Select the shapes that are similar to shape A.

The sum of the arithmetic sequence is S = 207 and the summation notation is S = ∑i=1 to 6 ( 5n + 17 )

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic sequence be represented as A

Now , the value of A is

A = 22 + 27 + 32 + 37 + 42 + 47

The number of terms n = 6

So , the value of i ranges from 1 to 6

Now , the summation is represented as ∑i=1 to 6 ( 5n + 17)

when n = 1

S₁ = 5 ( 1 ) + 17 = 22

when n = 2

S₂ = 22 + 5 ( 2 ) + 17

S₂ = 22 + 27

when n = 3

S₃ = 22 + 27 + 5 ( 3 ) + 17

S₃ = 22 + 27 + 32

Hence , the sum of the arithmetic sequence is S = 207

To learn more about arithmetic sequence click :

https://brainly.com/question/1522572

#SPJ1

The answer to the question would be D 5in^2

Answer:

yes

Step-by-step explanation:

brain

Answer:

Step-by-step explanation:

9x + 2y = 24  (A)

y = 6x + 19 ------ > y - 6x = 19 * (-2) -------> -2y + 6x = -38 (B)

(A) + (B)

15x = -14

x = -14/15

y = 6 * (-14/15) + 19 = -28/5 + 19 = 67/5

Answer:

A. 9x + 2y = 24  

Based on the scatter plot, the best model is: C. linear.

The equation of the line of best fit is: B. y = 1.98x + 1.07.

The value of y when x = 10 is: F. 20.87.

In order to write a linear equation that models the data point contained in the table, we would have to make use of a scatter plot and then determine the line of best fit.

In this scenario, the x-values would be plotted on the x-coordinate of the scatter plot while the y-values would be plotted on the y-coordinate of the scatter plot.

On the Excel worksheet, you should right click on a data point on the scatter plot, select format trend line and then tick the box to display a linear equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between data points in the table, a linear equation for the line of best fit is given by:

y = 1.98x + 1.07.

Next, we would use the linear equation for the line of best fit to predict the value of y when x = 10:

y = 1.98(10) + 1.07

y = 19.8 + 1.07

y = 20.87.

Read more on line of best fit here: brainly.com/question/28758241

#SPJ1

Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.

Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.

What is an Angle?

An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths

To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:

Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.

Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees

Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees

Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

For more questions on Measurement .

https://brainly.com/question/27233632

#SPJ8

Step-by-step explanation:

Each bag of crackers is 2 ounces, while each bag of pretzels is 3 ounces. Since there are 50 bags of crackers and 65 bags of pretzels, we can make an equation:

2(50)=100 oz of crackers

3(65)=195 oz of pretzels

195-100=95(difference in total)

Hope this helps!

Answer:

Step-by-step explanation:

m = 5d

m-6+d-6 = 60 substitute for m:

5d-6+d-6 = 60

6d-12 = 60

6d = 72

d = 12 The daughter is 12 and the mother is 5(12) = 60

hope this helps

Answer:

Explination:

So to find the answer to this problem

m(mother) = x

d(daughter) = y

If In 6 years the mother will be as 3 times as old as the daughter. We can use the process of elimination. Lets start of with the number 20. So the mother is 60(for now). Then in 6 years the mother will be 66. 66/3 = 22. This means the daughter was 22  - 6 = 16. But the mother has to be 5 times as old right now. SO this wouldnt make sense. If you reduced this number by 10's continuelly then you would see that the only other 10's form of this that is divisible is 36. So 30 + 6 is 36. 36/3 = 12. This means the daughter was 6.. So the mother was 30. The daughter was 6.

Hope this helped!

Answer:

The first one would be 9

The second one would be 4

Step-by-step explanation:

By adding the same numbers, you make the equations equal and therefore true.

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

Learn more about ratio on

brainly.com/question/2328454

#SPJ1

The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

Learn more on quadratic equations here: https://brainly.com/question/24628957

#SPJ1

The moment of inertia for rotation about the z axis is  \(I & =\frac{a^2 M}{3}\).

A triangular prism of mass m, whose two ends are equilateral triangles.

Two ends are equal.

The xy plane with side 2a, is centered on the origin with its axis along the z axis.

Find the moment of inertia for rotation the z-axis.

It is divide into 4 triangles with side 'a' k one side is 3cm.

\($$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$\)

It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.

Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.

\($$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$\)

\($$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$\)

⇒ Now, by using the \($I_{\text {Big }}=I$\)

⇒\(I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\\)

⇒\(4 I & =I+a^2 m\)

⇒\(4 I-I & =a^2 m \\\)

⇒\(3 I & =a^2 M . \\\)

⇒\(I \quad & =\frac{a^2 M}{3}\)

Therefore, the moment of inertia is \(I & =\frac{a^2 M}{3}\).

For more such questions on distance between points

https://brainly.com/question/15958176

#SPJ4

Step-by-step explanation:

T = 55 + 6w

after 8 week $103

To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

For more such questions on sequence.

https://brainly.com/question/7882626

#SPJ8

Answer:

5

Step-by-step explanation:

\(\triangle HBK \cong \triangle NBK\) by SAS. Using CPCTC, \(3x=x+10 \implies 2x=10 \implies x=5\).

The Central Limit Theorem states that if the population is normally distributed and the sample size is reasonably large, then the sample mean will be normally distributed.

The Central Limit Theorem states that if the sample size is reasonably large and the population is normally distributed, then the sample mean will be normally distributed. This means that we can use the normal distribution to make inferences about the population mean. Specifically, it allows us to calculate the probability that the population mean falls within a certain range, given the sample mean. This is useful because we can use the sample data to make assumptions about the population as a whole. For example, if the sample data is normally distributed, we can assume that the population mean is also normally distributed. This is especially useful when the population size is large and it would be difficult to collect data from every individual in the population. The Central Limit Theorem gives us an efficient way to make inferences about the population mean.

Learn more about mean here

https://brainly.com/question/29547409

#SPJ4

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer: I would say that the hotdogs cost $2 and the burgers cost $4

Step-by-step explanation: By the display of it, it that would be the normal cost of a hotdog and a hamburger

Answer:

The left hand is more accurate.

Step-by-step explanation:

If you look at the graph, it will look like the right hand is more accurate, due to the fact that it has a closer distance than the left. However, the right hand actually never have hit the target while the left did more than once.

Answer:

B

Step-by-step explanation:

You must multiply 1/4 to 2/8 so you can subtract

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

the final price after both discounts is $35.75.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

If the original price of an item is x, the price after the 45% off sale is:

0.55x

The price after the additional 35% off coupon is:

0.65(0.55x) = 0.3575x

Therefore, the final price after both discounts is 35.75% of the original price, or:

0.3575x

For example, if an item originally costs $100, the price after the 45% off sale is:

0.55($100) = $55

And the price after the additional 35% off coupon is:

0.65($55) = $35.75

So the final price after both discounts is $35.75.

Learn more about percentage, by the following link.

https://brainly.com/question/24304697

#SPJ1

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

Path A-B-C-E represents the distance traveled, which is 18 meters.

Path A-G-C-E represents the displacement, which is 17 meters.

From the given figure, we can identify the paths and calculate the distance and displacement.

Path A-B-C-E represents the distance traveled, and path A-G-C-E represents the displacement.

Let's calculate the lengths of both paths:

Distance traveled (Path A-B-C-E):

Length of AB = 9m

Length of BC = 3m

Length of CE = 6m

Total distance traveled = Length of AB + Length of BC + Length of CE

= 9m + 3m + 6m

= 18m

Therefore, the distance traveled along path A-B-C-E is 18 meters.

Displacement (Path A-G-C-E):

Length of AG = 5m

Length of GC = 6m

Length of CE = 6m

Total displacement = Length of AG + Length of GC + Length of CE

= 5m + 6m + 6m

= 17m

Therefore, the displacement along path A-G-C-E is 17 meters.

for such more question on distance

https://brainly.com/question/12356021

#SPJ8

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

In the given problem, the probability of getting a sundae with vanilla ice cream, caramel, and marshmallow is 1/8.

The probability of getting a sundae with vanilla ice cream, caramel, and marshmallow can be found by multiplying the probabilities of each event occurring:

P(Vanilla ice cream) * P(Caramel) * P(Marshmallow)

Since there are only two options for ice cream (vanilla or chocolate) and one option each for the toppings (caramel and marshmallow), the probabilities can be calculated as follows:

P(Vanilla ice cream) = 1/2

P(Caramel) = 1/2

P(Marshmallow) = 1/2

Therefore, the probability of getting a sundae with vanilla ice cream, caramel, and marshmallow is:

P(Vanilla ice cream) * P(Caramel) * P(Marshmallow) = (1/2) * (1/2) * (1/2) = 1/8

To draw a tree diagram to find the solution, we start with the choice of ice cream (vanilla or chocolate) and then branch out to the toppings (caramel or marshmallow) for each option of ice cream. The resulting tree diagram would look like this:      

                |-------Caramel-------Marshmallow

                |

Vanilla|----|

                |

                |-------Caramel-------Marshmallow

                        Chocolate not considered

Each branch represents a possible combination of ice cream and topping choices. The end of each branch shows the probability of that particular combination occurring. To find the probability of a specific combination, we multiply the probabilities of each event along the corresponding branch.

Mathematically, the solution can also be justified using the multiplication rule of probability. This states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the events of choosing vanilla ice cream, caramel, and marshmallow are all independent of each other. Therefore, the probability of all three events occurring together is the product of their individual probabilities:

P(Vanilla ice cream and caramel and marshmallow) = P(Vanilla ice cream) * P(Caramel) * P(Marshmallow)

Substituting the probabilities we calculated earlier, we get:

P(Vanilla ice cream and caramel and marshmallow) = (1/2) * (1/2) * (1/2) = 1/8

This confirms that the probability of getting a sundae with vanilla ice cream, caramel, and marshmallow is indeed 1/8.

Learn more about tree diagram here: https://brainly.com/question/23272868

#SPJ1

Answer:

I think the answer would be r=-9

Step-by-step explanation:

12+r=3

-12     -12

-------------

r=-9

Answer:

decay.

Step-by-step explanation:

decline means reduce, which is a negative term. decay is also negative.

decimal form= .113 or .11

Answer:

188.4 units²

Step-by-step explanation:

Hi there!

Part A

Surface area of a cone = \(3.14(rs+r^2)\) where r is the radius of the base and s is the slant height

⇒ r = 6

Replace r with 6

\(3.14(6s+6^2)\)

⇒ s = 4

Replace s with 4

\(3.14(6*4+6^2)\)

Part B

Evaluate the expression found in Part A:

\(3.14(6*4+6^2)\)

Find 6²:

\(=3.14(6*4+36)\)

Find 6*4:

\(=3.14(24+36)\)

Find 24+36:

\(=3.14(60)\\=188.4\)

Therefore, the surface area of the cone is 188.4 units².

I hope this helps!