Suppose the heights of the members of a population follow a normal distribution. If the mean height of the population is 68 inches and the standard deviation is 4 inches, 95% of the population will have a height within which of the following ranges?

Answer:

64.5A

Step-by-step explanation:

The x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.

To find the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4, we can use the slope formula:

slope = (change in y) / (change in x)

Given that the slope is -4 and the two points are (x, -9) and (0, 1), we can plug the values into the slope formula:

-4 = (-9 - 1) / (x - 0)

Now, simplify the equation:

-4 = -10 / x

Now, cross-multiply:

-4x = -10

Now, solve for x by dividing both sides by -4:

x = -10 / -4

x = 5/2

So, the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.

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4. -3

5. 3

4. For x > -2, the value of a is the slope of the line. The line goes down 3 units for each 1 to the right, so the slope is -3/1 = -3. Then a = -3.

___

5. The ordered pair (h, k) is typically used to name the point to which a function is translated. The vertex of the function f(x) = |x| is (0, 0). When it is translated to (h, k), the function becomes ...

... q(x) = |x -h| +k

If the new vertex is (3, 0), then h = 3 and k = 0. This is consistent with the equation shown. (k = 0 means q(x) = |x -h|.)

QUESTION 34

We want to find the variance of [tex]82,44,67,52,120[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{82+44+67+52+120}{5}[/tex]

[tex]\bar X =\frac{365}{5}[/tex]

[tex]\Rightarrow \bar X =73[/tex]

This means that,

[tex]\sigma^2=\frac{(82-73)^2+(44-73)^2+(67-73)^2+(52-73)^2+(52-73)^2+(120-73)^2}{5}[/tex]

This gives us,

[tex]\sigma^2=\frac{(9)^2+(-29)^2+(-6)^2+(-21)^2+(47)^2}{5}[/tex]

[tex]\sigma^2=\frac{81+841+36+441+2209}{5}[/tex]

[tex]\sigma^2=\frac{3608}{5}[/tex]

[tex]\sigma^2=721.6[/tex]

QUESTION 35

We want to find the variance of [tex]10,12,15,18,11,13,14,16,19,20[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{10+12+15+18+11+13+14+16+19+20}{10}[/tex]

[tex]\bar X =\frac{148}{10}[/tex]

[tex]\fRightarrow \bar X =14.8[/tex]

This means that,

[tex]\sigma^2 =\frac{(10-14.8)^2+(12-14.8)^2+(15-14.8)^2+(18-14.8)^2+(11-14.8)^2+(13-14.8)^2+(14-14.8)^2+(16-14.8)^2+(19-14.8)^2+(20-14.8)^2}{10}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-4.8)^2+(-2.8)^2+(0.2)^2+(3.2)^2+(-3.8)^2+(-1.8)^2+(-0.8)^2+(1.2)^2+(4.2)^2+(5.2)^2}{10}[/tex]

[tex]\sigma^2=\frac{23.04+7.84+0.04+10.24+14.44+3.24+0.64+1.44+17.64+27.04}{10}[/tex]

[tex]\sigma^2=\frac{105.6}{10}[/tex]

[tex]\sigma^2=10.56[/tex]

QUESTION 36

We want to find the variance of [tex]100,140,130,180,80,160[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{100+140+130+180+80+160}{6}[/tex]

[tex]\bar X =\frac{790}{6}[/tex]

[tex]\Rightarrow \bar X =131.67[/tex]

This means that,

[tex]\sigma^2=\frac{(100-131.6667)^2+(140-131.6667)^2+(130-131.6667)^2+(180-131.6667)^2+(80-131.6667)^2+(160-131.6667)^2}{6}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-31.6667)^2+(8.3333)^2+(-0.6667)^2+(48.3333)^2+(-51.6667)^2+(28.3333)^2}{6}[/tex]

[tex]\sigma^2=\frac{10325}{9}[/tex]

[tex]\sigma^2=1147.22[/tex]

To find the variance of a set of data, find the mean, subtract the mean from each data point, square the differences, and find the average of the squared differences. The standard deviation is the square root of the variance.

To find the variance of a set of data, follow these steps:

For the data set 82, 44, 67, 52, 120 (Question 34), the mean is 73, the squared differences are 81, 841, 36, 441, and 1849, and the average of the squared differences is 631.20, rounding to two decimal places.

For the data set 10, 12, 15, 18, 11, 13, 14, 16, 19, 20 (Question 35), the mean is 14.8, the squared differences are 23.04, 4.84, 0.64, 8.84, 12.96, 3.24, 1.44, 2.56, 19.36, and 29.16, and the average of the squared differences is 10.10, rounding to two decimal places.

To find the standard deviation of a set of data, take the square root of the variance. For the data set 100, 140, 130, 180, 80, 160 (Question 36), the variance is 9300, and the standard deviation is 96.49, rounding to two decimal places.

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Answer:B is the answer I think but I’m not sure sorry

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

There are 100 capsules and she can only buy 1/4

Multiply 100 * 1/4

100 * 1/4 =

100/4

25

We can check  by  calculating how many she leaves at the store

100 * 3/4 =

300 /4 = 75

The ones she bought , plus the ones she left behind should be 100 capsules

25+ 75 = 100

100 = 100

Check

Add up the expressions. Combine like terms wherever possible.

(f+g)(x) = f(x) + g(x)

(f+g)(x) = (x^2+10) + (x-3)

(f+g)(x) = x^2 + x + (10-3)

(f+g)(x) = x^2 + x + 7

Answer: Choice A

Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right by h units, then

 the new function g(x) = f(x - h)  

- If the function f(x) translated horizontally to the left by h units, then

 the new function g(x) = f(x + h)  

- If the function f(x) translated vertically up by k units, then the new

 function g(x) = f(x) + k  

- If the function f(x) translated vertically down by k units, then the

 new function g(x) = f(x) – k  

- A vertical stretching is the stretching of the graph away from the

 x-axis  

- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically  

 stretched by multiplying each of its y-coordinates by k.  

- A vertical compression is the squeezing of the graph toward  

 the x-axis.  

- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)

 vertically compressed by multiplying each of its y-coordinates by k.  

* Lets solve the problem

∵ f(x) = sin(x)

∵ f(x) is stretching vertically by a factor of 4

∴ f(x) multiplied by 4

∵ f(x) is shifting 3 units to the right

∴ We will change x to (x - 3)

∵ The new function is g(x)

∴ g(x) = 4 sin(x - 3)

- The attached graph for more understand

f(x) is the red graph

g(x) is the blue graph

Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

The given function is:

f(x) = sin(x)

Stretching by a factor of 4:

A vertical stretch or compression of f(x) can be expressed as:

cf(x), where c is any constant

if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.

Since, given function is being stretched by a factor of 4, the transformed function will become:

4f(x)

Shifting by 3 units right:

A shift of f(x) to right can be obtained by subtracting c from every occurrence of x in f(x) , where c is the number of units f(x) is being shifted in right direction. Since in this case f(x) is shifted 3 units to right, the transformed function will be:

f(x - 3)

Applying both the transformations to f(x), we get g(x) as:

g(x) = 4 f(x - 3)

g(x) = 4 sin(x - 3)

Answer:

(1,0)  (-2,-1)

Step-by-step explanation:

We need to find the midpoint of Segment BD

(-3,1) and (-1,-3)

the midpoint is (x1+x2)/2, (y1+y2)/2

                         (-3+-1)/2 , (1+-3)/2

                             -4/2  , -2/2

                                -2, -1

We need to find the midpoint of Segment cD

(3,3) and (-1,-3)

the midpoint is (x1+x2)/2, (y1+y2)/2

                         (3+-1)/2 , (3+-3)/2

                             2/2  , 0/2

                                1, 0

Answer:

45/63

Step-by-step explanation:

6 3/10=63/10,    4  1/2=45/10,

(45/10)/(63/10)=45/63

Answer:

x = 8

y = 1

Step-by-step explanation:

Slope = difference in y values / corresponding difference in x values

Slope =  (9 - 5) / (x - 10) = -2

-2x + 20 = 4

x = -16 / -2 = 8  (answer)

Question 4

(y - 6) /(1 - 2) = 5

y - 6 = -5

y = 1  (answer).

Answer:

-1  1/9 degrees Celsius

Step-by-step explanation:

Assuming we have 30 Fahrenheit, we need to plug it into the formula to find the degrees Celsius.

c=5/9 (f-32)

Substitute  f=30

c = 5/9 (30-32)

c = 5/9 (-2)

c = -10/9

c = -1 1/9 degrees Celsius

Answer:

32 houses will have a pool

Step-by-step explanation:

40% of 80 is 32

Answer:

a. -2, even mult. and 1, odd mult.

b.[tex](x+2)^2(x-1)[/tex]

c. Odd degree of 3 or higher, likely higher due to the turns in the graph.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -2,1

We can write them in intercept or factored form as (x-1) and (x+2).  

Because the graph never crosses the x-axis at x=-2 the zero has an even multiplicity of at least 2.  The opposite is true for x=1 because it crosses. Therefore it has an odd multiplicity of at least 1.

The graph is a sideways s shape and ends up so is positive.  

This means the function has a degree of 3 or higher with the degree being odd.

Answer:

The answer is A. 1 1/2

Step-by-step explanation:

You have 3 5/12  - 2 1/3

1/3 of 12 is 4.

So change 2 1/3 to 2 4/12

3 5/12 - 2 4/12 = 1 1/2

I hope this helps!

Cheers, July.

Answer: 173

Step-by-step explanation: 173 x 3 = 519. 520-173 = 347

Answer:

Approx. 48 cm

Step-by-step explanation:

The two horizontal sides of this parallelogram have length 12 cm each.

The length of one slanting side can be estimated by (eye:  the base of the triangle partially outlined with a dashed line is approx. 3 cm.  Then, using the Pyth. Thm., we estimate the hypotenuse of this triangle to be

sqrt(3^2 + 10^2), or sqrt(109), which is approx. 10.45.

Thus, the estimated perimeter is

P = 2L + 2W, which, here, is

P = 2(12 cm) + 2(10.45 cm), or 44.9 cm.

The fourth answer, 48 cm, is the one closest to this estimated 44.9 cm.

Answer:

-1< x< 3  x is an integer

Step-by-step explanation:

There are the dots on the number line.  Three points are represented

x= 0,1,2

We want an inequality

-1< x< 3  x is an integer

Answer:

Step-by-step explanation:

If ΔABC and ΔDEF are similar, then

AB is proportional to DE

BC is proportional to EF

CA is proportional to FD

and

angles A and D are congruent

angles B and E are congruent

angles C and F are congruent

Answer:

B.)Segment BC is proportional to segment EF, and angles A and D are congruent.

Step-by-step explanation:

Answer:

48/8=6 bags of chocolate chip cookies.

And 64/8=8 bags of vanilla wafer cookies.

8 bags.

Step-by-step explanation:

Linda is having a bake sale:

48 chocolate chip cookies and 64 vanilla wafer cookies to put in bags

She can fill the bag with same number of cookies and the same number of wafers in each bag

And condition is no wafers or cookies left over.

So, we will find the greatest common factor of 48 and 64  which is 8

Hence, she can fill 8 bags

And 48/8=6 bags of chocolate chip cookies.

And 64/8=8 bags of vanilla wafer cookies.

Answer:

Given two events A and B of a sample set :-

P[A] = 0.20  

P[not B]=0.40

[tex]P[B/A]=0.25[/tex]

To find P[A or B]:

[tex]P[A or B] = P[A] + P[B] - P[A \cap B][/tex]                ......[1]

Calculate for [tex]P[B][/tex] and [tex]P[A \cap B][/tex]

P[B] = 1- P[not B]

Substitute the value P[not B] we get;

P[B] = 1-0.40 = 0.60      

[tex]P[A \cap B] = P[B/A] \cdot P[A][/tex]

Substitute the given values we get;

[tex]P[A \cap B] = 0.25 \cdot 0.20 = 0.05[/tex]

Then;

[tex]P[A or B] = 0.20+0.60-0.05 = 0.80-0.05 =0.75[/tex]

Therefore, the value of P[A or B] is, 0.75.

The probability of P(A∪B) is 0.35.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Given

     P(A) = 0.20

     P(B) = 0.40

P(A∩B) = 0.25

The probability of P(A∪B).

We know the formula

P(A∪B) = P(A) + P(B) - (A∩B)

P(A∪B) = 0.20 + 0.40 - 0.25

P(A∪B) = 0.60 - 0.25

P(A∪B) = 0.35

Thus the probability of P(A∪B) is 0.35.

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[tex]f(x)=x^3+3x^2-10x-24\\\\y-intercept\ for\ x=0:\\\\f(0)=0^3+3(0)^2-10(0)-24=-24[/tex]

Answer:

The attached image shows he graph for given function.

Step-by-step explanation:

We are given the following expression in the question:

[tex]f(x) = x^3 + 3x^2-10x-24[/tex]

The zeroes of the given function can be calculated as:

[tex]x^3 + 3x^2-10x-24 = 0\\x = -4, x = -2, x=3[/tex]

Thus,the graph for the given function passes through the x-axis on the points (-4,0), (-2,0) and (3,0).

The function crosses the y-axis at the point (0,24)

The attached image shows the graph for given function.

Thus, the second option is the correct graph for given function.

Answer:

[tex]12\frac{1}{2}[/tex] hours.  

Step-by-step explanation:

We have been given that Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M.

Let us find the number of hours between 8:00 am to 1:00 pm.

There are 4 hours between 8:00 am to 12 noon and 1 hour from noon to 1:00 pm. So the total number of hours between 8:00 am to 1:00 pm is 5 hours.

Now let us find total number of hours worked by Phyllis Doran by adding 7 1/2 and 5.

[tex]\text{The total number of hours Doran worked}=7\frac{1}{2}+5[/tex]

[tex]\text{The total number of hours Doran worked}=12\frac{1}{2}[/tex]

Therefore, the total number of hours worked by Phyllis Doran is [tex]12\frac{1}{2}[/tex] hours.

Answer:i cant see it good

Step-by-step explanation:

Answer:

1 cm^2 = 100 mm^2

9 cm^2 = 900 mm^2

5.2 cm^2 = 520 mm^2

1 dm^2 = 100 cm^2

17 dm^2 = 1700 cm^2

4.3 dm^2 = 430 cm^2

1 m^2 = 10000 cm^2

7 m^2 = 70000 cm^2

2.5 m^2 = 25000 cm^2

1 km^2 = 1000000 m^2

50 km^2 = 50000000 m^2

8.5 km^2 = 8500000 m^2

Step-by-step explanation:

1 cm = 10 mm

1 [tex]cm^{2}[/tex] = 10×10 [tex]mm^{2}[/tex] = 100 [tex]mm^{2}[/tex]

9 [tex]cm^{2}[/tex] = 9×100 [tex]mm^{2}[/tex] = 900 [tex]mm^{2}[/tex]

5.2  [tex]cm^{2}[/tex] = 5.20×100 [tex]mm^{2}[/tex] = 520 [tex]mm^{2}[/tex]

1 dm = 10 cm

1 [tex]dm^{2}[/tex] = 10×10 [tex]cm^{2}[/tex] = 100 [tex]cm^{2}[/tex]

17 [tex]dm^{2}[/tex] = 17× 100 [tex]cm^{2}[/tex] = 1700 [tex]cm^{2}[/tex]

4.3 [tex]dm^{2}[/tex] = 4.3 × 100 [tex]cm^{2}[/tex] = 430 [tex]cm^{2}[/tex]

1 m = 100 cm

1 [tex]m^{2}[/tex] = 100×100 [tex]cm^{2}[/tex] = 10000 [tex]cm^{2}[/tex]

7 [tex]m^{2}[/tex] = 7×10000  [tex]cm^{2}[/tex] = 70000 [tex]cm^{2}[/tex]

2.5 [tex]m^{2}[/tex] = 2.5×10000 [tex]cm^{2}[/tex] = 25000 [tex]cm^{2}[/tex]

1 km = 1000 m

1 [tex]km^{2}[/tex] = 1000×1000 [tex]m^{2}[/tex] = 1000000 [tex]m^{2}[/tex]

50 [tex]km^{2}[/tex] = 50×1000000 [tex]m^{2}[/tex] = 50000000 [tex]m^{2}[/tex]

8.5 [tex]km^{2}[/tex] = 8.5×1000000 [tex]m^{2}[/tex] = 8500000 [tex]m^{2}[/tex]

Answer:

Sorry if this isnt helpful: Im just going off stuff i learned to see if this will help you at all. Im only in 7th so.. Sorry in advance!!

Step-by-step explanation:

To find the rate, you need to create a unit rate table thing, like this:

5/3 = ?/1 To do this, you would need to divide 5 by 3 and 3 by 3 to get y and x. You get: 1.666 continued. Rounded, about 1.7 . so your unit rate for part A is 1.7/1. You would do the same thing. 2/3 = ?/1. I will let you solve that :)))

Finished A! Now B:

To compare, we use the butterfly method! so 1.7/1 o ?1. cross multiply, and whichever number is bigger comes on top. Then you would explain why that number is bigger. BAM

Answer: 5, 3, [tex]\dfrac{1}{6}[/tex], D

Step-by-step explanation:

-5 < 0 so f(-5) = | -5 | = 5

-3 < 0 so f(-3) = | -3 | = 3

6 > 0 so f(6) = [tex]\dfrac{1}{6}[/tex]

graph D (since x can equal zero)