Write a polynomial f (x) that satisfies the given conditions.
Degree 3 polynomial with integer coefficients with zeros 7i and 9/5

The null hypothesis is rejected if the p-value is lower than or equal to the chosen significance threshold; otherwise, it is not. To put it another way, if p, reject  [tex]H_{0}[/tex]; if p>, do not reject [tex]H_{0}[/tex].

This criterion, known as (alpha) in null hypothesis testing, is often set to 05. The rejection of the null hypothesis is if there is less than a 5% probability that a result as dramatic as the sample result would occur if the null hypothesis is accepted. The outcome is referred to as statistically significant when this occurs.

If a statistical test is run with a threshold of significance = 0.1, 0.05, and 0.01 the null hypothesis was rejected.

The alternative hypothesis is taken into consideration instead of the null hypothesis if the P value is less than alpha, the predetermined level of statistical significance.

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The domain of the relation is 1,-1,-2, and 1. The range of the function is -2,2,4, and 3.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. The domain of the function is defined as the set of all the possible values of the function.

The domain of the relation is 1,-1,-2, and 1. The range of the function is -2,2,4, and 3.

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In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given,

Ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards:

Through combination:

²⁴C₅

24!/51(24-5)!

Simplifying:

24!/5!(19!)

24 × 23× 22× 21× 20×19!/5! × 19!
24 × 23 × 22 × 21 × 20/ 5× 4 × 3 × 2 × 1

42504

In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.

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Answer:

[19+7] / [2 x 6 + 1]

Step-by-step explanation:

[19+7] / [2 x 6 + 1]

[26] / [13]

[2]

If n is negative the value of the equation that we have below would be -18

We have to rewrite the equation in a way that it would be easier to understand first.

[tex]\frac{-2n+8}{4} =11[/tex]

Next we would have to cross multiply

this would give us

-2n + 8 = 11 * 4

-2n + 8 = 44

take the like terms

-2n = 44 - 8

-2n = 36

divide through by -2 from the above

-2n / -2 = 36 / -2

n = - 18

Therefore given that we have that the value of the equation after n is negative is -18.

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The required question based on number of posters is y = 109.95 + 65x.

The cost of additional posters = 65x, based on the mentioned information.The 100 posters make 1 set. Assuming the total number of posters be x. So, the additional sets will be calculated by the formula = (x - 100)/100.

Now, the equation will be the sum of the cost of first 100 posters and the cost of remaining posters.

y = 109.95 + 65x

Thus, the equation with the total cost (in dollars) as a function of the number (in hundreds) of posters ordered is y = 109.95 + 65x.

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Answer:

scale factor = 2

Step-by-step explanation:

the scale factor is the ratio of corresponding sides , polygon B to polygon A

in figure A the vertical side RS = 2 units

the corresponding vertical height in figure B = 4 units , then

scale factor = [tex]\frac{4}{2}[/tex] = 2

Answer:

5/12

6/15

10/18

Step-by-step explanation:

Answer: y=2x+1

Hope this helps

3(y-9)

3y-27

Factorizing

3(y-9)

Answer: Hence the answer is 27 square feet.

Please look at the images for more details.

Answer:

27 square feet

Step-by-step explanation:

Define the variables:

To increase a number by a certain percent, divide the percent by 100, add it to 1, then multiply the original number by this number.

If the length of the new flag is 20% greater than the length of the old flag:

[tex]\implies \textsf{Length}=\left(1+\dfrac{20}{100}\right) \timesl \times l=1.2l[/tex]

To decrease a number by a certain percent, divide the percent by 100, subtract it from 1, then multiply the original number by this number.

If the width of the new flag is 10% less than the width of the old flag:

[tex]\implies \textsf{Width}=\left(1-\dfrac{10}{100}\right) \times w =0.9w[/tex]

[tex]\boxed{\textsf{Area of a rectangle}=\sf width \times length}[/tex]

Therefore, given the area of the old flag is 25 ft²:

[tex]\implies wl=25[/tex]

To find the area of the new flag, substitute the expressions for width, length and wl into the formula for area of a rectangle:

[tex]\begin{aligned}\textsf{Area of new flag}&=\sf width \times length\\&=0.9w \times 1.2l\\&=0.9 \times 1.2 \times wl\\&=1.08 \times 25\\&=27\sf \;\; ft^2\end{aligned}[/tex]

Therefore, the area of the new flag is 27 square feet.

0.55 is the probability that a vacationer will visit at least one of these magnificent attractions.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

50% of the vacationers going to toronto visit the CN tower= 0.5

40% visit skydome= 0.4

35% visit both=0.35

P( At lease one) = P(Toronto) + P(Skydome) - P(Both)

P( At lease one) = 0.4 + 0.5 - 0.35

P( At lease one)  = 0.55

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Answer:

20°,70°

Step-by-step explanation:

X+y+90=180

X+y=90

20+y=90

y=70°

2x+180-40=180

2x=40

X=20°

The measures of angles of the triangle is x = 20° and y = 70°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , let the side be represented as BD , which cuts AC at point D

And , the measure of BD = measure of DC ( given )

And , the measure of ∠ABC = 90°

The measure of ∠BDA = 40°

So , the measure of angle ∠BDC = 140° ( angles on a straight line )

Now , the measure of angle ∠DBC = measure of ∠BCD ( given )

So , the measure of x = ( 180 - 140 ) / 2

x = 20°

And , the measure of y = 180° - 40° - 70°

y = 70°

Hence , the angles of triangle are x = 20° and y = 70°

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This is an example of stratified random sampling as the population is divided into two groups males and females and 200 samples are selected from each group.

Given that,

A researcher asks all 1000 employees to engage in a questionnaire survey to look at various areas of employee job satisfaction with the goal of selecting a sample of 200 males and 200 women.

A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata

Therefore, the population is separated into two categories, males and females, and 200 samples are chosen from each group in this stratified random sampling example.

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Answer:

119.5

Step-by-step explanation:

Since supplementary is 180 degrees, 180-60.5=119.5

Answer: 21 Tomatoes

Step-by-step explanation:

5 + 2 = 7

147 / 7 = 21

21 Tomatoes

Answer:

Step-by-step explanation:

-22.7

The positive slope is tilted towards the right on a coordinate plane and the negative slope is tilted towards the left on the coordinate plane.

When two variables have a positive slope, it means that they are positively correlated; that is, when x rises, y rises as well, and when x falls, y falls as well. A line on a line graph that has a positive slope rises as the line advances from left to right.

A line that slopes downward from left to right is said to have a negative slope. In other words, the rise-to-run ratio of the line is negative.

The graph of the two real-life situations is attached with the answer below. In which the equation y = 4x means that the value of y is increasing by 4. Similarly, the equation for negative slope is y = -4x means that the value of y is increasing in opposite direction by factor 4.

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The percentage increase in the number of pieces she saws on that day is 40%.

Here it is given that a seamstress sews 55 pieces per day.

But on a certain day, 77 pieces were sewn.

We have to find the percentage increase in the number of pieces she sews on that day.

So first we have to find the increase in the number of pieces she sews.

Increase in the number = 77 - 55

                                       = 22

The original number per day = 55

Formula to find the percentage increase in the number.

Percentage increase = Increase in number/ original number × 100

Now putting the values in the equation:

Percentage increase = 22 / 55 × 100

                                   = 2/5 × 100

                                   = 40%

Therefore there is a 40% increase in the number of pieces.

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Kevin favorite lemonade juice can't taste the same as Patricia's.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

1 table spoon = 0.5 ounce

Therefore, 24 ounces will be:

= 24 × 0.5

= 12 tablespoon

In this case, they have different tablespoon and therefore won't have same taste.

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Answer:

Range:  [tex]\text{y} \ge 0[/tex]

Domain: [tex]\text{x} \ge 0[/tex]

Both involve "greater than or equal to 0".

==============================================

Explanation:

The domain is the set of allowed inputs (x). The smallest input allowed in this case is x = 0, as it corresponds to the left-most point (0,0) on the blue graph. There is no largest x value since it stretches forever to the right.

Either x = 0 or x > 0 which condenses to [tex]\text{x} \ge 0[/tex] and this is the domain as an inequality.

--------

The range will have us look at the possible y values or possible outputs. We have y = 0 as the smallest output possible, which corresponds to the lowest point (0,0).

There is no largest y value since the blue graph goes forever upward.

Either y = 0 or y > 0 to give us the range of [tex]\text{y} \ge 0[/tex]

The relationship between variables p and q is given by p = kq. Also, the value of the variable p when q = 16 is 6 and when p = 2.4, the variable q is 6.4.

Mathematically, a proportional relationship can be represented with the following mathematical expression:

p = kq

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = p/q

Constant of proportionality (k) = 4.5/12

Constant of proportionality (k) = 0.375.

When q = 16, the variable p is given by:

p = kq

p = 0.375 × 16

p = 6.

When p = 2.4, the variable q is given by:

q = p/k

q = 2.4/0.375

q = 6.4

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The probability for Jacie or Robyn would consume cheese on a random day is 0.15.

The likelihood of Jacie eating cheese on any particular day is 0.6.

The likelihood of Robyn eating cheese on any particular day is 0.25.

Both events are independent.

As a result, the probability for Jacie or Robyn would consume cheese on a random day is;

P(Jacie or Robyn)  = P(Jacie). P(Robyn)

P(Jacie or Robyn)  = 0.6 x 0.25

P(Jacie or Robyn)  = 0.15

Thus, the probability for Jacie or Robyn would consume cheese on a random day is 0.15.

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Answer:

c = 11.46 yd

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

Answer:

abad

Step-by-step explanation:

Answer:

m=18

Step-by-step explanation:

The slope-Intercept form of the given line is y=1.5x.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The given line passes through (4, -2) and (2, 3). Therefore, the slope of the given line can be written as,

Slope of the line, m = (-2 - 3)/(4 - 2)

                                = 3 / 2

                                = 1.5

Now, the equation of the line passing through (2, 3) can be written as,

y = mx + c

(3) = 1.5(2) + C

3 = 3 + C

3 - 3 = C

C = 0

Substitute all the value in the equation of the line,

y = m(x) + c

y = 1.5(x) + 0

y = 1.5x

Hence, the equation of the given line is y=1.5x .

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