solve for x in the diagram

The volume of the packing material that luke will need is: 11 cubic feet

The formula for the volume of a box is expressed as:

V = length * width * height

Now, we are given:

Area of base = 15 square feet

height = 3 feet

Thus:

Volume of box = 15 * 3 = 45 cubic feet

If he is going to ship a toy that is 34 cubic feet, then it means that:

Volume of packing material Luke needs = 45 - 34 = 11 cubic feet

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Result:

Yes, the fifth-grade team will need to ship the order of 325 shirts for Field Day. They will need to package them in 16 boxes to ship them.

To evaluate the number of boxes needed to ship the order, we need to divide the total number of shirts by the number of shirts that can fit in one box.

where:

Number of shirts per box = 21

Total number of shirts = 325

Number of boxes needed = Total number of shirts / Number of shirts per box

Number of boxes needed = 325 / 21

Number of boxes needed = 15.47619

Since we cannot have a fraction of a box, we would round up to the nearest whole number.

Therefore, the fifth-grade team will need to ship the order in 16 boxes.

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The length the one-inch pipe should be cut to make a flute with a lowest desired note of 523.25 Hz, based on the acoustic length formula is 12.9 inches

The acoustic length is the length obtained from the sum of  the bore length and the corrections at the foot and the sound hole.

The frequency of the lowest note = 523.25 Hz

Whereby the frequency of the lowest note = The fundamental frequency

The acoustic length formula for finding the length of the pipe, L, can be presented as follows;

L = (v/(2·f)) × √(1 + 4·A²/v²)

Where;

L = The length of the pipe

f = The frequency = 523.25 Hz

A = The cross-sectional area of the pipe = π × 1.315²/4 ≈ 1.36 in²

v = The speed of sound ≈ 343 m/s ≈ 13503.9 in/s

L = (v/(2·f)) × √(1 + 4·A²/v²)

L = (13503.9/(2×523.25)) × √(1 + 4×1.26²/13503.9²) ≈ 12.9

The length of the pipe is about 12.9 inches

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Answer: The cost of a large pizza with 2 toppings depends on the pizza place. Let's say the cost is $15 per pizza, and each additional topping costs $2.

Let t be the number of toppings Anna has on her pizza. Then, the total cost of her pizza can be expressed as:

Total cost = $15 + $2t

Since Anna has 2 toppings on her pizza, we can substitute t = 2:

Total cost = $15 + $2(2)

Total cost = $15 + $4

Total cost = $19

Therefore, the total cost of Anna's pizza with 2 toppings is $19.

Answer:  5km

Step-by-step explanation:

The formula for Surface area of a square pyramid

SA= [tex]L^{2} + 2Ls[/tex]         where L is the length on the bottom and s is the slant height

                                L=1 km              s=2 km

SA = [tex]1^{2} +[/tex] 2(1)(2)

=1+4

=5km

Tom is installing 6 windows each day and Suzanne is installing 6 windows each day as well.

To find the number of days it takes for each homebuilder to install the windows, we need to solve for x in each equation.

Tom's equation: 42 = 7x + 2

Subtracting 2 from both sides:

40 = 7x

Dividing both sides by 7:

x = 5.71 ≈ 6

So it will take Tom approximately 6 days to install the windows on his home.

Suzanne's equation: 37 = 6x + 5

Subtracting 5 from both sides:

32 = 6x

Dividing both sides by 6:

x = 5.33 ≈ 6.

So it will take Suzanne approximately 6 days to install the windows on her home.

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The smallest approximate sample size required to obtain the desired margin of error is b. 180 Chihuahuas

The sample size is defined as the number of observations used for determining the estimations of a given population. It should be noted that the size of the sample has been drawn from the population. Sampling is the process of selection of a subset of individuals from the population to estimate the characteristics of the whole population.

The sample size will be:

= (2.576 × 26 / 5)²

= 180

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The statement that is not true is (c) The measure of ∠R is the same as ∠N.

From the question, we have the following parameters that can be used in our computation:

Looking at the above coordinates, we can see that the transformation rule is (x, y) = (-x, -y)

This is a rigid transformation

And so, the side lengths and the corresponding angle measures are equal

However, angles R and N are not corresponding angles

So, the false statement is (c) The measure of ∠R is the same as ∠N.

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The equation of the line for the given points is y= (1/2)x - 3.

An equation of a line can be written in slope-intercept form, which is:

y = mx + b

where:

y and x are the coordinates of any point on the line.

m is the slope of the line (the rate at which y changes with respect to x).

b is the y-intercept of the line (the y-coordinate of the point where the line intersects the y-axis).

The slope of the line is calculated as,

m = ( y₂ -y₁) / (x₂ - x₁)

m = ( -2+1) / (2-4)

m = 1/2

The y-intercept is calculated as,

y = mx + c

-1 = (1/2)x 4 + c

c = -3

The equation of the line will be,

y = mx + c

y = (1/2)x - 3

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The equation of the line of best fit for the set of data is given as follows:

y = 4.24773x - 0.32726

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

From the table in this problem, the points are given as follows:

(0.9, 3.51), (1.7, 6.61), (3, 12.27), (0.1, 0.15), (2.3, 9.59), (1.3, 5.35), (0.5, 1.65), (2.1, 8.8).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 4.24773x - 0.32726

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Answer:

Step-by-step explanation: However, say that the car loses 50% of its value every year. This means that if you originally bought a car for 2,000 dollars in 2015, in 2016 it would be world 2,000/2=1,000, 1,000/2=500 the year after that, and so on. We can try to put this into a linear function, but it's hard to put it into one equation because we're not subtracting or adding to the cost of the car by a specific amount each year. If we had our equation as y=-0.5*x+2000, this wouldn't work because it's adding to the original amount, not multiplying. However, if we used an exponential equation such as y=b(m^a), with y representing the end cost, b representing the starting cost, m representing the amount multiplied per year, and a representing the number of years. This works because we start with a value, and multiply it by an amount each year. Since 50%=0.5, we plug that into m to get y=2,000(0.5^a). Therefore, this works well here. If the minivan were to depreciate by 3,000 every year, starting at $29,248, this means that we first have to find out what we multiply by 29,248 by the first year to subtract 3,000. As, after one year, the value is 29,248-3,000=26,248, we have 26,248=29,248(m^1). Therefore, we can divide 29,248 by both sides to get around 0.9 as our answer form. Thus, our equation is y=29,248(0.9^a). This type of equation would not work if we subtracted an amount every year because we're not multiplying by the same amount then. For example, if a toy was valued at 3$ and gained a value of one dollar every year, we could multiply the toy by 4/3 the first year to get 4, but the next year we wouldn't get 5.

Answer:

There are 36 possible outcomes when two dice are rolled (6 outcomes for the first die and 6 outcomes for the second die). To find the probability that the sum of the two numbers on the dice will be greater than 9, we need to count the number of outcomes where the sum is greater than 9.

The possible outcomes where the sum is greater than 9 are (4,6), (5,5), (5,6), and (6,5), for a total of 4 outcomes. Therefore, the probability of getting a sum greater than 9 is 4/36 or 1/9.

Answer: C) 1/12.

Huai's monthly payment for the community college loan is $89.72 and $235.35.

To calculate the monthly payment for each loan, we need first to calculate the total amount borrowed and the total interest paid for each loan.

For the first loan

Total amount borrowed = $3700

Total interest paid = $3700 x 0.068 x (4 + 4/12 + 3/12) = $1,271.12

Total amount repaid = $3700 + $1,271.12 = $4,971.12

To find the monthly payment, we can use the formula for a loan payment

P = (r(PV))/(1-(1+r)⁻ⁿ)

Where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan, and n is the total number of payments.

For the first loan, r = 0.068/12, PV = $3700, and n = 48 (4 years x 12 months/year). Substituting these values into the formula, we get

P = (0.068/12 * $3700)/(1-(1+0.068/12)⁻⁴⁸) = $89.72

Therefore, the monthly payment on the first loan is $89.72.

For the second loan

Total amount borrowed = $12,000

Total interest paid = $12,000 x 0.074 x (3/12) = $222.00

Total amount repaid = $12,000 + $222.00 = $12,222.00

The second loan was acquired 2 years after the first, so the total repayment period is 5 x 12 - 2 x 12 - 3 = 51 months.

Using the same formula as before, but with r = 0.074/12, PV = $12,000, and n = 51, we get

P = (0.074/12 * $12,000)/(1-(1+0.074/12)⁻⁵¹) = $235.35

Therefore, the monthly payment on the second loan is $235.35.

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The area of the shaded region is 559 ft².

In order to find the area of the shaded region, we will subtract the area of the square from the area of the rectangle. That is:

area of the shaded region = area of rectangle - area of square

area of the shaded region = (32 * 20) - (9 * 9)

area of the shaded region = 640 - 81

area of the shaded region = 559 ft²

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Complete Question

See attached image

The approximate area of the mulch around the merry-go-round is 126.228 feet².

Diameter of the merry go round = 10.4 feet

Radius is half of the diameter.

Radius of the merry go round = 10.4/2 = 5.2 feet

Before the piece can be installed, a solid circular pad of mulch must be put down which extends 3 feet beyond the edge of the merry-go-round.

Radius of the merry go round with mulch = 5.2 + 3 = 8.2 feet

Total area of the merry go round with the mulch is,

Area = π (8.2)² = 67.24π feet²

Area of the merry go round = π (5.2)² = 27.04π feet²

Area of the mulch = 67.24π feet² - 27.04π feet² = 40.2π = 126.228 feet²

Hence the required area is 126.228 feet².

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The student can choose four questions from a question paper that contains six questions as follow:

a. 10 ways.

b. 5 ways.

c. 15 ways.

Combination is a way of selecting items from a collection where the order of selection does not matter.

a. If Question No. 1 is compulsory, then the student can choose three more questions from the remaining five. That is:

5C3 (i.e. 5 combination 3) ways =  10 ways.

b. If Question No. 2 should not be chosen, then the student can choose four questions from the remaining five. That is:

5C4 ways =  5 ways.

c. If there is no restriction on any of the questions, the student can choose any four questions from the remaining six. That is:

6C4 ways = 15 ways

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The probability of landing on a white square is 4/5.

We have toss board of measurement 5 x 5.

Total squares in board = 25

White square = 20

Black square= 5

So, the probability of landing on a white square

= 20 / 25

= 4/5

Thus, the required probability is 4/5.

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Answer:

yes

Step-by-step explanation:

log4(64)=3－0,4*4*4=64

The account's total value is $498,174.72.

The total interest paid is $174,174.72.

We can utilize the calculation for the future value of a compound interest annuity to resolve this issue:

FV = P*(((1 + r/n)(n*t))-1) / (r/n).

where

When we enter the values, we obtain:

FV = 600 * (((1 + 0.12/4)^(4*60)) - 1) / (0.12/4) = 498,174.72

After the 60th deposit, the account's total value is $498,174.72.

We can deduct the total amount deposited from the account's total value to calculate the cumulative interest:

Added interest is calculated as follows: FV - (P * t * n) = 498,174.72 - (600 * 60 * 4) = 174,174.72

Therefore, the total interest paid is $174,174.72.

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The number of chickens and pigs the farmer saw on the field are 37 and 16 respectively.

Let

Number of chickens = x

Number of pigs = y

x + y = 53

2x + 4y = 138

From (1)

x = 53 - y

Substitute x = 53 - y into (2)

2x + 4y = 138

2(53 - y) + 4y = 138

106 - 2y + 4y = 138

- 2y + 4y = 138 - 106

2y = 32

divide both sides by 2

y = 32/2

y = 16

Substitute y = 16 into

x + y = 53

x + 16 = 53

x = 53 - 16

x = 37

Therefore, there are 37 chickens and 16 pigs respectively.

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Statement " There will be 5 dots above 7" is true. Therefore, option D is the correct answer.

A line plot is an effective way to visualize and compare data in a table. In this case, the line plot would show the total number of people on each team, with dots representing the values.

The greatest value in the table is 11, but this would not be represented with a dot in the line plot. There will be 11 dots in total, representing the 11 teams listed in the table.

There will be 4 more dots above 7 than above 8, since there are 4 teams with 7 people on each team and only 3 teams with 8 people on each team.

Finally, there will be 5 dots above 7, since there are 5 teams with 7 or more people on each team.

Therefore, option D is the correct answer.

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The product of two given vectors is 48.

Given that, |v|=8, |w|=12 and the angle between v and w is 60 degrees.

We know that, |a|·|b|=|a|×|b|×cosθ.

Here, |v|·|w|=8×12×cos60°

= 96× 1/2

= 48

Therefore, the product of two given vectors is 48.

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Applying the leg rule, the length of BC in simplest radical form is: x = x = √390

The leg rule is used to find missing lengths in a right triangle when an altitude intersects the hypotenuse and form segments.

The leg rule is given as:

Hypotenuse / leg = leg / part

Thus, using the image given, we have:

Hypotenuse (AC) = 65

Part (DC) = 6

Leg = x

Plug in the values:

65 / x = x / 6

Cross multiply:

x * x = 6 * 65

x² = 390

x = √390

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The mean number of bikes sold by the company from January to June was 146.17.

The mean, also called average refers to data set found by adding all numbers in the data set and then dividing by the number of values in the set.

Given data:​ 110 ​ 158 ​ 112 ​ 176 ​ 119 ​ 202

The total number of bikes sold is:

= 110 + 158 + 112 + 176 + 119 + 202

= 877

The number of months (Jan - Jun) = 6

The mean number of bikes sold will be:

= Ef/x

= 877 / 6

= 146.166666667

= 146.17

Full question "The table shows the number of bikes sold by a company from January to June of last year.​

​Find the mean number of bikes sold by the company from January to June.

​January ​February ​March April​ May​ ​June

​ 110 ​ 158 ​ 112 ​ 176 ​ 119 ​ 202"

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The length of ZL and IL is 297.72 ft and 283.15 ft respectively.

The lengths of ZL and IL is calculated by applying trigonometry ratio as follows;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The hypothenuse side = ZL and the adjacent side = IL.

tan 18 = 92/IL

IL = 92/tan (18)

IL = 283.15 ft

sin 18 = 92/ZL

ZL = 92/si 18

ZL = 297.72 ft

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The area of the given trapezoid is 270 square units.

A trapezoid is a four-sided geometric shape that has two parallel sides (called the bases) and two non-parallel sides (called the legs). The area of a trapezoid is the amount of space inside the shape and can be calculated using the formula:

A = (a + b)h/2

Where:

a and b are the lengths of the two parallel sides of the trapezoid, and

h is the height (perpendicular distance) between the two parallel sides.

The area will be calculated as,

A = ( 10 + 8) x 30 /2

A = 270 square units

Therefore, the area is 270 square units.

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slope = -5, y intercept = 2

The graph is below.

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

Work Shown:

20x+4y = 8

4y = 8-20x

4y = -20x + 8

y = (-20x+8)/4

y = -20x/4 + 8/4

y = -5x + 2 is the final answer

slope = -5, y intercept = 2

Two points on this line are (0,2) and (1, -3)

The graph is below. I used GeoGebra to make it, but Desmos is another good choice.

The y-intercept for the function g(x) is 4.

The y-intercept of a function is a point where the line crosses the y-axis. The linear function can be given as below.

f(x) = mx+n

Where m is the slope of the line and n is a real number and y-intercept of the line.

The given function is f(x)=-4x—2.

The function is vertically translated 6 units up to g(x).

The y-intercept of the function f(x) is -2. Then the y-intercept for the function g(x) can be given as below.

y-intercept g(x) = -2+6

y-intercept g(x) = 4

Hence,  the y-intercept for the function g(x) is 4.

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Answer: on 1 = 0

on 2 = 0

on 3 = 3

on 4 = 0

on 5 = 0

on 6 = 2

on 7 = 1

on 8 = 4

Step-by-step explanation:

As the first, second, fourth and fifth do not have any numbers we will skip to the next number on the number line.

1/16 = 0

1/8 = 0

3/16 = 3

1/4 = 0

5/16 = 0

3/8 = 2

7/16 = 1

1/2 = 4