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Answer: There are 75 books.

Price of each book = $4.

Step-by-step explanation:

Let x = Number of books in the box.

Then as per given,

Cost of x books = $300

Cost of one book = [tex]\$(\dfrac{300}x)[/tex]

Books left after giving 15 of them = x-15

Selling price of (x-15) books=  $330

Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]

Profit on each book= $1.50

Profit = selling price - cost price

[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]

[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]

Number of books cannot be negative.

So, there are 75 books.

Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]

So price of each book = $4.

Answer:

Null Hypothesis: H0:μ ≤ 16.8

Alternative Hypothesis: Ha: μ > 16.8

Step-by-step explanation:

We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.

It means that the past value was not more than 16.8.

This follows that the null hypothesis is given as;

H0:μ ≤ 16.8

And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;

Ha: μ > 16.8

Answer:

ABC = 148, 3*148 = 444

Step-by-step explanation:

We know that 111 = 3*  37, so all numbers of the form BBB has the factor 37.

So we need a multiple of 37 such thant when multiplied, we get three digits the same as the middle digit.

Try 4*37 = 148, 148*3 = 444, bingo, we got the right combination.

So ABC is 148.

Answer:

Alpha (α) is used to measure the error for decisions concerning true null hypotheses, while beta (ß) is used to measure error for decisions concerning false null hypotheses.

Step-by-step explanation:

Suppose we have events X and Y.

1. If it is said that X equals Y, when X is actually not equal to Y, α is used in this case, the null hypotheses.

2. If X is said to not be equal to Y, when X is actually equal to Y, β is used in this case, the false null hypotheses.

Answer:

(C) 1 and 3

Step-by-step explanation:

Corresponding angles are angles that are at the same corner at the different intersections.

We can see that 1 is on the bottom right corner of the bottom line, now we need to see what angle is at the bottom right corner of the top line?

That's 3.

So 1 and 3 are congruent because they are corresponding.

Hope this helped!

Answer:

The unit price of the 20 pack is $0.79 and the unit price for the 8 pack is $0.80.

Step-by-step explanation:

Simply Take the price of the pack of batteries divided by the number within the pack.

$6.40 / 8 == $0.80

$15.80 / 20 == $0.79

Cheers.

The question is incomplete. You can find the missing content below.

A package of 8-count AA batteries costs $6.40. A package of 20-count Of batteries costs $15.80. Which statement about the unit prices is true?

A) The 8-count pack of AA batteries has a lower unit price of $0.79 per battery.

B) The 20-count pack of AA batteries has a lower unit price of $0.80 per battery.

C) The 8-count pack of AA batteries has a lower unit prices of $0.80 per battery.

D) The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.

The correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.

Inequality is the relation between two numbers or variables or expressions showing relationships like greater than, greater than equals to, lesser than equals to, lesser than, etc.

For example 2<9

A package of 8-count AA batteries has cost = $6.40.

cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries

= $6.40/8= $0.8

A package of 20-count AA batteries has cost = $15.80.

cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries

= $15.80/20= $0.79

As 0.79<0.8

cost of 20-count AA batteries <  cost of 8-count AA batteries

Therefore the correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.

Learn more about inequality

here: https://brainly.com/question/11613554

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Answer:

Step-by-step explanation:

According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e

F = mg where;

F is the force of gravity

m is the mass of the body

g is the proportionality constant known as the acceleration due to gravity.

If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;

F = m*32.2

F =32.2m

Hence the required equation is F = 32.2m

Answer:

a) Means: 24 and 2; Extremes: 4 and 12

b) Means: 6 and 16; Extremes: 24 and 4

c) Means: 8 and 8; Extremes: 4 and 16

d) Means: 50 and 3; Extremes: 6 and 25

Step-by-step explanation:

The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:

a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.

The Means are the values that appear in the middle of the one line expression, that is: b and c.

Recall as well that the proportion can also be written with fractions:

a : b = c : d  is the same as:   a / b = c / d

so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.

Answer:

151 9/19

Step-by-step explanation:

Step-by-step explanation:

Option A is the correct answer because it is equal to 151.47

Answer: 4150

Step-by-step explanation:

You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!

Answer:

y = 3 passes through (8, 3) and is therefore parallel to y = -2

Step-by-step explanation:

Any line parallel to y = -2 is a horizontal one, and it has the same slope (zero) as does y = -2.

We could invent the horizontal line y = 3 (which comes from the point (8, 3) and surmise that it is parallel to the given line y = -2.

Thus, y = 3 passes through (8, 3) and is therefore parallel to y = -2.

In the future, please share any answer choices that are give you.  Thank you.

Answer:

a) dV(s)  =  15,386 cm³

b) dS(s) = 4,396 cm²

c) dV(s)/V(s) = 1,07 %    and   dS(s)/ S(s)  =  0,71 %

Step-by-step explanation:

a) The volume of the sphere is

V(s) = (4/3)*π*x³        where x is the radius

Taking derivatives on both sides of the equation we get:

dV(s)/ dr  =  4*π*x²    or

dV(s)  =  4*π*x² *dr

the possible propagated error in cm³ in computing the volume of the sphere is:

dV(s)  = 4*3,14*(7)²*(0,025)

dV(s)  =  15,386 cm³

b) Surface area of the sphere is:

V(s) = (4/3)*π*x³  

dV(s) /dx  =  S(s) = 4*π*x³

And

dS(s) /dx  = 8*π*x

dS(s) = 8*π*x*dx

dS(s) = 8*3,14*7*(0,025)

dS(s) = 4,396 cm²

c) The approximates errors in a and b are:

V(s) =  (4/3)*π*x³     then

V(s) = (4/3)*3,14*(7)³

V(s) = 1436,03 cm³

And  the possible propagated error in volume is from a)  is

dV(s)  =  15,386 cm³

dV(s)/V(s)  = [15,386 cm³/1436,03 cm³]* 100

dV(s)/V(s) = 1,07 %

And for case b)

dS(s) = 4,396 cm²

And the surface area of the sphere is:

S(s) =  4*π*x³        ⇒   S(s) =  4*3,14*(7)²    ⇒ S(s) = 615,44 cm²

dS(s) = 4,396 cm²

dS(s)/ S(s)  =  [ 4,396 cm²/615,44 cm² ] * 100

dS(s)/ S(s)  =  0,71

Answer:

-12

Step-by-step explanation:

Answer:

3x^2

Step-by-step explanation:

3 x times the fraction 1 over x to the power of negative 4 => 3x * 1/x^-4

= 3x *x^4 = 3x^5

times x to the power of negative 3 => x^-3

3x^5 * x^-3 = 3x^2

Answer:

3x^2

Step-by-step explanation:

i got it right on the test on god!

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Answer:

17h+1.75m=522 m=40h

Step-by-step explanation:

Let h=  {the number of hours the driver drove}

Let m=  the number of miles driven

The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:

17h+1.75m=522

17h+1.75m=522

Since the driver drove an avearge of 40 miles per hour, if the driver drove  hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:

m=40h

m=40h

Write System of Equations:

​  

17h+1.75m= 522

m=40h

The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]

The following are the different costs of the truck that Luke must be pay while running a truck:

Let ' x ' be the total time of driving a truck in hours.

and ' y ' be the total mile distance that is covered by the truck.

Therefore, the system of the equation for the overall running cost for a truck is given below.

[tex]\rm{Cost}=17x+1.75y[/tex]

Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.

Thus,

The total distance traveled by truck is 40x.

That is,

[tex]y=40x[/tex]

Substitute the values and solve them further.

[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]

Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]

To know more about variables, please refer to the link:

https://brainly.com/question/14393109

Answer:

[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]

Step-by-step explanation:

First find the radius

Which is the distance between the 2 points.

Radius =5

The answer in the standad form is above.

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r²

where (a, b) is the center of the circle and r is the radius of the circle.

Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:

[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]

hence:

(x - 3)² + (y - (-5))² = 5²

(x - 3)² + (y + 5)² = 25

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

Find out more at: https://brainly.com/question/13658927

Answer:

C). $3523.83

Step-by-step explanation:

loan of principles p= $9,300,

at rate R= 12 1 /8 % interest

Rate R = 12.125%

for duration year T = 37.5 months

T= 37.5/12 = 3.125 years

Interest I=PRT/100

Interest I =( 9300*12.125*3.125)/100

Interest I = (352382.8125)/100

Interest I = 3523.83

Interest I= $3523.83

Answer:

24 = x+6

x = 18

Step-by-step explanation:

N = 24

T = x

N = x+6  

24 = x+6

Subtract 6 from each side

24-6 = x+6-6

18 = x

Time has 6 marbles

Nirja has 6 more than Tim,

So you can subtract 6 from 24 to find x:

24-6 = x

Or you can add 6 to x to equal 24:

x + 6 = 24

You don't list the choices but it should be one of these.

Solve:

24 - 6 = x

x = 18

Complete Question

In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?

Answer:

The  probability is  [tex]P(g) =0.72[/tex]

Yes the result is reasonably close

Step-by-step explanation:

From the question we are told that

   The  number of  of  green peas is  [tex]g = 436[/tex]

     The number of yellow peas is  [tex]y = 171[/tex]

   The sample size is  [tex]n = 171 + 436 = 607[/tex]

The probability of getting an offspring pea that is green is mathematically represented as

       [tex]P(g) = \frac{g}{n}[/tex]

        [tex]P(g) = \frac{436}{607}[/tex]

        [tex]P(g) =0.72[/tex]

Comparing  [tex]P(g) =0.72[/tex]  to   [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close

Answer:

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Step-by-step explanation:

Let the hours for which Tran family's sprinkler used is x hours

water output rate for the Tran family's sprinkler = 35L per hour

water output from  Tran family's sprinkler in x hours = 35*x L = 35x

Let the hours for which Green family's sprinkler used is y hours

water output rate for the Green family's sprinkler = 40L per hour

water output from  Green family's sprinkler in x hours = 40*y L = 40y

Given

The families used their sprinklers for a combined total of 50 hours

thus

x + y = 50 -------------------equation 1

y = 50-x

total water output of 1900L

35x+40y = 1900  -------------------equation 1

using  y = 50-x in equation 2, we have

35x + 40(50-x) = 1900

35x + 2000 - 40x = 1900

=> -5x = 1900 - 2000 = -100

=> x = -100/-5 = 20

y = 50-20 = 30

Thus,

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Answer:

1. When amount of schooling increases by one year, the number of pregnancies will decrease by 4.

Step-by-step explanation:

Regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, there is regression equation given. X and Y are considered as dependent variables. When number of schooling increases by 1 year then number of pregnancies will decrease by 4

Answer:

197 = 10(31-1) + a

197 = 300 + a

-103 = a

Answer:

85.36 far north from the center

10.36 far east from the center

Step-by-step explanation:

The extra direction taken in the north side is x

X/sin(360-315)=50/sin 90

Sin 90= 1

X/sin 45= 50

X= sin45 *50

X= 0.7071*50

X= 35.355 steps

X= 35.36

Then the west direction traveled

West =√(50² - 35.355²)

West = √(2500-1249.6225)

West= √1250.3775

West= 35.36 steps

But this was taken in an opposite west direction

From the center

He is 35.36 +50

= 85.36 far north from the center

And

25-35.36=-10.36

10.36 far east from the center

Answer:

[tex]\huge \boxed{x=3}[/tex]

Step-by-step explanation:

[tex]6(x+2)=30[/tex]

[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]

[tex]x+2=5[/tex]

[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]

[tex]x=3[/tex]

Answer:

3

Step-by-step explanation:

30 = 6(x+2)

30/6 = 5

5 = x+2

5-2 = 3

3=x

This is a pretty simple question and I tried to make it as simple as possible when explaining it.

This question is solved using proportions.

Doing this, we get that he should take 3 packs.

How many calories he burns in the hike?

In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?

45 minutes - 345 calories

360 minutes - x calories

Applying cross multiplication:

[tex]45x = 345*360[/tex]

[tex]x = \frac{345*360}{45}[/tex]

[tex]x = 2760[/tex]

He burns 2760 calories in the hike.

How many calories he wants to replace?

Roughly 1/3, so he have to find one third of 2760, that is:

[tex]\frac{2760}{3} = 920[/tex]

How many packs?

One pack recovers 310 calories, how many packs for 920 calories?

1 pack - 310 calories

x packs - 920 calories

Applying cross multiplication:

[tex]310x = 920[/tex]

[tex]x = \frac{920}{310}[/tex]

[tex]x = 2.97[/tex]

Rounding up, he should take 3 packs.

A similar question is found at https://brainly.com/question/14426926

Answer:

6

Step-by-step explanation:

Hello, please consider the following.

[tex](4+x)^2=4^2+2\cdot 4\cdot x+x^2=16+\boxed{8}x+x^2\\\\\text{ ... and not ...}\\\\16+\boxed{4}x+x^2[/tex]

So the correct equation becomes.

[tex]x^2+64=16+8x+x^2\\\\8x=64-16=48\\\\\text{ we divide by 8 both sides of the equation.}\\\\x=\dfrac{45}{8}=6[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Error : The expression ( 4 + x )² was expanded incorrectly.

Correct Solution : x = 6

Step-by-step explanation:

The planning of the solution is correct, by Pythagorean Theorem you can say that PQ² + QO² = PO², and hence through substitution x² + 8² = ( 4 + x )². Let's look into the calculations.

PQ² + QO² = PO²,

x² + 8² = ( 4 + x )²,

x² + 8² = 16 + 8x + x²,

64 = 16 + 8x,

48 = 8x,

x = 48 / 8 = 6, x = 6

As you can see, the only error in the calculations was expanding the expression ( 4 + x )². ( 4 + x )² = 4² + 2 [tex]*[/tex] 4 [tex]*[/tex] x + x² = 4² + 8x + x² = 16 + 8x + x², not 16 + 4x + x².

Answer:

1978.2 or 630π feet

Step-by-step explanation:

The Ferris wheel will rotate 3 * 5 = 15 times during the 5 minute ride and the radius is 42 / 2 = 21 feet. Since C = 2πr, r = 21 and π ≈ 3.14, C = 2 * 3.14 * 21 = 131.88. However, this only accounts for one rotation so the answer is 131.88 * 15 = 1978.2 or 630π feet.

Answer:

to provide interest in the subject

As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c

Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.

Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.

if you're next to your exams then just one thing, Start now!!

hope this helps!

Answer:

1/9

Step-by-step explanation:

easy 2/3 is equivalent to 6/9. So there is 1/9 of a pint left