If all the books on a shelf with fewer than 45 books were put into piles of five books each, no books would remain. If the same book were put into piles of seven books each, two books would remain. What is the greatest number of books that could be on the shelf?

Answer:

373.3333... in^3

Step-by-step explanation:

V = lwh / 3

V = 10 * 8 * 14 / 3

V = 1120 / 3

V = 373.3333... in^3

I'm probably wrong, I haven't done volume in a looong time.

Complete question is;

A trucking company determined that the distance traveled per truck per year in its entire fleet was normally distributed with a mean of 55 thousand miles and a standard deviation of 11 thousand miles.

a)A truck in the fleet traveled 42 thousand miles in the last vear. Calculate the z-score for this truck.

b) Interpret the z-score

c) The trucking company has a policy that any truck with mileage more than 2.5 standard deviations above the mean should be removed from the road and inspected. What is the probability that a randomly selected truck from the fleet will have to be inspected?

d) A randomly selected truck in the fleet traveled 85 thousand miles in the last year. Should this truck be removed from the road and inspected? Explain why or why not.

Answer:

A) z = - 1.18

B) Interpretation of the z-score in A above shows that the distance traveled per truck per year in its entire fleet is 1.18 standard deviations lesser than the distance traveled per truck on average

C) P(z > 2.5) = 0.0062

D) it's value of z is greater than 2.5 minimum and so the truck will be removed from the road and inspected

Step-by-step explanation:

A) We are given;

Population mean; μ = 55000

Sample mean; x¯ = 42000

Standard deviation; σ = 11000

Z-score formula is;

z = (x¯ - μ)/σ

z = (42000 - 55000)/11000

z = - 1.18

B) Interpretation of the z-score in A above shows that the distance traveled per truck per year in its entire fleet is 1.18 standard deviations lesser than the distance traveled per truck on average.

C) since it has a policy that any truck with mileage more than 2.5 standard deviations above the mean should be removed from the road and inspected, then it means that probability that it will be inspected is;

P(z > 2.5) = 1 - P(z < 2.5)

From p-values from z-score table, we have;

P(z > 2.5) = 1 - 0.9938

P(z > 2.5) = 0.0062

D) A randomly selected truck in the fleet traveled 85 thousand miles in the last year. Thus; x¯ = 85000.

Thus;

z = (85000 - 55000)/11000

z = 2.73

This value of z is greater than 2.5 minimum and so the truck will be removed from the road and inspected

Answer:

The answer is "94.3".

Step-by-step explanation:

Calculating the total numbers of cake eaters[tex]=50+3=53\\\\[/tex]

Calculating the total numbers of ill among them[tex]=50\\\\[/tex]

[tex]\therefore[/tex]

The attack rate for those who ate cake[tex]=\frac{50}{53}\times 100\%=94.3[/tex]

Answer:

Step-by-step explanation:

.007  = 7 x [tex]10^{-3}[/tex]

.07    = 7 x [tex]10^{-2}[/tex]

7      = 7 x [tex]10^{0}[/tex]

700 = 7 x [tex]10^{2}[/tex]

Answer:

(4x4) + (6x11) = 82 for area

4+4+10+11+7+6= 42

Step-by-step explanation:

You can calculate this by calculating the two squares separately, and on the bottom line, it is 10, so just subtract 4 to make the rectangle on the right, separate from the square on the left. (for area)

Answer:

9(1 +6)

Step-by-step explanation:

9 = 9 * 1

54 = 9 * 6

9 + 54 = (9*1 ) + (9*6)      {9 is common in both terms}

           = 9*(1 + 6)

Answer:

1st step, DON'T PANIC. You have plenty of time to study. When it's a big exam, I like to set aside 2 hours daily for studying. If you're confused by certain topics, watch a video or ask your professor how to properly complete the answer. One college tip I learned: ALWAYS ASK THE PROFESSOR IF YOU GET CONFUSED WHILE STUDYING! They can help clear up problems you have. On the night before the exam, make sure you get a good night's rest. On the day of your exam, make sure to eat a good breakfast.

You have plenty of time, you got this! :)

1. Have some healthy food...or junk food or food that you love... because with a hungry stomach no one can study...

2. Take a break after every 15min... while studying..

3. Call your friends and study together...i.e. make a study circle...

4.Study loudly and faster...

At last..if you feel you're prepared then... good..if not.. then have a corner and weep and cry...or

5. have advice of your best friend or genius friend... if he or she didn't picks up phone then again cry because he or she is studying seriously with concentration so he or she will not pick up your phone...

6. At last pick up your all the methods of cheating...

hope it helps..

3x+x^2=3x+x^2

3x-3x=x^2-x^2

which means x=0

Answer:

The answer is C. [tex]256\pi[/tex] [tex]in^2[/tex].

Step-by-step explanation:

To solve for the surface area of this cylinder, start by using the cylinder surface area formula, which is [tex]SA=2\pi rh+2\pi r^{2}[/tex]. Next, plug in the information given from the problem into the formula, which will look like [tex]SA=(2)(\pi )(8in)(8in)+(2)(\pi )(8in^{2})[/tex]. Then, simplify the equation, which will look like [tex]SA=(128in)(\pi) +(128in)(\pi)[/tex]. The next step is to simplify the equation further, which will look like [tex]SA= 256\pi[/tex] [tex]in^{2}[/tex]. The final answer is [tex]256 \pi[/tex] [tex]in^2[/tex].

Step-by-step explanation:

Using Pythagoras theorem:

[tex] = \sqrt{{20}^{2} - {12}^{2} } [/tex]

[tex] = \sqrt{400 - 144}[/tex]

[tex] = \sqrt{256} [/tex]

[tex] = 16[/tex]

Answer:

8p^3 ( 2p -3)

Step-by-step explanation:

16p^4 - 24p^3

8*2* p^3 *p - 3*8*p^3

Factor out the common terms

8p^3 ( 2p -3)

Answer:

According to me,

Answer:

The radius of the circle if the circumference is 44 cm will be 7 cm.

Step-by-step explanation:

➝ Circumference of the circle = 44 cm

➔ Circumference = 2πr [For finding radius]

Finding the radius:-

➜ Let radius be r.

➜ 44 = 2 × 22/7 × r

➜ Multiply 2 × 22/7

➜ 44 = 44/7 × r

➜ Taking 7 to LHS.

➜ 44 × 7 = 44 × r

➜ 308 = 44 × r

➜ Taking 44 to LHS.

➜ 308/44 = r

➜ 308/44 = 7

➜ 7 = r

➜ r = 7

Answer:

3/5

Step-by-step explanation:

Cos C = adjacent/hypotenuse

or, Cos C = 21/35 = 3/4

Answered by GAUTHMATH

Answer:

36

Step-by-step explanation:

a1 = 4

an=an-1 *3

a2 = a1 *3 = 4*3 = 12

a3 = a2*3 = 12*3 = 36

Answer:

it should be letter b sorry if its wrong

the answer should be choice B

Answer:

∠ HFG = 79°

Step-by-step explanation:

The inscribed angle HFG is half the measure of its intercepted arc, that is

∠ HFG = [tex]\frac{1}{2}[/tex] × 158° = 79°

Answer:

- 5

Step-by-step explanation:

Solve for x

4-2(×+7)=3(×+5)

We open the bracket :

4 - 2x - 14 = 3x + 15

Collect like terms

-2x - 3x = 15 + 14 - 4

-5x = 25

Divide both sides by - 5

-5x/-5 = 25 / - 5

x = - 5

Answer:

The fourth option.

x + b/2a = +- sqrt((b^2 - 4ac)/(4a^2))

Step-by-step explanation:

Answer:

[tex]-4x\sqrt{3}[/tex]

Step-by-step explanation:

One is given the following expression:

[tex]\sqrt{48x^2}[/tex]

Factor out the expression. Rewrite the expression as the product of a number times itself times another number. This will allow one to take factors out of the radical. Remember, the square root operation indicates that a number times itself equals the number under the radical. Bear in mind, the result of the square root operation must always be positive. Since (x) is negative, one has to multiply the result of the operation by (-1) to compensate for the fact that (x) is negative. Rewrite the value under the radical:

[tex]\sqrt{4*4*3*x^2}[/tex]

Take out the factors,

[tex]=-4x\sqrt{3}[/tex]

Answer:

Multiplication:

Step 1: Factor both the numerator and the denominator.

Step 2: Write as one fraction.  Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.

Step 3: Simplify the rational expression.

Step 4: Multiply any remaining factors in the numerator and/or denominator.

Division:

Step 1: Completely factor both the numerators and denominators of all fractions.

Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal.

Step 3: Cancel or reduce the fractions. Remember that to reduce fractions; you can cancel something in the numerator with something in the denominator, but in order to cancel something in the numerator and denominator the two factors must be EXACTLY the same.

Step 4: Rewrite the remaining factor. Notice that you do NOT need to actually multiply anything in the numerator or denominator.

Answer:

cost of a taco: $1.25

cost of a burrito: $2.50

Step-by-step explanation:

Let the cost of a taco be $t and the cost of a burrito be $b.

t +3b= 8.75 -----(1)

4t +2b= 10

Divide both sides by 2:

2t +b= 5

Making b the subject of formula:

b= 5 -2t -----(2)

Substitute (2) into (1):

t +3(5 -2t)= 8.75

Expand:

t +3(5) +3(-2t)= 8.75

t +15 -6t= 8.75

t -6t= 8.75 -15

-5t= -6.25

t= -6.25 ÷(-5)

t= 1.25

Substitute t= 1.25 into (2):

b= 5 -2(1.25)

b= 5 -2.5

b= 2.50

Thus, the cost of a taco is $1.25 and the cost of a burrito is $2.50.

Answer:

A = 616 cm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi (14)^2

A = pi (196)

Using 3.14 as an approximation for pi

A = 3.14 *196

A =615.44

The nearest approximation is

A = 616 cm^2

Answer:

D 616 cm^2

Step-by-step explanation:

Area = pi r^2

= 14^2 * 3.142

= 615.832

Answer:

The height of the tree is is 60m

Step-by-step explanation:

Let's answer a, as it is the only complete question.

We know that the angle of elevation of the top of a tree observed from a point 60m away, is 45°.

We can model this with a triangle rectangle, a sketch of it can be seen below (assuming that you are looking it from the ground).

You can see that the adjacent cathetus to the 45° angle is equal to 60m

And the opposite cathetus is the measure we want to find.

Now you can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus).

So to find the height of the tree we need to solve:

tan(45°) = H/60m

This is just:

tan(45°)*60m = H  =60m

The height of the tree is is 60m

The solution is, The format of this proof is C. flowchart proof.

Flowchart Proof. A type of proof that makes use of a graphical illustration. Statements are placed in boxes, and the justification for each statement is written below the box. Arrows imply the logical flow of the statements.

here, we have,

given that,

Given: AB = BC

Prove: B is the midpoint of AC.

now, we have to find that, the format of this proof is what.

now, we know that,

Flowchart proofs are organized with boxes and arrows; every "statement" is inside the field and every "reason" is below every field. each statement in evidence permits every other subsequent statement to be made.

In flowchart proofs, this development is proven through arrows.

Hence, The solution is, The format of this proof is C. flowchart proof.

Learn more about Flowchart Proof here

brainly.com/question/12611050

#SPJ7

$\sf\underline\bold\blue{Information\:given\:in\:the\:question:}$

$\space$

$\sf\underline\bold\blue{What\:we\:have\:to\:find?}$

$\space$

$\sf\underline\bold\blue{Answer:}$

$\space$

$\sf\underline\bold\blue{Calculations:}$

Here we have the value of the circle's diameter that is 20inches. So, first we have to calculate the radius of the circle using the formula :

$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{Diameter}{2}$

$\space$

$\sf\underline\bold\blue{Calculating\:the\:required\:values:}$

$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{20}{2}$

$\sf{Convert \: to \: the\:lowest\:term(Divide),}$

$\mapsto$ $\sf\underline\bold{Radius=10}$

☆Now we know the value of the radius . So now let's calculate the area of the circle.

$\space$

$\sf\bold{Area\:of\:circle:}$ π$\sf{ r \: ^{2} }$

$\sf\bold{Evaluating \: the\:required\:values:}$

$\sf\bold{Area\:of\:circle=3.1415(10)^2}$

$\space$

$\sf\bold{Area\:of\:the\:circle=3.1415\times10\times10}$

$\sf\bold{Now,}$

$\sf\bold{Area\:of\:the\:circle:3.1415\times100}$

$\space$

$\sf\underline\bold\green{Thus,Area\:of\:the\:circle\: is \: 314.15}$

____________________________

Answer:

Step-by-step explanation:

This Makes no sense but this is 4kg and 8g converted to Kg :

4kg - 8g = 4.008 kg

Answer:

[tex]\sqrt[2]{8}[/tex]

Step-by-step explanation:

Remember the basic format of a fraction raised to a fractional exponent:

[tex]a^\frac{b}{c}=\sqrt[b]{a^c}[/tex]

Some terms to keep in mind are the following:

(a) is the base

(c) is the exponent

(b) is the index

Apply this information to the given problem:

[tex]2^\frac{3}{2}[/tex]

In this case, (2) is the base, and the index; (3) is the exponent. Apply the general format of the fraction exponent to change the expression from an exponent to a radical.

[tex]2^\frac{3}{2}=\sqrt[2]{2^3}[/tex]

Simplify the term under the radical:

[tex]\sqrt[2]{2^3}=\sqrt[2]{8}[/tex]