suppose 44% of the doctors in a hospital are surgeons. if a sample of 738 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by more than 4% ? round your answer to four decimal places.

Answers

Answer 1

The probability of the the sample proportion of surgeons will be given as 1.

The z-score is a dimensionless variable that is used to express the signed, fractional number of standard deviations by which an event is above the mean value being measured. It is also known as the standard score, z-value, and normal score, among other terms. Z-scores are positive for values above the mean and negative for those below the mean.

For this case we can define the population proportion p as "true proportion of surgeons" and we can check if we can use the normal approximation for the distribution of p,

1) np = 738 x  0.44 = 324.72 > 10

2) n(1 - p) = 738 x  (1 - 0.44) = 413.28 > 10

3) Random sample: We assume that the data comes from a random sample Since we can use the normal approximation the distribution for P is given by:

psimN(p,[tex]\sqrt{\frac{p(1-p)}{n} }[/tex])

With the following parameters:

Hp = 0.44

[tex]\sigma_p=\sqrt{\frac{0.44(1-0.44)}{738} }[/tex]

= 0.01827

And we want to find this probability:

P(p > 0.04)

And we can use the z score formula given by:

[tex]z=\frac{p-\mu}{\sigma}[/tex]

And if we calculate the z score for p = 0.39 we got:

[tex]z=\frac{0.04-0.44}{0.01827}[/tex] = -21.893

And we can find this probability using the complement rule and the normal standard table or excel and we got:

P(p > 0.04) = P(Z > -21.893) = 1 − P(Z < −21.893) = 1 - 0 = 1.

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Related Questions

A farm grew 19.8 tons of wheat in 2013. the farm's wheat output increased by 9.8% from 2013-2014, and by 5.1 % from 2014 to 2015. which expression represents a strategy for estimating the farm's output for 2015?

Answers

The expression that represents a strategy for estimating the farm's output for 2015 is 1.153w, where w is the farm's wheat output in 2013.

Let w be the farm's wheat output in 2013. We know that the output increased by 9.8% from 2013 to 2014, so the output in 2014 can be estimated as:

w + 0.098w = 1.098w

This expression represents a strategy for estimating the farm's output for 2014.

Similarly, the output in 2015 can be estimated as:

(1.098w) + 0.051(1.098w) = (1 + 0.051)(1.098w)

Simplifying this expression, we get:

1.153w

Therefore, the expression that represents a strategy for estimating the farm's wheat output for 2015 is:

1.153w

where w is the farm's wheat output in 2013 (i.e., 19.8 tons).

So we can estimate the farm's wheat output in 2015 as:

1.153(19.8) = 22.82 tons (rounded to two decimal places)

Note that this is only an estimate, based on the assumption that the percentage increases from 2013 to 2014 and from 2014 to 2015 will continue to hold in the future.

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2. The zoologists want to investigate whether the current 4 different diets impact their weight gains of 6-month baby elephants. The weights (in lbs) of participating 6-month baby elephants at the Houston Zoo are presented below, Diet Weight 1 655.5 788.3 734.3 721.4 679.1 699.4 2 789.2 772.5 786.9 686.1 732.1 774.8 3 737.1 639.0 696.3 671.7 717.2 727.1 4 535.1 628.7 542.4 559.0 586.9 520.0 Table 1: 6-month baby elephant weights. 3. The amount of circumference growth in mm) of oak trees at three different nurseries are presented below. Investigate whether the nursery locations affect the growths.

Answers

For question 2, the zoologists can conduct an analysis of variance (ANOVA) test to investigate whether the four different diets impact the weight gains of the 6-month baby elephants. The ANOVA test will compare the mean weight of each diet group to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the zoologists can conclude that the diets are impacting the weight gains of the baby elephants.

For question 3, the researchers can also conduct an ANOVA test to investigate whether the nursery locations affect the growth of oak trees. The test will compare the mean circumference growth of the oak trees at each nursery location to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the researchers can conclude that the nursery locations are impacting the growth of the oak trees.

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The circumstances of the base of the cone is 6π cm. If the volume of the cone is 12π. what is the height?

Answers

Answer: 4

Step-by-step explanation:

[tex]\frac{1}{3} \pi 3^{2} h=12\pi \\3h=12\\h=4[/tex]

For the cost function C(x) = 6000 + 242 + 0.005.03 find: A) The production level that will minimize the average cost. B) The minimal average cost.

Answers

To find the production level that will minimize the average cost, we need to differentiate the cost function with respect to x and set it equal to zero. So:

C'(x) = 0.005x^2 + 242x + 6000
0 = 0.005x^2 + 242x + 6000
Using the quadratic formula, we get:
x = (-242 ± sqrt(242^2 - 4(0.005)(6000))) / (2(0.005))
x = (-242 ± sqrt(146416)) / 0.01
x = (-242 ± 382) / 0.01
x = -14,000 or 27,000

Since the production level cannot be negative, we can discard the negative solution and conclude that the production level that will minimize the average cost is 27,000 units.

To find the minimal average cost, we need to plug the production level back into the cost function and divide by the production level. So:

C(27,000) = 6000 + 242(27,000) + 0.005(27,000)^2
C(27,000) = 6,594,000
Average cost = C(27,000) / 27,000
Average cost = 6,594,000 / 27,000
Average cost ≈ 244.22

Therefore, the minimal average cost is approximately $244.22.
To answer your question, first, let's correct the cost function, which should be in the form of C(x) = Fixed cost + Variable cost. Assuming it is C(x) = 6000 + 242x + 0.005x^2.

A) To find the production level that will minimize the average cost, we need to first determine the average cost function, which is AC(x) = C(x)/x. So, AC(x) = (6000 + 242x + 0.005x^2)/x.

Now, find the first derivative of AC(x) concerning x, and set it equal to zero to find the minimum point:

d(AC(x))/dx = 0

The first derivative of AC(x) is:

d(AC(x))/dx = (242 + 0.010x - 6000/x^2)

Setting this to zero and solving for x will give us the production level that minimizes the average cost:

242 + 0.010x - 6000/x^2 = 0

Now, you can solve for x using numerical methods, such as Newton-Raphson or others. After solving for x, you will get the production level that minimizes the average cost.

B) To find the minimal average cost, plug the production level x you found in part A into the average cost function, AC(x):

Minimal Average Cost = AC(production level)

This will give you the minimal average cost for the given cost function.

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In Triangle JKL, ∠J is congruent to ∠L.

Answers

The measure of ∠L in Triangle JKL is 56.1 degrees.

What is the measures in triangles?

In geometry, the measures in triangles refer to the angles and sides within a triangle. Triangles are three-sided polygons, and the measures of their angles and sides are important properties that determine their shape and characteristics.

In a triangle, the sum of the measures of all three angles is always 180 degrees. Therefore, to find the measure of ∠L in Triangle JKL, we can use the information given:

∠J is congruent to ∠L, which means they have the same measure.

∠K is given as 67.8 degrees.

Since ∠J is congruent to ∠L, we can denote their measure as "x".

So, the sum of the measures of ∠J, ∠K, and ∠L is 180 degrees:

∠J + ∠K + ∠L = 180

Substituting the given values:

x + 67.8 + x = 180

Simplifying the equation:

2x + 67.8 = 180

Subtracting 67.8 from both sides:

2x = 180 - 67.8

2x = 112.2

Dividing both sides by 2:

x = 112.2 / 2

x = 56.1

Hence, the measure of ∠L in Triangle JKL is 56.1 degrees.

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Suppose you are doing a 5000 piece puzzle. you have already placed 175 pieces. every minute you place 10 more pieces. after 50 minutes, how many pieces will you have placed

Answers

After 50 minutes, you will have placed 675 pieces

Given, you are doing a 5000 piece puzzle. You have already placed 175 pieces, and every minute you place 10 more pieces. After 50 minutes, we need to find how many pieces you will have placed.

We can start by finding the number of pieces you place in 50 minutes.

Every minute, you place 10 more pieces, so in 50 minutes, you will place:

10 x 50 = 500 pieces

Adding the pieces you have already placed, we get:

175 + 500 = 675 pieces

Therefore, after 50 minutes, you will have placed 675 pieces

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Your family decides they have $400 per month to spend towards remodeling their house. the bank offers them a ten year(120 months) home equity loan for $30,000 with an interest rate of 6.5%. use p = p v ( i 1 − ( 1 + i ) − n ) to determine if your family can afford the monthly payment.

Answers

The monthly payment for the loan is $328.05. So we can determine that the family can afford the monthly payment.

Money spend =  $400

Time = 120 months

Loan amount = $30,000

Interest rate = 6.5%.

The formula is given P = [tex]PV*(i / (1 - (1+i)^{-n}))[/tex]

The interest should be calculated at the monthly rate. So, we can divide the interest rate by 12.

i = 0.065/12 = 0.00541667  

Substituting the values into the formula,

P = [tex]30000 * 0.00541667 / (1 - (1+0.00541667)^{-120})[/tex]

P = $328.05

Therefore, we can conclude that the monthly payment for the loan is $328.05.

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y=1.5 In(et.t+5) for t=1; round your answer to the whole number (exponent "t.t" read (means) t square)

Answers

when t=1, y is approximately equal to 5.

To solve for y when t=1 in the equation y=1.5 In(et.t+5), we first need to plug in t=1:

y=1.5 In(e(1)(1)+5)

We simplify the exponent e(1)(1) to just e:

y=1.5 In(e+5)

Using the properties of natural logarithms, we can simplify this further:

y=1.5(1+ln(5+e))

We can use a calculator to evaluate ln(5+e) to be approximately 2.063, so we can plug that in and simplify:

y=1.5(1+2.063)

y=1.5(3.063)

y=4.5945

Rounding this answer to the nearest whole number, we get:

y=5

Therefore, when t=1, y is approximately equal to 5.

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The green parallelogram is a dilation of the black parallelogram. What is the scale factor of the dilation?



A) 1/3



B) 1/2



C) 2

Answers

To determine the scale factor of the dilation between the green parallelogram and the black parallelogram, you would need to compare the corresponding side lengths of the two parallelograms. For example, if the green parallelogram has a side length that is half of the black parallelogram's side length, the scale factor would be 1/2 (Option B).

If the green parallelogram's side length is twice the black parallelogram's side length, the scale factor would be 2 (Option C). And if the green parallelogram's side length is one-third of the black parallelogram's side length, the scale factor would be 1/3 (Option A). Without specific measurements or a visual representation, it is not possible to accurately identify the scale factor between the two parallelograms. Please provide the side lengths or a diagram to help determine the correct scale factor.

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(x+2)^1/2-5=-2
Answers is x=7
SHOW WORK

Answers

[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{\text{x}+2} = -2+5\\\\\sqrt{\text{x}+2} = 3\\\\(\sqrt{\text{x}+2})^2 = 3^2\\\\\text{x}+2= 9\\\\\text{x}= 9-2\\\\\text{x}= 7\\\\[/tex]

-----------------------

Check:

[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{7+2}-5 = -2\\\\\sqrt{9}-5 = -2\\\\3-5 = -2\\\\-2 = -2 \ \ \ \checkmark\\\\[/tex]

The answer is confirmed.

-----------------------

Answer: x = 7

Find the maximum value of s=xy yz xz where x y z=21

Answers

The maximum value of s is 9261, which is obtained when x = y = z = 7.

To find the maximum value of s=xyz, we can use the AM-GM inequality, which states that the arithmetic mean of a set of non-negative numbers is greater than or equal to the geometric mean of the same set of numbers.

Mathematically, this can be represented as:[tex](1/3)(x + y + z) \geq (xyz)^(1/3)[/tex]Multiplying both sides of the inequality by[tex]3(xyz)^(1/3)[/tex],

we get: [tex](x + y + z) \geq 3(xyz)^(1/3)[/tex] Now,

we can substitute the given value of x + y + z = 21, to obtain: 21 ≥ [tex]3(xyz)^(1/3)[/tex]

Cubing both sides of the inequality, we get: [tex]21^3 \geq 27(xyz)[/tex]

Simplifying the expression, we obtain: s=[tex]xyz \leq (21^3)/27[/tex]= 9261.

The maximum value of s=xyz is obtained when x = y = z = 7, and the value of s is equal to 9261. This result is obtained using the AM-GM inequality, which is a useful tool for solving optimization problems involving non-negative numbers.

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.the function f(x) = 5^x is stretched vertically by a scale factor

of 2, shifted 3 units to the left and down 1 unit to produce the

function g(x). find g(x).

please help :d​

Answers

The transformation of the function g(x) is g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, a shift of 3 units to the left, and a downward shift of 1 unit applied to the original function f(x) = 5^x.

- Vertical stretch by a scale factor of 2: Multiply the output by 2.

- Shift 3 units to the left: Replace x with x + 3.

- Shift 1 unit down: Subtract 1 from the output.

Thus, the function g(x) can be written as:

g(x) = 2 * f(x + 3) - 1

Substituting f(x) = 5^x, we get:

g(x) = 2 * 5^(x + 3) - 1

Simplifying:

g(x) = 2 * 125 * 5^x - 1

g(x) = 250 * 5^x - 1

The function g(x) is given by g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, followed by a shift of 3 units to the left, and a downward shift of 1 unit, applied to the original function f(x) = 5^x.

The transformation increases the steepness of the graph, shifts it to the left, and shifts it downward. The expression 250 * 5^x represents the vertical scaling, and the -1 accounts for the vertical shift downward. Overall, g(x) is a modified version of f(x) with these transformations applied.

Therefore, the function g(x) is g(x) = 250 * 5^x - 1.

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Someone please help

(Composition of Transformations)

Answers

The image point of (6, 4) after the transformation R₉₀ T₁,₅ is (-3, 11).

Understanding the Composition of Transformation

The transformation R₉₀ T₁,₅  represents a rotation of 90° counterclockwise around the origin followed by a translation of 1 unit to the right and 5 units up.

To find the image point of (6, 4) under this transformation, we can apply the two transformations in order.

First, let's find the image of (6, 4) after rotating 90° counterclockwise around the origin.

Easy way to do this is by switching the x and y coordinates and negate the new x-coordinate. So, the image of (6, 4) after the rotation is (-4, 6).

Next, we apply the translation of 1 unit to the right and 5 units up. This moves the point (-4, 6) one unit to the right to get (-3, 6), and five units up to get the final image point:

Image point = (-3, 11)

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a certain company has 400 shoes. 20% of the shoes are black, One shoe is chosen and replaced. Then the second shoe is chosen. What is the probability that the shoes chosen are black

Answers

Answer: 4%

The probability of choosing a black shoe on the first draw is 20% or 0.2. Since the first shoe is replaced, the probability of choosing a black shoe on the second draw is also 20% or 0.2.

The probability of both events happening together is found by multiplying their probabilities. Therefore, the probability of choosing two black shoes in a row is:

0.2 x 0.2 = 0.04 or 4%

Therefore, the probability that the shoes chosen are black is 4%.

Answer: 80

Step-by-step explanation: The question is tell us that a certain company  we don't know which one, but it says a certain company has 400 shoes. that is important to note. also 20% of the shoes are black. and One shoe is chosen and replaced. Then the second shoe is chosen. The question is What is the probability that the shoes chosen are black?

Well, take 400 and mutipy it by 20% which changes to 0.20 in decimal form then mutiply your answer by one and you get 80. so the answer is the probability that shoes chosen are black is 80%.

Joshua's mail truck travels 14 miles every day he works


and is not used at all on days he does not work. At the


end of his 100th day of work the mail truck shows a


mileage of 76,762. Model Joshua's truck mileage as a


function of the number of days he has worked. When


will he reach 100,000 miles?

Answers

Solving the equation, Joshua will reach 100,000 miles after approximately 1,760 days of work.

To model Joshua's truck mileage as a function of the number of days he has worked, we can use the following equation:

Mileage (M) = 14 * Number of days worked (D) + Initial Mileage (I)

First, we need to determine the initial mileage on the mail truck. To do this, we can use the information given for his 100th day of work:

76,762 = 14 * 100 + Initial Mileage
76,762 = 1,400 + Initial Mileage
Initial Mileage (I) = 76,762 - 1,400
Initial Mileage (I) = 75,362

Now we can rewrite the equation as:

Mileage (M) = 14 * Number of days worked (D) + 75,362

To find when Joshua will reach 100,000 miles, we can set M equal to 100,000 and solve for D:

100,000 = 14 * D + 75,362
24,638 = 14 * D
D ≈ 24,638 / 14
D ≈ 1,759.857

Since Joshua cannot work a fraction of a day, he will reach 100,000 miles after approximately 1,760 days of work.

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Ide whole numbers
1
franny spent 35 minutes walking around a track. she made 7 laps around the track.
it took franny the same amount of time to walk each lap. how many minutes did it take her to walk each lap?
оа.
28
ов.
5
oc. 245
od. 1
reset
submit

Answers

It took Franny 5 minutes to walk each lap. The correct option is B.

Franny spent a total of 35 minutes walking around the track and made 7 laps around the track, so the total time for all 7 laps is 35 minutes. Let's assume it took Franny t minutes to walk each lap. Then, we can set up the following equation:

7t = 35

We can solve for t by dividing both sides of the equation by 7:

t = 35/7 = 5

Therefore, the correct option is B.

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If using the method of completing the square to solve the quadratic equation x^2-19x-39=0x 2 −19x−39=0, which number would have to be added to "complete the square"?​

Answers

We know that the solutions to the quadratic equation are x=21 or x=-12.

To solve the quadratic equation x^2-19x-39=0 using the method of completing the square, the number that would have to be added to "complete the square" is 91.

First, move the constant term to the right side: x^2-19x=39.

Then, take half of the coefficient of x, square it, and add it to both sides: x^2-19x+90.25=129.25.

This can be factored as (x-9.5)^2=129.25.

Taking the square root of both sides, we get x-9.5=±√129.25.

Solving for x, we get x=9.5±√129.25, which simplifies to x=9.5±11.5.

Therefore, the solutions to the quadratic equation are x=21 or x=-12.

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Homework:section 6c homework question 13, 6.c.21 hw score: 60%, 12 of 20 points points: 0 of 1 question content area top part 1 the scores on a psychology exam were normally distributed with a mean of 68 and a standard deviation of 9 . about what percentage of scores were less than ​50?

Answers

For a normal distribution with a mean of 68 and a standard deviation of 9, the percentage of scores less than 50 is 2.28%.

It is given that scores on a psychology exam have a normal distribution with a mean of 68 and a standard deviation of 9. The percentage of scores less than 50 can be determined as follows.

1. Calculate the z-score for 50 using the formula:

z = (X - μ) / σ

where

X = 50 (the value we're comparing to)

μ = 68 (mean)

σ = 9 (standard deviation)

2. Plug in the values:

z = (50 - 68) / 9 = -18 / 9 = -2

3. Use a z-table or calculator to find the area to the left of z = -2. This represents the percentage of scores less than 50.

4. Based on the z-table or calculator, the area to the left of z = -2 is approximately 0.0228, which means that around 2.28% of scores were less than 50.

So, about 2.28% of scores on the psychology exam were less than 50.

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The sum of five consecutive odd integers is 235. What is the greatest of
these integers?

Answers

Answer:

x + x + 2 + x + 4 + x + 6 + x + 8 = 235

5x + 20 = 235

5x = 215, so x = 43

The integers are 43, 45, 47, 49, and 51.

The greatest of these integers is 51.

In def x is a point on ef and y is a point on df so that xy ||de if xf =10 yf=5 and ef = 13 what is dy

Answers

DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

In the given figure, we have a triangle DEF, where EF is a transversal intersecting DE and DF at points X and Y, respectively, such that XY || DE.

    D

   / \

  /   \

 /     \

E-------F

Given that XF = 10, YF = 5, and EF = 13, we need to find DY.

We can start by using the property of similar triangles. Since XY || DE, we have the following similarity ratios:

EF / ED = EY / EJ  (where J is the intersection of XY and DF)

EF / DF = EJ / EY

Substituting the given values, we get:

13 / ED = EY / EJ

13 / DF = EJ / (13 - EY)

Multiplying the above two equations, we get:

13 / ED * 13 / DF = EY / EJ * EJ / (13 - EY)

169 / (ED * DF) = EY / (13 - EY)

Substituting the values of XF = 10 and YF = 5, we get:

169 / (ED * DF) = 5 / 8

ED / DF = 135 / 169

Using the Pythagorean theorem on triangles DEX and DFY, we get:

ED^2 = EX^2 + DX^2

DF^2 = FY^2 + DY^2

Since EX + DX = EF = 13, we have DX = 13 - EX. Substituting this in the first equation and simplifying, we get:

ED^2 = EX^2 + (13 - EX)^2

ED^2 = 2EX^2 - 26EX + 170

Similarly, substituting FY = 13 - EY in the second equation and simplifying, we get:

DF^2 = FY^2 + DY^2

DF^2 = 170 - 26EY + EY^2 + DY^2

Now, using the fact that ED/DF = 135/169, we can substitute ED^2 = (135/169)^2 * DF^2 in the above equation for ED^2, and simplify to get:

(135/169)^2 * DF^2 = 2EX^2 - 26EX + 170

DF^2 = 170 * 169^2 / (135^2 + 2EX^2 - 26EX)

DF^2 = 170 * 169^2 / (135^2 + 2(10^2) - 26EX)   (Substituting XF = 10)

Similarly, we can substitute EY = 5 in the above equation for DF^2 and simplify to get:

FY^2 + DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY)   (Substituting YF = 5)

DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) - FY^2

Substituting the given values, we get:

DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

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The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 42 meters. Find the length and width of the rectangle

Answers

the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters. So the dimensions of the rectangle are 10 meters by 11 meters.

what is  rectangle ?

A rectangle is a geometric shape that has four straight sides and four right angles (90-degree angles) between them. The opposite sides of a rectangle are parallel and have the same length, so the shape is symmetrical along its horizontal and vertical axes.

In the given question,

Let's assume that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is x + 1 meters, since the length and width are consecutive integers.

The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 42 meters, so we can write:

2(length + width) = 42

Substituting the expressions for the length and width in terms of x, we get:

2(x + x + 1) = 42

Simplifying this equation, we get:

4x + 2 = 42

Subtracting 2 from both sides, we get:

4x = 40

Dividing both sides by 4, we get:

x = 10

Therefore, the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters.

So the dimensions of the rectangle are 10 meters by 11 meters.

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Joey needs to buy chocolate milk they only sell it in pint containers how many pint containers of chocolate milk should he buy

Answers

To determin how many pint containers of chocolate milk Joey should buy, we need to know how much chocolate milk he wants in total.

Let's assume Joey wants to buy "x" pints of chocolate milk. Then, the total amount of chocolate milk he will get in quarts can be calculated as:

Total amount of chocolate milk = x pints/2 pints per quart = x/2 quarts

If Joey has a specific total amount of chocolate milk he wants to buy, we can solve for "x". For example, if Joey wants to buy 3 quarts of chocolate milk, we can set up the following equation:

x/2 = 3

Multiplying both sides by 2, we get:

x = 6

So, Joey needs to buy 6 pint containers of chocolate milk to get 3 quarts in total.

If Joey has a different desired amount of chocolate milk, we can adjust the equation accordingly to find the number of pint containers he needs to buy

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if y varies inversely as x and y = 18 when x = 1/2 then find x when y = -10

Answers

The value of x in the variation is -2/9

How to solve the variation?

y varies inversely as x and the value of y is 18 and x is 1/2

the first step is to calculate the constant k

k= y/x

k= 18 ÷ 1/2

k= 18 × 2/1

k= 36

From the calculation above the value of k which is the constant is 36

The next step is to calculate x. The value of x can be calculated as follows

k = y/x

36= -10/x

cross multiply

36x= -10

x= -10/36

x= -2/9

Hence the value of x in the variation is -2/9

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i need help with these 30 points

Answers

Answer:

0 hrs 32 mins

Step-by-step explanation:

Which of the following statements proves the series –128 + 96 – 72 + 54 – … is geometric? r equals negative three fourths r equals three fourths r equals negative four thirds r equals four thirds

Answers

Answer: To determine if the series –128 + 96 – 72 + 54 – ... is a geometric series, we need to check if the ratio between consecutive terms is constant.

Let's calculate the ratio between the second and first terms:

96 / (-128) = -3/4

Now let's calculate the ratio between the third and second terms:

-72 / 96 = -3/4

The ratio between the fourth and third terms is:

54 / (-72) = -3/4

We can see that the ratio between consecutive terms is always the same: -3/4. Therefore, the series –128 + 96 – 72 + 54 – ... is a geometric series with a common ratio of -3/4.

So the answer is r equals negative three fourths.

Step-by-step explanation:

Final answer:

The series provided is a geometric series because each term after the first is found by multiplying the previous term by -3/4. Therefore, the common ratio 'r' equals -3/4.

Explanation:

In a geometric series, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In the series given –128 + 96 – 72 + 54 – …, the second term (96) divided by the first term (-128) equals -3/4, the third term (-72) divided by the second term (96) also equals -3/4, and so on. This constant ratio between successive terms demonstrates that this is indeed a geometric series. Therefore, the statement that proves this is a geometric series is 'r equals negative three fourths' where r represents the common ratio.

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7.) The Goody's store manager charted
the number of coats sold compared
with the outside temperature. What
kind of relationship would you expect
between the variables?

Answers

It is also possible that there may not be a clear relationship between the two variables or that there may be other factors that influence the number of coats sold, such as seasonal trends or fashion trends.

What is variable?

In mathematics, a variable is a symbol or letter that represents a quantity that can vary or take on different values in a given situation or equation. Variables are commonly denoted by letters such as x, y, z, a, b, c, etc. They are used to represent unknown or changing quantities in mathematical expressions or equations.

For example, in the equation y = 2x + 3, x and y are variables. x represents an unknown value, while y represents the value that results from the equation for a particular value of x. In this case, the variable x can take on different values, and the corresponding value of y will change accordingly.

Variables are used in a wide range of mathematical concepts, such as algebra, calculus, and statistics, to represent and manipulate different quantities and relationships between them.

It is reasonable to expect that there is a negative correlation between the number of coats sold and the outside temperature. In other words, as the temperature gets colder, the number of coats sold would increase, and as the temperature gets warmer, the number of coats sold would decrease. This is because colder temperatures would typically prompt people to buy more coats to stay warm, while warmer temperatures would make people less likely to buy coats. However, it is also possible that there may not be a clear relationship between the two variables or that there may be other factors that influence the number of coats sold, such as seasonal trends or fashion trends.

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Construct angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm ii, Construct M the midpoint of XZ where XYZ= 60o

Answers

To construct angle XYZ with XY = 8.3 cm and YZ = 11.9 cm, follow these steps:

1. Draw a line segment XY of length 8.3 cm.
2. At point Y, draw a ray in any direction to form an angle with XY.
3. Using a compass, draw an arc with center at point Y and radius 11.9 cm. This arc should intersect the ray drawn in step 2 at point Z.
4. Draw the line segment YZ of length 11.9 cm.
5. Using a compass, draw an arc with center at point X and radius equal to the length of segment YZ. This arc should intersect segment XY at two points. Label the point of intersection closest to Y as M.
6. Draw a line segment XM and a line segment ZM.
7. Angle XYZ is the angle formed by segments XY and YZ.

To confirm that angle XYZ is 60 degrees, we need to show that XMZ is also a 60-degree angle. Since M is the midpoint of XZ, we have:

XM = MZ

Therefore, triangles XMY and ZMY are congruent by the Side-Side-Side (SSS) criterion. Thus, angles XMY and ZMY are congruent. Since they form a straight line, we know that:

angle XMY + angle ZMY = 180 degrees

Therefore, each of these angles measures:

angle XMY = angle ZMY = 180 degrees / 2 = 90 degrees

Since angle XYZ is the sum of angles XMY and ZMY, we have:

angle XYZ = 90 degrees + 90 degrees = 180 degrees

This means that angle XYZ is a straight angle, which measures 180 degrees. However, we know that XYZ is a 60-degree angle, so we must have made an error in the construction. Double-check the construction steps to make sure that each step was performed accurately.

The length of a rectangle is 3 cm less than twice it’s width. the perimeter of the rectangle is 48cm

Answers

The length of the rectangle is 15 cm and the width is 9 cm.

What is the width of the rectangle?

Let's start by setting up the equations we need to solve:

L = 2W - 3 (the length is 3 cm less than twice the width)

2L + 2W = 48 (the perimeter is 2 times the length plus 2 times the width)

Now we can substitute the first equation into the second equation and solve for W:

2(2W - 3) + 2W = 48

4W - 6 + 2W = 48

6W = 54

W = 9

Now that we know the width is 9 cm, we can substitute this value back into the first equation and solve for L:

L = 2(9) - 3

L = 15

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During an elbow flexion exercise, the relative angle at the elbow was 10 degrees at 0. 5s and 120 degrees at 0. 71s. What was the angular velocity of the elbow?

Answers

The angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s

To calculate the angular velocity of the elbow during an elbow flexion exercise, we'll use the information given about the relative angle at different times. Here's the step-by-step explanation:
First, find the change in relative angle: Δθ = Final angle - Initial angle = 120 degrees - 10 degrees = 110 degrees.
Next, find the change in time: Δt = Final time - Initial time = 0.71s - 0.5s = 0.21s.
Now, calculate the angular velocity: ω = Δθ / Δt = 110 degrees / 0.21s ≈ 523.81 degrees/s.
So, the angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s.

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Given that cos α = -8/17 and that 0° <= α <= 360°, find two values of α, to two decimal places.

Answers

Therefore, two possible values of α are approximately 138.19° and 221.81°.

What purpose does sin serve?

Sin 180 has a precise value of zero. One of the fundamental trigonometric functions is sine, which is used to calculate the angle or sides of a right-angled triangle.

Given that cos = -8/17, we must determine two potential values for.

We can construct a right triangle with the adjacent side equal to -8 and the hypotenuse equal to 17, and then use the Pythagorean theorem to calculate the opposite side since cos = adjacent/hypotenuse.

The Pythagorean theorem gives us:

opposite² = hypotenuse² - adjacent²

opposite² = 17² - (-8)²

opposite² = 225

opposite = ±15

Both the x and y coordinates are negative in the second quadrant, resulting in:

cos α = -8/17

sin α = -15/17

Consequently, may have the following value: = 180° - arccos(-8/17) 138.19° (rounded to two decimal places)

The x coordinate is negative and the y coordinate is positive in the third quadrant, resulting in:

cos α = -8/17

sin α = 15/17

Therefore, another possible value of α is:

α = 360° - cos(-8/17)

≈ 221.81°

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