Select the correct answer.

Answer:

x=4 and x=3

Step-by-step explanation:

The first step to find all factors of 12

1,2,3,4,6,12

and their negative form

-1,-2,-3,-4,-6,-12

we must add two of these numbers to get -7

and the two numbers that add up to -7 are -3 and -4

we can simply plot them into the polynomial (x-3)(x-4)

since x-3=0

we add three to both sides to get x=3

and since x-4=0

add four to both sides

we get x=4

and now check out work which

we can use First out in last (foil) method

(x-3)(x-4)

first

x^2

out

-4x

in

-3x

last

12

now we simplify to get x^2-7x+12

so it x=4 x=3 works

Answer:

x² - 7x + 12 = 0

doing middle term factorization

x²-4x-3x+12=0

taking common from each two term

x(x-4)-3(x-4)=0

taking common

(x-4)(x-3)=0

either

x-4=0

:. x=4

or

x-3=0

x=3

:.x=4,3

Answer:

x=6

Step-by-step explanation:

2x+4=16

2x+4-4=16-6

2x=12

x=6

Proof:

2x+4=16

2(6)+4=16

12+4=16

16=16

Hope this helps ;) ❤❤❤

Answer:

find out what x is and it is 6 it is 6 because 2 times 6 is 12 and 12 plus 4 is 16

Step-by-step explanation:

Answer:

  53

Step-by-step explanation:

Let's start with the given relation:

  2x -7 = (x+4) +5

  x = 16 . . . . . . . . . add 7-x

  3x +5 = 3(16) +5 = 53 . . . . . multiply by 3 and add 5

The value of 3x+5 is 53.

Answer:

Step-by-step explanation:

Let the point P is origin (0, 0), segment AB lies on the x-axis and segment PC on the y-axis,

Coordinates of A, B and C will be (1, 0), (2, 0) and (0, 2).

When triangle ABC is dilated by a scale factor 4 about the origin,

Rule for dilation;

(x, y) → (4x, 4y)

New coordinates of the points A, B and C will be,

A(1, 0) → A'(4, 0)

B(-2, 0) → B'(-8, 0)

C(0, 2) → C'(0, 8)

By plotting points A', B' and C' we can get the dilated image A'B'C'.

Dilation involves changing the size of a shape.

Assume point P is the center of origin, then we have the following coordinates of ABC

[tex]A = (1,0)[/tex]

[tex]B = (-2,0)[/tex]

[tex]C = (0,2)[/tex]

The scale factor (k) is given as:

[tex]k= 4[/tex]

So, the dilation rule is represented as:

[tex](x,y) \to (4 \times (x,y)[/tex]

Using the above dilation rule, the following coordinates represent the image of triangle ABC

[tex]A' = (4,0)[/tex]

[tex]B' = (-8,0)[/tex]

[tex]C = (0,8)[/tex]

See attachment for the image of the dilation.

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Answer:

The number of ways is 13860 ways

Step-by-step explanation:

Given

Senior Members = 10

Junior Members = 12

Required

Number of ways of selecting 6 students students

The question lay emphasis on the keyword selection; this implies combination

From the question, we understand that

4 students are to be selected from senior members while 2 from junior members;

The number of ways is calculated as thus;

Ways = Ways of Selecting Senior Members * Ways of Selecting Junior Members

[tex]Ways = ^{10}C_4 * ^{12}C2[/tex]

[tex]Ways = \frac{10!}{(10-4)!4!)} * \frac{12!}{(12-2)!2!)}[/tex]

[tex]Ways = \frac{10!}{(6)!4!)} * \frac{12!}{(10)!2!)}[/tex]

[tex]Ways = \frac{10 * 9 * 8 * 7 *6!}{(6! * 4*3*2*1)} * \frac{12*11*10!}{(10!*2*1)}[/tex]

[tex]Ways = \frac{10 * 9 * 8 * 7}{4*3*2*1} * \frac{12*11}{2*1}[/tex]

[tex]Ways = \frac{5040}{24} * \frac{132}{2}[/tex]

[tex]Ways = 210 * 66[/tex]

[tex]Ways = 13860[/tex]

Hence, the number of ways is 13860 ways

I used arm span as the x-axis and height as the y-axis; arm span is the independent variable because height is typically dependent on arm span. Although the opposite could be argued for.

The equation of the line of best fit is y= 12+(7/9)x. To get the slope I used the points (37,39) and (19,25). The slope is therefore 14/18=7/9. The slope represents that height increases by 7/9 inches when arm span increases by 1 inch. The y-intercept 12 represents roughly the height when arm size is very small. I tested the residuals of the points (47,49) and (58,61). The respective predictions are 48.556 and 57.111. The respective residuals are then (49-48.556)=0.444 and (61-57.111)=3.889. It seems that the line models the data well until the x values get larger, where the performance decreases. The line of best fit with its positive slope indicates that there is a positive correlation with arm span and height.

Using the model, a person with arm span 66 inches has a height of 12+(7/9)*66= 63.333 inches. A person with 74 inches height has an estimated arm span of 62*9/7= 79.714 inches.

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 \\with \; R^2 = 0.951[/tex]

The y  intercept 3.787 represents the  height of that is independent of Arm span.

The height of the person whose arm span is 66 inches is 66.817 inch.

The arm span of a person whose height is 74 inches is 73.52 inch

According to the given data the arm span  and heights are given in inches

Using Microsoft excel we can draw the scatter plot of both the variables such that arm span is on X axis and Height is on Y axis

The  image for the excel work done showing calculations and scatter plot  is attached.

Now we can fit the linear tread line and  to find out the equation of fitted line just tick on the " show equation" line option of trend line fitting

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 .....(1) \\with \; R^2 = 0.951[/tex]

Slope of line of best fit = 0.955

So we can conclude that height (Y) is related to Arm span according to equation (1)

Equation (1) shows the equation of line of best fit for the given data

The y  intercept 3.787 represents the  height of that is independent of Arm span.

So the height of the person whose arm span is 66 inches is given following

[tex]\rm y = 0.955 \times 66+ 3.787 \\y = 66.817 \; inch[/tex]

Similarly the arm span of a person whose height is 74 inches

[tex]\rm 74 = 0.955x +3.787 \\x = 73.52 \; inches[/tex]

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Answer: $1,540,194.30 .

Step-by-step explanation:

The formula to calculate the accumulated amount earned on principal (P) at rate of interest (r)[ in decimal] compounded monthly after t years :

[tex]A=P(1+\dfrac{r}{12})^{12t}[/tex]

Given:  P= $425,000

r= 4.3% = 0.043

t= 30 years

[tex]A=425000(1+\dfrac{0.043}{12})^{12(30)}\\\\=425000(1.003583)^{360}\\\\=425000\times3.62398657958\approx1540194.30[/tex]

Hence, the payment would be $1,540,194.30 .

Answer:

6

Step-by-step explanation:

The constant of variation is the slope

k = (y2-y1)/(x2-x1)

  = (30-18)/(5-3)

   =12/2

   = 6

The value of constant of variation, k, is,

⇒ k = 6

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Here, the constant of variation, k, of the line y = kx through (3,18) and (5,30)

Since, The constant of variation is the slope,

Hence, We get;

k = (y₂ - y₁)/(x₂ - x₁)

 = (30 - 18)/(5 - 3)

  = 12/2

  = 6

Thus, the value of constant of variation, k, is,

⇒ k = 6

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Answer:

[tex]\large \boxed{\sf No}[/tex]

Step-by-step explanation:

There are 365 days in 1 year.

The average person lives for about 78 years.

Multiply 78 by 365 to find the value in days.

[tex]78 \times 365= 28470[/tex]

The average person lives for about 28470 days.

Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

h = –21.962x + 114.655

As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.

Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

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Answer:

Step-by-step explanation:

Coordinates of the vertices of the given rectangle are,

A(-4, 5), B(-2, 5), C(-2,1) and D(-4, 1).

If the given rectangle ABCD is translated by 1 unit right and 4 units down,

Rule for the translation will be,

(x, y) → [(x + 1), (y - 4)]

Therefore, coordinates of A, B, C and D after translation will be,

A(-4, 5) → A'(-3, 1)

B(-2, 5) → B'(-1, 1)

C(-2, 1) → C'(-1, -3)

D(-4, 1) → D'(-3, -3)

Then A', B', C' and D' are reflected about the y-axis.

Rule for the reflection about y-axis will be,

(x, y) → (-x, y)

New coordinates after the reflection will be,

A'(-3, 1) → A"(3, 1)

B'(-1, 1) → B"(1, 1)

C'(-1, -3) → C"(1, -3)

D'(-3, -3) → D''(3, -3)

Finally these points are rotated 270° clockwise about the origin,

Rule to be followed,

(x, y) → (-y, x)

Therefore, new coordinates will be,

A"(3, 1) → A"'(-1, 3)

B"(1, 1) → B'"(-1, 1)

C"(1, -3) → C"'(3, 1)

D"(3, -3) → D"'(3, 3)

Answer:

step 2

Step-by-step explanation:

9 = -3(e - 2)

9 = -3e + 6

9-6 = -3e

3 = -3e

divide both sides by -3

-1 = e

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are there for the interviewer to create the list?

Since the question deals with selection, we will apply the combination rule. Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

According to the question, if the the interviewer is to select 6 applicants from a pool of 20 applicants that are interviewed for a job, this can be done in 20C6 number of ways.

20C6 = 20!/(20-6)!6!

20C6 = 20!/14!6!

20C6 = 20*19*18*17*16*15*14!/14!*6*5*4*3*2

20C6 =  20*19*18*1716*15/6*5*4*3*2

20C6 = 27,907,200/720

20C6 = 38,760 different ways.

Hence, the interviewer can create the list in 38,760 different ways.

Answer:

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]Sections = 10[/tex]

[tex]n(Gray) = 5[/tex]

[tex]n(Blue) = 5[/tex]

Required

Determine P(Gray and Blue)

Using probability formula;

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

Calculating P(Gray)

[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]

[tex]P(Gray) = \frac{5}{10}[/tex]

[tex]P(Gray) = \frac{1}{2}[/tex]

Calculating P(Gray)

[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]

[tex]P(Blue) = \frac{5}{10}[/tex]

[tex]P(Blue) = \frac{1}{2}[/tex]

Substitute these values on the given formula

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

  93

Step-by-step explanation:

First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.

_____

First differences are ...

  13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20

Second differences are ...

  8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4

When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.

Answer:

Credit remaining after 21 minutes = $30.4

Step-by-step explanation:

Credit remaining on a phone card is a linear function of the total calling time.

When graphed, let the linear function representing the line is,

y = mx + b

Where 'm' = slope of the line

b = y-intercept

From the graph,

Slope of the line = -0.12

y = -0.12x + b

If this line passes through a point (33, 28.96),

28.96 = -0.12(33) + b

b = 28.96 + 3.96

b = 32.92

Therefore, the linear function is,

f(x) = -0.12x + 32.92

where x = calling time

Credit left in the card after 21 minutes,

f(21) = -0.12(21) + 32.92

      = -2.52 + 32.92

      = $30.4

Answer:

[tex]Probability = 0.068[/tex]

Step-by-step explanation:

Let P(S) represent the probability that stock market will go up in a day

Given

[tex]P(S) = 51\%[/tex]

Required

Determine the probability that stock will go up 4 consecutive days

Start by converting P(S) from percentage to decimal

[tex]P(S) = 51\%[/tex]

[tex]P(S) = \frac{51}{100}[/tex]

[tex]P(S) = 0.51[/tex]

The above expression represents the probability in a day;

For 4 days; we have:

[tex]Probability = P(S) * P(S) * P(S) * P(S)[/tex]

[tex]Probability = (P(S))^4[/tex]

Substitute 0.51 for P(S)

[tex]Probability = (0.51)^4[/tex]

[tex]Probability = 0.06765201[/tex]

[tex]Probability = 0.068[/tex] -- Approximated

Hence, the probability that stock will rise for 4 consecutive days is 0.068

Answer:

6.25

Step-by-step explanation:

(x-a)^2=x^2-2ax+a^2

2a=5

a=2.5

2.5 ^ 2 = 6.25

Answer:

bde

Step-by-step explanation:

Answer:

B: The histogram shows there were 22 students in the class.

D: The histogram is symmetrical.

E:The histogram has a peak.

F: The histogram shows the data is evenly distributed.

Step-by-step explanation:

edg 2020

Answer: $2750

Step-by-step explanation:

Formula to calculate interest : I = Prt , where P = Principal amount , r = rate of interest ( in decimal) , t= time.

Given:  I= $495

t= 3 years

r= 6% = 0.06

Then, according to the above formula:

[tex]495 = P (0.06\times3)\\\\\Rightarrow\ P=\dfrac{495}{0.18}\\\\\Rightarrow\ P=2750[/tex]

Hence, the principal invested = $2750

Answer:

[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

Answer = A

Answer:

Please refer to the attached graph.

Slope = -3.125

Step-by-step explanation:

Given

Time is placed on x axis.

Initially, height of rock climber is 25 feet above sea level.

[tex]t_1 =0\ sec[/tex]

[tex]h_1[/tex] = 25 feet

After 8 seconds, he is at sea level.

[tex]t_2 =8\ sec[/tex]

[tex]h_2[/tex] = 0 feet

To find:

Graph of the given points and Slope of the line depicted.

Solution:

Kindly refer to the attached graph.

Here, we have been given two points to be plotted on the xy coordinate plane.

1st point is (0, 25): Time is 0 and height above sea level is 25 ft

2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)

First of all, mark these points and join them with a straight line.

Please refer to attached graph.

Slope of a line is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Here,

[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]

Using the formula:

[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]

Answer:

So this is giving us the slope the slope is y=-7x+150

Step-by-step explanation:

It is giving us the Y intercept which is $150  because thats how much he starts out with

It is giving us the slope -7 dollars because he is spending that everyday

Answer:

The probability is  [tex]p(n ) = 3.18*10^{-5}[/tex]

Step-by-step explanation:

From the question we are told that

     The population size is  N =  31

      The sample size  n =  4  

Generally the number of way by which the n  can be selected from N is mathematically represented as

          [tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]

The number of ways of selecting a particular sample size is  is   [tex]k = 1[/tex]

Therefore the probability of each simple random sample in this​ case is mathematically evaluated as  

           [tex]p(n ) = \frac{1}{31465}[/tex]  

           [tex]p(n ) = 3.18*10^{-5}[/tex]

Answer:

B

Step-by-step explanation:

1. Lets focus on 55^5

55^5 = 11^5 * 5^5

2. now on 65

65 = 5 * 13

3. now on 9^15

9^15=(3^2)^15 = 3^30

4. combine all three parts

11^5 * 5^5 * 5 * 13 * 3^30 = 11^5*5^6*13*3^30

so our answer is B

[tex]f(f(3))=2\cdot3^2+1=19\\f(f(f(f(3))))=2\cdot19^2+1=723[/tex]

Answer:

Percentage of home team supporters =65%

Percentage of visiting team supporters =35%

Step-by-step explanation:

Total attendees=2,000 people

Home team supporters=1,300

Visiting team supporters=700

What percentage of people attending supported the home team?

Percentage of people attending who supported the home team = home team supporters / total attendees × 100

=1,300/2,000 × 100

=0.65 × 100

=65%

Visiting team supporters = visiting team supporters / total attendees

× 100

=700/2000 × 100

=0.35 × 100

=35%

Alternatively,

Visiting team supporters = percentage of total attendees - percentage of home team supporters

=100% - 65%

=35%

Answer:

Number 1: A

Number 2:D

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Do 60*.80

60 represent the total points the test was worth

.80 represents the % number

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

100% = 60

80% = 48

The points Salema earned are 48 points.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Salema's score = 80%

Total score in the test = 60 points

Salema's score.

= 80% of 60 points

= 80/100 x 60

= 48

Thus,

The points Salema earned are 48 points.

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