Jill would like an increase in the hourly wage she receives from the Mathematics Research Center, where she works in the mail room. Her boss gives her an equation to solve, telling her that her raise is the solution to the equation, but only if she can solve it. The equation is x 2- 6x + 9 = 0. What was the amount of her raise per hour? Answer:

Answers

Answer 1

Answer:

Jill will receive an increase of $3 per hour

Step-by-step explanation:

The Quadratic Equation

The quadratic equation can be represented in the standard form as:

[tex]ax^2+bx+c=0[/tex]

being a,b, and c are constants.

It can be solved by using the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Jill would like an increase in her hourly wage. The increase will come as the solution for a maths equation.

She must solve the equation:

[tex]x^2-6x+9=0[/tex]

The solution to the equation, or value of x, is the increase in her hourly wage.

Comparing with the general form, we have a=1, b=-6, c=9. Thus, the solutions are:

[tex]\displaystyle x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(9)}}{2(1)}[/tex]

[tex]\displaystyle x=\frac{6\pm \sqrt{36-36}}{2}[/tex]

[tex]\displaystyle x=\frac{6\pm \sqrt{0}}{2}[/tex]

The square root is 0, therefore is only one solution:

[tex]\displaystyle x=\frac{6}{2}=3[/tex]

x = 3

Thus, her raise per hour is $3.


Related Questions

A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
A. (195 - 286) + 1.992 underroot46/45 + 58/40
B. (286 - 195) + 1.992 underroot46^2/45+ 58^2/40
C. (195 - 286)+ 1.992 underrot 140² 158²/45+40
D. (286 - 195) + 1.992 46 1582 45 +40
E. (195-286) +1.992 462 + 58 45 40

Answers

Answer:

(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))

Step-by-step explanation:

Given that:

NEWER CARS:

Sample size = n1 = 45

Standard deviation s1 = 46

Mean = m1 = 195

OLDER CARS:

Sample size = n2 = 40

Standard DEVIATION s2 = 58

Mean = m2 = 286

Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025

Confidence interval is calculated thus : (newer--older)

(m1 - m2) ± Tcritical * standard error

Mean difference = m1 - m2; (195 - 286)

Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)

Standard error (E) = sqrt((s1²/n1) + (s2²/n2))

E = sqrt((46^2/45) + (58^2/40))

Hence, confidence interval:

(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))

The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:

[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]

Given that:

The first sample consists of owners of newer cars

First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]

The second sample consists of owner of older cars.

Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:

95% confidence interval for difference between both samples' means.

Calculations and Explanations:

Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.

The CI is given as:

[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]

For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)

Thus,

[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]

Learn more about confidence interval here:

https://brainly.com/question/4249560

What is the solution to the equation x + 14 = 63? (Input a whole number only.) (3 points)

Answers

The answer is:

Substitute 49 for x

49 + 14 = 63

Hope this helps!

Answer:

49

Step-by-step explanation:

49 + 14 = 63

so that means:

x = 49

A music store marks up the instruments it sells by 30%.
If the price tag on a trumpet says $104, how much did the store pay for it?

Answers

A. $ 58.50

B. $ 80

C. No, it did not mark up 30%.

Step-by-step explanation:Since,

A. We have,

Mark up percentage = 30%

Actual price = $ 45,

B. We have,

SP = $ 104,

C.  We have,

AP = $ 75,

SP = $100,

Thus, mark up percentage =

= 33.33 %

Hence, store did not mark up the price by 30%.

What is an advantage to using debt snowball method

Answers

Answer:The advantage of the debt snowball is that it helps build motivation for debt repayment. The debt snowball method involves paying off the smallest debts first to get them out of the way before moving on to bigger ones. It's not easy to get excited about debt repayment.

Step-by-step explanation:

Advantages of the debt snowball method The primary advantage of the snowball method is the psychological boost. When you see debts disappearing, it can increase your motivation to continue paying off debt. And even if you’ve only paid off a small balance, your confidence in the progress you’re making grows.



Find the Lateral Area
A triangular prism and its dimensions are shown in the diagram.
5 cm
5 cm
8 cm
6 cm
What is the lateral surface area of this triangular prism in square centimeters?

Answers

Answer:

? please explain

Step-by-step explanation:

Answer:128 I think is the answer

Step-by-step explanation:

plz help !!!!! complete the function tables then graph

Answers

Answer:

Step-by-step explanation:

Given the function f(x) = 3|x - 2| + 6, for what values of x is f(x) = 18?
O x = -2, x = -8
O x = -2, x = -6
O x = -2, x = 6
O x = -2, x = 8

Answers

When x = -2, x = 6 is the answer.

please help asap please​

Answers

Answer:

abcdefghijklmnopqrstuvwxyz

Step-by-step explanation:

if x =20 and y =40 then x and y are

Answers

Answer:

Are directly proportional

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?

Answers

Answer

a. 0.856

b. 0.78071

c. It is not unusual

d. 13.65 years old

Step-by-step explanation:

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.

We solve this question using z score formula:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

a. Find the probability that a cat will live to be older than 14 years.

For x > 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x<14) = 0.144

P(x>14) = 1 - P(x<14) = 0.856

b. Find the probability that a cat will live between 14 and 18 years.

For x = 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x = 14) = 0.144

For x = 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x = 18) = 0.92471

The probability that a cat will live between 14 and 18 years is calculated as:

P(x = 18) - P(x = 14)

0.92471 - 0.144

= 0.78071

c. If a cat lives to be over 18 years, would that be unusual? Why or why not?

For x > 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x<18) = 0.92471

P(x>18) = 1 - P(x<18) = 0.075288

Converting this to percentage:

0.075288 × 100 = 7.5288%

Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.

d. How old would a cat have to be to be older than 90% of other cats?

From the question above, 10% of the cats would be older than 90% of other cats.

Hence, we find the z score of the 10th percentile

= -1.282

Hence,

-1.282 = x - 15.7/1.6

Cross Multiply

-1.282 × 1.6 = x - 15.7

- 2.0512 = x - 15.7

x = 15.7 -2.0512

x = 13.6488 years old

Approximately = 13.65 years old

Solve for a .

5.4 = a - (-1.8)


a =

Answers

5.4=a+1.8
5.4-1.8=a
a=3.6

Answer:

3.6 = a

Step-by-step explanation:

5.4 = a - ( -1.8)

Distribute minus sign.

5.4 = a + 1.8

Move constant to the left hand side and change their sign.

5.4 - 1.8 = a

3.6 = a

Mrs. Matthews wrote three math expressions on the board.



She asked her students which expression would result in a product greater than 7.

Enter the number of the expression that Mrs. Matthews's students should have chosen.
Expression
will result in a product greater than 7.

Answers

Answer:

expression 3

because expression 1 = 1

and expression 2 = 7

A school janitor has mopped
1/3 of a classroom in 5 minutes. At what rate is he mopping?

Answers

Answer:

1/3 of the school in 5 minutes or in 15 minutes he will mop the whole entire school.

Step-by-step explanation:

Answer:  1/15 of a classroom per minute

=================================================

Work Shown:

1/3 of a classroom = 5 minutes

3*(1/3 of a classroom) = 3*5 minutes

1 classroom = 15 minutes

It takes the janitor 15 minutes to mop a full classroom.

The rate is expressed in units of classrooms per minute. This means we'll need to divide both sides by 15 to get

1 classroom = 15 minutes

1/15 classroom = 15/15 minutes

1/15 of a classroom = 1 minute

The janitor's rate is 1/15 of a classroom per minute.

PLZ HELP
Do the ones you know!

Answers

the first one in the top is 180 degrees so 8(15) and 8x15=120 so x on the other side is 60.

You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.015. Can you be confident that your predicted value will be reasonably close to the actual value?

a. Yes, because the correlation is close to zero, it is strong.
b. Yes, No, because the correlation is close to zero, it is strong.
c. No, because the correlation is close to zero, it is weak.
d. No, because the correlation is negative, it is weak.

Answers

Answer:

Following are the solution to this question:

Step-by-step explanation:

For this set, the correlation coefficient is = -0.015.

It shows that financial variables have trust issues. Once a price rises, the other one is decreasing the value of -0,015 shows, that there are several fewer associations in the set of data among x and y and between y values. This interaction also can range between -1 to 1, to 0 being completely unrelated. But you'd never be sure, in this situation, 0.015 is very similar to 0.

It means that your prediction is nothing better than just a wild choice. Its odds of an estimated value being relatively close to the actual result are therefore much smaller as the points are it's hardly the best match.

If U is the set of all multiples of 3 less than 20, and M={3,12,18}, find Mc (the complement of M). Express your answer as a set in the roster form: i.e. {a,b,c...}.

Answers

Answer:

Step-by-step explanation:

U={3,6,9,12,15,18}

M={3,12,18}

M'={6,9,15}

The answer is,

U={3,6,9,12,15,18}

M={3,12,18}

M'={6,9,15}

What is set?

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

here. given that,

U is the set of all multiples of 3 less than 20,

i.e. U={3,6,9,12,15,18}

and M={3,12,18},

Mc (the complement of M),

i.e. M'={6,9,15}.

Hence, we get, U={3,6,9,12,15,18} ,  M={3,12,18} & M'={6,9,15}.

To learn more on set click:

https://brainly.com/question/4801204

#SPJ2

Rewrite the logarithm log8(2) as an exponential expression then find the value of the logarithm

Answers

Answer:

exponential expression:

8ᵇ = 2

log8(2) = 0.333333333 or 1/3

Answer:

log8(2) = 1/3

Step-by-step explanation:

I don't know if they mean this by an exponential expression but:

set x = log8(2), then

8^x = 8^(log8(2))

By logarithmic properties:

8^x = 2.

notice that 8 = 2^3.

By exponential properties:

8^x = (2^3)^x = 2^(3x)

So 2^(3x) = 2 = 2^1.

Comparing exponents gives:

3x = 1 <=> x = 1/3.

So log8(2) = 1/3.

1) What is the constant of proportionality that relates y to x
х
Y
8
6
20
15
28
21
a. 1.33
6,48
0.0.75
b. 14
f

Answers

Answer:  The Answer Is A Because if u just add the numbers then divide them

A USB stick can store 1.1x10 power of 3
megabytes of data.
A hard drive can store 4x10 power of 4
megabytes of data.
How much more can the hard drive store?
Give your answer in standard form

Answers

Answer:

uhhh

Step-by-step explanation:

Answer:

3.82 x 10

Step-by-step explanation:

divide 4 x 10^4 by 1.1 x 10^3

4 divided by 1.1 is 3.81818181... and you subtract exponents to get 1

-5b = -20 b= need help with homwork

Answers

Answer:

b = 4

Step-by-step explanation:

you must divide both sides of the equation by -5 to get b by itself. division cancels out multiplication but also keeps both sides equal

b = -20/-5

b = 4

the answer is b=4
hope this helped

Solve for x in the diagram shown.
A) 2.67
B) 4.5
C)5.625
D) 34.375

Answers

Answer: C

Step-by-step explanation:

2. Which of the following is the correct value of (0.22) - (0.4)? Show your reasoning. c. 0.088 d. 0.0088 w​

Answers

Answer:

C

Step-by-step explanation:

there would have to be one more zero between 0 and 8 for both of them

Pls help me with this ASAP

Answers

The answer is the first option, 3/1

Help help help help help help pls

Answers

Answer:

a.) 36

b.) 18

c.) 27

Step-by-step explanation:

The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:

C = 5 over 9(F − 32)

The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:

C = 5 over 9(F − 32)
Which of the following formulas correctly solves for F?

F = 9 over 5C + 32
F = 9 over 5C − 32
F = 9C + 32 over 5
F = 9C − 32 over 5

Answers

Answer:

F = 9 over 5C + 32

Step-by-step explanation:

Let's consider the following equation that shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F.

C = 5 over 9(F − 32)

C = 5/9 (F − 32)

To solve for F, first, we will multiply both sides by 9/5.

C × 9/5 = 5/9 (F − 32) × 9/5

9/5 C = F − 32

Now, we add 32 to both sides.

9/5 C + 32 = F − 32 + 32

9/5 C + 32 = F

F = 9 over 5C + 32

Answer:

F = 9 over 5C + 32

Step-by-step explanation:

I'm stuck with this question​

Answers

Answer:

Store A = 3.17

Store B = 3.25

Step-by-step explanation:

Hope this helps!

gyiftuerdtgyuhijovhfghdfgchbnm,

Answers

i’m pretty sure the answer is A:

A. 5/16

because 1/4 of 1 1/4 is 0.3125 which is 5/16 as a fraction.

0.3125 = 5/16

What’s the area? Please help :)

Answers

Answer:

252 sq. in.

Step-by-step explanation:

divide it into sections like this

12*15=180

3*6=18

6*9=54

then add it all together. sometimes it is more complicated, but as long as none of the divided parts overlap this will be correct for any shape, as long as you account for the whole shape.

The equation y - 3x - 5 = 0 when written in slope-intercept form is:
y = 3x - 5.
y=-3x + 5.
O y = 3x + 5.

Answers

Answer:

y = 3x + 5

Step-by-step explanation:

The zero seems to be a place holder to mess you up. Just ignore that it doesn't do anything. Add -3x and -5 to the both sides to create y = 3x + 5

I need help with like 3 or 4 questions please help

Answers

Answer:

x=3y-6

Step-by-step explanation:

x−3y=−6

Step 1: Add 3y to both sides.

x−3y+3y=−6+3y

x=3y−6

Answer:

x=3y−6

Anwser x=3y-6
That is the anwser trust me
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