One of the legs of a right triangle measures 8 cm and its hypotenuse measures 14 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.

Answer:

The prism has a length x and a width x. Since it is a square at the base both length and width are the same amount x. The height is "half the length of one edge of the base". Since the base is x, this makes it 1/2x.

The volume's prism is found using V = l*w*h. Substitute and simplify.

13.5 = x*x*1/2x

13.5 = 1/2 x^3

27 = x^3

3 = x

The prism is 3 by 3 by 1.5.

Step-by-step explanation:

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The probability that the current customer gets their coffee before another customer joins the queue, given that there is one customer already in the cafe, is 0.5.

(a) The transition diagram for the birth and death process N(t) with state-space S = {0, 1, 2, 3, 4, 5} is as follows:

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 ----> 0 ----> 1 ----> 2 ----> 3 ----> 4 ----> 5 ---->

  Un=60   An=0   Un=60   An=0   Un=60   An=0   Un=0

In this diagram, the transitions from state i to i+1 represent the arrival of a customer, denoted by An, with a rate of 60 per hour. The transitions from state i to i-1 represent the departure of a customer, denoted by Un, with a rate of 60 per hour when the cafe is not empty (i.e., i > 0). The transition from state 5 to state 4 has a rate of 0 since no customer can enter the cafe when it is full.

(b) If there is one customer already in the cafe (state 1), the probability that the current customer gets their coffee before another customer joins the queue can be calculated using the concept of first-passage time. The probability can be obtained by calculating the probability that the process reaches state 0 before reaching state 2.

Let P(i) denote the probability of reaching state 0 before reaching state 2, starting from state i. We have:

P(1) = An / (An + Un)

In this case, An = 60 and Un = 60, so:

P(1) = 60 / (60 + 60) = 0.5

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Answer:

1 1/2

Step-by-step explanation:

1 1/2 + 3 1/2 = 5

6 1/2 - 5 =1 1/2

Answer:

An expression for this would be 3y as length * breadth is the area of a rectangle.

Answer:

hi

Step-by-step explanation:

The entry to record the payment of salaries and wages on July 2 is a debit to Salaries and Wages Payable and a credit to Cash.

1. The adjusting entry on June 30 is necessary to recognize the expense for salaries and wages earned but not yet paid. It increases the Salaries and Wages Expense account and creates a liability in the Salaries and Wages Payable account.

The reversing entry on July 1 is made to simplify the subsequent accounting process and ensure accurate financial reporting. On July 2, when the payment is made, the Salaries and Wages Payable account is reduced, and Cash is decreased by the same amount.

2. Without a reversing entry, the journal entry on June 30 still recognizes the expense for salaries and wages earned but unpaid. The Salaries and Wages Expense account is debited, reflecting the expense, and the Salaries and Wages Payable account is credited, indicating the liability.

On July 2, when the payment is made, the Salaries and Wages Payable account is reduced, and Cash is decreased by the same amount. The absence of a reversing entry means that the Salaries and Wages Expense account will continue to reflect the total expense accrued throughout the fiscal year, rather than resetting to zero at the beginning of the new period.

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Answer:

114cm

Step-by-step explanation:

When you're in a situation like this, you use ratios!

If the father's height is 5cm, and actually 185cm, the ratio of photo height and actual height is 1:57.

When we use this, the father is 57 times taller than him inside the photo, so since the daughter (in photo) is 2 cm, her height should be 2*57 cm.

2*57 = 114, which concludes to 114 cm.

:)

Answer:

1) X = 10 Therefore, 10 + 2 + 10 = 22.

2) B = 2 Therefore, 15 = 8(2) - 5 + 2(2)

3) B = -0.9 Therefore, -10 + 4(3(-0.9) + 10) = 19.

Answer:

the answer is B

I hope you a good day!

Answer:

B

Step-by-step explanation:

You can't do anything in the parentheses because you can't add x to 15 yet since x is unknown. Thus, you add 5 to 15 and get 20 + x or B, x + 20

Answer:

(2x-7)(x+12)

Step-by-step explanation:

2x²+17x-84

(2x     )(x     )

We were told to use 7 and 12 to equal 84. Let's try 12 in the first bracket and 7 in the second:

(2x  12)(x   7): (2x)(7) and (12)(x) = 14x and 12x, which we cant make 17x from

Now let's try 7 in the first bracket and 12 in the second:

(2x   7)(x   12): (2x)(12) and (7)(x) = 24x and 7x, which we CAN use to make 17x if the 7x is negative, ie place a '+' before the twelve in the second bracket and a '-' before the seven in the first bracket.

(2x-7)(x+12)

Double check: (2x-7)(x+12)=2x(x+12)-7(x+12)=2x²+24x-7x-84=2x²+17x-84

Answer:

C) Line A does not intersect Line B.

Step-by-step explanation:

Line A passes through (6 ,-30) & (-2 , 10)

Line B passes through (-4 , 28) & (2 , -2)

Find the slopes for each line. To find the slope, use the slope formula:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Line 1:

Let:

[tex](x_1 , y_1) = (6 , -30) \\(x_2 , y_2) = (-2 , 10)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{10 - (-30)}{-2 - 6} = \frac{10 + 30}{-8} = \frac{40}{-8} = \frac{-5}{1}[/tex]

Line 2:

Let:

[tex](x_1 , y_1) = (2 , -2)\\(x_2 , y_2) = (-4 , 28)[/tex]

Plug in the corresponding numbers to the corresponding variables:

m = [tex]\frac{28 - (-2)}{-4 - (2)} = \frac{28 + 2}{-4 - 2} = \frac{30}{-6} = \frac{-5}{1}[/tex]

The two lines share the same slope, therefore, they are parallel to each other. This means that they do not intersect at any given point.

Answer:

Step-by-step explanation:

17*8= the entire rectangle which is 136

Area of triangle=(base*height)divided by 2

The base of the white triangle is 4 because 8-4=4 and the height is 17

17*4=68

68/2=34

34= the area of the triangle

Area of the rectangle-area of the triangle=102

102 is your answer.

hopefully i did this right:)

Answer:

$17.5

Step-by-step explanation:

Answer:

26.25

Step-by-step explanation:

I took the test

Answer:

just believe and ask for forgiveness

Step-by-step explanation:

god lovesyou amen you shall pass

Answer:

4,-4 I think

Step-by-step explanation:

My brain is off right now so might be wrong

Answer:

30 i think

Step-by-step explanation:

Answer:

(8,9)

Step-by-step explanation:

<|--------------------|--------------------------|>

(-2,-5)               (3,2)

-2-3 = -5 = | -5 | = 5

-5-2=-7 = | -7 | = 7

3+5=8

2+7=9

(8,9)

If a translation of the figure above is plotted 7 units to the right and 2 units up, the (12,3) point A' will be located on the new figure.

The process of changing the location of the image on the coordinate system will be known as the translation. Here the image is translated as;

The given coordinate of the point is:- (7, 2)

Then it is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x  because we  just count 7 units to the right and then 2 units up.

Hence If a translation of the figure above is plotted 7 units to the right and 2 units up, the (12,3) point A' will be located on the new figure.

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The value of y(1) is found to be approximately 2.6742 based on the approximate values obtained using Euler's method.

First, we divide the interval [0, 1] into 10 subintervals (h = 0.1), resulting in 11 points including the initial point.

Using the Euler's method, we start with the initial condition y(0) = 1 and iterate the following formula for each step:

y_(i+1) = y_i + h * (t_i * y_i + t_i^2)

Calculating the values iteratively, we obtain a table of values for t and y as follows:

t | y

0.0 | 1.0000

0.1 | 1.1000

0.2 | 1.2110

0.3 | 1.3343

0.4 | 1.4708

0.5 | 1.6228

0.6 | 1.7920

0.7 | 1.9802

0.8 | 2.1892

0.9 | 2.4202

1.0 | 2.6742

Therefore, using Euler's method with a step size of h = 0.1, the approximate value of y(1) is 2.6742.

Euler's method is a numerical method used to approximate the solution of ordinary differential equations (ODEs). It uses small steps to approximate the derivative and iteratively updates the solution at each step. In this case, we applied Euler's method with a step size of h = 0.1 to approximate the solution y(1) for the given initial value problem. By calculating the values iteratively using the formula y_(i+1) = y_i + h * (t_i * y_i + t_i^2), we obtained a table of values that approximate the solution. The value of y(1) is found to be approximately 2.6742 based on the approximate values obtained using Euler's method.

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The pool's hydrostatic force is 1,500 pounds at the shallow end, 4,500 pounds at the deep end, 1,500 pounds on each side from shallow to deep, and 0 pounds at the bottom.

(a) To compute the pressure the water exerts at that depth and multiply it by the shallow end's surface area, we must first measure the hydrostatic force on the shallow end. The equation P = gh, pressure is P, is the fluid's density, acceleration from gravity is g, the depth is h, determines the pressure that a fluid exerts at a given depth.

In this case, the depth of the shallow end is 3 ft. The weight density of water is given as 62.5 lb/ft³.

Plugging in these values, we have,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft)

P = 1,500 lb/ft².

To find the hydrostatic force, we multiply this pressure by the surface area of the shallow end, which is the width times the length,

Hydrostatic force = 1,500 lb/ft² * (20 ft * 40 ft)

Hydrostatic force = 1,500 lb. Therefore, the hydrostatic force on the shallow end is 1,500 lb.

(b) Using the same method as in part (a), we find that the pressure exerted by the water at the depth of the deep end, which is 9 ft, is ,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (9 ft)

P = 4,500 lb/ft².

Multiplying this pressure by the surface area of the deep end (20 ft * 40 ft), we get the hydrostatic force on the deep end,

Hydrostatic force = 4,500 lb/ft² * (20 ft * 40 ft)

Hydrostatic force = 4,500 lb.

Therefore, the hydrostatic force on the deep end is 4,500 lb.

(c) The depth of the side is varying linearly from 3 ft to 9 ft. Taking the average depth, we have (3 ft + 9 ft) / 2 = 6 ft.

Using the formula,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (6 ft),

We find that the pressure is 3,000 lb/ft².

Multiplying this pressure by the surface area of the side (20 ft * 6 ft), we get the hydrostatic force,

Hydrostatic force = 3,000 lb/ft² * (20 ft * 6 ft)

Hydrostatic force = 1,500 lb.

(d) Since the bottom of the pool is horizontal, the depth remains constant throughout, which is 3 ft. Plugging this value into the formul,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft),

p =  1,500 lb/ft², we find that the pressure is 1,500 lb/ft². However, since the bottom is horizontal, the surface area facing upward cancels out the surface area facing downward, resulting in a net force of 0 lb.

Therefore, the hydrostatic force on the bottom of the pool is 0 lb.

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No, the population does not have to be normally distributed to test the hypothesis in this scenario. The correct answer is OB. No, because n >= 30.

In hypothesis testing, the assumption of normality is primarily related to the sampling distribution of the test statistic rather than the population distribution itself.

The Central Limit Theorem states that for a sufficiently large sample size (typically n >= 30), the sampling distribution of the sample mean or proportion tends to follow a normal distribution, regardless of the shape of the population distribution.

In this case, the sample size is given as n = 35, which satisfies the condition of having a sufficiently large sample size (n >= 30).

Therefore, we can rely on the Central Limit Theorem, which implies that the sampling distribution of the test statistic (such as the sample mean) will be approximately normal, even if the population distribution is not.

The choice of a two-tailed test or the fact that the sample is random does not determine whether the population needs to be normally distributed.

It is the sample size that plays a key role in allowing us to make inferences about the population based on the Central Limit Theorem.

Hence, the correct answer is OB. No, because n >= 30. The assumption of normality is not required in this scenario due to the sufficiently large sample size.

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Answer:

A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the diagram attached

The sum of the two adjacent angles is 180 degrees. Hence;

8x-9 + 53 = 180

8x + 44 = 180

Subtract 44 from both sides of the equation

8x + 44 - 44 = 180 - 44

8x = 136

Divide both sides by 8

8x/8 = 136/8

x = 17

Hence the value of x is 17

Answer:

x = 35

m<PQR = 70

Step-by-step explanation:

This is an isoceles triangle so the base angles are the same and they all add up to 180 so:

2x + 2x + 40 = 180

4x + 40 = 180

4x = 140

x = 35

m<PQR:

2x

2(35)

70

Answer:

48

Step-by-step explanation:

60 students X 80%=48

20% is 12 students

40% is 24 students

60% is 36 students

so on and so forth.

Answer:

48.

Step-by-step explanation:

.80 x 60 = 48

Option C is correct: A one-unit increase in x1 will lead to a 0.5906 unit increase in y, when x2 is held constant. A one-unit increase in x2 will lead to a 0.498 unit increase in y, when x1 is held constant.

The estimated regression equation for a model involving two independent variables and 10 observations follows. Here SST = 6,724.125,

SSE = 507.75,

Sb1 = 0.0813, and

Sb2 = 0.0567.

ŷ = 29.1270 +0.5906x1 + 0.4980x2

Interpretation of Regression Coefficients:

Below are the explanations of the regression coefficients in the estimated regression equation:

1. The regression coefficient for x1 is 0.5906. A one-unit increase in x1 will lead to a 0.5906 unit increase in y, when x2 is held constant.

2. The regression coefficient for x2 is 0.4980. A one-unit increase in x2 will lead to a 0.498 unit increase in y, when x1 is held constant.

Therefore, Option C is correct: A one-unit increase in x1 will lead to a 0.5906 unit increase in y, when x2 is held constant. A one-unit increase in x2 will lead to a 0.498 unit increase in y, when x1 is held constant.

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Answer:

36

Step-by-step explanation:

if you have one board and divde it by 3 you get 3 equally sized boards

and if you cut all 12 of them you get 36 equally sized boards.