what is the area of the shaded region ? ​

Answer:

0.2159 = 21.59% probability this student’s score will be at least 1500.

Step-by-step explanation:

To solve this question, we need to understand the normal distribution and conditional probability.

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Recognized student(scored more than 1350)

Event B: Score of at least 1500.

SAT scores (out of 1600) are distributed normally with a mean of 1100 and a standard deviation of 200

This means that [tex]\mu = 1100, \sigma = 200[/tex]

Probability of being recognized.

1 subtracted by the pvalue of Z when X = 1350. So

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

[tex]Z = \frac{1350 - 1100}{200}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944.

1 - 0.8944 = 0.1056

So [tex]P(A) = 0.1056[/tex]

Probabibility of being recognized and scoring at least 1500.

Intersection between more than 1350 and more than 1500 is more than 1500. So this probability is 1 subtracted by the pvalue of Z when X = 1500.

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

[tex]Z = \frac{1500 - 1100}{200}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

So, [tex]P(A \cap B) = 0.0228[/tex]

What is the probability this student’s score will be at least 1500?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0228}{0.1056} = 0.2159[/tex]

0.2159 = 21.59% probability this student’s score will be at least 1500.

Answer:

116 miles

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-41,3)[/tex] --- Camp 1

[tex](x_2,y_2) = (75,3)[/tex] --- Camp 2

Required

The distance between both camps

This is calculated using:

[tex]d^2 = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}[/tex]

[tex]d^2 = \sqrt{(-41-75)^2 + (3-3)^2}[/tex]

[tex]d^2 = \sqrt{(-116)^2 + (0)^2}[/tex]

[tex]d^2 = \sqrt{116^2}[/tex]

[tex]d = 116[/tex]

The distance is 116 miles

Answer:

3015

Step-by-step explanation:

Answer:

Coordinates of G = [tex](2,0)[/tex]

Step-by-step explanation:

Given: Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3).

To find: coordinates of G

Solution:

Midpoints of a side joining points [tex](a,b),\,(c,d)[/tex] are given by [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]

Diagonals of a parallelogram bisect each other.

So,

Midpoint of DF = Midpoint of EG

Midpoint of DF = [tex](\frac{-4+3}{2},\frac{-2+3}{2})=(\frac{-1}{2},\frac{1}{2})[/tex]

Midpoint of EG = [tex](\frac{-3+x}{2},\frac{1+y}{2})[/tex]

Let coordinates of G be [tex](x,y)[/tex]

Therefore,

[tex](\frac{-1}{2},\frac{1}{2}) =(\frac{-3+x}{2},\frac{1+y}{2})\\\\\frac{-1}{2}=\frac{-3+x}{2},\,\frac{1}{2}=\frac{1+y}{2}\\\\-1=-3+x,\,1=1+y\\\\x=-1+3,\,y=1-1\\x=2,\,y=0[/tex]

So,

Coordinates of G = [tex](2,0)[/tex]

Answer: B

Step-by-step explanation:

The correct answer is B

The population of the bacteria at the value of P (5) is 384, and it represents that the time is 5 pm

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=a^x[/tex]

Here, a is the variable in the power of a number.

The population of a bacterium doubles every hour. At 9 am, the population is 12 bacteria.

The function models the bacteria population t hours after 9 am  is,

[tex]P (t) = 12\times2^t[/tex]

Put the value of t as 5 at P (5) in the above exponential function as,

[tex]P (5) = 12\times2^5\\P(5)=12\times32\\P(5)=384[/tex]

Hence, the population of the bacteria at the value of P (5) is 384, and it represents that the time is 5 pm.

Learn more about the exponential function here;

https://brainly.com/question/15602982

Answer:

x = 14.5°

Step-by-step explanation:

A+D = 180°

(8x-11) + (5y+2) = 180°

simplify:

5y + 8x = 189°

5y = 189 - 8x

D = B

(5y+2) = (4x+17)

simplify

5y = 4x + 15

then:

189 - 8x = 4x + 15

12x = 174

x = 14.5°

5y = 4(14.5) + 15

5y = 73

y = 14.6

check:

5(14.6) + 8(14.5) = 189

73 + 116 = 189

189 = 189

Answer:

it's not fair, because it's only a 1 in 6 chance of rolling gold.

it would be fair if 3 of the 6 sides were gold

Answer:

it aint fair it only 1/6 listen to the other guy

Step-by-step explanation:

i needed points sorry

Answer:

chale. necesita. 20 caracteres

Step-by-step explanation:

4a² - 8ab + 4b²

= (2a)² - 2 * 2a * 2b + (2b) ²

= (2a - 2b) ²

Hope it helps :)

Answer:

41

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

the total height is 12 and the first half of the shape has a height of 8 so the other part is 4.

Answer:

B

promise it's B trust me

The answer is 3) Pythagorean.

A trigonometric identity derived from the Pythagorean theorem is called a Pythagorean identity.

Mathematically, the Pythagorean theorem states that

Hypotenuse^2 = Adjacent^2 + Opposite^2

Divide through by Hypotenuse^2

This gives

1 = cos^2(x) + sin^2(x)

Rewrite as:

cos^2(x) + sin^2(x) = 1

As a general rule, the above represents the basic Pythagorean identity.

Hence, the word that completes the blank is Pythagorean.

Read more about Pythagorean identity at:

https://brainly.com/question/1969941

#SPJ2

Answer:

x = 9.7

Step-by-step explanation:

tan 68° = 24/x

2.4751 = 24/x

x = 9.7

Answer:

All parents in the school

Step-by-step explanation:

Answer:

b) The number of vinyl album sales in the country in the year 2020 will be 18.3 million.

Step-by-step explanation:

Given - The number of vinyl album sales (in millions) in a country x years after 2010 can be modeled by y = 0.12 x² + 0.3 x +3.3  for 2010 through 2016.

To find - Use this model to predict the number of vinyl album sales in the country in the year 2020 where  x = 10

a) The number of vinyl album sales in the country in the year 2020 will be 20.5 million.

b) The number of vinyl album sales in the country in the year 2020 will be 18.3 million.

c) The number of vinyl album sales in the country in the year 2020 will be 7.74 million.

d) The number of vinyl album sales in the country in the year 2020 will be 21.12 million.

Proof -

Given that,

The equation be - y = 0.12 x² + 0.3 x +3.3

Now,

Put x = 10 in above equation we get

y = 0.12×10² + 0.3×10 +3.3

  = 0.12×100 + 3 + 3.3

  = 12 + 6.3 = 18.3

⇒y = 18.3

∴ we get

The number of vinyl album sales in the country in the year 2020 will be 18.3 million.

So,

The correct option be - b) The number of vinyl album sales in the country in the year 2020 will be 18.3 million.

Answer: Y = -x/2 + 12.5

Step-by-step explanation:

You wrote the equation strange so i don't really know if the end of the equation is a 25 or not

Answer:

1/2 ft or 6 inches

Step-by-step explanation:

1/6 of 3 yards = 1/2 ft or 6 inches

Answer:

0.555

Step-by-step explanation:

you simply follow the linear equation rule and fill in

Answer:

✓2=1.41421

✓5=2.23607

✓8=2.82842

✓11=3.31662

✓14=3.74166

Step-by-step explanation:

Therefore the numbers are increasing by three so they cant be perfect square

9514 1404 393

Answer:

  squares are of the form 3n or 3n+1; the sequence is of the form 3n-1, so none of the sequence will be a square

Step-by-step explanation:

The given arithmetic sequence has first term 2 and common difference 3, so its explicit formula is ...

  an = 2 +3(n -1) = 3n -1 . . . . for counting numbers n

__

All integers are of one of these forms: 3n-1, 3n, 3n+1, for some integer n. The squares of these are ...

  (3n -1)² = 9n² -6n +1 = 3(3n² -2) +1 = 3k+1 for some k

  (3n)² = 3(3n²) = 3k for some k

  (3n +1)² = 9n² +6n +1 = 3(3n² +2) +1 = 3k+1 for some k

Note that none of these squares is of the form 3n -1.

Hence, the square of an integer cannot be in the given sequence.

Answer:

D

Step-by-step explanation:

Ed2021

Answer:

so the answer is 5

Step-by-step explanation:

the equation will be for this is

7x + 20 = 55

7x = 55-22

7x = 35

x = 35÷7

x=5

Answer:

M = kwh^2/L

k = 400

Step-by-step explanation:

Given that the maximum weight M that can be supported by a beam is jointly proportional to its width w in inches and the square of its height h in inches and inversely proportional to its length L in feet

Then

M ∝ wh^2/L

M = kwh^2/L

where k is the constant of proportionality

if a beam 4 in. wide, 6 in. high, and 15 ft long can support a weight of 3840 lb then

3840 = k * 4 * 6^2/15

k = 3840 * 15 / (4 * 36)

k = 400

Answer:

Basically this is because division can be thought of as how many times does the divisor have to be multiplied in order to produce the dividend.

So you would need to multiply 1 8 times in order to produce the dividend,

Similarly, 10 goes into 80 8 times. The zeros are simply cancelled out in the division.

Answer:B

Step-by-step explanation:  ok its B because i need some $$$

Answer:

D and E

Step-by-step explanation:

The question asks which one would always form an image that is congruent to the pre-image.

Note that Translation, Reflection, and Rotation do not change the size or shape of the pre-image while Dilation will change the size of your pre-image.

Therefore, the most likely answer would be options D and E that do not include dilation in their series of transformations so the image will not change its size making it congruent to the pre-image.