The table shows some values of a function of the form y
= ax² + bx + c.
V
4
21
5
32
6
45
7
60
8
77

The regression equation that represents the relationship between velocity and time is:

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (t,v), that is, time and velocity, are given as follows:

(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).

Hence, inserting these points into a calculator, the equation is given by:

v = 2.19t + 6.7.

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Answer:

64°

Step-by-step explanation:

This is a question on angle properties.

Angle y + 37 + 79 = 180 (Sum of angles in a triangle)

Angle y + 116 = 180

Angle y = 180 - 116 = 64°

the equation with these solutions is:

0 = x^2 - 6x + 6

Remember that a quadratic equation with the solutions a and b is written as:

0 = (x - a)*(x - b)

Here we have the solutions:

Then we can write a quadratic equation of the form:

0 = (x - (3 + √3) )*(x - (3 - √3) )

0 = (x - 3 - √3)*(x - 3 + √3)

Expanding that, we get:

0 = x^2 - 6x + 9 - 3

0 = x^2 - 6x + 6

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Answer:

h = 5 cm

Step-by-step explanation:

Givens

d = 6cm

V = 45cubic cm

Formula

V = pi * r^2 h                                  substitute values into the formula

Solution

d = 2*r

6 = 2*r                                            Divide both sides by 2

6/2 = 2r / 2

3 = r

45 pi cm^3 = pi * (3)^2 * h            Divide both sides by pi

45 pi/pi = pi * 9 * h / pi

45 = 9h                                         Divide both sides by 4

45/4 = 9h/9                                    

5 cm

The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

For given question,

We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]

We need to find the sum of given convergent series.

Given series is a geometric series with ratio r = sin(1)

The first term of the given geometric series is [tex]a_1=sin(1)[/tex]

So, the sum is,

= [tex]\frac{a_1}{1-r}[/tex]

= sin(1) / [1 - sin(1)]

This means, the series converges to sin(1) / [1 - sin(1)]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

= [tex]\frac{sin(1)}{1-sin(1)}[/tex]

= [tex]\frac{0.8415}{1-0.8415}[/tex]

= [tex]\frac{0.8415}{0.1585}[/tex]

= 5.31

Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

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Minimum: 59

Lower Quartile: 67

Median: 76

Upper Quartile: 86

Maximum: 92

Interquartile Range: 19

Answer:

a variable.

Seven is a number and cannot be a variable.

Answer:a

Step-by-step explanation: 20 x 25=500

Answer: Point D

Reason:

The circumcenter is found by intersecting the perpendicular bisectors of each segment of the triangle.

As you can see, the circumcenter is the center of the circumcircle. This special circle is the smallest possible that wraps the triangle so to speak. The vertices of the triangle are on the circle.  The distances AD, BD and CD are all the same.

More than 50% of Americans rely upon television broadcasts for their news.

News, current occasions and ancient programming can help make younger humans extra aware of other cultures and those. Documentaries can help increase vital thinking about society and the arena. television can help introduce teens to classic Hollywood movies and overseas movies that they might not otherwise see.

It broadens the know-how of various cultures, and promotes tolerance and international information of worldwide issues. Through contemporary affairs, discovery, lifestyle, cooking indicates and children's programs, television encourages medical and cultural interest.

Agree with and effect: television is the most relied on a form of marketing and stays maximumly probable to make consumers chortle, circulate them to tears or cause feelings. For example, television is with the aid of a long way the maximum relied on shape of video advertising in Canada. 70% of 18-34-year-olds named tv the most truthful compared to 12% for online video.

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Answer:

NMK= 22

Step-by-step explanation:

From N to K equals 177.

N to M equals x

K to M equals to 107

L equals 35

35    177

x        107

it equals to 21.158

Round up to the nearest ones or whole number

A dot plot displays the individual data values and a histogram displays data ranges along the x-axis and uses rectangular bars to show the frequencies of values that fall into each range.

It should be noted that dot plots, histograms, and box plots are all common graphical ways to represent data sets.

The dot plot represents data by placing a dot for each data point. Also, the histogram groups the data into ranges and then plots the frequency that data occurs in each range.

The similarities is that the dot plot and the histogram can more easily tell us the mode of our data set. A dot plot gives you a visual idea of your data, but histogram gives you additional information.

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The total pay for hours worked is $980.013

The method with which a daily worker's wage is being paid is by calculating the total hours worked and multiplying it with the fixed hourly pay.

From the information given:

In hours, we have:

= (38 + 0.9667) hours

= 38.9667 hours

If a fixed hourly pay of $25.15 is being paid, we have:

= $(38.9667 × 25.15)

= $980.012505

= $980.013 to the nearest hundredth.

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Answer:

Step-by-step explanation:

elastic, inelastic, inelastic

Answer: elastic, inelastic, inelastic

Step-by-step explanation:

Answer:

3 cans

Step-by-step explanation:

A = lw

a = 20 x 8 = 160[tex]ft^{2}[/tex]

a = 40 x 8 = 320 [tex]ft^{2}[/tex]

Together this is 480 [tex]ft^{2}[/tex]

I would need 3 cans.

Answer: B

Step-by-step explanation:

Answer:

3.4 units

Step-by-step explanation:

Using proportions, it is found that the value of n is of [tex]n \geq 11[/tex].

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

On the first 15 games, the team wins 2 games and losses 13. Then, in each week, the team plays 3 games, winning 2. Then:

The proportion of wins is given as follows:

[tex]\frac{2 + 2n}{15 + 3n}[/tex]

The proportion is of at least 50%, hence:

[tex]\frac{2 + 2n}{15 + 3n} \geq 0.5[/tex]

We solve the inequality for n, similarly to how we would solve an equality, applying cross multiplication. Then:

[tex]2 + 2n \geq 7.5 + 1.5n[/tex]

[tex]0.5n \geq 5.5[/tex]

[tex]n \geq \frac{5.5}{0.5}[/tex]

[tex]n \geq 11[/tex]

The value of n is of [tex]n \geq 11[/tex].

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Answer:

343.608 million to nearest thousand.

Step-by-step explanation:

Projected annual percent of growth = 3%  ( from the values 1.03 in the equation)

Worth is 2012 ( 12 years after 2000) is:

241(1.03)^12

= 343.608 million

The median of this box and whisker plot is 73

A box and whisker plot is defined as a graphical method of displaying variation in a set of data. In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph. Box and whisker plots are very effective and easy to read, as they can summarize data from multiple sources and display the results in a single graph. Box and whisker plots allow for comparison of data from different categories for easier, more effective decision-making.

From the given data, following can be inferred

which is demonstrated in the box and whisker plot below

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Answer:

Associative property of addition.

Step-by-step explanation:

The location of the parentheses makes no difference to the sum of these numbers.

The property shown in the statement "(46 + 17) + 3 = 46 + (17 + 3)" is the associative property of addition.

The associative property of addition states that when adding three or more numbers, the grouping of the numbers does not affect the sum

In the given statement, we have three numbers being added: 46, 17, and 3. The statement shows that the addition is grouped differently on each side of the equation, but the result is the same.

On the left side, we have (46 + 17) + 3.

This means we first add 46 and 17, which equals 63. Then we add 3 to the sum, resulting in 66.

On the right side, we have 46 + (17 + 3). Here, we first add 17 and 3, which equals 20. Then we add 46 to the sum, also resulting in 66.

As we can see, no matter how we group the numbers being added, the final sum is the same. This demonstrates the associative property of addition.

Therefore, the property shown in the given statement is the associative property of addition.

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we conclude that the linear equation represented by the given table is:

y = (1/2)*x + 2

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂), then the slope is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we can use just the first two points on the given line:

(-8, -2) and (-4, 0)

Then the slope will be:

[tex]a = \frac{0 - (-2)}{-4 -(-8)} = \frac{2}{4} = \frac{1}{2}[/tex]

Then the linear equation is something like:

y = (1/2)*x + b

To find the value of b, we can use one of the two given points, I will use (-4, 0), then:

0 = (1/2)*(-4) + b

0 = -2 + b

2 = b

Then we conclude that the linear equation represented by the given table is:

y = (1/2)*x + 2

Then the correct option is the first one.

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Based on these data, it is better to describe the centers of distribution in terms of: B. median for both coffee shops because the data distribution is not symmetric.

A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

Next, we would calculate the mean and median for the two coffee shops as follows.

For coffee shop A, we have:

Mean = [F(x)]/n

Mean = [12+15+33+45+46+51+52+57]/8

Mean = [311]/8

Mean = 38.875.

Median = (45+46)/2

Median = 91/2

Median = 45.5.

For coffee shop B, we have:

Mean = [F(x)]/n

Mean = [17+16+36+35+12+9+34+15]/8

Mean = [174]/8

Mean = 21.75.

Median = (16+17)/2

Median = 33/2

Median = 16.5.

Since both the mean and median are not close, we can infer and logically deduce that the data distribution isn't symmetric for both coffee shops A and B.

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m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft. This can be obtained using the Laws of cosine formula and Laws of sine formula.

In a triangle ABC,

⇒ a² = b² + c² - 2bc cos A

⇒ b² = a² + c² - 2ac cos B

⇒ c² = a² + b² - 2ab cos C

where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.

In a triangle ABC,

⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.

In the question we can use the laws of cosine formula and laws of sine formula,

5) Given that,

AB = c = 13 km

AC = b = 21 km

m∠A = 91°

By using Laws of cosine formula,

⇒ a² = b² + c² - 2bc cos A

a² = 21² + 13² - 2(21)(13) cos 91°

a² = 441 + 169 - 546 (-0.0174524064)    

a² = 610 + 9.52901391 = 619.529014

⇒ a = 24.89 km

By using Laws of sine formula,

⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

sin 91°/24.89 = sin B/21

sin B = 0.999847695×21/24.89 = 0.843583833

⇒ m∠B = 57.52°

6) Given that,

AB = c = 11 cm

BC = a = 13 cm

AC = b = 14 cm

By using Laws of cosine formula,

⇒ b² = a² + c² - 2ac cos B

14² = 13² + 11² - 2(13)(11) cos B

196 = 169 + 121 - 286 cos B

196 = 290 - 286 cos B

cos B = 94/286

cos B = 0.328671329

⇒ m∠B = 70.8°

7) Given that,

AC = b = 24 km

BC = a = 26 km

m∠C = 134°

By using Laws of cosine formula,

⇒ c² = a² + b² - 2ab cos C

c² = 26² + 24² - 2(26)(24) cos 134°

c² = 676 + 576 - 1248 (-0.69465837)

c² = 1252 + 866.933646 = 2118.93365

⇒ AB = c = 46.03 km

8) Given that,

AB = c = 26 ft

BC = a = 21 ft

m∠B = 112°

By using Laws of cosine formula,

⇒ b² = a² + c² - 2ac cos B

b² = 21² + 26² - 2(21)(26) cos 112°

b² = 441 + 676 - 1096 (-0.374606593)

b² = 1117 + 410.568826 = 1527.56883

⇒ AC = b = 39.08 ft

Hence m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft.

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Answer:

Step-by-step explanation:

assuming that he has an annual interest of 5% then his initial deposit would be rounded to $2,238.65

Answer:

the top 2 and the left bottom corner

Step-by-step explanation:

the first one in the first row is a reflection

the second one in the first row is a rotation

the one on the left bottom corner just moved a unit

Answer:

Option 3

Step-by-step explanation:

The first answer is a reflection across the y-axis, the second is a rotation, and the last one is two translations. So, the third one is correct because it's the only single translation.

There are 20! number of ways for everyone to do this so that at the end of the move, each seat is taken by exactly one person.

People are seated in a 2 by 10 rectangle grid. All 20 persons stand up from their seats and relocate to an orthogonally neighboring one upon the blowing of a whistle.

Now, we have to find the number of possible ways in which each seat is taken up by exactly one person after the move.

As the number of people is 20 and 20 seats are to filled exactly once.

So, the number of ways = 20!

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Answer: 26.39

Step-by-step explanation:

2xπxr

           [tex]\boldsymbol{\sf{-2x + 7x +34 = -2(1-7x) \ \ \longmapsto \ \ [Add \ -2x+7x]}}[/tex]

                        [tex]\boldsymbol{\sf{5x+34=-2(1-7x)}}[/tex]

Use the distributive property to multiply −2 by 1−7x.

                            [tex]\boldsymbol{\sf{5x+34=-2+14x}}[/tex]

Subtract 14x on both sides.

                              [tex]\boldsymbol{\sf{5x+34-14x=-2}}[/tex]

Combine 5x and −14x to get −9x.

                                [tex]\boldsymbol{\sf{-9x+34=-2 }}[/tex]

Subtract 34 from both sides.

                              [tex]\boldsymbol{\sf{-9x=-2-34 \ \ \longmapsto \ \ \ [Subtract] }}[/tex]

                               [tex]\boldsymbol{\sf{-9x=-36}}[/tex]

Divide both sides by −9.

                                      [tex]\boldsymbol{\sf{x=\dfrac{-36}{-9} \ \ \longmapsto \ \ [Split] }}[/tex]

                                       [tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ x=4 }}}}}[/tex]

[tex] \quad\quad\quad \huge \underline{ \tt{ANSWER}}[/tex]

[tex]\quad\quad\quad\quad\quad\quad[/tex]

[tex]\tt{- 2x + 7x + 34 = - 2(1 - 7x)}[/tex]

[tex]\tt{5x + 34 = - 2(- 7x + 1)}[/tex]

[tex]\tt{5x + 34 = - (- 2 * 7x + 2)}[/tex]

[tex]\tt{5x + 34 = - (- 14x + 2)}[/tex]

[tex]\tt{(5x + 34) + (- 34 - 14x) = (14x - 2) + (- 34 - 14x)}[/tex]

[tex]\tt{5x + 34 - 34 - 14x = 14x - 2 - 34 - 14x}[/tex]

[tex]\tt{5x - 14x + 34 - 34 =14x-14x-2 - 34}[/tex]

[tex]\tt{- 9x = - 36}[/tex]

[tex]\tt{\frac{9x}{9} = \frac{36}{9}}[/tex]

[tex]\tt{x = 4}[/tex]

The equation that solve for x is as follows;

70 + 60 + x = 180

The equation that can be used to find the measure of angle x can be found as follows:

60 + 70 + y = 180

Therefore,

130 + y = 180

subtract 130 from both sides

130 - 130 + y = 180 - 130

y = 50°

70 + 60 + x = 180

130 + x = 180

x = 180 - 130

x = 50°

x and y are  vertically opposite angles.

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