solve the following whole number is 9- 3 upon 5​

Answer:

\(\displaystyle \sin\Big(\frac{x}{2}\Big) = \frac{7\sqrt{58} }{ 58 }\)

\(\displaystyle \cos\Big(\frac{x}{2}\Big)=-\frac{3 \sqrt{58}}{58}\)

\(\displaystyle \tan\Big(\frac{x}{2}\Big)=-\frac{7}{3}\)

Step-by-step explanation:

We are given that:

\(\displaystyle \sin(x)=-\frac{21}{29}\)

Where x is in QIII.

First, recall that sine is the ratio of the opposite side to the hypotenuse. Therefore, the adjacent side is:

\(a=\sqrt{29^2-21^2}=20\)

So, with respect to x, the opposite side is 21, the adjacent side is 20, and the hypotenuse is 29.

Since x is in QIII, sine is negative, cosine is negative, and tangent is also negative.

And if x is in QIII, this means that:

\(180<x<270\)

So:

\(\displaystyle 90 < \frac{x}{2} < 135\)

Thus, x/2 will be in QII, where sine is positive, cosine is negative, and tangent is negative.

1)

Recall that:

\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\pm\sqrt{\frac{1 - \cos(x)}{2}}\)

Since x/2 is in QII, this will be positive.

Using the above information, cos(x) is -20/29. Therefore:

\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{1 + 20/29}{2}\)

Simplify:

\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{49/29}{2}}=\sqrt{\frac{49}{58}}=\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}\)

2)

Likewise:

\(\displaystyle \cos \Big( \frac{x}{2} \Big) =\pm \sqrt{ \frac{1+\cos(x)}{2} }\)

Since x/2 is in QII, this will be negative.

Using the above information, cos(x) is -20/29. Therefore:

\(\displaystyle \cos \Big( \frac{x}{2} \Big) =-\sqrt{ \frac{1- 20/29}{2} }\)

Simplify:

\(\displaystyle \cos\Big(\frac{x}{2}\Big)=-\sqrt{\frac{9/29}{2}}=-\sqrt{\frac{9}{58}}=-\frac{3}{\sqrt{58}}=-\frac{3\sqrt{58}}{58}\)

3)

Finally:

\(\displaystyle \tan\Big(\frac{x}{2}\Big) = \frac{\sin(x/2)}{\cos(x/2)}\)

Therefore:

\(\displaystyle \tan\Big(\frac{x}{2}\Big)=\frac{7\sqrt{58}/58}{-3\sqrt{58}/58}=-\frac{7}{3}\)

Answer:

1st year

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Answer:

a. 738.73

Step-by-step explanation:

hope that’s righttt.

What I did was 500x0.05 and with the answer I did x0.5 again and added it to the previous year until the 8th time each was 738.73 correct me if I’m wrong

edit so it’s wrong….not sure what I did wrong

Answer:

The chef cooked 1/3 pound of potatoes and

1/4 pound of green beans for

each customer.

so. Sum of all vegetables for one customer = 1/3 pound of potatoes + 1/4 pound of green beans

                                                                        = 1/3 + 1/4 pound

                                                                        = 7/12 pound

so. Sum of all vegetables for 22 customer = (7/12 pound ) 22

                                                                      = 22/12 pound

                                                                      = 11/6 pound

Step-by-step explanation:

The function g(x) = 2x² − x − 1 needs to be used to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval of [2, 4] using 4 rectangles. The two approximations of the area of the region between the graph of the function and the x-axis over the given interval are:12.125 < Area < 16.875.

To find the two approximations of the area using left and right endpoints and the given number of rectangles, use the following steps:

Find the width of each rectangle with the following formula: width = Δx = (b-a)/n where b is the upper limit of the interval, a is the lower limit of the interval, and n is the number of rectangles.

Substituting the given values into the above formula gives: width = Δx = (4 - 2)/4 = 0.5

Find the left endpoints for each rectangle by using the formula:x = a + iΔxwhere i is the index number of the rectangle.

Substituting the given values into the formula gives:x1 = 2 + 0.5(0) = 2x2 = 2 + 0.5(1) = 2.5x3 = 2 + 0.5(2) = 3x4 = 2 + 0.5(3) = 3.5

Find the right endpoints for each rectangle by using the formula:

x = a + (i+1)Δx

where i is the index number of the rectangle.

Substituting the given values into the formula gives:x1 = 2 + 0.5(1) = 2.5x2 = 2 + 0.5(2) = 3x3 = 2 + 0.5(3) = 3.5x4 = 2 + 0.5(4) = 4Using these left and right endpoints, calculate the area for each rectangle by using the formula:

Area = f(x)Δx,where f(x) is the height of the rectangle.

Substituting the x values obtained earlier into the function gives:

f(x1) = f(2) = 2(2)² - 2 - 1 = 5f(x2) = f(2.5) = 2(2.5)² - 2.5 - 1 = 10.75f(x3) = f(3) = 2(3)² - 3 - 1 = 14f(x4) = f(3.5) = 2(3.5)² - 3.5 - 1 = 18.75

Substituting the values obtained earlier into the area formula gives:Left endpoints approximation:

Area = f(x1)Δx + f(x2)Δx + f(x3)Δx + f(x4)ΔxArea = (5)(0.5) + (10.75)(0.5) + (14)(0.5) + (18.75)(0.5)

Area = 12.125

Right endpoints approximation:

Area = f(x2)Δx + f(x3)Δx + f(x4)Δx + f(x5)ΔxArea = (10.75)(0.5) + (14)(0.5) + (18.75)(0.5) + (23)(0.5)Area = 16.875 Therefore, the two approximations of the area of the region between the graph of the function and the x-axis over the given interval are:12.125 < Area < 16.875.

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Answer:

Step-by-step explanation:

Expected egg production is:

Correct choice is B

Answer:

Step-by-step explanation:

we have to find the value of the expected egg production for any one egg.

That is,

Hence,

OPTION B IS CORRECT.

Answer:

arithmetic sequence

Step-by-step explanation:

This is an arithmetic sequence since there is a common difference between each term. In this case, adding −16 to the previous term in the sequence gives the next term.

Answer:

Step-by-step explanation:

Since the swimming pool is cylindrical, we would find its volume by applying the formula for determining the volume of a cylinder which is expressed as

Volume = πr²h

Where

r represents radius of the cylinder

h represents height

π = constant = 3.14

From the information given,

Diameter = 12 feet

Radius, r = diameter/2 = 12/2 = 6 feet

h = 4 feet

Volume = 3.14 × 6² × 4 = 452.16ft³

Since 1 cubic foot is approximately 7.48 gallons, the number of gallons of water that the swimming pool can contain is

452.16 × 7.48 = 3382.16 gallons

Step-by-step explanation:

tan 32 = x/46

x = 46 tan 32 = 28.7

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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In a real piping system there are always losses due to viscosity.

These losses cause a drop in total pressure but the static pressure remains the same.

The "K" factor (i.e. loss factor) for a sudden contraction and a rapid expansion in fully developed turbulent flow are 0.50 and 1.0.

A single pipe of known diameter, surface roughness and length joins two reservoirs and the free water surface between them is 57m.

We have to first guess the Reynolds number as the flow rate is unknown, then calculate a value for f and iterate to get the answer.

The effect of rounding a pipe inlet (where the fluid flows from a reservoir into the pipe) on the loss coefficient K will not change the coefficient. To minimize pressure losses in a venturi meter, the shape change from the inlet to the outlet must be fast change in, slow change out.Viscosity always causes losses in a piping system due to which there is a drop in total pressure.

The “K” factor for sudden contraction and rapid expansion is 0.50 and 1.0 respectively. The flow rate of a single pipe can be calculated by first guessing the Reynolds number, then calculating a value for f, and iterating to get the answer. Rounding a pipe inlet does not change the coefficient of loss.

To minimize pressure losses in a venturi meter, the shape change from the inlet to the outlet must be fast change in, slow change out.

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Answer:

by distributing you need to multiple by using the 7 in front and use that 7 to multiply each number inside

1. -7(-4+x) -> 28-7x

2. 7(4+x) -> 28+7x

3. 7(-4-x) -> -28-7x

4. -7(4-x)-> -28+7x

The approximate area of the unshaded region under the standard normal curve is 0.86 the option third is correct.

It is given that the standard normal curve shows the shaded area in the curve.

It is required to find the approximate area of the unshaded region under the standard normal curve.

It is defined as the continuous distribution probability curve which is most likely symmetric around the mean. At Z=0, the probability is 50-50% on the Z curve. It is also called a bell-shaped curve.

In the curve showing the shaded region area between:

\(\rm P(1 < Z < 2)\)

First, we calculate the shaded region area:

From the data given the value of Ф(1) = 0.8413.

P(Z<1)  = 0.8413  and

P(Z<2) =  0.9772

The area of the shaded region:

= P(Z<2) - P(Z<1)

=  0.9772 - 0.8413

= 0.1359

The area of the unshaded region:

= 1 - The area of the shaded region  ( because the curve is symmetric)

= 1 - 0.1359

= 0.8641 ≈ 0.86

Thus, the approximate area of the unshaded region under the standard normal curve is 0.86 the option third is correct.

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Applying the formula for the slope of a line, the value of x = 4.

To find the slope of a line, the following formula or equation can be employed:

Slope (m) = change in y / change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\).

Given the following points, (6, z) and (-3, 5) lies on a line that has a slope of -1/9, to find the value of z, follow the steps below:

Let (6, z) be represented as \((x_1, y_1)\)

Let (-3, 5) be represented as \((x_2, y_2)\).

m = -1/9

Plug in the values:

-1/9 = (5 - z) / (-3 - 6)

-1/9 = (5 - z) / -9

Cross multiply:

-1 × -9 = (5 - z) × 9

9 = 45 - 9z

9 - 45 = -9z

-36 = -9z

Divide both sides by -9:

-36/-9 = -9z/-9

4 = z

z = 4

The value of z is: 4.

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Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

Hey there!

Guide:

• Negatives are BELOW 0

• Negatives are SMALLER than 0

• Negatives are also on the LEFT side of 0.

• Positives are ABOVE 0

• Positives are BIGGER than 0

• Positives are also on the RIGHT side of 0.

Thus, this means 7 is bigger than -9 because, your -9 is a negative number and 7 is a positive

That being said 7 > -9 (7 is the greater number out of the two numbers)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The perimeter of each polygon is 42.

Perimeter:

The whole distance around a shape is referred to as its perimeter. In essence, the length of any shape when it is expanded in a linear form equals its perimeter. A shape's perimeter in a two-dimensional plane is its complete circumference. Depending on their measurements, distinct shapes' perimeters may be equal in length. For instance, if a circle is built of a metal wire of length L, the same wire can be used to build a square with equal-length sides. Three sides make up the triangle. Any triangle's perimeter, whether scalene, isosceles, or equilateral, will therefore equal the sum of its three sides' lengths. And the space a triangle takes up in a plane is its area.

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Moving Average and Exponential Smoothing is a method used in a forecasting model for a time series when a trend, seasonal, or cyclical effect is not significant.

When trend, seasonal, or cyclical effects are not significant in a time series, the most appropriate method for forecasting is typically the Moving Average or Exponential Smoothing method. The Moving Average method involves calculating the average of a set of previous observations to forecast the next data point.

The number of previous observations to include in the average is determined by the chosen window size, which can be adjusted based on the level of smoothing desired. On the other hand, the Exponential Smoothing method assigns more weight to recent observations and less weight to older observations. This method assumes that recent data points are more relevant for forecasting future values than older data points.

The level of smoothing can be controlled by adjusting the smoothing parameter. Linear regression and Holt-Winters methods are better suited for time series with significant trends, and seasonal, or cyclical effects. Holt-Winters is a more complex method that considers both trend and seasonal effects in addition to the level of smoothing.

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Answer: Let's solve this problem step by step.

First, let's assume the salaries of An and B to be 5x and 3x, respectively, where x is a common multiplier.

According to the given information, they save Rs. 2600 and Rs. 1800, respectively. Since savings come from the remaining portion of their incomes after spending, we can calculate their expenditures as follows:

For An:

Income of An = Salary of An + Savings of An

Income of An = 5x + 2600

For B:

Income of B = Salary of B + Savings of B

Income of B = 3x + 1800

Now, let's consider the proportion of their expenditures. It is given that the proportion of their expenditures is 9:5. So, we can write the following equation:

(Expenditure of An)/(Expenditure of B) = 9/5

Since expenditure is the complement of savings, we have:

[(Income of An - Savings of An)] / [(Income of B - Savings of B)] = 9/5

Substituting the previously derived expressions for income, we get:

[(5x + 2600 - 2600)] / [(3x + 1800 - 1800)] = 9/5

Simplifying the equation, we have:

5x / 3x = 9/5

Cross-multiplying, we get:

5 * 3x = 9 * 3x

15x = 27x

Subtracting 27x from both sides, we have:

0 = 12x

This implies that x = 0, which is not a valid solution. Therefore, there seems to be an error or inconsistency in the given information or equations. Please recheck the problem statement or provide additional information to help resolve the issue.

In general, different refrigerants should not be mixed or recovered into the same cylinder.

Different refrigerants have unique chemical compositions and properties that make them incompatible with one another. Mixing different refrigerants can lead to unpredictable reactions, loss of refrigerant performance, and potential safety hazards. Therefore, it is generally recommended to avoid recovering different refrigerants into the same cylinder.

When recovering refrigerants, it is important to use separate recovery cylinders or tanks for each specific refrigerant type. This ensures that the refrigerants can be properly identified, stored, and recycled or disposed of in accordance with regulations and environmental guidelines.

The refrigerant recovery process involves capturing and removing refrigerant from a system, storing it temporarily in dedicated containers, and then transferring it to a proper recovery or recycling facility. Proper identification and segregation of refrigerants during the recovery process help maintain the integrity of each refrigerant type and prevent contamination or cross-contamination.

To maintain the integrity and safety of different refrigerants, it is best practice to recover each refrigerant into separate cylinders. Mixing different refrigerants in the same cylinder can lead to complications and should be avoided. Following proper refrigerant recovery procedures and guidelines helps ensure the efficient and environmentally responsible management of refrigerants.

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The number of different refrigerants that may be recovered into the same cylinder is zero.

When it comes to refrigerants, it is important to understand that different refrigerants should not be mixed together. Each refrigerant has its own unique properties and should be handled and stored separately. mixing refrigerants can lead to chemical reactions and potential safety hazards.

The recovery process involves removing refrigerants from a system and storing them in a cylinder for proper disposal or reuse. During the recovery process, it is crucial to ensure that only one type of refrigerant is being recovered into a cylinder to avoid contamination or mixing.

Therefore, the number of different refrigerants that may be recovered into the same cylinder is zero. It is essential to keep different refrigerants separate to maintain their integrity and prevent any adverse reactions.

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13 is the value of z from the given figure.

The properties of the triangle are:

From the given figure,

∠ABE + ∠EBC =. 180

∠EBC = 180- ∠ABE

∠EBC = 180 - 9z -----(1)

∠ECB + 115 = 180

∠ECB = 65-----(2)

IN ∆EBC

∠BEC + ∠ECB + ∠EBC = 180

4Z + 180- 9Z + 65 = 180 ---------(from eq i & ii)

-5Z = -65

Z = -65/-5y

Z = 13

The value of z from the given figure is 13.

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Complete question:

Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

If it takes 10 workers 2.5 years to build a 20 story building, it will take 2.5 sec 20 workers to build a 40 story building.

Given that a skyscraper's height and the number of workers needed to build it determine how long the project takes, We must make the time.

Allow the time t, height h, and number of workers to be ω.

Then, based on the relationship,

t = kh/ω

where k is constant.

The formula in the term of k is:

k = tω/h

Additionally, it takes 10 employees t0 2.5 years to construct a 20-story skyscraper.

Now putting the value

k = (2.5 × 10)/20

k = 25/20

k = 5/4

If a 40-story skyscraper requires 20 workers to construct, we have

t = kh/ω

t = (5/4) × (40/20)

t = 5/2

t = 2.5 sec

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The complete question is:

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 20 workers to build a 40 story building?

Answer:

x+5

Step-by-step explanation:

I thought what 2 numbers if multiplied made 15

also 2x+3 already has a 3

so I'm guessing 3 and 5

then I put them next to each other

(2x+3) ( +5)

I put a x in the second parenthesis as a guess because the area had a 2x^2 in it . that could only happen with 2x * x

so (2x+3) (x+5)

Answer:

yes it look right like the one you have to do 2x+5=39

Answer:

53

Step-by-step explanation:

Let yazid's score be x

x + x + 17 + 2x = 161

4x + 17 = 161

4x = 144

x = 36

jack = x + 17

jack = 53

Answer:

Jack:  36

Bonus:  Yazid:  53 and Susan:  72

Step-by-step explanation:

Let J, Y, and K stand for Jack, Yazin, Susan's scores.

We are told that:

J = Y + 17  [Jack scored 17 marks more than Yazid]

S = 2Y  [Susan scored twice Yazid's score]

J + Y + S = 161  [total score is 161]

Substitute the first two expressions into the last equation:

J + Y + S = 161

(Y+17) + Y + (2Y) = 161

4Y = 144

Y = 36

Use Y = 36 to find the other scores:

J = Y + 17

J = 36 + 17

J = 53

S = 2Y

S = 2*(36)

S = 72

CHECK:

Does 36+53+72 = 161?

YES

Answer: yes

Step-by-step explanation:

Answer:

perimeter = 14

Step-by-step explanation:

perimeter = ∑sides

                = x + (x + 3) + (x + 4)  --------eq.

                = 3x + 7

           3x = 7

            x = 7/3

plugin values into the equation:

perimeter = ⁷/₃ + (⁷/₃ + 3) + (⁷/₃ + 4)

                = 14

therefore, the perimeter of a triangle is 14

Answer:

Step-by-step explanation: The speed of reaction to differences between forecasts and actual results. is the answer i think