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.
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.
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.
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?
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
I'm stuck with this question
Answer:
Store A = 3.17
Store B = 3.25
Step-by-step explanation:
Hope this helps!
The equation y - 3x - 5 = 0 when written in slope-intercept form is:
y = 3x - 5.
y=-3x + 5.
O y = 3x + 5.
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
Solve for x in the diagram shown.
A) 2.67
B) 4.5
C)5.625
D) 34.375
Answer: C
Step-by-step explanation:
gyiftuerdtgyuhijovhfghdfgchbnm,
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
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
Answer: The Answer Is A Because if u just add the numbers then divide them
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.
Answer:
expression 3
because expression 1 = 1
and expression 2 = 7
Rewrite the logarithm log8(2) as an exponential expression then find the value of the logarithm
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.
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...}.
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}.
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-5b = -20 b= need help with homwork
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
please help asap please
Answer:
abcdefghijklmnopqrstuvwxyz
Step-by-step explanation:
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?
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%.
2. Which of the following is the correct value of (0.22) - (0.4)? Show your reasoning. c. 0.088 d. 0.0088 w
Answer:
C
Step-by-step explanation:
there would have to be one more zero between 0 and 8 for both of them
Solve for a .
5.4 = a - (-1.8)
a =
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
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
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:
What is an advantage to using debt snowball method
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.
plz help !!!!! complete the function tables then graph
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
if x =20 and y =40 then x and y are
Answer:
Are directly proportional
Pls help me with this ASAP
What is the solution to the equation x + 14 = 63? (Input a whole number only.) (3 points)
Answer:
49
Step-by-step explanation:
49 + 14 = 63
so that means:
x = 49
What’s the area? Please help :)
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.
A school janitor has mopped
1/3 of a classroom in 5 minutes. At what rate is he mopping?
Answer:
1/3 of the school in 5 minutes or in 15 minutes he will mop the whole entire school.
Step-by-step explanation:
=================================================
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.
Help help help help help help pls
Answer:
a.) 36
b.) 18
c.) 27
Step-by-step explanation:
I need help with like 3 or 4 questions please help
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
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?
Answer:
? please explain
Step-by-step explanation:
Answer:128 I think is the answer
Step-by-step explanation:
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
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
PLZ HELP
Do the ones you know!
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
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]
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