Lauren is going to a carnival that has games and rides. Each game costs $2 and each ride costs $4.75. Lauren spent $50 altogether at the carnival and the number of rides she went on is 2 more than the number of games she played. Write a system of equations that could be used to determine the number of games Lauren played and the number of rides Lauren went on. Define the variables that you use to write the system.

The values of x that makes the equation (x - 3)/x = - 8/(x + 3) true are x = - 9 and x = - 1.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given equation is (x - 3)/x = - 8/(x + 3).

(x + 3)(x -3) = - 8x.        (a² - b² = (a + b)(a - b))

x² - 9 = - 8x.

x² + 8x - 9 = 0.

x² + 9x - x - 9 = 0.

x(x + 9) - 1(x + 9) = 0.

(x + 9)(x + 1) = 0.

x + 9 = 0 Or x + 1 = 0.

x = - 9 Or x = - 1.

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2 measurements can be treated as continuous random variables. 1 discrete random variable, and a fourth that cannot be treated as a random variable. (option d)

There are a few ways that a continuous random variable differs from a discrete variable: Due to the fact that it can contain an infinite number of values within a given interval, continuous random variables are typically uncountable. Measurements like height, weight, distance, and a plethora of other decimal values are examples of these variables. On the other hand, discrete random variables have values that can be counted, and the values of successive values are typically whole numbers.

In the above scenario, The number of starfish is a discrete variable, whereas the starfish's weight and percentage of the plot's area are continuous variables.

It is not a random variable whether the plot is in progress or halfway between high tide and low tide.

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to get the equation of any straight line, we simply need two points off of it, let's use the provided ones

[tex]f(5)=-1\implies \underline{(\stackrel{x}{5}~~,~~\stackrel{y}{-1})}\hspace{5em}f(0)=-5\implies \underline{(\stackrel{x}{0}~~,~~\stackrel{y}{-5})} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}} \implies \cfrac{-5 +1}{-5} \implies \cfrac{ -4 }{ -5 } \implies \cfrac{4 }{ 5 }[/tex]

[tex]\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-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{4 }{ 5 }}(x-\stackrel{x_1}{5}) \implies y +1 = \cfrac{4 }{ 5 } ( x -5) \\\\\\ y-1=\cfrac{4 }{ 5 }x-4\implies {\Large \begin{array}{llll} y=\cfrac{4 }{ 5 }x-3 \end{array}}[/tex]

"-4(x-1)+6x=2(17-x)" for X

Exact Form: x= 15/2= 7-1/2

decimal form: X=7.5

Answer:

Step-by-step explanation:

1 ) multiply the number with the brackets (-4x -4 = 34 - 2x)

2) collect the like terms (-4x + 2x = 34 + 4)

3) -2x = 38

4) x = 38/-2

5) x = -19

Rochelle can make 2 party favors with 3/4 yards of wine.

According to the question,

We have the following information:

Rochelle had 3/4 yard of wine. Each party favor requires 3/8 yard.

Now, we will find how many parts of a party can 1 yard of wine favor using division.

So, we have the following expression:

1 party = 3/8 yards

1 yard = 8/3 party

Now, Rochelle has 3/4 yards of wine in total. So, we can find the number of party favors using multiplication.

3/4 yards = (3/4)*8/3

3/4 yards = 2 parties

Hence, Rochelle can make 2 party favors with 3/4 yards of wine.

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The individual statements which would provide enough information to conclude that line r is perpendicular to line p are m∠3 = m∠6, m∠6 = 90°, and m∠5 + m∠4 = 90°. Option B, option C, and option E are correct.

First, let us understand the angle formed by intersecting lines:

The types of angles formed by intersecting lines are adjacent angles, vertical angles, etc.

We are given;

The figure shows lines r, n, and p intersecting to form angles 1, 2, 3, 4, 5, and 6.

All 3 lines lie in the same plane.

If line r is perpendicular to line p, then;

m∠1 + m∠2 = m∠5 + m∠4 = 90° (Vertical angles)

m∠3 = m∠6 = 90° (Vertical angles)

Thus, the individual statements which would provide enough information to conclude that line r is perpendicular to line p are m∠3 = m∠6, m∠6 = 90°, and m∠5 + m∠4 = 90°. Option B, option C, and option E are correct.

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The rate of change, -7/3, in the equation means: the average weight of strawberry decrease by 7/3 grams at every 1°F increase in temperature.

A linear equation is often expressed in the form of y = mx + b, which is the slope-intercept form, where the rate of change is the value of the variable "m" in the equation, and b is the starting or initial value.

Given the equation, y = -7/3x + 72.75, in slope-intercept form, where:

Therefore:

-7/3 in the equation represents the rate of change.

72.75 represents the starting value or y-intercept.

The rate of change, -7/3, in the context of this situation as represented in the equation can be described as: 7/3 grams average weight that is decayed at every 1°F increase in temperature.

Therefore, the statement that best describes the rate of change is: There is 7/3 grams decrease in weight of the strawberry at every 1°F increase in temperature.

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The accuracy of the USA Today claim about the access the internet read the international news online by adults is 0.089.

We have provided in question that,

adults who access the internet read the international news online is 44% i.e 0.44

this provides the interval ( .344, .522)

Using the estimation formula (E) or margin error

= Z-value √(p (1-p)/n

where, p --> Sample proportion of sucess

1-p = q ----> sample proportion of failure

n ---> sample size

Now, a random sample of 120 adults is considered for survay.

i.e., n= 120 and 52 adults out of 130 are responded "yes" for reading international news online.

so, p = 52/120 = 0.433 and 1-p = q = 1-0.433

= 0.567

Confidence interval to test the newspaper's claim is 95% . Thus, the Z-value for 95% confidence interval is 1.96..

putting the value in above formula we get,

E = 1.96 √0.433×0.567/120 = 1.96√0.2455/120

= 1.96√0.00204 = 1.96× 0.0452 = 0.0889 ~ 0.089

So, accuracy is 0.089 to support the claim of newspaper.

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52 increased by 18 is basically 52 + 18 = 70

I hope this helps!

Answer:

-27

Step-by-step explanation:

6 * (-4) -3 =

= -24 - 3 =

= -27

The constant of proportionality in a graph, table or ordered pairs is divide y by x

Ising a graph, the constant of proportionality is the constant value of the ratio obtained from two proportional quantities.

How to obtain a constant of proportionality?

The constant of proportionality is the slope of the graph of a straight line.

The slope of a graph of a straight line is determined by:

Slope = rise /run or increase in y/increase in x or decrease in y/decrease in x

In conclusion, rise in y/run in x determines the constant of proportionality.

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Answer: I believe this is True!

Step-by-step explanation:

I know what associative property and that seems like a example.

And if its false then answer should be false.

Try True, if not True then False!

By using factor theorem it is obtained that,

x - 1 is not a factor f(x) =[tex]2x^5-9x-6[/tex]

What is factor theorem?

At first, it is important to know about remainder theorem

Remainder theorem states that if f(x) is divided by (x - a), then the remainder is f(a)

If the remainder is zero, then f(a) is a factor of f(x)

Factor theorem states that if f(a)  = 0, then (x - a) is a factor of f(x).

Here,

[tex]f(x)=2x^5-9x-6[/tex]

Divisor = x - 1

x - 1 = 0

x = 1

By remainder theorem,

Remainder = f(1)

f(1) =

      [tex]2(1)^5 - 9(1) - 6\\2 - 9 -6\\-13[/tex]

Which is not equal to zero

x - 1 is not a factor f(x) [By factor theorem]

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slope of a line that is perpendicular to the line y=-3x is 1/3

What is slope of line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.

y=-3x

tanθ=slope = y/x= -3

Slope(M) of this equation is -3

Let the slope of its perpendicular line is m

As we know that the product of the slopes of perpendicular lines is -1

so,

M*m =-1

-3 * m= -1

m=1/3

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Answer: 6 hours

to be honest i got 7 hours but i typed in 6 and it was correct so i cant really tell you how i got it right :/

From the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.

As given in the question,

Given distribution of annual profit :

Approximately normal with mean μ = $66,000

Standard deviation σ = $22,000

Profits in the top 5 percent

Apply z-score formula :

z = ( x - μ) / σ

Top 5% mean 95% and more.

Using normal distribution table,

z -score corresponding to 95% or 0.95 is equal to 1.65.

Substitute all value in the formula we get,

1.65 = ( x - 66,000 ) / 22,000

⇒ x - 66,000 = 1.65 × 22,000

⇒ x = 36,300 + 66,000

⇒ x = 102,300

Therefore, from the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.

The complete question is :

The distribution of annual profit at a chain of stores was approximately normal with mean μ = $66,000, standard deviation σ = $22,000. The stores with profits in the top 5 percent each had a reward party for the employees to celebrate.

What is closest to the minimum annual profit for a store that had a reward party?

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The largest possible total area of the four pens is 14,062.5 ft.²

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

Diagrams illustrating the situation can be formed adjusting the width of the included diagram illustrating the general situation.

The expression for the total area is  A=( 150- (2Y)/5 ) Y

Reasons:

The given parameter are;

Length of fencing available = 750 ft.

Area to be enclosed = Rectangular

Number of included pens with parallel fencing = Four

Let Y represent the width of the area and let X represent the breadth

Therefore, we have;

2·Y + 5·X = 750

Which gives;

X=(750/5)-(2Y/5)=150-(2Y/5)

The area is therefore;

A=Y [150-(2Y/5)] = 150Y-(2Y²/5)

Differentiate with respect to Y and equate to zero

dA/dY = 150- (4Y/5)=0

Y=(150*5)/4 = 187.5

The width of the maximum area, Y = 187.5 ft.

Which gives;

X=150- (2*187.5)/5 = 75

The breadth of the area, X = 75 ft.

The maximum area,  = Y × X, which gives;

= 187.5 ft. × 75 ft. = 14,062.5 ft.²

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Answer: 3 hours and 20 minutes

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Number sold at rs180 = x

Number sold at rs330 = y

x + y = 200

180x + 330y = 48000

x = 200 - y

180(200 - y) + 330y = 48000

36000 - 180y + 330y = 48000

48000 - 36000 = 330y - 180y

12000 = 150y

12000/150 = y

y = 80

x = 200 - 80

x = 120

Answer:

Students in her classes At the beginning of the semester, but 13 students withdraw from her classes before Test three. So now she has 150 students. If she has one classes in total, in each class has an equal number of students. How many students are in each class round your answer to the nearest ones? Well, first of all, if she only has one class, then there's 150 students in that class is or class, this is the middle school math teacher signing out.

lazyuser30

Answer:

a = -b - c + 8

Step-by-step explanation:

8 = a + b + c.  Solve for a.

Subtract b from both sides

8 - b = a + c

Subtract c from both sides

8 - b - c = a

It is customary to rearrange so that the variable we solved for is on the left side

a = -b - c + 8

Answer: The base is 4.8 sq inches.

Step-by-step explanation: The formula for a triangle is (B x H) x 1/2. Knowing this, we can double 8.64 to nullify the 1/2. This gives us 17.28. 17.28 divided by 3.6 gives us 4.8

Answer:

4.8

Step-by-step explanation:

The area of a triangle is half the base times the height.

[tex]0.5*b*3.6=8.64 \\ b = \frac{8.64}{0.5*3.6}[/tex]

The sum of angles 3 and 4 is equal to 180 degrees, therefore: A: true; this would be enough information to say that the lines are definitely parallel.

When two lines are intersected by a transversal, and the same-side interior angles are supplementary, that is are equal to 180 degrees, then we can state that the two lines are parallel to each other based on the converse of the same-side-interior angles theorem.

Given the following information:

Angle 4 and angle 3 are same-side-interior angles, thus:

89 + 91 = 180°

This means that, the sum of angle 4 and 3 are supplementary. Lines g and h are therefore parallel to each other.

In summary, our answer would be: A: true; this would be enough information to say that the lines are definitely parallel.

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Answer:

true

Step-by-step explanation:

Answer: $49

Step-by-step explanation: 5% of 980 = 0.05 × 980 = 49

Answer:

$931

Step-by-step explanation:

Discount = less money paid

100% - 5% = 95%

95% = 0.95

980 * 0.95 = 931

Assuming that other factors are held constant, the sample means difference Increases. (option C)

The null hypothesis and the alternative hypothesis are the two types of hypotheses for a test.

Step 1: The null hypothesis is based on the assumption that there is no difference between the true mean (µ) and the compare value ([tex]m_{o}[/tex]). The alternative hypothesis is based on this assumption.

Step 2: Increasing the sample mean difference would probably make it more likely that the null hypothesis will be rejected, as long as other factors stay the same.

As a result, option C is the right one.

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(Complete question)

Assuming that other factors are held constant, which approach would tend to increase the likelihood of rejecting the null hypothesis?​

a. ​Decrease the sample mean difference.

b. ​Increase the sample variance.

c. ​Increase the sample mean difference.

d. ​Decrease the sample size.

The probability that she will get the station between 9:25 and 9:30 is 1/2.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given: The time it takes a woman to travel from her apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.

She leaves home at 9:05 a.m.

Let x be the random variable denoting that travel time of a women from apartment to bus stop.

Here x ≈ U (20, 30)

⇒  F(x) = (x - 20) / (30 - 20)

To find, she leaves home at 9:25 at reach bus stop at 9:25 to 9:30

⇔ P(20 < x < 25)

= (25 - 20) / (30 - 20)

= 5 / 20

= 1/2

Hence, the probability is 1/2.

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Answer:

Step-by-step explanation:

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