What is the volume of a cone (in cubic inches) with a radius of 3 inches and a height of 6 inches in terms of pi

Answer:

Min C = 295x+ 416y;

Constraints (s.t):

Step-by-step explanation:

First, to find the Objective function of the linear programming problem we need to note that we are told, "the department wants to minimize cost (weekly cost)," meaning our objective function is Min C (Cost) = 295x+ 416y. Where x≥ 0, y≥ 0.

Constraints:

Let x denote the number of graduate research assistants hired and let y denote the number of professional researchers hired.

Note these statements that form the constraints for the different types of researchers:

1. Fieldwork hours constraints:

And the minimum (≥) number of hours needed per week for fieldwork is 154. Which implies this model, 23x+ 15y≥ 154.

2. University's research center hours constraints:

And the minimum (≥) number of hours needed per week at the research center is 140. Which implies this model, 17x+ 25y≥ 140.

The measure of angle is θ cannot determine the statements that are true about its reference angle.

There are two issues with the given statement.

First, it does not specify the measure of angle θ.

Second, the statement cos(0)=-3/10 is not related to the reference angle of θ.

The reference angle of θ is the acute angle between the terminal side of θ and the x-axis.

It is always positive and its measure is between 0 and 90 degrees or between 0 and π/2 radians.

The measure of the reference angle of θ is denoted by θ'.

To determine the reference angle of θ, we need to know the quadrant in which θ lies.

The reference angle of θ in standard position is the acute angle between the terminal side of θ and the x-axis.

If θ is in the first quadrant, then θ' = θ.

If θ is in the second quadrant, then θ' = π - θ.

If θ is in the third quadrant, then θ' = θ - π.

If θ is in the fourth quadrant, then θ' = 2π - θ.

The measure of angle θ, we can determine its reference angle using the above rules.

The statement cos(0)=-3/10 is not related to the reference angle of θ.

It is the value of the cosine function at 0 radians or 0 degrees.

This value does not correspond to any angle that has a reference angle.

The measure of angle θ cannot determine the statements that are true about its reference angle.

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Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

The nearest foot is 19

Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

Answer: I hope this helps!

Step-by-step explanation:

The volume of cone having diameter 18 units and height 8 units is 678.85 cubic units which is nearest to 648.17 cubic units which is option C.

Volume is basically amount of substance a container can hold in its capacity. Volume of cone is 1/3 *π\(R^{2}H\) in which R is the radius and H is height of cone.

We know that volume of cone is 1/3 *π*\(R^{2} H\)

We have to put the value of radius and height in the formula to get the value of volume of cone.

Radius=diameter/2

=18/2

=9 units.

Volume=1/3 * 3.14*9*9*8

=2034.72/3

=678.24 cubic units

Nearest option is 648.17 cubic units.

Hence the volume of the cone is 648.17 units.

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Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.

To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)

The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).

Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:

a = -4.9

b = 11

Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:

t = -11 / (2 * -4.9)

t = -11 / -9.8

t ≈ 1.122

Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.

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Answer:

(6,2)

Step-by-step explanation:

Start by plugging in 6 for x and 2 for y

4(6)-2(2) = ?

24-4 = 20

Answer:

512 ounces

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

multiply the volume value by 128

Answer: 360 containers

Step-by-step explanation: 1 5/8 in decimal form is 1.625 pounds. Divide 585 by 1.625 pounds you get 360. It takes 360 containers to hold 585 pounds of fruit

Answer:

2x

Step-by-step explanation:

Complete answer

Answer:

2x

Step-by-step explanation:

Mental math is just better

There is no true equation among the given equations.

An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.

Mathematical expressions are constants, numbers, values, or variables written with algebraic operands, including addition, subtraction, division, and multiplication.

A. 34 − 12 = 14.  This equation is not true because (34 - 12 = 22).

B. 916 − 48 = 58. This equation is not true since (916 - 48 = 868).

C. 78 − 34 = 18. This equation is not true since (78 - 34 = 44).

D. 715 − 13 = 615. This equation is not true because (715 - 13 = 702).

E. 12 − 20 = 10. This equation is untrue since (12 - 20 = -8).

Thus, since the solutions to the equations are not the same values given, we can conclude that none of the equations is true.

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A. 34 − 12 = 14

B. 916 − 48 = 58

C. 78 − 34 = 18

D. 715 − 13 = 615

E. 12 − 20 = 10

The possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

The given parameters are

Area = 15 square cm

The area is given as

Area = 15 square cm

The formula of area is

Area = Length x Width

Using the above formula, we have:

A) 1 cm and 15 cm ⇒ 15 square cm

B) 2 cm and 7 cm ⇒ 14 square cm

C) 3 cm and 5 cm ⇒ 15 square cm

D) 4 cm and 4 cm ⇒ 16 square cm

Hence, the possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

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Possible question

The area of a rectangle is 15 square cm

Which of the following could be the rectangle's length and width?

(Area = length x width)

Choose all answers that apply:

A) 1 cm and 15 cm

B) 2 cm and 7 cm

C) 3 cm and 5 cm

D) 4 cm and 4 cm

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

The length of the rectangle

is 2 units. The width of the rectangle

Is 11 units. The area of the rectangle

is 26 square units.

The area of the triangle is half the area of the rectangle, so the area of the triangle is 13 square units.

The required, area of the triangle can be determined by forming a rectangle and then finding half of the area of that rectangle. Option D is correct.

The area of the triangle is half the product of the base and height of the triangle.

here,
To determine the area of the triangle by forming a rectangle, we can use the following steps:

A. Copy and rotate the triangle and place it next to the existing triangle to form a rectangle.

B. The length of the rectangle is equal to the base of the triangle plus the height of the triangle. So, the length of the rectangle is (base + height) units.

C. The width of the rectangle is equal to the other side of the triangle. So, the width of the rectangle is the same as the base of the triangle. Thus, the width of the rectangle is base units. The area of the rectangle is length times width, which is (base + height) times base square units.

D. The area of the triangle is half the area of the rectangle. So, we can find the area of the triangle by dividing the area of the rectangle by 2. Thus, the area of the triangle is ((base + height) times base) / 2 square units.

So, the area of the triangle can be determined by forming a rectangle and then finding half of the area of that rectangle.

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The probability that the sample's mean length is greater than 6.3 inches is0.8446.

Here, we have,

Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.

We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.

Probability is the likeliness of happening an event.

It lies between 0 and 1.

Probability is the number of items divided by the total number of items.

We have to use z statistic in this question because the sample size is greater than 30.

μ=6.5

σ=0.5

n=46

z=X-μ/σ

where μ is mean and

σ is standard deviation.

First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.

z=6.3-6.5/0.5

=-0.2/0.5

=-0.4

p value from z table is 0.3446

Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.

Hence the probability that the mean length is greater than 6.3 inches is 0.8446.

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Answer:

  $5.59

Step-by-step explanation:

You want the unit price of a pair of socks, given that 5 pairs cost $27.95.

The unit price is found by dividing the price by the number of units.

  $27.95/5 = $5.59

The unit price of a pair of socks is $5.59.

Answer:

d = ±7i

Step-by-step explanation:

d^2 -1 = -50

Add 1 to each side

d^2 -1 = -50

d^2 = -49

Take the square root of each side

sqrt(d^2) = sqrt(-49)

d = sqrt(-1) sqrt(49)

d = i( ±7)

d = ±7i

Answer:

A.

Step-by-step explanation:

d^2-1= -50

First, add 1 to both sides.

d^2= -49

Take the square root of both sides:

d=√-49

Since i^2=-1

d=i√49

d= ±7i

Hope this helps!

Answer:

The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.

Step-by-step explanation:

The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Here, given that,

Robert's salary after working for n years can be determined using the equation

S = 5000n + 60000.

Hence, The slope is 5000,

this means that for each additional year Robert works at the company, he earns 5000 more dollars.

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Answer:

sorry

Step-by-step explanation:

Answer:

y=15

∠P=113

∠Q=67

∠R=113

∠S=67

Step-by-step explanation:

10y-37+4y+7=180

14y=210

y=15

∠P=10(15)-37=113

∠Q=180-113=67

Answer:

m=0

Step-by-step explanation:

the slope is calculated using two points on the line and the formula

m = (y2 - y1) ÷ (x2 - x1)

where

x1 and y1 are the coordinates of point 1

x2 and y2 are the coordinates of point 2

for example, you can take

point 1 = (x1;y1) = (-2;3)

point 2 = (x2;y2) = (-1;3)

then your slope is

m = (3 - 3) ÷ (-1 - (-2)) = 0

notice that x1 is always at the left of x2 on the x axis

and it makes sense that your slope is 0 because for each x your y is the same

The dimensions of the right circular cylinder of maximum volume that can be inscribed in a sphere of radius 20 cm are: radius = 20 cm, height = 10 cm, and the maximum volume is approximately 12566.37 cm³.

Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disc in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting two circular bases. Perpendicular distance is the measurement separating the two bases, and it is denoted by the letter "h," which stands for height. The distance between the two circular bases' centers and outer edges is known as the cylinder's radius and is denoted by the letter "r". A rectangle and two circles combine to form the cylinder.

h = (40 - 20)/2 = 10 cm

Now, we can calculate the volume of the cylinder:

Volume =\(\rm \pi^2h = \pi (20)^2(10) = 4000\pi \simeq 12566.37\ cm^3\)

Therefore, the dimensions of the right circular cylinder of maximum volume that can be inscribed in a sphere of radius 20 cm are: radius = 20 cm, height = 10 cm, and the maximum volume is approximately 12566.37 cm³.

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Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

1) Let's expand this expression below, distributing the factors (as FOIL technique):

2) Combining like terms we have:

3) Hence, the expanded form is the one above, with all the simplifications.

The lower quartile of the given data set is 63.

To find the lower quartile (Q1), we need to determine the value that divides the data set into the lower 25% of the values.

First, we need to sort the data set in ascending order: 61, 61, 62, 64, 66, 69, 69, 70, 72, 73, 74, 78.

Next, we calculate the position of the lower quartile using the formula: (n+1)/4, where n is the number of data points. In this case, we have 12 data points, so (12+1)/4 = 13/4 = 3.25.

Since 3.25 is not a whole number, we can find the lower quartile by taking the average of the data points at positions 3 and 4.

The data point at position 3 is 62, and the data point at position 4 is 64.

Therefore, the lower quartile (Q1) is the average of 62 and 64:

(Q1) = (62 + 64)/2 = 126/2 = 63.

Hence, the lower quartile of the given data set is 63.

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9514 1404 393

Answer:

  see below

Step-by-step explanation:

First row

Fill in the given x-value and solve for y:

  3(-4) +2y = -6

  -12 +2y = -6

  -6 +y = -3 . . . . . divide by 2

  y = 3 . . . . . . . . . add 6

__

Second row

Fill in the given y-value and solve for x:

  3x +2(0) = -6

  x = -2 . . . . . . . . . divide by 3

Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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Answer:

Step-by-step explanation:

Question

N

m

4

5

4

U

-

3-

Cu v

-5-4-3-2-1

2

-2

1 w

60

r

2345x

What is the domain of the function on the graph?

O all real numbers

O all real numbers greater than or equal to-2

O all real numbers greater than or equal to-5

O all real numbers greater than or equal to 0

Help please

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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Final conclusion would be that the difference between the means of the two samples is not statistically significant.

What is Null Hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

It is not possible to test the claim that the two samples come from populations with the same mean without more information about the samples themselves. In order to test this claim, you need to have the sample data, the sample sizes, and the standard deviations of the samples. You can then use a t-test for independent samples to determine whether the difference between the means of the two samples is statistically significant.

The t-test is a statistical test that is used to compare the means of two samples. The test statistic for the t-test is the difference between the means of the two samples divided by the standard error of the difference. The degree of freedom for the t-test is the sum of the sample sizes minus 2. The significance level, alpha, is the probability of making a type I error, which is the probability of rejecting the null hypothesis when it is true. The rejection region for the t-test is the set of values of the test statistic for which the null hypothesis is rejected.

If the test statistic does not fall in the rejection region, you cannot reject the null hypothesis, and you must conclude that the difference between the means of the two samples is not statistically significant.

Final conclusion would be that the difference between the means of the two samples is not statistically significant.

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