The sum of the interior angles of the 10-sided polygon on the left is ____

Answer:

The volume of the display case in cubic inches is 10,328 1/16 in.

The couple needs to deposit about $554.49 each month end until they retire to reach their goal.

To find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:

FV = PMT * [((1 + r)^n - 1) / r]

We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:

PMT = FV / [((1 + r)^n - 1) / r]

We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:

PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]

PMT ≈ 554.49

Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.

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The total distance traveled by the car between t = 0 and t = 3 is given as follows:

c. 15 mi.

The velocity function is given as follows:

v(t) = 20 - 10t.

The distance function is the integral of the velocity function, hence it is given as follows:

d(t) = 20t - 5t².

The distance at t = 0 is given as follows:

d(0) = 20(0) - 5(0)²

d(0) = 0.

The distance at t = 3 is given as follows:

d(3) = 20(3) - 5(3)²

d(3) = 15.

Hence the total distance is given as follows:

15 - 0 = 15 mi.

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If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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Answer:

K′(0, 0), L′(−2, 5), M′(5, 5), N′(−3, 0)

Step-by-step explanation:

To rotate a point $(x,y)$ by $270^{\circ}$ clockwise, we first swap the $x$ and $y$ coordinates and then negate the new $y$ coordinate.

Using this, we can find the image vertices of the given polygon as follows:

For vertex K(0, 0), we have $(0,0) \rightarrow (0,0)$. So K′ is at the origin.

For vertex L(5, 2), we have $(5,2) \rightarrow (2,-5)$. So L′ is at (-2, 5).

For vertex M(5, -5), we have $(5,-5) \rightarrow (5,5)$. So M′ is at (5, 5).

For vertex N(0, -3), we have $(0,-3) \rightarrow (-3,0)$. So N′ is at (-3, 0).

Therefore, the image vertices of the polygon KLMN after a $270^{\circ}$ clockwise rotation are K′(0, 0), L′(−2, 5), M′(5, 5), and N′(−3, 0).

Thus, the correct option is:

K′(0, 0), L′(−2, 5), M′(5, 5), N′(−3, 0)

Answer:

Since (2x, x + 17, x + 21, ...) is an arithmetic sequence, we know that the common difference between consecutive terms is constant.

The common difference can be found by subtracting any two consecutive terms in the sequence. Let's subtract the second term (x + 17) from the first term (2x):

2x - (x + 17) = x - 17

Now let's subtract the third term (x + 21) from the second term (x + 17):

(x + 17) - (x + 21) = -4

Since the common difference is constant, we can set the two expressions for the common difference equal to each other:

x - 17 = -4

Solving for x, we get:

x = 13

Therefore, the value of x that makes the sequence (2x, x + 17, x + 21, ...) an arithmetic sequence is x = 13.

Answer:

We can use the information provided to estimate the number of ducks that have red marks on the bottom.

If only 3 out of 50 people have won a small prize, then we can estimate that the probability of winning a small prize is 3/50 or 0.06. Since the person wins a small prize if there’s a red mark on the bottom of the duck, we can estimate that the proportion of ducks with red marks is also 0.06.

So, we can estimate the number of ducks with red marks as follows:

Number of ducks with red marks = 0.06 x 160

Number of ducks with red marks = 9.6

We can estimate that there are about 9 or 10 ducks with red marks on the bottom.

Using the model to estimate f(x) when x = 5 and x = 10, the vaues are 18.33 and 17.78

From the question, we have the following function that can be used in our computation:

f(x) = -0.11x + 18.88

Also, we have

x = 5 and x = 10

Substitute the known values in the above equation, so, we have the following representation

f(5) = -0.11 * 5 + 18.88 = 18.33

f(10) = -0.11 * 10 + 18.88 = 17.78

Hence, the values are 18.33 and 17.78

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Complete question

Question: A statistician calculated the following linear model to describe the data: f(x) = – 0.11x + 18.88 Use the model to estimate f(x) when x = 5

Answer:32mi/gal

Step-by-step explanation:

106485 - 106069 = 416mi (the distance that you traveled)

416/13 = 32

32mi/gal

Answer:

Table B is proportional since y = 1.5x:

4.5 ÷ 3 = 1.5

7.5 ÷ 5 = 1.5

10.5 ÷ 7 = 1.5

[tex] {( \frac{9}{4} )}^{3} [/tex]

=

[tex] \frac{729}{64} [/tex]

Answer: 11 25/64

Step-by-step explanation: 2 1/4 x 2 1/4= 5 1/16 x 2 1/4 = 11 25/64

The relative frequency of a person having the flu and testing positive for the flu is 0.1053/0.901 = 0.117, or approximately 11.7%. The relative frequency table is given below.

To get the relative frequencies, we divide each cell value by the total frequency of the table.

This is how we construct relative frequency table.

To construct a relative frequency table, we need to determine the different possible outcomes and their corresponding frequencies based on the given information.

Let's define the following events:

A: a person has the flu

B: a person tests positive for the flu

Then, using the information given in the problem, we can construct the following relative frequency table:

                   A (has the flu)   not A (does not have the flu) Total

B              0.13*0.81 = 0.1053          0.08*0.87 = 0.0696              0.1749

not B       0.19*0.81 = 0.1540           0.63*0.87 = 0.5471               0.7011

To                   0.2843                                 0.6171                         0.901

In this table, the values in the cells represent the product of the probability of the row event and the probability of the column event. For example, the value 0.1053 in the top left cell represents the probability of a person having the flu (event A) and testing positive for the flu (event B), which is calculated as 0.13 x 0.81.

The total frequency for each row and column is calculated by summing the values in that row or column. The total frequency for the entire table is the sum of all the values, which is 0.901 in this case.

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The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.

Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.

So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided

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Answer:

They would have gotten 2 full apples each. There would be 4 left over. If they decided to split those 4 apples, they would have gotten 2 1/2 apples each.

Step-by-step explanation:

20 ÷ 8 = 16 R 4

16 ÷ 8 = 2 (the full apples they got each_)

4 x 2 = 8 (split the 4 apples in half to make 8)

Therefore, each student would have gotten 2 full apples and 1/2 of an apple.

Answer:

Lana has completed 22 out of 32 puzzles in her book. To find the percentage of the puzzle she has completed, divide the number of puzzles she has completed by the total number of puzzles in the book and multiply by 100.

22/32 x 100 = 68.75%

Lana has completed 68.75% of the puzzles in her book.

Answer:

Lana has completed 68.75% of the puzzles in her puzzle book.

Step-by-step explanation:

Lana has completed a total of 22 puzzles and there are 10 puzzles remaining, so the total number of puzzles in the book is:22 + 10 = 32To find the percentage of puzzles Lana has completed, we can use the following formula:percentage = (completed puzzles / total puzzles) x 100%Substituting the values, we get:percentage = (22 / 32) x 100%

percentage = 0.6875 x 100%

percentage = 68.75%Therefore, Lana has completed 68.75% of the puzzles in her puzzle book.

The fractional part of 70/28 is 35/14 i.e., 2.5

Percentage:

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100

28 of 70 can be written as:

=> [tex]\frac{28}{70}[/tex]

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

[tex]\frac{28}{70}[/tex] × [tex]\frac{100}{100}[/tex]

=> (28 × 100) /70 ×[tex]\frac{1}{100}[/tex]

=> 40/100

Therefore, the answer is 40%

The fractional part of 70/28 is 35/14 i.e., 2.5

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The triangle which can be drawn as per the condition described is only option 2. an isosceles triangle with measure  20° and 80°.

Triangle which can be drawn as per the measurements are,

An acute triangle with sides measuring 7, 4, 2.

In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.

According to the Pythagorean theorem.

7²< 4² + 2²

49 < 16 + 4

49 < 20

This is a contradiction, since 49 cannot be less than 20.

It is not possible to draw triangle.

An isosceles triangle with measures of angle 20° and 80°.

Sum of interior angles  of a triangle is 180°

Here, third angle = 180° - ( 20° + 80° )

⇒Third angle = 80°

Two angles are congruent ⇒ opposite sides to congruent angles are also congruent.

It forms a isosceles triangle.

An obtuse triangle with sides measuring 5, 10 and 15.

Side lengths 5, 10, and 15 do not form a triangle at all.

Since the sum of the two shorter sides is less than the longest side.

5 + 10 = 15

It is not possible to have an obtuse triangle with sides measuring 5, 10, and 15.

An scalene triangle with angle measuring 110° and 35°.

Sum of the interior angles is always 180°.

Measure of the third angle ,

180° - 110° - 35° = 35°

Three angles of the triangle measure 110°, 35°, and 35°.

It represents isosceles triangle.

Therefore, the possible triangle as per the given condition is only option 2. isosceles triangle with measure 20° and 80°.

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Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

The statement The product of p is and -8 is less than 24 as an expression is -8p <  24

From the question, we have the following parameters that can be used in our computation:

The statement represented as

The product of p is and -8 is less than 24

Less than is represented using the symbol <

So, we have

The product of p is and -8 is less than 24: The product of p is and -8 is <  24

Represent products as *

So, we have

The product of p is and -8 is less than 24: -8p <  24

Hence, the expression is -8p <  24

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[tex] {(3x + 7)}^{2} - ((2x + 5) \times x) [/tex]

[tex] = 7 {x}^{2} - 5x + 49[/tex]

i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0

To use a graph to find the value of x for the given values of y in the equation y=-|x-2|+2, we can follow these steps:

i) When y<0:

The graph of y=-|x-2|+2 is below the x-axis when y<0. Therefore, there is no solution for x when y<0, because there is no point on the graph that has a negative y-coordinate.

ii) When y>0:

The graph of y=-|x-2|+2 intersects the x-axis at two points when y>0. To find the x-coordinates of these points, we can set y=0 in the equation y=-|x-2|+2 and solve for x, as shown in the previous answer.

The x-intercepts are at (4,0) and (0,0), which means that the graph crosses the x-axis at x=4 and x=0 when y>0.

iii) When y=0:

To find the x-coordinate(s) of the point(s) where the graph intersects the x-axis (i.e., where y=0), we can look at the x-intercepts that we found in part ii) above. The x-coordinate(s) of the point(s) where the graph intersects the x-axis are x=4 and x=0, so the solutions for x when y=0 are x=4 and x=0.

Therefore, i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0 (the x-intercepts).

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Answer: x^2+2x-63

Step-by-step explanation:

Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)

                                =x^2-(7-9)+(7*(-9))

                                =x^2+2x-63

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

For the transformation 1, we have a reflection, which keeps both the side lengths and the angle measure constant, just changing the orientation of the figure.

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The overall mean of data set is 49.57. Option D

The overall mean is all the sums of the means divided by the total number of set in the table.

All the mean in the table are 42. 75 + 51. 75 + 50.00 + 49.50 + 51.25 + 47.25 + 50.75 + 47.75 + 56.50 + 47.50 + 38.75 + 49.25 + 57.00 + 48.75 + 54.75 = 743.5

We see that there are 15 data set.

mean = 743.5/ 15

Overall mean = 49.57

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We can see here that the statements that are true are:

B. The symbol should be used because (8, 13, 22, 36) is a set and none of the elements in - 13 is a set.

C. The ∉ symbol should be used because ∉ is not an element of the set.

F. The ∈ symbol should be used because ∉ is not an element of the set.

A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.

Numbers, letters, words, forms, persons, and other mathematical things can all be included in a set.

We can see here that -13 ∉  (8, 13, 22, 36).

These statements are true because -13 is not actually an element of (8, 13, 22, 36). Thus, in the given set of data, -13 is not seen in the given set.

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Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

Answer: x ≥ 3

Step-by-step explanation:

Answer:

$1,000.

Step-by-step explanation:

200 kids divided by 25% or 4 = 50 then 50 x 20 = 1,000.

Answer:

[tex] \frac{210}{360} = \frac{7}{12} [/tex]

This figure represents 7/12 of the circle.

The book value of the automobile at the end of 3 years is $13,000.

The straight-line method is method of depreciation that allocates the same depreciation expense each year.

Straight line depreciation expense = (Cost of asset - Salvage value) / useful life

($32,500 - 0) / 5 = $6,500

Total depreciation in 3 years = $6,500 x 3 = $19,500

Book value = cost of the automobile - total depreciation

$32,500 - $19,500 = $13,000

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