What system of equations is shown on the graph below

Answer:

The score of a person who did better than 85% of all the test-takers was of 624.44.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

One year, the average score on the Math SAT was 500 and the standard deviation was 120.

This means that [tex]\mu = 500, \sigma = 120[/tex]

What was the score of a person who did better than 85% of all the test-takers?

The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.037 = \frac{X - 500}{120}[/tex]

[tex]X - 500 = 1.037*120[/tex]

[tex]X = 624.44[/tex]

The score of a person who did better than 85% of all the test-takers was of 624.44.

Answer:

b) y=x -2(w+z)

Step-by-step explanation:

multiply both sides, move the terms and write on parametric form

Answer:

a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

24​% say that they were too young when they got their tattoos.

This means that [tex]p = 0.24[/tex]

Six adults

This means that [tex]n = 6[/tex]

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]

0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]

0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

This is:

[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]

0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

Answer:

S/100r

Step-by-step explanation:

S% of 1/r = (1/r x S) : 100

(1/r x S) : 100

S/r : 100

S/100r

Answer:

2 = x          -7 = x

Step-by-step explanation:

f(x) = (x - 2)(x + 7)

y  = (x - 2)(x + 7)

Set y = 0

0 = (x - 2)(x + 7)

Using the zero product property

0 = x-2    0 = x+7

2 = x          -7 = x

Answer:

Zeros happen when f(x) = 0. There are two zeros in the given function:

Therefore solve both equations above and you'll get:

Answer:

-(x + 3)(x - 3)

Step-by-step explanation:

Using the difference of squares we can factor this expression.

[tex](9 - x^2)\\= (3^2 - x^2)\\= (3 + x)(3 - x)\\= -(3 + x)(-3 + x)\\= -(x + 3)(x - 3)[/tex]

Answer:

Hello,

Answer A (-4,0) and (0,0)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]

[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]

Answer:

0.5679

Step-by-step explanation:

From. The table Given above :

The probability of female Given an advanced degree ;

P(F|A) = p(FnA) / p(A)

From the table, p(FnA) = 322

P(Advanced degree), P(A) = (245 + 322) = 567

Hence,

P(F|A) = p(FnA) / p(A) = 322 / 567 = 0.5679

The missing side length is 10 unit.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have,

Perpendicular = 6

Base = 8

Using Pythagoras theorem

c² = P² + B²

c² = 6² + 8²

c²= 36 + 64

c² = 100

c= 10 unit.

Thus, the missing length is 10 unit.

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ7

Answer:

(x, y, z) = (-8,4,-2)

Step-by-step explanation:

.......................................

That's a question about exponentiation.

Answer:

Kenji is wrong because he does not aply the porperty correctly.

Step-by-step explanation:

A exponetiation has this form:

[tex]\boxed{a^b}[/tex]

a is the base

b is the power or exponent

To understand that situation it's important to know a property about exponentiation. When we have a multiplication with the same exponent and diferent bases, the result is the multiplication of the bases with the same exponent. Let's see this above, in mathematical language:

[tex]\boxed{a^b \cdot c^b = (a\cdot c) ^b}[/tex]

Examples:

Now, we can say why Kenji is wrong. It's easy simplify [tex]3^5 \cdot 4^5[/tex]! We know that the result is [tex](3 \cdot 4) ^5 = 12^5[/tex], but Kenji multiplied the bases and added the exponents, that's why he is wrong.

I hope I've helped. ^^

Enjoy your studies! \o/

Answer: -3/8

Step-by-step explanation:

Expanding z we get  

z = 4x^2 - 4xy + y^2 - 2y^2 - 3y

  = -y^2 - (4x + 3) y + 4x^2.

After Archimedes chooses x, Brahmagupta will choose

y=-(4x+3/2) in order to maximize z

Then  

z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2

z=8x^2+6x+9/4

To minimize this expression, Archimedes should choose x=-3/8

Answer:

10:3

Step-by-step explanation:

Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.

For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.

So make 5/2 to a 10/4.

Take the numerator 10 & 3.

Your answer will be 10:3

No problem.

Answer:

3:8

Step-by-step explanation:

i will gadit

that only

Answer:

1.6 Bitcoins

Step-by-step explanation:

Given data

We have the rate as

$1 USD to 0.004

Hence $400 will buy x bitcoins

Cross multiply to find the value of x

1*x= 400*0.004

x=1.6

Hence $400 will get you 1.6 Bitcoins

Answer:

10,-4

Step-by-step explanation:

not sure where the options are but if you were to solve this equation first bring everything to one side.

x^2 - 6x - 40 = 0

factor it

(x-10)(x+4) = 0

set each part to 0

x-10 = 0 and x+4 = 0

solutions are 10 and -4

Answer:

3.564 m^2

Step-by-step explanation:

The area of the original garden is

A = 5.4 * 1.5 = 8.1

The new garden is

5.4*1.2 = 6.48 by 1.5*1.2 =1.8

The area is

A = 6.48*1.8=11.664

The increase in area is

11.664-8.1=3.564

The given information is,

To find the increase in area of the garden.

Formula we use,

→ Area = Length × Width

Area of the real garden is,

→ 5.4 × 1.5

→ 8.1 m

The new garden will be,

→ 5.4 × 1.2 = 6.48 m

→ 1.5 × 1.2 = 1.8 m

The area of the new garden is,

→ 6.48 × 1.8

→ 11.664

Then the increase in area of the garden,

→ 11.664 - 8.1

→ 3.564 m²

Hence, 3.564 m² is the increase in area.

Answer:

3.1 gallons

Step-by-step explanation:

To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that

miles of gas / gallons = miles of gas / gallons

23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house

If we write the gallons needed to go to Bob's mother's house as g, we can say

23 miles / 1 gallon = 72 miles/g

multiply both sides by 1 gallon to remove a denominator

23 miles = 72 miles * 1 gallon /g

multiply both sides by g to remove the other denominator

23 miles * g = 72 miles * 1 gallon

divide both sides by 23 miles to isolate the g

g = 72 miles * 1 gallon/23 miles

= 72 / 23 gallons

≈ 3.1 gallons

Answer:

{(2,0),(-5,1),(7,8),(6,0),(-7,1)

Answer:

The point at the bottom has to move over 2 to the left to be aligned with the point at the top however they will have a 3 space in between the 2 same for the point at the top, the top point moves over 2 to the right to be aligned with the bottom point, then they will have a 3 square space between each other.

Answer:Around 3 spaces between?

Step-by-step explanation:

Answer:

The constant is StartFraction 5 over 6 EndFraction

Step-by-step explanation:

StartFraction 5 over 6 EndFraction + one-fourth x minus y

5/6 + 1/4x - y

A. The constant is StartFraction 5 over 6 EndFraction.

True

B. The only coefficient is One-fourth.

False

There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1

C. The only variable is y

False

There are 2 variables: variable x and variable y

D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.

False

5/6 and 1/4x are not like terms

The only true statement is: The constant is StartFraction 5 over 6 EndFraction

Answer:

It's A if you don't want to read. A). The constant is 5/6

Step-by-step explanation:

Answer:

1/425

Step-by-step explanation:

The first card can be any card, so we don’t have to evaluate the probability.

Now we can suppose that the exit card is a two

- For the second card we have 3/51 of possibilities that is a 2 = 1/17

- For the third card we have 2/50 of possibilities that is a 2 = 1/25

1/17 * 1/25 = 1/425

Answer:  Choice B)  [tex]\sqrt{2}[/tex]

Work Shown:

[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.

Answer:

5 ft

Step-by-step explanation:

The formula for Volume is V=lwh, or Volume = length x width x height.

The equation would be:

[tex]180=l(4)(9)[/tex]

or

[tex]180=36l[/tex]

To find the answer, divide by 36.

[tex]\frac{180}{36} =\frac{36l}{36}[/tex]

[tex]5=l[/tex]

Answer:

A, B, and E apply

Step-by-step explanation:

One thing we can do is to make everything in the same format, under one square root, with no non-square roots.

First, we can say that 6 is equal to √36 as 6² =36, and 6 ≥ 0. Therefore, 6√3 = √36 * √3 = √108

For A, √3 * √36 = √108, so this applies

For B, √18 * √6 = √108, so this applies

For C, 108² = √something bigger than 108 = √11664, so this does not apply

For D, √54 ≠ √108, so this does not apply

For E, √108 = √108, so this applies

For F, √3 * √6 = √18, so this does not apply

It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.

Answer:

You can cut the plank down from the size you buy to the

exact size, but you want to waste as little wood as possible.