Assume that adults have IQ scores that are normally distributed with a mean 105 of and a standard deviation 20 . Find the probability that a randomly selected adult has an IQ between 88 and 122 .

Answer:

b

Step-by-step explanation:

The y- intercept is the point on the y- axis where the graph crosses.

On the y- axis the x- coordinate is always zero.

From the table when x = 0 , y = 3, thus

(0, 3 ) is the y- intercept → b

Answer:

32

Step-by-step explanation:

[tex] 64= 2^6[/tex]

[tex] 96= 2^5\times 3[/tex]

[tex] 64= 2^7[/tex]

Common factor = [tex] 2^5[/tex]

Therefore,

H.C.F OF 64,96,128 = [tex] 2^5[/tex] = 32

Answer:

73.437= 74 437/1000

Step-by-step explanation:

73.437 to fraction.

Let's acknowledge the presence of a decimal and how many digit we have after the decimal point.

Actually, the numbers after the decimal point will determine the amount of 10s to be divided with.

What I'm saying is this

73.437= 74 437/1000

In this case, 437 is a prime number

So

73.437= 74 437/1000

If you have tickmarks on the segment, on a blank piece of paper, then you count out the spaces to get the length of the segment. This is assuming the tickmarks are properly spaced out. If there aren't any tickmarks, then you'll have to use a ruler to find the length. Either way, a ruler is encouraged.

The coordinate plane makes things easier to find the length of any segment. Use either the pythagorean theorem or the distance formula to find the length of the segment.

1 year = 52 weeks. 2 years would be 104 weeks.

$12 per week x 104 weeks = $1248 total.

1248 - 900 = $348

348 /900 = 0.3866 = 38.7%

The answer is B

Answer:

coordinates of the centroid = [tex](\frac{2}{3} , \frac{2}{3} )[/tex]

Step-by-step explanation:

The curves to be plotted are : y =2x, y = 0, x =1

The coordinates of the centroid ( visually estimated ) can be found by first calculating the area of the region

A = [tex]\int\limits^1_0 {2x} \, dx[/tex]  =   2[tex](\frac{x^2}{2} )[/tex] hence A = 1

attached below is the remaining part of the solution

Answer:

100 dinners

Step-by-step explanation:

There are 4 choices for the appetizer, 5 choices for the main course and 5 choices for the dessert so the total number of dinners that are possible is 4 * 5 * 5 = 100.

Complete Question: Which of the following is an example of the difference of two​ squares?

A x² − 9

B x³ − 9

C (x + 9)²

D (x − 9)²

Answer:

A. [tex] x^2 - 9 [/tex].

Step-by-step explanation:

An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.

Thus, difference of two squares takes the following form: [tex] a^2 - b^2 = (a + b)(a - b) [/tex].

a² and b² are perfect squares. Expanding [tex] (a + b)(a - b) [/tex] will give us [tex] a^2 - b^2 [/tex].

Therefore, an example of the difference of two squares, from the given options, is [tex] x^2 - 9 [/tex].

[tex] x^2 - 9 [/tex] can be factorised as [tex] x^2 - 3^2 = (x + 3)(x - 3) [/tex].

Answer:

or,6x+6=9x-9

or,6+9= 9x-6x

or,15=3x

or,15/3=X

therefore,X=5ans

Answer:

x=3

Step-by-step explanation:

32/24=(6x+6)/(9x-9)

simplify by 8 in the left

4/3=6(x+1)/9(x-1)

simplify by 3 in the right

4/3=2(x+1)/3(x-1)

*3           *3

4=2(x+1)/(x-1)

(x+1)/(x-1)=4/2=2

so x+1=2(x-1)=2x-2

-x                     -x

1=x-2

+2    +2

3=x

so x=3

verify  (6*3+6)/(9*3-9)=32/24

24/18=32/24

simplify by 6  in the left

4/3=32/24

simplify by 8   in the right

4/3=4/3   TRUE

Answer:

144

Step-by-step explanation:

Hello, please consider the following.

[tex]x^2-24x+c[/tex]

is a perfect square means that the discriminant is 0.

[tex]\Delta = b^2-4ac=24^2-4c=0\\\\<=>24^2-4c =0<=> 4c=576\\\\\text{We divide by 4}\\\\c= \dfrac{576}{4}=144[/tex]

Thank you

The value of c which make a perfect square trinomial is,

⇒ c = 144

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ x² - 24x + c

Now, We can it squared as;

⇒ x² - 24x + c

⇒ x² - 2 × 12x + 144

⇒ x² - 24x + 12²

⇒ (x - 12)²

Thus, The value of c which make a perfect square trinomial is,

⇒ c = 144

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Answer:

"proportional to"

Step-by-step explanation:

The sign ∝ means 'is proportional to'. This is used to show that one variable of value is proportional to another value or variable.

Example:

Hope this helps.

Answer:

-625,3125

Step-by-step explanation:

Im not saying this is correct but it looks like its multipling by 25

Answer:

17

Step-by-step explanation:

first find the value of N

The correct answer is C) 50 parents of college students from the state

Explanation:

The purpose of representative samples is to study a population by only selecting a small group in it. Due to this, the individuals selected as part of the sample need to match the characteristics of the population being studied.

In this context, if the focus is the opinion of parents about college tuition fees in a specific state, it is expected the sample includes parents of college students rather than students, citizens, etc. because the opinion of parents of college students is being evaluated. Moreover, those parents selected should have children in the state being studied. According to this, the correct option is C because this includes individuals who can appropriately represent the population that is being analyzed.

Answer:

50 parents of college students from the state.

Step-by-step explanation:

Sophia Statistics

Answer:

the simple multiplier is equal to 4

Step-by-step explanation:

In an economic model,

Y=  C + I + G + (X - M)

the average expenditure Y must be equal  to the totality of the output

If C = 3 + 0.75Y

where;

marginal propensity to consume MPC = 0.75

Then,

Y = 3 + 0.75Y + 2 + 1

Y = 6+0.75 Y

Y - 0.75 Y = 6

0.25 Y = 6

Y = 6/0.25

Y = 24

However,  the simple multiplier can be expressed as:

[tex]=\dfrac{1}{1 - MPC}[/tex]

[tex]=\dfrac{1}{1 - 0.75}[/tex]

[tex]=\dfrac{1}{0.25}[/tex]

= 4

Answer:

4917

Step-by-step explanation:

Given sequence:

This is AP with common difference of 1, the first term of 42 and the last term of 107

Number of terms:

Sum of the terms:

Answer is: 4917

Answer:

Yes, this is a function

Step-by-step explanation:

This relation is function because 1 x value corresponds to 1 y value

Division is one of the four fundamental arithmetic operations. Andrew is faster than Noah.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Andre can now complete 135 multiplication facts in 90 seconds.

A.) If Andre is answering questions at a constant rate, then the number of facts that Andre can answer per second can be written as,

Number of facts per seconds = 135 facts / 90 seconds

                                                 = 1.5 facts per seconds

B.) Noah also works at a constant rate, and he can complete 75 facts in 1 minute. Therefore, the number of facts that Noah can answer per second can be written as,

Number of facts per seconds = 75 facts / 60 seconds

                                                 = 1.25 facts per seconds

Now, since the number of facts that Andrew can read in a second is 1.5 facts, while the number of facts that Noah can read in a second is 1.25 facts.

Hence, Andrew is faster than Noah.

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Answer:

Step-by-step explanation:

Hello,

-1 <= -1 < 0

so f(-1)=-1

0 <= 0.5 < 1

so f(0.5)=0

1 <= 1 < 2

so f(1)=1

Thank you.

Answer: Hi!

So first, I'm going to convert "350 below ground level" to -350, as this is what "below ground level" represents.

Now, we should find the total distance traveled. Take the absolute value of -350 (350) and add it to 10, the metres above ground level. This is 360.

We already know the rate of travel; 6m/min. All we have to do now is divide the total distance (360) by the rate of travel (6)!

360 ÷ 6 = 60

So, it took 60 minutes, or one hour, for the elevator to travel down the shaft!

Hope this helps!

Step-by-step explanation: The figure shown here is a straight path between points that extends forever in both directions, so it's called a line.

Since a line doesn't have endpoints, it doesn't matter which

two points on the line we use to name the line.

I have attached 5 possible names for the line below.

Answer:

Step-by-step explanation:

e Because lines continue infinitely, we can name them forwards or backwards. We can also use any two points on a line to identify it, unlike with rays or segments. The l and the end of the line can also be used to identify it.

Different names for the line include: DE ED DF FD and line l.

Answer:

900cm^3

Step-by-step explanation:

1 cm= 10 mm

x=300mm (criss cross)

1cm*300mm/10mm= 10mm*x/10mm

30cm=x

30cm=300mm

1m=100cm

0.2m=x

1m*x/1m=0.2m*100cm/1m

x=0.2*100cm

x=20cm

0.2m=20cm

l=15cm

w=30cm

h=20cm

v=l*w*h

v=15cm*30cm*20cm

v=450cm^2*20cm

v=900cm^3

Answer:

9000cm^3

Step-by-step explanation:

Width:300mm=30cm

Height:15cm=15cm

Depth:0.2m=20cm

V=DxWxH

V= 20x30x15

V=9000cm^3

Answer:

sinθ = -5/√61

secθ = √61/6

tanθ = -5/6

Step-by-step explanation:

From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Let us get the value of the radius 'r' first before calculating the trigonometry identities.

Using the Pythagoras theorem;

[tex]r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}[/tex]

Using SOH, CAH, TOA to get the trigonometry identities;

Given x = 6, y =5 and r = √61

[tex]sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\[/tex]

Since sin θ, is negative in the fourth quadrant, [tex]sin \theta = -5/\sqrt{61} \\[/tex]

[tex]cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\[/tex]

[tex]sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}[/tex]

For tanθ:

[tex]tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\[/tex]

Since tan θ, is negative in the fourth quadrant, [tex]tan \theta = -5/6[/tex]

 [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex],

[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]  

[tex]TAN\Theta=\frac{-5}{6}[/tex].

Given coordinate of point be (6, -5).

So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.

By Pythagorean theorem, we find that the hypotenuse

[tex]H=\sqrt{6^{2} +(-5)^{2} }[/tex]

[tex]H=\sqrt{61}[/tex]

We know from trigonometric ratios,

[tex]SIN\Theta=\frac{Perpendicular}{hypotenuse} \\[/tex]

[tex]SIN\Theta=\frac{5}{\sqrt{61} }[/tex]

Since [tex]SIN\Theta[/tex] is negative in 4th quadrant,

so,

[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex]

Similarly,

[tex]SEC\Theta=\frac{hypotenuse}{base}[/tex]

[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]

And,

[tex]TAN\Theta=\frac{perpendicular}{base}[/tex]

[tex]TAN\Theta=\frac{-5}{6}[/tex]

Hence,  [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex], [tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]  and [tex]TAN\Theta=\frac{-5}{6}[/tex].

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Answer:

The original number is -7.

Step-by-step explanation:

In this section, we are trying to figure out a mysterious number. Let's call this number y. To find the value of y, we need to create an equation. Our equation will be based on clues hidden in the text. So, what do we know?

- A number, aka y, is increased by 3. (y+3)

-That number is doubled. 'That number' refers to the answer of y+3. So, (y+3)x2.

-Finally, the end result is -8.

Great! Now we know our equation: 2(y+3)=-8. We need to figure out what y equals, so let's isolate the y term with some algebra.

2(y+3)=-8; Original formula

2y+6=-8; Distribute the (y+3)

2y=-14; Carry the 6 to the other side of the equation.

y=-7: Divide

Thus, our mysterious number is -7. Hope this helps:)))

Answer:

5x^2 -2x +4

Step-by-step explanation:

(8x^2 + 9) - (3x^2 + 2x + 5)

Distribute the minus sign

(8x^2 + 9) - 3x^2 - 2x - 5

Combine like terms

5x^2 -2x +4

Hello,

First of all, dividing by 0 is not defined we will take x different from 1/3 (because -1+3x= 0 <=> x = 1/3)

Then, dividing this polynomial by (-1+3x) means that you have to have Q(x), a polynomial of degree 1 and R a real number such that

[tex]\dfrac{9x^2-6x+2}{-1+3x}=Q(x)+\dfrac{R}{-1+3x}\\\\\text{We can multiply by (-1+3x)}\\\\9x^2-6x+2=(-1+3x)Q(x)+R[/tex]

Either you do the division and you can select the correct answer or you check the different answer to identify the correct one.

For instance, for the first answer, let's estimate

[tex](-1+3x)(3x-3)+\dfrac{-1+3x}{3x-1}\\\\=-3x+3+9x^2-9x+1\\\\=9x^2-12x+4[/tex]

and this is not equal to our initial polynomial, so this is not the correct answer.

Second Answer.

[tex](-1+3x)(3x-1)+\dfrac{-1+3x}{3x-1}\\\\=-3x+1+9x^2-3x+1\\\\=9x^2-6x+2[/tex]

And this is our initial polynomial. So this is the [tex]\large \boxed{\sf \bf \text{correct answer}}[/tex]

Thank you.

PS: in this example, you can even notice the following (so it makes the division trivial)

[tex](3x-1)^x=9x^2-6x+1 \\\\\text{So}\\\\9x^2-6x+2= (3x-1)^2+1\\\\\text{And, then.}\\\\\dfrac{9x^2-6x+2}{-1+3x}=3x-1+\dfrac{1}{3x-1}[/tex]

Answer:

Step-by-step explanation:

Using the Distributive Property of Multiplication, we get

12

---- - 12x. or 4 - 12x, or 4(1 - 3x)

 3