A company is criticized because only 20 of 47 executives at a local branch are women. The company explains that although this proportion is lower than it might​ wish, it's not a surprising value given that only 45​% of all its employees are women. The company has more than 500 executives worldwide. Test an appropriate hypothesis and state the conclusion.

Answer:

23°

Step-by-step explanation:

We apply Pythagorean theorem to determine the missing length, Hypotenuse:

[tex]h^2+b^2=H^2\\\\70^2+30^2=H^2\\\\H=\sqrt{5800}\\\\=76.15773\ ft[/tex]

This hypotenuse corresponds to the right triangle and the tree's height, corresponds to the angle of elevation:

-We apply the law of Sines;

[tex]\frac{a}{Sin \ A}=\frac{b}{Sin\ B}\\\\\\\frac{76.15773}{Sin \ 90}=\frac{30}{Sin\ h}\\\\h=Sin^{-1}\frac{30}{76.15773}\\\\=23.19859\approx 23\textdegree[/tex]

Hence, the angle of elevation is 23°

The common ratio of the geometric sequence –1,-8, -64, ... is 8. This is calculated by dividing a term in the sequence by its preceding term and is same across all consecutive terms.

In a geometric sequence, the common ratio is found by dividing any term by its preceding term. Here, the sequence given is –1,-8, -64, ...

Let's calculate the ratio for this series: We divide the second term (-8) by the first term (-1), which is 8. Let's check it with the next terms, where we divide the third term (-64) by the second term (-8). We find the ratio to be 8 again.

Therefore, the common ratio of the given geometric sequence –1,-8, -64, ... is 8.

https://brainly.com/question/32555331

#SPJ2

The common ratio of the geometric sequence -1, -8, -64, ... is -8, which results from dividing any term of the sequence by its preceding term.

Geometric sequence: -1, -8, -64, ...

Common ratio:

To find the common ratio, we divide each term by its preceding term.

In this case, -8 ÷ (-1) = 8 and -64 ÷ (-8) = 8.

Therefore, the common ratio is 8.

Answer:

Step-by-step explanation:

The distance of point A from the top of the pole that will make the pole be  perpendicular position to the ground

so, for the pole to be in perpendicular position it must obey Pythagorean theorem

Then, using Pythagoras theorem

c² = a² + b²

x² = 10² + 6²

x² = 100 + 36

x² = 136

x = √136

x = 11.662ft

To nearest tenth

x = 11.7 ft.

So, the pole must be at a distance of 11.7 ft from the top of the pole to point A.

To justify,

10 font long board and an 18 foot long board. To make the ramp right triangle. How long should ramp

So, to calculate the ramp, which is the hypotenuse we will still apply Pythagorean theorem

Then, using Pythagoras theorem

c² = a² + b²

x² = 10² + 18²

x² = 100 + 324

x² = 424

x = √424

x = 20.59 ft

To nearest tenth

x = 20.6 ft.

So, the ramp is 20.6 ft long

Jalen needs to measure 8 feet from point A to the base of the pole to set it perpendicularly to the ground.

To make the pole perpendicular to the ground, Jalen needs to measure the distance from point A to the base of the pole, which forms a right angle at point B.

Using the Pythagorean theorem: Distance AB = √((10)^2 - (6)^2) = √(100 - 36) = √64 = 8 feet.

Therefore, Jalen needs to measure 8 feet from point A to the base of the pole for it to be positioned perpendicularly.

Answer:

$91,749.04

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 2.3% into a decimal:

2.3% -> [tex]\frac{2.3}{100}[/tex] -> 0.023

Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:

[tex]A=65,000(1+\frac{0.023}{12})^{12(15)}[/tex]

[tex]A=91,749.04[/tex]

You will have $91,749.04 in 15 years.

Answer:

254.5 Inches Cubed

Step-by-step explanation:

Formula for Finding the Volume of a Cylinder: [tex]V=\pi r^2h[/tex]

The radius is 3 inches.

[tex]r=3[/tex]

The height is three times the radius.

Multiply the radius by three to get the height.

[tex]h=3*3\\h=9[/tex]

The height is 9 inches.

Use the formula to find the volume.

[tex]\pi (3)^29= \pi (9)9=81\pi[/tex]

The exact volume is 81[tex]\pi[/tex] inches cubed.

[tex]81 * \pi[/tex] ≈ 254.47

254.47 ≈ 254.5

The volume of the cylinder should be about 254.5 inches cubed.

Given:

In ΔPQR, ∠Q = 90°

PQ = 8 cm

QR = 15 cm and

PR = 17 cm

To find the value of ∠P.

Formula

By Trigonometric ratio we get,

[tex]tan \theta=\frac{opp}{adj}[/tex]

Now let us take ∠P = θ

With respect to θ, QR be the opposite side and PQ be the adjacent side.

So,

tan θ = [tex]\frac{QR}{PQ}[/tex]

tan θ = [tex]\frac{15}{8}[/tex]

θ = [tex]tan^{-1} (\frac{15}{8} )[/tex]

θ = 61.93° (approx)

Hence, the value of ∠P is 61.93° (approx).

Answer:

61.93°

Step-by-step explanation:

Using cosine law:

15² = 8² + 17² - 2(8)(17)cosP

225 = 353 - 272cosP

cosP = 8/17

P = 61.92751306

Answer: his pay for the 4th year is $1453.16

Step-by-step explanation:

The landlord raises the rent 1.25% each year. It means that the rent is increasing in geometric progression.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = $1,400

r = 1 + 1.25/100 = 1.0125

n = 4 years

The 4th term(year), T4 is

T4 = 1400 × 1.0125^(4 - 1)

T4 = 1400 × 1.0125^3

T4 = $1453.16

Using an exponential function, the rent Joe will have to pay for the fourth year, with a 1.25% annual increase, is approximately $1,453.38.

To calculate the rent Joe will have to pay for the fourth year of living in the apartment with an annual rent increase of 1.25%, we will use an exponential function. The general formula for compounded growth is given by:

Future Value = Present Value ×(1 + rate)number of periods

In Joe's case, the Present Value is the initial monthly rent of $1,400, the rate is 1.25% or 0.0125 when expressed as a decimal, and the number of periods is 3 years since we are calculating the rent at the start of the fourth year. Plugging these values into the formula:

Rent for the fourth year = $1,400 × (1 + 0.0125)3

Let's calculate that:

Rent for the fourth year = $1,400 × (1.0125)3

Rent for the fourth year approximately = $1,400 × 1.038128

$1,453.38

Hence, Joe will have to pay about $1,453.38 for the fourth year of rent.

Hello.

The angle shown for 1 (and 3) is ∠40.

A straight line is shown, which is 180°. So the measure of ∠4 is 140°

Answer:

7*4

14*2

Step-by-step explanation:

Answer:

Answers will vary

Step-by-step explanation:

There are many possibilities, especially if you're going beyond whole numbers, meaning decimals work as well

Whole numbers

1 and 28

2 and 14

4 and 7

Decimals

3 and 9.33 or 9 1/3

5 and 5.6

6 and 4.67 or 4 2/3

8 and 3.5

9 and 3.11

10 and 2.8

These are just a few simple ones, it gets even more complicated if you have two numbers both with decimals

Answer:

30.10

Step-by-step explanation:

Answer:

$45,000

Step-by-step explanation:

Let Kevin's Salary=x

Ethan's Salary=$34,200.

Since Ethan is earning a salary that is 28% lower than the salary of Kevin.

Ethan is earning (100-24)%=76% of Kevin's Salary.

76% of Kevin's Salary=$34,200.

0.76x=34200

Divide both sides by 0.76

x=45000

Kevin's Salary is $45,000.

Answer:

horizontal and vertical

Step-by-step explanation:

if its the plus?

Answer:

360 miles

Step-by-step explanation:

15 times 8= 120 miles I. September

Times 3 in August=360 miles

Answer:

1.25 m.

Step-by-step explanation:

Given,

Area of base = 1.2 m²

Number of gold fish = 6

Density of the tank should be = 4 fish/m³

Height of the tank= ?

4 fish = 1 m³

6 fish = 1.5 m³

Volume required for 6 fish is 1.5 m³

V = area of base x height

1.5 = 1.2 x h

h = 1.25 m

Hence, height of the tank is equal to 1.25 m.

Answer:

1.25

Step-by-step explanation:

Step-by-step explanation:

Simple

If Amelia is 10 years old and so half of Amelia age = 5

Caleb is 2 years more so = 5 + 2 = 7

It means Caleb age = 7

And Amelia age = 10

From the information given, the area of the circle is: "113 sq. cm".

The formula to find the area of a circle is πr².

Using the side as the radius of the circle, we can calculate the area of the base area.

Note;

r = 6

Thus,

A = π * 6²

A = (22/7) * 36

A = 3.14285714286 * 36

Hence, The area of the circle A = 113.142857143 or 113 sq. cm.

Learn more about the area of a circle;

brainly.com/question/14068861

#SPJ5

Answer:

  y = 1/8(x -2)^2 -1

Step-by-step explanation:

The vertex form of the equation of a parabola can be written as ...

  y = (1/(4p))(x -h)^2 +k

for vertex (h, k) and vertex-to-directrix distance p. Here, the vertex has a y-value of -1, and the directrix has a y-value of -3, so the distance between them is -1 -(-3) = 2, and the desired equation with vertex (2, -1) is ...

  y = 1/8(x -2)^2 -1

_____

Comment on the graph

One description of a parabola is that it is the locus of points equidistant from the focus and the directrix. I like to show that a point on the parabola (not the vertex) meets that requirement. That is what the dashed orange lines are for in the diagram. You can easily see that each has length 4.

Answer:

The coffee Leah has left in percentage is 68.18%

Step-by-step explanation:

Given data

Total available coffee = 22 ounces

Amount She took out = 7 ounces

Let us carry out a simple subtraction arithmetic to find out the remainder

Hence remaining coffee = 22-7= 15

To expressing the remainder as a percentage we have

(15/22)*100=0.6818*100

= 68.1818%

To the nearest hundredths we have

= 68.18%

Answer: 68.18%

Step-by-step explanation:

Leah has a 22 ounce coffee and she drinks 7 ounces of the coffee. This means she will have:

22 - 7 = 15 ounces left.

The percentage of ounces of coffee Leah has left of her coffee will be the number of ounces left divided by the total number of ounces of coffee multiplied by 100. This will be:

= 15/22 × 100

= 0.6818 × 100

= 68.18%

The percentage of coffee Leah has left is 68.18%.

Answer:

8.75 per hour

you would put the overall money earned and divide it by how many hours he worked

example:

87.50 ÷ 10 = 8.75

Answer:

2.67 ounce of cashews are in the mix.

Step-by-step explanation:

Since we are dealing with a 32 ounce bag of mixed nuts and 1/12 of this bag is cashews (1/12 of the mix),

Then:

1/12 × 32 ounce = The actual quantity of cashew nuts in the mix.

= 1/12 × 32

= 32/12

= 2.67 ounce of cashews are in the bag.

Answer:

2.666ounce is contained in the bag

Step-by-step explanation:

Given that 32 ounce of bag has mixed nuts of which 1/12 of this bag contain cashews.

(1/12 of the entire mix),

Hence,

1/12 × 32 ounce

= 1/12 × 32

= 32/12

= 2.666ounce of cashews are in the bag.

Answer:

Median = 42  pounds

Step-by-step explanation:

It is given that the following are the weights,in pounds, of some dogs at a kennel: 36,45,29,39,51,49.

Arrange the data in ascending order.

29, 36, 39, 45, 49, 51

Total number of terms = 6 (even)

So, the formula for median is

[tex]Median=\dfrac{\frac{n}{2}\text{th term}+(\frac{n}{2}+1)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{\frac{6}{2}\text{th term}+(\frac{6}{2}+1)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{3\text{rd term}+4\text{th term}}{2}[/tex]

[tex]Median=\dfrac{39+45}{2}[/tex]

[tex]Median=42[/tex]

Hence, the median weight is 42 pounds.

To find the median, units of the data should be same. If one of the weights were given in kilograms, then we cannot find median.

Answer: the school paid $80 for the book.

Step-by-step explanation:

Let x represent the amount that the school paid for the book.

Her school charges a lost book fee equal to 75% of the cost of the book. It means that the amount that the school would charge on a book that cost $x is

75/100 × x = 0.75 × x = 0.75x

Sarah received a notice stating that she owed the school $60 for he lost book. It means that

0.75x = 60

x = 60/0.75

x = $80

Answer:

coefficient

Step by-step explanation:

Answer:

The correct answer is 2 inches.

Step-by-step explanation:

Let l inches and w inches be the length and width of a rectangle respectively.

According to the given problem, l - 8 = [tex]\frac{w}{2}[/tex].

Area of the rectangle is given to be, according to the question, 18 square inches.

Thus l × w = 18

⇒ l × (2l - 16) = 18

⇒ 2 [tex]l^{2}[/tex] - 16l - 18 = 0

⇒  [tex]l^{2}[/tex] - 8l - 9 = 0

⇒ ( l - 9) ( l + 1) = 0

The possible values of l are 9 and -1. As the length cannot be equal to -1, thus the value of the length is 9 inches.

Width of the rectangle is 2 inches.

Answer:

14 /3- fraction

(Decimal: 4.666667)

Step-by-step explanation:

The value of the numerical expression is 26

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the expression be A = (2/5)^2 • 100 ÷ 2/3 + [2^4 ÷ (13 - 5)]

Now , on simplifying the equation , we get

A = ( 2/5 )² x 100 / ( 2/3 ) + [ 2⁴ / 8 ]

A = ( 4/25 ) x ( 100 x 3 ) / 2 + 2

So , the equation will be

A = 4/25 x ( 300/2 ) + 2

A = 4/25 x 150 + 2

A = 4 x 6 + 2

A = 24 + 2

A = 26

Therefore , the value of A is 26

Hence , The value of the numerical expression is 26

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ2

Answer:

a. f(x) is continuous for all real numbers

Step-by-step explanation:

At x = 1

Piece 1:

f(x) = 1² + 4 = 5

Piece 2:

f(x) = 1 + 4 = 5

First piece ends at (1,5)

Second piece starts at (1,5)

So no discontinuity

Answer:

I would say add it up

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct answer would be C - h(x) = f(x) + g(x). The total cost for serving everyone at the barbecue would consist of adding the cost of both the buns and turkey burgers.

Answer: point B should be the 2nd number on the number line.

Step-by-step explanation:

the answer is shove it up your  whole

hAHA JK ITS B