A car travels at 50 mph until it is at a quarter (0.25) tank of gas. How far did the car travel if the uses gasoline at a rate of 1/8 tank per 1/2 hour of driving and started with a full tank.

Answer:

The asnwer in the bottom right corner is correct. When multiplying exponents with the same base all you do is add the exponent for example: For 9 to the 6 power times 9 to the 4 power the answer is 9 to the 10 since we just add 4 and 6

Step-by-step explanation:

The probabilities can be ordered from least to greatest as: (b) P(285 < X < 315) for n = 40, (c) P(285 ≤ X ≤ 315), and (a) P(2855 > X > 315) for n = 50.

To compare the probabilities, we need to consider the sample size and the type of inequality used in each probability.

For probability (b) P(285 < X < 315) with a sample size of n = 40, we are looking for the probability that the sample mean falls between 285 and 315. Since the sample mean distribution follows the same mean as the population, but with a reduced standard deviation (σ/√n), the probability of this range is higher compared to the other two probabilities.

For probability (c) P(285 ≤ X ≤ 315), the inequality includes the endpoints. This means that the probability includes the values of 285 and 315. Considering the same sample size of n = 40, this probability will be slightly lower than (b) since it covers a wider range.

For probability (a) P(285 > X > 315) with a sample size of n = 50, the inequality includes the exclusive endpoints, meaning that the values of 285 and 315 are not included. Since the sample size is larger compared to (b), the probability of this range will be lower than both (b) and (c).

Therefore, the probabilities can be ordered from least to greatest as: (b) P(285 < X < 315) for n = 40, (c) P(285 ≤ X ≤ 315), and (a) P(2855 > X > 315) for n = 50.

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Considering the curve x³y + y³ = sin y - x, the final i is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

Implicit differentiation is a technique used to differentiate equations that are not explicitly expressed in terms of one variable. It is particularly useful when you have an equation that defines a relationship between two or more variables, and you want to find the derivatives of those variables with respect to each other.

To find dy/dx for the curve x³y + y³ = sin y - x², the implicit differentiation will be used which involves differentiating both sides of the equation with respect to x.

It is expressed as follows;

\(\frac{d}{dx} x^3y + \frac{d}{dx} y^3 = \frac{d}{dx} sin(y) - \frac{d}{dx} x^2\)

Then we'll differentiate each term:

For the first term, x^3y, we'll use the product rule

\(\frac{d}{dx} x^3y = 3x^2y + x^3 \frac{dy}{dx}\)

For the second term, y^3, we'll also use the chain rule

\(\frac{d}{dx} y^3 = 3y^2 \frac{dy}{dx}\)

For the third term, sin(y), we'll again use the chain rule

\(\frac{d}{dx} sin(y) = cos(y) \frac{dy}{dx}\)

For the fourth term, x², we'll use the power rule

\(\frac{d}{dx} x^2 = 2x\)

Substituting these expressions back into the original equation, we get:

3x²y + x³(dy/dx) + 3y²(dy/dx) = cos(y)(dy/dx) - 2x

Simplifying the equation:3x²y + x³(dy/dx) + 3y²(dy/dx) - cos(y)(dy/dx) = -2x

Dividing both sides by 3y² - cos(y), we get:(x³ - cos(y))(dy/dx) = -2x / (3y² - cos(y))

Hence, the final answer is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

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The solution of f(x)=g(x) to the nearest hundredth if f(x)= x^2-2 g(x) = x-1 is 1.62 or -0.62

Given the following function below:

f(x) = x^2 - 2
g(x) = x - 1

Since f(x) = g(x), hence;

x^2 - 2 = x - 1
x^2 - x - 1 = 0

Factorize to have:

x = 1/2 +√5/2  or x= 1/2 - √5/2

x = 1.62 or -0.62

Hence the solution of f(x)=g(x) to the nearest hundredth if f(x)= x^2-2 g(x) = x-1 is 1.62 or -0.62

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Step-by-step explanation:

Here the value of x will be 55° as it is vertically opposite to 55°....

Now ,

y + 55° = 180° ( straight angle )

y = 180° - 55°

y = 125°

Now ,

z = y ( vertically opposite angle )

z = 125°

\(...\)

hence...the value of x is 55° and y and z is 125°

Answer:

Step-by-step explanation:

x = opposite angle = 55°

y+z = 360 - 55 - 55 = 250°

y+z = 250°

y = z (opposite angle)

y = z = 250° : 2 = 125

Linear regression forecasting is an algorithm used for identifying and predicting the future values of a dependent variable based on the independent variable.

The major restriction in linear regression forecasting is that it only takes into account the linear relationship between the dependent and independent variables.

The model assumes that the relationship between the dependent and independent variable is linear and not nonlinear. This assumption may not always be true because there might be cases where the relationship between the variables is non-linear, which can result in inaccuracies in the forecast.

The model's reliability is also based on the quality of the data used for regression analysis. If the data is incorrect, outdated, or incomplete, the accuracy of the model can be negatively affected. Another limitation is that the model assumes that the relationship between the dependent and independent variables is constant over time, which may not be true in the real world.

Also, linear regression is a parametric method that requires certain assumptions about the data, including the normality of the residuals and constant variance of the errors.Linear regression forecasts require data to be independent and unbiased and may not work well if data contains outliers or noise.

Linear regression cannot identify causality or differentiate between correlation and causality. Hence, it is recommended to use linear regression along with other techniques for better accuracy.

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There are four fundamental types of inequality: less than ( < ), larger than( > ), less than or equal to ( ≤ ), and more than or equal to( ≥ ).

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.

Steps to solve the inequality:

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The length of MN is 12 inches,  total surface area in square inches of the wooden blocks to be painted is 80400 square inches and

The formula for volume of a cuboid is:

Volume = Length× Width × Height

Thus 427 = (MN × 7× 3) + (5 × 5 × 7)

427 = 21MN + 175

21MN = 252

MN = 252/21

MN = 12

2) Surface area of entire object is:

TSA = 2(12 × 3) + 2(12×7) - (5 × 7) + 2(7×3) + 3(5 × 7) + 2(5 ×5)

= 402 in²

For 200 blocks:

TSA = 200× 402 = 80400 in²

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among the given options, the use of correlational statistics OPTION B is the most reliable indicator that a study employed a bivariate correlational design.

A bivariate correlational design is characterized by the examination of the relationship between two quantitative variables. In this context, the use of correlational statistics is a key indicator of this design. Correlational statistics, such as correlation coefficients (e.g., Pearson's r), are employed to assess the strength and direction of the relationship between the variables under investigation.

The presence of measured variables, inclusion of quantitative variables, or depiction of a bar graph are not definitive indicators of a bivariate correlational design. Measured variables can be present in various study designs, including experimental ones. Similarly, quantitative variables can be utilized in different types of studies, such as experimental, quasi-experimental, or observational designs. The depiction of a bar graph, which is commonly used to illustrate categorical data, does not inherently imply the use of a bivariate correlational design.

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Answer:

3

Step-by-step explanation:

The actual prime factors of 60 are 2, 3, and 5.

Answer:

3

Step-by-step explanation:

prime fatorizations are 2, 3, and 5

The couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.  The couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

a. The amount of money the couple needs to invest each year can be calculated using the present value of annuity formula. The future value of the university cost after 10 years can be calculated by compounding the current cost for 10 years at an annual inflation rate of 5.6%.

Then, the present value of this future cost can be found by discounting it back to the present using the effective annual interest rate of 6.75%. Finally, this present value can be divided by the present value of an annuity factor for 9 years (one year before the university starts) at an effective annual interest rate of 6.75%.

Using these calculations, the couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.

b. If the couple waits for one year, they will have nine years to save for their daughter's university education. This means they will have one less year to invest, so they will need to invest more each year to have enough money for their daughter's university education.

The additional amount they need to invest can be found by subtracting the present value of an annuity of $9,060.52 for 9 years from the present value of an annuity of $9,060.52 for 8 years.

Using these calculations, the couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

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Rounded to two decimal places, the percentage increase per year in the winner's check over this period is approximately 15,332.33%.

To calculate the percentage increase per year in the winner's check over the period from 1895 to 2016, we can use the following formula:

Percentage increase = [(Final value - Initial value) / Initial value] * 100

Initial value: $150

Final value: $2,300,000

Number of years: 2016 - 1895 = 121 years

Percentage increase = [(2,300,000 - 150) / 150] * 100

= (2,299,850 / 150) * 100

= 15,332.33%

Rounded to two decimal places, the percentage increase per year in the winner's check over this period is approximately 15,332.33%.

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Answer:
The cost of Jordan’s visits to the hair salon depends on the number of visits. The cost for 2 visits would be $60.00 (membership fee) + 2 * $26.00 (cost per visit) = $112.00. The cost for 4 visits would be $60.00 + 4 * $26.00 = $164.00. The cost for 5 visits would be $60.00 + 5 * $26.00 = $190.00. The cost for 8 visits would be $60.00 + 8 * $26.00 = $268.00.

Answer: 2 = 112 4 = 164 5 = 190 8 =268

Step-by-step explanation:

In order to solve this, the equation would be:

26x + 60

where x is the number of appointments, 26 is the amount each appointment costs, and 60 is the original price of the membership.

So...

2 visits would be $112

4 visits would be $164

5 visits would be $190

8 visits would be $268

Hope this is helpful

By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.

To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.

Since a van can ferry a maximum of 12 people, we can write the inequality as:

12v ≥ 80

Now, let's solve for "v":

Divide both sides of the inequality by 12.
v ≥ 80/12

Simplify the inequality.
v ≥ 6.67

Since we cannot have a fraction of a van, we need to round up to the nearest whole number:

v ≥ 7

Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.

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Answer:

D.10

s

Step by step explanation:

sana makatulong

Answer:

7/3

Step-by-step explanation:

i hope this works :)

Answer:

−4y

Step-by-step explanation:

Since the directrix is vertical, use the equation of a parabola that opens up or down.

(x−h)2=4p(y−k)

Find the vertex.

The vertex (h, k) is halfway between the directrix and focus. Find the y coordinate of the vertex using the formula y = y coordinate of focus + directrix 2. The x coordinate will be the same as the x coordinate of the focus.

(3,−1+1

    ___            

      2)

Simplify the vertex.

Add − 1 and 1. (3,0/2) Divide 0 by 2. (3,0).

Find the distance from the focus to the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is | p |. Subtract the y coordinate of the vertex from the y coordinate of the focus to find p. p = − 1 − 0 Subtract 0 from − 1 . p = − 1.

Substitute in the known values for the variables into the equation ( x − h ) 2 = 4 p (y − k). (x − 3) 2 = 4 (− 1) (y − 0).

Simplify.

(x − 3) 2= −4y

= −4y

Answer:

4(2x+3)

Step-by-step explanation:

Because 4 is the GCF

Answer:

x=11

Step-by-step explanation:

3x+28+5x+52+12=180

8x+92=180

-92 on both sides

8x=88

/8 on both sides

x=11

Answer:

Area of apothem is 8.33 inches

Step-by-step explanation:

Mathematically,

Area of hexagon = 1/2 * apothem * number of sides * length of side

Area = 50 in square

apothem = ?

number of sides = 6

Length of side = 2 inches

Substituting the values, we have;

50 = 1/2 * A * 6 * 2

50 = 6A

A = 50/6

A = 8.33 inches

Answer:

,,, hehe

Step-by-step explanation:

By dividing the polynomial f(x) = 3x⁴ + 7x³ - 10x² + 55 by (x + 2), the quotient is q(x) = 3x³ - 5x² + 10x + 45, and the remainder is r = -35.

To express the polynomial f(x) = 3x⁴ + 7x³ - 10x² + 55 in the desired form, we divide it by the linear factor (x + 2), representing k = -2. Using long division or synthetic division, we find that the quotient q(x) is equal to 3x³ - 5x² + 10x + 45.

This means that the term (x + 2) appears once in the expression of f(x), multiplied by q(x). The remainder r is -35, which represents the part of f(x) that is not divisible by (x + 2). Hence, the complete expression is f(x) = (x + 2)(3x³ - 5x² + 10x + 45) - 35.

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To answer this question, we need to take into account the reflection over the y-axis is given by the following rule:

If (x, y) is reflected over the y-axis, then the image is (-x, y).

Then, from the graph, we have that the coordinates are:

B(5, 5)

S(2, 2)

I(5,0)

Then, the image across the y-axis is:

B(5, 5) ---> Ry-axis ---> (-5, 5)

S(2, 2) ---> Ry-axis ---> (-2, 2)

I(5, 0) ---> Ry-axis ---> (-5,0)

Then, the rule for the new image is (-x, y).

The required value of the given function is (f ⋅ g)(4) = 130.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

f(x)=3x+1 and g(x)=x²-6

(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).

(f ⋅ g)(x) = f(x) × g(x)

So, substituting x = 4:

(f ⋅ g)(4) = f(4) × g(4)

= (3 × 4 + 1)×(4² - 6)

= 13 × 10

= 130

So, (f ⋅ g)(4) = 130.

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Which of the following is an accurate definition for the power of a statistical test is C. The power of a statistical test refers to the probability of rejecting a false null hypothesis. This means that the test is able to correctly identify when there is a significant difference between two groups or conditions.

statistical tests are used to determine whether the results of an experiment are likely due to chance or whether there is a real effect. The null hypothesis states that there is no significant difference, while the alternative hypothesis states that there is. The power of a statistical test refers to the ability of the test to correctly reject the null hypothesis when it is false, and thus support the alternative hypothesis.

, the power of a statistical test is the probability of correctly rejecting a false null hypothesis, which indicates that there is a significant difference between two groups or conditions.

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Answer:

decimal 0.13

percent is 13

Step-by-step explanation:

Answer:

Decimal: 13

Percent: 13%

Step-by-step explanation:

Sorry if it wrong

Answer:

A) (15 x $3) + (10 x $2) + (12 x $1) = X

B) $77      

Step-by-step explanation:

A) Each wrapping paper is 3 dollors, and they bought 15 (15 x 3)

Each greeting card is 2 dollors, and they bought 10 (10 x 2)

Each roll of ribbon is 1 dollors, and they bought 12 (12 x 1)

B) 15 times 3 is 45

10 times 2 is 20

12 x 1 is 12

45 + 20 + 12 = 77