If gasoline costs $ 3.77 per gallon when you pay with a credit card, but $0.08 per gallon less if you pay with cash, how much do you save by filling up a 8-gallon tank and paying for it with cash?

Answer:

I did this quickly, so please check carefully.

d/a = -(11/12)

Step-by-step explanation:

a/(b+c+d)=4/3

3a = 4(b+c+d)    [Cross multiply]

3a = 4((b+c)+d)   [Note that b and c can be grouped as (b+c)]

---------------------

We can see the second equation also has a (b+c) group.  Isolate it to one side:

a/(b+c)=3/5

5a = 3(b+c)

(b+c) = (5a/3)

------------------

Now use this definition of (b+c) in the first equation:

3a = 4((b+c)+d)

3a = 4((5a/3)+d)   [Use the new value of (b+c), which is (5a/3)]

3a = 4(5a/3+3d/3)

3a = 4((5a + 3d)/3)

3a = (4/3)(5a + 3d)

3a = (20/3)a + 4d

9/3a = (20/3)a + 4d

-(11/3)a = 4d

4d = -(11/3)a

d = -(11/12)a

d/a = -(11/12)

The height of the building is 5.33m.

The question is to calculate the height of the building.

Based on the information given, the height will be:

Madeline eye height/Distance from X = Height of building/Building distance from X

1.55/2.75 = x/9.45

x = (1.55 × 9.45)/2.75

x = 5.33 m

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The correct answer is Option A , D , E.

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

Ratio in it's simplest form means when the ratio can't be simplified anymore  by cancelling out the common factors.

The ratio in Option(A) can't be simplified anymore because 29 is a prime number.

The ratio in Option(B) can be simplified to 1 / 7.

The ratio in Option(C) can be simplified to 5 / 2.

The ratio in Option(D) can't be simplified.

The ratio in Option(E) can't be simplified because 19 is prime number.

Hence, the correct answer is Option A , D , E.

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IfIf it forms interior <6 measuring70. The measure of <4 is: B. 110°.

Using this interior angle theorem

Measure of <4=180° - <6

Where:

<6 measure 70

Hence:

Measure of <4=180°-70°

Measure of <4=110°

Therefore the measure of <4 is: B. 110°.

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Answer:

The graph increases.

Step-by-step explanation:

hope this helps!!

Answer: the graph increases

Step-by-step explanation: did test

Answer:

x = -2

Step-by-step explanation:

Subtract 7 from both sides :

6x = -12

Divide both sides by 6 :

x = -2

Hope this helped and have a good day

Answer:

x = 2

Step-by-step explanation:

1) If there is a number right next to a bracket, then it means that it should be multiplied. --> 4(5 -2x) = 25 - 10x

2) (20 - 8x) + 3 = 23 - 8x

3) 23 - 8x = 7

4) 16 = 8x

5) We divide both sides with 8 to leave x. --> 2 = x

6) x = 2

Answer:

$11.78

Step-by-step explanation:

14.89+9.33=24.22

36-24.22=11.78

The magnitude of the resultant vector is 27 miles

Resultant vector = Distance of A - Distance of B

This is so because of the opposite direction of the car's movement

A = 87 miles

B = 114 miles

Resultant vector = 114 - 87

Resultant vector = 27 miles

Thus, the magnitude of the resultant vector is 27 miles

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Answer:

5610

Step-by-step explanation:

unaffected people will be (100%-2.5\%-50.75%)=46.75% of 12000:

[tex]12000\cdot 46.75\%=12000\cdot \frac{46.75}{100} =120\cdot 46.75=5610[/tex]

Answer:

[tex]A) \sf \ \sf \dfrac{x^8}{16y^4}[/tex]

Explanation:

 [tex]\sf \left(\dfrac{2y}{x^2}\right)^{-4}[/tex]

inverse of the expression

 [tex]\sf \left(\dfrac{x^2}{2y}\right)^{4}[/tex]

distribute power inside parenthesis

 [tex]\sf \left(\dfrac{(x^2)^4}{(2y)^4}\right)[/tex]

apply exponent rules: [tex]\s(a^b )^c = a^{bc}[/tex]

   [tex]\sf \dfrac{x^8}{16y^4}[/tex]

Truth Value for p^ q when x is replaced by 2 is also true. (  p^q is True)

The prime numbers are those numbers that have only one factor namely 1 and the number itself.

Given that p = x is prime and q = x is even. If we replace x by 2 then we would get

p = 2 is prime

q = 2 is even

p^q will be held true only if p and q both are true.

The statement for p and q both are true because 2 only has two factors only 1 and 2 themselves.

2 is also considered an even number (2,4,6,8,...)

Since p = true and q = true then

p and q = p^q = true

Thus, p^q is True.

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Answer:

p^q is true

Step-by-step explanation:

If both p and q are true, the statement p^q is true. If both p and q are false, the statement p^q is still true. All other options yield a false result.

11. The value of x is [tex]13\frac{3}{4}[/tex]

12. From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x

From the question, we are to solve the given equation

The given equation is

[tex]5 + \frac{1}{2}(4x +5) = 35[/tex]

This becomes

[tex]\frac{1}{2}(4x +5) = 35-5[/tex]

[tex]\frac{1}{2}(4x +5) = 30[/tex]

[tex]4x +5 = 2 \times 30[/tex]

[tex]4x +5 = 60\\[/tex]

[tex]4x= 60-5[/tex]

[tex]4x= 55[/tex]

[tex]x = \frac{55}{4}[/tex]

[tex]x = 13\frac{3}{4}[/tex]

Hence, the value of x is [tex]13\frac{3}{4}[/tex]

12.

From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x

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Answer:

1.5x = 7.5   (a)

Step-by-step explanation:

If Billy has $7.50 remaining, then he can buy x no. of boxes.

Each box costs $1.50

So, 1.5x = 7.5

[tex]|\Omega|=12+5+6+4=27\\|A|=12\\\\P(A)=\dfrac{12}{27}=\dfrac{4}{9}=44.4\%[/tex]

Answer:  44.44% approximately

Work Shown:

P(red) = (number of red)/(number total)

P(red) = (12 red)/(12 red + 5 green + 6 yellow + 4 blue)

P(red) = (12 red)/(27 total)

P(red) = 12/27

P(red) = 4/9

P(red) = 0.4444 approximately

P(red) = 44.44% approximately

Answer:

-135689;456+((888888888

According to the information, it can be inferred that the answer is No, because informing the students that there will be a $10 increase... (option B).

This question is not valid because it specifies information that would surely change the answer of the respondent.

The information that the question reveals is that there is going to be a raise, this will cause a refusal in people to accept that raise just to see a live band.

According to the above, the question is invalid because it reveals information that will modify the answer of those who respond.

Note: This question is incomplete because the options are missing. Here are the options:

A. No, because questions about musical preferences are always invalid because you cannot measure people's opinions on subjective manners like music and other creative arts.

B. No, because informing the students that there will be a $10 increase in the cost of a prom ticket may make them more likely to say that they would not like a live band to perform.

C. No, because students should be given a sample of the band's music to allow them to offer a more informed opinion.

D. No, because a random sample of all seniors in the country should have been taken to determine if a live band should perform at this high school's senior prom.

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The probability that either the score on the green die is 1 or the score on the red die is 6, but not both, is 11/36.

To find the probability that either the score on the green die is 1 or the score on the red die is 6 (but not both), we can break it down into two mutually exclusive events and then calculate their probabilities separately.

Event A: The score on the green die is 1.

Event B: The score on the red die is 6.

We need to find the probability of either event A or event B occurring but not both.

The probability of event A occurring is the probability of rolling a 1 on the green die.

Since each die is six-sided, the probability of rolling a 1 on the green die is 1/6.

The probability of event B occurring is the probability of rolling a 6 on the red die. Similarly, the probability of rolling a 6 on the red die is 1/6.

To calculate the probability of either event A or event B occurring but not both, we need to subtract the probability of both events occurring simultaneously from the sum of their individual probabilities.

The probability of both event A and event B occurring simultaneously is the product of their individual probabilities, which is (1/6) x (1/6) = 1/36.

So, the probability of either event A or event B occurring but not both is:

Probability = (Probability of event A) + (Probability of event B) - (Probability of both events occurring)

= (1/6) + (1/6) - (1/36)

= 6/36 + 6/36 - 1/36

= 11/36

Therefore, the probability is 11/36.

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By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.

In this question we have an application of direct proportionality model, whose form is shown below:

y = k · x     (1)

Where:

If we know that x = 45 bu and k = 1/36.744, then the soybean quantity in tonnes is:

y = (1/36.744 t/bu) · (45 bu)

y = 1.225 t

By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.

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Answer:

m = 1 and n = 10.

Step-by-step explanation:

I  am assuming you mean -8, m , n, 19.

If they are in AP the 4 terms will have a common difference.

19 - (-8) = 19 + 8 = 27.

So the increase over 3 terms (from -8 to 19) is 27 so we have:

27 / 3 = 9

Therefore the common difference is 9 and the A P is

-8, 1, 10, 19.

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of linear equations:

(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0    

- c + d = 1      (1)

3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0    

3 · c + d = 117       (2)

The solution of this system is c = 29 and d = 30.

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

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It is true that exponent laws apply all the time when simplifying variables

The laws of exponent state that:

[tex](ab)^m = a^m * b^m[/tex]

[tex](a+ b)^m \ne a^m + b^m[/tex]

[tex](a- b)^m \ne a^m - b^m[/tex]

[tex](a/b)^m \ne a^m / b^m[/tex]

The above laws must be followed in all variables.

When any of the law is misinterpreted, misrepresented or misused in simplifying variables, the result would be incorrect

Hence, it is true that exponent laws apply all the time when simplifying variables

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By definition of logarithm the value of [tex]$3log _2(9n)[/tex] exists

[tex]$ 6(log _2(3) +3 log _2(n))[/tex].

A logarithm exists as an amount that conveys power to a specified number contains to be raised to create the assigned number.

From the definition of a logarithm, we get

aˣ = b exists the same as x = logₐb

Given: [tex]$3log _2(9n)[/tex]

Simplifying [tex]$log _2(9n) = 2log _2(3) + log _2(n)[/tex]

[tex]$= 3(2log _2(3) + log _2(n))[/tex]

Expanding the equation, we get

[tex]$3(2log _2(3) + log _2(n))[/tex]

[tex]$= 6(log _2(3) +3 log _2(n))[/tex]

[tex]$= 6(log _2(3) +3 log _2(n))[/tex]

Therefore, the value of [tex]$3log _2(9n)[/tex] exists [tex]$ 6(log _2(3) +3 log _2(n))[/tex].

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When one is looking at a map of the united states, and it is assumed that you already know which direction is north, this illustrates a theorem.

It should be noted that a theorem simply means a statement that has been proved.

In this case, when one is looking at a map of the United States, and it is assumed that you already know which direction is north, this illustrates a theorem. This is because it's proven.

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Answer: That raw vegetables are better for the rabbit's growth than rabbit food.

Answer:

The rabbit food that was strictly a diet of raw vegetables is healthier for the rabbits.

Step-by-step explanation:

The pooled estimate of the variance is 187.650 and the test statistic is -2.32

The dataset is given as:

Regular price 138 124 89 112 116 123 98

Reduced price 124 134 154 135 118 126 133 132

Let the regular price be dataset 1 and the reduced price be dataset 2.

So, we have:

#1: 138 124 89 112 116 123 98

#2: 124 134 154 135 118 126 133 132

Calculate the sample means and the sample standard deviations using a graphing calculator.

#1

[tex]\sigma_1 = 16.56[/tex]

[tex]\bar x_1 = 114.29[/tex]

[tex]\sigma_1^2 = 274.24[/tex]

#2

[tex]\sigma_2 = 10.65[/tex]

[tex]\bar x_2 = 132[/tex]

[tex]\sigma_2^2 = 113.43[/tex]

The pooled estimate of the variance is:

[tex]\sigma_p^2 = \frac{\sigma_1^2(n_1 - 1) + \sigma_2^2(n_2 - 1)}{(n_1 - 1) + (n_2 - 1)}[/tex]

This gives

[tex]\sigma_p^2 = \frac{274.24 * (7 - 1) + 113.43 * (8 - 1)}{(7- 1) + (8- 1)}[/tex]

Evaluate the factors

[tex]\sigma_p^2 = \frac{2439.45}{13}[/tex]

Divide

[tex]\sigma_p^2 = 187.65[/tex]

Hence, the pooled estimate of the variance is 187.650

This is calculated using:

[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\sigma_p^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]

This gives

[tex]t = \frac{114.29 - 132}{\sqrt{187.650} * \sqrt{\frac{1}{7} + \frac{1}{6}}}[/tex]

This gives

[tex]t = \frac{-17.71}{\sqrt{187.650} * \sqrt{\frac{13}{42}}}[/tex]

Evaluate the product

[tex]t = \frac{-17.71}{\sqrt{58.08214}}[/tex]

Evaluate the exponent

[tex]t = \frac{-17.71}{7.62}[/tex]

Divide

t = -2.32

Hence, the test statistic is -2.32

The critical value at 0.025 significance level is -1.96

-2.32 is less than -1.96

This means that we accept the null hypothesis

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Answer:

[tex]\sf C. - \dfrac{3}{4}[/tex]

Explanation:

[tex]\sf Given \ equation : 4x - 3y = 12[/tex]

Rewrite in slope intercept form "y = mx + b"

[tex]\rightarrow \sf 4x - 3y = 12[/tex]

[tex]\rightarrow \sf - 3y = 12 - 4x[/tex]

[tex]\rightarrow \sf y =\dfrac{ 12 - 4x}{-3}[/tex]

[tex]\rightarrow \sf y =\dfrac{ 4}{3}x - 4[/tex]

Here the slope is 4/3 and y-intercept is -4

Perpendicular lines has negatively inverse slope.

→ per. slope = -(slope)⁻¹ = -(4/3)⁻¹ = -3/4

Answer:

[tex]-\dfrac{3}{4}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

 [tex]y=mx+b[/tex]

where:

Given linear equation:

  [tex]4x-3y=12[/tex]

Find the slope of the given linear equation by rewriting the equation so that it is in slope-intercept form (i.e. make y the subject):

[tex]\implies 4x-3y=12[/tex]

[tex]\implies 4x-3y+3y=12+3y[/tex]

[tex]\implies 4x=12+3y[/tex]

[tex]\implies 4x-12=12+3y-12[/tex]

[tex]\implies 4x-12=3y[/tex]

[tex]\implies \dfrac{3y}{3}=\dfrac{4}{3}x-\dfrac{12}{3}[/tex]

[tex]\implies y=\dfrac{4}{3}x-4[/tex]

Therefore, the slope of the given line is 4/3.

If two lines are perpendicular to each other, the product of their slopes will be -1.   Therefore, the slope (m) of the line perpendicular to the given line is:

[tex]\implies m \times \dfrac{4}{3}=-1[/tex]

[tex]\implies m=-\dfrac{3}{4}[/tex]