A bag contains 7 red marbles, 8 blue marbles and 4 green marbles. If three marbles
are drawn out of the bag, what is the probability, to the nearest 100oth, that all three
marbles drawn will be blue?

Answer:

a) SAT score = 1075

b) ACT score = 19.2.

c) ACT score = 27.9.

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.

(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score

SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]

51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So

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

[tex]0.025 = \frac{X - 1070}{204}[/tex]

[tex]X - 1070 = 0.025*204[/tex]

[tex]X = 1075[/tex]

SAT score = 1075.

(B) What would be the equivalent ACT score for this student?

ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So

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

[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 0.025*5.2[/tex]

[tex]X = 19.2[/tex]

ACT score = 19.2.

(C) If a student gets an SAT score of 1417, find the equivalent ACT score.

Z-score for the SAT:

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

[tex]Z = \frac{1417 - 1070}{204}[/tex]

[tex]Z = 1.7[/tex]

Equivalent score on the ACT:

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

[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 1.7*5.2[/tex]

[tex]X = 27.9[/tex]

ACT score = 27.9.

Answer:

She needs a grade of 71 on her next text.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values in the data-set divided by the number of values.

Tammy has scored 82, 78, and 93 on her previous three tests.

Thus, her grades are 82, 78, 93 and x, in which x is her grade in the fourth test.

There are 4 tests.

What score does she need on her next test so that her average (mean) is 81?

We have to find x when the mean is 81. So

[tex]\frac{82 + 78 + 93 + x}{4} = 81[/tex]

[tex]253 + x = 324[/tex]

[tex]x = 324 - 253[/tex]

[tex]x = 71[/tex]

She needs a grade of 71 on her next text.

Answer:

2/45+1/9=

7/45

Have a great day

Given:

The given sum is:

[tex]\sum _{k=4}^9(5k+3)[/tex]

To find:

The expanded form and find the sum.

Solution:

We have,

[tex]\sum _{k=4}^9(5k+3)[/tex]

The expanded form of given sum is:

[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]

[tex]\sum _{k=4}^9(5k+3)=213[/tex]

Therefore, the correct option is C.

Answer:

[tex](a)\ Pr = \frac{2}{5}[/tex]

[tex](b)\ Pr = \frac{9}{20}[/tex]

[tex](c)\ E(Orange) = 100[/tex]

[tex](d)\ E(Orange) = 62.5[/tex]

Step-by-step explanation:

Solving (a): Theoretical probability of green or yellow

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 5[/tex] --- i.e. 5 sections

[tex]Yellow = 1[/tex]

[tex]Green = 1[/tex]

So, the probability is:

[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]

[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]

[tex]Pr = \frac{1}{5} + \frac{1}{5}[/tex]

Take LCM

[tex]Pr = \frac{1+1}{5}[/tex]

[tex]Pr = \frac{2}{5}[/tex]

Solving (b): Experimental probability of green or yellow

Here, we consider the result of the experiment

From the attached image, we have:

[tex]n= 40[/tex] --- i.e. 40 spins

[tex]Yellow = 12[/tex]

[tex]Green = 6[/tex]

So, the probability is:

[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]

[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]

[tex]Pr = \frac{12}{40} + \frac{6}{40}[/tex]

Take LCM

[tex]Pr = \frac{12+6}{40}[/tex]

[tex]Pr = \frac{18}{40}[/tex]

Simplify

[tex]Pr = \frac{9}{20}[/tex]

Solving (c): Expectation of orange outcomes in a spin of 500 times, theoretically.

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 5[/tex] --- i.e. 5 sections

[tex]Orange = 1[/tex]

So, the probability of having an outcome of orange in 1 spin is:

[tex]Pr = P(Orange)[/tex]

[tex]Pr = \frac{Orange}{n}[/tex]

[tex]Pr = \frac{1}{5}[/tex]

In 500 spins, the expectation is:

[tex]E(Orange) = Pr * 500[/tex]

[tex]E(Orange) = \frac{1}{5} * 500[/tex]

[tex]E(Orange) = 100[/tex]

Solving (c): Expectation of orange outcomes in a spin of 500 times, base on experiments.

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 40[/tex] --- i.e. 40 spins

[tex]Orange = 5[/tex]

So, the probability of having an outcome of orange is:

[tex]Pr = P(Orange)[/tex]

[tex]Pr = \frac{Orange}{n}[/tex]

[tex]Pr = \frac{5}{40}[/tex]

[tex]Pr = \frac{1}{8}[/tex]

In 500 spins, the expectation is:

[tex]E(Orange) = Pr * 500[/tex]

[tex]E(Orange) = \frac{1}{8} * 500[/tex]

[tex]E(Orange) = 62.5[/tex]

Answer:

3692.64 cm³

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

Given a tangent and a secant from an external point to a circle, then

The product of the external part and the whole of the secant is equal to the square of the tangent, that is

9(9 + x) = 15²

9(9 + x) = 225 ( divide both sides by 9 )

9 + x = 25 ( subtract 9 from both sides )

x = 16

Answer:

Solution given:

a = 12, b = 5, c = 9

We have

: a² = b² + c² – 2bc cos A

12²=5²+9²-2×5×9 cos A

12²-25-81=-90 cos A

cos A=38/-90

A=cos -1(-19/45)

A=115°

is a required answer.

Answer: the answer is 8 because

Step-by-step explanation:

Answer:

Belle is my fav.

Step-by-step explanation:

She loves to read books like me and I hate people who always go out there and try to impress me with something.

Answer:

1,408 packs can be made, and 2 pens will be left out.

Step-by-step explanation:

Given that a manufacturer has 5,634 pens to divide into packs of 4 pens, and the manufacturer makes as many packs as possible, to determine how many packs of pens does the manufacturer make, and how many pens are left over, the following must be done calculation:

5.634 / 4 = X

1,408.5 = X

5,634 - (1,408 x 4) = X

5.634 - 5.632 = X

2 = X

Therefore, 1,408 packs can be made, and 2 pens will be left out.

Answer: 1,408 packs can be made and 2 will be left out

Step-by-step explanation:

Answer: The  maximum   value is   -3.75  

Note: -3.75 = -15/4

=============================================================

Explanation:

The given quadratic is in the form y = ax^2 + bx + c, where,

We'll plug the values of 'a' and b into the formula below

h = -b/(2a)

h = -1/(2(-1))

h = 1/2

h = 0.5

This represents the x coordinate of the vertex. Recall the vertex is (h,k).

Plug this x value into the function to find its corresponding y coordinate

y = -x^2 + x - 4

y = -(0.5)^2 + 0.5 - 4

y = -3.75

The vertex is located at (0.5, -3.75)

Since a < 0, this means the parabola opens downward and that the vertex is the highest point on the parabola. Therefore, the largest y can get is y = -3.75 which we consider the maximum.

The graph visually helps confirm this (see image attachment).

Side note: -3.75 = -15/4

-------------------

Here's another way we can find the vertex (h,k). We'll complete the square to get the function into vertex form

y = -x^2 + x - 4

y + 4 = -x^2 + x

y + 4 = -(x^2 - x)

y + 4 = -(x^2 - x + 0)

y + 4 = -(x^2 - x + 0.25 - 0.25) .... see note below

y + 4 = -(x^2 - x + 0.25) -(-0.25)

y + 4 = -(x^2 - x + 0.25) + 0.25

y + 4 = -(x - 0.5)^2 + 0.25

y = -(x - 0.5)^2 + 0.25 - 4

y = -(x - 0.5)^2 - 3.75

This is in the form y = a(x-h)^2 + k where (h,k) = (0.5, -3.75).

Note: The x coefficient is -1 which cuts in half to -0.5, then that squares to 0.25

9514 1404 393

Answer:

  2. Given

  4. SAS postulate

Step-by-step explanation:

Reason 2: Statement 2 is one of the Given statements.

Reason 4: You have shown that two sides and the angle between them are congruent. The Side-Angle-Side (SAS) congruence postulate applies.

Answer:

The annual interest rate of return during his investment was 12.28%.

Step-by-step explanation:

Since Julio purchased 1,700 shares of a certain stock for $ 23,750 including commissions, and I have sold the shares 3 years later and received $ 32,500 after deducting commissions, to find the effective annual rate of return on his investment over the 3-year period the following calculation  must be performed:

23,750 = 100

32,500 = X

32,500 x 100 / 23,750 = X

3,250,000 / 23,750 = X

136.84 = X

(136.84 - 100) / 3 = X

36.84 / 3 = X

12.28 = X

Therefore, the annual interest rate of return during his investment was 12.28%.

Answer:

Step-by-step explanation:

First,

7 times 8 = 7 × 8 = 56

Then,

The product divided by 2 = 56 ÷ 2 = 28

Hence,

The required answer is 28

Answer:

The answer is LINEAR EQUATIONS

Step-by-step explanation:

Hope you have a great day :)

Answer:

B. -0.5

Step-by-step explanation:

I calculated it logically

Answer:

0.3269

Step-by-step explanation:

Number of spades = 13

Number of 5's = 4

17/52 =

Answer:

Step-by-step explanation:

Answer:

x = 2 , 1

Step-by-step explanation:

Answer:

2.5 or 3.5

Step-by-step explanation:

The quadratic formula is [tex]x = -b +/- \frac{\sqrt{b^2 + 4ac}}{2a}[/tex] .

a, b, and c are determined by the terms in the formula ax^2 + bx + c

They gave you the equation x^2 - 3x - 2, which fits that formula. a is 1, b is -3, and c is -2. So plug those values into the equation:

[tex]x = -(-3) +/- \frac{\sqrt{(-3)^2 + 4(1)(-2)}}{2(1)}[/tex]

[tex]x = 3 +/- \frac{\sqrt{9 -8}}{2}[/tex]

[tex]x = 3 +/- \frac{\sqrt{1}}{2}[/tex]

[tex]x = 3 +/- \frac{1}{2}[/tex]

So x is 3 plus or minus -1/2. 3 plus -1/2 is 2.5

3 minus -1/2 is 3.5

So the 2 possible x values are 2.5 and 3.5.

Answer:

9 ft

Step-by-step explanation:

Area of a a rectangle = length × width.

Plug in the information youhave.

45ft. = 5ft × ?

45 = 5x

9 = x

Answer:

x = -5/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

-4x = 5

Step 2: Solve for x

Answer:

x = -5/4

Step-by-step explanation:

-4x = 5

Divide both sides by -4

x = -5/4

Answer:

speed = 78 miles per hour

Step-by-step explanation:

Speed is distance divided by time

speed = 234 miles / 3 hours

speed = 78 miles per hour

Answer:

[tex]P(Work | Senior) = 0.14[/tex]

Step-by-step explanation:

Given

The attached table

Required

[tex]P(Work | Senior)[/tex]

This is calculated using:

[tex]P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}[/tex]

This gives:

[tex]P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}[/tex]

From the table:

[tex]n(Work \ n\ Senior) = 5[/tex]

[tex]n(Senior) = 25 + 5+ 5 = 35[/tex]

So:

[tex]P(Work | Senior) = \frac{5}{35}[/tex]

[tex]P(Work | Senior) = 0.14[/tex]

Answer:

14%

Step-by-step explanation:

add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

Answer:

90°

Step-by-step explanation:

It's simple, the angle of a line is 180°

∠EFG=90°

Line GD-∠EFG=180°-90°=90°

Please mark brainliest!

Answer:

He can lift 160 pounds

Step-by-step explanation:

125 (from last year) + 35 (more pounds) = 160 (total pounds)

125 + 35 = 160