the economic policy institute periodically issues reports on worker's wags. the institute reported that mean wags for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2020. assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. (12 points) what is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.97? what is the probability that a sample of 50 female graduates will provide a sample mean within $1.00 of the population mean $27.83? in which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population mean? why? what is the probability that a sample of 120 female graduates will provide a sample mean more than $0.60 below the population mean, 27.83?

The approximate mean and standard deviation of the number of chips meeting specifications are: μ = 16.2; σ = 1.273

In this question, we have been given a factory makes silicon chips for use in computers. it is known that about 90% of the chips meet specifications. every hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded.

we need to find  the approximate mean and standard deviation of the number of chips meeting specifications

Since 90% meet specifications we can say p = 0.9

So, q = 1 - p

q = 1 - 0.9

q = 0.1

here,  a sample size is n = 18

So, the mean would be,

μ = np

μ = 18 * 0.9

μ = 16.2

And the standard deviation would be,

σ = √npq

σ = √(18 * 0.9 * 0.1)

σ = 1.273

Therefore, the mean (μ) = 16.2 and the standard deviation (σ) = 1.273

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Answer:

it is linear

Step-by-step explanation:

i took the test.

The required percent decrease in the price of the skateboard is 40%.

What is the percentage?

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here, we have

Original price = $84.50

sale price = $50.70

Percent decrease = 84.50-50.70/84.50 × 100 = 40%

Hence, the required percent decrease in the price of the skateboard is 40%.

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The probability that the committee includes all 3 women is 0.00018

In this question, we have been given there are 97 men and 3 women in an organization.

A simple random sample of 5 people is taken to form a committee.

We need to find  the probability that the committee includes all 3 women.

Total number of people in the organization: 97 + 3 = 100

Usinng combination formula the possible number of 5 people committee:

100C5

= 100! / 5!(100 - 5)!

= 75287520

The number of outcomes for the committee includes all 3 women would be:

5C3 = (97C2)*3

       = 13968

So, the probability that the committee includes all 3 women would be,

P = 13968 / 75287520

P = 0.00018

Therefore, the required probability is 0.00018

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A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground, the height to which the ladder will reach the wall is 9.456 foot.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is a term used to describe everything that may be measured vertically, high or low.

From the lowest to the highest point to the lowest point, it calculates the vertical distance. In general, it refers to a coordinate geometry object's measurement along the y-axis.

let, h = height of ladder

Given that,

length of ladder = 12 ft

angle with the ground = 52°

As we know,

sinθ = h/12

or, sin (52°) = h/12

or, 0.7880 = h/12

or, h = 9.456 foot.

the height to which the ladder will reach the wall 9.456 foot.

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Answer:

x = 5

Step-by-step explanation:

Firstly, we know that corresponding angles are the same. So we can say that 25x + 5 = 26x

Let’s simplify this equation:

25x + 5 =26x

-25x -25x

5 = x

Therefore, x = 5.

Answer:

The area of the square is 225 square kilometres.

Step-by-step explanation:

So,

A = (15)² km

A = 225 km²

Thus, The area of the square is 225 square kilometres.

The measure of the angle x would be 30.26°.

What are inverse trigonometric functions?

Inverse trigonometric functions are functions that "undo" the action of the trigonometric functions. They allow us to find the angles of a right triangle given the values of the sides, or to find the values of the sides given the angles.

In the given triangle, by using sine ratio we can write

        sin(x°) = BC/AC

       [tex]sin(x^o)=39/74\\\\x^o=sin^{-1} \frac{39}{74}\\\\x^o=sin^{-1}{0.5270}\\\\x^o=30.26^o[/tex]

Hence, the measure of the angle x would be 30.26°.

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Answer:

greater

Step-by-step explanation:

972 is a higher number than 792 so the answer is greater

Answer:

972 is greater than 792

Step-by-step explanation:

972 > 792

First:

Quotient: [tex]2x^{2} -11x+58[/tex]

Remainder: [tex]-294[/tex]

Second:

Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]

Remainder: [tex]422[/tex]

Third:

Quotient: [tex]2x-3[/tex]

Remainder: [tex]12[/tex]

Answer:

10 years old

Step-by-step explanation:

The force on the object is 40N

Force can be described as the influence that can change the motion of an object.

It is seen as an external agent having the capability of changing a body's state of motion or rest.

It causes b in velocity of an object with mass , that is,  to accelerate. Force can also be described as either a push or a pull.

It is described as a vector quantity, that is, it has both magnitude and direction.

The formula for determining force is given as;

F = ma

Where;

Substitute the values

F = 10(4)

F = 40N

Hence, the value is 40N

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Answer:

84

Step-by-step explanation:

Let's call the number of cookies Mrs. Green sold "x". We can then write the following equation to represent the information given in the problem:

x - 36 - 48 = 0

Solving for x, we get:

x = 36 + 48

Mrs. Green sold 36 + 48 = 84 cookies.

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Answer:

Step-by-step explanation:

Answer:

-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.

Step-by-step explanation:

The equivalent ratios to tan F = EL/ EF = OS/OJ

Similar triangles are those with the same shape but different sizes. Similar triangles include all equilateral triangles and squares with any side length.

All related pairs of angles will be equal and corresponding sides of similar triangles will have the same ratio. The symbol '∼' is used to represent the similarity.

Given that

△FEL∼△JOS

That means △FEL and △JOS are similar triangles

As we know tan θ = Opposite side / Adjacent side

From the triangle △FEL,

=> tan F = EL/EF      

By the given information,

The similar triangle's corresponding sides will have the same ratio  

=> EL/ EF = OS/OJ

Therefore

The equivalent ratios to tan F = EL/ EF = OS/OJ

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An isosceles triangular prism, its surface area becomes: 568 feet²

The faces of a polyhedron called an isosceles triangular prism are made up of polygons. It has six edges, five faces, and five vertices. Isosceles triangles make up the two portions at the base that face each other and rectangles make up the vertical faces of the five faces.

where the isosceles triangle's base has equal sides measured in "a" units, each triangle's base measured in "b" units, the triangle's height measured in "h" units, and the length of the congruent rectangles measured in "l" units.

The surface area of an isosceles triangular prism is:

Surface area = (b × h) + (2× l × a) + (l × b)

here, b = the base of each of the triangle = 16 feet

h = the height of the triangle = 18 feet

l = length of the congruent rectangles = 10 feet

a = isosceles triangle in the base have the equal sides be "a" units = 6 feet

Now, Surface area = (16 × 18) + (2 × 10 × 6) + (10 × 16)

or, Surface area = 568 feet²

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The perimeter of the triangle XYZ according to the midsegment theorem is 37

The midsegment theorem states that the segment that is obtained by joining the midpoints of two sides of a triangle is parallel to the third side and it is half the length of the third side of the triangle.

The specified parameters are;

The midpoint of [tex]\overline{XY}[/tex] = A

The midpoint of [tex]\overline{YZ}[/tex] = B

The midpoint of [tex]\overline{XZ}[/tex] = C

The length of segment AC = 5

The length of segment BC = 6

The length of side XZ = 15

The segments AC, BC, and AB are midsegments of the triangle XYZ

According to the midsegment theorem, we get

AC = 0.5 × [tex]\overline{YZ}[/tex]

BC = 0.5 × [tex]\overline{XY}[/tex]

AB = 0.5 × [tex]\overline{XZ}[/tex]

Therefore;

2 × AC = [tex]\overline{YZ}[/tex]

2 × BC = [tex]\overline{XY}[/tex]

2 × AB = [tex]\overline{XZ}[/tex]

[tex]\overline{YZ}[/tex] = 2 × 5 = 10 (substitution property)

[tex]\overline{XY}[/tex] = 2 × 6 = 12 (substitution property)

The perimeter of the triangle = [tex]\overline{YZ}[/tex] + [tex]\overline{XY}[/tex] + [tex]\overline{XZ}[/tex]
Plugging in the values, of [tex]\overline{YZ}[/tex], [tex]\overline{XY}[/tex], and [tex]\overline{XZ}[/tex]  we get;

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The missing factor for A in the model is 3/4

From the question, we have the following parameters that can be used in our computation:

Length of column A = 4

Shaded region in column A = 3

This means that

The missing factor = Shaded region/Length of column A

Substitute the known values in the above equation, so, we have the following representation

The missing factor, A = 3/4

Here, we have

Length of column B = 5

Shaded region in column B = 1

This means that

The missing factor = Shaded region/Length of column B

Substitute the known values in the above equation, so, we have the following representation

The missing factor, B = 1/5

In (a) and (b), we have

The missing factor, A = 3/4

The missing factor, B = 1/5

So, we have

Pair = 3/4 * 1/5

Evaluate

Pair = 3/20

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Answer:

[tex]Circumcenter =(2,333, 1.3333) \;or\; \left(2\dfrac{1}{3}, 1\dfrac{1}{3}\right)[/tex]

[tex]Orthocenter = (2.3333, 2.3333) \;or\;\left(2\dfrac{1}{3},2\dfrac{1}{3}\right)[/tex]

Step-by-step explanation:

The equation of the parabola that has a vertex  (-3,4) and passes through  (2,8) is 25y = 4x² + 24x + 13.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the DirectX and focus, respectively.

Given:

The vertex = (-3, 4) and the point = (2, 8)

Write the equation using the standard form given below,

[tex]y = a (x - h)^2 + k[/tex]

y = a[x - (-3)]² + 4

y = a(x + 3)² + 4

Now put the coordinates,

8 = a (2 + 3)² + 4

8 = 25a + 4

a = 4 / 25

Put the value of a in the above equation,

y = 4/25 × (x + 3)² + 4

25y = 4 (x² + 9 +6x) + 100

25y = 4x² + 36 +24x + 100

25y = 4x² + 24x + 13

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△KML is congruent to △QNP (△KML ≅  △QNP) under SSA conditions.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

If two triangles meet all 5 requirements for congruence, then they are congruent.

They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) (RHS).

So, in the given triangle:

Prove that: △KML ≅  △QNP

∠L = ∠P = 90° (Equal: Given)

ML = QP = 12 units (Equal: Given)

Mk = QN = 15 units (Equal: Given)

So, △KML ≅  △QNP is under SSA condition.

Therefore, △KML is congruent to △QNP (△KML ≅  △QNP) under SSA conditions.

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The smallest representable positive number is 2149, or roughly 1.4*10-45.

Lets take a  32-bit floating point integer (IEEE 754) with the following bits,

0-22 for the mantissa (23 bits), 23-30 for the exponent ( 8 bits), and 31 for the sign (1bit)

The decimal counterpart of this expression would be if we put all zeros in the mantissa and all ones in the exponent.

The way of representing huge numbers in terms of powers is known as an exponent.

Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6.

The exponent is represented by the symbol  ^ . This symbol is known as a carrot . As an illustration, 4 raised to 2 can be expressed as 4^2 .

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Answer:

22 X 50= 1100 cards because 100 dived by 2 = 50.

Step-by-step explanation:

The lengths of the sides of the triangle are 5, 12, and 13.

So the correct option is the last one.

Remember that if we have two points (x₁, y₁) and (x₂, y₂), the distance between these two points is given by the formula:

d = √( (x₁ - x₂)² + (y₁ - y₂)²)

Here we know that the vertices of our triangle are the points:

(0, 0), (5, 0), (5, 12)

And we want to find the lengths of the sides.

We can get the length of the first side using the points  (0, 0), (5, 0)

d₁ = √( (0 - 5)² + (0 - 0)²) = 5

The length of the second side is: (5, 0), (5, 12).

d₂ = √( (5 - 5)² + (0 - 12)²) = 12

The length of the third is side is given by the points (5, 12) and (0, 0)

d₃ = √( (5 - 0)² + (12 - 12)²)

d₃ = √(25 + 144) = 13

Then the correct option is the last one:

5, 12, 13.

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The expression in terms of xx that represents the total amount that Hailey paid is (2912/625)xx .

What is business Mathematics?  

Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.

According to Question:

let the the subtotal on the bill was xx dollars

A tax of 8% is added on bill then Bill becomes xx + 8% of xx

The of 8% on bill = (108/100)xx

Now the Final bill = xx + (108/100)xx

                    = (208/100)xx

Hailey decides to leave a tip of 24% on the entire bill (including the tax)

So the Total Amount = (208/100)xx + 24% of Final bills

⇒

24% of (208/100)xx = (208/100)(124/100)xx

The Total amount = (208/100)xx +(208/100)(124/100)xx

Let the Amount be A

hence, expression in terms of xx that represents the total amount that Hailey paid is A = (208/100)xx +(208/100)(124/100)xx

⇒ A = (52/25)xx +(52/25)(31/25)xx

⇒ 625A = 625((52/25)xx +(52/25)(31/25)xx)

⇒ 625A = 1300xx + 1612xx

⇒ 625A = 2912xx

⇒ A = (2912/625)xx

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By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

What does testing your hypotheses mean?

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.

               First, a hazy assumption about the parameter or distribution is made.

What is hypothesis testing, and how can it be used?

A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.

                     The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.

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Answer:

22 divided by 2 is 11

Step-by-step explanation:

Answer:At the rate of 15% the amount of interest on $2000

Step-by-step explanation:

simple amount= Principle(1+rt)

where r= rate of inetrest

t= time

principal is initial amount

therefore, amount=2000(1+15*1)

Amount = $2,300.00

Interest = Amount - Principal = $300.00

Answer:

Step-by-step explanation:

Interest = Principle * Rate * Time /100

Principle =  $2000

Rate = 15 %

Time =  1 year

I = 2000 * 15 * 1/100

I = 300

Juan has to pay $300 in a year

It will take about 18 million years for Los Angles to be located next to san Francisco.

The distance traveled is 630km (380 miles), and the net distance moves is 36mm per year.

We can use this formula to determine the answer :

Time = distance/rate

630 km = 630,000 m = 630, 000,000 mm

Time = 630,000,000 mm/ 36mm/year = 17,500,000 year

We could also put these dimensional relationship together as follows and then cancel units that occur in both the numerator and the denominator .

We are left with an answer in number of years:

630 km × [tex]\frac{1000m}{1km 1m}[/tex]  × [tex]\frac{1000mm 1 year}{36mm}[/tex]  = 17,500,000 year

Hence, It will take about 18 million years for Los Angles to be located next to san Francisco.

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