Are the ratios of the number of people to the number of rollercoaster cars in a proportional relationship? Explain your reasoning.


Answer in 2 complete sentences.

183=61

305=61

366=61

488=61

Answer:

exactly one

Step-by-step explanation:

1. subtract 2x from the equation 2x + y = 1

2. now you should have y= -2x + 1

3. then on the second equation subtract 4x from 4x + 2y = 2

4. now you should have 2y = -4x + 2

5. divide everything by 2

6. now you should have y = -2x + 1

7. since you got an exact answer on both of them then it is exactly one

Answer:

3

Step-by-step explanation:

To solve this you have to work backwards with what you are given.

16-7=9

Then we know that a number has to be multiplied by itself to equal nine the only number that follows that criteria is 3

3*3=9+7=16

Answer:

3

Step-by-step explanation:

Work backwards. 16 Subtract 7. Take square root. We take the square root because that is how to undo a number that was multiplied by itself.

16-7=9 √(9)=3

Check this by going through the same steps listed in the question:

A positive number is multiplied by itself. then 7 is added. the answer is 16

3×3=9

9+7=16

The y-intercept is 1/3

I'll assume the function is the following:

[tex]f(x)=-\frac{2}{9}x+\frac{1}{3}[/tex]

As you can see, this is the equation of a line written in Slope-intercept form. The general rule of writing lines in this form is:

[tex]y=mx+b[/tex]

Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept, which is the point at which [tex]x=0[/tex]. By comparing our function with the written rule, we can say that the y-intercept is:

[tex]\boxed{b=\frac{1}{3}}[/tex]

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Answer:

[tex]b=\frac{1}{3}[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=-\frac{2}{9}x +\frac{1}{3}[/tex]

This given function is a linear function, because its variables have one as exponent, we can also say that its variables are linear.

This function, as a linear one, it's represented as a line.

Additionally, the form of this function is called slope-intercept form as

[tex]f(x)=mx+b[/tex]

Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

So, in this case

[tex]m=-\frac{2}{9}[/tex] and [tex]b=\frac{1}{3}[/tex]

Therefore, the y-intercept of the given function is

[tex]b=\frac{1}{3}[/tex]

Answer:

Area of ΔDEF is [tex]45\ cm^2[/tex].

Step-by-step explanation:

Given;

ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Length of AB = [tex]2\ cm[/tex] and

Length of DE = [tex]6\ cm[/tex]

Area of ΔABC = [tex]5\ cm^2[/tex]

Solution,

Since, ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Therefore,

[tex]\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}[/tex]

Where triangle 1 and triangle 2 is  ΔABC and  ΔDEF respectively.

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

[tex]\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2[/tex]

Thus the area of  ΔDEF is [tex]45\ cm^2[/tex].

Answer:

place

Step-by-step explanation:

Answer:

The answer is " Place value"

Step-by-step explanation:

The place value determines the value of the digit in a number, based on its position.

A standard form number is divided into groups of three digits using commad. Each of these groups is called a period.

Answer:

From what I can tell from the image, b is equivalent to B.) 50°

Step-by-step explanation:

So to start off 2a=80° there is 2 a's. so  you subtract 80° from 180° to get 100°.

now b=c and their is 100° left over. So 100°/2 is 50° because if b=50° and c=50° both angles equal 100°.

Answer : The correct option is, (B) 50

Step-by-step explanation:

As we are given :

2a = 80

b = c

As we know that:

The sum of interior angles of a triangle is equal to [tex]180^o[/tex].

That means,

[tex]\angle A+\angle B+\angle C=180^o[/tex]

[tex]80^o+\angle B+\angle C=180^o[/tex]

and, [tex]\angle B=\angle C[/tex]

So,

[tex]80^o+2\angle B=180^o[/tex]

[tex]2\angle B=180^o-80^o[/tex]

[tex]2\angle B=100^o[/tex]

[tex]\angle B=\frac{100^o}{2}[/tex]

[tex]\angle B=50^o[/tex]

Thus, the value of 'b' is [tex]50[/tex]

Answer:

[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]

Step-by-step explanation:

Succession can be understood as a sorted collection of values that respond to a general term or rule. We need to find if these numbers are in arithmetic progression or geometric progression.

In an arithmetic progression, every number is obtained as the previous number plus or minus a constant value called common difference. In a geometric progression, we get the next numbers as the previous one multiplied or divided by a constant value, called the common ratio.  

If we try to find a possible common difference between first and second terms we get:

[tex]2-(-3)=5[/tex]

If it was an arithmetic progression, third term should be

[tex]2+5=7[/tex]

Which is obviously not true. Now let's try to find a possible common ratio by dividing second by first term

[tex]r=\frac{2}{-3}=-\frac{2}{3}[/tex]

Testing our value to find the third term we get

[tex]a_3=2*(-\frac{2}{3})=-\frac{4}{3}[/tex]

Since we have more terms to test:

[tex]a_3=(-\frac{4}{3})*(-\frac{2}{3})=\frac{8}{9}[/tex]

The given value is just as predicted

The fourth term can be accurately predicted also:

[tex]a_4=(\frac{8}{9})*(-\frac{2}{3})=\frac{16}{27}[/tex]

Now we are sure it's a geometric progression, it can easily be stated the general term of the progression is

[tex]a_n=a_1*r^n \ n>=0[/tex]

[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]

The right answer is Option D.

Step-by-step explanation:

Given equations are;

2x+4y=3    Eqn 1

x+3y=13    Eqn 2

When we use subtraction-addition method, we make one of the variables same with opposite signs so that only one variable remains after addition or subtraction.

In the given problem, we will multiply Eqn 2 with "-2" so that the x variables become equal and then we can add both the equations and solve for y.

Therefore,

The first step will be to multiply the second equation by -2 to solve the linear system of equations.

The right answer is Option D.

Keywords: linear equations, subtraction

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Answer:

It's D.

Step-by-step explanation:

It was correct on my unit test review.

Answer:

x=2

Step-by-step explanation:

so if the bigger one is 16 and the other one is 4 that means you need to multiply 4 by 4 to get 16 so to find x you need to divide the 8 by 4 to find your answer

Answer:

x = 2

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x}{8}[/tex] = [tex]\frac{4}{16}[/tex] ( cross- multiply )

16x = 32 ( divide both sides by 16 )

x = 2

The solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]

To find the solutions for [tex]\( \csc^2x - 5\csc x = 0 \)[/tex], we can factor the expression:

[tex]\[ \csc x (\csc x - 5) = 0 \][/tex]

This equation is satisfied when either [tex]\(\csc x = 0\) or \(\csc x - 5 = 0\)[/tex].

1. For [tex]\(\csc x = 0\)[/tex], we know that [tex]\(\csc x\)[/tex] is the reciprocal of the sine function, and sine is 0 at multiples of [tex]\(\pi\)[/tex]. Therefore, [tex]\(x = n\pi\)[/tex] where n is an integer.

2. For [tex]\(\csc x - 5 = 0\)[/tex], solving for [tex]\(\csc x\)[/tex] gives [tex]\(\csc x = 5\)[/tex], and the sine of an angle is the reciprocal of its cosecant. Therefore, [tex]\(x = \sin^{-1}(1/5)\).[/tex]

In summary, the solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]

The complete question is probably:

What are the solutions for \( \csc^2x - 5\csc x = 0 \)?

Answer:

Step-by-step explanation:

B :because 11 pound in Ounces is 176

Answer:

C = 8 + 3x

The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.

The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.

Step-by-step explanation:

Let the admission cost of the fair is $x and each game is $3.

Now, Steven went to the state fair, played  4 games and spent a total of $20 on  admission and games.

So, we can write 20 = x + 4 × 3 {As the relation is linear}

⇒ x = $8

Therefore, the admission cost in the fair is $8.

Therefore, the equation that models the situation is  

C = 8 + 3x ............ (1)

Where C is the total cost and x is the number of games played.

So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.

Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)

Answer:

20 cups of broth are needed to make 30 servings of the soup.

Step-by-step explanation:

This is a typical proportion math problem.

Just set up the proportion and solve for the unknown variable, let it be x, because it's simple to use.

12/8=30/x

simplify 12/8 to 3/2,

3/2=30/x

cross product,

2*30=3*x

60=3x

x=60/3

x=20

Number of cups of broth needed for making 30 servings is 20.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

We have,

Cups of broth needed for 12 servings of soup = 8 cups

Let cups of broth needed for 30 servings of soup = x cups

Using the concept of proportion,

12 / 8 = 30 / x

Doing the cross multiplication,

12x = 8 × 30

12x = 240

x = 240 / 12

x = 20

Hence 20 cups of broth are needed to make 30 servings of the soup.

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Answer:

It goes up my $1.80

Step-by-step explanation:

You multiply $4.50 by 0.40 and you get 1.80 and that’s how much it goes up by

Answer:

[tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex]

Step-by-step explanation:

Given:

Dividend = [tex](-15)^{-1}[/tex]

Quotient =  [tex](-15)^{-1}[/tex]

We notice that the dividend and the quotient are equal. This means the divisor is 1.

By identity property of 1, any number divided by 1 is equal to the same number or the quotient of a number divided by 1 is equal to the number itself.

So, we can write this as:

[tex]\frac{(-15)^{-1}}{1}=(-15)^{-1}[/tex]

Thus [tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex] (Answer)

Answer:

Y- intercept is 5!

Final answer:

The simplified expression for 3.4m + 2.4m is 5.8m. You simply add the coefficients of like terms.

Explanation:

To simplify the expression 3.4m + 2.4m, we need to combine like terms. The term 'like terms' refers to terms that have the exact same variable raised to the same power. In this case, both terms have 'm' as the variable, and it's not raised to any power (which is the same as being raised to the power of 1).

Combine the coefficients (numerical parts) of the like terms:

3.4m + 2.4m = (3.4 + 2.4)m

Add the coefficients: 3.4 + 2.4 = 5.8

Therefore, 3.4m + 2.4m = 5.8m.

Answer:

see the explanation

Step-by-step explanation:

we know that

The rule of the reflection of a point across the y-axis is equal to

(x,y) -----> (-x,y)

The rule of the reflection of a point across the x-axis is equal to

(x,y) -----> (x,-y)

so

Verify each statement

1) Point (3,2) to (3,-2) is a reflection over the y-axis.

The statement is false

Because, is a reflection over the x-axis

A reflection over the y-axis will be

(3,2) -----> (-3,2)

2) A(1,3) to A'(-1,3) is a reflection over the y-axis

The statement is true

Answer:

40 and 50

Step-by-step explanation:

We know that River's mom drove for 45 minutes. Furthermore, at x miles per hour for a time amount y, she drove 10 miles, and at x+10 miles per hour for time amount z, she drove 25 miles. We can set up the equations like this:

x*y = 10

(x+10)*z = 25

y+z = 0.75

I knew to include time as the variable because time was given at the end, and is the only way possible to solve this. Furthermore, we can multiply x and y because we drive for x miles per hour for y hours, so

[tex]\frac{x miles}{hours}  * \frac{yhours}{1}  = xmiles*y[/tex]

I turned 45 into 0.75 as 45 is 3/4 of an hour, and y and z are in hours.

We're kind of stuck here, so it would be nice if we could limit the variables in an equation. One way to do this would be to solve for y in the first equation, so x=10/y. Then, we can plug that into the second equation to get

(10/y+10)*z=25

Combining that with the third equation, we can solve for z in the second equation to get that 25/(10/y+10)=z, and then plug that into the third to get that

y+25/(10/y+10) = 0.75

Multiplying both sides by 10/y+10 to get rid of the denominator, we get

10+10y+25=7.5/y+7.5

Then we multiply by y to get rid of the denominator

10y+10y²+25y=7.5+7.5y

Subtracting 7.5+7.5y to get everything on one side for a quadratic equation

10y²+27.5y-7.5=0

Plugging this into the quadratic equation, we get than y either equals -3 or 0.25. It's clear that you can't have negative time, so y = 0.25

Then, 0.75-0.25=0.5=z, and 10/0.25=40, so x=40, and x+10=50 for the 2 driving speeds

Answer:

Y = - 2

Step-by-step explanation:

Put your finger at x= 0 or (0,0) and go down until you hit the black line, thats your y

==================================

Explanation:

Simply pair each value given in the sequence with a0,a1,a2,etc like so

a0 = 4

a1 = 11

a2 = 18

a3 = 25

a4 = 32

a5 = 39

Answer:   using t - test value is 1.37<2.08( At 0.05 level of significance)

        The mean of the sample was drawn from the population.

Step-by-step explanation:

Here sample size n=22

Given sample mean =530

Given population mean   =500

[tex]t=\frac{sample mean-µ}{\frac{S}{\sqrt{n-1} } }[/tex]

given sample standard deviation s=100

a) null hypothesis:-  The mean of the sample was drawn from the population   µ =500

Alternative hypothesis:-

The most powerful test you can use is t - distribution.

The test statistic is  

[tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }  

here S is the standard deviation of the sample

b)  The value of the test statistic

           [tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }  

substitute given values sample size n=22

sample mean =530

sample standard deviation s =100

mean of the population µ =500

the calculated value of t =[tex]\frac{530-500}{\frac{100}{\sqrt{22} } }[/tex]

                      the calculated value=1.3748

c) The degrees of freedom =n-1 = 22-1 = 21

     The table value of t are 0.05 level of significance with 21 degrees of freedom is 2.08

       The calculated value 1.37<2.08

∴ we accept null hypothesis at 0.05 level of significance

conclusion:-

The mean of the sample was drawn from the  population.

A t-test is the most powerful test for this hypothesis. The test statistic value is calculated using t = (X - µ) / (s / √n). Based on a significance level of 0.05, we can conclude by comparing the calculated t-value with the critical t-value from t-distribution table.

The subjects of this question are hypothesis testing and statistics.

To answer your question: a) The most powerful test to use to test your hypothesis is the t-test for single mean. This is because you have one sample mean, one hypothesized population mean, and the population standard deviation is not known.

b) The value of the test statistic can be calculated using the formula: t = (X - µ) / (s / √n), where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size. Plugging in your values, the formula becomes t = (530 - 500) / (113/ √22).

c) With a = 0.05, we conclude by comparing the calculated t-value with t-distribution table (df = 22-1 = 21). If the calculated t-value exceeds the critical t-value from the t-distribution table, we reject the null hypothesis.

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Answer: 838% to the nearest percent

Step-by-step explanation:

225 - 24 =201

=201/24 * 100

= 838% to the nearest percent

If you are given the slope and y-intercept of a line, you can conclude several things about the line and use them to write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

For the values you've given:

- The slope (m) is 35.
- The y-intercept (b) is 550.

From these pieces of information, you can conclude:

1. **Slope (Steepness and Direction):** Since the slope is 35, this tells us that the line is relatively steep and rises quickly. The slope is positive, which means the line slants upwards from left to right. Specifically, for every one unit that x increases, y increases by 35 units.

2. **Y-intercept (Starting Point):** The y-intercept is where the line crosses the y-axis. Since the y-intercept is 550, it indicates that the line will cross the y-axis at the point (0, 550). This is the starting point of the line if you begin plotting from the y-axis.

With these conclusions, you can write the equation of the line in slope-intercept form:

\[ y = 35x + 550 \]

This equation allows you to predict or calculate the value of y for any given value of x along the line. It also enables you to graph the line by plotting the y-intercept and using the slope to determine the direction and steepness of the line. Remember, a line extends infinitely in both directions on the graph, so the portion you draw depends on the context or constraints of the particular situation you are modeling with the line.

Answer:

0.6 ounces

Step-by-step explanation:

Answer:

[tex] \frac{5}{2} \\ [/tex]

Step-by-step explanation:

[tex] \frac{ - 5 - 5}{ - 8 - - 4} [/tex]

Y - Y divided by X - X, the Y is 5 and the X is 2 (Rise over Run)

Answer:

[tex]\displaystyle 2\frac{1}{2} = m[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 5}{4 - 8} = \frac{-10}{-4} = 2\frac{1}{2}[/tex]

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The total number of college students was 17.94 million.

Step-by-step explanation:

Percentage of part time students = 34%

Number of part time students = 6.1 million

Let,

x be the total number of students

According to statement,

34% of x = 6.1 million

[tex]\frac{34}{100}x=6.1\ million\\0.34x=6.1[/tex]

Dividing both sides by 0.34

[tex]\frac{0.34x}{0.34}=\frac{6.1}{0.34}\\x=17.94\ million[/tex]

The total number of college students was 17.94 million.

Keywords: percentage, division

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Answer:

[tex]\displaystyle y = 7[/tex]

Step-by-step explanation:

Since the rate of change [slope] is zero, that automatically makes our equation set equal to the y-coordinate of the ordered pair, which in this case is the y-intercept.

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Answer:

22 people with red shirts and 10 people with yellow shirts