My math teacher,mr.numeric, went to the auto show last weekend. I made the mistake of asking him what he saw.here was his response: I’m glad you asked. I made several interesting observations. As you might have guessed, every red car was a sports car, but I found it odd that half of all the blue cars were sports cars. Interestingly, a salesman told me that half of all the sports cars were red. I counted 40 blue cars and 30 red cars. Now can you tell me how many sports cars were neither blue nor red?

Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean  Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 =  

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean  2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to  of the values.

Therefore, Scores between 72 and 90 =  

= 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 =  

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

Step-by-step explanation:

It is found that score of 62 is not within one standard deviation of the mean.

The Z-score measures how many standard deviations the measure is from the mean. If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have  [tex]X \sim N(\mu, \sigma)[/tex]then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

In a set with mean and standard deviation, the z- score of a measure X is given by:

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

Z-score, we look at the z-score table and find the p-value associated with this z-score.

Given that Mean score of 54 and a standard deviation of 6.

This means to see if a score of 62 is within one standard deviation of the mean.

Is Z between -1 and 1 when X = 62.

[tex]Z = \dfrac{X - \mu}{\sigma},\\Z = \dfrac{62 - 54}{6},[/tex]

Z = 1.33

Therefore, It is found that score of 62 is not within one standard deviation of the mean.

Learn more about z-score here:

https://brainly.com/question/21262765

#SPJ2

Answer:

-0.21428571428

Answer:

Negative 5 and 7 over 8

Step-by-step explanation:

Answer:

Negative 5 and StartFraction 7 over 8

Step-by-step explanation:

Answer:

0.45576

Step-by-step explanation:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Standard Deviation = √variance

Mean = 50

= √9

= 3

z = 51 - 50/3

= 0.11111

Probability value from Z-Table:

P(x<51) = 0.54424

P(x>51) = 1 - P(x<51)

= 1 - 0.54424

= 0.45576

The probability that the dealer will sell 51 or more cars is 0.45576

Answer:

Sophia is not correct

Step-by-step explanation:

The given situation represent the problem of a ratio and it is predicted to do the simplify the ratio by determining the smallest possible values

Here it can be presented 60:36 as a fraction i.e. [tex]\frac{60}{36}[/tex]

Now the fraction should be fall by dividing both the numerator and denominator by a common factor i.e. 6

Now after dividing it, the fraction would be [tex]\frac{10}{6}[/tex]

Now it can be further reduced by a common factor i.e. 2

So now the fraction is [tex]\frac{5}{2}[/tex]

Thus, the ratio is 5:2

Hence, she is not correct

Answer:

x=22

Step-by-step explanation:

180-77=103

103+55=158

180-158=22

x=22

Answer:

Question 1: 20,160 cookies

Question 2: 37,600 letters

Question 3: 252,396 squares on each tablecloth

Question 4: 138,762 points

Question 5: 4,652,352 shrimp

Step-by-step explanation:

Question 1: Multiply 315 and 64 to get amount of cookies

Question 2: Multiply 940 and 40 to get the number of letters

Question 3: Multiply 36 and 7,011

Question 4: Multiply 26 and 5,337 to get the number of points

Question 5: Multiply 96 and 48,462 to get the number of shrimp the chef prepared.

:)

Answer:

11/132 = 1/12

Step-by-step explanation:

just put the rise over the run and simplify

Answer:

1050 fish

Step-by-step explanation:

175(6 tanks) = 1050

Answer:

Pole of Inaccessibility

Answer:

true

Step-by-step explanation:

Your arms would be the line and your body would be the y-axis, and your arms are on either side of the y-axis which means your body is the line of reflection

Hope this helps.

Answer:

y+5 = -0.7 (x-1)

Step-by-step explanation:

m = (change in y) / (change in x) = (2-(-5)) / (-9-1) = 7 / (-10) = -0.7

Answer: See attachment

Step-by-step explanation:

The journal entry for Dilbert has-been prepared and attached. The journal entry shows the transaction that was done by Dilbert on a March 1st.

Check the attachment for the entry.

Answer:

The correct answer is -3

Step-by-step explanation:

attached is a number line to show diagrammatically how to count five units from the chosen point to point 2 on a number line.

Moving five units from -3 to 2 on a number line is given as follows:

-3 ⇒ -2 ⇒ -1 ⇒ 0 ⇒ 1 ⇒ 2

From the motion expression shown above, moving from -3 to 2 involves moving 5 units.

another way of determining the correct answer is to find the difference in interval between the two points as shown below:

Let the point be x

2 - x = 5 units

2 - 5 = x

∴ x = -3

Answer:

-3

Step-by-step explanation:

it was on quiz baby

Answer:

The jar contains 156 grams of zinc

Step-by-step explanation:

Ratios

Let's call

Z=gr of zinc

C=gr of copper

We know the ratio between them in a certain chemical is:

[tex]\displaystyle \frac{Z}{C}=\frac{4}{17}[/tex]

The jar of the chemical contains C=663 gr of copper. Calculate the grams of zinc by solving the above relation for Z:

Multiplying by C:

[tex]\displaystyle Z=\frac{4}{17}\cdot C[/tex]

Substituting the value of C:

[tex]\displaystyle Z=\frac{4}{17}\cdot 663[/tex]

Z=156 gr

The jar contains 156 grams of zinc

Answer:

80

Step-by-step explanation:

use the formula of arithmetic progression

Answer:

freeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

trump 20202020202020020202020

Answer:

The 98% confidence interval of the proportion = (0.312, 0.374)

Step-by-step explanation:

(Give answers accurate to 3 decimal places.)

The formula for Confidence Interval of Proportion is given as:

p ± z × √p(1 - p)/n

Where p = Proportion = x/n

x = 440

n = 1282

p = 440/1282 = 0.34321372854

Approximately = 0.343

z = z-score of 98 % confidence interval

= 2.326

Confidence Interval =

= 0.343 ± 2.326 × √0.343(1 - 0.343)/1282

= 0.343 ± 2.326 × √0.225351/1282

= 0.343 ± 2.326 × √0.00017578081

= 0.343 ± 2.326 × 0.01325823555

= 0.343 ± 0.03083865589

0.343 - 0.03083865589

= 0.31216134411

Approximately = 0.312

0.343 + 0.03083865589

= 0.37383865589

Approximately to = 0.374

Therefore, the 98% confidence interval of the proportion = (0.312, 0.374)

Answer:

9 1/66

Step-by-step explanation:

9 x 1 is 9 so its that but to add more proof the problem is 9 1/6, 1 1/11 multiply 6 and 11 it is 66 so the answer is 9 1/66

Answer:

30 pages

Step-by-step explanation:

Knowing she wrote 12 pages in 4 hours, we can do 12/4 to get 3 pages per hour. Multiply 3 pages by the 6 hours she spends writing and you get 18 pages in 6 hours. Add 12 pages and 18 pages and you have 30 pages.

Answer:

-24

Step-by-step explanation:

If you are struggling with this here's a tip!

-18+-6 is what you are trying to solve

The 6 is negative, so get rid of the plus sign -18-6

2 negative numbers are just added like positive numbers

So add 18 and 6, you should get 24

Don't forget about the negative!

-24

Answer:

a

[tex]N = 7.0 *10^{44} \ Ways [/tex]

b

[tex]U  = 2.85 *10^{26}\  ways [/tex]

Step-by-step explanation:

From the question we are told that

   The number of students are  n =  100

    The number of dormitories  is  k =  3

    The capacity of the first dormitory is  A =  25

     The capacity of the second dormitory is  B =  35

      The capacity of the third dormitory is  c =  40

Generally the number of way to fill the dormitory up is mathematically represented as

      [tex]N  =  \frac{n!}{A! B!C!}[/tex]

=>   [tex]N  =  \frac{100!}{25! 35! 40!}[/tex]

Here ! stands for factorial, so we will be making use of the factorial functionality in our calculators to  evaluated the above equation

=>   [tex]N  =  \frac{100!}{25! 35! 40!}[/tex]

[tex]N = \frac{9.332622* 10^{157}}{[1.551121* 10^{25}]* [1.0333148* 10^{40}] * [8.1591528*10^{47}]}[/tex]

[tex]N = 7.0 *10^{44} \ Ways [/tex]

From the question we are told that there are 50 men and  50  women and

     A is  all-men's dorm and  B is all-women's dorm while C is co-ed

So

When A is filled , the number of men that will be remaining to fill dorm C is  50-25 = 25

While when B is filled the number of women that will be remaining to fill dorm C is   50-35 = 15

Generally the number of ways there to fill the dormitories is equivalent to the number of ways of selecting the 25 men and 35 women to fill dormitory A and B plus one more way which is filling dorm C with the remaining students this is  mathematically represented as  

       [tex]U  =  ^{50}C_{35} * ^{50}C_{25}  +  1[/tex]

Here C stands for combination hence we will be making use of the combination functionality in our calculators

     [tex]U  = 2.250829575* ^{12}  * 1.264106064 * 10^{14} +  1[/tex]

=>    [tex]U  = 2.85 *10^{26}\  ways [/tex]

Answer: 10.2272727273

Step-by-step explanation:

Answer:

Each class = 225 glue sticks

22 classes = 225*25  

                   = 5625 glue sticks

Answer:

$8.85

Step-by-step explanation:

Step-by-step explanation: well if you take 23.60 and divide it by 8 you would get 2.95 times that by three and you would get 8.85 and there's your answer.

Answer:

7.35    

because my kid got the question wrong              

Answer:

The leading coefficient is 3

Step-by-step explanation:

Polynomials

Given the roots of a polynomial x1,x2,x3, it can be expressed as:

[tex]p(x)=a(x-x1)(x-x2)(x-x3)[/tex]

Where a is the leading coefficient.

We are given the roots x1=-6, x2=7i, x3=-7i, thus:

[tex]p(x)=a(x+6)(x-7i)(x+7i)[/tex]

Operating the product of the conjugated imaginary roots:

[tex]p(x)=a(x+6)(x^2+49)[/tex]

Knowing p(2)=1,272 we can find the value of a

[tex]p(2)=a(2+6)(4+49)=1,272[/tex]

Operating:

[tex]a(8)(53)=1,272[/tex]

[tex]424a=1,272[/tex]

Solving:

[tex]a=1,272/424[/tex]

a=3

The leading coefficient is 3

Answer:

3

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

use rise over run, from (-6,0) to (0,3) it rises 3 and runs 6. 3/6 = 1/2.

Answer:

the slope is two

Step-by-step explanation:

rise over run

Answer:

1

Step-by-step explanation:

1.26