7. During a person's commute to school, she spends 10 minutes driving 30 miles per hour (mph) and 5 minutes stopped at red lights. (a) (1 pt.) Find the distance of her commute.​

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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Answer:

He would have 48

Step-by-step explanation:

1 set: 8

2 sets: 16

3 sets: 24

4 sets: 32

5 sets: 40

5 sets: 48

OR

{4(8)} + 2(8)

32 + 2(8)

32 + 16

48

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Answers

48

Steps

4+2=6

8 times 6= 48

Part A

We are asked to write a system of equations to calculate the amount of tickets sold of each type (choldren and adults). We are told that 600 tickets were sold. Let's say the number of children's tickets is c, and the number of adult tickets is a. Then:

The total amount of money collected was $5500. The tickets for children cost $8, and $15 for adults. Then:

Now, we can create a system of two equations with two unknowns: c and a.

This system of equations will allow us to caluclate how many children tickets and how many adult tickets were sold.

Part B

We need to calculate how many of each type were sold. We have the system of equations that will allow us to do that. To use substitution method from the first equation we can solve for c:

Now that we have an expression for c, we can replace it in the second equation of the system:

In the previous expression, we have now only one unknown: a. Then, we can easily solve it:

Reducing like terms (-8a and 15a):

Now we have calculated the amount of adult tickets sold: 100. Now, knowing this value, we can recall the first equation of the system (c + a = 600) and estimate the number of children's tickets sold:

Now, we also know the number of children's tickets sold: 500.

We can prove this recalling the system of equations. The total number of tickets sold was 600. 500 for children plus 100 for adults give as the 600 tickets sold:

Also, calculating the total amount of money collected:

We obtain $5500, the same amount stated at the beggining of the problem. Now, those amounts are confirmed: 500 shildren tickets were sold, while for adults, only 1000 were sold.

Part C

Now, we are told to estimate how much more money would have been earned if the same amount of children and adult tickets were sold, but the children tickets costing $15.

The number of children and adults is kept the same: c = 500 and a = 100.

We can calulate the new hypothetical earnings:

With the new ticket fees, the total earning would have been $9000. Recalling that the earning with old fees were $5500, then:

Then, with the new fees, they wuold earn $3500 more than with the old fees.

Answer:

\(2a^{4} + 5a^{3} - 13a^{2} + 19a - 28\)

Step-by-step explanation:

Answer:

1/3 - (-5/3) = 2

Step-by-step explanation:

1/3 - (-5/3)

Subtracting a negative is the same as adding a positive.

1/3 + 5/3 = 6/3, or 2

Answer:

40

Step-by-step explanation:

The median is the middle number amoungst the numbers you have.  The lowest number is 30, the highest number is 50.  The median of the two numbers is 40 because it is exactly in between 50 and 30.

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35 is a reasonable prediction of the number of times he will select 2 yellow socks?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.

In the given question,

The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:

P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25

So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.

To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:

E(X) = n * p

where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.

In this case, n = 175 and p = 1/25. So,

E(X) = 175 * (1/25) = 7

Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.

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The measure of the angle MON in the figure is 102 degrees

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

The parallel lines and the transversal

From the parallel lines and the transversal, we have the following values

Angle JNO = (12x + 30) degrees

Angle MON = (9x + 48) degrees

From the figure we have

Angle JNO and Angle MON are opposite exterior angles

This means that both angles are congruent angles

So, we have the following representation

12x + 30 = 9x + 48

Evaluate the like terms

3x = 18

Divide by 3

x = 6

Substitute x = 6 in Angle MON = (9x + 48) degrees

Angle MON = (9 x 6 + 48) degrees

Evaluate

Angle MON = 102 degrees

Hence, the angle is 102 degrees

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Answer:

25.6667

Step-by-step explanation:

Divide the length value by 3.

77 divided 3 =

25.6667

Answer:

Step-by-step explanation:

25.66 SQM

The solution to the given system of equation is x < 4

Inequality expressions are expression that are not separated by an equal sign. Given the inequality expression

9(2x-5)-3<7x-4

Expand to have;

18x - 45 - 3 < 7x - 4

18x - 7x - 48 + 4 < 0

11x -44 < 0

x < 44/11

x < 4

Hence the solution to the given system of equation is x < 4

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Answer:

The slope is 2/9.

Step-by-step explanation:

(15, 10) and (60, 20)

m = 20-10/60-15

m = 10/45

m = 2/9

The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)

In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:

y = b · aˣ

Where:

By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.

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It can be inferred that the amount of nuts that Allen requires depends on the amount of the recipe that he wants to make.

According to the information provided, one serving of the recipe calls for one cup of nuts. According to this, it can be inferred that to make a smaller or larger portion of the recipe, this amount must be divided or multiplied.

For example, if Allen calls for making two servings of the recipe, he would use two cups of nuts, while if he calls for making a half serving, he would use half a cup of nuts.

Note: The question is missing because there is some missing information. However I can answer it based on my general prior knowledge.

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Answer:

1/6

Step-by-step explanation:

The probability she pulls out a purple piece of candy would be 0.22.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is Sam's fathers collection.

We can write the equations for upstream and downstream as -

x - y = 7/2

x + y = 21/10

Solving the equations graphically -

{x} = 2.8

{y} = 0.7
In still water, the speed would be -

S = 3 - 0.7

S = 2.3 Km/h

Distance peddled upstream -

D = 2.8 x 3.5 = 9.8 Km

Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.

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Answer:

60 slices

Step-by-step explanation:

1 pizza = 10 slices

6 pizzas = 10 slices * 6 = 60 slices

Answer:

The total weight of the sugar and water  is 20 grams

Step-by-step explanation:

Given;

weight of sugar Maya added, w₁ = 6 grams

weight of water contained in the bottle, w₂ = 14 grams

The total weight of the sugar and water = 6 grams + 14 grams

The total weight of the sugar and water = 20 grams

Therefore, the total weight of the sugar and water in the bottle is 20 grams.

Answer:

10.5 miles

Step-by-step explanation:

75 divided by 50 is 1.5

1.5 times 7 is 10.5

The probability that a person who tests positive actually has the disease is 0.012%

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

The probability that a person who tests positive actually has the disease is represented as

Probability = Incidence rate * False positive rate

Substitute the known values in the above equation, so, we have the following representation

Probability = 0.3% * 4%

Evaluate the products

Probability = 0.012%

Hence, the probability is 0.012%

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The compositions f(g(x)) and g(f(x)) simplify to x, suggesting that the functions f(x) = 8x - 6 and g(x) = (x + 6) / 8 are inverse functions.

We may apply a number of operations and compositions to find the following functions with f(x) = 8x - 6 and g(x) = (x + 6) / 8.

f(g(x)):

To get f(g(x)), we need to substitute x with g(x):

In the case where f(g(x)) = f((((x + 6) / 8) - 6 = x + 6 - 6 = x

f(g(x)) consequently becomes x.

g(f(x)): By substituting x with f(x) in g(x), we can find g(f(x)):

According to the formula g(f(x)) = g(8x-6) = (8x- 6 + 6) / 8 = 8x / 8 = x

As a result, g(f(x)) also drops to x.

Both f(g(x)) and g(f(x)) compositions result in x, demonstrating that they are identity functions. This implies that the two functions, f(x) and g(x), are inverses of one another.

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Hey!

For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)

This way, it will be able to graph and get the answers quicker!

The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).

Therefore ,  \(-4|x|\)   is the square root of \(-\sqrt{16x^{2} }\)

When a number is multiplied by itself, the result is known as the square root of the number. To represent the square root, use the radical symbol. For illustration, \(\sqrt\)16 = 4. Another name for the radical sign is the root symbol or surds.

given

- \(\sqrt{16x^{2}\) when \(x\) < 0,

In order to solve the given expression we will take the square root of the term inside the root.

Perfect squares (squares of integers) make up the word in the square root, thus we can express it as a square of the numbers.

⇒  \(-\sqrt{(4x)^{2} }\)    [ as \((4x)^{2}\) = \(16x^{2}\)]

On taking square root the square gets removed. So, we have,

\(-|4x|\)  =\(-4|x|\)

Since , so the value would be negative.

Therefore , \(-4|x|\) is the square root of \(-\sqrt{16x^{2} }\)

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The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

The reciprocal of the divisor: Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged, then it is said to be its reciprocal. Suppose a fraction is a/b, then its reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number.

The reciprocal of the divisor 5 1/5 divided by 1/10

To the reciprocal of the divisor.

Equation: 5 1/5 divided by 1/10

1st: Flip the 1/10 to become 10/1

2nd: Change division to multiplication

New equation: 5.1/5.10/1

⇒ 50/5

       ⇒ 10.

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

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Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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Answer:

It's D

Step-by-step explanation:

When you add the 19-50 and over 50 then you get the highest answer

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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