A car travels 120 mi on 6 gal of gasoline.
What is the car's unit rate and what does it mean?
Enter your answers in the boxes.
The unit rate is
This means the car travels
mi on 1 gal of gas.

Answer:

15

Step-by-step explanation:

90 points in 6 games

90/6 = points in one game

= 15 points in one game

Answer:

15 points per game

Step-by-step explanation:

You need to divide the full amount of points (90) by the amount of games played (6) to get the amount of points per game.

90÷6=15

So 15 is the answer

Answer:

yes

Step-by-step explanation:

A quadratic function has the general form

fx) = ax² + bx + c ( a ≠ 0 )

f(x) = x² - 2x + 3 ← is in this form and is a quadratic function

The statement P(70) = 0.76 refers to the cumulative distribution function representing the probability of an individual's age being less than or equal to 70.


In probability theory, a cumulative distribution function (CDF) is used to describe the probability distribution of a random variable. In this case, P(t) represents the CDF for the age of individuals in the US, where t is measured in years.

The statement P(70) = 0.76 indicates that the probability of an individual's age being less than or equal to 70 is 0.76, or 76%. This means that among the population in the US, approximately 76% of individuals have an age less than or equal to 70 years.

The CDF P(t) provides information about the probability distribution of ages and allows us to determine the likelihood of an individual falling within a certain age range. In this case, P(70) = 0.76 tells us the proportion of individuals in the US population who are 70 years old or younger.


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Answer:

x° = 99°

Step-by-step explanation:

The polygon is a hexagon and the sum of its internal angles is:

\(180(n-2)=180(6-2)=180(4)=720^{0}\)

subtract the 5 known angles:

\(x^{0} =720-145-164-59-132-121=99^{0}\)

Hope this helps

Answer: 20.25*10.5*12.5 = the answer

Step-by-step explanation: Hope this help :D

It took 1700 J of work to stretch a spring from its natural length of 2 m to a length of 6 m. The spring constant k will be 212.5 N/m.

The potential energy stored in a spring is given by the formula:

PE = (1/2) kx^2

where k is the spring constant, x is the displacement from the equilibrium position, and PE is the potential energy.

In this problem, the spring is stretched from its natural length of 2 m to a length of 6 m, so the displacement is x = 6 m - 2 m = 4 m.

The work done on the spring is equal to the change in potential energy, so:

Work = PE final - PE initial

1700 J = (1/2) k(4² - (1/2) k(0)²

1700 J = 8k

k = 212.5 N/m

Therefore, the spring constant is 212.5 N/m.

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This equation is in slope intercept form

where m is the slope and b is the intercept

If what you are asking is to solve for x in terms of y

Then, we will follow the steps below:

subtract b from both-side of the equation

y-b = mx + b- b

y-b = mx

divide both-side of the equation by m

y-b / m = mx/m

Answer: y-b / m = mx/m

Step-by-step explanation:

This equation is in slope intercept form

where m is the slope and b is the intercept

If what you are asking is to solve for x in terms of y

Then, we will follow the steps below:

subtract b from both-side of the equation

y-b = mx + b- b

y-b = mx

divide both-side of the equation by m

y-b / m = mx/m

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}\)

\(A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}\)

Product is the answer to a multiplication problem so we multiply g and 4.

4xg or 4(g). Or even simpler, you could do 4g.

hope it helps!

The number that makes the ratio equivalent to 7:5 is 70 when compared with 50. To find this, we can set up a proportion and solve for the unknown value.

Step 1: Set up the proportion
First, we can set up the proportion with the given ratio 7:5 and the unknown value (let's call it "x") compared to 50:
(7/5) = (x/50)

Step 2: Cross-multiply
Next, we can cross-multiply to find the equivalent value:
7 * 50 = 5 * x

Step 3: Solve for x
Now, we can solve for the unknown value "x":
350 = 5x
x = 70

So, the number that makes the ratio equivalent to 7:5 when compared with 50 is 70. The resulting equivalent ratio is 70:50.

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Answer:

This geometric series is convergent:

\( \frac{10}{1 - ( - \frac{1}{5}) } = \frac{10}{ \frac{6}{5} } = 10( \frac{5}{6} ) = \frac{25}{3} = 8 \frac{1}{3} \)

The geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent.

To determine if the geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent or divergent, we need to examine the common ratio (r) between consecutive terms.

The common ratio (r) can be found by dividing any term by its preceding term.

Let's calculate it:

r = (-2) ÷ 10 = -0.2

r = 0.4 ÷ (-2) = -0.2

r = (-0.08) ÷ 0.4 = -0.2

In this series, the common ratio (r) is -0.2.

For a geometric series to be convergent, the absolute value of the common ratio (|r|) must be less than 1. If |r| ≥ 1, the series is divergent.

In this case, |r| = |-0.2| = 0.2 < 1.

Since the absolute value of the common ratio is less than 1, the geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent.

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Answer:

Step-by-step explanation:

b

b

lol

hope this helps <3

Answer:

in y=mx + b, b is the y intercept. Sp answer choice d.

Answer:

4+(4-3y) to the power of 3, 4x(5.5+3y) since y = 3.

Step-by-step explanation:

Noah is using the 50/30/20 budgeting strategy because he is using 50% of his income for his basic needs, 30% for entertainment, and 20% for savings and debt repayment.

Money management in mathematics is the application of mathematical principles and techniques to the management of personal or corporate money. It entails the use of mathematical tools like equations, graphs, and statistics to analyse financial data and make educated decisions about budgeting, saving, investing, and spending. Mathematicians also use probability and risk analysis to manage money by estimating the likelihood of different financial events and making decisions based on the benefits and dangers of various financial options. Overall, mathematicians' understanding of money management enables people and organisations to better manage their financial resources and reach their financial objectives.

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Answer:

Step-by-step explanation:

1:3

Answer:

-3

Step-by-step explanation:

153÷-51=-3

-51÷17=-3

Answer:

240 degrees

Step-by-step explanation:

Mathematically, the area of a circle is

A = 2 * pi * r^2

we need to calculate the radius of the circle first

18pi = 2pi * r^2

divide both sides by 2pi

r^2 = 9

r = 3 inches

Area of sector = angle/360 * pi * r^2

6pi = angle/360 * pi * 3^2

6pi = angle/360 * 9pi

(360 * 6pi)/9pi = angle

40 * 6 = 240 degrees

The maximum expected increase in exam score if a student studies an extra 3 hours is 4.11 points.

Since we have a 99% confidence interval, we can assume a t-distribution with 31 degrees of freedom (n-1). Using this distribution, we can find the margin of error (E) for the mean difference in exam score (µD) between students who study for an extra 3 hours and those who do not.

E = t* (s/√n), where s is the sample standard deviation and n is the sample size.

We don't have the standard deviation, but we can estimate it using the range rule of thumb, which states that the standard deviation is approximately equal to the range of the data divided by 4.

s ≈ (6.96 - 3.59) / 4 = 0.8425

Using a t-value for a 99% confidence interval and 31 degrees of freedom, we have:

t = 2.750

E = 2.750 * (0.8425/√32) ≈ 0.929

So the 99% confidence interval for the true mean difference in exam score is (3.59 - 0.929, 6.96 + 0.929) = (2.66, 7.89).

To find the maximum expected increase in exam score if a student studies an extra 3 hours, we can subtract the mean difference in exam score from the previous 32 students from the mean difference in exam score between students who study for an extra 3 hours and those who do not.

Mean difference in exam score = (6.96 - 3.59) / 32 = 0.104

Max expected increase in exam score = 0.104 + 3 = 4.11

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The points to be graphed are  (0, 3.5) and (-2.8, 0). The graph of the equation is shown in the attached image

Given  y = x/8 + 3.5

In order to graph the equation of the line:

First, find the value of x when y = 0:

y = x/8 + 3.5, when y = 0:

0 = x/8 + 3.5

x/8 = -3.5

x = -28

Thus, x-intercept is (-28, 0)

Also, find the value of y when x = 0:

y = x/8 + 3.5, when x = 0:

y = 0/8 + 3.5

y = 3.5

Thus, y-intercept is (0, 3.5)

Therefore,  the values to be plotted on our graph are (0, 3.5) and (-2.8, 0). The image of the graph is attached

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Answer:

Below.

Step-by-step explanation:

i) (a + b)^2 = a^2 + 2ab + b^2

= (x + y)^2 + 2(x + y)(x - y) + (x - y)^2

=  x^2 + 2xy + y^2 + 2(x^2 - y^2) + x^2 - 2xy + y^2

=  x^2 + 2x^2 + x^2 + y^2 - 2y^2 + y^2 + 2xy - 2xy

= 4x^2.

ii) (a - b)^2 = a^2 + b^2 - 2ab

=  (x + y)^2 + (x - y)^2 - 2 - 2(x^2 - y^2)

= x^2 + 2xy + y^2 + x^2 - 2xy + y^2 - 2x^2 + 2y^2

=  x^2 + x^2 - 2x^2 + y^2 + y^2 + 2y^2 + 2xy - 2xy

=  4y^2.

Answer:

A' (-5, 5)

B' (20, 0)

C' (5, -15)

Step-by-step explanation:

Multiply each coordinate by 5, and your result is given above.

Answer:

Step-by-step explanation:

Answer:

x + 6

Step-by-step explanation:

Sum means to add the 2 terms , so

x + 6 ← represents the sum of 6 and x

The test statistic for the population mean has a t-distribution with 9 degrees of freedom. Correct option is D.

The test statistic for the population mean in this scenario is a t-distribution with 9 degrees of freedom (option D).

To determine the test statistic, we need to use the formula:

t = (x' - μ) / (s / √n)

where x' is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

In this case, the hypothesized population mean is 2.5 grams, the sample mean is 2.47 grams, the sample standard deviation is 0.04 gram, and the sample size is 10.

Plugging these values into the formula, we get:

t = (2.47 - 2.5) / (0.04 / √10) ≈ -1.58

Since the sample size is less than 30, we use a t-distribution instead of a standard normal distribution. The degrees of freedom for the t-distribution is equal to n - 1, which in this case is 10 - 1 = 9.

We can use this distribution to calculate the p-value and make inferences about the population mean based on the sample data. Therefore, the correct option is D.

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Answer: 2x + 0.5 unit

Step-by-step explanation:

A square has 4 equal sides. Therefore, its perimeter is calculated by adding the four sides.

Since the perimeter of a square is 8x +2 units, to get the length of one side, we divide the perimeter by 4. This will be:

= (8x + 2)/4

= 2x + 0.5

Therefore, the length of one side is 2x + 0.5 unit

Answer:

60° and 30°

Step-by-step explanation:

Complementary angles sum to 90°

sum the parts of the ratio, 6 + 3 = 9 parts

Divide 90° by 9 to find the value of one part of the ratio.

90° ÷ 9 = 10° ← value of 1 part of the ratio, then

6 parts = 6 × 10° = 60°

3 parts = 3 × 10° = 30°

The measure of the angles is 60° and 30°

Answer:

3 for every 45 students

Step-by-step explanation:

so 3 for 45

4 90

When a multiple regression model created incorrectly then leaves out one and more than one important factors are omitted.

Multiple regression is a statistical way that can be used to analyze the relationship between a single dependent variable and several independent variables. Equation is written as y =

We have regressors x₁ and x₂ where both variables are determinants of the dependent variable. you first regressor y on x₁ only and find no relationship. however when regressing y on x₁ and x₂.

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Complete question:

consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. you first regress y on x1 only and find no relationship. however when regressing y on x1 and x2, the slope coefficient changes by a large amount. this suggests that your first regression suffers from:

Answer: 6

Step-by-step explanation: you subtract the one time fee($16) from the 100 then divide the rest by the cost of a one month membership($14)

Answer:

8

Step-by-step explanation:

Factors of 16 = 1, 2, 4, 8, 16

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

The bolded numbers are the factors that both numbers share. 8 is the biggest one.

The population parameter will always be between lower and upper bounds of the confidence interval. - True, whereas sample statistic will always be between lower and upper bounds of the confidence interval - False

With a certain degree of certainty, the population parameter is anticipated to lie between the lower and higher limits of the confidence interval. The confidence interval, which gives an interval estimate of the unidentified population parameter, is created based on the sample data. The interval's level of confidence shows the amount of ambiguity we are prepared to accept when determining the actual population parameter.

The confidence interval's lower and upper limits may or may not be met by the sample statistic used to compute them. A single point estimate, the sample figure is susceptible to sampling error. On the other hand, based on the observed sample data and the selected degree of confidence, the confidence interval is a range of values that we can be fairly confident includes the true population parameter.

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Answer:

Angle AOE is a vertical angle to angle COD.

Answer:

Aoe is vertical to coe

Step-by-step explanation: