Express the series using sigma notation. 6 + 9 + 12 + 15.

Answer:

C

Step-by-step explanation:

Side a has a length of 5 and b has a length of 7. From the Pythagorean Theorem, 5² + 7² = c² which means c = 8.

Answer:

f(3) = 30

Step-by-step explanation:

f(3) = 3^(3) + 3

f(3) = 27 + 3

f(3) = 30

Answer:

A)The probability of randomly selecting a score less than X=51 is 0.3085

B)The probability of selecting a Random sample of n=4scores with a mean less than m=51 is 0.1587

C)The probability of selecting a sample of n=36scores with a mean less than m=51 is 0.0013

Step-by-step explanation:

Mean =[tex]\mu = 54[/tex]

Standard deviation =[tex]\sigma = 6[/tex]

A)What is the probability of randomly selecting a score less than X=51 i.e. P(x<51)?

Formula : [tex]Z =\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{51-54}{6}[/tex]

Z=-0.5

Refer the Z table for p value

So, P(x<51)=0.3085

So,the probability of randomly selecting a score less than X=51 is 0.3085

B)What is the probability of selecting a Random sample of n=4scores with a mean less than m=51?

Formula : [tex]Z =\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z=\frac{51-54}{\frac{6}{\sqrt{4}}}[/tex]

Z=-1

Refer the Z table for p value

So, P(x<51)=0.1587

So, the probability of selecting a Random sample of n=4scores with a mean less than m=51 is 0.1587

C) What is the probability of selecting a sample of n=36scores with a mean less than m=51?

Formula : [tex]Z =\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z=\frac{51-54}{\frac{6}{\sqrt{36}}}[/tex]

Z=-3

Refer the Z table for p value

So, P(x<51)=0.0013

So,the probability of selecting a sample of n=36scores with a mean less than m=51 is 0.0013

Answer:

The width is 7 cm

Step-by-step explanation:

The volume of a cereal box is

V = l*w*h

6860 = 35 * w * 28

6860 =980 w

Divide each side by 980

6860/980 = w

7 = w

Answer:

35*28=6,860

980 = 6,860

divide by 980 to both side

_980__ =  _6,860_

980                980

x = 7

Step-by-step explanation:

Answer:

The angle of ∠ABE is 40°.

Step-by-step explanation:

Given that ∠ABE and ∠CBD are opposite vertical angles so they have the same measure of angles.

Because ∠ABE and ∠CBD are vertical angles, ∠ABE = ∠CBD = 40°.

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Answer:

71% = P

Step-by-step explanation:

500/700 = P/100

500(100) =700p

50,000/700 = 700p/700

P=71%

The percent increase in enrollment is, 71.43%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The enrollment at the 21st Century High School increased from 700 students to 1,200 students over a period of 5 years.

Now,

Increased students = 1200 - 700

                              = 500

Hence, The increased percent is,

⇒ 500 / 700 × 100

⇒ 71.43%

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Step-by-step explanation:

1/2 on the first round, then 1 on the second. When you have 2 juice boxes on the first round, there is a 50/50 (reduce to 1/2) chance that you will get one or the other. But after one is chosen, there is one left, because there is no replacement, and it is guarantied that the one will be picked. 100/100 or 1.

Answer:

I am answering to this question: There are 15 cherry, 17 grape, and 14 orange juice boxes in the cooler. Find the probability of randomly selecting two grape juice boxes without replacement.

Step-by-step explanation:

136/1035

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Answer:

x = 135     y = 45

Step-by-step explanation:

The sum of the measure of interior angles can be found by equation  

(n - 2) x 180            n is the number of sides

(8 - 2)180 = 1080

Sum of measure of interior angles is 1080 degrees. Variable x, which we are solving for, it the measure of one interior angle. To find x, divide 1080 by 8 to find the measure of one interior angle.

1080 / 8 = 135

x = 135 degrees

We know that a trapezoid like the one formed in the octagon has 2 pairs of congruent angles. we know two of the angles already, as they are the measure of one interior angle, or 135 degrees. The sum of the measure of interior angles of a trapezoid is 360 degrees.

360 - 2(135) = 90

The sum of the remaining two angles of the trapezoid are 90 degrees. These two angles are equal, so divide 90 by 2.

90 / 2 = 45

y = 45 degrees.

135  45 Answer:

Step-by-step explanation:

Answer:

48 miles per hour

Step-by-step explanation:

Take the miles and divide by the time to get miles per hour

120 miles / 2.5 hours

48 miles per hour

Answer:

the bus is going 48 mile per hour

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

Since B is the midpoint of segment AC, then AB = BC.

AB = BC

3x - 8 = x + 12

2x - 8 = 12

2x = 20

x = 10

As per the given information, the value of x is 10. For understanding, check the calculations provided below.

A midpoint is a point that divides a line into two parts equally.

In the given diagram,

B is the midpoint of line segment AC. Midpoint B divides the line segment AC equally.

When a midpoint B divides equally then AB = BC

Given that,

AB = 3x-8 and BC = x+12

B is the midpoint of line segment AC.

So,

AB = BC

Substitute the expression and solve for x

AB = BC

3x-8=x+12

Subtract x,

⇒ 3x-x-8 = x-x+12

⇒ 2x-8=12

Add 8

⇒ 2x = 12+8

⇒ 2x = 20

divide by 2

∵ x = 10

Thus, the value of x is 10.

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Answer:

b) 65f

Step-by-step explanation:

Answer:

b. 65° F

Step-by-step explanation:

option B is correct answer

Answer: 50 miles

Step-by-step explanation:

On maps one inch is a mile

Answer:

1) 22

2) 19.5

3) 26

4) 12

5) False

6) True

7) Mean

8) False

9) Add all the numbers and divide by the total number of numbers

10) Bimodal

Step-by-step explanation:

1)Use the data to calculate the mean. 24, 31, 12, 38, 12, 15 *

To calculate mean you add all the numbers up and divide by the total number of numbers.

[tex]\frac{24 + 31+12+38+12+15}{6} = 22[/tex]

2) Use the data to calculate the median. 24, 31, 12, 38, 12, 15 *

For median, arrange the numbers from lowest to largest

12, 12, 15, 24, 31, 38

use (n+1) / 2 to figure out which value is the median

(6+1) / 2 = 3.5 (median is in between the 3rd and 4th value)

(15+24) / 2 = 19.5

3) Use the data to calculate the range. 24, 31, 12, 38, 12, 15 *

Range is max value - min value

38 is max and 12 is min

38 - 12 = 26

4) Use the data to calculate the mode. 24, 31, 12, 38, 12, 15 *

Mode is the value that appears most frequently

In this case 12 appears 2 times, therefore it is the mode

5) the mode represents the number that appears the least *

False, mode is the number that appears the most

6) To calculate the range we use the highest and lowest number ? *

True

7) Average is another word for *

mean

8) the range indicates the middle number ? *

False, range is the max value - min value

9) which statement best describes the mean. *

add all the numbers and divide by the total number of numbers

10) A data set with two modes is known as *

bimodal

___________________________________

hey!!

summation fX=132

N(total no.of items)=6

Now,

Mean=summation FX/N

=132/6

=22

2. Arranging the data in ascending order

= 12,12,15,24,31,38

N=6

Median=(N+1/2)th item

= (6+1/2) th item

=(7/2)th item

=3.5 th item

Again,

median=3 rd item + 4th item/2

=15+24/2

= 39/2

=19.5

3.Range= highest score- lowest score

=38- 12

=26

4. Mode= 12 because it has more frequency.

______________________________________

Good luck on your assignment

________________________________

Answer:

a)   45

The sequence  3 , 5, 9 , 15 , 23 , 33 , 45

Step-by-step explanation:

Given The sequence  3 , 5, 9 , 15 , 23 , 33

First term = 3

Add 2  of first term  

Second term  = 3 +2 = 5

Add 4  of second term  

Third term = 5 + 4 = 9

Add 6  of Third term  

Fourth term  = 9 + 6 = 15

Add 8 of  fourth term

fifth term = 15 + 8 = 23

Add 10 of fifth term

sixth term = 23 + 10 = 33

Add 12 of sixth term

seventh term = 33 +12 = 45

Final answer:-

Now the sequence   3​, 5​, 9​, 15​, 23​, 33​, ​__45___

Answer: 2.25 km

Step-by-step explanation:

2 cm = 0.5 km

9 cm = (9 x 0.5)/2

= 2.25 km

Answer:

2.25 km

Step-by-step explanation:

Since 2 cm represents 0.5 km on the ground we cross multiply to find how much ground will be represented by 9 cm on the map

9cm=?

NOTE: since the cm are the same they will cancel each other out in the division stage

Answer:

g(5)=17

Step-by-step explanation:

g(x)=3x+2

Let x = 5

g(5) = 3*5+2

      = 15+2

      = 17

Answer:

17

Step-by-step explanation:

Just substitute 5 into the position of X

b. c=4s

you multiply x times 4 to get y

Answer:

Option (B). Perimeter of the quadrilateral ABCD= 14.6 units

Step-by-step explanation:

From the figure attached,

Coordinates of the vertices are A(3, 5), B(1, 3), C(3, -1), D(5, 3).

Length of AB = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

                      = [tex]\sqrt{(3-1)^2+(5-3)^2}[/tex]

                      = [tex]\sqrt{8}[/tex]

                      = 2.83 units

Length of AD = [tex]\sqrt{(3-5)^2+(5-3)^2}[/tex]

                      = [tex]\sqrt{8}[/tex]

                      = 2.83 units

Length of BC = [tex]\sqrt{(1-3)^2+(3+1)^2}[/tex]

                      = [tex]\sqrt{20}[/tex]

                      = 4.47 units

Length of DC = [tex]\sqrt{(5-3)^2+(3+1)^2}[/tex]

                       = [tex]\sqrt{20}[/tex]

                       = 4.47 units

Perimeter of the quadrilateral = AB + AD + DC + BC

                                                 = 2.83 + 2.83 + 4.47 + 4.47

                                                = 14.6 units  

Option (B) is the answer.

Answer:

$250

Step-by-step explanation:

200/80=2.50

2.50*100=250

Answer:

$250.

Step-by-step explanation:

By proportion the cost should be 200 * 100/80

= 200*5/4

= 50 * 5

= $250.

Answer:

[tex]r = 4[/tex]

Step-by-step explanation:

Given: Direct Variation

(0,0) ,(3,12),(9,36)​

Required

Constant of Variation

Provided that the given data is a direct variation, the constant variation is represented by r.

r is calculated as thus;

[tex]y = rx[/tex]

Divide both sides by x

[tex]r = \frac{y}{x}[/tex]

Point (0,0) is the center of origin and cannot be used

When x = 3, y = 12

and

[tex]r = \frac{12}{3}[/tex]

[tex]r = 4[/tex]

When x = 3, y = 12

and

[tex]r = \frac{36}{9}[/tex]

[tex]r = 4[/tex]

Notice that the value of r remain constant in both cases; Hence, the constant of variation is; [tex]r = 4[/tex]

The business requires $124,200 to pay its employees each week.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

A small company employs 98 workers. Every employee works 8 hours a day, 5 days a week. Eleven employees are paid $45 per hour, while the remaining employees are paid $30 per hour. 

As per the given question, the required solution would be as:

No. of employees at $30hr: 98 -11 = 87

⇒ 8 hours × 5 days = 40 hour a week

⇒ 40 hour × $30 × 87 =104,400

⇒ 40 hour × $45 × 11 = 19,800

⇒ 104,400 + 19,800 = 124,200

Thus, the business requires $124,200 to pay its employees each week.

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Answer:

0 , 120 , 120 , 150

Step-by-step explanation:

Lets consider in step by step

For Time = 0 hours

At t= 0, the train has not moved from its initial spot. The amount of distance travelled by train is 0

For Time = 2 hours

The train is travelling at a constant speed of 60 miles per hour. As the train travels for 2 consecutive hours at the same speed without stopping, it means that it covers a distance of 60 miles in 1st hour and another 60 miles in 2nd hour. Total distance covered is 120 miles.

For Time = 2.5 hours

The train stops after 2 hours and remain at the same place for 30 mins. So, after 2.5 hours the distance remains the same i.e 120 miles , as the train was stopped.

For Time = 3.5 hours

After 2.5 hours, train travels at a speed of 30 miles per hour. Which means that it covers another 30 miles to reach the destination.

Total Distance covered = 120+30 = 150 miles

Answer:

-85n - 7  = -92

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

I tried to solve this by doing the square root of [tex]x^{2} +49[/tex], which is x+7. x+7≠x+5

Answer:

1/8th

Step-by-step explanation:

Answer:

1/8 of the sub or 1.5 inches

Step-by-step explanation:

One foot=12 inches, but the teacher eats half, so we are left with only six inches. then, divide the six inches with the number of students, which is 4. if you divide 12 and 1.5, you'll see that there are a total of 8 pieces, so one student gets 1 out of the 8

Answer:

Not a solution.

Step-by-step explanation:

2=-3/4(3)+3

2=-9/4+3

2 does not equal 3/4.

Therefore, it is not a solution.

Answer:

False

Step-by-step explanation:

Just plug it in.

[tex]2 = -\frac{3}{4}*3 + 3[/tex]

2 = -2.25 + 3

2 ≠ 0.75

It is not equal so it's false.

Answer:

6

Step-by-step explanation:

3x2

Answer:

its D

Step-by-step explanation:

Just did the test. Goodluck

Answer:

d

Step-by-step explanation: