keith drove 320 miles using 12 gallons of gas. at this rate, how many gallons of gas would he need to drive 296 miles?

Answer:

[tex]c = \frac{d}{a} - b[/tex]

Step-by-step explanation:

Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, divide a from both sides of the equation:

[tex]a(c + b) = d\\\frac{a(c + b)}{a} = \frac{d}{a} \\c + b = \frac{d}{a}[/tex]

Next, isolate the variable, c, by subtracting b from both sides of the equation:

[tex]c + b = \frac{d}{a} \\c + b (-b) = \frac{d}{a} (-b)\\c = \frac{d}{a} - b[/tex]

[tex]c = \frac{d}{a} - b[/tex] is your answer.

~

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Answer:

c = (d/a) - b

Step-by-step explanation:

Now we have to,

→ Find the required value of c.

The equation is,

→ a(c + b) = d

This can be distributed as,

→ a(c + b) = d

→ a(b) + a(c) = d

→ ab + ac = d

Then the value of c will be,

→ a(c + b) = d

→ a × (c + b) = d

→ c + b = d/a

→ c = -b + (d/a)

→ [ c = (d/a) - b ]

Hence, value of c is (d/a) - b.

On Monday, for completing the daily target Philip needs to travel 9/8 more miles.

As per the question,

As Philip wants to run a total of 3 miles each day.

As on Monday morning, he ran only 1(7/8) miles.

First, we will convert the given mixed fraction in form of improper fractions.

So, converting 1(7/8),

It will become equal to (8*1+7)/8 = 15/8

From above,

We can say, out of the 3 miles he only travel 15/8 miles on Monday.

So, for calculating the required distance we need to subtract the given value 15/8 from 3

Thus we will get it as:

3-15/8 = (24-15)/8 = 9/8 miles.

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The speed of the car is 59 miles per hour. Anna might have made an error by using change in y-coordinates/change in x-coordinates to find a unit rate, instead of change in x-coordinates/change in y-coordinates.

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Answer:

18

Step-by-step explanation:

To find a percent of a number, change the percent to a decimal by dividing the percent by 100 and multiply by the number.

25% of 72 =

= 25/100 × 72

= 0.25 × 72

= 18

Answer: it would be 18

Step-by-step explanation:

Answer:

x=71; y=19

Step-by-step explanation:

x+y = 90 so x =90-y = 14+3y

so  90=14+4y

90-14 = 4y

76=4y

y=19

x=71

Answer:

x = 71

y = 19

Step-by-step explanation:

I solved by graphing and got (71,19) as included in the image. A more mathematical way to solve is by substitution. You try to find x with one of the equations, plug in x and then solve for y.

x + y = 90

x = 90 - y

90 - y = 14 + 3y

90 - y + y= 14 + 3y + y

90 = 14 + 4y

90 - 14= 14 + 4y - 14

76= 4y

19 = y

x + y = 90

x + (19) = 90

x + 19 - 19= 90- 19

x = 71

The height of the trapezoid that has an area of 24 cubic cm is: 3 cm.

The formula for the area of a trapezoid is 1/2(a+b)h, where a and b are the lengths of the bases and h is the height.

Given that the area of the trapezoid is 24 cubic centimeters and the base lengths are 9 cm and 7 cm, we can plug in those values to the formula and solve for h:

24 = 1/2(9+7)h

24 = 1/2(16)h

24 = 8h

To find h, we divide both sides of the equation by 8:

h = 24/8

h = 3

So the height of the trapezoid is 3 cm.

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Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true is that: A. it cannot be proportional because a straight line through the point does not go through the origin.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

In conclusion, the relationship between the x-value and y-value isn't proportional because the straight line does not pass through the origin (0, 0).

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For two similar triangular sculptures having leg l1 = 4.5 ft, l2 = 6 ft, and base b1 = 7.2 ft, the measurement of b2 is 9.6 ft.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

Two triangles are similar.

Let the two similar triangles sculptures be ΔABC and ΔDEF.

The length of the leg ΔABC, AB = 4.5 feet

The length of the base of ΔABC, BC = 7.2 feet

The length of the leg ΔDEF, DE = 6 feet

The length of the base of ΔDEF, EF = x feet

To find the measure of base of ΔDEF, use the formula for indirect measurement.

According to indirect measurement the formula will be -

AB/DE = BC/EF

Substitute the values in the equation -

4.5/6 = 7.2/x

4.5 × x = 7.2 × 6

4.5x = 43.2

x = 43.2/4.5

x = 9.6

Therefore, the value for x is obtained as 9.6 feet.

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There are 153 parking spaces on each level of the parking garage.

Equation

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that a parking garage has 612 parking spaces on 4 levels, and each level has about the same number of parking spaces, to determine the number of parking spaces on each level the following calculation must be performed: -

so the equation is ,

612/4 = X

153 = X

X = 153.

Thus, there are 153 parking spaces on each level of the parking garage.

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The value of x that best represent this expression √x = 11 is 121.

The square root of a number is the part of the number that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents. The portion of a number that yields the original number when multiplied by itself is known as the square root of the number.

Examples of special exponents include squares and square roots. Think about the number 9. Nine is the result of multiplying 3 by itself. This can be expressed as either or 3*3. We refer to this as a square since it has a 2 exponent. When the exponent is now 1/2, the integer's square root is being discussed.

An integer or number (not a fraction) multiplied by itself produces a "Square Number," which is the result. For instance, 3 x 3 = or 3 squared is the result of 3 times 3.

Given:

√x+11 = 0

√x = -11

can be written as

x = -11²

x = 121

The value of x that best represent the expression √x+11 = 0 is 121.

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Correct question:

For which values of x does the expression √x + 11 = 0 make sense? ​

The percentage of students that prefer drama is 52%.

The percentage of students that go to the movies three times or more is 34%.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to percentage, multiply the number by 100.

The percentage of students that prefer drama = (total number of students that prefer drama / total number of students surveyed) x 100

= [(70 + 34) / 200] x 100

= (104 / 200) x 100 = 52%

The percentage of students that go to the movies three times or more = (total number of students that go to the movies three times or more / total number of students surveyed) x 100

[(34 + 34) / 200] x 100

(68 / 200) x 100 = 34%

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Answer:

Step-by-step explanation:

The expression that represents the ratio between the total number of seagulls standing on the pier and the 51 gulls in the air is given as follows:

g/51.

The ratio between two amounts a and b is found applying a proportion, which is the division between them.

The amounts for this problem are given as follows:

Hence the ratio is given as follows:

g/51.

The problem asks for the expression for the ratio the total number of seagulls standing on the pier and the 51 gulls in the air.

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Answer:

8.75

Step-by-step explanation:

The number of bicycles there is given as follows:

63.

The number of bicycles and tricycles is obtained using a system of equations, for which the variables are given as follows:

The number of bicycles is 1 less than 4 times the number of tricycles, hence:

x = 4y - 1.

There is a total of 174 wheels, hence:

2x + 3y = 174.

The number of tricycles is obtained as follows:

2(4y - 1) + 3y = 174

11y = 176

y = 176/11

y = 16.

Hence the number of bicycles is of:

x = 4(16) - 1

x = 63.

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The mathematical statement that accurately depicts how value of philipine peso is less than the value of one US dollar is: p < d. The Option C is correct.

The Less-than symbol is used to compare two values where the first number is less than the second number, for example, in ascending order. The opening angle bracket is approximated by the less than symbol.

"<" is the symbol used to represent the less than inequality. The less than sign is a universally recognized math symbol composed of two equal measure strokes intersecting in an acute angle at the left.

For example: If given 2< 5: 2 is less than 5

Missing options "Which of the following mathematical statement represents the given situation? a. d = p b. p>d c. p <d d. none of these​

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The equation of the straight line perpendicular to the line 3x - 6y = - 8 is y-2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y=0.

The general equation of a straight line is -

y=mx+c

where -

m is slope of line which tells the unit rate of change of y with respect to x.

c is the y - intercept i.e., the point where the graph cuts the y axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

[tex]y=\frac{-A}{B} x-\frac{C}{B}[/tex]

Given that: -

[tex]3x-6y=8\\\\6y=3x-8\\\\y=\frac{1}{2}x-\frac{4}{3}[/tex]

then,

[tex]m=\frac{1}{2}\\\\c=\frac{4}{3}[/tex]

For a parallel line,

[tex]m=\frac{1}{2}\\and,(4,2)[/tex]

[tex]y-y_{1}=m(x-x_{1})\\\\y-2=\frac{1}{2}(x-4)\\\\2y-4=x-4\\\\y=\frac{x}{2}[/tex]

The equation of parallel line is y=0.5x

For a perpendicular line

[tex]m=2\\\\y-2=2(x-4)\\\\y-2=2x-8\\y-2x=-6\\y-2x+6=0\\[/tex]

Therefore, the equation of the line perpendicular to the line 3x - 6y = - 8 is y -2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y = 0.5x.

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Compared to Ann and Bob, Colin has more. Thus, Ann is not have most money.

In the given question, we have to find Ann have the most money or not.

Three people Ann, Bob and Colin have a total of $1.80 between them, each having a different amount.

Ann has $0.6 amount and Bob has $0.5 amount.

Ann + Bob + Colin = 1.80

0.6 + 0.5 + Colin = 1.80

1.1 + Colin = 1.80

Subtract 1.1 on both side, we get

Colin = 0.70

So Colin has $0.70.

So, Colin has more amount than Ann and Bob. So Ann does not have most money.

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The inequality model of the question will be -13 > x > -3

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

9|x + 8| > 45

now when we remove the modulus there will be two terms.

|x + 8| > 45/9

|x + 8| > 5

-5>x + 8>5

-5-8>x >5-8

-13 > x > -3

Hence, the inequality model will be -13 > x > -3

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Answer:

s³ - 15s² + 50s - 125

Step-by-step explanation:

yes

The two-way frequency table to display the data will be:

                         Fishing         Not Fishing Total

Swimming        15                     30           45

Not Swimming 5                 45           50

Total                  20                 75         95

20% of 120 people is 24 people, but since 20% of the people went fishing, we know that 24 people went fishing.

75% of 24 people who went fishing is 18 people.

50% of 96 people who did not go fishing is 48 people.

Total number of people who went swimming is 45 (15+30)

Total number of people who did not go swimming is 50 (5+45)

Total number of people in the survey is 95 (24+71)

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In a survey of 120 people who visited the a lake, 20% went fishing.of those who went fishing,75% also went swimming. Of those who did not go fishing ,50% went swimming. Construct a two-way frequency table to display the data.

The probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected is 65.53%.

This can be calculated using the normal distribution. The mean of the normal distribution is the population means, which in this case is 21,604 dollars per annum. The standard deviation is 727 dollars per annum. Using this information, we can calculate the z-score of 21635 dollars per annum by subtracting the population mean from it and dividing it by the standard deviation. This gives us a z-score of 0.42.

21635-21329/727=0.42

Using a z-table, we can calculate the probability of the sample means being less than 21635 dollars to be 0.6553.

This can also be written as 65.53%. This means that there is a 65.53% probability that the sample mean of 193 persons randomly selected would be less than 21635 dollars per annum.

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The number of possible sandwiches does is 6.

What is combination ?

In arithmetic, a combination is a way of choosing gadgets from a set where the order of selection does no longer count. suppose we've got a hard and fast of 3 numbers P, Q and R. Then in what number of methods we can select two numbers from every set, is described via combination.

Given ,

Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef.

The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese.

factorial of n! = n*(n-1) !

The number of possible sandwiches does  =  3!

=3*2 = 6.

Therefore, The number of possible sandwiches does is 6.

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a) The old monthly payment was =  9.27 × 50 = 463.5

b) The new monthly payment is = 11.10 × 50 = 555

c) The percent increase in his monthly payment is 1.947 %

With a 25-year, 10.25% adjustable rate mortgage, Sandra Williams purchased a property. She made monthly payments of $9.27 per thousand on his initial debt.

According to the question,

The per thousand value of $65000 is, 50000/1000 = 50

Now, the old monthly payment was =  9.27 × 50 = 463.5

She makes the decision to renew and will now make monthly loan payments of $11.10 per thousand.

So, the new monthly payment is = 11.10 × 50 = 555

The percent increase in his monthly payment is = 11.10 /9.27 - 1 × 100

⇒ 19.7411 %

And to nearest tenth it is 1.947%

Hence, the old monthly payment was =  9.27 × 50 = 463.5

The new monthly payment is = 11.10 × 50 = 555

Thus, the percent increase in his monthly payment is 1.947%.

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The UCL and LCL are 1.00434 and 0.99566. The process is not in control and the z-value is 2.17.

We already know that the mean, x = 1.0, and the standard deviation of the process, σ = 0.01.

We already know that according to the central limit theorem, the standard deviation of sample means is equal to the standard deviation of the population divided by the square root of the sample size.

So, it is equal to = 0.01 / √25 ⇒ 0.002

For a sample size of 25. The z value, or the z-score, is about 2.17 for a confidence level of 97 percent.

So, UCL = 1.0 + 2.17 * 0.002 = 1.00434

LCL = 1.0 - 2.17 * 0.002 = 0.99566

Lastly, the process is not in control because the sample means 1.005 and 0.995 are outside the control range.

The complete question that you must be looking for is given below.

An automatic filling machine is used to fill 1-liter bottles of cola. The machine output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations.

a. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control.

b. Given these sample means: 1.005, 1.001, .998, 1.002, .995, and .999, is the process in control.

c. What is the z-value we should use if the control limits will include roughly 97% of the sample means?

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The amount of type A used is A=31 lbs.

Assign variables for unknowns.

Let A be the number of pounds of Type A coffee.

Let B be the number of pounds of Type B coffee.

If one pound of Type A costs $4.10 then A pound costs 4.10A

If one pound of Type B costs $5.45 then B pounds cost 5.45B

At this point, you have two equations with A and B as variables.  You can use the substitution or elimination method to solve for A.

Equations:

B = 2A----(1)

4.10A + 5.45B = 465.00

4.10A + 5.45(2A) = 465.0

4.10A + 10.9A = 465.00

15A = 465.00

A = 31 lbs (amt. of type A coffee used)

To know the amount of type B coffee used just plug the A value in equation(1) we get:

B=2(31)

B=62.

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Answer:

x = 8

Step-by-step explanation:

0.75 * ( x+4) = 9

0.75x + 3 = 9

0.75x = 9 - 3

0.75x = 6

x = 6 / 0.75

x = 8

At a distance of 72.5 meters above the water's surface, the anchor was let go.

It takes 29 seconds to reach the water's surface.

The anchor dropped for 45 seconds at a speed of 2.5 m/s.

112.5 metres are equal to (2.5 m/s) x (45 s).

It must have dropped if it ended up only 40 meters under the water.

(112.5 m - 40 m) equals 72.5 m

Before it ever got to the water, it was in storage on the large cruise ship.

It took longer because it was descending at a speed of 2.5 m/s.

29 seconds are equal to 72.5 m / (2.5 m/s)

it began to drop, to get down to the water's surface.

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

see image

The quotient from 4,096 divided by 61  is between 66 and 67.