at a high school movie night, the refreshment stand sells popcorm and soft drinks. Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. 38 students bought both popcorn and a drink. What is the probability that a student buys a drink?

Answer:  [tex]Range:[/tex]{[tex]1,3,4,7[/tex]}

Step-by-step explanation:

We know that, by definition, the Domain is the set of all the x-coordinates of the ordered pairs  and the Range is the set of all the y-coordinates of the ordered pairs.

Therefore, given [tex]f=(2,3),(5,7),(5,4),(9,1)[/tex], you can observe that the set of all second elements of ordered pairs (the values of "y") is the following:

{[tex]3,7,4,1[/tex]}

 Therefore, we can conclude that if [tex]f=(2,3),(5,7),(5,4),(9,1)[/tex] , then the range is:

 [tex]Range:[/tex]{[tex]1,3,4,7[/tex]}

Answer:

The range of f is {1 , 3 , 4 , 7}

Step-by-step explanation:

* Lets revise the relation

- f is a relation between x and y

- x is the input of the relation

- y is the output of the relation

- x is called the domain of the relation

- y is called the range of the relation

- The range is the corresponding value to x

* Now lets solve the problem

∵ f = {(2 , 3) , (5 , 7) , (5 , 4) , (9 , 1)

∵ x = {2 , 5 , 9}

∴ The domain of f is {2 , 5 , 9}

∵ y = {1 , 3 , 4 , 7}

∴ The range of f is {1 , 3 , 4 , 7}

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=5(2)^{x}[/tex]  

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]  

where

a is the initial value

b is the base

In this problem

a=5

b=2

using a graphing tool

see the attached figure

Answer:

A

Step-by-step explanation:

Edge

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-2)}{1-3}\implies \cfrac{4+2}{1-3}\implies \cfrac{6}{-2}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=-3(x-3) \\\\\\ y+2=-3x+9\implies y=-3x+7[/tex]

Answer:

[tex]\large\boxed{(F\circ F)(n)=4n+6}[/tex]

Step-by-step explanation:

[tex]F(n)=2n+2\\\\(F\circ F)(n)\to\text{Replace n with 2n + 2 in F(n)}:\\\\(F\circ F)(n)=2(2n+2)+2\qquad\text{use the distributive property}\\\\(F\circ F)(n)=(2)(2n)+(2)(2)+2=4n+4+2=4n+6[/tex]

Answer:

the Bision is 10 miles / hour faster if he could keep it up

Step-by-step explanation:

There are 60 minutes in an hour.

Therefore the bison can run [3520 feet / min] * [60 min ] =211288 feet in an hour.

Now you have to convert 212200 to miles. Do this by dividing by 5280

212200/5280 = 40 miles.

Kind of hard to believe isn't it. 40 miles is a long way when you are running it.

The bison is faster by 10 miles / hour.

This can be done all in 1 step if you know how to do dimensional analysis

3520 feet / minute * [ 60 min/ hour ] * [ 1 mile / 5280 feet] = 40 miles

Answer:

A bison is 10 miles per hour faster than a deer.

Answer:

C

Step-by-step explanation:

looking at the graph, we see a parabola shifted up 6 units. the function is f(x) = x² + 6

we also see a line with a reflection on the y axis and a vertical shift up 6 units. the function is f(x) = -x + 6

x² + 6 is graphed like a normal parabola (u shaped graph) with an open circle on (3,15). the x coordinate is whats important here, which is 3. we see that there are no values to the right of 3, and only to the left of 3. we can say that the statement x < 3 is true of the parabola, as any value less than 3 is a solution to the parabola.

for -x + 6, we see a line graphed with an closed circle on approximately (3,3). again, the x-coordinate is important here which is 3. the line only goes to the right of 3, meaning the inequality x ≥ 3 is true of the line as any value greater than or equal to 3 is a solution

looking at our answer choices we need to find the following answer:

x² + 6 x < 3 and -x + 6 x ≥ 3

this answer would be C

Answer:

C

Step-by-step explanation:

Copied what the person aboved one said

Answer:

the answer is the second one (6, 9)

Answer: The answers are (9, -1) and (6, 1)

Step-by-step explanation:

Answer:

3, 50%

Step-by-step explanation:

The interquartile range is the top of the box minus the bottom of the box.  

5-2 = 3

Each part is 25 %

From the bottom of the whisker to the bottom of the box is 25%

From the bottom of the box of the middle of the box( median) is 25%

From the median to the top of the box is 25%

From the top  of the box of the last of the whisker of the box( is 25%

Adding from the bottom of the box to the top of the box  

25% + 25% = 50%

Answer:

4x=6

Step-by-step explanation:

The value of the equation is 4x = 6.

The two equations in the system are added or subtracted to produce a new equation with just one variable when using the addition/subtraction method. The other variable must cancel out for the new equation to have just one variable.

Given

eq 1 :8x+3y=14

eq 2 :4x+3y=8

eq1 - eq 2

(8x+3y=14) - (4x+3y=8)

=> (8x-4x) + ( 3y-3y) = (14-8)

=> 4x + 0 = 6

4x = 6.

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Answer:

The solution is [tex](3, -2)[/tex]

Step-by-step explanation:

We have the following system of equations

Equation 1) [tex]d + e = 1[/tex]

Equation 2) [tex]-d + e = -5[/tex]

To solve the system of equations add equation 1 with equation 2 and solve for variable e.

[tex]d + e = 1[/tex]

       +

[tex]-d + e = -5[/tex]

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

[tex]0d + 2e = -4[/tex]

[tex]e = -2[/tex]

Now substitute the value of e in equation 1 or equation 2 and solve for d.

[tex]d + (-2) = 1\\\\d = 3[/tex]

Therefore the solution of the system is the ordered pair

[tex](3, -2)[/tex]

I’m not sure but I think it’s C

ANSWER

[tex]6{a}^{3} {b}^{4} {c}^{2} [/tex]

EXPLANATION

The given polynomials are:

[tex]3 {a}^{3} c = 3 \times {a}^{3} \times c[/tex]

[tex]6 {b}^{4} = 2 \times 3 \times {b}^{4} [/tex]

[tex]{b}^{2} {c}^{2} ={b}^{2} \times{c}^{2} [/tex]

The least common multiple (LCM) is the product of the highest powers of the common factors;

[tex]2 \times 3 \times {a}^{3} \times {b}^{4} \times {c}^{2} [/tex]

This simplifies to,

[tex]6{a}^{3} {b}^{4} {c}^{2} [/tex]

The LCM is

[tex]6{a}^{3} {b}^{4} {c}^{2} [/tex]

Answer:

6a³b⁴c²

Step-by-step explanation:

Given the polynomials, to find the Lowest Common Multiple of the polynomials, we need to find factors that can go in at least one of the given polynomials and multiply the resulting variables and constant gotten.

Check the attachment for the diagram

The LCM is 6a³b⁴c²

Answer:

Width = [tex]1\frac{1}{3}[/tex] ft

Step-by-step explanation:

The tank holds 150 gallons of water.

7.5 gallons holds 1 ft³ of water.

So 150 gallons will hold;

[tex]\frac{150}{7.5}[/tex] × 1 ft³ = 20 ft³

The volume of the tank = Length(l) × Width(w) × Height(h) = 20 ft³

i.e 5 ft × w × 3 ft = 20 ft³

15w ft² = 20 ft³

w = [tex]\frac{20 ft^3}{15 ft^2}[/tex] =  [tex]1\frac{1}{3}[/tex] ft

Answer:

adult = £5

child = £2

Step-by-step explanation:

a = adult c = child

3a + 4c = 23

1a + 5c = 15

multiply second equation by 3 and rewrite

3a + 4c = 23

3a + 15c = 45

subtract

0 - 11c = - 22

-11c = -22

11c = 22

c = £2

subsitute into one of the equations and solve for a

1a + 5c = 15

a + 5(2) = 15

a + 10 = 15

a = £5

The question can be solved using systems of linear equations. The cost of an adult's ticket is £5, and the cost of a child's ticket is £2.

The problem given can be solved using systems of linear equations. We can denote the cost of an adult's ticket as 'a' and the cost of a child's ticket as 'c'. Then you set up two equations:

To solve the system, we can multiply the second equation by 3:

Now we subtract the first equation from this one:

If you divide by 11, you get c=2. Now, substitute c into the second initial equation: a + 5*2 =15, and you get that a=5. Therefore, the cost of an adult's ticket is £5 and the cost of a child's ticket is £2.

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Answer:

Answer: There are 21 eggs left.

Step-by-step explanation:

One carton has 12 eggs.

2 cartons are two times one carton, so two cartons have 2 times 12 eggs.

2 * 12 = 24

There are 24 eggs in two cartons.

Margot uses 3 eggs. We subtract 3 eggs from 24 eggs.

24 - 3 = 21

Answer: There are 21 eggs left.

There are 21 eggs are left if each carton 12 eggs. There are 2 full cartons in the refrigerator. Margot uses 3 eggs to make a quiche.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Each carton contains = 12 eggs

Number of carton = 2

Number of total eggs = 12×2 = 24

Margot uses 3 eggs to make a quiche.

Remaining eggs = 24 - 3 = 21

Thus, there are 21 eggs are left if each carton 12 eggs. There are 2 full cartons in the refrigerator. Margot uses 3 eggs to make a quiche.

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Answer:

Well the answer is 857.4 meters per minute

Step-by-step explanation:

The reason is because 1.429 times 60= 85.74 That means that you walk 85.74 meters per second. Then that times 10 is 857.4 . Can I get brainliest

The answer would be A

Step-by-step explanation:

[tex]4 {x}^{4} - 28 {x}^{3} + 59 {x}^{2} - 2x + c \: | 2x - 5[/tex]

-

[tex]4 {x}^{4} - 10 {x}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | 2 {x}^{3} [/tex]

then continue

[tex]0 - 18 {x}^{3} + 59 {x}^{2} - 2x + c \: \: \: \: \: \: \: | 2x - 5[/tex]

-

[tex] \: \: \: \: - 18 {x}^{3} + 45 {x}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | - 9 {x}^{2} [/tex]

continue

[tex] \: \: \: \: \: \: 0 + 14{x}^{2} - 2x + c \: \: \: \: \: \: \: \: \: \: \: \: \: | 2x - 5[/tex]

-

[tex] 14{x}^{2} - 35x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | 7x[/tex]

continue

[tex] 0 + 33x + c \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | 2x - 5[/tex]

-

[tex]33x - \frac{165}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | \frac{33}{2} [/tex]

[tex]0 +( c + \frac{165}{2} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: |[/tex]

Since 2x+5 is a factor then

[tex]c + \frac{165}{2} = 0 \\ = > c = - \frac{165}{2} [/tex]

The answer is:

There are 17.6 ounces in 0.5 kilograms.

To calculate how many ounces are in 0.5 kilograms, we need to use the following factor:

[tex]1Kg=35.274ounces[/tex]

So, converting we have:

[tex]0.5Kilogram*\frac{35.274ounces}{1Kilogram}=17.637ounces=17.6ounces[/tex]

Have a nice day!

Answer:

Step-by-step explanation:

11.5 + 12.5 - 10 - 75*x  = 0

               4  

multiply both sides by 4

11.5 + 12.5 - 10 - 75x = 0     Combine the first 2 terms.

24 - 10 - 75x = 0                 Subtract 10    

14 - 75x = 0                         Subtract 14 from both sides

-75x = - 14                           Divide by - 75

-75x/-75 = -14/75                Do the division

x = 0.187

Final answer:

Diego's method may introduce bias by not representing all student subgroups, suggesting that a random, stratified random, or systematic sampling method would better reflect student satisfaction with cafeteria food.

Explanation:

The question asks if selecting the first 25 students who purchase a lunch at the cafeteria is a good way for Diego to sample students to determine satisfaction with the cafeteria food. This sampling method may lead to bias because it does not represent all subgroups within the school population equally. For instance, it may only capture the opinions of students who already have a preference for cafeteria food, thus overlooking those who avoid it due to dissatisfaction. A better approach would be a random sampling method, where every student has an equal chance of being selected, ensuring a more accurate reflection of the entire student body’s opinion.

To improve the survey, Diego could consider using a stratified random sample, where the school population is divided into strata, such as grade levels or lunch periods, and then a random sample is taken from each stratum. This approach helps ensure that all segments of the student population are represented. Alternatively, a systematic sampling method, where every nth person is selected from a list or a line, could provide a more structured yet still random selection process compared to Diego's original plan.

Diego's approach is convenient but prone to bias. Random sampling across various days would improve representativeness and accuracy.

Diego's approach to surveying the students about cafeteria satisfaction has both strengths and weaknesses. Let's break down the pros and cons step by step:

1. **Convenience**: Approaching students during lunchtime in the cafeteria is convenient because it allows Diego to access a large number of students in one place and at a time when they are likely to be available.

2. **Sampling Bias**: However, selecting only the first 25 students who purchase lunch on a Monday might introduce sampling bias. For example, if there is a rush in the cafeteria during that time, Diego might end up surveying students who are in a hurry and may not accurately represent the entire student population.

3. **Limited Sample Size**: The sample size of 25 students is relatively small. While a larger sample size is not always necessary for accurate results, a larger sample size generally leads to more reliable findings. With only 25 students surveyed, there's a risk of the results being skewed by chance variations.

4. **Day of the Week Bias**: Monday might not be the best day to conduct the survey. Students' satisfaction with cafeteria food might vary depending on the day of the week due to factors like menu rotation or weekend leftovers. Therefore, surveying only on Mondays might not provide a comprehensive picture of overall satisfaction.

5. **Response Bias**: There's also the potential for response bias. Students who are particularly satisfied or dissatisfied with the food might be more likely to respond to Diego's survey, leading to results that don't accurately reflect the general sentiment of all students.

6. **Alternatives**: A better approach might be to conduct the survey at different times and days of the week to capture a more diverse range of student experiences. Additionally, Diego could use random sampling techniques to ensure that every student has an equal chance of being surveyed, reducing the risk of bias.

In summary, while Diego's approach is convenient, it may not yield the most accurate or representative results due to potential sampling bias, limited sample size, and other factors. To improve the validity of the survey findings, Diego should consider adjusting his sampling method and survey timing.

Answer:

80% markup

Step-by-step explanation:

You first subtract the original amount from the final to get:

54-20 = 24

Then you divide it by the original:

24/30 = .80

You multiple this by 100% to get 80%

Answer:

The markup is 80%

Let's start with y = 4x + b (since 4 is the slope);

We need to find what number should be put instead of b;

Then, let's see what needs to be done;

Plug in the y and x values from the coordinate (22,12) into y=4x+b;

12 = 4(22) + b

Solve;

12 = 88 + b

12 - 88 = b

b = -76

Remember the equation y = 4x + b? Put the -76 instead of b:

y = 4x + -76

or: y = 4x - 76

That is the equation.

To make it standard form, put x and y both in the left side, with x first then y:

-4x + y = -76

^^Answer!

Final answer:

The equation of the line which passes through the point (22, 12) with a slope of 4, when written in standard form, is -4x + y = -76.

Explanation:

To write the equation of a line that includes the point (22, 12) and has a slope of 4 in standard form, we begin with the point-slope form of a line equation, which is y - y1 = m(x - x1). Substituting the given point and slope values, we have y - 12 = 4(x - 22).

Next, we simplify and convert this equation to standard form Ax + By = C. Standard form requires that x and y terms are on the left side and the constant is on the right:

y - 12 = 4x - 88
Add 12 to both sides:
y = 4x - 76
Subtract 4x from both sides:
-4x + y = -76

This is now in standard form and matches one of the given choices.

Answer:

The factors are: (3a+2b +ab-6)(3a+2b -ab+6)

Step-by-step explanation:

[tex](a^2-4)(9-b^2)+24ab[/tex]

We need to solve the above expression using factorization.

Multiplying (a^2-4)(9-b^2)

9(a^2-4)-b^2(a^2-4) + 24ab

9a^2 -36 -a^2b^2+4b^2 + 24ab

Rearranging:

9a^2 + 4b^2 +24ab -36 -a^2b^2

We try to make perfect square of the form a^2+2ab-b^2

We have 24ab that can be written as 12ab + 12ab

Now, we can arrange the above equation:

9a^2 +12ab+ 4b^2 -(a^2b^2-12ab +36)

(3a)^2 +2(3a)(2b) + (2b)^2 -((ab)^2 -2(ab)(6)+(6)^2)

The perfect square will be:

(3a+2b)^2 - (ab-6)^2

Now We know a^2 - b^2 = (a+b)(a-b)

Here a = 3a+2b , b=ab-6

So,

(3a+2b +(ab-6))(3a+2b - (ab-6))

(3a+2b +ab-6)(3a+2b -ab+6)

So, the factors are: (3a+2b +ab-6)(3a+2b -ab+6)

Answer:

a=14.63

c=13.63

Step-by-step explanation:

a = sinA*b

c = sinC*b

Answer is a and c girl

Answer:

$199.99 multiply by .20 = 39.998

$199.99 minus $39.99 or $40

the sale price of the four wheeler is $159.99

Step-by-step explanation:

The second is ones.

The third is tens.

I don’t know the first one 100% so I don’t want to guess and have you get it wrong!! But pls mark me love(:

1. Hundred thousands

2. Ones

3. Tens

The balance in the account after 4 years, compounded continuously at 11%, is approximately $3884.25.

The formula for continuous compounding is given by [tex]\(A = Pe^{rt}\)[/tex], where:

- [tex]\(A\)[/tex] is the final amount,

- [tex]\(P\)[/tex] is the principal amount (initial investment),

- [tex]\(e\)[/tex] is the mathematical constant approximately equal to 2.71828,

- [tex]\(r\)[/tex] is the interest rate, and

- [tex]\(t\)[/tex] is the time in years.

In this scenario, [tex]\(P = $2500\)[/tex], [tex]\(r = 0.11\)[/tex] (11% expressed as a decimal), and [tex]\(t = 4\)[/tex] years. Plugging these values into the formula:

[tex]\[ A = 2500 \times e^{(0.11 \times 4)} \][/tex]

Calculate the exponent:

[tex]\[ A = 2500 \times e^{0.44} \][/tex]

Using the approximate value of [tex]\(e \approx 2.71828\):[/tex]

[tex]\[ A \approx 2500 \times 2.71828^{0.44} \][/tex]

[tex]\[ A \approx 2500 \times 1.5537 \][/tex]

[tex]\[ A \approx 3884.25 \][/tex]

Therefore, the balance in the account after 4 years, with an initial investment of $2500 at a continuously compounded interest rate of 11%, is approximately $3884.25.

The question probable maybe:

If $2500 is invested at a rate of 11% compounded continuously, find the balance in the account after 4 years. Use the formula A=Pe^(rt)

Answer:

110 in. = 9  1/6 ft, or 9 ft 2 in

Step-by-step explanation:

Please try to do a better job of formatting your next question.  Thanks.

110 in       1 ft

-------- * --------- = 9 1/6 ft  or  9 ft 2 in

   1          12 in

110 in = 9 ft  2 in.

To convert 110 inches to feet and inches, we need to know the conversion factor that:

[tex]1\ foot = 12\ inches[/tex]

So, first, divide the total inches by 12 to get the number of feet:

[tex]\frac{110\ inches}{12\ inches/foot} = 9\ feet[/tex] with a remainder.

The remainder represents the inches that do not make up a full foot. The remainder can be calculated as follows:

[tex]110\ inches - (9\ feet \times 12\ inches/foot) = 110\ inches - 108\ inches = 2\ inches[/tex].

So, 110 inches is equal to 9 feet and 2 inches.

Therefore, 110 inches = 9 feet 2 inches.

f(5) means to replace x in the equation with 5 then solve.

f(x) = x^2 +2x

f(5) = 5^2 + 2(5)

f(5) = 25 +10

f(5) = 35

The answer is D)35