can anyone help me with this its driving me nuts.

The unit rate he can drive in mile per gallon is 22 miles per gallon.

Unit rate can be defined as the ratio between two measurements with the second term as 1.

In other words, a unit rate describes the ratio of two different units for the quantity of one.

Therefore, the  unit rate in miles per gallon can be calculated as follows:

Hence,

unit rate = number of miles / number of gallons

number of miles = 330 miles

number of gallons = 15 gallons

unit rate = 330 / 15

Therefore,

unit rate =  22 miles per gallon

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The interest paid on the loan and the total amount paid are $84,320 and $152,320 respectively.

It is given in the question that:-

Money borrowed by the company (Principal) = $68,000

Time period for which the money is borrowed = 8 years

Simple Interest rate = 15.5 %

We have to find the interest paid on the loan and the total amount paid.

We know that,

Simple interest = (Principal * Interest * Rate)/100

Hence, we can write,

Simple interest = (68000 * 15.5 * 8)/100 = $84,320

Also, we know that,

Amount = Principal + Interest

Hence, we can write

Amount = 68,000 + 84,320 = $152,320

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EXPLANATION

Given the expression:

Applying the cubic power to both sides:

Simplifying the cubic root with the cubic power:

Subtracting -a to both sides:

Adding z to both sides:

Simplifying terms:

Switching sides:

We are asked to determine the equation of a line that passes through the point (-3, -1) and has a slope 2/5. To do that we will use the point-slope form of a line equation:

Where:

Now, we plug in the values:

Simplifying we get:

Now, we apply the distributive law:

Now, we subtract 1 from both sides:

and thus we get the equation of the line.

The price per ticket, excluding the convenience charge, is  $65.

the rush delivery is given as $15.

The total cost of the tickets is said to be put at $352.50

Then the value that we would have for the the 5 tickets wpould be 352.50 - 15 = $337.50.

There is the convenience charge of $2.50 per ticket. This charge is excluded from the convenience charge that is to be paid.

Hence you would have to make the payment of

337.50 - 5*2.50

= 325.

Next we are to solve for the price of the ticket whioch is independent of the convenience charge

= 325 / 5

= $65

Hence the price per ticket is given as 65 dollars

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By rewritting the 6 as 5 + 1 we will get:

1 + 5 + 5 = 1 + (5 + 5) = 11

One trick we do a lot when we do additions os making tens (or hundreds, thousands, etc... depending on the case).

This means that we play with the numbers in such a way that we can make tens, in this case we have the sum:

6 + 5

We can rewrite this as:

6 + 5 = 1 + 5 + 5

Using the associative property we rewrite:

1 + 5 + 5 = 1 + (5 + 5)

1 + (5 + 5) = 1 + 10 = 11

The sum is equal to 11.

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Answer:

36

Step-by-step explanation:

-2(-3)(6)

6(6)

36

Answer:

-8/2 / 6/-3 -8/2 x -3/6 24/12= 2

Step-by-step explanation:

Answer:

$89 dollars per uniform

Step-by-step explanation:

Total amount of money raised= $6,764.

Money spent on new instruments= $6,764÷1/2 = $3382

The number of new uniforms bought with the remaining money= 38.

How much was spent on one= $3,382÷38 = $89

The transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.

So, the difference between the vertices of triangle FGH and F’G’H is the y-coordinates of the F’G’H triangle are inverse of the y-coordinates of the FGH triangle.

Therefore, the transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.

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Answer:

-16

Step-by-step explanation:

b) -x²;                   x = -4

-(-4)²

-(16)

-16

I hope this helps!

Answer: -16

Step-by-step explanation:

The first five terms of the given sequence are 4, 1, 6, 13, 22

We can solve this problem by following a few steps.

The formula to find the next four terms is, a =  (n)²- 3, (n ≥2) as per the question.

Where n is the sequence of the number ( n = 2, 3, 4, 5, 6, etc. )

So, for the 2nd term A₂ = 2² - 3 = 4 - 3 = 1  [As n = 2 for the second term ]

Similarly, for the 3rd term A₃ = 3² - 3 = 9 - 3 = 6  [ As n = 3 for the third term ] ,

for the 4th term A₄ = 4² - 3 = 16 - 3 = 13  [ As n = 4 for the second term ] ,

for the 5th term A₂ = 5² - 3 = 25 - 3 = 22  [As n = 5 for the second term ]

Now, we can conclude that the first five terms of the given sequence are 4, 1, 6, 13, 22

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The correct question is :

a₁ = 4; a = (n)²-3 (n ≥2) list the first five terms

The graph is attached below.

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The expected value for the amount chosen from the bag is $5.90

We have

So in total, we have 1 + 2 + 3 +4 = 10 bills.

The expected value will be then given by the sum of the products between the value of each bill and the number of bills of that type, divided by the total number of bills.

EV = (1*$20 + 2*$10 + 3*$5 + 4*$1)/10 = $5.9

The expected value is $5.9

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Answer:

The value of x will be 90°

The probability of the next car not being a white car is 0.92

The probability of an event is the chance or the likelihood that the event would occur.

Note that the chance or the likelihood is represented as a numerical value

The complete question is added as an attachment

From the attached question, we have the following parameters

P(White Vehicle) = 0.25

P(Car) = 0.36

P(White Car) = 0.08

Using the complement rule of probability, we have the following equation

P(White Car) + P(Not White Car)  = 1

Substitute the known values in the above equation

So, we have the following equation

0.08 + P(Not White Car)  = 1

Subtract 0.08 from both sides of the equation

So, we have

P(Not White Car)  = 1 - 0.08

Evaluate the difference

P(Not White Car)  = 0.92

Hence, the probability that the next car will not be a white car is 0.92

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The person is therefore using more water for bathing than for showering, according to the conclusion.

Half of the tub's total water is consumed while taking a bath.

Water used divided by volume equals

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

= [tex]\frac{(5)(3)(2.8)}{2}[/tex]

=[tex]\frac{42}{2}[/tex]

=21 cubic feet.

The following will provide the total amount of water utilized while having a shower:

Total water Equals rate ×time

= 1.52 × 12

= 18.24 gallons.

So, if there are 7.5 gallons in a cubic foot, the amount of water in cubic feet will be amount

=[tex]\frac{18.24}{7.5}[/tex]

=2.432 cubic feet.

The person is therefore using more water for bathing than for showering, according to the conclusion.

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When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones, it's important to regroup in order to correctly multiply the values.

Using partial products or multiplying in parts is how the conventional method does multiplication. A word that also signifies multiplication is "product," so keep that in mind. Any two numbers, regardless of how tiny or how large, can be multiplied using this standard technique.

The top number is multiplied by the bottom number, one digit at a time, working your way from right to left, using this procedure.

In this case, it should be noted that the value of 5,917 × 29 is 171593.

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Answer:

C. 0.16

Explanation:

In the table there are 59 students that prefer tacos and there are 367 students in total because

187 + 59 + 23 + 98 = 367

Then, the estimated population proportion of students that prefer tacos is calculated as

P = 59/367 = 0.16

Therefore, the answer is

C. 0.16

Answer:

"Simplify" is an instruction to rewrite the expression with as few symbols as possible. 5y-4 and 5/y4 have the same number of symbols.

A possible alternative direction might have been to rewrite without the negative exponent.

Answer:

[tex]\frac{1}{y}[/tex]

Step-by-step explanation:

using the rule of exponents

•  [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]\frac{y^{-5} }{y^{-4} }[/tex]

= [tex]y^{(-5-(-4))}[/tex]

= [tex]y^{(-5+4)}[/tex]

= [tex]y^{-1}[/tex]

= [tex]\frac{1}{y}[/tex]

Using an exponential function and a differential equation, the constant k for the situation is given by:

k = 0.03.

An increasing exponential function is modeled according to the following rule:

[tex]A(t) = A(0)e^{kt}[/tex]

In which:

This exponential function is the solution to the following differential equation:

A'(t) = kA(t)

One example of application of these functions is for continuous compounding, in which the value of an investment of P(0) after t years is given by:

[tex]P(t) = P(0)e^{kt}[/tex]

For the continuous compounding situation in this problem, the interest rate is of 3%, hence k = 0.03, which is the desired parameter.

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1.25 is the probability that the aircraft Will last 100 hours.

The area of mathematics described as probability concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty. 

Given Data

Mean = 80

Standard deviation = 16

P( x < 100)

P( x < 100) = P( Z< [tex]\frac{x- mean}{standard deviation}[/tex])

P(x<100 ) = P( Z < [tex]\frac{100-80}{16}[/tex])

P(x< 100) = P(Z< [tex]\frac{20}{16}[/tex])

P(x < 100) = 1.25

1.25 is the probability that the aircraft Will last 100 hours.

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.............................

The graph of the linear equation:

y = -3x + 4

Can be seen in the image at the end.

Here we know that the equation for the line is:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above line so we get the value of k.

-2 = k*2 + 4

With this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

Then the line is:

y = -3*x + 4

If we evaluate in x = 0, we get:

y = -3*0 + 4 = 4

So, at this point we know that the line passes through points (0, 4) and (2, -2), so to graph the line, we just need to graph these two points and draw a line that connects them, like in the example below.

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The constant variation of hight(y) to seconds(x) is 3y/2x.

So, let the second be 'x' and the height is 'y'.

At 4 seconds the wavelength is 6 ft high.

Constant variation:

So,

Therefore, the constant variation of hight(y) to seconds(x) is 3y/2x.

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Probability - The value of P(AUB) =  0.557

What is Probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

P(A) = 0.2,

P(B) = 0.31 and

P(A/B) = 0.152,

Since, we know that

P(A⋃B) = P(A)+P(B)-P(A⋂B)

So, we have to find P(A⋂B)

We know that,

P(A/B) = P(A⋂B)/P(B)

Putting the values we get,

0.152 = P(A⋂B) / 0.31

P(A⋂B) = 0.152 x 0.31

P(A⋂B) = 0.047

Now, lets find the value of P(A⋃B)

P(A⋃B) = P(A)+P(B)-P(A⋂B)

Putting the values we get,

P(A⋃B) = 0.2 + 0.31 + 0.047

P(A⋃B) = 0.557

Hence the value of P(A⋃B) = 0.557

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The equation as a function of x is y = 9280 -20x

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement. It shall be taken into account as an expression.

The equation is =[tex]\frac{1}{16}x + \frac{1}{320}y - 29= 0[/tex]

Now rearranging the function we write

[tex]\frac{y}{320}= 29 -\frac{x}{16}[/tex]

y = 9280 -20x

The equation as a function of x is y = 9280 -20x

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The numerical value of each of the four given shapes filled in the rows and columns are;

let

Row 1: There are 2 stars, one pentagon and one spiral shape.

A + 2B + C = 23 .....(equation 1)

Row 2: There are 2 spiral shapes and 2 rectangle shape.

2C + 2D = 16 ......( equation 2)

Row 3: There are 1 star, one pentagon and 2 rectangle shape.

A + B + 2D = 24 ....(equation 3)

Row 4: There are 3 spiral shapes and one star shape.

B + 3C = 15 ....(equation 4)

Column 1:

2C + A + D = 19 ....(equation 5)

Column 2:

2B + C + D = 20 .....(equation 6)

From equation 4;

B = 15 - 3C

From equation 2:

D = 8 - C

A + 2B + C = 23

A + 2(15 - 3C) + C = 23

A + 30 - 6C + C = 23

A = 5C - 7

2C + A + D = 19

2C + (5C - 7) + 8 - C = 19

6C + 1 = 19

6C = 18

C = 3

A = 5C - 7

A = 5(3) - 7

A = 8

B = 15 - 3C

B = 15 - 3(3)

B = 6

D = 8 - C

D = 8 - 3

D = 5

Therefore, there are 8 pentagon shape, 6 star shapes, 3 spiral shapes and 5 rectangle shape.

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Jack's percentage decrease on his measurement of painting by 18%.

What is meant by percentage change?

Measures of percent change include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.

Given that,

Jack's measurement for his room =  5 ft (taking this as old value)

Actual measurement for Jack's room = 4.1 ft (taking this as new value)

Using formula for Percent change =  [tex]\frac{new - old}{old}[/tex]  × 100% =  [tex]\frac{4.1 - 5}{5}[/tex] × 100%

                                                       =  [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%

                                                       = -18%

Here, minus sign represents the decrease in percentage.

Hence, Jack's percentage decrease on his measurement of painting by 18%.

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Correct question will be :

Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?

The quadratic formula is given by th following formula:

where a, b and c are the coefficients of the quadratic equation. In this case, you have:

a = 6

b = 9

c = -22

replace the previous values into the quadratic formula and simplify:

Hence, the solutions for the given equation are 1.31 and -2.81

We have to use the simple interest formula.

Where P = 2,000, r = 0.04, t = 25. Let's solve for A