Find m2. The diagram is not to scale.
770
270
a
76
b
104

С C
103
86

Answer:

[tex]Mean = 68.9[/tex]

[tex]s^2 =18.1[/tex] --- Variance

Step-by-step explanation:

Given

[tex]\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}[/tex]

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

[tex]x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5[/tex]

For 59 - 66

[tex]x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5[/tex]

For 67 - 74

[tex]x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5[/tex]

For 75 - 82

[tex]x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5[/tex]

For 83 - 90

[tex]x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5[/tex]

So, the table becomes:

[tex]\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}[/tex]

The mean is then calculated as:

[tex]Mean = \frac{\sum fx}{\sum f}[/tex]

[tex]Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}[/tex]

[tex]Mean = \frac{2547.5}{37}[/tex]

[tex]Mean = 68.9[/tex] -- approximated

Solving (b): The sample variance:

This is calculated as:

[tex]s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}[/tex]

So, we have:

[tex]s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}[/tex]

[tex]s^2 =\frac{652.8}{36}[/tex]

[tex]s^2 =18.1[/tex] -- approximated

Answer:

15. 12

Step-by-step explanation:

just multiply them

Answer:

n=-18

Step-by-step explanation:

subtract 8 from both sides.

then you do -10 subtracted by 8 and thats -18.

Answer:

40

Step-by-step explanation:

A rhombus diagonals form perpendicular angles. It also bisects and form 4 right triangles. Looking at triangle MAS, we can use pythagorean theorem to find the side MA.

[tex]ms {}^{2} + sa {}^{2} = {ma}^{2} [/tex]

ms=6, sa =8 so we plug that in.

[tex]6 {}^{2} + {8}^{2} = ma {}^{2} [/tex]

Simplify

[tex]36 + 64 = ma {}^{2} [/tex]

[tex]100 = ma {}^{2} [/tex]

take sqr root

[tex] \sqrt{100} = ma[/tex]

[tex]ma = 10[/tex]

Now let find the perimeter

Since perimeter of a Rhombus is 4a where a is the length of a side. We plug it in

[tex]4(10) = 40[/tex]

The answer is 40

Answer:

Hello your question is poorly written below is the complete question

An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. If The number of claims filed has a Poisson distribution. Compute the variance of the number of claims filed. You can use, without a proof, what is the variance of a Poisson distribution is equal to its mean

answer : variance = 2

Step-by-step explanation:

compute the variance of the number of claims filed

x = number of claim filed

For Poisson distribution

mean = variance = Л

∴ Variance = 2

Answer:

3)x=−9  and x=4

4)x=−12  and x=−5

5)x=8  and x=14

6)x=−7  and x=3

7)x=-1 2/3 and x = 1/4

8)x=2/5

Step-by-step explanation:

Hope this helps

Answer:

45 cups

Step-by-step explanation:

Answer:

b= -15

Step-by-step explanation:

First combine like terms 9-16= -7

Left 3b-7= -52

Next add 7 to both sides

Left 3b= -45

Finally divide

So b= -15

Answer:

3

Step-by-step explanation:

30 + 18 = 48

5 + 3 = 8, 6 x 8 = 48

If this was helpful vote brainliest :)

Answer:

Step-by-step explanation:

Adjacent angles when a line crosses another line must have a sum of 180 degrees.

52+2^(3x+1)=180

2^(3x+1)=128, 128=2^7 so

2^(3x+1)=2^7 which means

3x+1=7

3x=6

x=2

Answer:

3.53

Step-by-step explanation:

I checked it using a calculator. :)

Answer:

its the second one bc if u multiply 8.34 times 5305 it equals to 44243.7 the diameter of the pool was jus to throw u off it was unneeded information.

Step-by-step explanation:

Answer:

Rounded to whole numbers, if he slept for 33% of the year, he slept for a total of 4 months.

Step-by-step explanation:

Given that in a year there are a total of twelve months, if he slept for 33% of the year, to determine how many months are spent sleeping the following calculation must be performed:

12 - (12 x 33/100) = X

12 - (12 x 0.33) = X

12 - 3.96 = X

8.04 = X

12 - 8.04 = 3.96

Thus, rounded to whole numbers, if he slept for 33% of the year, he slept for a total of 4 months.

Answer:

20

Step-by-step explanation:

reasoning; you can see that all three of them form a 180 angle so you add 125+35 which is 160 then 180- 160 which is 20 that is the answer

hope it helps!

pls give brainliest

Answer:

10

Step-by-step explanation:

-7y + 35 + 8 = -27

collect like terms

-7y = -27 - 35 - 8

-7y = -70

y= -70/-7

y= 10

Answer:

10x+30

Step-by-step explanation:

Distributive property is distributing what is in the parentheses.

To do that on this problem you have multiply each of these numbers by 10!

10 times x is 10x

10 times 3 is 30

Put them back together and you get 10x+30!

I hope this helps, and have a great day! :)

P.S. If you need a better explanation I can help. I just didn't want to make this to long.  :D

Answer:

286 minutes

Step-by-step explanation:

can you give brainlest or good review

Answer:

Hello!

Let's call X to the number of minutes of long-distance calls you plan to make.

The cost of plan A is given by 25%2B0.05X

The cost of plan B is given by 5%2B0.12X

Plan B is advantageous when its cost is lower than plan A's. Therefore, we set the inequality

5%2B0.12X+%3C+25%2B0.05X

And then solve for X. This will give us the range of minutes for which B is more convenient.

Subtract 5 from both sides of the inequality to get:

0.12X+%3C+20%2B0.05X

Now subtract 0.05X:

0.12X+-+0.05X+%3C+20

0.07X%3C20

Finally, divide by 0.07 to get:

X+%3C+20%2F0.07

X++%3C+285.71

So plan B is advantageous if you plan to use less than 286 minutes of long distance calls.

I hope this helps!

Step-by-step explanation:

The selling price should be $88

Given that,

= $55 + (60% of $55)

= $55 + $33

= $88

Learn more about the price here: https://brainly.com/question/25300841?referrer=searchResults

Answer:

88

Step-by-step explanation:

Answer:

Should be $11.25

Step-by-step explanation:

Since 25% is 1/4 you can just divide 45 by 4.

45/4 = 11.25

Answer: 33.75. 25% of 45 is 11.25. So 45-11.25=33.75

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

You can use cross multiply.

8x = 6 x 4

8x = 24

x = 3

Answer:

x = 3

Step-by-step explanation:

Multiply x by 8 to get 8x

Multiply 6 by 4 to get 24

Place 8x and 24 into an equation to get 8x = 24

Divide 8x and 24 by 8

The 8 from 8x is canceled out, leaving the answer:

x = 3

Answer and Step-by-step explanation: This function is a probability density function of a random variable X:

[tex]f(x)=\frac{3(8x-x^{2})}{256}[/tex]

and to calculate probabilities, we will have to integrate it:

[tex]P(X<x)=\int\limits^x_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

Solving:

[tex]P(X<x)=\frac{3}{256}(4x^{2}-\frac{x^{3}}{3} )[/tex]

Then:

a. P(X < 5)

[tex]P(X<5)=\int\limits^5_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]P(X<5)=\frac{3}{256}(100-\frac{125}{3} )[/tex]

[tex]P(X<5)=\frac{3}{256}(\frac{300-125}{3} )[/tex]

[tex]P(X<5)=\frac{175}{256}[/tex]

P(X < 5) = 0.683

b. P(X < 9)

Since density function's upper limit is 8, probability of x < 9 is 100% or 1.

So, P(X < 9) = 1

c. P(5 < X < 7)

[tex]P(5<X<7)=\int\limits^7_5 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]P(5<X<7)=\frac{3}{256}[4(7)^{2}-\frac{7^{3}}{3}-4(5)^{2}+\frac{5^{3}}{3}][/tex]

[tex]P(5<X<7)=\frac{3}{256}[96-\frac{218}{3} ][/tex]

[tex]P(5<X<7)=\frac{70}{256}[/tex]

P(5 < X < 7) = 0.273

d. P(X > 3)

[tex]P(X>3)=\int\limits^8_3 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]P(X>3)=\frac{3}{256}[256-\frac{512}{3}-36+9 ][/tex]

[tex]P(X>3)=\frac{3}{256}(229-\frac{512}{3} )[/tex]

[tex]P(X>3)=\frac{175}{256}[/tex]

P (X > 3) = 0.683

e. P(X < x) = 0.95

[tex]0.95=\int\limits^x_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]

[tex]\frac{3}{256}[\frac{12x^{2}-x^{3}}{3} ] =0.95[/tex]

[tex]\frac{12x^{2}-x^{3}}{256}=0.95[/tex]

[tex]12x^{2}-x^{3}=243.2[/tex]

[tex]-x^{3}+12x^{2}-243.2=0[/tex]

Solving this cubic equation, we have three values for x:

x₁ = -3.909

x₂ = 8.992

x₃ = 6.917

The value of x will the one between 0 and 8, which are the limits of the function. So, value of x which gives a probability of 0.95 is x = 6.917.

Answer:

84

Step-by-step explanation:

7-5=2

2u-> 14

1u->7

7+5=12

12u-> 84

Answer:

boy=5  girls=7 + 14= 21 girls

Step-by-step explanation:

Answer:

he is the answer

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

25 7 x 5 is 35

Step-by-step explanation:

hope this helps have a good rest of your afternoon :) ❤

Answer:

5 times 5 is 25.

Step-by-step explanation:

Hope this helps you dude

s h r e k (in a maid outfit)

Answer:

8 ounces

Step-by-step explanation:

Since there was 1 pint left, that means the mug had 1/2 pints of coffee.

Now, convert this to ounces. There are 16 ounces in a pint, so we can find how many ounces there were by multiplying 16 by 1/2

16(1/2)

= 8

So, there were 8 ounces of coffee in the mug

Answer:

No they are equivalent

Step-by-step explanation:

3/7 =21/35

3/5=21/35

Answer:

no

Step-by-step explanation:

find a common denominator we are going to do 35

3/7= 15/35

3/5= 21/35