Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.

Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?

A. d= 163 + t

B. d= 163/2 × t/2

C. d= 163t

D. d= 81.50t

To find the margin of error, we can use the formula: E = z√((p(1-p))/n)

where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.

From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.

Plugging in the values, we get:

E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385

So the margin of error is 0.0385.

To find the confidence interval, we can use the formula:

p ± E

where p is the sample proportion and E is the margin of error.

Plugging in the values, we get:

0.696 ± 0.0385

So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].

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The equivalent speed in still water for the boat is 30.26 km/h.

The equivalent speed of the boat in still water is calculated as follows;

The boat needs to travel North at 30 km/h,

The speed of the wave = 4 km/h

The equivalent speed of the boat in still water is calculated by applying Pythagoras theorem;

v² = (4 km/h)² + (30 km/h)²

v = √ [(4 km/h)² + (30 km/h)²]

v = 30.26 km/h

Thus, the equivalent speed of the boat is calculated by applying vector addition principle.

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Some poetic elements found in the poem are:

Poetic elements are described as  the devices used that characterize a piece of writing as a poem and  are integral to categorise a piece of writing as poetry, such as poetic meter and rhyme scheme.

In the poem, the author uses Imagery which is described as use of sensory details to create vivid mental images in the reader's mind.

The author made use of metaphor as a  comparison between two things that are not alike, in order to create an image or deepen understanding.

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Where the following triangle problem is given, note that:

A) α [tex]\approx[/tex] 11.0

β  β [tex]\approx[/tex] 9.4

B) 25.59 yrds

C) 0.38 yrds

A) To determine the near post angle and the far post angle when the striker is 24 yards from the near post

1/2 (24²) + 1/2 (28²) - 1/4(10²) = 655 (central line length formula)

Cos  α = (24² + 655 - 5²)/ (2 x 24 x √655)

= 0.98171498561

α = Cos ⁻¹ 0.98171498561

α = 10.973603643623608717848651724941

α [tex]\approx[/tex] 11.0° (Cosine Law)

For   28 yards from the far post.

Cos   β   = (28² + 655 - 5²)/ (2 x 28 x √655)

= 0.98659913977

 β  = Cos ⁻¹ 0.98659913977

 β  = 9.3905311636838307510867912796592

 β  [tex]\approx[/tex] 9.4°

B)  Distance between the goalie from the ball is

√655 = 25.592967784139454896443137575823

Distance  [tex]\approx[/tex] 25.59 yrds

C)  5-10 * ((24)/(24+28)) = 0.38 yrds (Angular Bisector Theorem)

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The answer is option A. That is, the time taken in hours if the train traveled 13 miles in 30 minutes is 4.5 hours.

The relation between distance traveled and time is given by the formula:

Distance = Speed x Time

where distance is the total distance traveled, speed is the rate at which the distance is covered, and time is the duration for which the distance is covered. This formula applies to any type of motion, whether it is linear or circular, and it is often used to calculate the distance covered by an object given its speed and the time it traveled. Alternatively, the formula can also be used to calculate the time required to travel a certain distance given the speed at which the object is traveling.

Given that the total distance = 117 miles. We need to find the time taken in hours if the train traveled 13 miles in 30 minutes.

For that we can use the equation, distance = rate x time

Now, rate = distance/time

Distance = 13 miles, time = 30 minutes = 30/60 hours = 0.5 hours

Therefore, rate = 13 miles / 0.5 hours = 26 miles per hour

Now to find the time it took to travel the entire 117 miles:

time = distance/rate

time = 117 miles/ 26 miles per hour

time = 4.5 hours

Therefore, the answer is (A) 4.5 hours.

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The May raw materials purchases for May in Rensing Ltd., in dollars terms, is $32,620.

The cost of raw materials purchased in May is determined by computing the required production units and multiplying the result by 2 units and the unit raw material cost.

                                     April     May      June

Sales                           2,520   2,440   2,390

Ending inventory       2,280    2,170    2,330

Goods available for

 sale                          4,800    4,610    4,720

Beginning inventory              2,280    2,170

Production units                     2,330

Raw materials purchases      4,660 (2,330 x 2)

Raw materials price per unit = $7

Total purchases of Raw Materials for May = $32,620 (4,660 x $7)

Thus, we can conclude that in May Rensing Ltd. purchased raw materials worth $32,620.

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Answer:

25

Step-by-step explanation:

range = largest number - smallest number

38-13=25

The probability that exactly 2 of them say job applicants should follow up within two weeks is 33.02%.

We can use the binomial probability formula:

P(x) = C ( n, x ) × p ^ x × ( 1 - p ) ^ ( n - x )

Solving then gives:

P ( 2 ) = C ( 7, 2 ) x 0.49 ^ 2 x ( 1 - 0. 49 ) ^ ( 7 - 2)

P ( 2 )  = 21 x 0. 49 ^ 2 x ( 1 - 0. 49) ^5

=  21 x 0. 2401 x 0. 078109

=  0. 3302

In conclusion, the probability that 2 of the 7 human resource managers say job applicants should follow up within two weeks is approximately 0.3302 or 33.02%.

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Answer:

x + 5 + 7x - 5 + x = 180

9x = 180

x = 20

So the measure of angle M is x + 5 = 20 + 5 = 25°

The height of the building when the surveyor is standing that far is D.)41ft​

The tangent function would be best to use to find the height because we would be able to use the adjacent and and opposite.

Assuming that 5 feet is the height and the angle of elevation is 41. 7 degrees, and the distance of 40 feet, we have :

tan ( A ) = (h - x) / D

tan ( 41. 7° ) = ( h - 5 ) / 40

h - 5 = 40 x tan ( 41. 7 ° )

h - 5 = 40 x 0.8895

h = 35.58 + 5

= 40.58

= 41 feet

The height of the building is 41 feet.

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The distance for boat is,

=  43.2 miles

Given that;

Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour

Now, For Walk DATA:

Rate = 2 mph ; time = x hrs.

Then, distance = 2x miles

For Boat DATA:

Rate = 10 mph ; time = 5 - x hrs

Then, distance = 10 (5 - x) miles

Hence, We can formulate;

distance + distance = 12 miles

2x + 10 (5 - x) = 20

2x + 50 - 10x = 20

30 = 8x

x = 3.6

Hence, Boat time ,

5 - x = 5 - 3.6 = 1.4 hr (boat time)

And, The value of Boat distance = 12x = 12 x 3.6 = 43.2 miles

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so, we know the diameter is 8, so that means its radius is half that, or 4.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2[/tex]

The minimum variance unbiased estimator of the parameter,λ of a poisson population is λ = Σxi/n.

Variance is a measure of how spread out a set of data is. In statistics, it is the average of the squared differences from the mean of a set of values. It is calculated by taking the sum of the squared deviations from the mean and dividing it by the number of data points.

Let X1, X2, ..., Xn be a random sample from a Poisson distribution with mean λ. The likelihood function is given by:

[tex]L(\lambda | x) = \pi[e^{(-\lambda)} \lambda^{(xi)} / xi!][/tex]

Taking the natural logarithm and differentiating with respect to λ:

ln L(λ | x) = -nλ + ln(λ) Σxi - Σln(xi!)

d/dλ ln L(λ | x) = -n + Σxi/λ

Setting the derivative equal to zero and solving for λ, we get:

λ = Σxi/n

This is the sample mean of the Poisson distribution, which is an unbiased estimator of λ. Moreover, using the Cramer-Rao lower bound, we can show that it is also the minimum variance unbiased estimator of λ.

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the number of gallons of water it can pump inn 45 minutes is

The given parameters that will help us to determine the quantity are

Powejet pumps 420 gallons of water per hour

how many gallons of water will it pump in 45 minutes  = ?

1 hour = 60 minutes

This means = 450/60  = 7 gallons

Therefore in  45 minutes it can pump 7*45 = 315 gollons

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The probability that the sample mean would be greater than 70.8 kilograms is given as follows:

0.1762 = 17.62%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 70, \sigma = 8, n = 87, s = \frac{8}{\sqrt{87}} = 0.8577[/tex]

The probability is one subtracted by the p-value of Z when X = 70.8, hence:

Z = (70.8 - 70)/0.8577

Z = 0.93

Z = 0.93 has a p-value of 0.8238

1 - 0.8238 = 0.1762.

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The two values which are located at the same point on a number line as required to be determined are; 4/1 and 4.

It follows from the task content that the answer choice which represents two values located at the same point on the number line be determined.

On this note, such two values must be equivalent.

Hence, by observation; the answer choice which represents two equivalent values is; 4/1 and 4 and they represent values located at the same point on the number line.

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4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral ​.

What do math quadrilaterals mean?

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.

                                   There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.

2X + 2 = 4

   2X = 4 -2

      2X = 2

        X = 1

2x + 2 = 2 * 1 + 2  = 4

4x + 3 = 4 * 1 + 3 = 7

2x = 2 * 1 = 2

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4 , 7 , 2 are the values of variables then find the lengths of the sides of each quadrilateral ​.

What do math quadrilaterals mean?

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. The vertices on them total four. The sides of them are four. 360 degrees is the total number of interior angles.

                                   There are two diagonals between them. A polygon having four sides is referred to as a quadrilateral. A line segment whose endpoints are the opposing vertices of a quadrilateral is said to be the diagonal of the quadrilateral.

2X + 2 = 4

   2X = 4 -2

      2X = 2

        X = 1

2x + 2 = 2 * 1 + 2  = 4

4x + 3 = 4 * 1 + 3 = 7

2x = 2 * 1 = 2

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The end behavior of f(x) is described as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The function for this problem is given as follows:

f(x) = 4(5/7)^x.

It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:

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The balance at the end of the month was $7046.93.

To determine the balance at the end of the month, we need to:

Data

Starting balance = $9145.87

Deposits = $2783.71

Interest earned = $11.15

Checks written = $4871.90

Maintenance fee = $12

Balance at the end of the month will be:

= Starting balance + Deposits + Interest earned - Checks written - Maintenance fee

= $9145.87 + $2783.71 + $11.15 - $4871.90 - $12

= $7046.93.

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Answer:

-4.7854909e+52

Step-by-step explanation:

how do i know

cuz i used a calculator

what evevn is your equation

Step-by-step explanation:

If Sarah buys the oil and oil filter separately, she would spend:

Cost of oil = $37.54

Cost of oil filter = $9.47

Total cost = $37.54 + $9.47 = $47.01

Therefore, Sarah can save:

Coupon price - Total cost = $49.95 - $47.01 = $2.94

So, Sarah can save $2.94 by doing the oil change herself instead of using the coupon.

Answer:18

Step-by-step explanation:18

The other angle that is congruent to  ∠DFA is: ∠BFC

Congruent angles are defined as two or more angles that are said to be identical to each other. This means that the measure of these angles is equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.

Now, we want to find the angle that is congruent to ∠DFA.

By inspection, we can see that ∠BFC is an opposite angle to ∠DFA.

We know that Opposite angles are the two angles opposite each other when two lines cross. They can also be called vertical angles due to sharing a vertex, which is the point where the two lines connect. Opposite angles always have the same measurement, making them congruent.

Thus, ∠BFC is congruent to  ∠DFA.

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Answer:

In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg.

A = (1/2)Pa

= (1/2)(2)(8/√3)(6)(8)

= (384√3)/3 = 128√3 = 221.7 units^2

Answer:

arc PTR = 277°

Step-by-step explanation:

PS is the diameter of the circle , then arc PS = 180°

arc PTR = PS + SR = 180° + 97° = 277°

Answer:

arc PTR = 277°

Step-by-step explanation:

PS is the diameter of the circle , then arc PS = 180°

arc PTR = PS + SR = 180° + 97° = 277°