Quadratic Inequalities

The expression that shows how many beads are on the necklace in all is:

b + 12.

An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.

In the given question,

To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:

Start with the initial number of beads on the necklace, which is 12.

To this, add the number of beads Josie added, which is b.

Combine the two terms to form the final expression: 12 + b.

Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.

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Answer:..

Step-by-step explanation:Use the distance formula to find the length of each side and then add the lengths.

Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.

Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.

Use the distance formula to find the length of the sides, and then multiply two of the side lengths.

Answer:

275 miles

Step-by-step explanation:

Answer: 344cm²

Step-by-step explanation:

7x7=49

49x5=245

3x2=6

49-6=43

245+43=288

5x2=10 10x2=20

5x3=15 15x2=30

288+30+20+6=344

The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.

To model the total amount of money Victoria will have in her bank account as interest accrues after depositing her $200, you can combine the two functions h(x) and s(x). The given functions are h(x) = 200 and s(x) = (1.05)^x−1.

First, note that s(x) represents the growth factor of the interest, which is 5% (1.05) compounded annually. To find the total amount after x years, you need to multiply the initial amount by the growth factor raised to the power of x.

So, the combined function T(x) can be written as T(x) = h(x) * s(x).

Substitute the given functions into the combined function:

T(x) = (200) * ((1.05)^x−1)

This function, T(x), models the total amount of money Victoria will have in her bank account after x years with interest accrued on her $200 deposit. The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.

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There are 252 different combinations of shirts, the correct option is B.

Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:

[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]

There are 252 different combinations, so the correct option is B.

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Answer:

$1.01

Step-by-step explanation:

We Know

A 2-quart carton of pineapple juice costs $8.08

1 quart = 4 cups

2 quarts = 8 cups

So, 8 cups of pineapple juice cost $8.08.

What is the price per cup?

We Take

8.08 / 8 = $1.01

So, the price per cup is $1.01

If the sum of the roots of a quadratic equation is 1 and the product of the roots is -35/4 and the equation is [tex]4x^2-4x-35=0[/tex] and the roots are 3.5 and -2.5

If the quadratic equation is [tex]ax^2+bx+c=0[/tex]

The sum of the roots = [tex]-\frac{b}{a}[/tex]

The product of the roots = [tex]\frac{c}{a}[/tex]

Sum of the roots = 1 = [tex]-\frac{b}{a}[/tex]

Product of the roots = [tex]-\frac{35}{4}[/tex] = [tex]\frac{c}{a}[/tex]

If we assume a as 1, then the equation comes out to be:

[tex]x^2-x-\frac{35}{4} =0[/tex]

Multiply the equation by 4 to get a simplified equation:

[tex]4x^2-4x-35=0[/tex]

[tex]4x^2[/tex] - 14x + 10x - 35 = 0

2x (2x - 7) + 5 (2x - 7) = 0

(2x - 7)(2x + 5) = 0

x = 3.5 and -2.5

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The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:

1) $20, $40, $50

2) $30, $60, $75

3) $64, $128, $160

To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.

Total bill: $110

The total ratio is 2+4+5=11.

Greg's share: (2/11) * $110 = $20

Harry's share: (4/11) * $110 = $40

Ian's share: (5/11) * $110 = $50

Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.

Total bill: $165

The total ratio is still 2+4+5=11.

Greg's share: (2/11) * $165 = $30

Harry's share: (4/11) * $165 = $60

Ian's share: (5/11) * $165 = $75

Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.

Total bill: $352

The total ratio remains the same: 2+4+5=11.

Greg's share: (2/11) * $352 = $64

Harry's share: (4/11) * $352 = $128

Ian's share: (5/11) * $352 = $160

Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.

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The mean of the fifth-grade jump distance data set.

To determine the mean of the data set for fifth-grade jump distances, we need the actual data values. Without the specific data set, it is not possible to calculate the mean.

The mean is the sum of all the values in a data set divided by the number of values. Therefore, we would need the individual jump distances for each fifth-grade student to calculate the mean accurately.

Once we have the complete data set, we can add up all the distances and divide by the total number of students to find the mean. Without the specific data, we cannot provide a numerical answer for the mean of the fifth-grade jump distance.

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The graph of the exponential function [tex]y = 2^{3x}[/tex] is given as follows:

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The function in this problem is given as follows:

[tex]y = 2^{3x}[/tex]

Hence the parameter values are:

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1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.

2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.

3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.

The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.

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The absolute maximum will be at (11, 10373).
The absolute minimum is at (-1.963, -25.294).

What in are the absolute maximum maxime off on the given interval?

To determine the location and value of the absolute extreme values of the function f(x) = 8x³+ 22x² - 24x on the interval (-7, 11), follow these steps:

Find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x) = 24x² + 44x - 24

Solve for x:
Factor the equation: 4(6x² + 11x - 6) = 0
Using the quadratic formula, x = (-11 ± √(121 + 144))/12
x ≈ -1.963, 0.630

Check the endpoints and the critical points to find the absolute maximum and minimum:
f(-7) ≈ 461
f(-1.963) ≈ -25.294
f(0.630) ≈ -16.102
f(11) ≈ 10373

Compare the values:
The absolute maximum is at x = 11, with a value of 10373.
The absolute minimum is at x ≈ -1.963, with a value of ≈ -25.294.

Answer:
The absolute maximum is at (11, 10373).
The absolute minimum is at (-1.963, -25.294).

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The system of equations is.

x + y = 80

12x + 10y = 900

And the solutions are y = 30 and x = 50

Let's define the two variables:

x = number of calculators.

y = number of calendars.

With the given information we can write two equations, then the system will be:

x + y = 80

12x + 10y = 900

Now let's solve it.

We can isolate x on the first equation to get:

x = 80 - y

Replace that in the other equation to get:

12*(80 - y) + 10y = 900

-2y = 900 - 960

-2y = -60

y = -60/-2 = 30

Then x = 50

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The company's profit in the year 2005 would be approximately $10.5 million.

Let's calculate the company's profit for the year 2005 using the given information.

Initial profit in 2001: $7.2 million
Annual profit increase: 11%

We need to find the profit for 2005, which is 4 years after 2001.

Step 1: Identify the formula for compound interest, which can be applied to profit increase:
Future Profit = Initial Profit * (1 + Profit Increase Rate)^Number of Years

Step 2: Plug in the values:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Step 3: Calculate the result:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Future Profit = $7.2 million [tex]* 1.4641[/tex]
Future Profit = $10.54152 million

Step 4: Round the result to the nearest tenth of a million dollars:
Future Profit ≈ $10.5 million

So, the company's profit in the year 2005 would be approximately $10.5 million.

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A 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.

Let's start by defining some variables. Let "r" represent the radius of the tire and "n" represent the number of revolutions it makes over a fixed distance. We are given that the number of revolutions is inversely proportional to the radius of the tire. This means that as the radius increases, the number of revolutions decreases, and vice versa. We can express this relationship mathematically as follows:

n = k/r

Here, "k" is the constant of variation, which remains the same for any given tire traveling over the same distance. To solve the problem, we need to find the value of "k" first. We know that a 12-inch radius tire makes 100 revolutions to travel a certain distance. Substituting these values into the equation, we get:

100 = k/12

Solving for "k," we get k = 1200. Now we can use this value to find the number of revolutions required by a 16-inch radius tire to travel the same distance:

n = 1200/16 = 75

Therefore, a 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.

In summary, we defined the variables, identified the constant of variation, wrote the equation (n=k/r), found the value of the constant by using the given information, and used it to solve the problem by finding the number of revolutions required by a tire with a different radius.

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Answer:

7/5

Step-by-step explanation:

Lily's age in months: 2×12+4=28mo

Hugo's age in months=12+8=20

Lily's age over Hugo's age: 28/20

Simplify:

28/20=14/10=7/5

Answer: Diffusion

Step-by-step explanation:

The Equation of the line which is parallel to the line "y = 3x + 6", and also passes through (4,7) is "y = 3x - 5".

In order to find an equation of a line which passes through point (4,7) and is parallel to line "y = 3x + 6", we use the fact that parallel lines have the same slope.

The given line ""y = 3x + 6" has a slope of 3,

So, the "parallel-line" we want to find must also have a slope of 3.

Now, by using the "point-slope" form of the equation of a line, which is : y - y₁ = m(x - x₁),

where m is slope and (x₁, y₁) is a point on the line,

So, we substitute "m = 3" and (x₁, y₁) = (4,7) to get:

⇒ y - 7 = 3(x - 4),

⇒ y - 7 = 3x - 12,

⇒ y = 3x - 5

Therefore, the equation of the required line is y = 3x - 5.

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Since the population standard deviation is unknown, we use a t-distribution to find the critical value. The degrees of freedom for the t-distribution is n-1, where n is the sample size. In this case, n = 7, so the degrees of freedom is 7-1 = 6. The critical value for a t-distribution with 6 degrees of freedom and a significance level of α = 0.200 (two-tailed) can be found using a t-table or calculator. The critical value is approximately ±1.94.

To model the volume of a rectangular prism with length 26cm and width w and height h such that the sum of the width and height is 32cm, we can use the following function:

V(w, h) = 26wh

subject to the constraint:

w + h = 32

We can solve for one of the variables in the constraint equation and substitute it into the volume equation, giving us:

w + h = 32  =>  h = 32 - w

V(w) = 26w(32 - w) = 832w - 26w^2

To find the maximum possible volume, we can take the derivative of this function with respect to w and set it equal to zero

dv/dw= 832 - 52w = 0

Solving for w, we get:

w = 16

Substituting this value back into the constraint equation, we get:

h = 32 - w = 16

Therefore, the maximum possible volume of the prism is:

V(16, 16) = 26(16)(16) = 6656 cubic cm

So the function to model the volume of the rectangular prism is V(w) = 832w - 26w^2, and the maximum possible volume is 6656 cubic cm when the width and height are both 16cm.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]

An expression for the sequence of operations described "Subtract three from the product of seven and eight." is (7 × 8) - 3.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

Expression: (7 × 8) - 3

56 - 3

53

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Yermin's point is the best approximation of the square root of 0.50.

To know whose point is the best approximation of the square root of 0.50 on a number line. We have the points plotted by Pedro, Lena, Harriet, and Yermin.

Step 1: Calculate the square root of 0.50.
[tex]\sqrt{0.50} = 0.707[/tex]

Step 2: Compare the plotted points to the calculated square root value.
Pedro: Between 0.2 and 0.3
Lena: Between 0.4 and 0.5
Harriet: At 0.5
Yermin: Just to the right of 0.7

Step 3: Determine the closest approximation.
Yermin's point (just to the right of 0.7) is the closest to the calculated value of 0.707.

Your answer: Yermin's point is the best approximation of the square root of 0.50.

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Answer:

If Mohal waits on 16 tables, he can expect to earn $25 wages + ($15 tips x 16 tables) = $265 in a day.

If Mohal waits on 1 table, he can expect to earn $25 wages + ($15 tips x 1 table) = $40 in a day.

If the cake is in the shape of a rectangular prism, the total surface area of the cake that will be covered in frosting is 314 sq. inches.

To find the total surface area of the cake that will be covered in frosting, we need to calculate the area of all sides except the bottom. A rectangular prism has 6 sides, and we will be considering 5 of them.

Surface area of top: length × width = 13 × 8 = 104 sq. inches
Surface area of front: length × height = 13 × 5 = 65 sq. inches
Surface area of back: length × height = 13 × 5 = 65 sq. inches
Surface area of left side: width × height = 8 × 5 = 40 sq. inches
Surface area of right side: width × height = 8 × 5 = 40 sq. inches

Now, we will sum the areas of all these sides:
104 + 65 + 65 + 40 + 40 = 314 sq. inches

So, the total surface area of the cake that will be covered in frosting is 314 sq. inches. None of the provided options match this answer, so it is important to double-check the question for any discrepancies.

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Answer: C Distribution is symmetric

Step-by-step explanation:

Therefore, the missing value of G is 7.608 cm, which is option A.

If G is two and one-half times smaller than 19.02 cm, we can find the value of G by multiplying 19.02 cm by 2/5, since two and one-half is equal to five halves, or 2/5 when expressed as a fraction.

G = (2/5) x 19.02 cm

Simplifying this expression:

G = 7.608 cm

Therefore, the missing value of G is 7.608 cm, which is option A.

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