On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 14. Suppose one individual is randomly chosen. Let X = IQ of an individual.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly selected person's IQ is over 107. Round your answer to 4 decimal places.

c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.

d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.
Q1:
Q3:
IQR:

Answer:

f(x) = -5/9x - 11/9

Step-by-step explanation:

Consider f(x) = y

so if x = -4 => y = 1 and x = 5 => y = -4

so (-4,1) and (5,-4) should be on the same linear equation

Slope m = (y2 - y1)/(x2 - x1)

m = (-4 - 1)/(5 -  -4) = (-5)/(9) = -5/9

y = mx + b

given m = -5/9, x = -4, y = 1

1 = -5/9(-4) + b

b = 1 - 20/9

b = 9/9 - 20/9 = -11/9

so y = -5/9x - 11/9

or f(x) = -5/9x - 11/9

the answer is

\(B. \: {v}^{2} {w}^{2} + {15v}^{2} {w}^{3} + 2\)

Hope this helps you!

The LCD of 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) is (x+2)^2(x-2)^2(x+2)(x-2) = (x+2)^3(x-2)^3.

To find the lowest common denominator (LCD) of three fractions, we need to identify the factors of each denominator and select those factors that are common to all denominators.The given fractions are: 1/ (x+2)^2, 3/ (x-2)^2, and 4/ (x^2-4).

The first denominator (x+2)^2 can be factored using the formula for the difference of two squares. The denominator of 3/(x-2)^2 can also be factored using the formula for the difference of two squares.

Finally, the denominator of 4/(x^2-4) can be factored using the formula for the difference of two squares and the formula for the sum of two squares.

So, 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) can be rewritten as follows:1/ (x+2)^2 = A/(x+2) + B/(x+2)^2. Multiplying both sides by (x+2)^2 gives:1 = A(x+2) + B ... (1)3/ (x-2)^2 = C/(x-2) + D/(x-2)^2.

Multiplying both sides by (x-2)^2 gives:3 = C(x-2) + D ... (2)4/ (x^2-4) = E/(x-2) + F/(x+2). Multiplying both sides by (x^2-4) gives:4 = E(x-2)(x+2) + F(x+2)(x-2) ... (3)

Now, we need to solve these equations for A, B, C, D, E, and F. First, we will solve equation (1) for A and B by substituting x = -2, which gives A = -1/4. Then we will substitute x = -2 again and solve for B, which gives B = 1/4. Next, we will solve equation (2) for C and D by substituting x = 2, which gives C = 3/4.

Then we will substitute x = 2 again and solve for D, which gives D = -3/4. Finally, we will solve equation (3) for E and F by substituting x = 2 and x = -2, which gives E = 1/2 and F = 1/2.

Now, we have A = -1/4, B = 1/4, C = 3/4, D = -3/4, E = 1/2, and F = 1/2. The LCD is the product of all the factors that appear in the denominators of the fractions, each raised to the highest power that appears.

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Answer:

x^6 y^3

Step-by-step explanation:

(x²y)³

We know that (ab) ^c = a^c * b^c

(x²y)³ = x^2 ^3  * y^3

We know that a^b^c = a^(b*c)

(x²y)³ = x^2 ^3  * y^3 = x^( 2*3) y^3 = x^6 y^3

If the first term of a geometric sequence is 8 and the common ratio is 3. Then the fifth term of the geometric sequence will be 648.

There are three parameters that differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.

The second parameter is the quantity by which we multiply the previous term to get the next term.

The third parameter is the length of the sequence. It can be finite or infinite.

Suppose the initial term of a geometric sequence is 'a' and the term by which we multiply the previous term to get the next term is 'r' (also called the common ratio)

The first term of a geometric sequence is 8 and the common ratio is 3.

Then the fifth term of the sequence will be

\(\rm T_n = a_1 \ r^{n-1}\)

Then we have

T₅ = 8 x 3⁵⁻¹

T₅ = 8 x 3⁴

T₅ = 8 x 81

T₅ = 648

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Answer:

a. 8 cm

Step-by-step explanation:

Given:

EH = 6 cm

FG = 4.00 cm

Based on the mid-segment theorem of a trapezoid, we have:

EH = ½(FG + DI)

Plug in the values

6 = ½(4 + DI)

Multiply both sides by 2

6*2 = 4 + DI

12 = 4 + DI

12 - 4 = 4 + DI - 4

8 = DI

DI = 8 cm

Answer:150?

Step-by-step explanation:

Answer: 7.937

Step-by-step explanation: Calculator...

Answer:

slope = 2.25

Step-by-step explanation:

This equation is written in slope-intercept form, which has the general structure: y = mx + b.

In this form, "m" = slope and "b" = y-intercept.

Therefore, the slope is 2.25 since it is replacing the "m" variable.

Answer:

>

Step-by-step explanation:

-3+7= 4

-10-2= -12

4> -12

Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

Answer:

a = 1.8 to the nearest tenth.

Step-by-step explanation:

Remark

I don't think this case is ambiguous. It has only 1 solution, I think.

Step One

Find the top angle.

All triangles have 180 degrees.

15 + 105 + x = 180

120 + x = 180                     Subtract 120 from both sides

x = 180 - 120

x = 60

Step Two: Find a

a/sin(60) = 2/Sin(105)       Multiply both sides by sin(60)

a = 2 *  Sin(60) / sin(105)

a = 2 * .8660 / 0.9659

a = 1.793

Answer:

it is A

Step-by-step explanation:

I took this test when I was in middle School

Answer: they need to feed 9 animals

Step-by-step explanation: if you solve the equation for x, you will get x=9. so, they need to feed 9 animals to spend the same amount.

The average rate of change for the interval from x =  7 to x =  8 is 35.  

To calculate the average rate of change for the interval from x =  7 to x =  8, we need to find the difference in y- values and divide it by the difference inx-values within that interval.

Let's calculate it step by step using the given table  

For the interval from x =  7 to x =  8  x1 =  7, y1 = -37  x2 =  8, y2 = -2   Difference in y- values Δy =  y2- y1 = -2-(- 37) =  35  

Difference inx-values Δx =  x2- x1 =  8- 7 =  1  

Average rate of change =  Δy/ Δx =  35/ 1 =  35  

Thus, the average rate of change for the interval from x =  7 to x =  8 is 35.   Note: It's important to mention that the values calculated then are grounded solely on the given data. Please  insure you  corroborate the  delicacy of the  handed data and  environment before using the answer in any important or critical  operations.

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In Southwest Direction, the left side of the graph of this function point.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

f(x)= \(x^{4}\)-x³+4x-2

it will not pass through the origin, as, f(0)=-2

It is a polynomial of degree four.

The function in question contains two genuine roots and two fictitious roots.

In the third quadrant and a small portion of the fourth quadrant, the left side of the function is located after drawing a line of symmetry. A line of symmetry is at approximately x=0.14.

Hence, In Southwest Direction, the left side of the graph of this function point.

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Answer:

the answer is x =1 mark me as brainliest

Answer:

7 lawns

Step-by-step explanation:

Given:

⇒ Total cost of trip = airfare + transportation + 4 x food

                                = 198 + 56 + (4 x 45)

                                = $434

Given:

⇒ Amount to make from mowing lawns = total cost of trip - savings

                                                                  = 434 - 189

                                                                  = $245

Therefore, he needs to make $245 from mowing lawns to have enough money to pay for the trip.

Given:

⇒ number of lawns = amount needed ÷ amount earned per lawn

                                = 245 ÷ 35

                                = 7

So he needs to mow 7 lawns to have enough money to pay for the trip.

Answer:

7 lawns

Step-by-step explanation:

Let us do this. replace l with lawns mowed and replace day with 4 since the trip is a 4-day trip.

What is 198 + 56?

254.

35l + 189 must be equal to or more than 45(4) + 254.

(45 x 4) + 254 = 180 + 254 = 434

434 - 189 = 245

35l = 245

35/35 = 245/35

l = 7

He has to mow 7 lawns.

Answer: Angle 3 and Angle 2

Step-by-step explanation:

The angles form a linear pair, which means they are supplementary.

Answer:

I dont know

Step-by-step explanation:

still dont know

Answer:

Time taken by kangaroo to travel 5 km = 4.27 minutes.

Step-by-step explanation:

Speed of kangaroo is 44 mph.

Speed of kangaroo = 44 mph = 44 x 1.6 = 70.4 kmph = 19.5 m/s

We need to find how much time it takes to travel 5 km

Distance traveled = 5 km = 5000 m

We have

          Distance traveled =  Speed x Time taken

          5000 = 19.5 x Time taken

          Time taken = 256.41 seconds

           Time taken = 4.27 minutes.

Answer:7.5

Step-by-step explanation:

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

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The temperature when the plane reaches an altitude of 9,000 ft is 43.5°F.

Temperature is the degree of hotness and coldness in a body.

In this case, there is a 1.3°F drop in temperature for every thousand feet that an airplane climbs into the sky.

The temperature when it reaches 9000 feet will be:

= Ground temperature - Drop on temperature

= 55.2 - 1.3(9000 / 1000)

= 55.2 - 1.3(9)

= 55.2 - 11.7

= 43.5°

This illustrates the concept regarding calculation of temperature.

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a) Evaluate the given function at each value of x. We have f(x) = 2x + 3.

• If x = -2, then

f(-2) = 2 (-2) + 3 = -4 + 3 = -1

• If x = -1, then

f(-1) = 2 (-1) + 3 = -2 + 3 = 1

• If x = 0, then

f(0) = 2 (0) + 3 = 0 + 3 = 3

and so on.

b) Kind of a silly question. Of course f(x) is a function, the instructions for part (a) say so!

But the real reason f(x) is indeed a function is that no single value of x returns more than one value of f(x).

By using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

Given

\(\sin \text{x}^\circ= \ ?\)

\(\tan \text{x}^\circ=\dfrac{\text{a}}{4}\)

\(\cos \text{x}^\circ=\dfrac{4}{\text{b}}\)

Formula to find \(\sin \text{x}^\circ\)

\(\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}\)

\(\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}\)

Therefore, by using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

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