what is the sum of the first fifteen terms of the sequence $2, 8, 14, \dots$, in which each term is six more than the preceding term?

The frequency table is:-

Data        Frequency

10             1

11              2

12             2

13             4

14             6

15             5

The frequency table determines the frequency of the data. In other words, it tells us how many times the same data is repeated.

The given data set is, 13, 14, 12, 15, 15, 14, 15, 11, 13, 14, 11, 13, 15, 12, 14, 14, 10, 14, 13, 15

The frequency table can be written as:-

Data        Frequency

10             1

11              2

12             2

13             4

14             6

15             5

The distribution's shape for the next data set you provided is left- or negatively skewed. This is due to the fact that as a number's value increases, so does its frequency.

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The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To fill in the blanks, we need to use the given information to complete the probability distribution table.

We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

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Answer:

So the solution to the system of equations is (x,y) = (3,-2).

Step-by-step explanation:

To solve for x and y using substitution, we can first substitute y=-2 into the second equation to find the value of x, and then use that to find y.

Starting with the second equation:

4x - 3(-2) = 18

Expanding the -3(-2) using the distributive property:

4x + 6 = 18

Subtracting 6 from both sides:

4x = 12

Dividing both sides by 4:

x = 3

Now that we have x = 3, we can substitute that back into the first equation to find y:

y = -2

So the solution to the system of equations is (x,y) = (3,-2).

Answer:

c

Step-by-step explanation:

trust me

The triangles ΔIGH and ΔGFE are similar triangles. So, GJ / GE = HG / FG, then the side FE is parallel to the side HI.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the corresponding sides will be constant then the triangles will be similar triangles and the third sides of the triangles will be parallel.

GJ / GH = GK / GI, then the side KJ is parallel to the side HI.

In triangles ΔIGH and ΔGFE, then we have

∠IGH = ∠FGE        (Vertival angle)

∠1 = ∠2                         (Given)

Then the triangles ΔIGH and ΔGFE are similar triangles. Then we have

GJ / GE = HG / FG, then the side FE is parallel to the side HI.

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Answer: 6 containers

Step-by-step explanation:

Fraction division.

2/3 divided by 1/8.

Keep-change-flip. (or a similar method for dividing fractions)

2/3 times 8/1 is 16/3.

He will fill 5 and 1/3 containers, so 6 containers will have paint in them.

(っ◔◡◔)っ ♥

Hope this helps.

MM4343

The expression is there are 2 chocolates and 5 lollypops having a total cost of $5. The expression is 2C + 5L = $5.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Suppose the real-time situation is if there are 2 chocolates and 5 lollypops having a total cost of $5.

The mathematical form of the expression can be written as:-

2C + 5L = 5

Here, C is the cost per chocolate and L is the cost of per Lollypop.

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The complete question is given below.

Write the expression if there are 2 chocolates and 5 lollypops having a total cost of $5.

The equation of the line of the best fit  for the data will be, y=2.07x-7.5.

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.

The equation of the line is;

y=mx+c

y=2.07x-7.5

Hence, the equation of the line of the best fit will be, y=2.07x-7.5

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Answer:

a: Angle 1 and Angle 3

b: Angle 8 and Angle 5

c: Angle 2 and Angle 9

d: Angle 5 and Angle 3

e: none of the above

Answer:  Therefore, we purchased 4 adult tickets and 7 child's tickets.

Step-by-step explanation:

Through the information provided, we set up a system equation:

a + c = 11

7.50a + 5.00c = 65

By the first equation, we convert it into a form, then we get a = 11 - c. Then we plug in the a = 11 - c to the second equation:

  7.50(11 - c) + 5.00c = 65

82.5 - 7.50c + 5.00c = 65

            82.5 - 2.50c = 65

                     - 2.50c = 65 - 82.5

                     - 2.50c = - 17.5

                               c = - 17.5/- 2.50

                               c = 7

And we plug c = 7 back into the first equation, which is a + c = 11.

a + c = 11

a + 7 = 11

      a = 11 - 7

      a = 4

Therefore, we purchased 4 adult tickets and 7 child's ticket.

Answer:

$24.96

Step-by-step explanation:

The question was incomplete. If you are asking how much is the book worth after 8 years, here's how to do it

Original cost  = $58
Since the rate of decrease = 10%, the cost of the book after 1 year is 90% of the original price

90% = 90/100 = 0.9

Therefore after 1 year, the book cost is 58(0.9)

After another year(effectively 2 years) the above cost will drop by another 10% to 90% of the first year value: 58(0.9)(0.9) = 58(0.9)²

So the value of the book after a period of n years is modeled by the function

V = 58 (0.9)ⁿ

After 8 years the value is
58 (0.9)⁸ = 58 x 0.43046721

V = $24.96 rounded to the nearest cent

Answer: A=71°

Step-by-step explanation:

A+B+C=180°

A+38°+C=180°

A+C=180°-38°

A+C=142°

142°/2=71°

∴A=71°

∴C=71°

The probability that no one in the United States will be struck and killed by lightning tomorrow is approximately 0.835, or 83.5%.

To find the probability that no one in the United States will be struck and killed by lightning tomorrow, we can use the Poisson distribution, which models the number of rare events occurring in a fixed period of time, given the average rate of occurrence.

The Poisson distribution has the following probability mass function:

P(X = k) = (e^(-λ) * λ^k) / k!

where:

X is the random variable representing the number of events (in this case, the number of people struck and killed by lightning)

λ is the average rate of events per unit of time (in this case, the average number of people struck and killed by lightning per day)

We can use the data given in the problem to estimate the value of λ:

λ = (2457 deaths) / (36 years * 365 days/year) ≈ 0.18 deaths/day

Now we can use the Poisson distribution to find the probability that no one in the United States will be struck and killed by lightning tomorrow:

P(X = 0) = (e^(-0.18) * 0.18^0) / 0! ≈ 0.835

This means that there is a high likelihood that no one will be killed by lightning tomorrow, given the historical average rate of lightning deaths.

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You solve it using your brain.

Answer:

2. 3(x + 9) = 48

Step-by-step explanation:

We are given

If each playlist has 9 rock songs and x pop songs, then each playlist has 9 + x songs.

If there are three playlists, there are three playlists which each have x + 9 songs. In other words, 3(x+9). This represents the total number of songs, which is 48. Therefore the answer is 3(x+9)=48.

Hope this helps!

Answer as a mixed number =  1   1/8  mph

Answer as a decimal = 1.125 mph

Work Shown:

(3/4) of a mile : (2/3) of an hour

12*(3/4) of a mile : 12*(2/3) of an hour

9 miles : 8 hours

9/8 miles : 8/8 hours

1.125 miles : 1 hour

His speed is 1.125 miles per hour. This converts to the mixed number 1 1/8

If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

However, the frog slips back 1 foot while resting for an hour, so the frog would only have covered 5 feet of the well after each hour of climbing. The frog would need to climb for a total of

40/5 = 8 hours

to reach the top of the well. Additionally, the frog would need to take 8 hours of rest to make up for the slipping back.

So the total time it would take the frog to get out of the well would be 8 hours + 8 hours = 16 hours.

If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

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Answer:

We can start by finding the total number of learners who participate in jogging and cycling by multiplying the ratio by the total number of learners. Let's say x is the number of learners who jog. Then, the number of learners who cycle is 2x.

The total number of learners who jog and cycle is 125, so:

x + 2x = 125

3x = 125

x = 125 / 3

x = 41.67

Since x represents the number of learners who jog, there are 41.67 learners who jog. Since the number of learners who cycle is 2x, there are 2 * 41.67 = 83.33 learners who cycle.

Since these are whole numbers of learners, we round up to the nearest whole number to get 42 joggers and 83 cyclists.

The number of students participating in each of the sports will be 75 for jogging and 50 for cycling.

Solution:

Let's assume that the number of students who participated in jogging will be 3x and those in cycling will be 2x

Given,

3x + 2x = 125

5x = 125

So, x = 25

Therefore, the number of students in jogging will be 3*25 = 75 and in cycling will be 2*25 = 50

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The sum of the measures of angles A, D, and F is:

A + D + F = 360°

First, we know that the sum of the interior angles of any triangle is always equal to 180°, then we can write:

B + C + E = 180°

We also can see that:

A + B = 180°

C + D = 180°

E + F = 180°

Then we can rewrite:

E = 180° - F

C = 180° - D

B = 180° - A

And replace that on the equation above:

B + C + E = 180°

( 180° - F) + (180° - D) + (180° - A) = 180°

Moving the variables to the right side we will get:

3*180° = 180° + A + D + F

3*180° - 180° = A + D + F

360° =  A + D + F

That is the sum of the 3 measures.

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The probability of drawing a black card in a standard deck of 52 cards is 1/2.

Probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1. There are total 52 cards out of which 26 are black cards and 26 are red cards.

There are 26 black cards (13 spades and 13 clubs) in a standard deck of 52 cards.

Therefore, the probability of drawing a black card from a standard deck of 52 cards is 26/52.

Probability = 26/52 = 1/2

So, the probability of drawing a black card is 1/2.

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The value of x in the triangle is 8 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, the sides x of the triangle can be found using proportion as follows:

x / x + 8 = x + 8 / 32

cross multiply

32x = (x + 8)(x + 8)

32x = x² + 8x + 8x + 64

x² + 16x - 32x + 64 = 0

x² - 16x + 64 = 0

Therefore,

x² - 16x + 64 = 0

x² - 8x - 8x + 64 = 0

x(x - 8) - 8(x - 8) = 0

(x - 8)(x - 8) = 0

Therefore,

x = 8

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Answer: 2.25 per gallon

Step-by-step explanation:

4.50 divided by 2 = 2.25

Turning 180° counterclockwise is essentially the same thing as a horizontal flip about the y axis.

That means C will find itself on the opposite side of the x axis, with negative inputs. However, it is still above the x axis, so it will have a positive y coordinate.

Your answer should be (-3,1)

Answer:

Step-by-step explanation:

time take for 1 dough = 16kg/4hours= 4kg/hour

Dough in 5 hours = 4 x 5 = 20

She prepared 20kilograms of dough in 5 hours

Answer: The value of the sum of x and y is (a) 144.

Step-by-step explanation:

Given, The sequence is a Geometric Sequence.

Initially,

=> 4x3 , x , y , 324, 324x3

=> 4x3, x, y, 4x3x3x3x3, 4x3x3x3x3x3

From above,

We can deduce that,

=> x = 4 x 3 x 3

=> x = 36

Also,

=> y = 4 x 3 x 3 x 3

=> y = 108

The values of x and y are 36 and 108

Now, We can evaluate the sum of x and y,

=> x + y = 36 + 108

=> x + y = 144

Therefore, The sum of x and y is 144. Hence, option (a) is correct.

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Surface area of a rectangular prism is 444 square unit.

A rectangular prism is a three-dimensional shape with six faces (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular. As an outcome, there really are three sets of exactly equal faces here. A rectangular prism is also recognized as a cuboid due to its shape.

The sides of a rectangular prism is 5, 4, 3, 3.7.

This can be calculated by multiplying each of the side lengths together and then multiplying that result by two.

Surface area of a rectangular prism = 2 × (5 × 4 × 3 × 3.7)

Surface area of a rectangular prism = 2 × 222

Surface area of a rectangular prism = 444 square unit

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the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

One side of rectangle is 200m

When the measure of the other side is 50 m

the area will be 50*200 = 1000m².

The expression of area A(x) = 200x,

hence the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,

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If there are 15 boys and 17 girls in a math class then, the ratio of boys to girls is Option A. 15:17

The ratio of boys to girls in the math class is 15:17. This can be found by dividing the number of boys by the number of girls, which gives:

15/17

This ratio cannot be simplified because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls is 15:17.

The ratio of boys to girls in a math class is the relationship between the number of boys and the number of girls. The ratio is a way of expressing the comparison between two quantities. In this case, there are 15 boys and 17 girls in the class. To find the ratio of boys to girls, we divide the number of boys by the number of girls, which gives 15/17. This ratio cannot be simplified further because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls in the math class is 15:17. This means that for every 15 boys in the class, there are 17 girls.

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 The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

The number of solutions for a system of linear equations depends on the relationship between the slopes and y-intercepts of the lines represented by the equations. If the lines are intersecting, then there is exactly one solution where the lines cross. If the lines are parallel, then there are no solutions, as the lines will never intersect.

If the lines are coincident, then there are infinitely many solutions, as the lines represent the same line.

Therefore,  The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.

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