3.4 MIXED FACTORING

1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.

a. x² - 4x-2x+8

The system of equations where the combination of the candies gives you a total of 22 points are:

x + y = 9

2x + 3y = 22

To create the equations, we shall first define the variables:

x = the number of purple candies

y = the number of yellow candies

Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.

Then, we would make sure that the total number of candies selected is 9.

The first equation represents the total number of candies selected:

x + y = 9

The second equation represents the total number of points obtained:

2x + 3y = 22

Therefore, the system of equations is:

x + y = 9

2x + 3y = 22

This is a system of linear equations.

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Answer:

So we can be 95% confident that the true proportion of people with kids in the population is between 0.044 and 0.096.

Step-by-step explanation:

To construct a confidence interval, we need to use the formula:

CI = p ± zsqrt((p(1-p))/n)

Where:

CI = confidence interval

p = sample proportion (in this case, 42/600 = 0.07)

z = the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval)

n = sample size (in this case, 600)

Plugging in the numbers, we get:

CI = 0.07 ± 1.96sqrt((0.07(1-0.07))/600)

Simplifying this, we get:

CI = 0.07 ± 0.026

Therefore, the 95% confidence interval for the true population proportion of people with kids is:

0.044 ≤ p ≤ 0.096

Cell 1 is in the "7th grade" row and "Pets" column. Have your student circle these labels or highlight them. Then it should be clear why choice E is the final answer.

Another way to rephrase it: the 35 people in cell 1 represent the number of 7th graders with pets.

The measures of the trigonometric relations and reference angles are solved

Given data ,

Let the measure of the angle be θ = 2π/3

Now , from the trigonometric relation ,

The tangent of the function tan ( 2π/3 ) = -√3

And , the reference angle of the θ = 2π/3  is given by A = π/3

So , A = 60°

Hence , the reference angle is 60°

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The measure of x is 36.

We have,

The angle opposite to equal sides is equal.

And,

The sum of the triangle.

27 + 90 + (x + 27)= 180

27 + 90 + x + 27 = 180

x = 180 - 144

x = 36

Thus,

The measure of x is 36.

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Answer:

Step-by-step explanation:

first, take 1/2+1/3 + 1/4+2/3

1/2+1/3=5/6 , 1/4+2/3=11/12

5/6+11/12=22/12

2/5-4=-18/5

-18/5*5/6=-3

22/12/3=22*3/12

=11/2

11/2/3/7=11/2*7/3

=77/6=12.8

Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.

Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.

Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.

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The limit of the function will be:

lim f(x) = ∞ as x → ∞

lim f(x) = 0 as x → -∞

The limit of f(x) as x goes towards infinity is infinite while the limit of f(x) approaches 0 when x tends to a negative value. Mathematically speaking,

lim f(x) = ∞ as x → ∞

lim f(x) = 0 as x → -∞

We can comprehend such behavior because the function's base is greater than 1 which explains how its growth accelerates as x increases and diminishes quickly as x declines towards zero.

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Answer:

1. # of people who predicted they would pass = 30

2. # of people who predicted they would fail = 20

3. # of people who predicted they would pass and actually passed = 27

4. # of people who predicted they would pass and actually failed = 3

5. # of people who predicted they would fail and actually passed = 11

6. # of people who predicted they would fail and actually failed = 9

Step-by-step explanation:

1. # of people who predicted they would

I also filled in the frequency table by extracting it from Brainly and drawing on it to show how the math works and fits in the table.

Answer:

Step-by-step explanation:

We can calculate the t-statistic and the p-value as follows:

If we assume that the null hypothesis is true, then the t-statistic will follow a t-distribution with 19 degrees of freedom. We can compare the calculated t-statistic with the critical t-value at the 0.05 level of significance using a t-distribution table or statistical software.

If the calculated t-statistic is greater than the critical t-value, then we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the population mean reading rate is greater than 96 words per minute.

The p-value is the probability of obtaining a t-statistic as extreme or more extreme than the calculated t-statistic, assuming the null hypothesis is true. We can use the t-distribution table or statistical software to find the corresponding p-value.

If the p-value is less than the significance level of 0.05, then we can reject the null hypothesis at the 0.05 level of significance and conclude that the probability of obtaining a random sample of 20 second grade students with a mean reading rate of more than 96 words per minute is statistically significant.

Answer:

All lines are parallel

Step-by-step explanation:

Get each equation in Slope-Intercept form:

 1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]

 2. No change

 3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]

Notice:

a. All slopes are -4/3, AND

b. All y-intercepts are different

The value of x in the chord is 3 units.

The chord intersection theorem states that the products of the lengths of the line segments on each chord are equal.

Therefore,

6(x + 5) = 4(2x + 6)

Open the brackets

6x + 30 = 8x + 24

subtract 8x from both sides of the equation

6x - 8x + 30 = 24

-2x + 30 = 24

subtract 30 from both sides of the equation'

-2x + 30 - 30 = 24 - 30

-2x = -6

divide both sides by -2

x = -6 / 2

x = 3

Therefore,

x = 3

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Answer:

20 : 4 : 15

Step-by-step explanation:

1 : 0.2 : 0.75

1 : 2/10 : 75/100

1 : 20/100 : 75/100

(×100)

100 : 20 : 75

(÷5)

20 : 4 : 15

Answer:

The length of the straw will be 5.91607 inches long in radical form.

What is Length of diagonal in cuboid?

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 5 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X= 5.91607 (in radical form)

Step-by-step explanation:

Hence, the length of the straw will be  5.91607 inches.

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Answer:

how many points will you give?

Step-by-step explanation:

The values of x and y of the given transverse lines are:

x = 44.25° and y = 7.25°

We know that there are different classification of angles such as:

Corresponding angles

Alternate angles

Opposite angles

Supplementary angles

Complementary angles

Now, we also know that sum of angles on a straight line is 180 degrees. Thus:

5x - 9y - 16 = 140

5x - 9y = 156   -----(1)

We also know that alternate angles are defined as two angles, that are formed when a line crosses two other lines, that lie on opposite sides of the transversal line and on the opposite relative sides of the other lines. If the two lines crossed are parallel, then the alternate angles are equal.

Thus:

3x + y = 5x - 9y - 16

2x - 10y - 16 = 0

2x - 10y = 16  ----(2)

Solving simultaneously gives us:

x = 44.25° and y = 7.25°

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The statement that is not true is: C. The translation of a line is a pair of parallel lines.

In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.

Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.

In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.

The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.

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The probability that a single randomly selected value is greater than 31.9 is 0.511.

The probability that a sample of size 66 is randomly selected with a mean greater than 31.9 is 0.641.

Probability that a single randomly selected value is greater than 31.9:

z = (31.9 - 32) / 3.9 = -0.026

We can find the probability:

P(X > 31.9) = P(Z > -0.026) = 0.511

Also, μ = 32, σ = 3.9, n = 66

z = (31.9 - 32) / (3.9 / √66) = -0.363

Using a standard normal distribution table or calculator, we can find the probability:

P(M > 31.9) = P(Z > -0.363) = 0.641

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To prove that the left cosets of H constitute a partition of G, we need to show that they satisfy two conditions:

1) Each element of G belongs to some left coset of H.

2) Any two distinct left cosets of H are disjoint.

Let g be any element of G. Then, by definition of a left coset, there exists an element h of H such that g = h·x for some x in G. Therefore, g belongs to the left coset H·x. Since this holds for any element g of G, we have shown that the left cosets of H cover all of G, satisfying the first condition.

Now, let H·x and H·y be two distinct left cosets of H. Suppose there exists an element z in both H·x and H·y.

Then, z = [tex]h_{1}[/tex]·x = [tex]h_{2}[/tex]·y for some [tex]h_{1}[/tex], [tex]h_{2}[/tex] in H.

Solving for x,

x = [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] · y.

Since H is a subgroup, [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] is also in H, and therefore x belongs to H·y.

Thus, H·x is contained entirely in H·y, and the two cosets cannot intersect.

This satisfies the second condition, and hence the left cosets of H constitute a partition of G.

A similar argument can be used to show that the right cosets of H also constitute a partition of G. This completes the proof.

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Answer:

Step-by-step explanation:15

Answer:

Step-by-step explanation:

2(y+5)=24

The objective function that can be used to maximize the profit is Profit = 15a + 8b

Let a is the number of units of product A and b is the number of units of product B.

Profit = 15a + 8b

This function represents the total profit earned by producing a units of product A and b units of product B

Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.

To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1000\\ P=\textit{original amount deposited}\\ r=rate\to 1.3\%\to \frac{1.3}{100}\dotfill &0.013\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]1000 = P\left(1+\frac{0.013}{52}\right)^{52\cdot 3} \implies 1000=P(1.00025)^{156} \\\\\\ \cfrac{1000}{(1.00025)^{156}}=P\implies 961.76\approx P[/tex]

Answer:

Step-by-step explanation:To solve this problem, we can use similar triangles. Let the side length of the cube be s, and let the midpoints of AB, AC, and BC be P, Q, and R, respectively. Then OP, OQ, and OR are the diagonals of the faces of the cube, and so they are equal to .Consider triangle AOB. By the Pythagorean theorem, we have , so . Since angle AOB is 90 degrees, we can use similarity to see that triangle OAP is similar to triangle OAB, so . Solving, we find that .Using similar triangles, we can find that . Since the sum of the squares of the lengths of the diagonals of a cube is equal to three times the square of the side length, we have

$$(0P2 + 0Q? + OR?) = 35388 Substituting the values we found for $OP$, $OQ$, and $OR$, we haveSimplifying and solving for , we find that . Thus, the side length of the cube inscribed in the tetrahedron is .

Answer:

$10,359.73.

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the amount of money after the specified time

P = the principal amount (the initial amount of money)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $4,000.00

r = 15% = 0.15

n = 1 (compounded annually)

t = 6 years

Substituting into the formula, we get:

A = 4000(1 + 0.15/1)^(1*6)

A = 4000(1.15)^6

A ≈ $10,359.73

Therefore, the amount in the account after 6 years, rounded to the nearest cent, is $10,359.73.

Answer:

C

Step-by-step explanation:

It mentions that they charge 1.20 per kg of lettuce

Answer:

Naida's statement is true

Step-by-step explanation:

Since the elevation of Lima, Peru is a positive number, you can automatically tell that it is above sea level since sea level is zero