Mathematics College

A truck has a full 50-gallon gas tank. It uses 7 1/4 gallons on the first part of its journey, 13 1/2 gallons on the second part of its journey, and 15 1/4 gallons on the third part of its journey. How many gallons of gas remain in the gas tank?

Answers

Answer 1

50 -7 1/4 -13 1/2 -15 1/4 = 14 . . . . gallons remain

Answer 2

14 gallons would remain in the gas tank after the third part of his journey.

Related Questions

You have 10 different video games. how many different ways can you arrange the games side by side on a shelf

Answers

Consider, please, this options:
option 1.
for the 1st place 10 games, for the 2d place - 9 games, for the 3d - 8, etc., for the 10th place - 1 game. Then, using the rule of 'logic &': 10*9*8*7*6*5*4*3*2*1=3628800 ways.
option 2.
using formula of permutations (Pₓ=x!): P₁₀=10!=3628800 ways.

Answer: 3628800.

You can arrange the games side by side on a shelf in "3628800" ways.

According to the question,

Number of video games,

Now,

The amount of possible ways could you place the games side by side on some kind of shelf will be:

= [tex]10![/tex]

= [tex]10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1[/tex]

= [tex]3628800[/tex]

Thus the response above is appropriate.

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What has an infinite number of points extending in opposite directions that has only one dimension

Answers

I believe it is a line

Hello there!

The answer to your question is a line. A line infinitely extends in opposite directions and it has an infinite number of points. It only has one dimension.

Now because the question doesn't say 'extends infinitely' and it JUST SAYS 'has an infinite number of points, a line segment could be a correct answer too because points are infinitely small. Don't write this answer though because I know the answer your teacher is looking for is a 'line.'

I really hope this helps!
Best wishes :)

Angle D is a vertical angle to F. The measure of D is 53° . What is the measure of F?

Answers

The measure of F is 53°

Final answer:

Angle F will have the same measure as angle D, which is 53°, because they are vertical angles and thus congruent.

Explanation:

The question asks about the measure of angle F given that it is a vertical angle to angle D, which measures 53°. In geometry, vertical angles (also known as opposite angles) are pairs of non-adjacent angles formed when two lines intersect. Vertical angles are congruent, which means they have the same measure. Therefore, since angle D is 53°, angle F, being its vertical angle, will also have a measure of 53°.

Angle D and angle F are vertical angles, which means they are congruent. If angle D measures 53°, then angle F will also measure 53°. This is because vertical angles are equal in measure.

the price of a tablet was reduced from $250 to $200. By what percentage was the price of the tablet reduced? Please help me solve this.

Answers

(250-200)/250=20%
it doesn't interfere with 200.

which of the following shows an equivalent expression to (5 times 3)times 12 if only associative property was used to transform the expression

Answers

There are no choices for this question, but the correct answer would be to re-write the exact same phrase only putting a parentheses around 3×12 instead. The associative property says that you can group your multiplication problem in any order it without changing the value. If we are only applying The associative property then the order it is written in would remain the same. Only the grouping would change.

⇒Associative Property states

A × (B ×C)=(A×B)×C=(A×C)×B

Now, we have to find equivalent expression of

[tex](5 \times 3) \times 12 \\\\1.\rightarrow 5 \times (3 \times 12)\\\\2.\rightarrow (5 \times 12) \times 3\\\\3 \rightarrow 180[/tex]

Where a is determined by the conditions x2 + y2 ≤ 1 and x + y ≥ 1?

Answers

See, pls, the attached picture, the area determined by the conditions marked by yellow lines.

The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds and a standard deviation of 100 seconds. what is the probability that an auditor will spend more than 12 minutes on an invoice?

Answers

Answer: 11.5%

Explanation:

Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.

Now, we get the z-score for 720 seconds by the following formula:

[tex]\text{z-score} = \frac{x - \mu}{\sigma} [/tex]

where

[tex]t = \text{time for the auditor to finish his work } = 720 \text{ seconds} \\ \mu = \text{average time for the auditor to finish his work } = 600 \text{ seconds} \\ \sigma = \text{standard deviation } = 100 \text{ seconds}[/tex]

So, the z-score of 720 seconds is given by:

[tex]\text{z-score} = \frac{x - \mu}{\sigma} \\ \\ \text{z-score} = \frac{720 - 600}{100} \\ \\ \boxed{\text{z-score} = 1.2}[/tex]

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

[tex]P(t \ \textgreater \ 720) \\ = P(z \ \textgreater \ 1.2) \\ = 1 - P(z \leq 1.2) \\ = 1 - 0.885 \\ \boxed{P(t \ \textgreater \ 720) = 0.115}[/tex]

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.

The probability that an auditor will spend more than 12 minutes on an invoice is approximately 88.49%.

Calculate the probability an auditor will spend more than 12 minutes on an invoice using the Z-score formula for a normal distribution.

The probability that an auditor will spend more than 12 minutes on an invoice can be calculated using the Z-score formula for a normal distribution.

Calculate the Z-score: Z = (12*60 - 600) / 100 = -1.2.Find the probability corresponding to this Z-score using a standard normal distribution table. P(Z > -1.2) = 0.8849.Therefore, the probability that an auditor will spend more than 12 minutes on an invoice is approximately 88.49%.

Create a pattern with the rule n x 2 + 1

Answers

To create this pattern, you can start with the number zero and apply this math. 0 x 2 +1 = 1. The next number would be found by taking 1 x 2 + 1=3. After that 3 x 2 + 1 = 7. The next number in the pattern would be found by taking 7 x 2 +1. Essentially, you are just taking the answer you just got and doubling it and then adding 1. Here is the pattern that would be created beginning with 0. 0, 1, 3, 7, 15, 31, 63, etc...

The pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11

Given:

n × 2 + 1

= 2n + 1

where

n = number of terms

when n = 0

2(0) + 1

0 + 1

= 1

when n = 1

2(1) + 1

= 2 + 1

= 3

when n = 2

2(2) + 1

4 + 1

= 5

when n = 3

2(3) + 1

6 + 1

= 7

when n = 4

2(4) + 1

8 + 1

= 9

Therefore, the pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11

Learn more about number pattern:

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Your friend earns $10.50 per hour. This is 125% of her hourly wage last year. How much did your friend earn per hour last year?

Answers

I believe it is 8.40

Ms Cohen gave a riddle: A string is 2 meters longer than a rod. Half of the rod is 1 meter shorter than half of the string. Is this true or false?

Answers

We are going to define the following variables.
y: length of the string.
x: length of the rod.
We have the following equation:
y = x + 2
Half of the rod is 1 meter shorter than half of the string
x/2 = y/2-1
Let's rewrite equation 1 to see if it's true:
y = x + 2
(1/2) * y = (1/2) * (x + 2)
(1/2) * y = (1/2) * x + 1
(1/2) * x = (1/2) * y-1
Answer
this is true
(1/2) * x = (1/2) * y-1

Rhoads earned $324.65 delivering newspapers. She promised her sister 0.2 of her earnings for helping her.How much does Rhoads owe her sister?

Do I have to subtract?? if not help me solve plz

Answers

In math problems, "of" usually means "multiplied by."

(owed to sister) = 0.2*(earnings)
.. = 0.2*$324.65
.. = $64.93

Rhoads owes her sister $64.93.

Suppose you have two credit cards. The first has a balance of $410 and a credit limit of $1,000. The second has a balance of $510 and a credit limit of $1,000. What is your overall credit utilization? 36% 56% 46% 16% 26%

Answers

The question asked for overall credit utilization, so instead of considering individual credit cards for computation, I will use the credit limits of two cards as if it is just one credit card. That will give me a total limit of $2000.

In the same way, I will add the balances of each card for a total of $920 and get the percentage of remaining balance:

(sum of balances of two cards) ÷ (sum of credit limits of two cards)

($410 + $510) ÷ ($1000 + $1000) = 0.46 or 46%

Note:

But I have an argument because isn't it that credit utilization is the "percentage used" of the credit limit and for that, I have to subtract 46% from 100% which is 54% and that is not an included in the option

Your have a balance of $410 on one card and $510 on the other. Together (add) this is a balance of $920. Your total credit limit is $2000 (add the limits of each card).

That means you use [tex] \frac{920}{2000} [/tex]. Percent means "out of 100" so we wish to write this fraction with 100 in the denominator (the bottom). We do this by dividing the top (numerator) and bottom (denominator) by the same number. Here we use 20. That gives us [tex]\frac{920}{2000}= \frac{46}{100} =46%[/tex]

a total of 324 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adults tickets sold how many adult tickets were sold?

Answers

The correct answer is 81

Final answer:

To find the number of adult tickets sold when a total of 324 tickets were sold for a school play and student tickets were three times the number of adult tickets, we set up the equation x + 3x = 324, solved for x, and found out that 81 adult tickets were sold.

Explanation:

The question is asking us to find out how many adult tickets were sold when a total of 324 tickets were sold for a school play, with the number of student tickets being three times the number of adult tickets sold. To solve this, we let x represent the number of adult tickets. Therefore, 3x will represent the number of student tickets since there are three times as many student tickets as adult tickets.

The equation representing the total number of tickets sold would be: x (adult tickets) + 3x (student tickets) = 324. Simplifying, we have 4x = 324. Dividing both sides by 4 gives us x = 81.

Therefore, the number of adult tickets sold is 81.

Efetue as divisões X ao cubo+10x+29x+20:x ao quadrado+5x+4

Answers

                                x + 5
                           ---------------------------------
   x^2 + 5x + 4    | x^3 + 10x^2 + 29x + 20
                         - x^3 + 5x^2 +   4x
                        ----------------------------
                                        5x^2 + 25x + 20
                                 - 5x^2 + 25x + 20
                                 -------------------------
   0

(x^3 + 10x^2 + 29x + 20) / (x^2 + 5x + 4) = x + 5

(Multiple Choice Worth 4 points) (05.01)A flower bed is in the shape of a triangle, with a base of 13 feet and a height of 5 feet. What is the area of the flower bed?

A 18 square feet
B 32.5 square feet
C 65 square feet
D 130.5 square feet

Answers

Hey there!

So, when finding area, we need to remember that the key point if this is to (multiply).

We would need to make sure that we do not get confused with (perimeter) and area.

We are going to multiple, sense the question stated "What is the area of the flower bed?".

To begin, what are the [tex](formula) [/tex] that we would use?

We will use . . . [tex] \left[\begin{array}{ccc}\boxed{A= \frac{ h_{b}b }{2}} \end{array}\right] [/tex]

By using this, we would plug in the numbers to get your area.

[tex] \left[\begin{array}{ccc}\boxed{\boxed{13*5=65/2=32.5}}\end{array}\right] [/tex]

Your correct answer would be (option B)

[tex]\boxed{32.5} \ square \ feet[/tex]

I hope this helps you!

Answer:

Step-by-step explanation:

I need help !! This packet is due tomorrow and I have no idea what I’m doing .

Answers

The proof would be as follows:

Given: angle M congruent to angle X; angle N congruent to angle Y; YO congruent to NZ.

1. YZ=YO+OZ; reason: segment addition postulate (YZ is made up of YO and OZ).

2. ON=NZ+OZ; reason: segment addition postulate (ON is made up of NZ and OZ).

3. YO=NZ; reason: given.

4. ON=YO+OZ; reason: substitution (since NZ is congruent to YO, we substitute YO for NZ).

5. ON=YZ; reason: substitution (since YZ=YO+OZ, we substitute YZ for YO+OZ).

6. MNO is congruent to XYZ; reason: AAS (we have 2 sides and a non-included angle in each triangle congruent, which is the angle-angle-side theorem).

Answer:

Given is :

∠M≅∠X

∠N≅∠Y

YO≅NZ

We have to prove that ΔMNO≅ΔXYZ

Using segment addition postulate we get YZ=YO+OZ and ON=NZ+OZ and YO=NZ is already given. Using substitution of YO for NZ; we get ON=YO+OZ

Now substituting YZ for YO+OZ we get ON=YZ and also YZ=YO+OZ.

Now applying AAS we get ΔMNO is congruent to ΔXYZ because of angle-angle-side theorem as we have already proved that two sides are congruent and a non-included angle in each triangle is congruent.

What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?

Answers

$1,500/(0.03)^10 = $1,116.14

General Idea:

We need to make use of the below formula to find the present value.

[tex] PV=\frac{FV}{(1+\frac{r}{n})^{nt}} \\ \\ Where:\\ FV \; is \; Future\; Value\; of \; money\\ r \; is\; Annual\; rate\; of\; interest\\ t\; is\; number\; of\; years\\ n\; is\; Number\; of\; periods\; based\; on\; compounding \; frequency [/tex]

Applying the Concept:

We are given the below information:

[tex] FV= \$11,500\\ \\ t=5\; years\\ \\ r=4.5 \%\\ \\ n=2\; (because\; given\; compounded\; semi-annually) [/tex]

We need to substitute the above information in the formula to find the Present value.

[tex] PV=\frac{11500}{(1+\frac{0.045}{2})^{2 \times 5}} =\frac{11500}{(1+0.0225)^{10}} =\frac{11500}{1.0225^{10}} \\ \\ PV \approx \$9206 [/tex]

CONCLUSION:

The present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually is approximately 9206 dollars

A magazine claims that 75% of all teenage boys have their own cellphones. A researcher wished to test the claim and selected a random sample of 60 teenage boys. She found that 54 had their own cell phones. At α = 0.01, should the claim be rejected?

Answers

yes, it is a comparison of .75 to .9 (I think?)

Not sure sorry!! Wish I could help

Find the reference angle for 697 degrees

Answers

The answer is c. 23 degrees. 697-360 is 337. 360-337 is 23.

A student is raising money for a homeless shelter. A local business agrees to donate an additional 20% of what the student raises, while a local politician also agrees to donate an additional 10% of what the student raises. If the student raises $600.00, how much will be donated?

Answers

Answer: the answer is $780.00

Step-by-step explanation:

$600.00 x .20 = $120.00

$600.00 x .10 = $60.00

Total:

$600.00 + $120.00 + $60.00 = $780.00

Answer:

780

Step-by-step explanation:

A website is offering a promotion, during which customers can buy up to 100 photos for a flat fee. The cost per photo varies inversely with the number of photos a customer buys, as shown in the table below. What functions model the data?

Answers

the complete question in the attached figure

we have that
for c=5 and n=20------------> n*c=20*5=100
for c=2.5 and n=40------------> n*c=40*2.5=100
for c=2 and n=50------------> n*c=50*2=100
for c=1.25 and n=80------------> n*c=80*1.25=100

therefore
the function that models the data is n*c=100

the answer is nc=100

Your answer is nc=100

Factor.x ^2 + 17x + 72

Answers

so we need to factor it into (ax+b)(cx+d)
since we have 1x^2, a and c=1

so factor into (x+b)(x+d)
if we expand, we get
[tex](x+b)(x+d)=x^2+(b+d)x+bd[/tex]

so we need 2 numbers that add to get the middle number and multiply to get the last number

I would factor the last number and see which ones add to the middle one

what 2 numbers multily to get 72 and add to get 17?
hmm, list factor of 72 and add them
1+72=73, nope
2+36=38, nope
3+24=27, nope
4+13=17, yep

so it facotrs to (x+4)(x+13)

Find factors of x^2 and 72, that, when combined, will give you 17x

x ^2 + 17x + 72

x 9

x 8

(x + 9)(x + 8) is your factor.

hope this helps

In a multiple regression analysis what would likely be the culprit of a dramatic increase in the P-value of one of the variables?

Answers

This can happen if you add another independent variable to your regression model that is strongly correlated to some other variable already in the model.
This is called multicollinearity.
If there is a high correlation between your independent variables can lead to problems.
It can lead to increased variance of the coefficient estimates and make the estimates very sensitive to minor changes in the model.

If a salesperson sells 3/4 of an acre for $80,000, what was the price per square foot rounded to two decimal spaces?

Answers

if
1 acre=43560 foot
3/4 acre=32670 foot
now we know that
32670 sq foot............................80,000 dollars
1 sq foot...........................................?

the price is=80,000/32670=2.4487
rounded =2.45

Following are the calculation to the given question:

Given:

salesperson sells[tex]\bold{= \frac{3}{4}}[/tex]

acre= 80,000

To find:

price per square foot rounded to two decimal spaces=?

Solution:

Therefore

[tex]1 \ acre=43560\ foot \\\\ \frac{3}{4}\ acre=32670\ foot[/tex]

Calculation

[tex]32670 \ sq \ foot = \$80,000 \\\\1 \ sq \ foot =? \\\\[/tex]

Calculating the price:

[tex]=\frac{80,000}{32670}=2.4487 \approx 2.45[/tex]

Therefore, the final answer is "$2.45".

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Could someone help me with this?

Answers

Distributive property was the first property used in STEP 1, where -4 was distributed to -3x+ 2 resulting in the equation in STEP 1. Next in STEP 2, commutative property of addition no matter how 12x and 6x are arranged, when you add them together the result will be the same.
*Take note that 12x and 6x are put together because they are like terms.

For Steps 3 and 4, you will see that the addition property of equality was used in STEP 3. To keep the equation equal, you will add the same number on both sides.

STEP 4 uses Division property of Equality. Like Step 3, to keep both sides of the equation equal, you must divide both sides with the same number. It keeps the statement true by doing so.

STEP 4 and 5 uses transitive property if you examine both as a whole.
Transitive property assumes that if a = b and b = c, then a = c

If 18/18 (a) = 1 (b), and x (c) = 18/18(a) then, x (c) = 1 (b).

Please help me with question 26

Answers

Answer: B) 65 degrees

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

angle AEB = angle GEC
5x = 3x+10
5x-3x = 10
2x = 10
x = 5

angle GEC = 3x+10
angle GEC = 3*5+10
angle GEC = 25 degrees

Angle FEG = 90 - (angle GEC)
Angle FEG = 90 - 25
Angle FEG = 65 degrees

what is the coefficient of the term 13a in the expression 13a+6b

Answers

The coefficient is 13.

Factor each expression: 5a-25

Answers

5a-25
= 5(a-5)

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

5a-25 = 5(a - 5)

hope it helps

the value of the building owned by two veterinarians went from 125000 to 117500. What is the percent decrease

Answers

The decrease:
125000 - 117500 = 7500

Percentage of decrease = 7500/125000 x 100 = 6%

Finally, 43 is 5% of what number?

Use the simplified ratio to find the equivalent ratio with a numerator of 43.

Enter your answer in the box.

43 is 5% of __?

Answers

5% = 5/100 = 1/20

43 ÷ 1/20 = 43 * 20/1 = 860 ← answer

Final answer:

43 is 5% of 860.

Explanation:

To find out what number 43 is 5% of, we can set up a proportion where 5% (or 0.05 when written as a decimal) is equal to 43 over an unknown total number X.

The formula to calculate this is part = percentage imes total, which in this case turns into 43 = 0.05 * X.

To solve for X, divide 43 by 0.05, giving us X = 43 / 0.05 which equals 860.

Therefore, 43 is 5% of 860.

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The ksp of tin(ii) hydroxide, sn(oh)2, is 5.45 10-27. calculate the molar solubility of this compound. identify the sentence with the correct end punctuation A.Did you see the elephants B.I saw a baby kangaroo, c.who found the way to the penguins: d.i missed the monkeys! solve the systems of linear equations by graphing y=-5/2x-7 x+2y=4 what is the solution to the system of linear equations A. (-4.5,4.25) B. (-1.7,-2.8) C. (0,-7) D. (3,0.5) What is the probability that a card randomly drawn from a standard deck of 52 cards is NOT a king? Which demonstrates conduction? -A marshmallow held over fire? -I cream melting in the sun? -Cool feet walking across the hot pavement? -A bulb releasing light energy? Which algebraic expressions are polynomials? Check all that apply. PLEASE HELP If f is differentiable at x = c, then f is continuous at x = c.True False What happens if you place human red blood cells in a concentrated salt solution Define the following: a. Cardiorespiratory endurance b. Muscular strength c. Muscular endurance d. Flexibility e. Body composition What are two examples of good stress in your life? Is it possible for good stress to turn into bad stress? Explain. What are two examples of bad stress in your life? How can physical activity affect your overall stress level? What are some stress management techniques that you currently use in your life? Why is sleep so important in regards to your overall health? Which answer represents the series in sigma notation? Henry conducted a survey on an ad done by his company. In the survey, he asked people to evaluate the ad and state whether they found it extremely poor, poor, good, very good, or excellent. What kind of test is Henry conducting in this survey?day-after recall testinterview testrating scale testopen-ended test What was the most important contribution that the Disney Studios made to America during World War II? Suppose you wanted to do a transaction from a remote client to a server as fast as possible. would you use udp or tcp? why? Which character do you think is more powerful- macbeth or lady macbeth. cite evidence? 1. For the balanced equation shown below, how many moles of O2 will react with 0.3020 moles of CO2?2C2H5OH + 6O2 4CO2 + 6H2OA. 0.151 moles O2B. 0.201 moles O2C. 0.302 moles O2D. 0.453 moles O22. How much heat is required to convert 74 grams of ice at -4 C into 74 grams of water at 52 C?Use the information below: Hf= 334 J/gA. 606 JB. 24,716 JC. 4000 JD. 41, 406 J tiny structures inside of cells such as ribosomes and chloroplast that have specialized roles are called solve the right triangle shown in the figure BC = 1.6in< A=48.8 C =90 name the stages of a complete metamorphisis.egg, larva, pupa, adultegg, nymph, adultegg, larva, nymph, adult egg, nymph, pupa, adult A sample of potassium chlorate (15.0 g) is dissolved in 201 g of water at 70 c with precautions taken to avoid evaporation of any water. the solution is cooled to 30.0 c and no precipitate is observed. this solution is __________.a.hydrated A 6 mile walking trail has a distance marker every 1/3 mile.