Two groups of friends went to the local movie theater. The first group bought four large buckets of
popcorn and five boxes of candy and spent $42.75. The second group spent $25.50 on two boxes of
candy and three large buckets of popcorn.
How much would one large popcorn and one box of candy cost?

The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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Answer:

A.32.10

Step-by-step explanation:

You have to remember to subtract the $35 then start to figure out how much he paid every month for a year.

Answer:

A is 15, B is 1, and c is 4!

Step-by-step explanation:

This is because 15 (rooted number) would be the main focus, and since the x (normally by the rooted number) doesn't have a label (like 2x, 3x, etc.) it will be one. Then, the 4 (last number) is c (since it is on the outside and is likely the divisor.

Good luck!

Answer:

\( \huge{ \boxed{ \tt{ \frac{4}{7} }}}\)

Step-by-step explanation:

Let the points be A and B

\( \sf{A(2 \: , - 1) \longrightarrow \: (x1 \:, y1)}\)

\( \sf{B(9 \: ,3 \: ) \longrightarrow \: (x2 \:, y2)}\)

\( \underline{ \text{Finding \: the \: slope}}: \)

\( \boxed{ \rm{Slope \: ( \: m \: ) \: = \frac{y2 - y1}{x2 - x1} }}\)

\( \rm{Slope = \frac{3 - ( - 1)}{9 - 2} }\)

\( \rm{Slope = \frac{3 + 1}{9 - 2}} \)

\( \rm{Slope = \boxed{ \rm \frac{4}{7} }}\)

Hope I helped!

Best regards! :D

~TheAnimeGirl

Answer:

the third side is \(\sqrt{85}\)

Step-by-step explanation:

root 85 is already the simplest form

Answer:

20.41

Step-by-step explanation:

I got the answer by doing 102.05 divided by 5 the took that number and multiplied it by 3 to get the answer 61.23

Answer:

17

Step-by-step explanation:

Range is the biggest number minus the smallest number. So 20-3=17

The indefinite integral of x√(x-9) dx is \((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\), where C is the constant of integration.

To find the indefinite integral of ∫x√(x-9) dx, we can use the substitution method.

Let u = x - 9, then du = dx.

Substituting these values into the integral, we have:

∫x√(x-9) dx = ∫(u + 9)√u du

Expanding the expression, we get:

∫(u√u + 9√u) du

Now we can integrate each term separately:

∫u√u du = ∫ \(u^{(3/2)}\) du = \((2/5)u^{(5/2)} + C1\)

∫9√u du = 9∫ \(u^{(1/2} du\) = \(9(2/3)u^{(3/2) }+ C2\)

Combining the results and substituting back u = x - 9, we have:

∫x√(x-9) dx = \((2/5)(x-9)^{(5/2)} + 9(2/3)(x-9)^{(3/2) }+ C\)

Simplifying further, we get:

∫x√(x-9) dx = \((2/5)(x-9)^{(5/2) }+ (6/3)(x-9)^{(3/2)} + C\)

                  = \((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\)

Therefore, the indefinite integral of x√(x-9) dx is\((2/5)(x-9)^{(5/2)} + 2(x-9)^{(3/2)} + C\), where C is the constant of integration.

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Answer:

15%

Step-by-step explanation:

Price of daily tickets entrance

Adult=£55

Children=£45

Family (2 adults and 2children)=£170(discount price)

Let

price for adults=a

Price for Children=c

Price of tickets without discount for 2 adults and 2 children=2(a+c)

=2(55+45)

=2(100)

=£200

Percentage discount offered with the family tickets=difference in price/original price×100

=£200-£170/200×100

=30/200×100

=30/2

=15%

The Percentage discount offered with the family tickets=15%

Probabilities associated with this distribution are

(a) P(Z < 0.5) = 0.6915

(b) P(Z = 0.5) = 0

(c) P(Z ≥ 2.3) = 0.0107.

(d)  P(-1.4 ≤ Z ≤ 0.6) = 0.6449.

(e) The value of z0 such that P(|Z| ≤ z0) = 0.32 is 0.9945.

The statement "~(0,1)" refers to a standard normal distribution with mean 0 and standard deviation 1.

We can use the standard normal distribution table or a calculator to find probabilities associated with this distribution. Here are the solutions to the given problems:

(a) P(Z < 0.5) = 0.6915, where Z is a standard normal random variable.

(b) P(Z = 0.5) = 0, since the probability of a continuous random variable taking any specific value is always zero.

(c) P(Z ≥ 2.3) = 0.0107.

(d) P(-1.4 ≤ Z ≤ 0.6) = P(Z ≤ 0.6) - P(Z ≤ -1.4) = 0.7257 - 0.0808 = 0.6449.

(e) The value of z0 such that P(|Z| ≤ z0) = 0.32 is the 0.16th percentile of the standard normal distribution.

From the standard normal distribution table, we can find that the 0.16th percentile is approximately -0.9945. Therefore, z0 = 0.9945.

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Answer:1/25

Step-by-step explanation: do 5 to the second power which will get all combinations then do 1 as the numerator over the denominator which is the number of combinations.

Answer:

840

Step-by-step explanation:

7000×2×6 ÷ 100. since it is 2%

= 840

Ella's bait and tackle shop sells 230,385 in April and May.

Based on the given conditions, formulate:

Bait and tackle sold in 128,278 live worms in April

Bait and tackle sold in 102,278 live worms in May

So the total number of Bait and tackles sold in April and May =

                                                                                             =128,107+102,278

                                                                                              = 230,385

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Answer:x − x^{2} − 1.

Step-by-step explanation:

.

Answer:

subtract/multiply

Step-by-step explanation:you subtract number of passengers and multiply weight of the passengers..hope this helps :)

Based on the given sample, there is sufficient evidence to suggest that the home team has a higher probability of winning in football games.

To test the claim that the probability of the home team winning is greater than one-half, a significance test can be conducted using the given sample of 45 football games, where 28 were won by the home team. The test will determine if the observed proportion of home team wins is statistically significant enough to support the claim.

To test the claim, we can use a hypothesis test with the following null and alternative hypotheses:

Null Hypothesis (H0): The probability of the home team winning is equal to one-half or less (p <= 0.5).

Alternative Hypothesis (Ha): The probability of the home team winning is greater than one-half (p > 0.5).

To conduct the test, we can use the z-test for proportions since we have a large sample size (n = 45). The test statistic, z, can be calculated using the formula:

z = (p - p0) / sqrt[(p0 * (1 - p0)) / n],

where p is the sample proportion, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.

In this case, p is the observed proportion of home team wins, which is 28/45, or approximately 0.622. Since the null hypothesis states that p <= 0.5, we use p0 = 0.5 in the calculation.

Using the formula, the calculated z-value is:

z = (0.622 - 0.5) / sqrt[(0.5 * (1 - 0.5)) / 45] = 1.911.

Next, we compare the calculated z-value to the critical z-value at the chosen significance level. Let's assume a significance level of α = 0.05 for a one-tailed test.

Looking up the critical z-value for a one-tailed test with α = 0.05, we find it to be approximately 1.645.

Since the calculated z-value (1.911) is greater than the critical z-value (1.645), we have evidence to reject the null hypothesis. This means that the observed proportion of home team wins (0.622) is statistically significant and supports the claim that the probability of the home team winning is greater than one-half.

Therefore, based on the given sample, there is sufficient evidence to suggest that the home team has a higher probability of winning in football games.

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The expression that represents the net yardage for these plays is given as follows:

19.8x - 11.1y.

The net yardage is given by the sum of all yards gained for the sum of all yards lost.

For example, if Josh Allen passes for 350 yards but loses 20 yards on sacks, his net yardage is given as follows:

350 - 20 = 330 yards.

Then the expression that gives the total net yardage for this problem is given as follows:

25x + 0.9y - 12y - 5.2x.

The expression can be simplified combining the like terms, as follows:

25x - 5.2x + 0.9y - 12y.

(25 - 5.2)x + (0.9 - 12)y

19.8x - 11.1y.

(as combining the like terms means that all the terms with the same letter  and same exponent are added/subtracted).

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Answer:(-4, -2)

Step-by-step explanation:

Answer:

We have 3 variables to solve for.  We will start by writing two equations in three variables but, with the given information, will eventually have those equations written in 2 variables.  The strategy is to set up equations from the given information and solve the equations simultaneously.  Let's assign variables...

c= #children total

s= #students total

a= #adults total

c+s+a=900.............Eq1, total attendance, given

4c+6s+8a=5600....Eq2, total receipts, given

a=(1/2)(c+s)

 =(1/2)c+(1/2)s.....Eq3, #adults total, given

Let's substitute Eq3 into each Eqs1,2 to get two equations in two variables...

c+s+(½c+½s)=900.........Eq1, substitute for"s"

      1.5c+1.5s=900.......combine like terms

            3c+3s=1800.....Eq4, multiple equation

                                      by 2 to eliminate fraction

4c+6s+8(½c+½s)=5600...Eq2, substitute for "s"

   4c+6s+(4c+4s)=5600...distribute 8

               8c+10s=5600...Eq5, combine like terms

Let's solve newly arrived at Eq4,5 simultaneuously...

    3c+3s=1800......Eq4

  8c+10s=5600......Eq5

-24c-24s=-14400...Eq4 multiplied by (-8)

24c+30s=16800...Eq5 multiplied by 3

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

          6s=2400.....add all terms vertically

        ∴ s=400.......divide both sides by 6

Substitute value back into Eq4, solve for "c"...

      3c+3s=1800...Eq4

3c+3(400)=1800...substitute for"s"

  3c+1200=1800

            3c=600.....subtract 1200, both sides

          ∴ c=200....divide both sides by 3

Substitute values back into Eq3, solve for "a"...

  a=(1/2)(c+s).............Eq3

    =(1/2)(200+400)...substitute for "c,s"

    =(1/2)(600)

∴ a=300.....................simplify

We now have our three variables solved.  Let's substitute those values back into original Eqs1,2 to check against the problem requirements...

          c+s+a=900.......Eq1

200+400+300=900....substitute for "c,s,a"

               900=900......true, √check

                  4c+6s+8a=5600.....Eq2

4(200)+6(400)+8(300)=5600...substitute for

                                                  "c,s,a"

        800+2400+2400=5600...simplify

                         5600=5600......true, √check

So our calculated values are correct. Always check your solutions and work!

In summary, we have...

200 children, 400 students, and 300 adults in attendance at the theater for the screening.

Step-by-step explanation:

There were total 150 childrens, 450 students and 300 adults.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a theater that has a seating capacity of 900 and charges $2.50 for children, $4 for students, and $5.50 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The total money brought in was $3825.

Assume that there were [x] childrens, [y] students and [z] adults. Then, we can write the equations as -

x + y + (1/2)(x + y) = 900

2.5x + 4y + (5.5)(1/2)(x + y) = 3825

Plot the graph. We will get x = 150 and y = 450.

Then -

z = (1/2)(150 + 450) = (1/2)(600) = 300

Therefore, there were total 150 childrens, 450 students and 300 adults.

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Step-by-step explanation:

Multiply numerator by numerator, denominator by denominator.

\( \frac{2}{4} \times \frac{9}{3} = \frac{18}{12} \)

Divide each side by 6:

\( \frac{18 \div 6}{12 \div 6} = \frac{3}{2} \)

3/2 also represents 1 1/2 as a mixed fraction.

Answer:

\(y=|x-(-2)|+2\)

Step-by-step explanation:

Hope this is helpful.

The required absolute function is given as y = |x - 2| + 2.

Given that,
From the graph, y = |x - h| + k, values of h and k is to be determined,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the graph and function, h represents the shift on the x-axis, which 2 units left so the value of h is 2, while k is given the shift of the function over the y-axis which 2 units up means that k = 2

Thus, The required absolute function is given as y = |x - 2| + 2.

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Answer:

i think you got it by now

Step-by-step explanation:

Answer:

Step-by-step explanation:

four shortcuts allow students to know two triangles must be congruent: SSS, SAS, ASA, and AAS. Knowing only side-side-angle (SSA) does not work because the unknown side could be located in two different places. ... Because there are 6 corresponding parts 3 angles and 3 sides, you don't need to know all of them.

In a transformation called a translation, the pre-image is slid either vertically or horizontally.

A translation is a type of transformation in geometry where the pre-image (original figure) is moved or slid to a new position in a specific direction. The movement can be either vertical or horizontal.

When a pre-image is translated vertically, it means that it is moved up or down without any change in its orientation. The entire figure maintains the same shape and size, but its position on the coordinate plane is shifted vertically.

On the other hand, when a pre-image is translated horizontally, it is moved left or right while preserving its original shape and size. The orientation of the figure remains the same, but its position on the coordinate plane is shifted horizontally.

In both cases, the translation occurs without any rotation, reflection, or resizing of the pre-image. The resulting image is a new figure that is congruent to the original but located at a different position on the plane.

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Answer:

C. No solutions exist Because the situation describes two lines that have the same slope and different y-intercepts

Step-by-step explanation:

it is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope so there is no solution.

Answer: 10 Days

Step-by-step explanation:

Answer:

B=14hrs 30min

A=5hrs 30min

Step-by-step explanation:

let's A be x and B be 9+x then follow the method used in the picture above and you'll get the answer.

good day.

the probability that the next 3 cards are also spades is 0.0156.

There are 13 spades in a deck of 52 cards. The probability of each card being a spade is 13/52 or 0.25. The probability that the next 3 cards are also spades is 0.25 x 0.25 x 0.25 = 0.016. Therefore, the probability that the next 3 cards are also spades is 0.0156.

1. Calculate the probability of one card being a spade: 13/52 or 0.25

2. Calculate the probability of the next 3 cards being spades: 0.25 x 0.25 x 0.25 = 0.016

3. Round the answer to four decimal places: 0.0156

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In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.

In this question we need to analyze an exponential function of the form:

y = a · (1 + r)ˣ      (1)

Where r is the growth rate. Please notice that there is a decay for r < 0. Thus, we find the following finding by comparing the given expression to (1):

y = 0.84 · (1 + 1/6)ˣ

In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.

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Answer:

Just take the opposite of the number in the factor.

x = 7, x = -1, x = 9

The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

What is a binomial distribution?

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

Formula to calculate the binomial distribution

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ

Here, we know that

Solar-heat installations successfully reduce the utility bill 60% of the time.

We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.

We have 60% = 0.6 = p and n = 10.

We have a binomial distribution: X : (10, 0.6).

We use the binomial distribution formula to calculate the probability

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get

P(x ≥ 9) = 1 - P(x < 9)

P(x ≥ 9) = 1 - P(x ≤ 8)

P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)

P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ

P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)

P(X ≥ 9) = 1 -0.95365

P(X ≥ 9) = 0.04635

Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

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