5 gallons of gas cost $16.25 the cost per gallon is $3.25

the question what unit rate describes the number of gallons per dollar?

Answer: This is a quadratic function in standard form:

f(x) = x^2 - 10x + 9

The vertex form of a quadratic function is given by:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

To rewrite the given function in vertex form, we need to complete the square:

f(x) = x^2 - 10x + 9

= (x - 5)^2 - 16

Now we can see that the vertex is at (5, -16) and the axis of symmetry is x = 5.

To find the x-intercepts, we set y = 0:

0 = (x - 5)^2 - 16

16 = (x - 5)^2

±4 = x - 5

x = 1 or x = 9

Therefore, the x-intercepts are (1, 0) and (9, 0).

To find the y-intercept, we set x = 0:

f(0) = 9

Therefore, the y-intercept is (0, 9).

The graph of the function is a parabola that opens upward with vertex at (5, -16), x-intercepts at (1, 0) and (9, 0), and y-intercept at (0, 9).

Step-by-step explanation:  

the vertex is at (5, -16)

y-intercept is (0, 9).

the x-intercepts are (1, 0) and (9, 0).

axis of symmetry is x = 5

the range of the function is all real numbers greater than or equal to -16. In interval notation, we can write this as [-16, ∞).

the domain of the given function f(x) = x^2 - 10x + 9 is all real numbers.

Let's start by setting up an equation to represent the problem.

Let's say Jake started with x amount of money.

After giving 1/3 to his wife, he has 2/3 left: (2/3)x

After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600

We can solve for x by isolating it:

(1/4)(2/3)x = $600

Multiplying both sides by 12/2 gives:

(2/3)x = $3600

Dividing both sides by 2/3 gives:

x = $5400

So Jake started with $5400.

To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:

(1/4)(2/3)($5400) = $900

So he gave his mother $900.

Step-by-step explanation:

x = original amount of money

the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.

x - (1/3)x - (1/4)x = 600

so let's bring every fractional term to .../12.

12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600

12x/12 - 4x/12 - 3x/12 = 600

5x/12 = 600

5x = 600×12

x = 600×12/5 = 120×12 = $1440

he gave to his mother

(1/4) × 1440 = $360

Using elimination,  the solution to the system of linear equations is x = -16/29 and y = -75/87.

What is a linear equation, exactly?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It is an algebraic equation that can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.

Now,

To solve the system of equations 8x + 3y = -7 and 7x + 2y = -3 using elimination, we need to eliminate one of the variables by adding or subtracting the two equations.

One way to do this is to multiply the second equation by a suitable constant so that the coefficient of one of the variables is the negative of the corresponding coefficient in the first equation. In this case, if we multiply the second equation by 3, we can eliminate y by adding the resulting equation to the first equation:

8x + 3y = -7

(3)(7x + 2y = -3) -> 21x + 6y = -9

Adding the two equations, we get:

29x + 0y = -16

Simplifying, we get:

x = -16/29

Now, we can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:

8x + 3y = -7

Substituting x = -16/29, we get:

8(-16/29) + 3y = -7

Simplifying, we get:

-128/29 + 3y = -7

Multiplying both sides by 29, we get:

-128 + 87y = -203

Solving for y, we get:

y = -75/87

Therefore, the solution to the system of equations is x = -16/29 and y = -75/87.

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Step-by-step explanation:

35/7   is an IMPROPER FRACTION ....  it REDUCES to an INTEGER = 5

The fraction 35/7 equals to 5, which is an integer because it is a whole number without a fractional or decimal component.

The fraction 35/7 equals to 5. The number 5 is a whole number that can be written without a fractional or decimal component, hence it is classified as an integer.

In general, an integer includes all whole numbers and their negative counterpart excluding fractions or decimals. Examples of integers are ...-3, -2, -1, 0, 1, 2, 3... and so on.

So the answer to your question is, 35/7 is an integer.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$700\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 700[1+(0.04)(2)] \implies A=700(1.08)\implies A = 756[/tex]

Answer:

y = x - 1

Step-by-step explanation:

to determine the equation of the line we require to find the slope of the line and its y- intercept, where it crosses the y- axis.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (1, 0) ← 2 points on the line

m = [tex]\frac{0-(-1)}{1-0}[/tex] = [tex]\frac{0+1}{1}[/tex] = [tex]\frac{1}{1}[/tex] = 1

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = x - 1

Answer:

if i answered it would be 0

Step-by-step explanation:

The probability that the two chairpersons chosen are of the same gender is 9/36.  

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It involves quantifying the likelihood of an event or outcome by assigning a numerical value between 0 and 1.

A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

Probabilities between 0 and 1 indicate the likelihood of the event occurring, with higher probabilities indicating a greater likelihood.

This can be calculated by looking at the number of possibilities when selecting two members from a group of nine (6 men, 3 women):

Total possibilities = 9C2 = 9!/(2!*7!) = 9*8/2 = 36

Ways of selecting two of the same gender = 6C2 + 3C2 = 6*5/2 + 3*2/2 = 15

Therefore, the probability of selecting two of the same gender is 15/36, which reduces to 9/36.

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The equation can be rewritten using the same base as: 3⁻³ =  3⁻⁴ˣ⁺⁶.

The solution for x is: x = 9/4

An equation is a mathematical statement that indicates that two expressions are equal. It consists of two sides, a left-hand side and a right-hand side, separated by an equal sign (=).

1) To rewrite an equation using the same base, we need to apply the following property of exponents:

(1/27)ˣ = 3⁻⁴ˣ⁺⁶

(1/3³) =  3⁻⁴ˣ⁺⁶

3⁻³ =  3⁻⁴ˣ⁺⁶

2) We can equate the exponents and then solve for x. That is:

3⁻³ =  3⁻⁴ˣ⁺⁶

-3 = -4x + 6

4x = 6 + 3

4x = 9

x = 9/4

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Answer:

Step-by-step explanation:

You want to know which of the listed statements is true of a 30°-60°-90° triangle.

The ratios of side lengths in a 30°-60°-90° triangle are 1 : √3 : 2.

This makes the following statements true:

To produce 36% solution, 50 gallons of pure acid should be added to 480 gallons of 22% acid solution.

To solve the problem find out how many gallons of acid are there in the 22% solution

           480*0.22= 105.6

       Let the amount of pure acid required to produce 36% solution be x gallons.

        So, the total amount of acid in the new solution will be

         480 + x.

 Write the equation for concentration:

    (Total acid in the new solution)/ (Total volume of new solution) = 36/100

       Using the above equation, we get;

        [105.6+x]/[480+x] = 36/100

  Cross multiply and simplify, we get;

       3600 + 100x = 423.6 + 36x63.6x

                              = 3176.4x

                              = 3176.4/63.6x

                           x = 50

        Therefore, the amount of pure acid required to produce 36% solution is 50 gallons.

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Answer: 12a + 6b

-2b

-8ab

Check: 48a^2 - 24b^2

Step-by-step explanation:

Therefore, the population mean, u, is the mean of 340 runners' times, regardless of the sample size. The correct answer is (B) 340.

In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data, which represents the average value of the data. It is commonly known as the arithmetic mean and is calculated by adding up all the values in the data set and then dividing by the number of values.

Here,

The population mean, u, is the mean of the times for all 340 runners in the population. If a sample of 226 runners is taken from the population, then the mean of the sample will be an estimate of the population mean. However, the population mean itself is not affected by the size of the sample.

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The equation of the transformed function, after being compressed horizontally by a factor of 3 and translated up 2 units, is g(x) = sqrt(x/3) + 2.

If f(x) is a function, and we want to compress it horizontally by a factor of 3 and translate it up 2 units, we can apply the following transformations:

Horizontal compression by a factor of 3 means that we need to replace x with x/3 in the function.

Translation up 2 units means that we need to add 2 to the function.

The equation of the transformed function is g(x) = sqrt(x/3) + 2, which represents a function that has been compressed horizontally by a factor of 3 and translated up 2 units from the original function f(x) = sqrt(x).

Therefore, the equation of the transformed function is:

g(x) = sqrt(x/3) + 2

Note that g(x) represents the transformed function, and we have used the square root symbol to indicate that the function is the square root of x/3.

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The product of 32 and 0.9 is 28.8.

The product of a set of numbers is the result of multiplying all the numbers together. For example, the product of 2, 3, and 4 is:

2 x 3 x 4 = 24

In general, if we have n numbers, the product is:

a1 x a2 x a3 x ... x an

where a1, a2, a3, ..., an are the individual numbers.

The product of two negative numbers is positive, while the product of a negative and a positive number is negative. The product of any number and 0 is always 0.

To find the product of 32 and 0.9, you can multiply these two numbers together:

32 x 0.9 = 28.8

Therefore, the product of 32 and 0.9 is 28.8.

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Answer:

Step-by-step explanation:

domain = x

range = y

when the domain is -1

y = 2(-1) - 3

y = -2 - 3

y = -5

range is -5

When the domain is 0

y = 2(0) - 3

y = 0 - 3

y = -3

range is -3

when the domain is 5

y = 2(5) - 3

y = 10 - 3

y = 7

range is 7

The range is { -5, -3, 7 }

[tex]X+1-\frac{2}{x+1}[/tex]

Step-by-step explanation:

when we use the way like this because the 2 was left by it own at the end so we need to do like this, by we cannot divide it by x

 steps for long division :Long division can also be used to divide decimal numbers into equal groups. It follows the same steps as that of long division, namely, – divide, multiply, subtract, bring down and repeat or find the remainder.

Let us consider the ratio to be x

So, as per the question's statement, we can write it as;

[tex]5x+4x=36[/tex]

[tex]\implies 9x=36[/tex]

We will divide 9 on both the sides, we get;

[tex]\implies x=\dfrac{36}{9} =4[/tex]

So, for getting the number of puppy sold we have to multiply it with 5, we get:

[tex]5x=5\times4=20[/tex]

They have sold 20 puppies.

Hence, the answer is [tex]20[/tex] puppies.

Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100.

Ratios can be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided any more.

Pls Add A Picture : Will Update.

Answer: (x-3)(2x+7)

Step-by-step explanation:

Answer:

(2x + 7 )(x - 3)

Step-by-step explanation:

You can find the original expression by using the box method on the factors.

The measure of angle P in the accompanying diagram is 0.072, when the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees. This is determined by using the formula for the measure of a central angle: M/P = (arc measure)/(360°).

Angle is a measure of the amount of turn between two straight lines or planes that have a common point or line of intersection. It is usually measured in degrees, radians, or gradians. An angle can be measured in different ways, such as the angle between two lines, the angle between two planes, or the angle between two points. Angles are important in mathematics, engineering, and physics as they help describe the shape and size of objects.

Since the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees, we can use the formula for the measure of a central angle:

M/P = (arc measure)/(360°)

Therefore, the measure of angle P is:

M/P = (26°)/(360°) = 0.072

Therefore, the measure of angle P is 0.072.

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The null-hypothesis (H₀) in a two-tailed hypothesis test states that there is no significant difference between the treatment group and the control group, the correct option is (c)The treatment has no effect on scores.

The "Null-Hypothesis" assumes that any difference between the treatment group and control group is due to chance, and that  treatment has no real effect on the outcome variable being measured.
The "Alternative-Hypothesis" (H₁) says that the treatment does have an effect on scores, but it does not specify whether the effect is positive or negative.

The null hypothesis is typically assumed to be true until there is sufficient evidence to reject it in favor of the alternative hypothesis.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a two-tailed hypothesis test, what does the null hypothesis (H₀) say about the treatment?

(a) The treatment increases scores.

(b) The treatment causes a change in scores.

(c) The treatment has no effect on scores.

(d) The treatment adds a constant to each score.

(e) The treatment decreases scores.

The option that shows a two-way conditional frequency table is option B as shown in the image attached.

A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:

Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.

The correct option is option B because it meets the following requirements:

We need 3 liters of water to fill the cylinder up to 2/3 of its capacity.

The formula for the volume of a cylinder is V=π r2 h, where V is the volume, π is pi, r is the radius and h is the height. The radius of the cylinder is half of the diameter, so the radius of this cylinder is 6 cm, and the height is 25 cm. Applying the formula, the volume of the cylinder is V=π[tex]*6^2*25[/tex]

=4500π cm3.

To fill it up to 2/3 of its capacity, we need 3000π cm3 of water. To convert this to liters, we need to divide by 1000, so the answer is 3000π/1000=3 liters of water.

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• Domain: All real numbers

• Range: (-∞, ∞)

• To find the local minimum/maximum and intervals of increase/decrease, we need to take the first and second derivatives of the function:

First derivative: -4x^3 + 6x + 2

Setting this equal to zero and solving for x, we get critical points at x ≈ -1.23, x ≈ 0.65, and x ≈ 1.23.

Second derivative: -12x^2 + 6

• At x ≈ -1.23, the second derivative is negative, so we have a local maximum.

• At x ≈ 0.65, the second derivative is positive, so we have a local minimum.

• At x ≈ 1.23, the second derivative is negative, so we have a local maximum.

• As x —> -∞, the function approaches ∞.

• As x —> ∞, the function approaches ∞.

• To find the x-intercepts, we set the function equal to zero and solve for x:

-x^4+3x^2+2x+2 = 0

This is a quartic equation that can be solved using various methods, such as factoring or using the quadratic formula. One solution is x ≈ -1.38. The other three solutions are complex numbers.

• To find the y-intercept, we set x = 0:

-y^4 + 2 = 0

Solving for y, we get y ≈ ±1.19. So the y-intercepts are (0, 1.19) and (0, -1.19).

Answer:

Domain- (−∞,∞),{x|x∈R}

Range-  (−∞,17+6√3(over)4], {y∣y≤17+6√3(over)4}

Local Minimum/Maximum- (−1,2) is a local maxima

(1+√3(over)2 ,17+6√3(over)4) is a local maxima

(1−√3(over)2 ,17−6√3(over)4)is a local minima

Intervals of Increase/Decrease- Increasing on: (−∞,−1)(1−√3(over)2,1+√3(over)2)

Decreasing on: (−1,1−√3(over)2),(1+√3(over)2,∞)

Step-by-step explanation:

i hope this helps !

Perimeter of quadrilateral: P = 20 m and Total area = 18 sq. m.

Quadrilaterals have the following two qualities:

Using Pythagorean theorem in  two given right triangles for finding the missing sides.

In triangle PQR

PR² = QR² + QP²

PR² = 8² + 1²

PR² = 64 + 1

PR = √65

Now,

In triangle PRS

PR² = PS² + RS²

PS² = PR² - RS²

PS² = 65 - 16

PS = 7

Perimeter of quadrilaterals:

P = sum of all exterior sides

P = 8 + 1 + 4 + 7

P = 20 m

Total area = area of triangle PQR +  area of triangle PRS

Total area = 1/2 *QR*PQ + 1/2 * PS *SR

Total area = 1/2*8*1 + 1/2*7*4

Total area = 18 sq. m

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A. The equation d = s * t shows relationship between the quantities.

B. They would cover a distance of 10 miles in 20 minutes.

C. Rounded to the nearest tenth, the biker would bike for 96.0 minutes.

What is distance?

Distance is the measure of the physical space between two objects or points. It is a scalar quantity that is usually measured in units such as meters, kilometers, miles, etc. In physics, distance is considered to be a fundamental concept and is often used in conjunction with time to calculate other physical quantities, such as speed and acceleration.

a. We can define the following variables:

t: time in minutes

d: distance traveled by the biker in miles

s: speed of the biker in miles per minute

Using these variables, we can write the equation d = s * t to represent the relationship between them.

b. If the biker rides for 20 minutes, we can use the equation d = s * t to find the distance traveled. Assuming the biker's speed is 0.5 miles per minute, we get:

d = 0.5 * 20 = 10 miles

Therefore, the biker would travel 10 miles in 20 minutes.

c. If the biker traveled 48 miles, we can use the equation t = d / s to find the time taken, where s is again assumed to be 0.5 miles per minute:

t = 48 / 0.5 = 96 minutes

Rounded to the nearest tenth, the biker would have ridden for 96.0 minutes to cover 48 miles.

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