For which of the following value(s) of p is the following function NOT defined:

Answer:

  84.5 cubic meters

Step-by-step explanation:

You want the volume of a pyramid with a base area of 42.25 m² and a height of 6 m.

The formula for the volume of a pyramid is ...

  V = 1/3Bh

Using the given values, we find the volume to be ...

  V = 1/3(42.25 m²)(6 m) = 84.5 m³

The volume of the pyramid is 84.5 cubic meters.

Final answer:

The percentage increase in the perimeter of the rectangle is 6%.

Explanation:

To find the percentage increase in the perimeter of the rectangle, we need to calculate the new perimeter and compare it to the original perimeter.

The original length is 20 and the width is 30. The original perimeter is 2(20+30) = 100.

When the length is increased by 10%, it becomes 20 + 10% of 20 = 20 + 2 = 22. The width is increased by 5%, so it becomes 30 + 5% of 30 = 30 + 1.5 = 31.5.

The new perimeter is 2(22+31.5) = 106. The percentage increase in the perimeter is (106-100)/100 * 100 = 6%.

Answer:

7.5 gallons

Step-by-step explanation:

2^-3= 0.125

0.125*60= 7.5

Final answer:

The gas pump fills 7.5 gallons of gasoline in one minute.

Explanation:

If a gas pump fills 2-3 gallon of gasoline per second, we first need to understand how much that is in gallons. 2-3 is the same as 1/23 or 1/8. Therefore, the pump fills 1/8 gallon per second.

To find out how many gallons the pump fills in one minute, we multiply the amount filled per second by the number of seconds in a minute:

Gallons per minute = gallons per second × seconds per minute

Gallons per minute = 1/8 gallon/second × 60 seconds/minute

Gallons per minute = 60/8 gallons

By reducing this fraction, we get:

Gallons per minute = 7.5 gallons

Thus, the gas pump fills 7.5 gallons of gasoline in one minute.

Answer: 260 downloads of the standard version were there.

Step-by-step explanation:

Let x represent the number of downloads of the standard version.

Let y represent the number of downloads of the high-quality version.

Yesterday, the high-quality version downloaded four times as often as the standard version. It means that

y = 4x

The size of the standard version is 2.9 megabytes (MB). the size of the high-quality version is 4.6 MB. the total size downloaded for the two versions was 5538 MB. It means that

2.9x + 4.6y = 5538- - - - - - - - - - - -1

Substituting y = 4x into equation 1, it becomes

2.9x + 4.6 × 4x = 5538

2.9x + 18.4x = 5538

21.3x = 5538

x = 5538/21.3

x = 260

Final answer:

To determine the number of standard version song downloads, we set up and solved a system of linear equations. We found that the standard version was downloaded 260 times.

Explanation:

The student's question involves solving a system of linear equations to find out how many times the standard version of a song was downloaded. We have two versions of a song: a standard version (2.9 MB) and a high-quality version (4.6 MB). We are told that the high-quality version was downloaded four times as often as the standard version and that the total size downloaded was 5538 MB. To solve this, we set up two equations:

Let x represent the number of standard version downloads, and 4x represent the number of high-quality version downloads.

The total size equation would be 2.9x + 4.6(4x) = 5538

Combining like terms and solving for x, we have:

2.9x + 18.4x = 5538

21.3x = 5538

x = 5538 / 21.3

x = 260

So, there were 260 downloads of the standard version of the song.

Answer:

Alex has 110 shells

Benji has 132 shells

Carmen has 66 shells

Step-by-step explanation:

In this question, we are tasked with calculating the number of shells each of the friends have.

We proceed as follows;

Since Alex is the linking point between the other two friends, we say that let the number of shells Alex has be A

Now, Benji has 20% more shells

This mathematically means that the number of shells owned by Benji = (20% × A) + A = 0.2A + A =  1.2A

Carmen has 40% fewer shells than Alex;

Mathematically, this means that the number of shells owned by Carmen is A - (40% × A) = A - 0.4A = 0.6A

To find A, we simply add all together and equate to 308

Mathematically, we have;

A + 1.2A + 0.6A = 308

2.8A = 308

Divide both sides by 2.8

A = 308/2.8

A = 110

This means Alex has 110 shells

Benji has 1.2A = 1.2 × 110 = 132 shells

Carmen has 0.6A = 0.6 × 110 = 66 shells

Answer:

4 5/6 (the last option)

Step-by-step explanation:

to ensure and find out you can dive 5/6 then add 4 and you get 4.833333333333

Answer:

Row 2

Step-by-step explanation:

6+5+3+0+4=16

4+5+3+5+6=23

7+1+4+5+3=20

4+2+5+6+3=20

23 is bigger than all of those so it would be row two.

Answer:

Row 2

Explanation:

Answer:

The confidence level of the study is 99.9%

The confidence level is 99.9% of the margin error is 8%

Step-by-step explanation:

Explanation:-

Candy has observed 250 sports cars

The sample size 'n' = 250

Sample proportion 'p' = 15% = 0.15

The margin of error = 8% = 0.08

The margin of error  is determined by   = [tex]\frac{z_{\alpha }\sqrt{p(1-p)} }{\sqrt{n} }[/tex]

                                                 [tex]0.08 X \sqrt{250} = z_{\alpha } \sqrt{0.15 (1-0.15)}[/tex]

                                                    [tex]\frac{ 0.08 X \sqrt{250}}{ \sqrt{0.15 (1-0.15)}} = z_{\alpha }[/tex]

                                                    [tex]z_{\alpha }= \frac{ 0.08 X \sqrt{250}}{ \sqrt{0.15 (1-0.15)}} = \frac{1.2649}{0.35707}[/tex]

                                                    [tex]z_{\alpha } = 3.5431[/tex]

Conclusion:-

The z- score of 99.9% level of significance = 3.54 for two tailed test

Hence the confidence level is 99.9% of the margin error is 8%.

Answer:

Step-by-step explanation:

Let the no of cars be x and no of buses be y.

x + y = 60 -> y = 60 - x

6x + 30y = 600

with the available equations let us calculate the values of x and y.

6x + 30 * (60-x) = 600

6x + 1800 - 30x = 600

24x = 1200

x cars = 50

y buses = 10

maximum profit = 50 * 2.5 + 10 * 7.5 = $200

a) The objective function to maximize profit is: 2.5C + 7.5B using constraints 6C + 30B ≤ 600 and C + B ≤ 60. b) The parking lot should accept 50 cars and 10 buses to maximize profit. The maximum profit will be $200.

We need to set up a linear programming model to maximize profit from parking cars and buses.

A. Model Formulation:

Let C represent the number of cars and B represent the number of buses.

Objective Function: Maximize Profit = 2.5C + 7.5B

Constraints:

B. Solution:

First, we convert the inequalities to equations and solve:

We solve these equations simultaneously:

1. C + 5B = 100 (Equation 1)

2. C + B = 60 (Equation 2)

Subtract Equation 2 from Equation 1:

(C + 5B) - (C + B) = 100 - 60

⟶ 4B = 40 ⟶ B = 10

From Equation 2, we get:

C + 10 = 60 ⟶ C = 50

Maximum Profit Calculation:

Substituting C = 50 and B = 10 into the objective function:

Profit = 2.5(50) + 7.5(10) = 125 + 75 = 200

Therefore, to maximize profit, the attendant should accept 50 cars and 10 buses.

Maximum profit is $200.

Complete question:

The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50. How many of each should be accepted to maximize Profit?

a. Set up for the solution of this Linear Programming (LP) problem.

b. Using part (a), how many of each should be accepted to maximize Profit? What is the maximum profit?

Answer: 1.6x + 1.75y ≤ 10

Step-by-step explanation:

Let x represent the number of pounds of strawberries that Joey can buy.

Let y represent the number of pounds of raspberries that Joey can buy.

Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. It means that the cost of x pounds of strawberry and y pounds of raspberry is expressed as

1.6x + 1.75y

if she only has $10 to spend on berries, then the inequality that can be used to represent the situation is

1.6x + 1.75y ≤ 10

Answer:

b and d

Step-by-step explanation:

Answer:

67,500 residents

Step-by-step explanation:

The population density is defined as the average number of people living per square unit area.

-Given the density is 225res/sq mile and the area is 300 sq mile, the area's population is:

[tex]\rho=\frac{Population}{Area}\\\\Population=Area \times \rho\\\\=300 \ mi^2\times 225\ res/mi^2\\\\=67500\ residents[/tex]

Hence, there are 67,500 residents in Flint county.

To calculate the population of Flint County, the population density (225 residents/mile2) is multiplied by its area (300 mile2), resulting in a population of 67,500 residents.

To find the population of Flint County, we need to multiply the population density by the area of the county. The population density is given as 225 residents per square mile, and the area of Flint County is 300 square miles. By multiplying these two values together, we can determine the total population.

Population of Flint County = Population Density × Area = 225 residents/mile2 × 300 mile2

Population of Flint County = 225 × 300 = 67,500 residents

Therefore, the population of Flint County is 67,500 residents.

Answer

y = 2(x - 8)(x + 2)

Step-by-step explanation:

A(x - 8)(x + 2)

A × -8 × 2 = -32

-16A = -32

A = 2

y = 2(x - 8)(x + 2)

Answer:

10 Yards

Step-by-step explanation:

In every yard there is 3 feet

If you have 30 feet you have ____ yards

Divide 30 by 3 to get 10 yards!

Hope this Helps!

The instantaneous velocity of the baseball 3 seconds after it is hit is [tex]\( 24 \)[/tex] feet per second.

To find the instantaneous velocity of the baseball 1 second and 3 seconds after it is hit, we need to differentiate the height function [tex]\( s(t) \)[/tex] with respect to time [tex]\( t \)[/tex] to get the velocity function [tex]\( v(t) \).[/tex]

The height function is given by:

[tex]\[ s(t) = -16t^2 + 88t + 4 \][/tex]

1. Find the Velocity Function:

[tex]\[ v(t) = s'(t) \][/tex]

Differentiate [tex]\( s(t) \)[/tex] with respect to [tex]\( t \)[/tex]:

[tex]\[ v(t) = -32t + 88 \][/tex]

2. Evaluate the Instantaneous Velocity at [tex]\( t = 1 \)[/tex] second:

[tex]\[ v(1) = -32(1) + 88 = 56 \][/tex]

The instantaneous velocity of the baseball 1 second after it is hit is [tex]\( 56 \)[/tex] feet per second.

3. Evaluate the Instantaneous Velocity at [tex]\( t = 3 \)[/tex] seconds:

[tex]\[ v(3) = -32(3) + 88 = 24 \][/tex]

The answer is [tex]\( 24 \)[/tex] feet per second.

So, after differentiating the height function to get the velocity function, we substituted the given values of time [tex](\( t = 1 \)[/tex] and [tex]\( t = 3 \))[/tex] into the velocity function to find the corresponding instantaneous velocities.

The instantaneous velocity provides information about the speed and direction of the baseball at a specific moment in time. In this case, 1 second after being hit, the baseball is moving upward with an instantaneous velocity of [tex]\( 56 \)[/tex] feet per second, and 3 seconds after being hit, it is still moving upward but with a reduced instantaneous velocity of[tex]\( 24 \)[/tex] feet per second.

The complete question is given here :

A foul tip of a baseball is hit straight upward from a height of 4 feet with an initial velocity of 88 feet per second. The function [tex]s(t) = -16t^2 + 88t + 4[/tex] describes the ball's height above the ground, s(t), in feet, t seconds after it was hit. What is the instantaneous velocity of the ball 1 second after it is hit? 3 seconds after it is hit?

Answer:

11

Step-by-step explanation:

8.7A+10=105.7

8.7A=95.7

A=11

Answer:

2/3

Step-by-step explanation:

To know the fraction of men over women, we just need to divide the total number of men in the academy by the total number of women in the academy. So, we have that:

Fraction = men / women = 24 / 36 = 2/3

So the fraction we want to know is 2/3, that is, for every 2 men, there are 3 women in the academy.

Answer: Yes and No

When the longest side is not longer than the sum of the two shorter

Step-by-step explanation:

Let first convert mile to kilometre

1 mile = 1.609km

AB = 0.5mile = 0.8045 km

BC = 1/3 miles = 0.53633 km

DE=0.205 kilometer

EF=0.01 kilometer

AC=1/4 mile = 0.40225

DF=0.02 kilometer

When the longest side is not longer than the sum of the two shorter sides , then a triangle can be made

Let's first consider AB, BC and AC Each set of line segments AB, BC and AC can form a triangle

Also DE, EF and DF

Each set of line segments DE, EF and DF can't form a triangle because the longest side is greater than the sum of the two shorter sides.

Answer:

8 × 7

Step-by-step explanation:

(4 × 2) × 7

We can multiply what is inside the parentheses

(8) × 7

Answer:

8*7

Step-by-step explanation:

Multiply what is inside the parentheses first, (PEMDAS)

(4*2)*7

8*7

Hope this helps! :)

Answer:

Each Exterior Angle = (360 degrees) ÷ (Number of Sides)

Each Exterior Angle = 360 / 30

Each Exterior Angle = 12 degrees

Step-by-step explanation:

The measure of each exterior angle of a regular 30-gon will be 12°.

Based on the information, it should be noted that the value of the total angles will be 360°.

Therefore, the measure of each exterior angle of a regular 30-gon will be:

= 360/30

= 12°

Therefore, the measure of each exterior angle of a regular 30-gon is 12°.

Read related link on:

https://brainly.com/question/11024992

Answer: (A) The longer side in the rectangle is 45 units.

(B) The line LP measures 14 cm.

Step-by-step explanation: In the rectangle, two sides are given as 2x and 3x + 3, respectively. The perimeter is also given as 146 units. The formula to determine the perimeter is

Perimeter = 2(L + W)

We can now substitute for the values

146 = 2(2x + 3x + 3)

146 = 2(5x + 3)

146 = 10x + 6

Subtract 6 from both sides of the equation

140 = 10x

Divide both sides of the equation by 10

14 = x

With the value of x now known as 14, the sides of the rectangle are,

L = 2x

L = 2 x 14

L = 28

And the other side is

W = 3x + 3

W = 3(14) + 3

W = 42 + 3

W = 45

Therefore the longer side is 45 units.

In question B;

The rhombus has all sides congruent as one of its properties. This simply implies that the diagonal from point M to point O, is the same length as the diagonal from point L to point N. Hence, at point P, where both diagonals intersect, both diagonals are divided into two equal lengths each. If line LN is 28 cm, then line LP which is half of LN shall be 28 divided by 2, and that gives us 14 cm.

Answer:

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Answer: the surface area of the larger cylinder is 16 times that of the smaller cylinder.

Step-by-step explanation:

The formula for determining the total surface area of a cylinder is expressed as

Total surface area = 2πr² + 2πrh

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant

Considering the larger cylinder,

radius = 8 cm

Height = 12 cm

Therefore,

Total surface area = (2 × π × 8²) + (2 × π × 8 × 12)

= 128π + 192π = 320π

Considering the smaller cylinder,

Total surface area = 56π

radius = 8/4 = 2cm

Height = 12/4 = 3 cm

Therefore,

Total surface area = (2 × π × 2²) + (2 × π × 2 × 3)

= 8π + 12π = 20π

Ratio of the surface area of the larger cylinder to the smaller cylinder is

320π/20π = 16

Answer:

x = 6

Step-by-step explanation:

cos 60° = JK/JL

cos 60° = 7 / (3x-4)

(1/2) = 7 / (3x-4)

(1/2) = 7 / (3x-4)

(3x-4) = (2)(7)

3x-4 = 14

3x = 14+4

3x = 18

x = 18/3

x = 6

Answer:

Step-by-step explanation:

If the columns span R^6, this says that every b in R^6 is in the span of the columns, which is another way of saying that any b is a linear combination of the columns. Then the equation is consistent for some b or all b in R^6.

If an augmented matrix can be transformed by elementary row operations into reduced echelon form, then the equation Ax = b is consistent.

Any matrix can be transformed by elementary row operations into reduced echelon form, but not every matrix equation Ax = b is consistent

For example, after echelon reduction we have

1 6. 7. 8. 8.

0 1. 5. 4. 9

0. 0. 1. 3. 6

0. 0. 0. 1. 6.

0. 0. 0. 0. 1

0. 0. 0. 0. 0

In this case, the matrix doesn't have a solution, then the matrix is inconsistent

But if the matrix echelon reduction gives

1 6. 7. 8. 8.

0 1. 5. 4. 9

0. 0. 1. 3. 6

0. 0. 0. 1. 6.

0. 0. 0. 0. 1

0. 0. 0. 0. 1

Then, the system have a solution but not unique, the system have a solution for some b in R^6.

Then, the solution is II and III

So the correct option is D.

Answer: The modes of that set of data are both 8 and 2

Step-by-step explanation: The mode is the number that appears most often in a data set and 8 and 2 are the only number that appear more than once in that set of data

Answer:

8 and 2

Step-by-step explanation:

I got this for a quiz and the answer was 8 and 2.

Answer:

17.5  yds =r

Step-by-step explanation:

Circumference is given by

C = 2*pi*r

35pi = 2 *pi*r

Divide each side by 2pi

35pi/2pi = 2*pi*r/2pi

17.5 =r

Answer: I believe the answer is 9 days.

Step-by-step explanation: 16 divided by 1.75 (1 and three-fourths) is equal to 9.143, which is only enough to feed him 9 full days.

Answer:

The answer to your question is 9 days.

Step-by-step explanation:

Data

Food needed = 1 3/4 cups

Total food = 16 cups

Number of days = ?

Process

1.- Convert the mixed fraction into an improper fraction

              1 3/4 = (4 + 3)/4 = 7/4

2.- Divide the total food by the food needed

              16/1 ÷ 7/4 = 64/7

-Simplify                     9        Quotient

                          7   64

                                 1          Remainder

3.- Mark can feed his dog 9 days and there will be 1/7 of the bag left.

Answer:

3 ft by 4/3 feet.

Step-by-step explanation:

We have been given that a card is 9 inches by 4 inches. A printing shop will enlarge it so that the longer side is any lengths up to 3 ft. We are asked to find the dimensions of biggest enlargement.

We will use proportions to solve our given problem.

[tex]\frac{\text{Card width}}{\text{Card length}}=\frac{\text{Enlarged width}}{\text{Enlarged length}}[/tex]

Upon substituting our given values, we will get:

[tex]\frac{\text{4 inches}}{9 \text{ inches}}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]

[tex]\frac{4}{9}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]

[tex]\frac{4}{9}\times \text{3 ft}=\frac{\text{Enlarged width}}{\text{3 ft}}\times \text{3 ft}[/tex]

[tex]\frac{4}{3}\times \text{ft}=\text{Enlarged width}[/tex]

Therefore, the dimensions of the biggest enlargement  would be 3 ft by 4/3 feet.