Plz answer correctly !

The 95% confidence interval for the average starting salary of all accountants in New York City is:

($47,589 - $7,285) to ($47,589 + $7,285)

or

$40,304 to $54,874

To construct a 95% confidence interval for the average starting salary of all accountants in New York City, we can use the formula:

\(CI = x $ \pm t*(s/\sqrt{n)\)

where x is the sample mean, s is the sample standard deviation, n is the sample size, t is the t-value from the t-distribution with n-1 degrees of freedom and a 95% confidence level, and \($\pm\) represents the margin of error.

In this case, x = $47,589, s = $11,364, and n = 10. The t-value with 9 degrees of freedom and a 95% confidence level is approximately 2.262 (from a t-distribution table or a calculator).

Substituting the values into the formula, we get:

\(CI = $47,589 $\pm 2.262*($11,364/\sqrt{10)\)

Simplifying the expression, we get:

CI = $47,589 \($\pm\) $7,285

Therefore, the 95% confidence interval for the average starting salary of all accountants in New York City is:

($47,589 - $7,285) to ($47,589 + $7,285)

or

$40,304 to $54,874

We can be 95% confident that the true average starting salary of all accountants in New York City falls within this interval.

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The probability that a household watches more than 3 hours of television a day is 0.0478.

The mean daily viewing time of television is 8 hours per household. Use a normal probability distribution with a standard deviation of 3 hours to answer the following questions about daily television viewing per household.

(a) Probability that a household views television between 5 and 11 hours a day:P(5 < x < 11) = P(z < (11-8)/3) - P(z < (5-8)/3) = P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826(b) Hours of television viewing must a household have in order to be in the top 3% of all television viewing households:

The top 3% of all households correspond to z = 1.88. Therefore, the number of hours that a household must watch television to be in the top 3% is:1.88 = (x - 8) / 3x - 8 = 5.64x = 13.64

(c) Probability that a household views television more than 3 hours a day:P(x > 3) = P(z < (3-8)/3) = P(z < -5/3) = 0.0478.the probability that a household watches more than 3 hours of television a day is 0.0478.

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Answer:

3.545 represents a value of 0.04

The set of all real numbers greater than or equal to -5.4 can be represented as [-5.4, +∞). This means that any number greater than or equal to -5.4, including -5.4 itself, belongs to this set.

In interval notation, the square brackets indicate that -5.4 is included in the set, and the infinity symbol (∞) represents all numbers greater than -5.4. The plus sign (+) indicates that there is no upper bound to the set, meaning it extends indefinitely.

To visualize this set on a number line, you would start from -5.4 and continue indefinitely to the right, encompassing all real numbers greater than or equal to -5.4.

In summary, the set of all real numbers greater than or equal to -5.4 is represented as [-5.4, +∞) and includes -5.4 as well as all numbers greater than it.

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Answer:

c)3pi/4

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

4(2x-1)=36

first distribute

8x-4=36

add 4 to both sides

8x=40

divide both sides by 8

x=5

Answer: To find the equation of a line passing through two points, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of one of the points, and m is the slope of the line.

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, let's plug in the values we have:

m = (-8 - 3)/(-8 - (-10)) = (-8 - 3)/2 = -11/2

Now we can use either point to find the equation. Let's use (-10, 3):

y - 3 = (-11/2)(x - (-10))

y - 3 = (-11/2)x - 55/2

y = (-11/2)x - 49/2

So the equation of the line through (-10, 3) and (-8, -8) is:

y = (-11/2)x - 49/2.

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Answer: 216 in ^3

Explanation:

18 x 3 x 12 = 648

648 / 3 = 216 in ^3

I hope this helped!

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Answer:

1. a. 2 KM ; b. 9000 m

2. a. 9 L ; b. 3000 g

3. a.   6000 ml  ; b. 9

4. a. 60 mm ; b. 4000 m

5. a. 1 km     ; b. 2 kg

6. a. 5      ;    b. 4 m

7. a. 4000 ml  ; b. 3000

8. a. 10 kg ; b. 20 mm

9. a. 10 km ; b. 9kg

10. a. 4 kg ; 8 l

Answer:

A. Conditional Statement

Step-by-step explanation:

In a conditional statement, A would be the premise, and B would be the conclusion.

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Have a great summer :)

Answer: Sara = 29/53

Fiona = 24/53

Step-by-step explanation: because that amount is how much they have won and how much its out of so for example ‘i played 26 games i only won 17 and John won the rest’ the probability that i win is

17/26 and Johns would be 9/26

Answer:

a) \(\frac{dA}{dt} = 48 \pi\frac{in^{2}}{min}\)

b) \( \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}\)

c) \(\frac{dh}{dt} = - 2\frac{h}{r} \frac {dr}{dt}\)

Step-by-step explanation:

In order to solve this problem, we must first picture a cylinder of height h and radius r (see attached picture).

a) So, in order to find the rate at which the area of the circular surface of the dough is increasing with respect to time, we need to start by using the are formula for a circle:

\(A=\pi r^{2}\)

So, to find the rate of change of the area, we can now take the derivative of this formula with respect to the radius r:

\(dA = \pi(2) r dr\)

and divide both sides into dt so we get:

\(\frac{dA}{dr} = 2\pi r \frac{dr}{dt}\)

and now we can substitute:

\(\frac{dA}{dr} = 2\pi(12in)(2\frac{in}{min})\)

\(\frac{dA}{dt} = 48\pi\frac{in^{2}}{min}\)

b) In order to solve part b, we can start with the formula for the volume:

\(V=\pi r^{2} h\)

and solve the equation for h, so we get:

\(h=\frac{V}{\pi r^{2}}\)

So now we can rewrite the equation so we get:

\(h=\frac{V}{\pi}r^{-2}\)

and now we can take its derivative so we get:

\(dh=\frac{V}{\pi} (-2) r^{-3} dr\)

we can rewrite the derivative so we get:

\(\frac{dh}{dt}=-2\frac{V}{\pi r^{3}}\frac{dr}{dt}\)

we can take the original volume formula and substitute it into our current derivative, so we get:

\(\frac{dh}{dt}= -2\frac{\pi r^{2} h}{\pi r^{3}} \frac{dr}{dt}\)

and simplify:

\(\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}\)

so now we can go ahead and substitute the values  provided by the problem:

\(\frac{dh}{dt} =-2\frac{13in}{12in} (2\frac{in}{min})\)

Which simplifies to:

\( \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}\)

c)

Part c was explained as part of part b where we got the expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of the height h and the radius r:

\(\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}\)

The rate of change of the height of the pizza with respect to (w.r.t.) time

can be found given that the volume of the pizza is constant.

Reasons:

The height of the dough when t = k is 13 inches

Radius of the dough = 12 inches

Rate at which the radius of the dough is increasing, \(\dfrac{dr}{dt}\) = 2 in.²/min

(a) Required: The rate of increase of the surface area with time

Solution:

The circular surface area, A = π·r²

By chain rule of differentiation, we have;

\(\dfrac{dA}{dt} = \mathbf{\dfrac{dA}{dr} \times \dfrac{dr}{dt}}\)

\(\dfrac{dA}{dt} = \dfrac{d ( \pi \cdot r^2)}{dr} \times \dfrac{dr}{dt} = 2 \cdot \pi \times 2 = 4 \cdot \pi\)

The rate of increase of the surface area with time, \(\mathbf{\dfrac{dA}{dt}}\) = 4·π in.²/min.

(b) Required: The rate of decrease of the height with respect to time

The volume of the pizza is constant, given by; V = π·r² ·h

Therefore;

\(h = \mathbf{ \dfrac{V}{\pi \cdot r^2}}\)

\(\dfrac{dh}{dt} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} \times \dfrac{dr}{dt} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} \times \dfrac{dr}{dt} = \mathbf{-2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt}}\)

\(\dfrac{dh}{dt} = -2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt} = -2 \times \dfrac{13}{12} \times 2 = \dfrac{13}{3} = 4. \overline 3\)

The rate at which the height of the dough is decreasing, \(\mathbf{\dfrac{dh}{dt}}\)= \(\underline{4.\overline 3 \ in./min}\)

(c) Required:]The expression for the rate of change the height of the dough with respect to the radius of the cone.

Solution:

\(\dfrac{dh}{dr} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} = -2 \cdot \dfrac{h}{r}\)

\(\dfrac{dh}{dr} = \mathbf{ -2 \cdot \dfrac{h}{r}}\)

The rate of change the height of the dough w.r.t. the radius is \(\underline{\dfrac{dh}{dr} = -2 \cdot \dfrac{h}{r}}\)

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We have 3 triangles that are related in the image

We will use the sine relations to determine the value of x

For triangle ABD

For triangle ABC

For triangle ACD

Now solving the system of equations we have

The answer would be x = 4 units

Answer:

PLEASE MARK AS BRAINLIEST

Z = 130

Y = 50

X = 130

Step-by-step explanation:

hope this helped

Answer: 35 is 70% of 50

Step-by-step explanation:

Steps to solve "35 is 70 percent of what number?"

We have, 70% × x = 35

or,

70

100

× x = 35

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 35 ×

100

70

x = 50

If you are using a calculator, simply enter 35×100÷70, which will give you the answer.

Answer:

50

Step-by-step explanation:

35 + 15 = 50

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

15 is 30% of 50 There fore 50 is the correct answer

I took this exam, its the 5.08 Ratios and rates practice exam right?

Have an amazing Day and good luck (:

The sample mode might be greater, smaller, or equal to the population mode. Even if the sample is genuinely random, it does not have to be equal. The sample size is 50 rather than 500.

The mode of a population or sample is the value that occurs the most frequently within the set. A sample's mode might be greater, less, or equal to the population's mode. This is due to the fact that the sample is a subset of the population and may not include the same values, even if it is genuinely random. If the population's mode is 10, the mode of a sample drawn from it may be 12. The sample mode does not have to be identical to the population mean because they are computed differently. The mode is the most common value, whereas the mean is an average. Lastly, the sample size must be 50, not 500. This is due to the fact that the sample is a subset of the population and comprises just 50 items.

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Answer:

Points R(4,1) S(7,3) T(6,4) after translation

R(4-3, 1) S(7-3, 3) T(6-3, 4)

R'(1, 1) S'(4, 3) T'(3, 4)

Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection

R''(1, -3) S''(4, -5) T''(3, -6)

Step-by-step explanation:

Answer:Step-by-step explanation:Points R(4,1) S(7,3) T(6,4) after translation R(4-3, 1) S(7-3, 3) T(6-3, 4) R'(1, 1) S'(4, 3) T'(3, 4) Points R'(1, 1) ...

The volume of water in the pool is 10230 cubic feet.

Given : Swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and increases linearly from 5 ft at the south end to 10 ft at the north end.

To find : The volume of water in the pool?

Swimming pool is circular with a 40-ft diameter.

The radius of the pool is 40/20 = 20 ft

The depth is constant along east-west lines and increases linearly from 5 ft at the south end to 10 ft at the north end.

Depth average is:

Da = 5+10/2

= 7.5

The volume is given by:

V = π × r² × Da

V = 3.41 × (20)² × 7.5

V = 10230 ft²

The volume of water in the pool is 10230 ft² cubic feet.

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Answer:

1.30cm.

2.7 children.

3.8 children.

4.148 cm.

Answer: -449/50

Step-by-step explanation:

-9.98

1) Put in fraction form.

-998/100

2) Simplify.

-449/50

Answer:

-9.98/1

Step-by-step explanation:

The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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The required number is 94.

Let the digit on unit's place be 'x'

Digit on ten's place be 'y'

Therefore,

Original number = 10y + x

Given, the sum of the digits = 11

=> x + y = 11 →(I)

When the digits are reversed, new number = 10x + y

Therefore,

(10y + x) - (10x + y) = 63

10y + x - 10x - y = 63

9y - 9x = 63

=> y - x = 7 →(II)

Adding (I) and (II) we get

2y = 18

y = 9

Substituting the value of y in (I) we get

x + 9 = 11

x = 2

Therefore,

Original number = 10y + x = 10(9) + 4 = 94

The required number is 94.

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Answer:

18 and 21 (I think)

Step-by-step explanation:

So, lets assume the equation is x + x + 3 is the 2 numbers (number 1 is x)

then divide by 3

You get:  (2x+3)/3 = x-5

then, multiply both sides by 3:

2x+3=3x-15

Simplify:

18 = x

18 is the smaller number

21 is the bigger one. (18+3)

We have here a perpendicular bisector of GH, so it divides this segment into two equal parts, that is. GB = 8, and BH = 8.

We also have that the formed triangles BCG and BCH are congruent since GB is congruent to BH And they share the same side BC. The angles Therefore, we have:

GH = GB + BH ---> GH = 8 + 8 = 16

GC = CH = 12 (since we have congruent figures here.)

In summary, we have that

GH = 16

CH = 12

If f(x) = arcsec(3x), then

sec(f(x)) = sec(arcsec(3x))

sec(f(x)) = 3x

But bear in mind that the right side reduces in this way only if 0 ≤ f(x) ≤ π.

Differentiating both sides using the chain rule gives

sec(f(x)) tan(f(x)) f'(x) = 3

so that

f'(x) = 3 cos(f(x)) cot(f(x))

f'(x) = 3 cos(arcsec(3x)) cot(arcsec(3x))

We *could* stop here, but we can usually simplify these nested trig and inverse trig expressions to end up with an simpler algebraic one. Consider a right triangle with a reference angle measuring θ = f(x) = arcsec(3x). Then sec(θ) = 3x. It follows from the definition of secant, and subsequently the Pythagorean identity, that

• cos(θ) = 1/sec(θ) = 1/(3x)

• sin(θ) = √((3x)² - 1²) = √(9x² - 1)/(3x)

but remember that we assume 0 ≤ θ ≤ π. Over this interval, sin(θ) can be either positive or negative, which we account for by replacing x with |x|, so that

• sin(θ) = √(9x² - 1)/(3|x|)

So, we have

cos(arcsec(3x)) = 1/(3x)

cot(arcsec(3x)) = (1/(3x)) / (√(9x² - 1)/(3|x|)) = |x|/(x √(1 - 9x²))

and so

f'(x) = 3 • 1/(3x) • |x|/(x √(1 - 9x²))

It's easy to show that |x|/x = x/|x|, so we can rewrite this as

f'(x) = 3 • 1/(3x) • x/(|x| √(1 - 9x²))

f'(x) = 1/(|x| √(1 - 9x²))

Answer:

12 dimes, 8 nickels

Step-by-step explanation:

1. Set up an equation. Since we know the relationship between how many dimes and how many nickels that he has, we can create values for them.

2. Say that the number of nickels is x, so the number of dimes would be 2x-4.

3. Since we know that all of the coins that he has is 20 coins, we can say that 2x-4+x=20.

4. Solve the equation. We get 3x=24, and x=8.

5. That means that the number of nickels is 8, and the number of dimes is 2(8)-4, which is 12.

Answer: Timmy has 12 dimes and 8 nickels.

the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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