Charity is ordering a sundae at a restaurant, and the server tells her that she can have up to five toppings: chocolate chips, butterscotch sauce, strawberries, a cherry, and hot fudge. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Charity gets just chocolate chips and a cherry? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer:

605

Step-by-step explanation:

11x55=605

The first term \(a_{1}\) = 2 and the sum of first 30 terms \(s_{30}\) = 930

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Arithmetic sequence is gotten by adding a known term by a constant value.

if \(a_{33}\) = 66 and d = 2 and \(a_{n}\) = \(a_{1}\) + (n -1)d and n = 33

Then

\(a_{33}\) =  \(a_{1}\) + 32d,

making  \(a_{1}\) subject of the equation we have

\(a_{1}\) =66 - 32 x 2

\(a_{1}\) = 66 - 64

\(a_{1}\) = 2

if n = 30,  \(a_{1}\) =-2, d = 2

Then

\(a_{30}\) = 2 + ( 30 - 1) x 2

\(a_{30}\) = 2 + 29 x 2

\(a_{30}\) = 60

if \(s_{n}\) = n/2(\(a_{1}\) + \(a_{n}\))

Then,

\(s_{30}\) = n/2 ( \(a_{1}\) + \(a_{30}\)) where n = 30

\(s_{30}\) = 30/2( 2 + 60)

\(s_{30}\) = 930

In conclusion, the sum of he first 30 terms is 930 and the first term is 2

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Answer:8.5

Step-by-step explanation:

There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members

If a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:

14Cr3 = \(\frac{14!}{3! 11!}\) = \(\frac{14x13x12}{3x2x1}\) = 364

Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.

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Answer: $24.34

Step-by-step explanation:

28/X=115/100

Part/Whole= %/100

28=1.15*x

Answer:

y=2/1+7

Step-by-step explanation:

Answer: 95.5

Step-by-step explanation:

If you order the numbers from least to greatest and alternate revoking numbers the number in the middle, or median will be 95.5

True, Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.

What does a response variable in an experiment mean?

Response Continuum In an experimental investigation, this is the result that is assessed after manipulating the explanatory variable; it is also referred to as the dependent or outcome variable.

                                Its value is expected or its variation is explained by the explanatory variable.

What other name would you give the answer variable?

The term "dependent variable" is one more typical moniker for the response variable. The response variable is frequently referred to as just "the response" for short.

                        There are several more terms for the predictor variables, including "explanatory variables," "independent variables," "predictors," and "regressors."

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Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

Answer:

Domain is A

Range is D

Step-by-step explanation:

it's all x because the line will go up and down on both directions infinitely hitting every x coordinate. The range is all y because it will also extend infinitely upwards and downwards. This is not a parabola so there i no limitation

The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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The condition probability of a given b must be smaller than the intersection of the same two events a and b:

This statement is False.

The condition probability of event "b" given event "a" (P(b|a)) must be less than or equal to the probability of event "b" (P(b)). This is because the occurrence of event "a" restricts the sample space to only those outcomes that belong to event "a", and thus the probability of event "b" given event "a" cannot be greater than the unconditional probability of event "b".

The concept of conditional probability is used to describe the probability of an event given that another event has already occurred.

The formula for conditional probability is

where P(b|a) represents the probability of event "b" given that event "a" has already occurred.

In order for this to be meaningful, it is required that P(b|a) <= P(b). This means that the probability of event "b" given that event "a" has already occurred cannot be greater than the unconditional probability of event "b".

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Answer:

There were 96 guests at the wedding.

Step-by-step explanation:

Let,

x be the total number of guests at the wedding.

People who chose pasta = 1/3 of the guests = \(\frac{1}{3}x\)

People who chose chicken = \(\frac{5}{12}x\)

People who chose beef = 24

Now,

\(\frac{1}{3}x+\frac{5}{12}x+24=x\\\\\frac{4x+5x+288}{12}=x\\9x+288 = 12x\\288=12x-9x\\288=3x\\3x=288\)

Dividing both sides by 3

\(\frac{3x}{3}=\frac{288}{3}\\x=96\)

Hence,

There were 96 guests at the wedding.

Answer:

9.26 per quart

Step-by-step explanation:

A 3-gallon bucket of paint costs $111.12.

  Find the price of per quart.

3 gallons equal 12 quarts. We divide 111.12 for 12 quarts by 12:

111.12 / 12 = 9.26

Answer:

65.5

Step-by-step explanation:

Answer:

65.5

Step-by-step explanation:

Answer:

To find the probability of selecting a Coke person from this group, we need to divide the number of people who prefer Coke by the total number of people in the group.

The number of people who prefer Coke is 29. The total number of people in the group is 29 + 21 + 37 + 28 + 19 + 16 + 150 + 150 + 2 = 452.

Therefore, the probability of selecting a Coke person from this group is:

P(Coke) = Number of people who prefer Coke / Total number of people in the group = 29 / 452 ≈ 0.064

So the probability of selecting a Coke person from this group is approximately 0.064.

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Answer:

301.59 units or 301.6 after rounding

Answer:

The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

In this question:

\(\mu = 68, \sigma = 15\)

Middle 68.26% of the grades:

From the

50 - (68.26/2) = 15.87th percentile

To the

50 + (68.26/2) = 84.13rd percentile.

15.87th percentile:

X when Z has a pvalue of 0.1587. So X when Z = -1.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1 = \frac{X - 68}{15}\)

\(X - 68 = -1*15\)

\(X = 53\)

84.13rd percentile:

X when Z has a pvalue of 0.8413. So X when Z = 1.

\(Z = \frac{X - \mu}{\sigma}\)

\(1 = \frac{X - 68}{15}\)

\(X - 68 = 1*15\)

\(X = 83\)

The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.

The function of the number of DVDs Angel owns (a) will be a = p + 10

From the information, Angel owns 10 more DVDs than Philip.

The number of DVD that Philip owns was represented asp.

Therefore, the function of the number of DVDs Angel owns (a) will be:

a = p + 10

Therefore the function is a = p + 10

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It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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Answer:

31/6

Step-by-step explanation:

Step 1:

13/24 × 3 5/9

Step 2:

13/24 × 32/9

Step 3:

62/12

Answer:

31/6

Hope This Helps :)

The product of powers of exponents cannot be used to simplify the binomial expansion

Given data ,

Let the binomial expansion be represented as A

A = ( 3z + y )³

According to the property of products of powers, exponents can be multiplied when a power is increased to a higher power.

The product of powers characteristic cannot be applied to the equation (3z + y)³. This is due to the fact that (3z + y)³ is a binomial raised to the power of 3, not just a power of a single word.

These terms cannot be simplified further using the product of powers property because they involve different variables or variable combinations.

In this case, it is more appropriate to expand the expression using the binomial expansion

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Answer:

Step-by-step explanation:

hope it help you

follow me please

Answer:

the answer is 35

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

From the question, we have the following parameters that can be used in our computation:

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

  86.75

Step-by-step explanation:

Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.

The grade for the course, with fourth test score x, will be ...

  0.20(63.5 +76 +87) +0.40x = 80

  0.40x +45.3 = 80

Solving for x, we get ...

  0.40x = 34.7 . . . . subtract 45.3

  x = 86.75 . . . . . . . divide by 0.4

The minimum score you need on the fourth test is 86.75.

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

undefined

Step-by-step explanation:

division by zero is undefined

Division Property of zero

For any nonzero real number a

The quotient of "a" and 0 is undefined. That is a/0 is undefined