10. Sarah and three friends were hired to organize books in the library. The librarian divided the amount paid equally between the four of them. Each person received $16. Write an equation for this situation. How much did the librarian pay all together?

The value of the expression in scientific format is 6.3 x 10¹⁷

From the question, we have the following parameters that can be used in our computation:

(9x10 to the 7th power) (7x10 to the 9th power)

To start with, we need to represent the above expression using numbers and mathematical operators

So, we have the following representation

(9 x 10⁷) (7 x 10⁹)

Next, we combine the brackets using a product sign

This gives

(9 x 10⁷) x (7 x 10⁹)

Next, we remove the brackets from the expression

This gives

9 x 10⁷ x 7 x 10⁹

Evaluate the products of 9 and 7

63 x 10⁷ x 10⁹

Apply the law of indices to evaluate the final products

63 x 10¹⁶

Rewrite as

6.3 x 10¹⁷

Hence, the solution is 6.3 x 10¹⁷

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Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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To find a(100), the values of functions a(1), a(2)....... a(99) must be calculated

Recursive functions are functions that derive their value from with the function formula

This means that the current term of a recursive definition is dependent on the previous terms

The recursive function is given as

a(100)

This means that the current term of the recursion is 100

As stated above that:

The current term of a recursive definition is dependent on the previous terms

This means that we must find the previous terms before we can find a(100)

In this case, it means that we must determine the values of functions a(1), a(2)....... a(99), before the value of a(100) can be calculated

Hence, to find a(100), the values of functions a(1), a(2)....... a(99) must be calculated

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Answer:$2

Step-by-step explanation:

For the function f(x) = x³ - 6x², we have that:

In the context of this function, we have that it is increasing to the left of x = 0 and to the right of x = 4, hence the interval is given by:

(-∞, 0) U (4, ∞).

On the remaining interval, that is, (0,4), the function is decreasing.

The critical points are given as follows:

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Step-by-step explanation:

2(5x + 4) = 8

[10]x +[8]= 8

The inverse of f(x) is f⁻¹(x) = (x - 3)/3.

To find the inverse of the function f(x), we need to switch the roles of x and y and solve for y.

Given:

f(x) = 3x + 3

Step 1: Replace f(x) with y:

y = 3x + 3

Step 2: Swap x and y:

x = 3y + 3

Step 3: Solve for y:

x - 3 = 3y

3y = x - 3

y = (x - 3)/3

Therefore, the inverse of f(x) is f⁻¹(x) = (x - 3)/3.

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The sequence of the terms is -7,-1+5, and +11. A series is a collection of sequences.

A sequence is a collection of items that have been arranged in a logical order, with members appearing either before or after each other.

Given equation ;

\(\rm a_n = a_{n-1}+6\)

If,

\(\rm a_1 = -13\)

The next term in the sequence is;

\(\rm a_2 = a_{2-1}+6 \\\\ \rm a_2 = a_{1}+6 \\\\ a_2 = -13 +6 \\\\ a_2 =-7\)

\(\rm a_3 = a_{3-1}+6 \\\\ \rm a_3 = a_{3}+6 \\\\ a_3 = -7 +6 \\\\ a_3 =-1\)

\(\rm a_4 = a_{4-1}+6 \\\\ \rm a_4 = a_{3}+6 \\\\ a_4 = -1 +6 \\\\ a_4 =+5\)

\(\rm a_5 = a_{5-1}+6 \\\\ \rm a_5 = a_{4}+6 \\\\ a_5 = 5 +6 \\\\ a_5 =11\)

Hence, the sequence of the terms is -7,-1+5, and +11.

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Answer: Pretty sure it's A

Step-by-step explanation: If you find the square root of 282 you get 16.7

Answer:

It is A

Step-by-step explanation:

It is A because you need to take the square roots of every number the square root of 282 is 16.7985562

Answer:

(-5, 5)

Step-by-step explanation:

The function increases from x = -11 to x = -5.

The function decreases from x = -5 to x = 5.

the function increases from x = 5 to x = 11.

Answer: (-5, 5)

Answer:

  (d)  240/289

Step-by-step explanation:

The trig identity for the sine of a double angle can be used to find the desired value.

  sin(2θ) = 2sin(θ)cos(θ)

__

The cosine of this 3rd-quadrant angle is negative:

  cos(θ) = -√(1 -(-8/17)²) = -(√(289 -64))/17 = -15/17

Then the desired sine value is ...

  sin(2θ) = 2(-8/17)(-15/17) = 240/289

_____

Additional comment

The attached calculator result comes from the principal value of the arcsine function resulting in a 4th-quadrant angle for negative sine values. Double that angle will still be a 4th-quadrant angle. When the translation is made to the appropriate quadrant, the desired double angle will be a 1st-quadrant angle with a positive sine.

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

Kenyon could make a total of 7 bouquets.

Step-by-step explanation:

To find the greatest number of bouquets we need to find GCF.

We need to find GCF for 21 and 28.

The factors of 21 are: 1,3,7, and 21.

The factors of 28 are: 1,2,4,7,14, and 28

1 and 7 are the common factors between 21 and 28.

From the factors, the greatest common factor is 7.

The area between 415 pounds and a mean of 400 pounds is 0.4332, The area between the mean and 395 pounds is 0.1915 and the probability of selecting a value at random and discovering that it has a value of less than 395 pounds is:  0.3085.

Given data:

Mean = 400 pounds

Standard deviation = 10

a. Area

First step is to find the z-score

z = 415 - 400 / 10

z = 15 /10

z = 1.5

Hence,

P(400 < x < 415) = P(0 < z < 1.5) =   0.4332

b. Area

First step is to find the z-score

z = 395 - 400 / 10

z = -5 /10

z = -0.5

Hence,

P (395 < x < 400) = P (-0.5 < z < 0) = P (0 < z < 0.5) = 0.1915

c. Probability

P (x < 395) =  P (z < -0.5)

P (x < 395) = 0.5 - P (-0.5 < z < 0)

P(x < 395) = 0.5 - P (0 < z < 0.5)

P(x < 395) = 0.5 - 0.1915

P(x < 395) = 0.3085

Therefore the area is 0.4332 , 0.1915 and the probability is 0.3085.

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The complete question  is :

The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds.

a. What is the area between 415 pounds and a mean of 400 pounds?

b. What is the area between the mean and 395 pounds?

c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

Answer:

it will produce 6400 newspapers

Step-by-step explanation:

800 x 8 = 6400

Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

Answer:

The expected number of hunters who hit the duck they aim at is 3.6

Step-by-step explanation:

Given;

number of hunters, n = 6

the probability of killing a duck, p = 0.6

The expected number of hunters who hit the duck they aim at?

In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.

The expected number of hunters who hit the duck they aim at is calculated as follows;

E = np

E = 0.6 x 6

E = 3.6

Therefore, the expected number of hunters who hit the duck they aim at is 3.6

Answer:

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Step-by-step explanation:

I clicked on the black picture. thought is was the box to enter the answer.

The length of line having mid point B ⇒  7x - 2.

Given that,

B is the mid point of AC

And also given that

length of segment AB = 2x+5

And length of segment BC = 5x - 7

A straight path established by linking a group of points in a plane is known as a line. It is a one-dimensional form with only a length and no width or height. A line can extend indefinitely in both ends in opposite directions. To indicate a line, we can use upper case characters.

Now since B is the mid point of AC,

So, The line AC is sum of the line segment AB and line segment BC.

Therefore,

AC = AB+BC

     = (2x+5)+(5x - 7)

     = 7x - 2

Hence,

The length of AC is 7x - 2

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The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

The population propose will match the pattern mean's proposal. The population trendy deviation divided by the rectangle root of the sample length yields the same results as the standard deviation of the distribution of the sample means, also known as the same old mistakes of the proposed (n).

The general sample recommends factors to be included in the pattern mean calculation.

The population suggest is calculated using the sum of all values within the population denoted with the aid of the summation of X divided by the number of values in the population that is denoted with the aid of N. The population suggest is the mean or average of all values within the given population.

Therefore,

The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

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Answer:

y = -3x + 10

Step-by-step explanation:

slope of perpendicular line = -3

y-1 = -3(x-3)

y-1 = -3x + 9

y = -3x + 9 + 1

y = -3x + 10

Answer:

Step-by-step explanation:

tan x= opp./adj.

tan x = 12/5 so

     x = tan^-1 (12/5)

second choice

Answer:

B

Step-by-step explanation:

Answer:

B C F

Step-by-step explanation:

If you reduce those answer and try to find the square roots, the decimals are terminating and never ending, while the others are perfect squares.

Answer:

true

Step-by-step explanation:

plz mark brainlyest

Carissa's salary when she sells $2,400 worth of merchandise is $732.

The first step is to determine the base pay and the commission rate.

In order to determine these values, form a system of equations that represent the information in the question:

a + 500b = 390 equation 1

a + 100b = 480 equation 2

Where:

a = base pay

b -= commission rate

Subtract equation 1 from equation 2:

500b = 90

Divide both sides by 500:

b = 90 / 500

b = 0.18

Substitute for b in equation 1:

a + 500(0.18) = 390

a + 90 = 390

a = 390 - 90

a = 300

Salary = 300 + (0.18 x 2400)

Salary = 300 + 432 = $732

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