Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.

Answer:

2.3

Step-by-step explanation:

.5 - .3 = .2

.8 - .5 = .3

1.2 - .8 = .4

1.7 - 1.2 = .5

We should add .6 next

1.7+.6 = 2.3

Answer:

P( yellow) =  8/23

P( blue or green) =  9/23

P(orange) = 0

Step-by-step explanation:

6 red, 5 green, 4 blue, and 8 yellow M&M's = 23  total

P( yellow) = yellow / total = 8/23

P( blue or green) = (blue+green) / total = (5+4)/23 = 9/23

P(orange) = orange/ total = 0/23

Answer:

there are 23 m&m's.

Step-by-step explanation:

Probability of getting red is 6/23

Probability of getting  green is 5/23

Probability of getting blue is  4/23

Probability of getting yellow is 8/23

Orange = red + yellow = 6+8/23

Probability of getting Orange = 14/23

Step-by-step explanation:

I do hope that you understand through the steps in the attachment, if not kindly reach out!

Answer:

July 4th, 1776.

Step-by-step explanation:

By issuing the Declaration of Independence, adopted by the Continental Congress on July 4, 1776, the 13 American colonies severed their political connections to Great Britain. The Declaration summarized the colonists' motivations for seeking independence.

Answer:

B Trevor isn't correct because -2i must also be a root

Step-by-step explanation:

A Trevor is correct.

B Trevor is not correct because –2i must also be a root.

C Trevor is not correct there cannot be an odd number of roots.

D Trevor is not correct because there cannot be both rational and complex roots.

statements^^^^^^

The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Since one of the roots is complex (2i), it follows that the coefficients of f(x) must be complex as well, and therefore f(x) must be a polynomial with complex coefficients.

However, it is possible for f(x) to have a higher degree than 3.

For example,

The polynomial (x + 7)(x - 2i)(x + 2i)(x - 7) has degree 4 and has the given roots of -7, 2i, and 7. Therefore, f(x) could be a polynomial with degree 4 or higher.

Thus,

The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.

Learn more about functions here:

https://brainly.com/question/28533782

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Answer:

Step-by-step explanation:

Answer:

The point estimate of the proportion of the population that would provide Yes responses is 0.28.

Step-by-step explanation:

Point estimate of the proportion of the population that would provide Yes

The sample proportion of yes responses.

In the sample:

112 yes responses in the sample of 400, so:

[tex]p = \frac{112}{400} = 0.28[/tex]

The point estimate of the proportion of the population that would provide Yes responses is 0.28.

Answer:

No, because the ratio of pay to hours is not the same for each pair of value.

Answer:

the the 3rd one Is the one

Answer:

d. The average exam scores for each group.

Step-by-step explanation:

The dependent variable, also called the measured or predicted variable is the variable which is being tested or measured in an experiment. It is the variable with which an experiment is being conducted. The outcome of the dependent variable however, relies on another variable called the independent variable.changes in the independent variable affects the outcome of the dependent variable. In the scenario above, the dependent variable is the average exam scores obtained which depends on how the amount of lavender sprayed brings an effect. Ounces of lavender sprayed is the independent variable.

Answer:

B

Step-by-step explanation:

Use pythagorean theorem

4^2+5^2=AC^2, AC= 6.4

7^2+9^2=CB^2, CB=11.4

Answer:

622,080

Step-by-step explanation:

The total number of subjects is 3

= 3×2×1

= 6

Six maths book

= 6×5×4×3×2×1

= 720

Four physics book

= 4×3×2×1

= 24

Three chemistry book

= 3×2×1

= 6

6×720×24×6

= 622,080

Hence if the books are grouped together 622,080 arrangement is possible

Answer:

100

Step-by-step explanation:

well you can put 5 students in each class guaranteed 5 times over so it would make sense because 5 for each class 9th-12th 5 times over again and again will eventually give you the answer of 100 5•20

If we take 5 students are in each class.

Then let minimum number of students be x

ATQ

1/20()x = 5

x = 5 × 20

x = 100

Answer: 100 people

Must click thanks and mark brainliest

Answer:

t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks

S = V * t

V = S / t = 20 mi * 5280 ft/mi / 2800  sec  = 37.7 ft/sec

Since 88 ft/sec = 60 mph

the speed is 60 * 37.7 / 88 = 25.7 mph

Answer:

A)

Step-by-step explanation:

the solution of a squared equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = 8

c = 22

x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =

= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =

= -4 ± sqrt(-6) = -4 ± i×sqrt(6)

Answer:

2x + 30° = 40°

4x + 30° = 50°

Step-by-step explanation:

2x + 30° and 4x + 30° are complementary angles.

Complementary angles sum up to give 90°.

Therefore,

2x + 30° + 4x + 30° = 90°

Add like terms

6x + 60 = 90

6x = 90 - 60

6x = 30

6x/6 = 30/6

x = 5

✔️2x + 30°

Plug in the value of x

2(5) + 30

10 + 30

= 40°

✔️4x + 30°

4(5) + 30°

20 + 30

= 50°

Answer:

17ft

Step-by-step explanation:

5*2 + 3.5*2=17

Answer:

A. x = 1/2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4x² + 3 = 4x + 2

Step 2: Solve for x

Answer:

[tex]s=6\sqrt{3}[/tex]

Step-by-step explanation:

In any 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.

In the given diagram, the hypotenuse is marked as 12 miles. Therefore, the side opposite to the 30 degree angle must be [tex]12 \div 2=6[/tex] miles. The final leg, [tex]s[/tex], must then represent the [tex]x\sqrt{3}[/tex] part of our ratio, hence [tex]\implies \boxed{6\sqrt{3}}[/tex]

Answer:

a = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos60° = [tex]\frac{1}{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

a = 4[tex]\sqrt{3}[/tex]

Answer:

44/3

Step-by-step explanation:

V=L*W*H

WH=22/3

V=2*(22/3)

Answer:

616.2442

area to the nearest whole number=616

Step-by-step explanation:

using formula 1/2absinx

where a =44,b=29 ,x=105

1/2x44x29xsin105

44x29=1276

1276÷2=638

638 x sin 105

the sin of 105 is 0.9659

if u are using a four figure table where u can't find 105 under sin of angle

u simply subtract 105 from 180=75

638 x 0.9659 =616.2442

approx.616

Answer:

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Step-by-step explanation:

Before building the confidence intervals, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

In the morning:

Sample of 57, mean of 5.2, standard deviation of 0.6, so:

[tex]\mu_1 = 5.2[/tex]

[tex]s_1 = \frac{0.6}{\sqrt{57}} = 0.0795[/tex]

In the afternoon/evening:

Sample of 70, mean of 4.5, standard deviation of 0.4, so:

[tex]\mu_2 = 4.5[/tex]

[tex]s_2 = \frac{0.2}{\sqrt{70}} = 0.0239[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 5.2 - 4.5 = 0.7[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0795^2 + 0.0239^2} = 0.083[/tex]

Confidence interval:

The confidence interval is:

[tex]\mu \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower bound of the interval is:

[tex]\mu - zs = 0.7 - 1.96*0.083 = 0.5[/tex]

The upper bound of the interval is:

[tex]\mu + zs = 0.7 + 1.96*0.083 = 0.9[/tex]

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Answer:

Hi! I'll provide the answers in the explanation.

Step-by-step explanation:

a) The table is in the attachment.

b) The percentage is 40%. Looking at the table, we can see that the total of teachers who voted is 30. You'll be able to find the percentage if you divide 30/75, since 75 is the total people who took the survey.

c) The percentage is 40%. For this situation, we have to divide the total of the people who voted for NO by the teachers who voted NO. So it'll be 20/50, which is 0.4. We can simplify that and the solution is 40%.

d) It represents the students who took the survey voted NO for a later start.

Hope this helps! :D

Answer:

5. Use the following information to answer the questions.

A survey asked 75 people if they wanted a later school day start time.

45 people were students, and the rest were teachers.

50 people voted yes for the later start.

30 students voted yes for the later start.

a) Use this information to complete the frequency table. (5 points: 1 point for each cell that was not given above)

Vote YES for later start

Vote NO for later start

Total

Students

30

15

45

Teachers

20

10

30

Total

50

25

75

b) Use the completed table from Part a. What percentage of the people surveyed were teachers? (2 points)

40%

c) Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time? (2 points)

40%

d) What does the number in the bolded cell represent? (1 point)

The number of students that said no to a later start.

Step-by-step explanation:

A p E x

9514 1404 393

Answer:

  a. Definition of bisector.

Step-by-step explanation:

Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.

The conclusion is justified by the definition of a bisector.

9514 1404 393

Answer:

  73 ft²

Step-by-step explanation:

The ratio of areas is the square of the ratio of linear dimensions.

  smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)

  smaller area = 73 1/3 ft² ≈ 73 ft²

Answer:

Area of the smaller triangle = 73 square feet

Step-by-step explanation:

Area of the larger triangle = 165 square feet

Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]

[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]

Height = 22 ft

Since, both the triangles are similar.

By the property of similar triangles,

Corresponding sides of the similar triangles are proportional.

Let the height of smaller triangle = h ft

Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]

h = [tex]\frac{22\times 10}{15}[/tex]

h = 14.67 ft

Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]

                                              = 73.33

                                              ≈ 73 square feet

Answer:

Step-by-step explanation:

3

Answer:

1.572

Step-by-step explanation:

For a standard normal distribution,

P(z > c) = 0.058

To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;

Using technology or table,

Zscore equivalent to P(Z > c) = 0.058 is 1.572

Hence, c = 1.572