Find the value of x.
3
4
6
8

The equation of the polynomial function is P(x) = (x- 10)(x² + 10x + 21)

The given parameters are

Leading coefficient, a = 1

Zeros = 5, -2 + 2i

There are complex numbers in the above zeros

So, the other zeros are

Zeros = -2 - 2i

The equation of the polynomial is then calculated as

P(x) = Leading coefficient * (x - zero)^multiplicity

So, we have

P(x) = 1 * (x - 5) * (x - (-2 + 2i)) * (x - (-2 - 2i))

This gives

P(x) = 1 * (x- 10) * ((x + 5)² - 4)

So, we have

P(x) = 1 * (x- 10) * (x² + 10x + 25 - 4)

Evaluate the products and the difference

P(x) = (x- 10)(x² + 10x + 21)

Hence, the equation is P(x) = (x- 10)(x² + 10x + 21)

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Answer: x=12

Step-by-step explanation:

Add 5 to both sides.  7 + 5 is 12

The linear inequality on the graph is:

2y - 3x ≥ 3

So the correct option is the third one.

Here we have a linear inequality, we can see a solid line and the region above the line is shaded.

We can assume that the line is something like:

y = a*x + b

Where a is the slope and b is the y-intercept.

We can see that the line intercepts the y-axis at y = 3, then:

y = a*x + 3

And the x-axis at x = -2, then:

0 = a*-2 + 3

2a = 3

a = 3/2

Then the line is:

y = (3/2)*x + 3

And the inequality is:

y ≥ (3/2)*x + 3

If we multipy it all by 2 we will get:

2y ≥ 3x + 3

If we move the term with x to the left:

2y - 3x ≥ 3

That is the graphed inequality.

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Answer:

To determine the truth value assignments for the primitive statements that make the compound statement false, we need to consider the truth table for the conditional operator (→).

The truth table for the conditional operator is as follows:

p q p→q

T T T

T F F

F T T

F F T

According to the truth table, a conditional statement of the form "p → q" is only false when p is true and q is false.

For the compound statement [(p^q) ^r] → (s / t) to be false, we need the antecedent [(p^q) ^r] to be true and the consequent (s / t) to be false.

Thus, the truth value assignments that make the compound statement false are:

p q r s t

T T T F F

Note that there is only one truth value assignment that makes the compound statement false.

The compound statement [(p^q) ^r] → (s / t) is false only when the antecedent (the part before the arrow) is true and the consequent (the part after the arrow) is false.

The antecedent, [(p^q) ^r], is true only when p, q, and r are all true. The consequent, (s / t), is false only when both s and t are false.

Therefore, the only truth value assignments that make the compound statement false are:

p = T, q = T, r = T, s = F, t = F

p = F, q = T, r = T, s = F, t = F

p = T, q = F, r = T, s = F, t = F

p = F, q = F, r = T, s = F, t = F

Any other truth value assignment will make either the antecedent or the consequent true, and the compound statement will be true.

Here is a truth table that shows all the possible truth value assignments for the compound statement and the values of the statement:

p | q | r | s | t | [(p^q) ^r] → (s \/ t)

-- | -- | -- | -- | -- | --

T | T | T | F | F | F

T | T | F | F | F | F

T | F | T | F | F | F

T | F | F | F | F | F

F | T | T | F | F | F

F | T | F | F | F | F

F | F | T | F | F | F

F | F | F | F | F | T

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No, the difference between the sample result and what we expected is not extreme enough. The probability of it occurring by chance alone is not unlikely (0.3664 > 0.05).

The correct option is A.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Given:

According to a recent national poll, 22% of US adults get an average of 7 or more hours of sleep per night.

Let x = Number of US adult get an average of 7 or more hours of sleep per night.

Assume this is the parameter value for the population.

That means,

Proportion of number of US adults get an average of 7 or more hours of sleep per night in population = p =0.22

Suppose you select a random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night.

1) The shape of this sampling distribution is approximately normal.

2) Let a = Number of US adults get an average of 7 or more hours of sleep per night in sample = 10

Sample size n = 50.

So, [tex]\hat {p}[/tex] = 10/50

[tex]\hat {p}[/tex] = 0.2

Option a) is correct.

3) σ[tex]_{\hat p}[/tex] = √(pq)/n

= √(0.22)(1 -0.22)/50

= 0.0586

The difference between the sample result and what we expected is not extreme enough.

Therefore, the probability of it occurring by chance alone is not unlikely (0.3664 > 0.05).

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Answer: 7

Step-by-step explanation:

315 divided by 45= 7

I hope this helps!

Answer: 47

Step-by-step explanation: 2,3,5,8,12,17,23,30,38,47,57

Answer:

57

Step-by-step explanation:

The sequence starts out 2 , 3 which is the 1st term of the sequence because from the number 2, 3 is one number away. . Then 3, 5 which is the 2nd sequence because 5 is two numbers away from the number 3. 5 to 8 is the 3rd sequence because 5, 6 , 7, 8.... three numbers away from the number 5 is 8. The problem continues from 8 to 12 is four numbers away, the next sequence is five numbers away. And the number 47 is 10 numbers away from 57 making 57 the 10th term.

Answer:

C = 62.8 in

A = 314.2 in²

Step-by-step explanation:

r = D/2 = 20/2 = 10 in

C = 2πr = 2π(10) = 62.8 in

A = πr² = π(10)² = 314.2 in²

Answer:

3 batches of meatloaf requires 6 pounds of beef

and 3 cups of bread crumbs.

Step-by-step explanation:

For pounds of beef

1 batch meatloaf = 2 pounds of beef

3 batches of meatloaf = x

Cross Multiply

x = 3 x 2 pounds of beef

x = 6 pounds of beef

3 batches of meatloaf requires 6 pounds of beef

For bread crumbs

1 batch meatloaf = 1 cup of bread crumbs

3 batches of meatloaf = x

Cross Multiply

x = 3 × 1 cup of bread crumbs

x = 3 cups of bread crumbs

3 batches of meatloaf requires 3 cups of bread crumbs.

Therefore, 3 batches of meatloaf requires 6 pounds of beef and 3 cups of bread crumbs.

All the ordered pairs that represent points on the graph of this equation include the following:

A. (-4, 4).

C. (-2, 1)

E. (2, -5)

F. (0, -2)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the solutions are include following;

Ordered pair = (-4, 4).

Ordered pair = (-2, 1).

Ordered pair = (2, -5).

Ordered pair = (0, -2).

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Complete Question:

Which ordered pairs represent points on the graph of this equation? Select all that apply.

2y= –3x–4

(-4, 4)

(7, 6)

(-2, 1)

(0, 7)

(2, -5)

(0, -2)

Answer:

7.5

Step-by-step explanation:

A trapezoid is a quadrilateral where the bases are parallel, but the legs are not parallel.

Given vertices of trapezoid STUV:

The parallel bases of the trapezoid are TU and SV.

Find the lengths of TU and SV using the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

[tex]\begin{aligned}TU&=\sqrt{(x_U-x_T)^2+(y_U-y_T)^2}\\&=\sqrt{(6-2)^2+(10-7)^2}\\&=\sqrt{(4)^2+(3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}SV&=\sqrt{(x_V-x_S)^2+(y_V-y_S)^2}\\&=\sqrt{(8-0)^2+(6-0)^2}\\&=\sqrt{(8)^2+(6)^2}\\&=\sqrt{64+36}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]

The midsegment of a trapezoid is the segment parallel to the bases that connects the midpoints of the legs.

[tex]\boxed{\begin{minipage}{6.5cm}\underline{Midsegment of a Trapezoid}\\\\$M=\dfrac{b_1+b_2}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the length of the midsegment. \\\phantom{ww}$\bullet$ $b_1$ and $b_2$ are the parallel bases. \\\end{minipage}}[/tex]

Substitute the found lengths of the bases into the midsegment formula:

[tex]\implies M=\dfrac{5+10}{2}[/tex]

[tex]\implies M=\dfrac{15}{2}[/tex]

[tex]\implies M=7.5[/tex]

The length of the midsegment is 7.5.

Answer: (C)

Step-by-step explanation: By viewing the diagram, we can see that f(x) is the line drawn, and as that line heads down to negative infinity, the line is also heading towards positive infinity, and we can see this by comparing the line (f(x)) and the x-axis :)

The standard deviation of the sampling distribution of a sample proportion is about 0.00687.

Sampling Distribution of a Sample Proportion: When a distribution is formed by taking random samples of size N

from a population where the proportion in the category of interest is p

, and finding the proportion of the category of interest in each sample, it is called the sampling distribution of a sample proportion.

Standard Deviation: The standard deviation is a measure of how spread out data is. When referring to the standard deviation of the sampling distribution of a sample proportion, the standard deviation measures how far from the population proportion the sample proportions are on average.

P  =X/n

   =34%/45%

   = 34/45

   =0.75

N = 35 + 28

σp=√p(1−p)/N

    = √0.75(1- 0.75)/63

    = √0.75(0.25)/63

    = 0.433/63

    =0.00687

The standard deviation of the sampling distribution of a sample proportion is about 0.00687.

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Answer:

30,30,30,30,30,30,45,45,45,45

Step-by-step explanation:

The sum of the exterior angles is 360.

Let x = the equal one of the six equal angles

6x + 4( x + 15) = 360  Distribute the 4

6x + 4(x) + 4(15) = 360

6x + 4x + 60 = 360  subtract 60 from both sides

6x + 4x + 60 - 60 = 360 - 60

6x + 4x = 300  Combine like terms

10x = 300  Divide both sides by 10

[tex]\frac{10x}{10}[/tex] = [tex]\frac{300}{10}[/tex]

x = 30

30 + 15 = 45

Answer:

-8g2 - 8g + 3

Step-by-step explanation:

Answer:

−8g2 − 12g

Step-by-step explanation:

-4g(2g + 3)

-8g^2 - 12g

Answer:

he point (-1, 0) is a valid solution, and the inequality is correctly written

Step-by-step explanation:

There are three standard forms for linear inequalities:

Standard form: Ax + By > C

Slope-intercept form: y > mx + b

Point-slope form: y - y1 > m(x - x1)

To write an inequality in standard form, you need to know the coefficients of the variables (A and B) and the constant term (C). You can find these values by examining the slope and the y-intercept of the line representing the inequality. For example, suppose the graph of the inequality shows the solution set to be all the points that lie above the line y = 2x + 1. To write this inequality in standard form, we can set A = 2, B = 1, and C = 1. The resulting inequality is 2x + y > 1. To check our work, we can substitute a test point, such as (-1, 0), into the inequality to see if it is a valid solution. In this case, we have 2(-1) + 0 > 1, which simplifies to -2 > 1, which is not true. Therefore, the point (-1, 0) is not a valid solution, and the inequality is correctly written.

To write an inequality in slope-intercept form, you need to know the slope (m) and the y-intercept (b) of the line representing the inequality. For example, suppose the graph of the inequality shows the solution set to be all the points that lie above the line y = 2x + 1. To write this inequality in slope-intercept form, we can set m = 2 and b = 1. The resulting inequality is y > 2x + 1. To check our work, we can substitute a test point, such as (-1, 0), into the inequality to see if it is a valid solution. In this case, we have 0 > 2(-1) + 1, which simplifies to 0 > -2 + 1, which is true. Therefore, the point (-1, 0) is a valid solution, and the inequality is correctly written.

To write an inequality in point-slope form, you need to know the slope (m) and a point (x1, y1) on the line representing the inequality. For example, suppose the graph of the inequality shows the solution set to be all the points that lie above the line y = 2x + 1. To write this inequality in point-slope form, we can choose a point on the line, such as (0, 1), and set x1 = 0 and y1 = 1. The slope of the line is m = 2, so the resulting inequality is y - 1 > 2(x - 0). This simplifies to y > 2x + 1, which is the same as the inequality written in slope-intercept form. To check our work, we can substitute a test point, such as (-1, 0), into the inequality to see if it is a valid solution. In this case, we have 0 > 2(-1) + 1, which simplifies to 0 > -2 + 1, which is true. Therefore, the point (-1, 0) is a valid solution, and the inequality is correctly written.

Answer:

The tax for each taxable income of a head of household depends on the tax rate that applies to that income and the applicable deductions and credits available to the taxpayer. The tax rate applied to a taxpayer's income depends on the taxpayer's taxable income and filing status. The tax rate for a head of household is generally lower than the tax rate for a single filer, but higher than the tax rate for a married taxpayer filing a joint return.

To determine the tax for a taxable income of a head of household, you can use the Internal Revenue Service (IRS) tax tables or a tax calculator. The tax tables provide tax rates and income ranges for each tax bracket, and you can use them to determine the tax on a given income. Alternatively, you can use a tax calculator to input your taxable income, filing status, and any applicable deductions and credits to determine the tax owed.

It's important to note that the tax rate for a head of household may change from year to year, as the IRS adjusts the tax brackets and rates. Additionally, the deductions and credits available to a head of household may change from year to year, so it's important to consult the IRS guidelines for the most current information.

Step-by-step explanation:

Answer:

$25.20

Step-by-step explanation:

($5.40) / ($0.30/day) = 18 days

It took 18 days for Gill to save $5.40 more than Devi.  So in those 18 days Devi saved:

$1.40/day x 18 days = $25.20

a). The equation of a function h(x) as required to be determined is; h (x) = 20,000 (0.85)^x.

b). The function h (x) as required to be described in terms of the parent function f(x) is a dilation of the parent function using a scale factor of 20,000.

c). The difference between the values of the $12,000 and the $20,000 car after 5 years is; $3549.6.

It follows from the task content that the equation of the function g (x) is given as;

g (x) = 12,000 (0.85)^x.

a). To start with, since the rate of depreciation is same for the $20,000 car too; it follows that the exponential function which represents the situation is;

h (x) = 20,000 (0.85)^x.

b). It follows from transformations that; since the parent function f (x) = 0.85^x, the function g(x) can be described relative to the parent function as a dilation of the parent function using a scale factor of; 20,000.

c). The value of the $12,000 item after 5 years is;

g (5) = 12,000 (0.85)⁵ = $5324.5.

Also, the value of the $20,000 car after 5 years is;

h ( 5 ) = 20,000 (0.85)⁵ = $8874.1.

Ultimately, the difference between the values of the two items as required is; 8874.1 - 5324.5 = $3549.6.

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Answer:b a

Step-by-step explanation:

The formula for volue is length x width x height.

The volume of the sand needed to fill the space is 240 feet³.

The total cost of the sand is $1240.

The brick patio is the shape of a rectangular prism. In order to determine the volume of the brick patio, determine the product of the length, width and the height.

Volume of the brick patio = length x width x height

= 10 x 12 x 2 = 240 feet³

Total cost of the sand = (volume x cost per cubic foot) + delivery fee

Total cost of the sand = (240 x $5) + $40

Total cost of the sand = 1200 + 40

Total cost of the sand = $1240

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The y-coordinate matched with the given x-coordinate:

x = 100  → y = 3

x = 1/10   → y = 0

x = 10  → y = 2

x = 1   → y = 1

x = 1/100  → y = -1

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

Given:

Logarithmic function,

y = log(10x).

(1).

x = 100

So,

y = log{(10)(100)}.

y =  log(1000)

y = 3

(2).

x = 1/10

So,

y = log{(10)(1/10)}.

y = log(1)

y = 0

(3).

x = 10

So,

y = log{(10)(10)}.

y = log(100)

y = 2

(4).

x = 1

So,

y = log{(10)(1)}.

y = log(10)

y = 1

(5).

x = 1/100

So,

y = log{(10)(1/100)}.

y = log(1/10)

y = -1

Therefore,  the y-coordinate matched with the given x-coordinate

x = 100  → y = 3

x = 1/10   → y = 0

x = 10  → y = 2

x = 1   → y = 1

x = 1/100  → y = -1

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Answer:

13, 15 17

Step-by-step explanation:

Let x = 1st number

Let x + 2 = 2nd number

Let x + 4 = 3rd number

x + x + 2 + x + 4 = 45  Combine like terms

3x + 6 = 45  Subtract 6 from both sides

3x + 6 - 6 = 45 - 6

3x = 39  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{39}{3}[/tex]

x = 13

Check:

13 + 15 + 17 = 45

A graph of the solution to this inequality (x < 5) is shown on the number line in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for the comparison of two (2) or more numerical data, numerals, and variables that are contained in an algebraic equation, especially based on the following inequality symbols:

Generally speaking, a number line is a type of chart which primarily decreases in numerical value towards the right from zero (0) and increases in numerical value towards the left from zero (0).

Next, we would solve the given inequality by adding eight to both sides as follows;

−8 + x < −3

−8 + x + 8 < −3 + 8

x < 5

Therefore, the solution is x is less than five.

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The algebraic expression that represents the number of beads per necklace is given as follows:

250/8.

The algebraic expression representing the number of beads per necklace is obtained applying the proportion in the context of the problem.

The proportion is given by the division of the total number of beads by the total number of necklaces, as follows:

Beads per necklace = Number of beads / Number of necklaces.

The parameters for this problem are given as follows:

Hence the algebraic expression that represents the number of beads per necklace is given as follows:

250/8.

(dividing the number of beads by the number of necklaces given in this problem).

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Based on the information, it can be inferred that Sylvia buys 75 pens for $6.00 (option C).

To calculate the number of pens that Silvia can buy we must carry out the following mathematical procedure

According to the above, $6.00 is enough to buy 15 groups of 5 pens. So, that's why we multiply 15 by 5 to find the number of pens Sylvia can buy. In this case there are 75 pens. Additionally, the first procedure we divide the total money in the value of each group of pens to identify how many groups we can buy.

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The right triangle drawings are used to model the shadow scenarios. Each side length of the triangle represents a different part of the scenario.

The hypotenuse represents the distance from the sun to the object casting the shadow, the side adjacent to the hypotenuse represents the length of the shadow, and the side opposite the hypotenuse represents the height of the object casting the shadow. In the real world, the hypotenuse is used to calculate the angle of the sun relative to the object casting the shadow.

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Option (c) In the given Poem "Hope is the thing with a feather" Hope symbolizes a Strong-willed bird

"Hope" is described by the speaker as a winged creature that resides within the human spirit. This feathered monster sings a tune without any words and never stops. Its song is most enjoyable when heard in strong gusts. This bird's chirping could only be silenced by a storm that was quite intense. Many people have experienced warmth from the "Hope" bird. The narrator has heard the song of the bird in the coldest climates and on the most unusual seas. But even in the most extreme instances, according to the speaker, the bird never demanded anything in return.

The well-known poem "Hope is the thing with feathers" by American poet Emily Dickinson was composed sometime about 1861. In the poem, "Hope" is figuratively changed into a tenacious bird that dwells inside the human soul and sings its song despite everything. The poem basically aims to remind readers of the strength of optimism and how little it demands of people. Hope, according to the speaker, has always been a comfort in trying times and has never required anything in return. The poem "Hope is the Thing with Feathers" is one of many by Emily Dickinson that reinterprets an abstract idea using novel imagery and figurative language.

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