A data set is normally distributed with a mean of 115 and a standard deviation of 23. What is the probability that a value in the data set is greater than or equal to 162?
The probability is about __

Answer:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4

Step-by-step explanation:

Step 1:  Solve using the first point

(2, 28)

[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]

[tex]28 = 8a + 4b + 2c + d[/tex]

Step 2:  Solve using the second point

(-1, -5)

[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]

[tex]-5 = -a + b - c + d[/tex]

Step 3:  Solve using the third point

(4, 220)

[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]

[tex]220 = 64a + 16b + 4c + d[/tex]

Step 4:  Solve using the fourth point

(-2, -20)

[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]

[tex]-20 = -8a + 4b - 2c + d[/tex]

Step 5:  Combine the first and fourth equations

[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]

[tex]8 = 8b + 2d[/tex]

[tex]8 - 8b = 8b - 8b + 2d[/tex]

[tex](8 -8b)/2 = 2d/2[/tex]

[tex]4 - 4b = d[/tex]

Step 6:  Solve for c in the second equation

[tex]-5 + 5 = -a + b - c + d + 5[/tex]

[tex]0 + c = -a + b - c + c + d + 5[/tex]

[tex]c = -a + b + d + 5[/tex]

Step 7:  Substitute d with the stuff we got in step 5

[tex]c = -a + b + (4 - 4b) + 5[/tex]

[tex]c = -a + b + 4 - 4b + 5[/tex]

[tex]c = -a - 3b + 9[/tex]

Step 8:  Substitute d and c into the first equation

[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]

[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]

[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]

[tex]6 / 6 = (6a - 6b) / 6[/tex]

[tex]1 + b = a - b + b[/tex]

[tex]1 + b = a[/tex]

Step 9:  Substitute a, b, and c into the third equation

[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]

[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]

[tex]220 - 100 = 60b + 100 - 100[/tex]

[tex]120 / 60 = 60b / 60[/tex]

[tex]2 = b[/tex]

Step 10:  Find a using b = 2

[tex]a = b + 1[/tex]

[tex]a = (2) + 1[/tex]

[tex]a = 3[/tex]

Step 11:  Find c using a = 3 and b = 2

[tex]c = -a - 3b + 9[/tex]

[tex]c = -(3) - 3(2) + 9[/tex]

[tex]c = -3 - 6 + 9[/tex]

[tex]c = 0[/tex]

Step 12:  Find d using b = 2

[tex]d = 4 - 4b[/tex]

[tex]d = 4 - 4(2)[/tex]

[tex]d = 4 - 8[/tex]

[tex]d = -4[/tex]

Answer:  [tex]a = 3, b = 2, c = 0,d = -4[/tex]

Step-by-step explanation:

I think 40 should be the first term in the sequence because it is given 40.. 6n - 1

Answer:

Area is a size measurement of a two-dimensional surface. Those dimensions (x and y) are perpendicular to each other, and thats why it is squared.

Answer:

$43.8

Step-by-step explanation:

Large necklace = LN

Small necklace = SM

LN sells for 5.60

SN sells for 4.50

LN = 5.60

SN = 4.50

you have 3 LN and 6 SN.

LN total = 3 x $5.60 = 16.8

SN total = 6 x 4.50 = 27

Add both the totals.

27 + 16.8 = 43.8

Hope this helps!

Answer:

HE/SHE earns $43.80.

Step-by-step explanation:

5.60 x 3 = $16.80

4.50 x 6 = $27.00

In totle:

Answer:

653.45

Step-by-step explanation:

Answer:

A≈653.45in

A=2πrh+2πr2=2·π·2·50+2·π·22≈653.45127in²

Answer:

x = 20

Step-by-step explanation:

assuming if this was a triangle

3x + 4x +2x = 180

9x = 180

180/9 = 20

Answer:

20

Step-by-step explanation:

You know that the angle measurements in a triangle add up to 180 degrees.

using the equation 3x+4x+2x= 180, you can find x

Simplify:

9x=180

x=20

Your answer is B) x = 20

Hope this helps!

Answer:

a number less than five

Answer:

So the number that has the greatest probability is a

Number less than 5

Step-by-step explanation:

odd numbr is [tex]\frac{3}{6}[/tex] or [tex]\frac{1}{2}[/tex]

Even number is [tex]\frac{3}{6}[/tex] or [tex]\frac{1}{2}[/tex]

a number less than 5 is [tex]\frac{4}{6}[/tex] or [tex]\frac{2}{3}[/tex]

A number greater than 3 is [tex]\frac{3}{6}[/tex] or [tex]\frac{1}{2}[/tex]

Answer:

11.56m²

Step-by-step explanation:

3.4×3.4=11.56m²

Answer:

11.56

Step-by-step explanation:

Answer:

17/20

Step-by-step explanation:

Answer:

x^2 - 24x + 144

Step-by-step explanation:

24/2(1)= 24/2= 12

(12)^2= 144

Step-by-step explanation:

the answer is

A,72

B,739

D,-11

Answer:

40

Step-by-step explanation: 13 + 6 + 15 + 6 = 40 ( : - ]

Answer:

4.0800*10^4

Step-by-step explanation:

4.9*10^4=49000

49000-8200=40800

since we can only have base numbers 1-9 in scientific notation, we need to move the decimal left 4 places:

4.0800*10^4

Hope this helps!

The scientific notation, of the given number is 4.0800×10⁴

Given the number is 4.9×10⁴-8200

4.9×10⁴ = 49000

49000-8200 = 40800

Since we can only have base numbers 1-9 in scientific notation, we need to move the decimal left 4 places:

4.0800×10⁴

Hence, the scientific notation, of the given number is 4.0800×10⁴

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Answer:

27648inches÷64inches=432 tiles

Step-by-step explanation:tiles cost 3456

Answer:

A and E

Step-by-step explanation:

I would plug in N as any number just to see if they are equal. I did 5.

A. 28(5)-35= -105

B. 28(5-35)= -840

C. 28(5-7)= -56

D. 7(4*5-35)= -105

E. 7(4*5-5)=  105

Answer:

3.5

Step-by-step explanation:

0 1 1 3 3 3 4 5 7

median= 3

Q1= 1

Q3= 4.5

4.5-1= 3.5

Answer:3.5

0,1,1,3,3,3,4,5,7

Answer:

The description that best compares the graph of the two function is:

         The line for function A is steeper.

Step-by-step explanation:

Answer:

The line for function a is a steeper

Step-by-step explanation:

526.36 rounded will be =

= 530

Answer:

[tex]-\sqrt{5}[/tex]

I hope that this helps anyone in the future! I took the test and got a good grade thanks to the anwser above

Answer:

Hello There Again. The correct answer is B. C. And E.

Explanation:

Because it shows that Stacy section of the numbers 2, 3, 4, 5, and 6 to play they game. but the statement Is D. but why is D. because it say that it is less likely that the power will on add numbered section and why i pick E. because it shows that Stacy use the spinner of the six number to play the game. And why it B. because of the pointer of the landing is a even-numbered section. Hope It Helps! .ω.

Answer:

Value of y > 0 at [tex]x = \{0, 1, 2, 3, 4\}[/tex]

Step-by-step explanation:

As seen from the graph attached in answer area as well, The graph is above  x-axis (i.e. y value of equation) only when x has values {0, 1, 2, 3, 4}.

At x = 0:

[tex]y = -|0-2| + 2 \\\Rightarrow -2 + 2\\ \Rightarrow y = 0[/tex]

At x = 1:

[tex]y = -|0-1| + 2 \\\Rightarrow -1 + 2\\ \Rightarrow y = 1[/tex]

At x = 2:

[tex]y = -|2-2| + 2 \\\Rightarrow 0 + 2\\ \Rightarrow y = 2[/tex]

At x = 3:

[tex]y = -|3-2| + 2 \\\Rightarrow -1 + 2\\ \Rightarrow y = 1[/tex]

At x = 4:

[tex]y = -|4-2| + 2 \\\Rightarrow -2 + 2\\ \Rightarrow y = 0[/tex]

Value of y > 0 at [tex]x = \{0, 1, 2, 3, 4\}[/tex]

Answer:

The probability that an incoming freshman scores between 61.6 and 80.2 is 0.7498

Step-by-step explanation:

We are given that Scores on a math placement exam at UGA are normally distributed with a mean of 76 and a standard deviation of 6.

Mean = [tex]\mu = 76[/tex]

Standard deviation =[tex]\sigma = 6[/tex]

we are supposed to find the probability that an incoming freshman scores between 61.6 and 80.2 i.e. P(61.6<x<80.2)

Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]

At x = 61.6

So,[tex]Z=\frac{61.6-76}{6}[/tex]

Z=-2.4

Refer the z table for p value

So,p value =0.0082

At x = 80.2

So,[tex]Z=\frac{80.2-76}{6}[/tex]

Z=0.7

Refer the z table for p value

So,p value =0.7580

P(61.6<x<80.2)=P(x<80.2)-P(x<61.6)=0.7580-0.0082=0.7498

Hence the probability that an incoming freshman scores between 61.6 and 80.2 is 0.7498

Answer:

can you fix the post so that it is not formatted weird?

Step-by-step explanation:

PLEASE MARK BRAINIEST!!

The required value of cos θ is approximately -0.95.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

We are given that sin θ = -0.31 and π < θ < 3π/2.

Since sin θ = -0.31 is negative, we know that θ is in the third quadrant.

Using the identity 2θ + 2θ = 1,

We can rewrite it as:

2θ = 1 - 2θ.

Squaring both sides, we get:

4θ² = 1 - 4θ + 4θ²

Simplifying, we get 8θ = 1, which means θ = 1/8π.

Since θ is in the third quadrant, we have cos θ < 0.

Using the identity cos² θ + sin² θ = 1, we can solve for cos θ as follows: cos² θ = 1 - sin² θ

cos² θ = 1 - (-0.31)²

cos² θ = 0.9039

cos² θ ≈ -0.95

Therefore, the value of cos θ is approximately -0.95.

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Answer:

580 cm squared

Step-by-step explanation:

(20 x 10)2 = 400

(20 x 3)2 = 120

(10 x 3)2 = 60

400 + 120 + 60 =

580

Answer:

A. linear

Step-by-step explanation:

A linear model is the best-fitting regression  model for the data plot because for similar variations in x values, the variation in y values are also similar, that is, if you take points (x1, y1), (x2, y2) and (x3, y3) the y1 - y2 is similar to y2 - y3, when x2 - x1 is also similar to x3 - x2.

Answer:

Linear

Just took the quiz!

Answer:

Answer: No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

Step-by-step explanation:

Let n equal the number, and let x equal the smaller number. Let's put this into equation form to make everything easier to understand.

x < n

n = 2x + 3

n = 2x + 1

Note how n equals two different things. In other words, how can n equal 2x + 3, but also equal 2x + 1? The equations have different y-intercepts but the same slope, meaning there are no solutions, or points where the lines would intercept. The only answer that highlights this is the third option.

To further clear things up, let's go through the other answers to make sure we're correct.

Answer 1: Two situations do not describe the exact same line; all parts of the question are unique.

Answer 2: The equations do not have different slopes, so this reasoning is invalid.

Answer 4: The situations describe two equations with the same slope but different y-intercept, not the other way around. In equation form, 2 = 2, but 3 ≠ 1.

Therefore, the only correct answer is option 3.

Answer:     x = 4

       or       x= -2/3 = -0.667

Step-by-step explanation:

Answer: [tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{3}-(-5)=[/tex]

Convert the mixed number to improper fraction. You can do this by multiplying the whole number times the denominator and adding the numerator; over the same denominator.

[tex]-\frac{2*3+1}{3} -(-5)=[/tex]

Solve;

[tex]-\frac{6+1}{3} -(-5)=[/tex]

[tex]-\frac{7}{3} -(-5)=[/tex]

Now, get rid of the two negatives by multiplying.

[tex]-\frac{7}{3} +5=[/tex]

Remember 5 has a 1 below; therefore, we can subtract these two fractions by getting both to a same denominator. Let's rewrite 5 as a fraction.

[tex]-\frac{7}{3}+\frac{5}{1} =[/tex]

To be able to convert 1 to 3, we have to multiply by 3. Remember that if you change the denominator, you have to change the numerator as well.

[tex]-\frac{7}{3}+\frac{5}{1} (\frac{3}{3} ) =[/tex]

Solve;

[tex]-\frac{7}{3}+\frac{15}{3} =[/tex]

Subtract numerators and keep the same denominator.

[tex]\frac{-7+15}{3}=\frac{8}{3}[/tex]

Convert to a mixed number. To do this, first, divide:

8/3=2

6

----

2

The 2 after the equal sign is the whole number, the two in the remainder is the numerator and the 3 is the denominator. Leaving our result as: [tex]2\frac{2}{3}[/tex]

Answer:

Do u have like a worksheet for the problem because that kinda confusing , but I would love to help if you could screens shot or post the pic.

Step-by-step explanation: