please help!!! Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents.


Month f(x) = No. of imports g(x) = No. of exports
January (1). 2 3
February (2) 4 4
March (3) 6 5
April (4) 8 6

Answer:

11331 non fiction books

Step-by-step explanation:

Given :

Total books = 67982

Childrens section = 1/3 of total

Number of children's books :

(1/3 * 67982) = 22660 books (approximately)

Books left :

67982 - 22660 = 45,322 books

Fiction books:

75% of remaining

0.75 * 45322

33991.5

= 33991 books

If the only section left is non - fiction, then

Non - fiction books = (45322 - 33991) = 11331

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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Answer:

0.0093 square inches

Step-by-step explanation:

The value of p when q is 2 is 1

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means that has x increases y will decrease and vice versa.

If p is inversely proportional to q , then p = kq

when p = 2, q = 4

2 = k4

k = 2/4

k = 1/2

When q = 2

p = 1/2 × 2

p = 1

Therefore the value of p is 1

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Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

The nearest foot is 19

Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

The most appropriate choice for combination will be given by-

Models can wear 112 different types of outfit.

What is combination?

Combination determines the number of ways of selecting some number of particular items from a group of given item, here the order of selection do not matter.

If there are n objects and from there, r objects are chosen, number of ways will be given by

                                  \(n \choose r\) = \(\frac{n!}{(n - r)! \times r!}\)

Here,

Number of tops = 7

Number of pants = 2

Number of jackets = 8

From 7 tops the designer can choose 1 top in \(7 \choose 1\) ways

                                                                        = \(\frac{7!}{(7-1)!\times 1 !}\)

                                                                        = \(\frac{7!}{6!}\)

                                                                        = \(7\)

From 2 pants the designer can choose 1 pant in \(2 \choose 1\) ways

                                                                        = \(\frac{2!}{(2-1)!\times 1 !}\)

                                                                        = \(\frac{2!}{1!}\)

                                                                        = \(2\)

From 8 jackets the designer can choose 1 jacket in \(8 \choose 1\) ways

                                                                        = \(\frac{8!}{(8-1)!\times 1 !}\)

                                                                        = \(\frac{8!}{7!}\)

                                                                        = \(8\)

Total number of different outfits models can wear = \(7 \times 2 \times 8\)

                                                                             = 112

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Answer:

70,000

Step-by-step explanation:

Median= 345,000

Higest selling house= 415,000

415,000-345,000= 70,000

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer

Inverse trig will be used to solve for this unknown angle.

Unknown angle = 32.6°

Explanation

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

For this question,

Hypotenuse = 38

Opposite = ?

Adjacent = 32

So, to get the angle marked, we will use inverse-trig to say CAH means

Cos x = (32/38)

x = Cos⁻¹ (32/38)

x = 32.6°

Hope this Helps!!!

1.)

a. The probability that a randomly selected value will be greater than 1,550 is 0.0026 or about 0.26%.
b. The probability that a randomly selected value will be less than 1,430 is 0.00005 or about 0.005%.

c. The probability that a randomly selected value will be between 1,380 and 1,620 is approximately 1 or 100%.

d. The lowest value of the upper 35% of the random variable is approximately 1,507.93.

2.)

a. The area below 80 is approximately 0.6293 or 62.93%.

b. The area below 95 is approximately 0.9082.

c. The area below 68 is approximately 32.12%.

d. The area below 99 is approximately 5.48%.

What is probability?

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain.

1)

a. We need to find the probability that a randomly selected value will be greater than 1,550. We can use the standard normal distribution to calculate this probability. First, we need to standardize the variable X using the formula:

Z = (X - μ) / σ

where X is the variable, μ is the mean, and σ is the standard deviation.

So,

Z = (1550 - 1500) / 18 = 2.78

Using a standard normal distribution table or calculator, we find that the probability of a Z-score being greater than 2.78 is approximately 0.0026.

Therefore, the probability that a randomly selected value will be greater than 1,550 is 0.0026 or about 0.26%.

b. Similarly, we can find the probability that a randomly selected value will be less than 1,430 by standardizing the variable and using the standard normal distribution table or calculator.

Z = (1430 - 1500) / 18 = -3.89

Using the standard normal distribution table or calculator, we find that the probability of a Z-score being less than -3.89 is approximately 0.00005.

Therefore, the probability that a randomly selected value will be less than 1,430 is 0.00005 or about 0.005%.

c. To find the probability that a randomly selected value will be between 1,380 and 1,620, we first need to standardize the variables.

Z1 = (1380 - 1500) / 18 = -6.67

Z2 = (1620 - 1500) / 18 = 6.67

Using the standard normal distribution table or calculator, we find the probability of a Z-score being less than -6.67 is very close to 0 and the probability of a Z-score being greater than 6.67 is also very close to 0. Therefore, the probability of a Z-score being between -6.67 and 6.67 is approximately 1.

Therefore, the probability that a randomly selected value will be between 1,380 and 1,620 is approximately 1 or 100%.

d. We need to find the lowest value of the upper 35% of the random variable. To do this, we need to find the Z-score that corresponds to the 65th percentile (since the upper 35% is the complement of the lower 65%).

Using the standard normal distribution table or calculator, we find that the Z-score corresponding to the 65th percentile is approximately 0.385.

So,

0.385 = (X - 1500) / 18

Solving for X, we get:

X = 1500 + (0.385 x 18) = 1507.93

Therefore, the lowest value of the upper 35% of the random variable is approximately 1,507.93.

2.)

a. The standard value for X = 80 can be calculated as follows:

Z = (X - μ) / σ

Z = (80 - 75) / 15 = 0.33

The area below 80 can be found using the standard normal distribution table or calculator.

P(Z < 0.33) = 0.6293

Therefore, the area below 80 is approximately 0.6293 or 62.93%.

b. For X = 95, we can calculate the standard value and find the area below 95 using the same method as in part (a).

Z = (95 - 75) / 15 = 1.33

Using a standard normal distribution table or calculator, we can find the area below 95 to be approximately 0.9082. Therefore, the answer is:

b. The area below 95 is approximately 0.9082.

c. For X = 68, we can calculate the standard value and find the area above 68 as follows:

Z = (68 - 75) / 15 = -0.47

Using a standard normal distribution table or calculator, we can find the area above -0.47, which is equivalent to the area below 0.47, as 0.3212 or approximately 32.12%.

d. For X = 99, we can calculate the standard value and find the area above 99 as follows:

Z = (99 - 75) / 15 = 1.6

Using a standard normal distribution table or calculator, we can find the area above 1.6 as 0.0548 or approximately 5.48%.

Hence,

1.)

a. The probability that a randomly selected value will be greater than 1,550 is 0.0026 or about 0.26%.
b. The probability that a randomly selected value will be less than 1,430 is 0.00005 or about 0.005%.

c. The probability that a randomly selected value will be between 1,380 and 1,620 is approximately 1 or 100%.

d. The lowest value of the upper 35% of the random variable is approximately 1,507.93.

2.)

a. The area below 80 is approximately 0.6293 or 62.93%.

b. The area below 95 is approximately 0.9082.

c. The area below 68 is approximately 32.12%.

d. The area below 99 is approximately 5.48%.

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Step-by-step explanation:

Hope you understand this

2 feet: 3 inches

1 feet: 3/2 inches

4*5 feet: 3x4*5/2

=6.75 Inchea

Answer:

∠1 = ∠8

Step-by-step explanation:

Because they are ALTERNATE EXTERIOR ANGLE

Answer:

∠1 = ∠8

Step-by-step explanation:

Because alternate exterior angles are equal.

Also there is no angle given so you cant work them out.

simply put:

∠1 = ∠8

∠1 = ∠4

∠3 = ∠2

∠1 = ∠5

∠2 = ∠6

∠2 = ∠7

∠5 = ∠8

∠4 = ∠8

∠7 = ∠6

∠7 = ∠3

Let me know if I missed out on anymore! It was long that's why.

Hope this kind of explained it :)

The number 1234567 cannot be written as a sum of two squares.

Let q = x^2+y^2,

Let a and b be two even numbers, such that

a= 2x and b = 2y

then

n = (2x)^2 + (2y)^2 = 4 (x^2+y^2)

implies n = 4q

Let a and b be two odd numbers, such that

a = 2x+1 and b = 2y+1

then

n = (2x+1)^2 + (2y+1)^2 = 4x^2+4y^2+1 = 4q+2

Let a be an even number and b be an odd number, such that

a= 2x and b = 2y+1

then

n = (2x)^2 + (2y+1)^2 = 4q+1

But, the given number 1234567 = (4×308641)+3 which is of the form 4q+3, hence it cannot be written as the sum of two squares.

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Answer:

10.3 years

Step-by-step explanation:

The Rule of 72 is a rule used to determine the period of time it would take an investment to double at a given fixed annual rate of return. The rule of 72 helps investors to have an estimate of how long an initial investment would double. The rule of 72 is given by the formula:

t = 72 / r

where r is the annual rate of return and t is the approximate time in years required for the investment to double.

t = 72 / r

Given that r = 7%

t = 72 / r = 72 / 7 = 10.3 years

Therefore it would take 10.3 years for an investment of $5,000 earning 7% annually to double to about $10,000

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

Step-by-step explanation:

8x^2 + xy - 8xy - y^2

8x^2 - 7xy - y^2

Answer: he has 4 apples now

Step-by-step explanation:

He has 12 apples to begin with and he gives away 8 to his friend

So, 12 - 8

This gives you 4

Answer:

4

Step-by-step explanation:

12 - 8 = 4

To double check: 8 + 4 = 12

Have an amazing day!

PLEASE RATE!!

Answer:

25% were knives

Step-by-step explanation:

Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

Answer:

1 solution

Key:

Assume x is the the range x > 0 ≥ 1, in other words, assume x is equal to 1.

Step-by-step explanation:

\(y = -x - 8x - 16\\= -x - 8x\\= 9x\\= 9x - 16\)

Answer:

The slope is 1/2.

Step-by-step explanation:

To find the slope of a line, use the equation (y2-y1 / x2-x1)

Let's say (4,3) is x2 and y2. That means (0,-2) is x1 and y1.

(3 - 0) / (4 - -2)

(3 - 0) / (4 + 2)

3/6, which simplifys to 1/2

Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.

Therefore option A is correct.

The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.

With reference to the table, the occupations that do not require a college degree are:

We were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.

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The solution to the system of inequalities 2x − y < 4 and x + y < −1 is the intersection of the shaded regions below the lines 2x - y = 4 and x + y = -1, labeled AB on the graph. Regions A and B represent the solutions to each individual inequality.

To solve the system of inequalities 2x − y < 4 and x + y < −1, we can use the following steps

Solve each inequality for y in terms of x

2x - 4 < y

-x - 1 < y

Plot the boundary lines for each inequality as dotted lines. To do this, we can use the equality signs instead of the inequality signs.

2x - 4 = y

-x - 1 = y

Shade the region that satisfies each inequality. To do this, we can test a point that is not on the boundary line in each inequality. For example, we can test (0,0) in the first inequality

2(0) - 0 < 4

0 < 4

Since (0,0) satisfies the first inequality, we shade the region below the line 2x - y = 4. Similarly, we can test (0,-2) in the second inequality

(0) + (-2) < -1

-2 < -1

Since (0,-2) satisfies the second inequality, we shade the region below the line x + y = -1.

The solution to the system of inequalities is the intersection of the shaded regions, which is labeled AB in the graph. The shaded region labeled AB is the region that satisfies both inequalities, which is the region below both lines.

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Answer:

x=6

Step-by-step explanation:

7+5(×-3)=22

expand the brackets:

7 + 5x - 15 = 22

simplify:

5x - 8 = 22

add 8 to both sides:

5x = 30

divide both sides by 5

x = 6

hope this helps

brainliest plz?

x

Answer:

7+5 (x-3)=22

7+5x-15=22

5x+ -8=22

5x=30

x=6

Step-by-step explanation:

PEMDAS

First distribute in the parentheses

Then add like terms together

once you have -8, add it on both sides

then divide 5 from both sides to leave the unknown variable by itself

Finally you have the answer

I hope this helps! :)