At the city museum, child admission is 5.70 and adult admission is 9.80. On Friday, 114 tickets were sold for a total sales of 912.20. How many adult tickets were sold that day?

Answer: 2  and 321 or  3  and 214

Step-by-step explanation:

One number is between 200-225.

Now, back up just a bit.  The product of the two numbers is 642.  Product comes from multiplying the two numbers.  So, if we divide 642 by the number that is between 200-225, we will get the other number.

 So, divide 200 into 642 and get 3 with a remainder of 42

     divide 225 into 642 and get 2 with a remainder of 192

This means that the other number must be either 2 or 3.  (note: this is because dividing by 200 gives the biggest value it could be and dividing by 225 gives the lowest value it could be -- think about sharing a bag of candy, dividing it between 2 friends gets each person the most candy and dividing it between more friends (3) gives each person less candy).

Well. if the other number is either 2 or 3, and the product of the two numbers is 642, the numbers must be either: 2  and 321 or  3  and 214

a) A × B is the Cartesian product of A and B, given by the set

A × B = {(a, b) | a ∈ A and b ∈ B}

Then for A = {4, 6, 8} and {4, 5, 6}, we have the product

A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}

b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...

Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is

A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}

and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set

Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}

Answer:

In 30 days she will do both again

Step-by-step explanation:

It's the first multiple of 15 that can also be a multiple of 2

Answer:

b,a,c

Step-by-step explanation:

Answer:

n + m = 4

Step-by-step explanation:

If m = 5 and n = -1 then that means 5 + (-) which equals 4

hope that helps ❤️

The limit of the function (cos(xy) -1)/(\(x^2\)\(y^2\)) as (x,y) approaches (0,0) is not defined.

We can see that the denominator \(x^2\)\(y^2\) goes to 0 as (x,y) approaches (0,0), and that can cause the function to go to infinity. However, the numerator (cos(xy) -1) does not have a specific value as (x,y) approaches (0,0) the cosine function oscillates between -1 and 1 as xy approaches zero, and therefore it does not approach a specific value.

The term (x,y) → (0,0) means that x and y are approaching 0 independently. There are different paths in which x and y can approach zero. Hence, by the squeeze theorem, we can see that if we approach (x,y) to (0,0) along the path y = mx, where m is a nonzero constant, the function goes to infinity, but if we approach (x,y) to (0,0) along the path x = 0 or y = 0, the function goes to -1.

Therefore, the limit of the function (cos(xy) -1)/(\(x^2\)\(y^2\)) as (x,y) approaches (0,0) is not defined, as the function does not approach a specific value along all paths.

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A total of 192 students voted altogether.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as an addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

Given:

The number of students who voted for Morgan = 64.

Let the number of students who voted for Whitney = n.

According to the question,

n = 2 times the number of students who voted for Morgan

n = 2 x 64

n = 128.

The total number of students who voted = 64 + 128

The total number of students who voted = 192.

Therefore, the required number of votes is 128.

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Answer:

-3

Step-by-step explanation:

Answer: The slope whould be 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept:

(0,0)

x|y

----

0|0

1|3

The volume of the cylinder is 1020.5 cu.yards .

A cylinder is a three dimensional figure , wit no vertices and edges , it as two similar circular bases and a curved surface.

It is given that :

Radius of the cylinder is 5 yards

Height = 13 yards

The volume of the cylinder is given by

V = π R²h

V = 3.14 *(5 *5) * 13

V = 1020.5 cu.yards

The volume of the cylinder is 1020.5 cu.yards .

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The amount of the first alloy is 450 grams and the amount of the second alloy is 30 grams.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

A chemist has two alloys, one of which is 5% gold and 20% lead and the other which is 30% gold and 50% lead.

Let's suppose the x is the amount of the first alloy and y is the amount of the second alloy:

We can make two linear equation in two variables:

0.05x + 0.3y = 31.5  ...(1)

0.2x + 0.5y = 105  ...(2)

After solving the above two linear equations by substitution method, we get:

x = 450 grams

y = 30 grams

Thus, the amount of the first alloy is 450 grams and the amount of the second alloy is 30 grams.

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Answer:

Step-by-step explanation:

4x + 2x = 180

6x = 180

x = 30

Answer:

first one is 4

second is   2

Step-by-step explanation:

let me know if you need to  show work

Answer:

first one is 4, 2nd one is 2

Step-by-step explanation:

Answer:

The 90% confidence interval is  \(0.445< p < 0.456\)

Step-by-step explanation:

From the  question we are told that

  The sample  size is  \(n = 17592\)

  The number of  binge  drinkers is  \(k = 7851\)

Given that the  confidence level is  90%  then the level of significance is mathematically represented as

          \(\alpha = (100 - 90)\%\)

          \(\alpha = 0.10\)

The critical value  of  \(\frac{\alpha }{2}\)  from the normal distribution table  is  \(Z_{\frac{\alpha }{2} } = 1.645\)

The  sample  proportion is mathematically represented as

      \(\r p = \frac{ 7851}{ 17592}\)

      \(\r p = 0.45\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{ \frac{x}{y} } * \sqrt{\frac{\r p(1 - \r p )}{n} }\)

       \(E =1.645 * \sqrt{\frac{ 0.45 (1 - 0.45 )}{17592} }\)

      \(E =0.00617\)

The  90%  confidence interval is mathematically represented as  

      \(\r p -E < p < \r p +E\)

      \(0.45 -0.00617 < p < 0.45 + 0.00617\)

      \(0.445< p < 0.456\)

Answer:50 minutes

Step-by-step explanation:

Answer:

Irrational.

Step-by-step explanation:

The square root of 35 is not a perfect integer.

The conclusion of the hypothesis testing is that; there is not enough evidence to support the claim that the mineral changes a person’s cholesterol level.

Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample.

Let us first define the hypothesis in this problem;

Null Hypothesis; H₀: μ_d = 0

Alternative Hypothesis; Hₐ: μ_d ≠ 0 (Claim)

The degree of freedom is;

DF = n - 1

DF = 6 - 1

DF = 5

At a significance level of α = 0.10, with a DF of 5, the critical values are ±2.015.

Using a computer software, we can calculate the mean from the attached table as;

D' = ∑d/n

D' = 100/6 = 16.7

Similarly, the standard deviation is calculated from the formula;

S_d = √(n∑d² - (∑d)²)/(n(n - 1))

s_d = √(6.489 - 100²)/(6(6 - 1))

s_d = 25.4

The test statistic is gotten from the formula;

t = (D' - μ_d)/(s_d/√n)

t = (16.7 - 0)/(25.4/√6)

t = 1.610

This is less than the critical value and we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mineral changes a person’s cholesterol level.

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Answer:

A satellite state is a country that is formally independent in the world, but under heavy political, economic and military influence or control from another country.

Answer:

c. could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest

Step-by-step explanation:

Nirav just opened a savings account paying 2 percent interest, compounded annually. After four years, the savings account will be worth $5,000. Assume there are no additional deposits or withdrawals. Given this information, Nirav:

a. will earn simple interest on his saving every year for four years

False. Problem states it's compound interest.

b. has an account currently valued at $5,000

False. Problem states account will be worth $5,000 in 4 years.

c. could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest

True. With a higher interest rate, he would earn more interest, so he could start with less money and still end up with $5000 at the end of 4 years.

d. could earn more interest on this account if the interest earnings were withdrawn annually

False. If he withdraws money periodically, there is less principal to earn interest on, so he will earn less interest overall.

e. will earn the same amount of interest each year for four years

False. Since compound interest earns interest on interest, all else being equal, compound interest earns more interest than simple interest.

Answer:

say there are 2 colors, it is 50/50.

if there are 3 it would be a 1/3. 4 colors would be 1/4. now multiply your probability by two. i.e: 1/4 ×2 = 2/8

If Matt and Jan each create 10 gallons of punch, Jan uses 2 liters more orange juice as a result than Matt.

Using the unitary approach, an issue can be resolved by first figuring out the value of a single unit, then multiplying that value by the number of units needed to solve the problem. The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.

given

For his 10-gallon punch, Matt uses gallons of orange juice, which adds up to 3x=3*2 = 6.

Using the formula Jan uses gallons of orange juice to create 10 gallons of punch and Matt uses gallons of orange juice to make 10 gallons of punch, we can calculate that Jan uses 2 gallons more orange juice than Matt.

If Matt and Jan each create 10 gallons of punch, Jan uses 2 liters more orange juice as a result than Matt.

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Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

We have ,

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

Hence, Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

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complete question:

A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?

b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?

d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?

e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?

f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?

g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?

Answer:

Step-by-step explanation:

82.296

I believe it's A

I hope this helps and if I'm wrong I apologize

From the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .

As given in the question,

Given pair of lines,

Condition given that two angles are congruent ,

∠5 ≅ ∠7

Angle 5 is congruent to vertical opposite angle and to make a pair of parallel line Opposite angle should be congruent to angle 7.

Opposite angle and Angle 7 are pair of corresponding angles.

Line l should be parallel to the line m to satisfied the condition of

∠5 ≅ ∠7.

Therefore, from the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .

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The height of the tree after 6 years can be expressed as "3 feet + 6f feet."

The correct answer is A. 3f + 6 feet.

To determine the current height of the tree in terms of "f,"

let's analyze the given information.

We know that the tree was initially 3 feet tall when it was planted 6 years ago.

Since the tree grows every year, we can assume that its growth rate is consistent.

Let's denote the current height of the tree as "h" (in feet).

After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").

Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."

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Step-by-step explanation:

2 1/4 = 9/4

2 × 2 1/4 = 2 × 9/4 = 9/2

Answer:

3

Step-by-step explanation:

In this expression, the first term is 2x, then 4y, then 8-2 (which simplifies to 6).

Answer:

6

Step-by-step explanation:

take 3/8 to the other side

27/56+3/8

take the LCM which is 56

21/56+21/56

=48/56

=6/7

If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

Using this formula

Margin of error=Standard deviation×Mean

Let plug in the formula

Margin of error=205 × 9.5%

Margin of error = 19.475

Margin of error = 19.5 (Approximately)

Therefore If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

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