What is the component form of the vector whose tail is the point (-3,2) and whose head is the point (1, -6)?

[tex]x^4 +2x^3 -11x^2-12x+36\\ \\=x^4-2x^3+4x^3-8x^2-3x^2 +6x-18x+36\\\\=x^3(x-2) +4x^2(x-2) -3x(x-2) -18(x-2)\\\\=(x-2)(x^3 +4x^2 -3x -18)\\\\=(x-2)(x^3+3x^2+x^2+3x-6x-18)\\\\=(x-2)\textbf{[}x^2(x+3)+x(x+3)-6(x+3)\textbf{]}\\\\=(x-2)(x+3)(x^2 +x -6)\\\\=(x-2)(x+3)(x^2 +3x -2x-6)\\\\=(x-2)(x+3)\textbf{[}x(x+3) -2(x+3)\textbf{]}\\\\=(x-2)(x-2)(x+3)(x+3)\\\\=(x-2)^2(x+3)^2[/tex]

There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.

In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

It Is said That 60% of families own a pet.

Of a sample of 95 families, 70 owned pets.

Whether the percent of families who own pets is different than 60%.

Let P be a proportion of the family who owns pets

Then by the test, we have

H₀: P = 0.60

Hₐ: P ≠ 60

Then by the test statistic, we have

[tex]z_o = \dfrac{\bar{P} - P_o}{\sqrt{\dfrac{P_o(1 - P_o)}{n}}}[/tex]

Where

[tex]\bar P[/tex]  = sample proportion

P₀ = hypothesis proporion

n = sample size

Then we have

[tex]\bar P[/tex] = x/n

[tex]\bar P[/tex] = 70/95

[tex]\bar P[/tex] = 0.74

Then the test statistic will be

[tex]z_o = \dfrac{0.74-0.60}{\sqrt{\dfrac{0.60(1-0.60)}{95}}}[/tex]

z₀ = 2.785

Then the critical region will be

Critical value = ± [tex]z_{\alpha /2}[/tex]

α = 0.05

α/2 = 0.025

Then we have

z₀.₀₂₅ = 1.96

Then the critical value will be

Critical value = ± 1.96

We reject if [tex]|z_o| > |z_{\alpha /2}|[/tex]

We have

[tex]|z_o| > |z_{\alpha /2}|\\[/tex]

2.79 > 1.96

We reject the null hypothesis at a 5% significance level.

There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.

More about the null hypotheses and alternative hypotheses link is given below.

https://brainly.com/question/9504281

#SPJ4

The statements that describe the fraction bar diagram shown are:

B. Each part of the whole fraction bar is equal to one-seventh.

C. The shaded portion of the fraction bar represents a unit fraction.

E. Each part represents a unit fraction.

A fraction bar is a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions.

Here,  each part of the whole fraction bar is equal to one-seventh, the shaded portion of the fraction bar represents a unit fraction, and each part represents a unit fraction.

Learn more about fraction on:

https://brainly.com/question/78672

#SPJ1

The given,matrix is [1  -4  5  -7] Thus, the correct option is A [3  -12  15  -21].

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

The given, a matrix is

[1  -4  5  -7]

The product will be

3. [1  -4  5  -7]

[3  -12  15  -21]

Thus, the correct option is A [3  -12  15  -21].

Learn more about multiplications;

https://brainly.com/question/14059007

#SPJ1

The given sum for n = 1 to n = 15 is equal to 255, so the correct option is B.

We want to find the sum of the series whose elements are of the form:

(2n + 1)

From n = 1 to n = 15.

Then our sum will be:

(2*1 + 1) + (2*2 + 1) + ... + (2*15 + 1).

3 + 5 + ... + 31

This is the sum of all odd numbers in the interval [3, 31]

Which gives:

[tex]S = 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 = 255[/tex]

So the correct option is B.

If you want to learn more about sums:

https://brainly.com/question/24295771

#SPJ1

Answer:

When 6x - 4 = 8, x = 2.

Step-by-step explanation:

6x - 4 = 8

Add 4 to both sides.

6x = 12

Divide both sides by 6.

x = 2

Proof:

6x - 4 = 8

Substitute variable.

6(2) - 4 = 8

Multiply 6 and 2.

12 - 4 = 8

Subtract 4 from 12.

8 = 8

Answer:

x is 2

Step-by-step explanation:

Simplify equation

What happens to one side must happen to the other

Add 4 to both sides

This tells us 6x is 12

Divide both sides by 6

X is 2

Answer:

the length of DE is 1/2*9 = 4.5

Answer:

66

Step-by-step explanation:

this is actually an almost trick question because it wants to confuse you!

Here's the trick

to work out a mean (average) you add all the components together then divide by the amount of groups.

but here they didn't give you components just the mean of the classes...both of them.

the question says "The mean fpor class A is 66, the mean score for BOTH classes is 66"

so this means that Class B's mean score is 66 too

hope this helps

Answer:

the radius is 2.02

Step-by-step explanation:

use the formula to solve the radius of a cylinder

The multiplicative inverse of 1000/450 is 9/20

The multiplicative inverse of a number x is:

Inverse = 1/x

The number is given as: 1000/450.

So, we have:

Inverse = 1/(1000/450)

Evaluate the expression

Inverse = 450/1000

Simplify

Inverse = 9/20

Hence, the multiplicative inverse of 1000/450 is 9/20

Read more about multiplicative inverse at:

https://brainly.com/question/1682347

#SPJ1

There are 18 blocks in the first row

Calculate the number of blocks on the first row

The ruin is given as:

Ruin = 49

The common difference is given as:

d = -2

The number of block on each row is then represented as:

Blocks = 48 - 2n

Where n represents the number of rows.

In this case, the first row would have a value of n = 15

So, we have:

Blocks = 48 - 2 * 15

Evaluate

Blocks = 18

Hence, there are 18 blocks in the first row

Read more about sequence at:

https://brainly.com/question/6561461

#SPJ1

The conclusion about the cylinder volume when the radius is half is that the volume is one-fourth of the original

The volume of a cylinder can be represented as follows;

volume = πr²h

volume = π × 10² × 14

volume = 1400π cm³

Let's half the radius as follows:

radius = 10 / 2 = 5 cm

volume = π × 5² × 14

volume = 350π cm³

Therefore, the new volume is one fourth of the original when the radius is halved.

learn more on cylinder here: https://brainly.com/question/15164997

#SPJ4

Answer:

a

Step-by-step explanation:

Answer:

[tex]a=1\\\\b=7[/tex]

Step-by-step explanation:

[tex]\dfrac{x^2 (y^3)^4}{xy^5}\\\\\\=x^{2 -1} \cdot \dfrac{y^{3 \times 4}}{y^5}\\\\\\=x^1 \cdot \dfrac{y^{12}}{y^5}\\\\\\=x^1 \cdot y^{12-5}\\\\\\=x^1 \cdot y^7\\\\\text{Hence a = 1, b = 7}[/tex]

Answer:

a. 10.

Step-by-step explanation:

27 / 3 = 9

90/10 = 9

So it's 10.

Based on the distance to the end of the hike and the distance to the scenic lookout, we can calculate that the straight route is 2 km shorter than the scenic lookout route.

If Maria took the straight route to the end of the Hike from the coordinates, (4, -4) to (-5, 5), she would have to walk 13 km.

If she went the scenic lookout route, she would have to first go to (2,3) before going to (-5,5) which is 15 km.

The difference is:

= 15 - 13

= 2 km

A more readable version of the question is:
Maria is on a hike. If she hikes to the scenic lookout on the following map first, she will have to hike farther than if she went straight to the end of the hike.

3 connected points on a coordinate plane. The point labeled, "Maria," is at 4, -4. The point labeled, "end," is at -5, 5.

A solid line connect the points "Maria" and "end." The point labeled, "scenic lookout," is at 2, 3. Dashed lines connect "Maria" to "scenic lookout" and connect "scenic lookout" to "end."

Find out more calculations involving the shorter distance at https://brainly.com/question/19544173.

#SPJ1

Answer:

2KM

Step-by-step explanation:

Answer:

3,-8

Step-by-step explanation:

x: from -3 to 0   is  +3    add +3 more     3

y: from -2 to -5 is   -3     add -3 more    -8

By using any two of the points in the table, we will see that the slope is -2.

A general linear relationship is:

y = a*x + b

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

Remember that if the line passes through (x₁, y₁) and (x₂, y₂), the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we can use the first two points on the table:

(-4, 11) and (2, -1), so the slope is:

[tex]a = \frac{11 - (-1)}{-4 - 2} = 12/-6 = -2[/tex]

Then the slope of the line is -2.

If you want to learn more about linear relationships:

https://brainly.com/question/4025726

#SPJ1

So we replace "x" with the necessary value (-7):

[tex]f( - 7) \: = \: 5(4 \: - \: ( - 7))[/tex]

[tex]f( - 7) \: = \: 5(4 \: + \: 7)[/tex]

[tex]f( - 7) \: = \: 5 \: \times \: 11[/tex]

[tex]f( - 7) \: = \: \boxed{ \bold{55}}[/tex]

[tex] \boxed{ \bold{55}}[/tex]

[tex]\huge\sf\color{red}{Answer:}[/tex]

Formula:

Lets solve : )

So the answer would be [tex]\large\sf\color{red}{16}[/tex]

The percent increase of going from 40 to 60 is 50%.

We have the Formula

Percent Increase = (New Value - Original Value) / Original Value x 100

As, the values changes from 40 to 60.

So, Percent Increase = (60 - 40) / 40 * 100

Percent Increase = 20 / 40 * 100

Percent Increase = 0.5 * 100

Percent Increase = 50%

Therefore, going from 40 to 60 represents a percent increase of 50%.

Learn more about percent increase here:

https://brainly.com/question/25098379

#SPJ2

Answer:

Lamar wants to predict the number of customers who may be interested in going to a music festival when a ticket to the festival costs $25. Using survey data, Lamar drew a line of best fit to make his prediction. Which should Lamar predict to be the number of customers interested in attending the music festival when the ticket price is $25?/

The measure of angle ∠1 will be 68 degrees.

The missing graph is given below.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The diagram is given below.

Then the measure of angle ∠1 will be

68° + 44° + ∠1 = 180°

                  ∠1 = 68°

The measure of angle ∠1 will be 68 degrees.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ1

The order in which the two transformations in a composite transformation affect the final answer

To determine if order matters or not, I will use the following example and illustration.

Let the coordinate of point A be:

A = (2, 5)

Perform the following transformations:

First order: Translation before dilation

The translation by (x, y + 1) would give:

A' = (2, 5 + 1)

A' = (2,6)

The dilation by a scale factor of 2 would give

A" = 2 * (2,6)

A" = (4,12)

Second order: Dilation before translation

The dilation by a scale factor of 2 would give

A' = 2 * (2,5)

A' = (4,10)

The translation by (x, y + 1) would give:

A'' = (4, 10 + 1)

A'' = (4,11)

See that the final coordinates in both orders are not the same.

Hence, the order in which the two transformations in a composite transformation affect the final answer

Read more about transformation at:

https://brainly.com/question/1548871

#SPJ1

The probability that the next customer will pay with a credit card is 0.61.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.

Given that Cristian's customers pay using, cash, debit cards and credit cards,

He knows that in the last week 10 customers paid cash, 14 customers used a debit card, and 38 customers used a credit card.

We need to find the probability that the next customer will pay with a credit card,

Therefore,

The favorable outcomes = 38

Total outcomes = 38+10+14 = 62

Therefore,

P(credit cards) = 38/62 = 0.61

Hence the probability that the next customer will pay with a credit card is 0.61.

Learn more about probability click;

https://brainly.com/question/30034780

#SPJ2

The two column proof for the given angle addition has been carried out below.

1) m∠CZE = m∠1 + m∠2

Reason: Angle Addition Property

2) m∠FXH = m∠3 + m∠4

Reason: Angle Addition Property

3) m∠CZE = m∠FXH

Reason: Given

4) m∠1 + m∠2 = m∠3 + m∠4

Reason: Substitution Property

5) m∠1 = m∠3

Reason: Subtraction Property

6) m∠3 + m∠2 = m∠3 + m∠4

Reason: Substitution Property

7) m∠2 = m∠4

Reason: Subtraction Property

Read more about Two Column Proof at; https://brainly.com/question/1788884

#SPJ1

Answer:

$1605

Step-by-step explanation:

Because this is simple interest, you can convert the 7% into a decimal

Because she payed an EXTRA 7% she payed 107% total

107% is the equivalent to 1.07

By multiplying 1500 x 1.07 = 1605

The Probability that the mean childhood asthma prevalence for the sample is greater than 2.7% is 0.0357.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

For a Normal Distribution, the z-score formula

[tex]z = \dfrac{X-\mu}{\sigma}[/tex]

Here X is the mean and sigma is the standard deviation.

Mean of 2.25​% = 2.25​

The standard deviation of 1.27%, sigma = 1.27

For Sample 31 the value of the standard deviation is

s = 1.27/√31

s = 0.2442

Substituting the values

Z = ( 2.25 -1.27)/0.2442

Z = 1.8

the p-value from the graph of z and p = 0.9643

To determine value of probability greater than X is 1 - 0.9643 = 0.0357

The Probability that the mean childhood asthma prevalence for the sample is greater than 2.7% is 0.0357.

To know more about Probability

brainly.com/question/11234923

#SPJ1

Answer:

y = -(2x+16) / 5

Step-by-step explanation:

2x + 5y = -16

5y = -2x - 16

y = (-2x - 16) / 5

y = -(2x+16) / 5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6\div2(1 + 2)}[/tex]

[tex]\mathsf{= \dfrac{6}{2}(1 + 2)}[/tex]

[tex]\mathsf{= \dfrac{6}{2}\times(1 + 2)}[/tex]

[tex]\mathsf{= \dfrac{6}{2}\times \bf 3}[/tex]

[tex]\mathsf{= \bold{3}\times3}[/tex]

[tex]\mathsf{= \bf 9}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{9}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Step-by-step explanation:

cos(a) = 1/2 or 0.5

that means a = 60°

the cosine value is the x coordinate, the sine value the y coordinate.

so, only an answer with 1/2 as x coordinate can be right.

and therefore, the 4th answer (bottom right) is correct.