I have a test to do today and I need help with it, i don't understand any of it. I will copy and paste it here: IQ scores are normally distributed with a mean of 100 and standard deviation of 15. 1) About what percent of people would have IQ between 85 and 115? 2) About what percent of people would have IQ between 70 and 130? 3) About what percent of people would have IQ above 130? 4) If a school had 255 students, about how many would you expect to have an IQ less than 70? 5) If a school had 1531 students, about how many would you expect to have an IQ greater than 145? 6) If a school has 354 students with an IQ between 100 and 130, about how many students does the whole school have?

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)  

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2  

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4  

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16    

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17  

The required answer is 17.  

The value of m+n in which m and n are relatively prime positive integers is 17.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the base rule of logarithmic function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the Power rule of logarithmic function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The number x can be written as

[tex]\dfrac{m}{n}[/tex]

Here, m and n are relatively prime positive integers. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of m+n in which m and n are relatively prime positive integers is 17.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

Step-by-step explanation:

The said tower is not shown.

But to find the percentage of the surface area that is green, since this excludes the surface area underneath the tower, we find the surface area of the total area subtract the surface area underneath the tower, calculate the surface area that is green, divide this last result by the surface are of the whole area that doesn't include underneath the tower, and multiply by 100. This is the percentage we are looking for.

Answer:

0° and 90°

Step-by-step explanation:

Bearing is simply the angle, clockwise, between the north direction and any other direction;

In the first image (on the left) B is exactly in the north direction as compared to A so the bearing is 0°;

In the other image, B is to the right of A, which is a clockwise rotation of 90° from the north direction.

Answer: 8 (2y-1)

Step-by-step explanation: first start by writing like this below:

16y-8

Then factorise the numbers(cut the numbers)

2×2×2×2×y - 2×2×2

Now take all which is common like:

2×2×2=8

Then,take the remained numbers and add it into the brackets.

8 (2y - 1) Here, why we should put 1,because there's nothing left.

If you want to check the answer, factorise this expression and see:

8 (2y-1)

16y-8.

Hope it helps you!!

Answer:

(-2,11) (1,-1) (5,-17)

Step-by-step explanation:

the range of this relation is 11,-1,-17

Answer:

2 1/3 ft^2

Step-by-step explanation:

Take the area of the rectangle

A = l *w

   4 * 1 1/6

   4 * 7/6

  28/6

Divide this in half since the rectangle is cut in half by using the diagonal

28/6 *1/2

28/12

7/3

Changing to a mixed number

2 1/3

Answer:

Step-by-step explanation:

First of all, a continuous variable only admits whole numbers, not decimals.

Now, in statitics, there are several way to reprepsent some data collected from a survey. The most popular tool are bar-graphs or histograms, they are used to show frequency distributions through graphs, where we use interval classes.

Therefore, the right answer is a.

Answer:

No, Justin isn't correct

Step-by-step explanation:

Because Justin added everything even the money he spent, and when he spent the money meaning subtracting them, he should get $21.46.

($25.67+$37.85)-($19.99+$22.07)=$21.46

↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑

Money earned      Money spend     Money left

Answer:

74°

Step-by-step explanation:

The blue angle and the red angle are supplementary angles (meaning they add up to 180°) because these two lines are parallel. Therefore, 106° + ? = 180°, and the red angle is 74°. Hope this helps!

Answer:

71° will be your answer

Answer:

infinite

Step-by-step explanation:

no solution would be something like 8=4 because it is not true

Answer:

Infinite solutions

Step-by-step explanation:

Answer:

No, she will earn 16.50/hr after the raise

Step-by-step explanation:

Catie's raise will be 15*0.10, which is $1.50

Caitie currently earns $15.00 an hour at her job, her boss is going to give her a 10% raise. she will earn 16.50/hr.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Caitie currently earns $15.00 an hour at her job. Thanks to her hard work, her boss is going to give her a 10% raise. Caitie thinks that this means she will earn about $25.00 an hour.

10% of 15

= 15 × 0.10

= $1.50

The total amount will be = 15 + 1.50

                                         = 16.50

Learn more about percentages;

https://brainly.com/question/13450942

Answer:

A- isosceles

B- equilateral

C- scalene

Answer:

Triangle A

Isosceles

Triangle B

Equilateral

Triangle C

Scalene

Hope this helped

Answer:

it 4968

Step-by-step explanation:

because you have to multiply 92 by 54 hopes this helped

2 = 2????

Thats what Im getting it from.

Since x is 2 then it would still be 2=2 in simple term.

Answer:

y = 4

Step-by-step explanation:

-1y = -4

Divide both sides by -1 to get y by itself.

-1/-1 = -4/-1

y = 4

It's positive because there are two negatives, which mean they cancel out.

Answer:

C. The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.

Step-by-step explanation:

It's a given that f(x) = x^2 so that means g(x) = f(x) - 9 means g(x) = x^2 - 9

in slope intercept form y = mx + b, b is the y-intercept

since g(x) is just f(x) with the y-intercept as -9 we know that the vertex of the parabola moves downwards 9 units

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Hope this helps! :) If so, please mark my answer as brainliest

Function g(x) is the translation of function f(x). The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f(x). The correct statement is C.

[tex]f(x)=x^{2}[/tex].

[tex]g(x) = f(x) - 9.[/tex]

From the above functions it is clear that the equation for the graph of g(x) will be,

[tex]g(x)=x^{2} -9[/tex].

The equation [tex]y=mx+c[/tex] is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

Since The y intercept of function f(x) is zero.

Hence in the function g(x), it is 9 units below the intercept of the function f(x). Thus the correct option is C.

For more details on y-intercept follow the link:

https://brainly.com/question/329422

Answer:

Step-by-step explanation:

Answer:

-7/2

Step-by-step explanation:

Answer:

x < .6

Step-by-step explanation:

1+5x<4

Subtract 1 from each side

1-1+5x<4-1

5x<3

Divide each side by 5

5x/5 <3/5

x < .6

Answer:

6

Step-by-step explanation:

because 36 is a perfect square root.

Answer:

the answer: 280ci

Step-by-step explanation:

:] [:

Answer:

280

Step-by-step explanation:

Answer:

There are 10 fourths.

Step-by-step explanation:

There are four 1/4ths in 1. So 2.5 x 4 = 10.

Answer:

2 1/2 is the same as 5/2 which is the same as 10/4, so 10 is the answer :)

Step-by step solution

Answer:

6(4a−3b)

Step-by-step explanation:

You have to factor out this expression, so i would recommend the UMBRELLA  method.

Answer:

6(4a-3b)

Step-by-step explanation:

This is the answer because

Answer:

Yes

Step-by-step explanation:

The inputs in a function should have only one output. In other words, each x value should only be assigned to one y value.

For example, (−2, −1),(1, 0),(1, 5),(2, 0) would not be a function because x value 1 is assigned to both number 0 and number 5.

In (1, 1)(2, 2)(3, 3)(4,4), non of the X values repeat themselves, so it IS a function.

Answer: [tex]14w+28y-7[/tex]

Step-by-step explanation:

multiply everything by -7

Answer:

Step-by-step explanation:

14w+28y-7

Answer:

40 mph

Step-by-step explanation:

To find the maximum speed at which the car can travel, as the distance it requires to stop is 168 feet, we just need to use the value of d = 168 in the equation, and then find the value of s:

168 = 0.05s^2 + 2.2s

0.05s^2 + 2.2s - 168 = 0

Using Bhaskara's formula: we have:

Delta = 2.2^2 + 4*0.05*168 = 38.44

sqrt(Delta) = 6.2

s1 = (-2.2 + 6.2)/0.1 = 40 mph

s2 = (-2.2 - 6.2)/0.1 = -84 mph (a negative value does not make sense as 's' is the speed of the car)

So the maximum speed of the car is 40 mph

Answer:

(4x+1)(4x-1)

Step-by-step explanation:

Answer:

[tex]\sin B=\dfrac{3\sqrt{58}}{58}[/tex]

[tex]\cos B=\dfrac{7\sqrt{58}}{58}[/tex]

[tex]\tan B=\dfrac{3}{7}[/tex]

Step-by-step explanation:

The sine of an angle is the length of the opposite side divided by the length of the hypotenuse, which in this case is[tex]\frac{3}{\sqrt{58}}=\frac{3\sqrt{58}}{58}[/tex]. The cosine is the adjacent side divided by the hypotenuse, which in this case is [tex]\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}[/tex]. The tangent is the length of the opposite side divided by the length of the adjacent side, which in this case is simply [tex]\frac{3}{7}[/tex]. Hope this helps!

Answer:

x=10

Step-by-step explanation:

3(4x-12) = 84

Divide each side by 3

3/3(4x-12) = 84/3

4x-12 =28

Add 12 to each side

4x-12+12 = 28+12

4x= 40

Divide each side by 4

4x/4 = 40/4

x = 10