What are the medians for the height and weight distribution, respectively?

Answer:

[tex] \large{ \boxed{ \tt{ - 20a {z}^{2} - 2 {z}^{3} - 2 {a}^{3} + 11 {a}^{2} z }}}[/tex]

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The measure of angle A is 144.3 degrees and the angle to cut the molding is 54.3 degrees

Start by solving the acute part of angle A using the following sine function

sin(Ax) = (30 - 4)/32

Evaluate the quotient

sin(Ax) = 0.8125

Take the arc sin of both sides

Ax = 54.3

The measure of angle A is then calculated as:

A = 90 + Ax

This gives

A = 90 + 54.3

Evaluate

A = 144.3

Hence, the measure of angle A is 144.3 degrees

In (a), we have:

Ax = 54.3

This represents the angle where the molding would be cut

Hence, the angle to cut the molding is 54.3 degrees

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Step-by-step explanation:

1825%

and percentage means 100

so 1825/100=73/4

Answer:

75

Step-by-step explanation:

Step-by-step explanation:

f(x) = x2-7x+10

f(x) = -5x+10 = -5(x-2)

= 10-5x

Let, f(x) = 0

0 = 10-5x

5x = 10

x = 2

f(2) = 10 - 10 = 0

f(5) = 10-5(5) = 10-25 = -15

Let, f(y) = f(x)

= 10-5x

y = -0

So, the correct answer is I. (- , 2) ✔✔

The 8% of us states have names that start with the letter w the answer is 8%.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The complete question is:

Of the 50 us states 4 have names that start with the letter w what percentage of us states have names that start with the letter w.

The percentage of the US states that have names that start with the letter W can be calculated:

Percentage = (No of US states starting with W/Total no of US states)×100

Percentage = (4/50)×100

Percentage = 8%

Thus, the 8% of us states have names that start with the letter w the answer is 8%.

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An interpretation of the relationship between the variables in this graph is that: C. you leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally, you continue at a slower (but constant) speed than before.

A graph can be defined as a type of chart which is used to graphically represent the relationship between the variables in a data set, on both the horizontal and vertical lines of a cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph attached in the image below, we can infer and logically deduce that an interpretation of the relationship between the variables in this graph is that you drove at a constant speed for 2 hours, and then stopped for 1 hour. Finally, you continued at a slower, but constant speed than before.

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Using the disk method, the volume of the solid is

[tex]\displaystyle \pi \int_3^8 \left(\dfrac1{2x-1}\right)^2 \, dx = \pi \int_3^8 \frac{dx}{(2x-1)^2}[/tex]

Substitute [tex]u = 2x-1[/tex] and [tex]du=2\,dx[/tex].

[tex]\displaystyle \pi \int_3^8 \frac{dx}{(2x-1)^2} = \frac\pi2 \int_5^{15} \frac{du}{u^2} \\\\ ~~~~~~~~ = -\frac\pi2 \frac1u \bigg|_5^{15} \\\\ ~~~~~~~~ = -\frac\pi2 \left(\frac1{15} - \frac15\right) = \boxed{\frac\pi{15}}[/tex]

1. 18

2.8

3.-1

An expression is a set of terms combined using the operations +, – , x or ,/.

Given:

1. 22 − 1 (4)

=22- 1*4

= 22-4

= 18

2. 2 + 2 (3)

=2+2*3

=2+6

=8

3. 1 − 2

= -1

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Answer:

248.00

Step-by-step explanation:

A = P(1 + rt)

A = the future value

P = the initial principal

r = annual interest rate (decimal)

t = the time in years

A=200(1+0.2*12)

Answer:

corresponding angles

Step-by-step explanation:

i dont cap

Answer:

19/20

Step-by-step explanation:

He got 4 incorrect, meaning he got 80-4 correct.

80-4 = 76.

Fraction = 76/80 = 38/40 = 19/20.

Answer:

19/20

Step-by-step explanation:

[tex]\frac{80-4}{80} =\frac{76}{80} =\frac{19}{20}[/tex]

Hope this helps

l don't know if you know it tell please

Answer:

C

Step-by-step explanation:

57+57+34=148

Answer:

Step-by-step explanation:

hello :

f(x) = -3x³ + x² - 3, find f(1).

f(1) = -3(1)³ +(1)² - 3=-3+1+3 = -5

The graph is shown in the attached image.

The midrange of the weekly salaries is $902.50.

Midrange is a measure of variation of a data set. Midrange is the mean of the lowest and highest salary.

Midrange + (lowest salary + highest salary) / 2

(692 + 1113) / 2 = $902.50

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1) given

2) given

3) Definition of linear pair

4) If alternate interior angles are congruent, then the lines are parallel.

a. The expression for profit is p(x) = -0.5x² + 40x - 300

b. The two values of x that will create a profit of $300 is 20 and 60

c. it is not possible for the company to make a profit of $15,000

The profit is the selling price minus the cost price.

Therefore,

Profit = revenue - cost

a.

The expression for profit is as follows;

p(x) = 90x − 0.5x² - (50x + 300)

p(x) = 90x − 0.5x²  - 50x - 300

p(x) = -0.5x² + 40x - 300

b.

The two values of x that will create a profit of $300 is as follows;

-0.5x² + 40x - 300 = 300

-0.5x² + 40x - 600 = 0

0.5x² - 40x + 600 = 0

x² - 80x + 1200 = 0

(x - 20)(x - 60)  = 0

x = 20 and 60

Therefore, the two value of x are 20 and 60

c.

-0.5x² + 40x - 300  = 15000

-0.5x² + 40x - 300 - 15000 = 0

-0.5x² + 40x - 15300 = 0

x² - 80x + 30600 = 0

There is no real solution. Therefore, it is not possible for the company to make a profit of $15,000

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Using the x-intercept concept, the function has x-intercept of 4 when c = -2.

The x-intercepts of a function are the values of x when y = 0.

In this problem, the function is:

cx - 5y + 8 = 0.

When y = 0, we have that:

cx + 8 = 0

x = 4, hence:

4c = -8

c = -2.

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Length of AB = 18. 92

Length of AC = 26. 15

Length of BC = 32. 552

Using the Pythagorean theorem, we have that

[tex](20 x-2)^2 = (12x + 20)^2 + (25x)^2[/tex]

Expand the bracket

[tex]400x^2- 4 = 144x^2 + 400 + 625x^2[/tex]

Collect like terms

[tex]400x^2 - 144x^2 - 625x^2 = 400 + 4[/tex]

[tex]-369x^2 = 404[/tex]

Make x^2 subject

[tex]x^2 = \frac{404}{369}[/tex]

[tex]x = \sqrt{1.0948}[/tex]

[tex]x = 1. 046[/tex]

Thus,

Length of AB = 20x -2 = 20(1. 046) - 2 = 18. 92

Length of AC = 25x = 25* 1.046 = 26. 15

Length of BC = 12x + 20 = 12(1. 046) + 20 = 32. 552

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The required value of function F(x), when x=18 is -2

A line of best fit is f(x) ≈ −0.86x + 13.5 for the set of points in the table
x     = 2   3   5   6  7  8  9
F(x) = 21  10 10  8  9  5  6

What is line?
line, is curve showing the shortest distance between 2 points.

Now, putting x = 18 in f(x) ≈ −0.86x + 13.5
f(x) ≈ −0.86(18) + 13.5

= -1.98
≅ -2 (approximation)

Thus, the required values of x=18 in a line of best fit is -2.

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Answer:

(y - x)/(y + x)

Step-by-step explanation:

(1/x - 1/y)/(1/x + 1/y) =

= (1/x - 1/y)/(1/x + 1/y) × (xy)/(xy)

= (y - x)/(y + x)

Answer:

9/20

Step-by-step explanation:

Total number of candies =60

Number of Green candies, n(G)=36

Number of candies with caramel, n(C)=45

Since the events are independent, the probability of selecting two candies where the first is green and the second has caramel is given by:

P(GC)=P(G) X P(C)

\begin{gathered}=\dfrac{n(G)}{n(S)} X \dfrac{n(C)}{n(S)} \\=\dfrac{36}{60} X \dfrac{45}{60}\\ =\dfrac{9}{20}\end{gathered}=n(S)n(G)Xn(S)n(C)=6036X6045=209

The probability in its lowest form is 9/20.

Answer:

Step-by-step explanation:

To find the total perimeter of the parallelogram we must add 200+200+150+150

This equals 700. Then, since squares have side lengths that are all equal, we have to divide by 4.

700 / 4 = 175

So, the length of a side of a square having this perimeter would be 175mm

Hope this helps!

Answer:

  1/4

Step-by-step explanation:

The inverse function tells you the input value that corresponds to the given output value of the function.

You want f^-1(3), which is the value of x such that f(x) = 3.

  f(x) = 3 = 4x +2

  1 = 4x . . . . . . subtract 2

  1/4 = x . . . . . divide by 4

The inverse function of 3 is 1/4:

  [tex]\boxed{f^{-1}(3)=\dfrac{1}{4}}[/tex]

Answer:

  80.7 mph

Step-by-step explanation:

In order to catch the car at the exit, the officer must cover the distance in 30 seconds less time than the car does. The time, speed, distance relation can be used.

The relation between time, speed, and distance is ...

  time = distance/speed

Here, speed is in miles per hour, and distance is in miles. That means time will be given in hours by the straightforward application of this formula.

  time = (3.6 mi)/(68 mi/h) = (3.6/68) h = 9/170 h

There are 3600 seconds in 1 hour, so 30 seconds represents this fraction of 1 hour:

  30/3600 = 1/120

The motorcycle will have this amount of time less than the time the car takes to reach the exit, so ...

  (9/170 -1/120) h = (9(120)-170)/(170×120) h = 910/20400 h = 91/2040 h

The speed required to cover 3.6 miles in 91/2040 hours is ...

  speed = distance/time

  (3.6 mi)/(91/2040 h) = 3.6×2040/91 mph = 7344/91 mph ≈ 80.7 mph

The officer's average speed in pursuit must be 80.7 miles per hour (or faster).

__

Additional comment

There are other ways the problem can be worked. One of them is to consider the remaining distance the car must travel when the officer begins pursuit. That will be 3.6 mi less (1/120 h)(68 mi/h) = 17/30 miles. The ratio of the officer's speed to the car's speed will be the same as the ratio of the officer's miles to the car's miles: 3.6/(3.6 -17/30) × 68 mph ≈ 80.7 mph.

Intermediate values used in the calculations should be kept at full calculator precision. Rounding should only be done at the end. Here, the actual speed required is 80.7032967... mph, rounded down for the above result.