Susan made $208 miles in 13 hours. At the same rate, how many hours would she have to work to make $114​

Answer:

We want to expand the expression:

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

We can just do it by brute force, this is:

First, rewrite our expression as the product of two square factors:

[tex](x - \frac{1}{x^2} )^4 = (x - \frac{1}{x^2} )^2*(x - \frac{1}{x^2} )^2[/tex]

Now we can expand each one these two factors:

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

That can be simplified to

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

Now we can replace that in our original expression to get:

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

Now we can expand that last product, to get:

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

We can simplify that to:

[tex]x^4 - 4x + 2x^2 - \frac{4}{x^5} + \frac{4}{x^2} + \frac{1}{x^8}[/tex]

That is the expanded expression.

Answer:

98

Step-by-step explanation:

The absolute value of a number different from 0 is always positive

- * - = +

15 + 83 = 98

Answer:

15 pounds of plaster

Step-by-step explanation:

First, convert ounces to pounds.

In 1 pound, there are 16 ounces. Create a proportion to convert 12 ounces to pounds.

[tex]\frac{1}{16}[/tex] = [tex]\frac{x}{12}[/tex]

Cross multiply and solve for x:

16x = 12

x = 0.75

So, each student will need 0.75 pounds of plaster. Multiply this by 20 to find the total amount the teacher will need:

20(0.75)

= 15

So, the teacher will need 15 pounds of plaster

Answer:

15 pounds

Step-by-step explanation:

Answer:

x = -15,46 thì y ≈ 34,46

x = 2,46 thì y ≈ 16,54

Step-by-step explanation:

x + y = 19 => x = 19 - y (1)

thay x = 19 -y vào phương trình 11x + x^2 = 2y ta có:

11 * (19 - y) + (19 - y)^2 =2y

=> 209 - 11y + 361 - 38y + y^2 = 2y

=> y^2 - 51y + 570 = 0

=> y ≈ 34,46 và y≈16,54

thay y ≈ 34,46 vào phương trình (1) có:

x = 19 - 34,46 = -15,46

thay y ≈ 16,54 vào phương trình (1) có:

x = 19 - 16,54 = 2,46

Answer:

Step-by-step explanation:

11x+x^2= 2y

Y + x = 19

Multiply and re-arrange second equation:

2y = 38 - 2x

Substitute into first equation:

11x + x^2 = 38 - 2x

Re-arrange:

x^2 + 13x - 38 = 0

Solve using quadratic formula:

x = (-13+(13^2-4*(-38))^(1/2))/2 or (-13-(13^2-4*(-38))^(1/2))/2

x = 2.46 or -15.46

Substitute back to solve for y:

y = 19 - 2.46 or 19 + 15..46

y= 16.54 or 34.46

Answer:

The answer is:

0.18

0.92

0.15

1.80

Answer:

17 and 32

Step-by-step explanation:

x + (x + 15) = 49

2x + 15 = 49

2x = 34

x = 17

x + 15 = 32

Answer:

think it's the last one

Step-by-step explanation:

sorry if i'm wrong

Answer:

A. 3 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Answer:

Mean will be affected.

Step-by-step explanation:

The mean value of the data set will be affected as it depends on the magnitude of data points and not its position. The median however will not change since it depends on the relative position of data points.

Answer:

x = 3.2

Step-by-step explanation:

Since they are similar the ratio of the side lengths must be the same

Using the bottom side and the unknown side from the left figure and the right figure

5            4

----- = --------

4            x

Using cross products

5x = 4*4

5x = 16

Divide by 5

x = 16/5

x =3.2

Answer:

30 years

Step-by-step explanation:

Given data

P=$17,000

A= $41,000

R=2.95%

the expressio for the time is

t= ln(A/P)/r

t= ln(41,000 /17000)/0.0295

t= ln(2.41176)/0.0295

t= 0.8803/0.0295

t= 29.8

about 30 years

Answer:

x=3

Step-by-step explanation:

Log base 5 of 125=x

that is equal to 5x5x5 which is 125

5 is multiplied 3 times so x is 3

Answer:

C. 16oz container

Step-by-step explanation:

I can explain my answer in the comments if needed, but C is the correct answer :)

Answer:

x = -1

y = 6

Step-by-step explanation:

We can multiply the second equation by two, so we can have opposite y terms:

2 (3x - 2y = -15)

6x - 4y = -30

Now, we can add the equations, and the y terms can cancel out:

  7x + 4y = 17

+ 6x - 4y = -30

13x = -13

x = -1

Now, we can plug in x:

3(-1) - 2y = -15

-3 - 2y = -15

-2y = -12

y = 6

9514 1404 393

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relationships between triangle sides and trig functions. These abbreviations tell you that ...

  Sin = Opposite/Hypotenuse   ⇒   sin(x) = b/c

  Cos = Adjacent/Hypotenuse   ⇒   cos(x) = a/c

  Tan = Opposite/Adjacent   ⇒   tan(x) = b/a

Answer:

Step-by-step explanation:

25+125+(-5x)=180 degree(sum of interior angles of a triangle is 180 degree)

150-5x=180

-5x=180-150

x=30/-5

x=-6

Answer:

0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.

88.54% of shoppers are expected to spend between $30 and 80 per week.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of $50 and a standard deviation of $15.

This means that [tex]\mu = 50, \sigma = 15[/tex]

Find the probability that any shopper selected at random spends more than $80 per week?

This is 1 subtracted by the p-value of Z when X = 80. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 50}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.

Find the percentage of shoppers who are expected to spend between $30 and 80 per week?

The proportion is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 30.

X = 80

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 50}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 30

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 50}{15}[/tex]

[tex]Z = -1.33[/tex]

[tex]Z = -1.33[/tex] has a p-value of 0.0918

0.9772 - 0.0918 = 0.8854

0.8854*100% = 88.54%

88.54% of shoppers are expected to spend between $30 and 80 per week.

Answer:

[tex]C=25^{\circ},\\a\approx 10.72,\\b\approx 11.83[/tex]

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be [tex]180-90-65=25^{\circ}[/tex].

In any triangle, the Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex].

Therefore, we have:

[tex]\frac{\sin 90^{\circ}}{b}=\frac{\sin 25^{\circ}}{5},\\\\b=\frac{5\sin90^{\circ}}{\sin 25^{\circ}}=11.8310079158\approx \boxed{11.83}[/tex]

[tex]\frac{a}{\sin 65^{\circ}}=\frac{5}{\sin25^{\circ}},\\a=\frac{5\sin 65^{\circ}}{\sin25^{\circ}}=10.7225346025\approx \boxed{10.72}[/tex]

The required value of P would be 64 for the given linear relationship.

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

Given that P varies inversely with the square of Q

P = k/Q²

As per the question, if Q is 8 and P is 9,

So 9 = k/8²

⇒ 9 = k/64

Apply cross-multiplication operation,

⇒ k = 576

If Q is 3, then

⇒ P = 576/3²

⇒ P = 576/9

Apply division operation, and we get

⇒ P = 64

Thus, the required value of P would be 64.

Learn about the linear relationship here :

https://brainly.com/question/11663530

#SPJ2

Answer: 72x(elevated 4)y(elevated 3)

Step-by-step explanation:

4xy(2x2y)(3xy)(3)

Answer:

The sample size should be:

c. 204

Step-by-step explanation:

This is based on the assumption that in this campus, there are no more than 2040 students.  The sample size should be around 10% of the population, which is considered a good representative of the real population for the specific study.  If, however, the population is so large that 10% of the population will be more than 1,000, then the sample size should be limited to 1,000.

Answer:

see explanation

Step-by-step explanation:

Given

x² , then when x = - 4

x² = - 4 × - 4 = + 16

[ the product of a negative and a negative results in a positive ]

Answer:

153.93804 in^2

Step-by-step explanation:

Area = radius^2 π = 7^2 π = 153,93804 in^2

Answer:

[tex]area = \pi \: r \:^{2} \\ = \pi(7) ^{2} \\ = 153.938 \: in ^{2} [/tex]

Answer:

-40% change

Step-by-step explanation:

9514 1404 393

Answer:

  x = 48

Step-by-step explanation:

The sum of the angles in a pentagon is 540°, so you have ...

  90° +100° +110° +2x° +3x° = 540°

  5x = 240 . . . . . . . divide by °, subtract 300

  x = 48 . . . . . . . . . divide by 5

_____

Additional comment

The sum of angles in a convex n-gon is (n -2)×180°. For a pentagon, that's 3×180° = 540°.

Answer:

15.9 units

Step-by-step explanation:

use the pathagorean theorem to find x.

a^2 + b^2 = c^2

6^2 + b^2 = 17^2

36 + b^2 = 289

-36             -36

[tex]\sqrt{b^{2} }[/tex]= [tex]\sqrt{253}[/tex]

b = 15.90597372

b = 15.9

Answer:

π in²

Step-by-step explanation:

We'll begin by calculating the radius of the circle. This can be obtained:

Area of sector (A) = 4π in²

Angle (θ) = 120 °

Radius (r) =?

The radius of the circle can be obtained by using the formula for calculating the area of a sector. This is illustrated below:

A = θ/360 × πr²

4π = 120/360 × πr²

4π = ⅓ × πr²

Cross multiply

3 × 4π = πr²

12π = πr²

Divide both side by π

r² = 12π / π

r² = 12

Take the square root of both side

r = √12 in

Thus, the radius is √12 in.

Finally, we shall determine the area of the sector created by 30 °. This can be obtained as follow:

Radius (r) = √12 in

Angle (θ) = 30 °

Area of sector (A) = ?

A = θ/360 × πr²

A = 30/360 × π(√12)²

A = 1/12 × 12π

A = π in²

Therefore, the area of the sector created by 30 ° us π in².

Answer:

I got ya :D

the answer is

[tex] \binom{ - 18 \: \: \: 10 }{5 \: \: \: - 3} [/tex]

explanation in the attachment