8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.

(h+3)² simplified is:(h+3)² = h² + 6h + 9

What is binomial?

Binomial refers to a type of probability distribution that describes the number of successes in a fixed number of independent trials.

The expression (h+3)² is a binomial squared. When we square a binomial, we use the formula:

(a+b)² = a² + 2ab + b²

where a and b are any numbers or variables. In this case, our binomial is (h+3), so we can use the formula with a=h and b=3:

(h+3)² = h² + 2h3 + 3²

The first term, h², comes from squaring the h in the binomial. The second term, 2h3, comes from multiplying the two terms in the binomial together and then doubling the result. Finally, the third term, 3^2, comes from squaring the 3 in the binomial.

Simplifying the expression, we can combine like terms. We have h² as the first term, 23h as the second term, and 3^2 as the third term. 23h is equal to 6h, so we can rewrite it as:

(h+3)² = h² + 6h + 9

And that is the simplified form of the expression (h+3)².

Therefore,  (h+3)² simplified is:(h+3)² = h² + 6h + 9

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The empirical probability of rolling a 2 should approach 1/6 as the number of trials increases.

The empirical probability of an event is the number of times the event occurs in a given number of trials divided by the total number of trials.

Since a fair die has six equally likely outcomes, the probability of rolling a 2 on a single roll is 1/6.

Therefore, if Shawn rolls the die many times, the empirical probability of rolling a 2 should approach 1/6 as the number of trials increases.

For example, if Shawn rolls the die 100 times and gets a 2 on 16 of those rolls, the empirical probability of rolling a 2 would be:

Empirical probability = Number of times event occurred / Total number of trials

Empirical probability = 16 / 100

Empirical probability = 0.16 or 16%

The empirical probability of Shawn rolling a 2 in a die is dependent on the number of trials or rolls of the die.

As the number of trials or rolls increases, the empirical probability should approach the theoretical probability of 1/6.

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Answer:

B. 15x - 45 = 15x + 75

Step-by-step explanation:

B. 15x - 45 = 15x + 75

15x = 15x + 120

0 = 120

This is wrong, so option B has no solution.

All the other options have solutions. Only option B has no solution!

Answer: B has no solution

Step-by-step explanation: since 15x - 15x = 75 +45 ' meaning 0= 120 giving us no solution, the rest of the options have solutions

The similes in the story are:

A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.

Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.

Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.

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Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:

(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth

To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:

(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth

To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):

50/16 = 3.125 gallons of milk

30/16 = 1.875 gallons of broth

Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.

Step-by-step explanation:

2298 divided by 24 using long division shows what is the quotient and remainder while 2298 divided by 24 and the complete steps for how to find it.

Question:

2298/24 = (?)

what is 2298 divided by 24?

the quotient is 95 and the remainder is 18 when 2298 is divided by 24.

Answer:

To find the height of the building, we can use the following formula:

height = y(d-x)/x

Substituting the given values, we get:

height = 6(6-3)/3

height = 6(3)/3

height = 6 meters

Therefore, the height of the building is 6 meters.

1267.1 ml = 1.2671 L.

A little amount of liquid is measured in milliliters. You can utilize liters for larger amounts of liquid. One milliliter, or 1 ml, is equal to one liter. Milliliter can be written as ml or mL.

Large amounts of liquid are measured in liters. Kg is the unit for measuring mass, m is the unit for measuring length, and km is the unit for measuring distance among the ones provided.

To convert milliliters (ml) to liters (L), we divide the number of milliliters by 1000:

1267.1 ml ÷ 1000 = 1.2671 L

Therefore, 1267.1 ml is equal to 1.2671 L.

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1267.1mL is equal to 1.2671 L.

The term "equal" is used to indicate that two values or expressions have the same numerical value or meaning. When we say that two quantities are equal, we mean that they are exactly the same in terms of their value or magnitude. This is denoted by the symbol "=". For example, if we say that 2 + 3 = 5, we mean that the sum of 2 and 3 is exactly equal to 5. Similarly, if we say that x + 4 = 10, we mean that the value of x that satisfies this equation is exactly equal to 6. The concept of equality is fundamental to many areas of mathematics, including algebra, calculus, and geometry.

1L =1000mL

1mL=(1/1000)L

Therefore 1267.1 mL= (1267.1/1000)L

So, 1267.1 mL= 1.2671L

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Nora covered a total distance of 13 miles during these sessions.

The parameter is represented by the line plot.

We can find the following frequency table from the line plot:

Distance   Frequency

0                    0

1/2                  4

1                     3

1 1/2               1

2                    2

2 1/2               1

3                    0

The overall separation from the line plot is then shown as

Total distance = sum of the distance-frequency product

The following equation can be found in mathematics.

Total distance = (0 * 0) + (1/2 * 4) + (1 * 3) + (1 1/2 * 1) + (2 * 2) + (2 1/2 * 1) +

(3 * 0)

Rank the total number of products

Total distance = 13

The total distance is therefore 13 units.

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Answer:

AB: y = 2x + 4

Step-by-step explanation:

Line AB is parallel to the line y = 2x + 3

When 2 lines are parallel they have the same coefficient of x.

=> AB: y = 2x + m (1)

Because line AB passes through the point (0, 4)

Replace x = 0; y = 4 into (1) => 2 × 0 + m = 4 => m = 4

So AB: y = 2x + 4

2x + 3/x + 5 is the value of expression .

What is an expression in mathematics?

A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:

                                     The expression is (number/variable, arithmetic operator, number/variable). For example, x + y is an expression whose term has an addition operator between x and y. There are two kinds of formulas in mathematics. Numeric expression - contains only numeric values. An algebraic expression containing both numbers and variables.  

g(x) = -5+2x/1+x

g(x+4) = -5+2(x + 4)/1+(x + 4 )

          = -5 + 2X + 8/1 + X + 4

          = 2x + 3/x + 5

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The absolute maximum value of f(x) is 4.5 and it occurs at x = -0.5, and the absolute minimum value of f(x) is -0.241 and it occurs at x = 0.833

To find the absolute maximum and minimum of the function f(x) = 4x^3 - 2x^2 - 5x + 3, we need to take the derivative of the function and set it equal to zero to find the critical points.

f(x) = 4x^3 - 2x^2 - 5x + 3

f'(x) = 12x^2 - 4x - 5

Setting f'(x) = 0, we get:

12x^2 - 4x - 5 = 0

Using the quadratic formula, we get:

x = -0.5 or x = 0.833

Now we need to check the values of f(x) at the critical points and the endpoints of the interval

f(-0.5) = 4(-0.5)^3 - 2(-0.5)^2 - 5(-0.5) + 3 = 4.5

f(0.833) = 4(0.833)^3 - 2(0.833)^2 - 5(0.833) + 3 = -0.241

So the absolute maximum it occurs at x = -0.5, and the absolute minimum occurs at x = 0.833

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Since the discriminant is negative, the equation has two complex conjugate roots is -19.

To find complex conjugate roots of a polynomial, you can follow these steps:

Identify the complex roots of the polynomial: Use the quadratic formula or any other method to find the roots of the polynomial. If the roots are complex, they will be of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Check for conjugate pairs: If a complex root is of the form a + bi, then its complex conjugate will be a - bi. Check if the polynomial has any other root of the form a - bi. If so, then the two roots are complex conjugates.

For example, suppose you have a polynomial with the equation:

[tex]x^3 - 4x^2 + 7x - 10 = 0[/tex]

Using a calculator or other methods, you can find that one of the roots of this polynomial is approximately 1.72 + 0.98i. To check if this is part of a complex conjugate pair, you can check if the polynomial has another root of the form a - bi.

One way to do this is to use polynomial long division to divide the original polynomial by the quadratic factor (x - (1.72 + 0.98i)) (x - (1.72 - 0.98i)).

To determine the number and type of roots of the equation x^2 - 3x + 7 = 0, we need to use the discriminant, which is given by the formula b^2 - 4ac.

In this case, a = 1, b = -3, and c = 7. Substituting these values into the formula, we get:

[tex]b^2 - 4ac = (-3)^2 - 4(1)(7) = 9 - 28 = -19[/tex]

Since the discriminant is negative, the equation has two complex conjugate roots.

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Answer:

5 degrees

Step-by-step explanation:

88-83=5

Emily's situation can be represented by the linear-equation in y =  [tex]\frac{-1}{10}[/tex]x + 15, where 'x' represents the time in seconds & 'y' represents the number of steps.

What is linear-equation?

An equation is linear if the maximum power or the degree of equation or of the variable is 1. The equation forms a straight line on the graph. A linear equation in one variable has the general or standard form mx + b = 0, where'm' stands for the slope and 'b' for the intercept.

To form a linear equation using points on the graph, we can use the general form as y=mx+b or [tex]\frac{Y-Y1}{X-X1}[/tex] =[tex]\frac{Y2-Y1}{X2-X1}[/tex]

The y intercept(b), is 15 as the linear graph intersects y-axis at (0,15)

b=15

For slope m, we can use point (150,0)

Substituting coordinates of point in equation y = mx + b

y = mx + b

0 =m(150) + 15

0 = 150m + 15

150m = -15

m = [tex]\frac{-15}{150}[/tex]

m = [tex]\frac{-1}{10}[/tex]

Using the slope & intercept to form equation:

y =  [tex]\frac{-1}{10}[/tex]x + 15

Where 'x' denotes time in seconds & 'y' denotes number of steps.

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Refer to the attachment for the complete question.

The perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

To find the perimeter of the regular octagon inscribed in a circle with radius 14 inches, we need to use the formula:

Perimeter of octagon = 8 x length of one side

Since the octagon is regular, all sides are congruent. Let s be the length of one side of the octagon.

The radius of the circle is 14 inches, which is also the distance from the center of the circle to any vertex of the octagon. We can divide the octagon into eight congruent isosceles triangles, each with base s and legs of length 14 inches. We can then use the Pythagorean theorem to find the length of the base s:

s² = 14² - (s/2)²

s² = 196 - s²/4

5s²/4 = 196

s² = 156.8

s ≈ 12.52

Therefore, the perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches (rounded to 2 decimal places).

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Answer:

A) y = [tex]\frac{-3}{4} x[/tex] - 3

Step-by-step explanation:

You need two things to write the equation.  You need the slope and the y intercept.

The slope is -3/4.  If you start at the point (-4,0) and to go the point (0,-3) and you can only move up, down, right or left, you would go down 3 spaces and right 4 spaces.  Down is negative and right is positive.  

The y-intercept is -3.  this is where the graph crosses the y axis. It crosses at point (0,-3).  -3 is the slope

y = mx + b  Substitute -3/4 for m and -3 for b

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

Helping in the name of Jesus.

Answer:

$4500

Step-by-step explanation:

Find out 25% of $6000. 25/100 × 6000 = 1500

6000 - 1500 = 4500

Step-by-step explanation:

Vertex at  -4,3 would result in vertex form of parabola  

g(x) = (x+4)^2 + 3

Answer:

y=2x

Step-by-step explanation:

equation formula is y=mx+b

m is slope

b is y-intercept

you know that slope is 2

y intercept is 0

so plug it into the equation

y=2x+0 or just y=2x

Answer: First, let's calculate the total cost of all the inputs:

Cost of grape concentrate = 2,450 * $0.07 = $171.50

Cost of granulated sugar = 54 * $0.50 = $27

Cost of lemons = 60 * $0.85 = $51

Cost of yeast tablets = 200 * $0.29 = $58

Cost of nutrient tablets = 250 * $0.11 = $27.50

Cost of water = 2,900 * $0.005 = $14.50

Next, let's calculate the amount of each input that is actually used:

Grape concentrate used = 2,450 * (1 - 0.02) = 2,401 oz

Sugar used = 54 * (1 - 0.10) = 48.6 lbs

Lemons used = 60 * (1 - 0.25) = 45

Yeast tablets used = 200

Nutrient tablets used = 250

Water used = 2,900 oz

Now, we can calculate the total cost of the inputs that are actually used:

Total cost of inputs used = $171.50 + $27 + $51 + $58 + $27.50 + $14.50 = $350.50

Finally, we can calculate the standard cost per gallon:

Standard cost per gallon = Total cost of inputs used / Number of gallons produced

Number of gallons produced = 50

Standard cost per gallon = $350.50 / 50 = $7.01 per gallon

Therefore, the standard cost per gallon of wine is $7.01.

Step-by-step explanation:

.............................

Axis of symmetry: x = 1[tex]\\[/tex]

Vertex: (0,1)

Y-intercept: (0,1)

Min / Max: 0 / infinity

Domain: -infinity ≥ x ≥ infinity

Range: 0 ≥ y ≥ infinity

The solutions of the equation are  [tex]\frac{\pi}{6}.\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}[/tex].

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given equation is ,

=> [tex]4cos^2x-3=0[/tex]

Now solving the equation,

=> [tex]4 cos^2x = 3[/tex]

=> [tex]cos^2x=\frac{3}{4}[/tex]

=> [tex]cos x=\pm\frac{\sqrt3}{2}[/tex]

=> cos x = ±0.866

=> x = [tex]\frac{\pi}{6}.\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}[/tex].

Hence the solutions of the equation are  [tex]\frac{\pi}{6}.\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}[/tex].

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The amount of money that each student group would need to raise in order to purchase the swing set is $60.32.

The amount they need to purchase the swing set = $682.56

The amount they receive = $200.00 donation.

The total amount to be raised by the 8 student groups is gotten from;

Total Amount to be raised = Total amount required - Donation

Total Amount to be Raised = $682.56 - $200.00

Total Amount to be raised = $482.56

Thus, Amount to be raised by each group = Total amount to be raised by the 8 groups/8

Amount to be raised by each group = 482.56/8

Amount to be raised by each group = $60.32

Therefore, The amount of money that each student group would need to raise in order to purchase the swing set is $60.32

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Answer:

Step-by-step explanation:it is 5/5 because it is a whole number and all the others aren’t

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

P = 42in

Step-by-step explanation:

P=2w+2 A/w=2 ·9+2 · 108/9 = 42in

The values accurate to two decimal places for -2  standard deviation, mean, and +2  standard deviation are 0.30, 0.40, and 0.49, respectively.

We can use the following formulas to calculate the mean and standard deviation of the sampling distribution:

Mean: μ = p = 0.40 (since the population proportion is 0.40)

Standard deviation: σ = √((p(1-p))/n)

σ = √((0.40(1-0.40))/165)

σ = 0.049

Now we can calculate the values for -2SD, mean, and +2SD as follows:

-2SD: μ - 2σ = 0.40 - 2(0.049) = 0.30

Mean: μ = 0.40

+2SD: μ + 2σ = 0.40 + 2(0.049) = 0.49

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