Please help

Solve the equation.
Give your simplified answer as an improper fraction.
7(x + 1) = 1 – 2(5 – x)
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Answer:

Gym: A=100 P=41

Cafeteria: A=144 P=48

Locker room: A=75 P= 37

Ahab's total change to funds is -$175, which means he spent more than he gained.

Ahab spent 3 tires at $50 each, which is a total of 3 x $50 = $150.

Later, he returned one tire, so he gets $50 back.

He also found a $5 bill, so he has an extra $5.

He then bought 2 jackets at $40 each, which is a total of 2 x $40 = $80.

The total amount Ahab spent is $150 + $80 = $230.

However, he also received $50 back and found $5, so his total change to funds is $50 + $5 - $230 = -$175.

Therefore, Ahab's total change to funds is -$175, which means he spent more than he gained.

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We can write g in terms of f as: g(x) = f(x) - 3 = x² - 3

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

To write g in terms of f, we can use function composition, which involves plugging the function f(x) into g(x) wherever we see x.

So, we have:

g(x) = f(x) - 3

where f(x) = x².

Substituting f(x) into g(x), we get:

g(x) = (x²) - 3

Therefore, we can write g in terms of f as:

g(x) = f(x) - 3 = x² - 3.

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A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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Answer:

Let the cost of each shirt be s.

Would assume each  shirt was discounted by 3.66

Amount to be paid for each:    s - 3.66

Total =    3*(s - 3.66)

3*(s - 3.66) = 62.31

s - 3.66 = 62.31/3

s - 3.66 =  20.77

s = 20.77 + 3.66

s = 24.43

Each shirt cost $24.43  before the discount.

Step-by-step explanation:

Answer:

for 8/24 the answer will be 1/3.

and for 8/32 the answer will be 1/4.

and for 6/30 the answer will be 1/5.

and for 12/24 the answer will be 1/2.

and for 9/21 the answer will be 3/7.

and for 5/20 the answer will be 1/4

Step-by-step explanation:

The system of equations are given as

The graph of the system of equations is

The point which is the solution is

12. Then X is 2. a continuous variable, 13. A subset of a population is 4) a sample, 14. The median is a better measure of central tendency than the mean if 2) the distribution is skewed.

Data gathering, organization, analysis, interpretation, and presentation are all topics covered in the field of statistics. It is hence customary to start with a statistical population or a model to be studied when using stats to solve a scientific, industrial, or social problem.

There are as of now two main types of statistical analysis: descriptive stats explains and visualizes the data you have, while inferential stats extrapolates the data you have to a larger population.

Statistical analysis has a number of advantages for businesses, including cost-cutting and increased productivity. The central tendency measure and the dispersion measure are fundamental concepts in stats.

Mean, median, and mode are the three primary central tendencies, and variance and standard deviation are the main central dispersions. The observational average is referred to as mean. When observations are arranged in order, the median represents the central value.

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A is either 45° or 135°.

To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.

Using the distance formula, we have:

AB² = x₁² + y₁²

AC² = x₂² + y₂²

According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:

(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]

Expanding and simplifying the equation, we get:

x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)

This equation can be further simplified to:

(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)

Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.

In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.

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Answer:

The probability that at least one of the 5 donors has Group O blood type is 0.9497.

Step-by-step explanation:

We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.

The probability that exactly k donors have Group O blood type in the sample can be written as:

\(P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{5}{k} 0.45^{k} 0.55^{5-k}\\\\\\\)

We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:

\(P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497\)

Answer:

A) 0.5

B) 10

Step-by-step explanation:

A) First, you need to Combine Like Terms on the right side of the =

98-248 = -150

Now, you need to Isolate the variable by getting rid of the -178. What you do to one side, you must do the the other.

56a-178(+178) = -150(+178)

56a = 28

Finally, you must remove that 56 on the a. Since it stands for 56 x a, you must do the same you did with the -178 except with Division.

56a/56 = 28/56

a = 0.5

B) Combine Like terms

640+70 = 710

Isolate the variable

710(-20) = 69y+20(=20)

690 = 69y

Remove the 69 with division

690/69 = 69y/69

10 = y

Answer:

Step-by-step explanation:

Hello,

\(-2a^2b+a^2-5ab+3ab^2-b^2+2(a^2b+2ab)\\\\=-2a^2b+a^2-5ab+3ab^2-b^2+2a^2b+4ab\\\\=a^2+3ab^2-ab-b^2\)

Thanks

Answer:

900 eggs

Step-by-step explanation:

75x12=75x10=750

          75x2  =150

total=750+150=900 eggs

Answer:

approximately 7 cm

Step-by-step explanation:

I’m not absolutely sure so double check

The expression factors completely into (9 + 2x)(9 - 2x).

What is factorization?

Factorization is the process of expressing a mathematical expression as a product of simpler expressions or factors. In other words, it is the process of breaking down a complex expression into smaller, more manageable pieces. This is an important technique in algebra and other branches of mathematics because it allows us to simplify expressions, solve equations, and understand the properties of functions and equations.

We can write the given expression as the difference of two squares:

81 − 4x^{2} = (9)^{2} − (2x)^{2}

Using the formula for the difference of two squares, we can factor this

expression as:

81 − 4x^{2} = (9 + 2x)(9 - 2x)

Therefore, the given expression factors completely into (9 + 2x)(9 - 2x).

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Answer:

y = -4/9x - 10/9

Step-by-step explanation:

(-7, 2) and (2, -2)

slope: y2-y1/x2-x1

-2-2 / 2+7

-4/9

y = mx + b

y = -4/9x + b

plug in (2,-2)

-2 = -8/9 + b

b = -10/9

y = -4/9x - 10/9

Answer:

\(y=-\frac{4}{9} x-\frac{10}{9}\)

Step-by-step explanation:

(-7, 2) and (2, -2)

Slope:

m=(y2-y1)/(x2-x1)

m=(-2-2)/(2+7)

m=(-4)/9

m= -4/9

y - y1 = m(x -x1)

y - 2 = -4/9(x + 7)

y - 2 = -4/9x - 28/9

y = -4/9x -10/9

The distance between the points (-1, 5) and (-7, -3) is 10 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Point 1 (-1,5)

Point 2 (-7,-3)​

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √[(-7 - (-1))² + (-3 - 5)²]

D = √[(-7 + 1)² + (-3 - 5)²]

D = √[-6² + (-8)²]

D = √[36 + 64]

D = √100

D = 10

Therefore, the distance is 10 units.

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Answer:

1. No

2. yes

3. yes

4. yes

Step-by-step explanation:

1. 2×3=6, 7×3=21 (The product of two (or more) prime numbers cannot result in another prime number. By definition, a prime number is a number that is divisible by 1 or itself - multiplying two or more primes together will always yield a number divisible by 1, itself and the prime numbers multiplied together to achieve it.

2.When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.

3. 1×3=3, 3×5=15 (odd numbers are not divisible by 2)Therefore, every prime number other than 2 is an odd number

4. 2×4=8, 6×8=48

Answer:

Question 1: Add the volumes

100 + 80 = 180 meters^3

Questions 2: Subtract the volumes

100 - 80 = 20 meters^3

Step-by-step explanation:

The formula for volume is:

V = lwh

The volume for figure A:

V = 5 x 5 x 4

V = 100 meters^3

The volume for figure B:

V = 4 x 4 x 5

V = 80 meters^3

Question 1: Add the volumes

100 + 80 = 180 meters^3

Questions 2: Subtract the volumes

100 - 80 = 20 meters^3

Answer:

first multiply 2 by 1 then devide both sides easyyyy

The value of square root of x + y squared + z squared is 30

x = 2, y = 3 and z = -5

\(( \sqrt{x + y} )^{2} + z ^{2} \)

substitute the value of x, y and z

\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)

simplify the square root and square

\( = (2 + 3) + 25\)

\( = 5 + 25\)

\( = 30\)

Ultimately, x + y squared + z squared is 30

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Answer: 2

Step-by-step explanation:

Answer:

the answer is 2

a)The smaller break even quantity is 10

b)The quantity that must be sold to maximize the profit= 14.25

c)The maximum profit = $36.13

STEP - BY - STEP EXPLANATION

What to find?

• The smaller break even quantity is

• The quantity that must be sold to maximize the profit

• The maximum profit.

Given:

C(x)= 13x + 370

R(x)=70x - 2x²

a) At the break even quantity, the revenue = cost, that is no profit and no loss.

R(x) = C(x)

So that we have;

70x - 2x² = 13x + 370

Re-arrange.

-2x² + 70x - 13x - 370 =0

-2x² +57x - 370 =0

2x² - 57x + 370 = 0

We can now solve the quadratic equation above.

Using the qudaratic formula

a=2 b=-57 c=370

Substitute the values into the formula and evaluate.

Or

x = 37/2 or x=10

We take the smaller value.

Hence, x=10

Therefore, the smaller break even quantity is 10.

b)To find the quantity that will maximize the profit, find the profit function.

p(x) = R(x) - C(x)

P(x) = 70x - 2x² - (13x +370)

= 70x - 2x² - 13x - 370

P(x) =-2x² + 57x - 370

Equate to zero

-2x² + 57x - 370 = 0

2x² - 57x + 370 =0

The maximum is at x = -b/2a

b= -57 and a=2

Substitute the values

x= - (-57) /2(2)

x= 57 /4

x= 14.25

c) To find the maximum profit, simply substitute x=14.25 into the profit function and simplify.

That is;

P(x) =-2x² + 57x - 370

P(14.25) =-2(14.25)² + 57(14.25) - 370

= -406.125 + 812.25 - 370

= 36.125

≈ 36.13

Hence, the maximum profit is $36.13

Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option

A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.

The figure is a composite figure comprising of a square and a circle

The radius of the circle, r = 5 meters

The side length of the square = 10 meters

The value of π = 3.14

The area of the square = 10 m × 10 m = 100 m²

The area of the circle = π × (5 m)² = 25·π m²

The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;

The area of the shaded region = (100 - 25·π) m²

The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²

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