Carla drove her truck 414 miles on 18 gallons of gasoline. How many miles did she drive per gallon?

Answer:

(1+y^2) /2y

Step-by-step explanation:

arithmetic mean is the average of x and y

(x+y)/2

Using the equation

xy = 1

and solving for x

x = 1/y

Replacing x in the first equation

(1/y + y) /2

Multiply by y/y

(1/y + y) /2 * y/y

(1/y + y)*y /2y

(1+y^2) /2y

Answer:

In the error term.

Step-by-step explanation:

A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).

Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.

Answer:

4

Step-by-step explanation:

I got it right on Khan

The value of x is 4.

A triangle is a polygon in two dimensional geometry. I has three sides and three angles along with three vertices.

Area of a triangle = [tex]\frac{1}{2}[/tex] × b × h

where b is the base of the triangle and h is the length of height of the triangle.

The given triangle is an obtuse triangle which has an angle equal to greater than 90 degrees. So the height of the triangle is found by drawing a perpendicular line from the base to the opposite vertex.

Here, height = x and base length = 6

Area = 12 units²

[tex]\frac{1}{2}[/tex] × 6 × h = 12

6 × h = 12 × 2

6 × h = 24

h = 24/6

h = 4 units.

Hence the length of the height which is x is 4 units.

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Answer:

C.

Step-by-step explanation:

[tex]\frac{7x}{3y}+\frac{12x}{9y}[/tex]

We can reduce the second term:

[tex]\frac{7x}{3y} +\frac{4x}{3y}[/tex]

Since they now have a common denominator, we can add them:

[tex]=\frac{7x+4x}{3y}=11x/3y[/tex]

The answer is C.

So, yes, you're answer was correct!

Answer:

x is approximately 2.220744

Step-by-step explanation:

This can be simplified a little using properties of logarithms, and then solve it by graphing:

[tex]log(x)-log(x-1)^2=2\,log(x-1)\\log(x)-2\,log(x-1)=2\,log(x-1)\\log(x)=4\,log(x-1)[/tex]

So we use a graphing tool to find the intersection point of the graph of [tex]log(x)[/tex], and the graph of [tex]4\,log(x-1)[/tex]

Please see attached image for the graph and solution.

The value of x is approximately 2.220744

Answer:

  x = 2.32011574011

Step-by-step explanation:

The problem with your original equation is that it is a long way of saying ...

  log(x) -log(x) -1 = 2log(x-1)

  0 -1 = 2log(x-1)

which has the solution ...

  -1/2 = log(x -1)

  1/√10 = x -1

  x = 1 + 1/√10 ≈ 1.3162278

__

We have asked for clarification, and what we got was ...

  [tex]\log{(x)}-\log{(x-1^2)}=2\log{(x-1)}[/tex]

which, again, is a long way of saying ...

  [tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]

The other reasonable interpretation of your 'clarified' equation is ...

  [tex]\log{(x)}-\log{((x-1)^2)}=2\log{(x-1)}[/tex]

which you already have an answer to. You have declared that a "misconception."

So, we are left with the interpretation that the equation you want a solution to is ...

  [tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]

_____

When solving these graphically, I like to write the equation as a function whose zero(s) we're trying to find. For this, when we subtract the right side, we get ...

  [tex]f(x)=\log{(x)}-3\log{(x-1)}[/tex]

A graphing calculator shows that f(x) = 0 when ...

  x ≈ 2.32011574011

__

If you don't like my interpretation, check out the second attachment. It has your x-1² as the argument of the middle term. You can see that the calculator interpreted that the same way I did (as required by the order of operations).

Answer:

see below

Step-by-step explanation:

√p = 9/16

We need to square each side, not take the square root

(√p)^2 =( 9/16)^2

p = 81/256

Answer:

P(identical colours) =  160/1771   (0.0903 to four decimals)

Step-by-step explanation:

Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)

Choose three without replacement.

Need probability three identical colours.

Use the multiplication rule.

P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253

P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771

P(BBB) = 8/23 * 7/22 * 6/21 = 8/153

Probability of getting identical colours

= P(RRR)+P(WWW)+P(BBB)

= 160/1771   (0.0903 to four decimals)

Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.

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

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

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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

The desired outcomes can be:

Thus:

[tex]D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160[/tex]

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

The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:

[tex]T = C_{23,3} = \frac{23!}{3!20!} = 1771[/tex]

The probability is:

[tex]p = \frac{D}{T} = \frac{160}{1771} = 0.0903[/tex]

0.0903 = 9.03% probability all three marbles are the same color.

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Answer:

(2,2) (-1,-1)

Step-by-step explanation

i think this is there answer im sorry if im wrong

Complete Question

Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n=150

Answer:

Normal sampling distribution can not be used

Step-by-step explanation:

From the question we are told that

    The  null hypothesis is  [tex]H_o : p = 0.015[/tex]

     The  alternative hypothesis is    [tex]H_a : p < 0.015[/tex]

The  sample size is  n= 150

Generally in order to use  normal sampling distribution  

     The value  [tex]np \ge 5[/tex]

So  

         [tex]np = 0.015 * 150[/tex]

         [tex]np = 2.25[/tex]

Given that  [tex]np < 5[/tex]   normal sampling distribution  can not be used

Based on the normal sampling assumption, the product of the sample size and the proportion must be greater than or equal to 5. Hence, since, the condition isn't met, then the normal sampling cannot be used.

Given the Parameters :

Test if np ≥ 5 :

2.25 < 5

Hence, np < 5 ;

Hence, the normal sampling distribution cannot be used.

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Answer:

Look at that picture

Step-by-step explanation:

Answer:

$3,717

Step-by-step explanation:

Hello, in 1 year there are 12 months.

Let's note I the Initial amount.

So, after 1 month we will get the following, because we compute the interest amount for one month only.

I * ( 1 + 6% * (1/12) )

And the next month, we will have interest of the amount available from previous month so it gives

[tex]I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2[/tex]

... and after n months ...

[tex]I*(1.005)^n[/tex]

8 years is 8*12 = 96 months. so we are looking for I such that

[tex]I*(1.005)^{96}=6000\\\\<=> I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}[/tex]

Thank you.

Answer:

1.05km/min

Step-by-step explanation:

[tex]Distance = 84 km\\\\Time = 1hr 20 min= 80minuttes\\\\Average \: Speed = \frac{Distance}{Time} \\\\A.S =\frac{84}{80} \\\\A.S = 1.05km/min[/tex]

we, know that

➺ Average Speed = Total Distance/Total Time taken

where,

♛ Substituting these values ♛

◗Average Speed = Distance/Time

◗Average Speed = 84000/4800

◗Average Speed = 840/48

◗Average Speed = 70/4

◗Average Speed = 17.5m/s

Answer:

Step-by-step explanation:

Given x = 5, y = 3/4 and z = -1/7, 2=we are to calculate [tex]\frac{xz}{y}[/tex]. Substituting the value of x, y and z into the expression will give;

[tex]= \frac{xz}{y}\\\\ \frac{5(-1/7)}{3/4} \\= \frac{-5/7}{3/4}\\\\= \frac{-5}{7} * \frac{4}{3}\\ \\ = \dfrac{-20}{21}\\[/tex]

Hence the value of the expression is -20/21

Answer:

El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.

Step-by-step explanation:

Sea [tex]c[/tex] el coste máximo que puede asumir el comensal, medido en pesos, el cual es representada por la siguiente suma:

[tex]c = c_{o} + c_{i} + c_{ii}[/tex]

Donde:

[tex]c_{o}[/tex] - Coste del consumo, medido en pesos.

[tex]c_{i}[/tex] - Coste del impuesto en el condado, medido en pesos.

[tex]c_{ii}[/tex] - Coste de la propina, medido en pesos.

Ahora, los costes por impuesto y por propina se determinan en función del coste de consumo:

Coste del impuesto en el condado

[tex]c_{i} = r_{i}\cdot c_{o}[/tex]

Donde [tex]r_{i}[/tex] es la razón entre el coste del impuesto en el condado y el coste del consumo, adimensional.

Coste de la propina

[tex]c_{ii} = r_{ii}\cdot (c_{o}+c_{i})[/tex]

[tex]c_{ii} = r_{ii}\cdot (c_{o}+r_{i}\cdot c_{o})[/tex]

[tex]c_{ii} = r_{ii}\cdot (1 + r_{i})\cdot c_{o}[/tex]

Donde [tex]r_{ii}[/tex] es la razón entre el coste de la propina y la suma de los costes de consumo y del impuesto del condado, adimensional.

Entonces, la suma completa queda representada por:

[tex]c = c_{o} + r_{i}\cdot c_{o}+r_{ii}\cdot (1+r_{i})\cdot c_{o}[/tex]

[tex]c = [1+r_{i}+r_{ii}\cdot (1+r_{i})]\cdot c_{o}[/tex]

A continuación, se despeja el coste de consumo (valor máximo de los platos):

[tex]c_{o} = \frac{c}{1 +r_{i}+r_{ii}\cdot (1+r_{i})}[/tex]

Si [tex]c = \$\,25[/tex], [tex]r_{i} = 0.07[/tex] y [tex]r_{ii} = 0.15[/tex], entonces:

[tex]c_{o} = \frac{\$\,25}{1+0.07+0.15\cdot (1+0.07)}[/tex]

[tex]c_{o} = \$\,20.32[/tex]

El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.

Answer:

1/4 miles

Step-by-step explanation:

Hey there!

Well starting at Campbell and going to Morristown it is 1/4 miles.

Going from Campbell to Clarksville it is 2/4 miles.

So to find the difference we’ll subtract.

2/4 - 1/4

= 1/4 miles

Hope this helps :)

Answer:

s  is [tex]s =15.3[/tex]

Step-by-step explanation:

From the question we are told that

    The data is  

Generally the mean is evaluated as

           [tex]\= x = \frac{84+ 85+ 83+​ 63+ 61+​100+ 98}{7}[/tex]

           [tex]\= x = 82[/tex]

The standard deviation is mathematically represented as

    [tex]s = \frac{\sum (x- \= x)^2}{n-1}[/tex]

[tex]s =\sqrt{ \frac{ (84-82)^2+​ (85-82)^2 +( 83-82 )^2 +(​63-82) ^2 + ( 61-82)^2,+ (100-82)^2 + (98-82)^2}{7-1}}[/tex]

 [tex]s =15.3[/tex]

Answer:

B) 5

Step-by-step explanation:

Proportions:

8 ⇒ 10

20 ⇒ 5x

5x = 20*10/8

5x = 25

x = 25/5

x = 5

Answer:

There has been no significant change in the number of students in each major between the last school year and this school year.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: There has been no change in the number of students.

Hₐ: There has been a significant change in the number of students.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

Here,

[tex]O_{i}[/tex] = Observed frequencies

[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.

The chi-square test statistic value is, 1.662.

The degrees of freedom is:

df = 4 - 1 = 4 - 1 = 3

Compute the p-value as follows:

[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]

*Use a Chi-square table.

The  p-value is 0.645.

The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.

Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.

Answer:

[tex] \sqrt{4 {}^{2} + ( - 4) {}^{2} } [/tex]

[tex] \sqrt{32} [/tex]

and the angle

[tex] \tan( \alpha ) = - 4 \div 4 = - 1[/tex]

and since the sin component is -ve, we have our angle on 4th quadrant, which equals 315 degrees

Options:

Determine two pairs of polar coordinates for the point (-4, 4) with 0° ≤ θ < 360°. (5 points)

Group of answer choices

(4  , 135°), (-4  , 315°)

(4  , 45°), (-4  , 225°)

(4  , 315°), (-4  , 135°)

(4  , 225°), (-4  , 45°)

Step-by-step explanation:

The guy asking forgot to provide the options you can comment the awnswe in the comments just do it before brainly turns off comments to try and prevent people from learning

Answer:

If something is guaranteed, it has a probability of 100%, or 1.

Step-by-step explanation:

A standard deck has 52 cards. Of these, half are red cards (diamonds and hearts) and half are black cards (clovers and spades)

Half of the deck is 26 cards (52 ÷ 2 = 26), so you have 26 red and 26 black cards.

What this means in our context is, if we draw 27 cards, even if we drew all 26 black cards, we would still have 1 red card.

So the probability is 100%, or 1, of drawing a red card when we pick 27 cards from a deck, no matter how it's shuffled

The probability of getting a red card is 1.

No matter how you shuffle the cards, the no of cards will remain the same.

Therefore, it will not affect the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Answer:

x = 450

510/170 = 3

x/150 = 3

x = 450

Answer:

X=450 is the answer.

Step-by-step explanation:

Answer:

y = 4x + 21

Step-by-step explanation:

Hello!

Point-slope form is y - y1 = m(x - x1)

y1 is the y point

x1 is the x point

m is the slope

Put in what you know

y - -3 = 4(x - -6)

Subtracting a negative is the same as adding

y + 3 = 4(x + 6)

Distribute the 4

y + 3 = 4x + 24

Subtract 3 from both sides

y = 4x + 21

The answer is y = 4x + 21

Hope this helps!

Answer:

8 cm

Step-by-step explanation:

x:y= 2:5

x/y = 2/5

5x = 2y

y is the longer side

5x=2(20)

x=8 cm

The length of the shorter side is 8 cm.

What is rectangle?

A rectangle more generally than any quadrilateral whose axes of symmetry pass through each pair of opposite sides.This definition includes both right-angled rectangles and rectangles. Each has an axis of symmetry that is parallel and equidistant from a pair of opposite sides and a second that is a perpendicular bisector of those sides, but in the case of a crossed rectangle the first axis is not the axis of symmetry of either side. . that it divides.

Quadrilaterals that have two axes of symmetry, each passing through a pair of opposite sides, belong to the larger class of quadrilaterals that have at least one axis of symmetry through a pair of opposite sides. These quadrilaterals consist of isosceles trapezoids and crossed isosceles trapezoids (crossed quadrilaterals with the same arrangement of vertices as an isosceles trapezoid).

Given, sides of a rectangle are in ratio 2:5.

Let length of a rectangle be 5x cm and breadth of a rectangle be 2x cm.

We know length of a rectangle is longer than breadth.

So, length of the rectangle is 20 cm.

According to question,

[tex]5x = 20 \\ x = \frac{20}{5} \\ x = 4[/tex]

So, length of the rectangle (5×4) = 40 cm and breadth of the rectangle (2×4) = 8 cm.

Breath is shorter side of rectangle.

Therefore,The length of the shorter side is 8 cm.

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Answer:

=Vlookup'B13' A11' 7'false

Press enter.

Step-by-step explanation:

Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:

=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.

where true is approximate match and false is exact match.

Answer:=VLOOKUP(J2,A2:G23,2,FALSE)

Step-by-step explanation:

a. In cell J3, begin to enter a formula using the VLOOKUP function.

b. Use the Project ID (cell J2) as the lookup value.

c. Use the Projects table (range A2:G23) as the table_array.

d. Use the Project Name column (column 2) as the col_index_num.

e. Specify an exact match (FALSE) for the range_lookup.

Answer:

A) Reject H0 if F > 5.417

B) we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms

Step-by-step explanation:

A) From the table, we can see that we have df1 = 3 and df2 = 15. And we are given a significance level of α = 0.01

We are also given f-value of 1.75

Thus,from the f-distribution table attached at significance level of α = 0.01 and df1 = 3 and df2 = 15, we have;

F-critical = 5.417

Normally, we reject H0 if F > 5.417

But in this case, F is 1.75 < 5.417 and so we conclude that we do not reject H0 at the 0.01 level of significance

B) for 0.05 level of significance, df1 = 3 and df2 = 15, from the 2nd table attached, we have;

F-critical = 3.2874

Again the f-value is less than this critical one.

Thus, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms

Answer:

The exact distance is [tex]\sqrt{109}[/tex] miles.

The distance is approximately 10.4 miles.

Step-by-step explanation:

It is given that a rectangular city is 3 miles long and 10 miles wide. So,

Length = 3 miles

Width = 10 miles

We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.

Using Pythagoras theorem, the length of diagonal is

[tex]d=\sqrt{l^2+w^2}[/tex]

where, l is length and w is width.

Substitute l=3 and w=10.

[tex]d=\sqrt{(3)^2+(10)^2}[/tex]

[tex]d=\sqrt{9+100}[/tex]

[tex]d=\sqrt{109}[/tex]

The exact distance is [tex]\sqrt{109}[/tex] miles.

Now,

[tex]d=\sqrt{109}[/tex]

[tex]d=10.4403065[/tex]

[tex]d\approx 10.4[/tex]

The distance is approximately 10.4 miles.

Answer:

b

Step-by-step explanation:

only b has 10 didgets. it could be a since the didgets aren't very random, but then again, i think it's b

Let favorable event“1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.

Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste to determine.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

While going throughout the option in options C and D number so the sample is not equal to 10 so both the statement is false. Option B is the correct option because the sample space is also equal to 10 and the number of the favorable events is also 3 which is mentioned in the question.

Thus, let favorable event “1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.

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Answer:

APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.

Step-by-step explanation:

Answer:

[tex]a = 6m/s^2[/tex]

Step-by-step explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

[tex]a\ \alpha\ \frac{1}{m}[/tex]

Convert variation to equality

[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)

Make F the subject of formula;

[tex]F = ma[/tex]

When mass = 4kg; Acceleration = 15m/s²

[tex]F = 4 * 15[/tex]

[tex]F = 60N[/tex]

When mass = 10kg; Substitute 60 for Force

[tex]F = ma[/tex]

[tex]60 = 10 * a[/tex]

[tex]60 = 10a[/tex]

Divide both sides by 10

[tex]\frac{60}{10} = \frac{10a}{10}[/tex]

[tex]a = 6m/s^2[/tex]

Hence, the acceleration is [tex]a = 6m/s^2[/tex]