Express 15$ for 10 gallons as a unit rate

Answer:

The answer is 72.578 :))

Step-by-step explanation:

I got it right in my exam

Isolate the x. Note the equal sign. What you do to one side, you do to the other. First, add 1/3y to both sides

8x - 1/3y (+1/3y) = 15 (+1/3y)

8x = 15 + 1/3y

Divide 8 from both sides

(8x)/8 = (15 + 1/3y)/8

x = 15/8 + 1/24y

x = 1/24y + 1.875

x = 1/24y + 1.875 is your answer

hope this helps

40 mins is the answer

10 mins-4

20mins-8

30mins-12

40mins-16

answer=2X8+3X5=16+15=31

B. is the graph that fills the requirements

Graph2 with slope of 25 is the graph that shows the relationship on the table.

To find the equation of the line passing through points A(3, 75) and B(12, 300) follow these steps:

1. Calculate the slope m:

m = (y₂ - y₁)/x₂ - x₁)

m = (300 - 75)/(12 - 3)

m = 225/9

m = 25.

Graph2 with same slope as the calculated slope is the graph that shows the relationship on the table.

2. Use the point-slope form with one of the points (e.g., A(3, 75)

y - y₁ = m(x - x₁)

y - 75 = 25(x - 3)

3. Simplify the equation:

y - 75 = 25x - 75.

4. Isolate y

y = 25x.

So, the equation of the line passing through points A(3, 75) and B(12, 300) is y = 25x

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Answer:

4606.48 $

Step-by-step explanation:

Amount invested P = 3500 $

Rate of interest r = 6.12%

Compounding monthly

Monthly rate of interest = 6.12/12 =0.51%

Time = 4.5 years = 4.5 (12) = 54 months

Hence final amount would be

P(1+0.01r)^t

Here r = 0.51 and t = no of months = 54

Hence final amount

= 3500(1.0051)^54

= 3500(1.31613)

=4606.48 $

Thus 3500 if invested now will become 4606.48 in 4.5 years at the rate of interest of 6.12% compounding monthly.

To find the cost of each concert ticket for a family of four, divide the total cost, $104, by the number of tickets, which is 4. The resulting cost per ticket is $26.

The student is asking for help with a simple division problem. A family purchased concert tickets for a total of $104, and we know there are four tickets purchased since it's a family of four. To find the cost of each ticket, we have to divide the total cost ($104) by the number of tickets (4).

Step-by-Step Solution:

Determine the total spent: $104.

Determine the number of tickets: 4.

Calculate the cost per ticket: $104 ÷ 4 = $26.

Therefore, the cost of each concert ticket was $26.

∠C and ​ ∠D ​ are vertical angles

so <C = <D because vertical angles are equal

Substitute

−3x + 58  = x−2

Solve for x

Subtract x from both sides

-4x + 58 = - 2

Subtract 58 from both sides

-4x = - 60

Divide both sides by -4

x = 15

<D = x−2  = 15 - 2 = 13

Answer

<D = 13°

Answer:

The measure of angle D is 13°

Step-by-step explanation:

-3x+58=x-2

+3x to each side

58=4x-2

Add 2 to each side

60=4x

Divide each side by 4

X=15

Now substitute that in:

-3(15)+58=13

(15)-2=13

The measure of angle D is 13°

Answer: C

Step-by-step explanation:

A) not completely factored because 2 can be factored out of 2x + 4

B)  not completely factored because 3 can be factored out of 3x - 9

C) CORRECT

D) not factors because the terms are added instead of multiplied

Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.

It is a polynomial of maximum power 2. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

A.  (2x + 4)(x - 3)

On multiplying

2x² - 2x -12

B.  (x - 1)(3x - 9)

On multiplying

3x² -12x + 9

C.  (x + 4)(x - 3)

On multiplying

x² + x - 12

D.  (x - 2) + (x + 3)

On multiplying

2x + 1

Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.

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Answer:

Refer below

Step-by-step explanation:

a) a and b are the lower and higher values of the interval for which uniform distribution is defined.

Here a= 6 and b =10

b) Mean of the uniform distribution= (a+b)/2 = (6+10)/2 =8

Or int x (1/4) dx = x^2/8 = 8

c) Variance of the uniform distribution = (b^2-a^2)/12 = (100-64)/12

= 36/12 =3

Std dev = sq rt of 3 = 1.732

d) To find total area

PDF of the distribution = 1/(b-a) = 1/4, 6<x<10

Area = \int 6 to 10 of 1/4 dx

= x/4

Subtitute limits

= (10-6)/4 =1

So total area = 1

d)P(X>7) = int 7 to 10 of 1/4 dx = 3/4

e) P(7<x<9) = Int 7 to 9 of 1/4 dx = 2/4 = 1/2

Probabilities are used to determine the chances of events

The values of a and b

The interval is given as 6 to 10.

So, the values of a and b are 6 and 10, respectively.

The mean

For a uniform distribution, the mean is:

[tex]\bar x = \frac{a + b}{2}[/tex]

So, we have:

[tex]\bar x = \frac{6 + 10}{2}[/tex]

[tex]\bar x = 8[/tex]

Hence, the mean is 8

The standard deviation

For a uniform distribution, the standard deviation is:

[tex]\sigma = \sqrt{\frac{b^2 - a^2}{12}}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{10^2 - 6^2}{12}}[/tex]

[tex]\sigma = 2.31[/tex]

Hence, the standard deviation is 2.31

The total area

This is calculated as:

[tex]A = \int\limits^b_a \frac{1}{b - a}\ dx[/tex]

So, we have:

[tex]A = \int\limits^{10}_6 \frac{1}{10 - 6}\ dx[/tex]

[tex]A = \int\limits^{10}_6 \frac{1}{4}\ dx[/tex]

Factor out 1/4

[tex]A = \frac{1}{4}\int\limits^{10}_6 \ dx[/tex]

Integrate

[tex]A = \frac{1}{4} * x|\limits^{10}_6[/tex]

Expand

[tex]A = \frac{1}{4} * (10 - 6)[/tex]

[tex]A = 1[/tex]

Hence, the total area of the distribution is 1.00

The probability of a value more than 7

This is calculated as:

[tex]P(x > 7) = \frac{1}{4} * x|\limits^{10}_7[/tex]

Expand

[tex]P(x > 7) = \frac{1}{4} * (10 - 7)[/tex]

[tex]P(x > 7) = 0.75[/tex]

Hence, the probability of a value more than 7 is 0.75

The probability of a value between 7 and 9

This is calculated as:

[tex]P(7 < x < 9) = \frac{1}{4} * x|\limits^9_7[/tex]

Expand

[tex]P(7 < x < 9) = \frac{1}{4} * (9 - 7)[/tex]

[tex]P(7 < x < 9) = 0.50[/tex]

Hence, the probability of a value between 7 and 9 is 0.50

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Answer:

A) x + 0

Step-by-step explanation:

In triangle ABC, the coordinates are: A(1, -1), B(1, -5) and C(4, -5)

In triangle A'B'C', the coordinates are: A(1, -5), B(1, 1) and C(4, 1)

Look at the x-coordinates in both the triangles remains the same because the triangles are reflected over x-axis, therefore, only the y-coordinate changes.

Therefore, the rule for x-coordinates = x + 0

Answer: A) x + 0

Hope this will helpful.

Thank you.

Answer:a

Step-by-step explanation:

Answer:

6:8, 9:12

Step-by-step explanation:

Answer:

6:8 9:12

Step-by-step explanation:

That triangle has a horizontal base with y=2.  The length of that base is RS=1-(-4)=1+4=5.  The height of the triangle is the vertical distance  from line y=2 to T(-5,-4).  That height is  2-(-4)=2+4=6.  The area of the triangle is  base * height/2 = 5*6/2= 15

The answer is 15 units ^2

Answer:

The answer is 15 units².

Step-by-step explanation:

I am a hundred percent sure. I did the math and got it right on my test.

Answer:

Given equation is:

x/4 = 16

Multiply both side of equation by 4

4* x/4 = 16*4

x= 64

Step-by-step explanation:

This is called Multiplication property of Equality.

If you multiply equation by a number on both sides, it remain same or balance.

The equation x/4 =16 is solved by multiplying both sides by 4, resulting in x = 64. This action is justified by the Multiplication Property of Equality.

To solve the equation x/4 =16, the action one would use is to multiply both sides of the equation by 4. This operation will isolate the variable 'x'.

Your equation would thus be transformed as: 4 * (x/4) = 16 * 4. This simplifies to x = 64.

The property that justifies this action is the Multiplication Property of Equality, which states that multiplying both sides of an equation by the same non-zero number does not change the equality.

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Algebraically, you have to factor the square root of 7 to see why you're wrong:

[tex] 3\sqrt{7}-\sqrt{7} = \sqrt{7}(3-1) = 2\sqrt{7} [/tex]

Conceptually, think that any object - say an apple - represents the square root of seven.

So, you have three apples, and you take away one apple. You have two apples remaining, i.e. [tex] 2\sqrt{7} [/tex]

[tex]3\sqrt{7} - \sqrt{7}[/tex]

Let x represent [tex]\sqrt{7}[/tex], then you can rewrite the expression as 3x - x.

3x - x = 2x.  Now replace "x" with  [tex]\sqrt{7}[/tex] and you get 2[tex]\sqrt{7}[/tex].

The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.

Using complex numbers, you can have negative squares, since [tex] i^2=-1 [/tex]

So, you can find the solutions to

[tex] x^2+20=0 \iff x^2 = -20 \iff x=\pm\sqrt{-20}=\pm i \sqrt{20}=\pm 4i\sqrt{5} [/tex]

So, using the factorization [tex] (x-x_1)(x-x_2) [/tex] where [tex] x_{1,2} [/tex] are the roots of the quadratic equation, you have

[tex] x^2+20 = (x-4i\sqrt{5})(x+4i\sqrt{5})[/tex]

This expression can't be further factorized, because all terms have degree 1.

To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.

To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.

Using the quadratic formula, we start by finding the values of x that satisfy the equation x^2 + 20 = 0.

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 1, b = 0, and c = 20. Substituting these values into the quadratic formula, we get: x = ± √-20.

Since we are factoring over the complex numbers, we can express the solution as: x = ± √20i.

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ANSWERS

Find out the how many weeks will it take for Mary and Joe to have the same amount saved.

To proof

Let us assume that the number of week take for Mary and Joe to have the same amount saved be x.

As given

Mary start with $10 and earns $10 each week mowing lawn.

Joe already has $20 from birthday gifts and earns five dollars a week pulling weeds.

than the equation

10 + 10x = 20 +5x

5x = 10

x = 2 weeks

therefore 2 weeks will it take for Mary and Joe to have the same amount saved.

Hence proved

The number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number.

Total letters = 26

Total numbers = 10

As the repetitions are allowed.

Number of ways = 26×26×26×10×10×(26+10)

N=63,273,600 Ways

P(abc123 or 123abc) = P(abc123)+P(123abc) - P(abc123 and 123abc)

The intersection of abc123 and 123abc is zero because both license plates are not possible at a time

P(ABC123 or 123ABC)=P(ABC123)+P(123ABC)

[tex]\rm P=\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}\dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8} + \dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8}\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}[/tex]

P= 2/5616000

or

P = 1/2,808,000

Thus, the number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

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D

a direct linear variation equation has the form f(x) = kx

f(x) = x - 12 is not in this form thus does not show a direct linear variation

x^2 - 3(x^2 + 3x - 1)

Distributive property.

x^4 + 3x^3 - x^2 - 3x^2 - 9x + 3

Combine like terms.

x^4 + 3x^3 - 4x^2 - 9x + 3

The tax on a $9.95 purchase with a 6.8% tax rate, rounded to the nearest hundredth, is approximately $0.68.

To calculate the tax on a purchase, you can multiply the purchase amount by the tax rate. In this case, $9.95 is being multiplied by 6.8% (or by 0.068 as a decimal). So, the calculation would look like this: $9.95 * 0.068 = $0.6766. However, the question asks to round to the nearest hundredth. So, the final tax would be approximately $0.68.

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Final answer:

A division equation that has a solution of -20 can be written by dividing a negative number by a positive number, such as -100 divided by 5.

Explanation:

To write a division equation with a solution of -20, you can choose any two numbers such that the division of one number by the other equals -20. For example, if we take -100 and divide it by 5, we get -20 as the solution. Thus, a sample division equation could be:

-100 / 5 = -20.

This is because when you divide a negative number by a positive number, the result is negative, and -100 \/ 5 leads to the desired solution of -20.

Answer:

The correct option is A.

Step-by-step explanation:

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]          ..... (1)

Where, (h,k) is vertex and a is a constant.

From the given graph it is clear that the vertex of the graph is (3,-7) and y-intercept is (0,2).

Substitute h=3 and k=-7 in equation (1).

[tex]y=a(x-3)^2-7[/tex]

The y-intercept is (0,2). So, substitute c=0 and y=2 in the above equation to find the value of a.

[tex]2=a(0-3)^2-7[/tex]

[tex]2+7=a(3)^2[/tex]

[tex]9=9a[/tex]

Divide both sides by 9.

[tex]1=a[/tex]

The value of a is 1.

Substitute a=1, h=3 and k=-7 in equation (1).

[tex]y=1(x-3)^2-7[/tex]

[tex]y=x^2-6x+9-7[/tex]

[tex]y=x^2-6x+2[/tex]

The equation of the parabola is [tex]y=x^2-6x+2[/tex].

Therefore the correct option is A.

Given that Bart and Melinda are grand children and Bart lives

6 blocks from his grand parents.

Also given that Melinda lives 8 blocks farther from her grandparents as Bart does .

This means Melinda lives 6+8 = 14 blocks from her grand father house

This question involves addition because farther as Bart does means , Melinda lives 8 +6 hence we get 14

Answer is: Melinda lives 14 blocks from her grandfathers

I know that i had it on a test its -2.11 Hope you ace it!

-2.11 hope this helps

If you distribute the multiplication, your function is written as

[tex] y=f(x)=3x-6 [/tex]

Like every function in the form [tex] y = mx+q [/tex], this function represents a line. A line has no vertex and no axis of symmetry (actually, it is symmetric with respect to every perpendicular line).