Evaluate the following.​

Answer:

9 and 11  

Step-by-step explanation:

First number = x -2

Second number = x

  and   2x = 3(x-2)  - 5

            2x = 3x - 6 - 5

             x = 11

              first number = 11-2 = 9

Using it's concept, the desired probability is:

P(Female|Junior) = 75%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 8 Junior Students, out of which 6 are Female, hence the probability is:

P(Female|Junior) = 6/8 = 0.75 = 75%.

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The value of x in the given expression is; x = wz/y

We are given the expression;

w/x = y/z

Now, we want to find the value of x which means we want to make x the subject of the formula. Thus;

Multiply both sides of the given expression by x to get;

(w/x)*x = (y/z)*x

⇒ w = xy/z

Now, multiply both sides by z/y to get;

w(z/y) = (xy/z) * (z/y)

wz/y = x

Thus, the value of x in the given expression is;

x = wz/y

The correct question is;

If w/x = y/z, then what is the value of x

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Answer: B

Step-by-step explanation:

The area of entire rectangle is (9)(4)=36.

The area of the square inside is [tex]x(x)=x^2[/tex]

Subtracting the areas, we get [tex]36-x^2[/tex]

the price that they should charge on the 2 year extended warranty is in order to break even is $10.

the price at which the company would breakeven is:

= percentage of product that will fail x replacement cost

solving gives:

= 4% x 250

= $10

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Answer:

AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle

The cost of 45 packets of instant noodles given the direct variation is $52.335

let

n = k × p

k = constant of proportionality

34.88 = k × 30

34.88 = 30k

k = 34.88/30

k = 1.16266666666666

Approximately,

k = 1.163

Find n when p = 45

n = k × p

= 1.163 × 45

n = $52.335

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Hello !

Look at the picture

The simplified expression of [tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex] is [tex]\frac{8a}{a^8 - 1}[/tex]

The expression is given as:

[tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Add the first two terms

[tex]\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate the first two terms

[tex]\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}[/tex]

Take the LCM

[tex]\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}[/tex]

Evaluate the like terms

[tex]\frac{8a}{a^8 - 1}[/tex]

Hence, the simplified expression is [tex]\frac{8a}{a^8 - 1}[/tex]

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Using proportions, it is found that the coordinate that is not marked is given by:

c. 3

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

There are 6 congruent segments between -2 and 10, hence the length of each segment is given by:

l = (10 - (-2))/6 = 2.

Then the points are: -2, 0, 2, 4, 6, 8, 10. 3 is not marked, hence option c is correct.

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Answer:

5

Step-by-step explanation:

2 × 2 = 4

3× 3 = 9

4 × 4 =16

5 × 5 =25

16 is the only number and closest number to 21 to subtract from

Answer:

any # where -2<=x<7

Step-by-step explanation:

(x-7) would be negative and (x+3) positive, resulting in f(x) being negative.

Answer:

D

Step-by-step explanation:

to determine the relationship between these two lines you have to find the slope.

=> if they have the same slope ,then they are parallel.

=> if they have negative inverse slope relative to each other ,then they are perpendicular.

=> if the slope for both equations is neither of the above cases ,then the two equations are neither parallel nor perpendicular.

so if we divide the first equation by 3 which is the commen factor for the whole equation and arrange it in the form y=mx +b it would give us y =5x +4. and since the two have the same slope which is 5 ,then we can conclude they are parallel lines.

Answer:

If the x-6 is all under the sqrt, the last answer is right:

6<= x <= infinity

If only x is under the sqrt and - 6 is NOT under the sqrt, then:

0 <= x <= infinity is the correct answer.

Step-by-step explanation:

You can look at the equation and or graph to determine the domain of a function. The domain is all the x's that may go into the equation or all the x's on the graph of the function. Inside of a squareroot symbol the number inside there must be positive. While considering the equation, only x's that keep that inside positive can be used.

For sqrt(x-6), x has to be 6 or bigger.

For sqrt(x) - 6, x has to be 0 or bigger.

Answer: None

Step-by-step explanation:

There is no triangle with an angle measure of 0 degrees.

Answer:

0.026

Step-by-step explanation:

Twenty-Six = 26 ( But for simplicity in the Next Step write it as 26.)

Then Twenty-Six Thousandths = 0.026

For the given systems we have:

1) Just swap the equations in system A.

2) Yes, the systems are equivalent.

Here we have the systems:

A:

-3x - 2y = 4

5x - 8y = -1

B:

5x - y = -1

-3x - 2y = 4

Notice that we have the same equations, just in a different order. So if we swap the first and second equations in system A, we get system B.

Are the systems equivalent?

Yes, because both systems are defined by the same equations.

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The number of minutes Samantha needs to run on Friday to reach her goal is 45 minutes.

Average = (Monday + Tuesday + Wednesday + Thursday + Friday) / 5

40 = (45 + 30 + 55 + 25 + x) / 5

40 × 5 = 155 + x

200 = 155 + x

200 - 155 = x

45 = x

x = 45 minutes

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Answer:

C. 29

Step-by-step explanation:

[tex]f(x) = -3x^3 + 2x^2 +24[/tex]

• To calculate [tex]f(-1)[/tex] , we have to replace x with -1 in the definition of [tex]f(x)[/tex] , and calculate the value:

[tex]f(-1) = -3(-1)^3 + 2(-1)^2 + 24[/tex]

         ⇒ [tex]-3(-1) +2(1) + 24[/tex]

         ⇒ [tex]3 + 2 + 24[/tex]

         ⇒ [tex]29[/tex]

[tex]\huge\boxed{\textsf{C.}\ 29}[/tex]

We have this equation:

[tex]f(x)=-3x^3+2x^2+24[/tex]

Substitute [tex]x=-1[/tex]:

[tex]f(-1)=-3(-1)^3+2(-1)^2+24[/tex]

Simplify to find the final answer:

[tex]\begin{aligned}f(-1)&=-3(-1)+2(1)+24\\&=3+2+24\\&=5+24\\&=\boxed{29}\end{aligned}[/tex]

Step-by-step explanation:

to be a tangent, it would have to have a 90° angle with the radius (12).

and that would make the triangle ABCenter of the circle a right-angled triangle.

and then Pythagoras must apply :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle). in our case the 20-line.

so,

20² = 12² + 16²

400 = 144 + 256 = 400

yes, it is confirmed, because the Pythagoras principle applies, it is a right-angled triangle, and therefore AB is indeed a tangent.

Answer:

the line AB is tangent to the circle

Step-by-step explanation:

we have :

16² + 12² = 256 +144 = 400

On the other hand:

20² = 400

Then

16² + 12² = 20²

Then

According to the Pythagorean theorem:

The line AB is perpendicular to the radius of the circle

Which means the line AB is tangent to the circle.

The graph of the inequality can be seen in the image at the end.

Here we have the inequality:

y ≥ 4x - 3

To graph this we need to graph the line:

y = 4x - 3

With a solid line (because the points on the line are solutions) and then shade the region above that line.

The graph of the inequality can be seen below.

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Step-by-step explanation:

Answer

a - 8

------------+

2

Answer:

50%

Step-by-step explanation:

In rhe beginning, there were 24 + 20 = 44 students trying out in total. After a week, there are 44 - 6 - 2 = 36 students remaining. Of those 36 students, 18 of them are trying out for the basketball team. The percentage of students trying out for the basketball team would be 18/36 = 0.5 = 50%

Answer:

1/100

Step-by-step explanation:

The answer is 1/100 because we don't know how many people are in the group but do know that only 1 person has been taken from the group and the probability will be 1 out of how many people are in the group so we just put 100 there as we don't know how many people are in the group.

Ps: Sorry if this is wrong, this is just a guess.

Hello,

    9k - 2  88

⇔ 9k - 2 + 2 ≥ 88 + 2

⇔ 9k ≥ 90

⇔ 9k/9 ≥ 90/9

⇔ k ≥ 10

S = [10 ; + ∞ [

Answer:

k ≥ 10

Step-by-step explanation:

9k - 2 ≥ 88

Step 1 : Add 2 on both sides.

9k - 2 + 2 ≥ 88 + 2

9k + 0 ≥ 90

9k ≥ 90

Step 2 : Divide 9 on both sides.

9k/9 ≥ 90/9

k ≥ 10

Using the Empirical Rule, it is found that 49.85% of buyers paid between $150,000 and $154,800.

It states that, for a normally distributed random variable:

Considering the given mean and standard deviation, the interval between $150,000 and $154,800 corresponds to the interval between the mean and 3 standard deviations above the mean.

The normal distribution is symmetric(50% above the mean, 50% below), hence the percentage corresponding to this interval is:

P = 0.5 x 99.7% = 49.85%.

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Answer:

156 : 48

Step-by-step explanation:

Solution:

Since

169 : 52 = 156 : X

Then we know

52/169 = X/156

Multiplying both sides by 156 cancels on the right

156 × (52/169) = (X/156) × 156

156 × (52/169) = X

Then solving for X

X = 156 × (52/169)

X = 48

Therefore

169 : 52 = 156 : 48