Question 8 of 10
What is the complete factorization of the polynomial below?
x3+3x²+ 9x+27
OA. (x+3)(x+3/)(x-3)
OB. (x-3)(x+3)(x+3)
OC. (x-3)(x+3)(x-3/)
D. (x+3)(x+3)(x+3/)

The value of the test statistic of the hypotheses is; -17.969

The test statistic is defined as a number, calculated from a statistical test, which is used to find if your data could have occurred under the null hypothesis.

We are given;

Sample size; n = 1160

Sample proportion; p^ = 88% = 0.88

Population proportion; p = 97% = 0.97

The claim is about the population proportion (p) in the hypotheses. Since we are told that fewer than 97% of adults have a cell phone, then the claim is; p < 0.97

The null hypothesis is expressed as;

H₀: p = 0.97

The alternative hypothesis is expressed as;

Hₐ: p < 0.97

The value of the test-statistic is gotten from the formula;

z = (p^ - p)/(√(p(1 - p)/n))

z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))

z = -17.969

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Step-by-step explanation:

speed = distance / time

to get distance, we have to multiply by time.

the speed the 2 busses are moving seat from each other is

x + (x + 17) = 2x + 17

x = the speed of one bus

x + 17 = the speed of the other bus.

so, after 4 hours the distance between them is

(2x + 17) × 4 = 836

2x + 17 = 209

2x = 192

x = 96 km/h

bus 1 travels at 96 km/h.

bus 2 travels at 96+17 = 113 km/h.

Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6

Information given in the question

f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity

This is written as (x + 6) / ( x² - 9x + 18 )

factorizing the denominator gives

(x + 6) / {( x - 6)( x - 3)}

In the denominator

At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:

f(x) is decreasing for all x < 6: contains  x = 3 and result to a higher value

f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing

f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4

Therefore the correct option is f(x) is increasing for all x > 6

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Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.

An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.

Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:

y = -3(-3) - 1

y = 9 - 1

y = 8

The missing value in the ordered pair is: (-3, 8).

To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:

2 = -3x - 1

2 + 1 = -3x

3 = -3x

3/-3 = x

x = -1

The missing value is (-1, 2).

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For the given polynomial the degree is 1, the leading coefficient is 1, and the constant term is 5.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The given polynomial is x+5.

(1) The degree is the highest power of the polynomial.

Degree = 1

(2) The leading coefficient is 1.

(3) The constant term is 5

Therefore, the given polynomial degree is 1, the leading coefficient is 1, and the constant term is 5.

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64x³+125y³

= (4x+5y)( 16x²-20xy+25y²)

a³ + b³ = ( a + b )( a² - ab + b² )

64x³ + 125y³

= ( 4x )³ + ( 5y )³

= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]

= (4x+5y)( 16x²-20xy+25y² )

In the proportional relationship table, x would represent distance and y, weight.

The complete table is given in the explanation below.

If two variables that have quantities that vary proportionately are x and y, then the constant of proportionality that lies between both varies can be calculated as k = y/x. The equation for the proportional relationship would be expressed as y = kx.

x represents distance (cm)

y represents weight (newtons).

Using the pair of value that is given in the table, (20, 28), the constant of proportionality, k, would be:

k = y/x = 28/20

k = 1.4

The equation would be y = 1.4x.

Use the equation to complete the table by substituting the value of each missing variables:

Row 2, when x = 55:

y = 1.4(55)

y = 77

Row 3, when y = 140:

140 = 1.4x

140/1.4 = x

100 = x

x = 100

Row 4, when x = 1:

y = 1.4(1)

y = 1.4

The table would be:

           Distance (cm)     Weight (newtons)          

Row 1        20                     28

Row 2       55                     77

Row 3       100                    140

Row 4        1                        1.4              

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Answer:Say w= the amount of water in oz, then the 60% of the solution is 250 - w

Set up the equation:

Use distributive property first

0.60(250-w) = 0.15 x 250

Isolate to solve for w

150- 0.60w= 37.5

-0.60w= 37.5-150

0.60w= -112.5

w= 187.5 ounces

250-187.5= 62.5 ounces salt solution



Therefore, she must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.

Hope this helps!

Step-by-step explanation:

The volume of the fish tank required = 0.154 m^3.

A fish tank has a capacity = 154L.

Capacity of fish tank in Litre = Volume of the fish tank in meter cube

So the volume of the fish tank required in cubic meter.

For the volume we required a conversion of litre into meter cube.

Cubic meters and liters are two common metric units of volume.

1 cubic meter is 1000 liters.

To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters.

1L = 0.001 m^3

So 154L = 0.154 m^3

So the volume of the fish tank required = 0.154 m^3.

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Answer: 15 books

Step-by-step explanation:

Given that the weight of 6 books is 1.260 kg

⟹ weight of each book is [tex]\frac{1.260}{6}[/tex] = 0.210kg

Let the number of books that will weigh 3.150 kg be x

as we know that

weight of x books is 0.210x kg

⟹0.210x=3.150

⟹x= [tex]\frac{3.150}{0.210}[/tex] = 15

The number of books is 15

15 books will weigh 3.150 kg.

Given the weight of 6 books is 1.260 kg

⟹ weight of each book is  

1.260/6

=0.210 kg

Let x be the total number of books that weigh 3.150 kg.

as we are aware

weight of x books is 0.210x kg

⟹0.210x=3.150

⟹x= 3.150/0.210

=15

So, the number of books is 15.

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Answer:

[tex]\frac{7}{4}[/tex] or 1 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

I am not sure if you meant 6x or 6+x at the end of the equation. I went with what was written.

5x -3(x-3) = -5 +4x +6x  Distribute the -3

5x -3x + 9 = -5 + 4x + 6x  Combine like terms

2x + 9 = -5 + 10x  Subtract 2x from both sides

9 = -5 + 8x  Add 5 to both sides

14 = 8x  Divide both sides by 5

[tex]\frac{14}{8}[/tex] = x

[tex]\frac{7}{4}[/tex] o r 1 [tex]\frac{3}{4}[/tex]

Answer:

Step-by-step explanation:

570.675

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]

As per the proportional relationship, the constant of the proportionality is 1/3

Proportional relationship

A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.

The standard form of proportional relationship is written as.

y = k x

where k refers the constant of proportionality.

Given,

The table shows the proportional relationship between h and j.

Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.

We know that the standard form of the proportionality is written as,

y = k x

So, here y takes the value of j and x takes the values of h.

Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,

=> 6 = k (18)

Here we need the value of k, so move the number to the other side then we get,

=> k = 6/18

When we reduce this, then we get,

=> k = 1/3

Therefore, the constant of proportionality is 1/3.

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Step-by-step explanation:

10 hours per week: $10.50 x 10 = $105.00

20 hours per week: $105.00 x 2 = $210.00

40 hours per week: $210.00 x 2 = $420.00

The marginal cost is the labor utilized in order to provide an additional cost of a haircut.

The marginal cost is the extra cost of generating one additional unit of output.

The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.

Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.

Change in cost / Change in quantity Equals Marginal cost.

The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.

Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.

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The expression that shows the result of applying the distributive property is 21y - 7/11 (option D).  

The distributive property states that an expression that has this form a(b + c) can be solved as a x (b + c) which becomes ab + ac.  

Thus, to solve an expression using the distributive property, multiply the term in the brackets by the term outside the brackets. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.

7(3y - 1/11)

= 7 x (3y - 1/11)

= 21y - 7/11

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Answer:

IT IS A FUNCTION

It is specifically a Surjective/ onto Mapping/function

Step-by-step explanation:

surjective or onto function is when y has an image in x

Answer:

The graph is a function

Step-by-step explanation:

-For every input (x) there is only one output value (y)

Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.

Ex.

X: 2, 4, 7 , 2, 5         This is not a function. More than one input for each output.

Y: 1, 2, 4, -3, 7

Ex.

X: 5, 6, -5, 8  this is a function. Exactly one input for every output.

Y: 1, 4, 5, 9

The given points gives us a line with constant slope of -2.

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

The points are in the form of ( x, y) , where y= g(x)

Plot these points on the graph and join the points through a line.

Refer to the attachment for the graph.

The slope is constant.

consider any 2 points:

(x,y) = (0,7)

(m,n) =(2,3)

Slope = change in y values/ change in x values

         = (7-3)/(0-2) = 4/-2 = -2

The given points gives us a line with constant slope of -2.

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simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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Answer:

x° = 34°

Step-by-step explanation:

First, find the interior angle supplementary to the given exterior angle 124°.

I will label it y.

124° + y° = 180°

y° = 180° - 124°

y° = 56°

Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.

x° + y° + 90° = 180°

x° + y° = 90°

x° + 56° = 90°

x° = 90° - 56°

x° = 34°

Answer:

---------------------------

The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.

The identity is presented as follows:

[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]

Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:

[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]

The following identity relates the square of the secant and of the tangent:

[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]

Hence:

[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]

Thus the remaining expression is:

[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]

The equations of the cotangent, secant and tangent are given as follows:

Hence:

[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]

One divided by the sine is the cosecant, as follows:

[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]

Hence the simplified expression is:

[tex]\csc{\beta} + 1[/tex]

Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.

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Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.

In the given question,

The measurements of two sides of a triangle are 12 cm and 17 cm.

We have to find which side length could be the measurement of the third side of the triangle.

We know that,

The sum of the length of any two sides is always greater than the third side.

The given sides of triangles are 12 cm and 17 cm.

Hence, the length of the third side should be shorter than the total of the other two sides,

12 + 17 = 29 cm.

Considering that the third side must be less than the difference between the first two sides,

17 – 12 = 5 cm

So, the length of the third side falls between 5 cm and 29 cm.

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Answer:

x = -11

Step-by-step explanation:

2x - 7 = 3x - 2x - 18

2x - 7 = x - 18

collect like terms

2x - x = 7 - 18

x = -11

The hypothesis are given as follows:

H0: p = 0.301; H1: p ≠ 0.301.

a) The level of significance is of 0.05.

b) The sampling distribution is given by: The standard normal, since np > 5 and nq > 5.

The test statistic is of: z = -2.09.

c) The p-value is of: 0.0366.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the proportion has changed, hence:

[tex]H_0: p = 0.301[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion has changed, hence:

[tex]H_1: p \neq 0.301[/tex]

The test statistic is given by the equation presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

The parameters of the equation are listed as follows:

The values of these parameters for this test are:

[tex]\overline{p} = \frac{52}{220} = 0.2364, p = 0.301, n = 220[/tex]

Hence the value of the test statistic is of:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.2364 - 0.301}{\sqrt{\frac{0.301(0.699)}{220}}}[/tex]

z = -2.09.

We have a two-tailed test, as we are testing if the proportion is different of a value.

Hence, using a z-distribution calculator, with z = -2.09, the p-value is of 0.0366.

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Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total socks= 10

White socks= 8

Total T- shirts= 9

White T- shirts = 2

Now, The probability of choosing a white pair of socks is

= 8/10

= 4/5

and, The probability of choosing a white tee shirt is

= 2/9

and, The probability of both being white is

= 4/5 x 2/9

= 8/45

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The probability that the sum is 5/9.The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa).

The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa). Given that this is feasible 4 times out of 36, the probability calculated by adding the two dice is 4/36, or 1/9.

I am assuming that you are rolling two dice.

Probability of even: 18 "evens" out of 36 total outcomes = 18/36

→(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5),(4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

Probability of greater than 9: 6 ">9s" out of 36 total outcomes = 6/36

→(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)

Probability of both evens and >9s: 4 "both" out of 36 total outcomes = 4/36

→(4,6), (5,5), (6,4), (6,6)

evens   OR    >9s    NOT both

18/36 + 6/8 - 4/36 = 20/36 = 5/9.

The probability that the sum is 5/9.  

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