If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question?
(b) in how many ways can a student check off one answer to each question and get all the answers wrong?

Answer:

[tex]y = mx + b[/tex]

≡ For instance, I have the equation, y = 9x + 5, and I must find the slope. The slope is 9, because 9 is in the m area of the equation, making these equations easier to determine and have less steps than before.

Answer:

6 inches

Step-by-step explanation:

Formula for surface area of a cylinder:

[tex]SA=2\pi r^{2} +2\pi rh[/tex]

Plug in values and solve for the radius:

[tex]180\pi =2\pi r^{2} +2\pi r(9)\\[/tex]

Divide both sides by [tex]2\pi[/tex]

[tex]90=r^{2} +r(9)[/tex]

Subtract 90 from both sides

[tex]0=r^{2} +9r-90[/tex]

Use the quadratic equation to find the roots

[tex]x=(-b[/tex]±[tex]\sqrt{b^2-4ac})*\frac{1}{2a}[/tex] (sorry for formatting, Brainly doesn't

                                           allow equations with ± in them)

[tex]x=\frac{-9+\sqrt{9^2-4*1*90} }{2(1)}[/tex]        and          [tex]x=\frac{-9-\sqrt{9^2-4*1*90} }{2(1)}[/tex]

[tex]x=\frac{(-9+\sqrt{81+360})}{2}[/tex]          and          [tex]x=\frac{(-9-\sqrt{81+360})}{2}[/tex]

[tex]x=\frac{(-9+\sqrt{441})}{2}[/tex]               and          [tex]x=\frac{(-9-\sqrt{441})}{2}[/tex]

[tex]x=\frac{(-9+21)}{2}[/tex]                   and          [tex]x=\frac{(-9-21)}{2}[/tex]

[tex]x=\frac{12}{2}[/tex]                           and          [tex]x=\frac{-30}{2}[/tex]

[tex]x=6[/tex]                             and          [tex]x=-15[/tex]  

We can't have a negative radius, so that leaves us with r=6 in.

Answer:

BB

Hope that helps!

Answer:

A

Step-by-step explanation:

hope this help

[tex]3^2+y^2=8^2\\9+y^2=64\\y^2=55\\\\x^2+3^2=y^2\\x^2+9=55\\x^2=46\\x=\sqrt{46}=2\sqrt5\approx6,8[/tex]

Let May's age be represented with m

Lilian's age 2/3m

Ratio of May's age to Lilian's age = m : 2/3m

Multiply both sides by 3 : 3  : 2

Ratio of Lilian's age their total age: 2 : 5

Lilian's age = 2/5 x 25 = 10 years

May's age = 3/5 x 25 = 15 years

Let the mass of carrots be represented with c

The mass potatoes would be represented with 5/2c

Ratio of carrots to potatoes : 2 : 5

Ratio of the mass of potatoes to the total mass : 5 : 7 = 5/7

Mass of carrots = 5/2c - c = 9

3/2c = 9

3c = 18

c = 6

Mass of potatoes = 5/2 x 6 = 15

Total mass = 15 + 6 = 21 kilograms

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Answer:

see the attachment photo!

Answer:

b

Step-by-step explanation:

Answer: Heyaa!  :))

60/50 as a percentage is.. 120%

Step-by-step explanation:

Hopefully this helps you! ~

Add -5 to each side of the inequality:

-3 ≤ x + 5 ≤ 8

-3 - 5 ≤ x + 5 - 5 ≤ 8 - 5

-8 ≤ x ≤ 3

Since x is an integer, there are 12 possible solutions belonging to {-8, -7, ..., 1, 2, 3}. In the sum of these solutions, the integers -3 to 3 cancel out, and the rest give

-8 - 7 - 6 - 5 - 4 = -30

Answer:

Step-by-step explanation:

Comment

The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.

Formula

Sin(A) = Sin(68 = opposite / hypotenuse     Substitute values.

Solution

sin(68) = altitude (side opposite) / 20       multiply both sides by 20

20*sin(68) = 20* altitude / 20                     substitute for sin(68)

20* 0.9272 = altitude

altitude = 18.5

Answer: 18.5 to the nearest tenth

It is true that the line segment AB equals 26

The given parameters are:

AB = x +16

BC = 4x + 11

AC = 77

The two-column proof is as follows:

AC = AB + BC                     Line segment formula

77 = x + 16 + 4x + 11            Substitution property of equation

77 = 5x + 27                        Addition property of equation

5x = 50                               Subtraction property of equation  

x = 10                                    Division property of equation

AB = 10 +16                          Substitution property of equation

AB = 26

Hence, the line segment AB has been proved to equal 26

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The simple interest rate​ is 8% if the Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.

It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.

We have:

Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.

We know the formula for simple interest is:

A = p(1 + rt)

We have A(final amount) = 35000

P(initial amount0 = 25000

t(time)  = 5 years

35000 = 25000(1 + 5r)

1.4 = 1 + 5r

0.4 = 5r

r = 0.08 or

r = 8%

Thus, the simple interest rate​ is 8% if the Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.

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The probability of selecting a jack and a queen is 1/169.

Probability calculates the odds that an event would happen. The odds that the event would happen lies between 0 and 1.

The probability of selecting a jack and a queen = (number of jacks / number of cards in a deck) x (number of queens / number of cards in a deck)

4/52 x 4/52 = 1/169

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Answer:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

Step-by-step explanation:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

Answer:

3 XD

Step-by-step explanation:

The expression for the profit is -x^2/30 + 9x - 103 and the percentage profit on 20 bags of rice is 11.1%

The cost and the selling price are given as:

C(x) = 24x + 103

S(x) = 33x - x^2/30

The profit is calculated using:

P(x) = S(x) - C(x)

This gives

P(x) = 33x - x^2/30 - 24x - 103

Evaluate the like terms

P(x) = -x^2/30 + 9x - 103

Hence, the expression for the profit is -x^2/30 + 9x - 103

When x = 20, we have:

Cost: C(20) = 24 * 20 + 103 = 583

Profit: P(20) = -(20)^2/30 + 9(20) - 103 = 64.67

The percentage profit is then calculated as:

Percentage = P(x)/C(x) * 100%

This gives

Percentage = 64.67/583 * 100%

Evaluate

Percentage = 11.1%

Hence, the percentage profit on 20 bags of rice is 11.1%

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The line that contains an example of assonance is C. He fell asleep under the oak tree, feeling fine.

This refers to the similarity of sounds that can be found in nearby words in a sentence, between their vowels and/or consonants.

Furthermore, alliteration means the occurrence of similar words or sounds in a sentence at the beginning of closely connected words.

With this in mind:

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Answer: 64

Step-by-step explanation:

[tex]10x+8+5x-4=12x+16\\15x+4=12x+16\\3x+4=16\\3x=12\\x=4\\\\LN=12(4)+16=\boxed{64}[/tex]

Callie will have $104.12 less than what she earned each month.

A number which can be represented in the form p/q where q ≠ 0 are called Rational Numbers.

The complete question is

Callie was billed $416.48 for car repairs. She will pay the service center in 4 equal monthly installments from her bank account.

What is the net change in her bank account balance after each monthly payment? The net change to Callie’s bank account is -$416.48.

The negative sign indicates money leaving Callie’s account. Which rational number represents the number of months that Callie has to pay off the bill? What does the sign on the number mean?

Write an expression to represent the net change to Callie’s account balance each month.

The number of months Callie has to pay the bill is for 4 months, as there are 4 equal installments

The net change in account in Callie's Account balance each month is

-$416.48  / 4 = -$104.12.

The (-) sign indicate the reduction of the net balance from her account.

Callie will have $104.12 less than what she earned each month.

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The volume of the rectangular prism is exactly (3/8) of a cubic inch.

Remember that for a rectangular prism of height H, length L, and width W, the volume is:

V = H*L*W

In this case, we have:

Then the volume of the rectangular prism is given by:

[tex]V = (1 in)*(\frac{3}{4} in)*(\frac{1}{2} in)= \frac{3}{4*2} in^3 = \frac{3}{8} in^3[/tex]

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find D which is the discriminant and with D < 0.

therefore the equation has an imaginary root and not a real root.

Answer:

45q^10

Step-by-step explanation:

First, we can separate the equation to make it simpler to understand.

5*q^4*9*q^6

Then we group terms that we can multiply:

(5*9)*(q^4*q^6)

Then we simplify

45*q^10

45q^10

The annual percent rate(APR) to purchase a living room set for $4,900 at 8% add-on interest for 4 years is 8. 6

Using the formula

APR = ((Interest + Fees / Loan amount) / Number of days in loan term)) x 365 x 100

Note that Interest expense = Original amount / interest rate

Interest amount = $4, 900

Rate = 8% = 0. 08

Interest expense = $4, 900× 0. 08 = $392

Loan amount is also the principal amount ,  P = I / (RT)

where I is Interest Amount, R is Rate of Interest and T is Time Period.

Principal amount = $4, 900 ÷ 0. 08 × 4 = $4, 900 ÷ 0.32 = $ 15,313. 5

Substitute the values into the formula for APR

APR = [tex]\frac{392+ 4900}{15312.5} / 1460 * 365* 100[/tex]

APR = [tex]0.345 / 1460 *365*100[/tex]

APR = [tex]2. 36* 10^-4 *365* 100[/tex]

APR = [tex]8. 625[/tex]

To the nearest tenth is, 8. 6

Therefore, the annual percent rate(APR) is 8. 6

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Step-by-step explanation:

so, "- 1" is also part of the square root ?

sqrt(x - 1) = x - 3

it is clear that for any value x < 1 we have no solution in R (as this makes the argument of the square root negative, and there is so real number solution for the square root of negative numbers).

now square the whole equation.

x - 1 = (x - 3)² = x² - 6x + 9

x² - 7x + 10 = 0

the general solution for quadratic equations is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -7

c = 10

x = (7 ± sqrt(49 - 4×1×10))/(2×1) =

= (7 ± sqrt(49 - 40))/2 = (7 ± sqrt(9))/2

x1 = (7 + 3)/2 = 10/2 = 5

x2 = (7 - 3)/2 = 4/2 = 2

x2 is probably (given the answer options) not a valid solution for the original problem, as it represents the negative solution of sqrt(x - 1).

sqrt(2 - 1) = 2 - 3

± 1 = -1

remember, every square root has always 2 solutions : a positive and a negative one.

your teacher clearly only wanted the positive solution, which is x1 = 5.

so, yes,

C. x = 5

is the correct answer.

but please send your teacher my regards and comments. he/she has to state that only the positive solution to the square root is required/allowed.

because, formally, also x = 2 is a valid solution.

and therefore, C. AND D. are correct answers !!!!

Step-by-step explanation:

remember, the number of possible combinations to pick m out of n elements is C(n, m) = n!/(m! × (n-m)!)

50,000 transistors.

4% are defective, that means 4/100 = 1/25 of the whole.

so, the probability for one picked transistor to be defective is 1/25.

and the probability for it to work properly is then 1-1/25 = 24/25.

now, 500 picks are done.

to accept the shipment, 9 or less of these 500 picks must be defective.

the probability is then the sum of the probabilities to get

0 defective = (24/25)⁵⁰⁰

1 defective = (24/25)⁴⁹⁹×1/25 × C(500, 1)

= 24⁴⁹⁹/25⁵⁰⁰ × 500

2 defective = (24/25)⁴⁹⁸×1/25² × C(500, 2)

= 24⁴⁹⁸/25⁵⁰⁰ × 250×499

3 defective = 24⁴⁹⁷/25⁵⁰⁰ × C(500, 3) =

= 24⁴⁹⁷/25⁵⁰⁰ × 250×499×166

...

9 defective = 24⁴⁹¹/25⁵⁰⁰ × C(500, 9) =

= 24⁴⁹¹/25⁵⁰⁰ × 500×499×498×497×496×495×494×493×492×491 /

9×8×7×6×5×4×3×2 =

= 24⁴⁹¹/25⁵⁰⁰ × 50×499×166×71×31×55×494×493×41×491

best to use Excel or another form of spreadsheet to calculate all this and add it all up :

the probability that the engineer will accept the shipment is

0.004376634...

which makes sense, when you think about it, because 10 defect units in the 500 is only 2%. and since the whole shipment contains 4% defect units, it is highly unlikely that the random sample of 500 will pick so overwhelmingly the good pieces.

is the acceptance policy good ?

that completely depends on the circumstances.

what was the requirement about max. faulty rate in the first place ? if it was 2%, then the engineer's approach is basically sound.

it then further depends what are the costs resulting from a faulty unit ? that depends again on when the defect is usually found (still in manufacturing, or already out there at the customer site, or somewhere in between) and how critical the product containing such transistors is. e.g. recalls for products are extremely costly, while simply sorting the bad transistors out during the manufacturing process can be rather cheap. if there is a reliable and quick process to do so.

so, depending on repair, outage and even penalty costs it might be even advisable to have a harder limit during the sample test.

in other words - it depends on experience and the found distribution/probability curve, standard deviation, costs involved and other factors to define the best criteria for the sample test.

Profit percentage for weaver after selling mat is equals to 140%.

" Percentage is defined as the hundredth part of the whole given quantity. It is represented by symbol %."

Formula used

Profit% = [tex](\frac{Profit }{cost price} )[/tex]×   100

According to the question,

Given,

Cost price of bundle of grass = $50.00

Number of mats made = 8

Selling price of each mat = $15.00

Therefore,

Selling price of 8 mats = 15 × 8

                                     = $120

Selling price > Cost price

Therefore,

Profit = Selling price - Cost price

         = 120 - 50

         = $70

Substitute the value in the formula to get profit percentage we get,

Profit% = [tex]\frac{70}{50}[/tex] ×100

            = 140%

Hence, profit percentage for weaver after selling mat is equals to 140%.

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The statement that matches the vector operation shown on the coordinate grid is v + w = u.

In order to add two vectors a and b graphically by using the tail and tip method, we must draw the tail of b at the tip of vector a.

Then we must draw a line that goes from the tail of vector a to the tip of vector b.

This line represents the sum of a + b.

In the given problem, we notice that the tail of the vector w is on the tip of the vector v.

The line that joins the tail of vector v with the tip of vector w is vector u.

Therefore we can say that v + w = u

The statement that matches the vector operation shown on the coordinate grid is v + w = u.

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The domain of the function is all real numbers, the range of a function is y ≤ 4

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = –(x + 6)(x + 2)

If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.

Here the no other details are given.

But we can say:

Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4

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Answer:

Mean = 3.125 ≈ 3.13

Step-by-step explanation:

Mean = Sum of numbers =  1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13

           Amount of number                     8                             8