Ms. Mather filled 8 3/4 gallons of gas in her car's fuel tank. The car used up 3 1/2 gallons when she visited a friend in a neighboring town. How many gallons of gas are left in Ms. Mather's fuel tank?

Answers

Answer 1

Answer: [tex]5\frac{1}{4}[/tex] gallons are left

Step-by-step explanation:

convert to mixed number...

[tex]8\frac{3}{4} = \frac{35}{4}[/tex]

[tex]3 \frac{1}{2} = \frac{7}{2}[/tex] or [tex]\frac{14}{4}[/tex]

[tex]\frac{35}{4} -\frac{14}{4}=\frac{21}{4}[/tex]

[tex]\frac{21}{4} =5\frac{1}{4}[/tex]

therefore, [tex]5\frac{1}{4}[/tex] gallons are left in Ms. Mather's fuel tank

Answer 2

Answer:

5 1/4 gallons are left... correct


Related Questions

Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.

Answers

Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.

The domain of the function is t ≥ 0

The greatest concentration of the medication is 5mg/L

Given that:

C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]

(a): The domain of the function

Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.

t, cannot take negative values (i.e. it is not possible to have a negative time).

The least possible value of t is 0

So, the domain of the function based on the context is: t ≥ 0

(b) The greatest concentration of the medication

From the graph (see attachment), the maximum y-value is 5.

Hence, the greatest concentration of the medication is 5 mg/L

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segment CD has endpoints at C(0, 3) and D(0, 7). If the segment is dilated by a factor of 3 about point C, what is the length of the image of segment CD question mark (1 point)

Answers

The length of CD is 7-3=4.

Therefore, if we dilate by a scale factor of 3, the length is 4(3) = 12

Answer:

b) 12

Step-by-step explanation:

the length of the image is 12. i just know. trust me.

a straight line passes through points A(-2,6) and B(4,2). M is the midpoint of line AB.Find the coordinates of M​

Answers

Answer:

(1,4)

Step-by-step explanation:

A trapezoid is a quadrilateral with one or more pairs of parallel sides.
O A. True
OB. False

Answers

The answer is B. False
The answer is B credits to the other guy

what figure was rotated

Answers

Answer: Rectangles

Step-by-step explanation:

Whenever rectangles are rotated about an axis, a cylinder is formed.

Which standard form of the equation of the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y equals plus or minus five twelfths times x question mark

y squared over 25 minus x squared over 144 equals 1
y squared over 144 minus x squared over 25 equals 1
x squared over 25 minus y squared over 144 equals 1
x squared over 144 minus y squared over 25 equals 1

Answers

The equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.

What is hyperbola?

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have:

Vertices of the hyperbola = (0, 5) and (0, -5)

Asymptotes: y = ±(5/12)x

The equations we have:

[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]

[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]

[tex]\rm \dfrac{x^{2}}{25}-\dfrac{y^{2}}{144}=1[/tex]

[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]

From the equation first:

[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]

The value of a and b are:

a = 12

b = 5

Vertices of the hyperbola = (0, b) and (0, -b)

Vertices of the hyperbola = (0, 5) and (0, -5)

Asymptotes: y = ±(b/a)x

Asymptotes: y = ±(5/12)x

Thus, the equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.

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Answer:

A

Step-by-step explanation:

What is the sum?
2/x^2+4/x^2

Answers

Answer:

6/x2

Step-by-step explanation:

Answer:

[tex]\mathsf {\frac{6}{x^{2}}}[/tex]

Step-by-step explanation:

[tex]\mathsf {\frac{2}{x^{2}} + \frac{4}{x^{2}} }[/tex]

[tex]\mathsf {\frac{2+4}{x^{2}}}[/tex]

[tex]\mathsf {\frac{6}{x^{2}}}[/tex]

n studying the sampling distribution of the mean, you were asked to list all the different possible samples from a small population and then find the mean of each of them. Consider the following: Personal phone calls received in the last three days by a new employee were 2, 4, and 7. Assume that samples of size 2 are randomly selected with replacement from this population of three values. What different samples could be chosen? What would be their sample means?

Answers

The Total outcome with replacement will be given by ,3² = 9, the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

What is Mean ?

Mean predicts the central tendency of a data set , It is determined by the ratio of sum of all the numbers to the total numbers in the data set.

On the basis of given data

The number given is 2,4,7

Size of the sample = 2 with replacement

The Total outcome with replacement will be given by

3² = 9

Possible outcome can be

2,2   2,4   2,7   4,4  4,2  4,7  7,7  7,2  7,4

The sample mean can be calculated as

(a+b)/2

(2+2)/2 = 2

similarly the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

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ary
S
Homework: Homework Chapter
7 Section C
h
In a large casino, the house wins on its blackjack tables with a probability of 50.4%. All bets at blackjack are 1 to 1, which means that if you win, you gain the amount
you bet, and if you lose, you lose the amount you bet
a. If you bet $1 on each hand, what is the expected value to you of a single game? What is the house edge?
a. The expected value to you of a single game is $ -0.008
(Type an integer or a decimal)
The house edge is $ 0.008
(Type an integer or a decimal)
b. If you played 150 games of blackjack in an evening, betting $1 on each hand, how much should you expect to win or lose?
c. If you played 150 games of blackjack in an evening, betting $5 on each hand, how much should you expect to win or lose?
d. If patrons bet $4,000,000 on blackjack in one evening, how much should the casino expect to earn?
b. You should expect to lose $1.2
(Type an integer or a decimal)
c. You should expect to lose $6.00
(Type an integer or a decimal.)
d. The casino should expect to earn $ 32,000
ere to search
Help me solve this View an example Get more help -
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Answers

Answer:

the answer is D

Step-by-step explanation:

least common denominator of 1
[tex] \frac{1}{6} \: and \: \frac{7}{9} [/tex]

Answers

The least common denominator of 1/6 and 7/9 is 18. Why? Well, we can start by listing the multiples of both denominators (the numbers on the bottom of the fractions) which are 6 and 9.


Multiples of 6:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Multiples of 9:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

By identifying the multiples of these numbers, we can see that the lowest multiple these integers have in common is 18. Because of this, the least common denominator of 1/6 and 7/9 is 18.

Your final answer: 18.

What are m and b in the linear equation y=16+6x

Answers

Answer: B=16 and m=6

Step-by-step explanation:

in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.

find the area for this pls

Answers

Answer:

3,36 in^2

Step-by-step explanation:

The geometric shape shown in image is called a trapezoid

to calculate the area of a trapezoid we use the following formula:

1/2*(a+b)*h (a and b are bases, h: height)

bases are 1.3 and 3.5 and height is 1.4

1/2(1.3 + 3.5)*(1.4) = 3,36 the area is stated in square units so the answer is

3,36 in^2

Please help me with this hard problem

Answers

Part 1: Finding [tex](g\circ h)(x)[/tex]

Note that [tex](g\circ h)(x)=g(h(x))[/tex]

In this case, it is [tex]g(\sqrt{x+4})=(\sqrt{x+4})^{2}-3=x+4-3=\boxed{x+1}[/tex]

Part 2: Domain

For the domain, we need to make sure the radicand of h(x) is greater than or equal to 0, so we get [tex]x+4 \geq 0 \longrightarrow \boxed{x \geq -4}[/tex]

The composition (g ο h) = x+ 1 and the domain of the composition (g ο h) is = (-∞ , ∞).

The composition (g ο h) means that the function g(x) composes of h(x) that is g(h(x)). So we have to put the the values of h(x) in the function g(x).

Now here it is given that

g(x) = [tex]x^{2} -3[/tex] and h(x) = [tex]\sqrt[2]{x + 4}[/tex]

so to get (g ο h) we have to replace the x with the value of h(x)

That gives :

g(h(x)) = [tex]\sqrt[2]{x+4} ^{2} - 3[/tex]

g(h(x)) = x + 4 - 3 = x +1

So the composition (g ο h) = x+ 1

The domain of the function is the values of x for which the function is defined.

so the domain of the composition (g ο h) is :

g(h(x)) = x+ 1

This function is undefined for no value of x .

So its domain is (-∞ , ∞).

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Find the value of d.

Answers

Answer:

Step-by-step explanation:

Comment

The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.

Givens

Arc 1 = 94

Arc2 = d

interior angle = 75

Formula

(d + 94)/2 = interior angle/1

Solution

(d + 94)/2 = interior angle/1               Cross Multiply

1*(d + 94) = 75 *2                           Combine

d + 94 = 150                                        Subtract 94 from both sides

d + 94 - 94 = 150 - 94                         Combine

d = 56

Answer: d = 56

Find dy/dx if y =x^3+5x+2/x²-1

How would I go about finding this? I would appreciate if you could be as detailed as possible!

Answers

Differentiate using the Quotient Rule

[tex]\qquad[/tex][tex]\pink{\twoheadrightarrow \sf \dfrac{d}{dx} \bigg[\dfrac{f(x)}{g(x)} \bigg]= \dfrac{ g(x)\:\dfrac{d}{dx}\bigg[f(x)\bigg] -f(x)\dfrac{d}{dx}\:\bigg[g(x)\bigg]}{g(x)^2}}\\[/tex]

According to the given question, we have –

f(x) = x^3+5x+2 g(x) = x^2-1

Let's solve it!

[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{d}{dx}\bigg[ \dfrac{x^3+5x+2 }{x^2-1}\bigg]} \\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1) \dfrac{d}{dx}(x^3+5x+2) - ( x^3+5x+2) \dfrac{d}{dx}(x^2-1)}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1)(3x^2+5) - ( x^3+5x+2) 2x}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex] \pink{\sf \because \dfrac{d}{dx} x^n = nx^{n-1} }\\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-(2x^4+10x^2+4x)}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-2x^4-10x^2-4x}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}\\[/tex]

[tex]\qquad[/tex][tex]\pink{\therefore \bf{\green{\underline{\underline{\dfrac{d}{dx} \dfrac{x^3+5x+2 }{x^2-1}} = \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}}}}\\\\[/tex]

If x=3 y=4 z=6 then 4x+8yz+3y equals

Answers

Answer:

216

Step-by-step explanation:

4x+8yz+3y

Let x=3 y=4 z=6

Substitute the values into the expression

4(3)+8(4)(6)+3(4)

Multiply first

12+192+12

Then add

216

which law would you use to simplify the expression...​

Answers

Answer:

Power of a quotient

PLS HELP!!
The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days.
How do the functions in the table compare?
Since x-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since y-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since the maximum value in the table for bacteria A
is greater than the maximum value in the table for
bacteria B, bacteria A has a faster growth rate than
bacteria B.
O Since the minimum value in the table for bacteria A
is less than the minimum value in the table for
bacteria B, bacteria A has a slower growth rate than
bacteria B

Answers

The correct answer are as follows:

A. False

B. True

C. False

D. False

What is Function?

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

False, it is the y-intercept of the function that indicates the amount at the start of the experiment.

B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

True, the y-intercept is given when x = 0, indicating the initial value of the function.

C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.

False, because the maximum value of each table is given in different times, and also the initial value of each table is different.

D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.

False, the growth rate is not given by the initial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.

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A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 1-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 3600 ft2 (including the margins).

If x denotes the left-right width (in feet) of the billboard, determine the value of x that maximizes the area of the printed region of the billboard.

Answers

An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,

The total area of the billboard, A= x·y

The total printed area of the billboard, [tex]A_p=(x-2)(y-8)[/tex]

Given in problem that the area of the billboard is 3600 ft².

x·y = 3600

y = (3600)/x

Substituting the value of y in the equation of the total printed area of the billboard,

[tex]A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}[/tex]

Now, the value of x is needed to be minimum, therefore, differentiating the given function,

[tex]\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}[/tex]

Equate the differentiated function with 0,

[tex]0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.[/tex]

Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

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solve for a
(log(a-1))^2 =log10

Answers

A function assigns the values. The value a is 11.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The given logarithmic function can be solved as shown below.

[tex](\log(a-1))^2 =\log10\\\\(\log(a-1))^2 =1\\\\(\log(a-1)) =\sqrt1\\\\\log(a-1) = 1\\\\10^1 = a-1\\\\a = 11[/tex]

Hence, the value a is 11.

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can someone help me asap :)

Answers

Answer:

Option 2 - TU is perpendicular to MN and MN is parallel to PQ

angle M = angle P ( 90°)

so MN is parallel to pq

MN makes 90° with UT so it is perpendicular

50% of 42 students are girls. How many of the students are girl's​

Answers

Answer:

21 girls.

Step-by-step explanation:

50% of 42 students are girls.

So 42/2 = 21.

Therefore 21 of the students are girls.

Hope I helped

The following confidence interval is'obtained for a population proportion p: 0.87 < p < 0.93 What is the margin error E. The following confidence interval is'obtained for a population proportion p : 0.87 < p < 0.93 What is the margin error E.​

Answers

The margin error of the confidence interval 0.87<p<0.93 is 0.03.

Given confidence interval 0.87<p<0.93.

We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random  sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.

Confidence interval is 0.87<p<0.93.

Width of the interval= 0.93-0.87

=0.06

=0.03

Hence the margin of error is equal to 0.03.

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only 1st main ,please do solve this asap ​

Answers

Answer:

(i) 8b-32

(ii) 7z^3+12z^2-20z

(iii) –q+p

(iv) a+ab

(v) 8x^2y+8xy^2-4x^2-7y^2

(vi) 4y^2-3y

Step-by-step explanation:

Need number 8 please!!

Answers

Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are given as follows:

f(x) = x².g(x) = f(x) - 2 = x² - 2.

Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.

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Another quick geometry question! Thanks!

Answers

cross multiply.
14/12=x/18
14 x 18 = 252
252/12= 21
so x=21

The following table shows the probability distribution for a discrete random
variable.
13
16
17
21
23
25
26
31
P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08
What is the mean of this discrete random variable? (That is, what is E(X), the
expected value of X?)
A. 21.5
B. 22
) C. 21
D. 20.42

Answers

A the other ones really don’t make sense

Find the degree of a polynomial.

Answers

Answer:

What is Poly in gender. Gender is Gender "Female" "Non-binary" "Male". Poly is Triangle gender which means random gender.

Answer: Explanation: To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

Step-by-step explanation:

Which of the following terms describes the measure indicated by the black
arrow below?
4
A. Median
B. Range
C. Mean
D. Minimum

Answers

Answer:

the answer is A

Step-by-step explanation:

The line is the middle point of the graph/ the middle number of all therefore it's the median.

Use the point-slope formula to write an equation of the line that passes through (4,10) and has a slope of m= 3. Write the
answer in slope-intercept form (if possible).
The equation of the line is

Answers

Answer:
3x --y -2= 0
Step-by-step explanation:
We have formula Y - y 1 = m ( X --x1) => Y - 10 = 3(X-4)
3X - Y - 2 = 0 Ans .


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solve the following inequality ( algebra 1 ) Triangle P R Q is shown. Angle R P Q is 39 degrees. The length of P R is 6, the length of R Q is p, and the length of P Q is 8.Law of cosines: a2 = b2 + c2 2bccos(A)Which equation correctly uses the law of cosines to solve for the missing side length of TrianglePQR?62 = p2 + 82 2(p)(8)cos(39)p2 = 62 + 82 2(6)(8)cos(39)82 = 62 + p2 2(6)(p)cos(39)p2 = 62 + 62 2(6)(6)cos(39) Vikram drinks 6/10 of a litter of water after gym class and 33/100 of a litter of juice with his lunch Vikram says he drank a total of 39 hundredths of a litter. use the drop-down menus to explain why Vikram is not correct? The TCP\IP protocol was invented by who _______ are subpopulations within a society that are systematically excluded from full participation in society and denied equal opportunities to power, prestige, and wealth. How did the mountainous geography of Athens influence the economy? Find the energy u of the capacitor in terms of c and q by using the definition of capacitance and the formula for the energy in a capacitor How do we investigate translocation using the ringing experiment? why care should be taken to use wild mushroom If 343* = 494-x, what is the value of x?5/88/528 In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle RST is congruent to triangle RSQ given that RS ST, RS SQ, and STR SQR. Which hybrid orbitals overlap to form the sigma bonds between the indicated atoms in xanthine?Correct Answer is B How does the authors diction contribute to the tone of the excerpt?Informal diction creates a passionate tone.Colloquial diction creates a regretful tone.Poetic diction creates a perturbed tone.Scholarly diction creates a serious tone. Which of these groups was one that hadmany of its members moving westward fora better and more prosperous life?A. christiansB. immigrantsC. Native Americans Sphingosine is not a component of: What determines the number of blocks or points that an image is saved as? Pixels Raster images Resolution Vector graphics Please answer step by step. MALCOLM. What will you do? Let's not consort with them.To show an unfelt sorrow is an officeWhich the false man does easy. I'll to England.DONALBAIN. To Ireland, I. Our separated fortuneShall keep us both the safer. Where we are,There's daggers in men's smiles. The near in blood,The nearer bloody.MALCOLM. This murderous shaft that's shotHath not yet lighted, and our safest wayIs to avoid the aim. Therefore, to horse,And let us not be dainty of leave-taking,But shift away. There's warrant in that theftWhich steals itself when there's no mercy left.-William Shakespeare, Macbeth, Act II, scene iiiWhich lines would support the answer to the question of why Malcolm and donalbain feel they need to leave Scotland?A). To show an unfelt sorrow is and office / which the false man does easy B). theres warrant in that theft / which steals itself when theres mo mercy leftC). Therefore, to horse, / And let us not be dainty of leave-takingD). What will you do? Lets not consort with them. Will a stand that can hold up to 40 pounds support a21-kilograms television? Explain. Use 2.2 lb=1kg. How many dogs were in the sample?