:

y - 3875 = -1/695(31250 - 19375)

y = 17.086 + 3875

y = $3892.086.

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For every 1 orange in the fruit bowl there are three bananas.

According to the question,

We have the following information:

In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.

Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:

4 oranges = 12 bananas

Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.

So, we have the following expression:

1 orange = 12/4 bananas

1 orange = 3 bananas

Hence, for every 1 orange in the fruit bowl there are three bananas.

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Answer: f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Step-by-step explanation: Using the given recursive formula:

f(1) = 0

f(n) = f(n-1) + 2

We can find the values of f(n) for different values of n:

f(1) = 0

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

f(5) = f(4) + 2 = 6 + 2 = 8

And so on.

We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:

f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Answer:

Point A does not lie on the curve y = x²

Step-by-step explanation:

Given points:

 \(\sf A: \left(\dfrac{3}{2}, \dfrac{9}{2}\right)\)

 \(\sf B: \left(-1,1 \right)\)

 \(\sf C: \left(4,16 \right)\)

 \(\sf D: \left(\dfrac{1}{2}, \dfrac{1}{4}\right)\)

To determine if the given points lie on the curve y = x², simply substitute the x-value of each point into the equation and compare y-values.

Point A

\(\boxed{\begin{aligned}x=\dfrac{3}{2} \implies y&=\left(\dfrac{3}{2} \right)^2\\\\y&=\dfrac{3^2}{2^2}\\\\y&=\dfrac{9}{4}\end{aligned}}\)

As 9/4 ≠ 9/2, point A does not lie on the curve.

Point B

\(\boxed{\begin{aligned}x= -1\implies y&=\left(-1 \right)^2\\y&=1\end{aligned}}\)

As 1 = 1, point B does lie on the curve.

Point C

\(\boxed{\begin{aligned}x=4 \implies y&=\left( 4\right)^2\\y&=16\end{aligned}}\)

As 16 = 16, point C does lie on the curve.

Point D

\(\boxed{\begin{aligned}x=\dfrac{1}{2} \implies y&=\left(\dfrac{1}{2} \right)^2\\\\y&=\dfrac{1^2}{2^2}\\\\y&=\dfrac{1}{4}\end{aligned}}\)

As 1/4 = 1/4, point D does lie on the curve.

Answer:

Side A is 7

Side B is 15

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

384 *.25=96

384-96=288

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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The correct expanded form for the following expression is 7/8 × 7/8.

The division of numbers into their component ones, tens, hundreds, thousands, ten thousand, and so forth creates the expanded form of the number. The expanded version of the number is the sum of each digit times its place value, which is used to represent the number. A number is broken down to show the value of each of its digits in order to be written in expanded form. 144 would then be converted to 100 + 40 + 4 = 144. It can be used to compute sums as well. When a number is expanded to show the value of each digit, it is written in expanded form. The numerical value of each digit in the number we are writing is represented using extended form.

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