An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places. r=

Answer:

105 mi

Step-by-step explanation:

distance = speed x time

total distance = (62 mi/hr)(1.5 hr) + (24 mi/hr)(0.5 hr) = 105 mi

30 min = 0.50 hr

The height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.

The formula for the surface area of a cylinder is:

where r is the radius of the base, h is the height, and π is approximately 3.14.

In this case, the radius is given as 2 inches, and we want to find the height that will give us a surface area as close to 100 square inches as possible. So we need to solve for h in the equation:

100 = 2π(2)² + 2π(2)h

Simplifying this equation:

100 = 8π + 4πh

92 = 4πh

h = 23/π

h ≈ 7.32

Rounding this answer to the nearest inch, we get:

h ≈ 7 inches

Therefore, the height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.

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Answer:

4.5

Step-by-step explanation:

6+2=8

8/2=4

1.5x4=6

6-1.5=4.5

Answer:

160 miles

Step-by-step explanation:

To find the unit rate, we want to know how many miles can we go in i hour.

96 ÷ 1 [tex]\frac{1}{2}[/tex]

1 [tex]\frac{1}{2}[/tex] can be written

[tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex]      1 is the same as [tex]\frac{2}{2}[/tex]

Now we have

96 ÷ [tex]\frac{3}{2}[/tex]  if we get a common denominator, in this case 2, we can just divide a cross.

96 is equal to [tex]\frac{192}{2}[/tex]   ([tex]\frac{96}{1}[/tex] x [tex]\frac{2}{2}[/tex])

Now we have

[tex]\frac{192}{2}[/tex] ÷ [tex]\frac{3}{2}[/tex] =  [tex]\frac{64}{1}[/tex] = 64

We now know the unit rate is 64 miles in one hour.

The distance in 2 [tex]\frac{1}{2}[/tex] hours would be

64 + 64 + [tex]\frac{1}{2}[/tex](64)

64 + 64 + 32

160

Helping in the name of Jesus.

The algebraic expressions that are equivalent to 7x-2 are -2 + 7x, 14x/2 - 4/2 and 5x + 2x - 2

The expression in the question is given as

7x - 2

The above expression is linear

Here are some algebraic expressions that are equivalent to 7x-2:

14x/2 - 4/2

When evaluated, we have

14x/2 - 4/2 = 7x - 2

5x + 2x - 2:

We can break up 7x into 5x and 2x, then combine 5x and 2x to get 7x.

So, we have

5x + 2x - 2 = 7x - 2

Hence, the expressions are 14x/2 - 4/2 and 5x + 2x - 2

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Answer:

[tex]\boxed{\textsf{y = 3}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for y.}[/tex]

[tex]\textsf{We should begin by \underline{simplifying} the equation.}[/tex]

[tex]\textsf{First, begin by dividing 750 from \underline{both sides} of the equation.}\\[/tex]

[tex]\Large\underline{\textsf{Divide:}}[/tex]

[tex]\mathtt{\frac{162000}{750} = \frac{750 \times 6^y}{750} .}[/tex]

[tex]\mathtt{216=6^y}[/tex]

[tex]\Large\underline{\textsf{Continue Dividing By 6:}}[/tex]

[tex]\mathtt{\frac{216}{6} = 36 (^{y-1})}[/tex]

[tex]\mathtt{\frac{36}{6} = 6 (^{y-2} )}[/tex]

[tex]\Large\underline{\textsf{Identify y:}}[/tex]

[tex]\mathtt{6^1 = 6. \ 6^{1+2} = 216. \ (6^3)}[/tex]

[tex]\boxed{\textsf{y = 3}}[/tex]

value from least to greatest is

A<B<C<D

A fraction is a numerical quantity that represents a part of a whole or a ratio of two quantities. It is expressed in the form of one number, called the numerator, divided by another number, called the denominator, and is typically written as a/b, where "a" is the numerator and "b" is the denominator.

Part a)

Let 5.7 (bar on 7) be x

x=5.777777... .....(1)

Multiply the equation by 10,

10x=57.77777... ....(2)

(2)-(1),

9x=52

x=52/9=5.777777778

Partb)

Let 5.75 (bar on 75) be x

x=5.75757575... .....(1)

Multiply the equation by 100,

100x=575.75757575.. ....(2)

(2)-(1),

99x=569.99

x=190/33=5.757575758

Part c)

Let 5.75 (bar on 5) be x

x=5.7555555... .....(1)

Multiply the equation by 10,

10x=57.55555555... ....(2)

Multiply the equation by 10,

100x=575.5555.. ....(3)

(3)-(2),

90x=52

x=259/45=5.755555556

Hence, value from least to greatest is

A<B<C<D

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The answer of the given question based on the ordering from the least to greatest  the answer is the correct answer is (A) DBCA.

The decimal system is a number system that uses the base 10, meaning that there are 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used to represent any quantity. This system is also called the base-10 numeral system, denary system, or Hindu-Arabic numeral system.

In the decimal system, each digit represents a different power of 10. For example, in the number 357, the 7 represents the units, 5 represents the tens, and 3 represents the hundreds.

This system is widely used in everyday life, in which numbers are expressed in decimal form, such as money, time, and measurements. It is also used in mathematics, science, and engineering as the standard way of expressing numbers.

The correct order from least to greatest will be :

A. 5.7

D. 5.75

B. 5.75

C. 5.75

Therefore, the correct answer is (A) DBCA.

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The fourth expression 3⁻⁷/3⁻⁵ is equivalent to  3⁻².

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, operators, and functions that are combined in a particular way to represent a mathematical value or relationship. Expressions can be simple or complex, and they can involve any number of mathematical operations.

Expressions can be used to represent many mathematical concepts:

Now,

To find the equivalent expression of 3⁻², we can simplify each of the given choices using the rules of exponents:

1. 3⁻²/3³ = 1/3²⁺³ = 1/3⁵

2. 3⁻⁷/3⁵ = 3⁻⁷⁻⁵ = 3⁻¹²

3. 3³/3⁻¹² = 3³⁺¹² = 3¹⁵

4. 3⁻⁷/3⁻⁵ = 3⁻⁷⁺⁵ = 3⁻²

Out of the given choices, the fourth choice 3⁻⁷/3⁻⁵ is equivalent to 3⁻².

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Answer:

The answer would be 8.1% (8.108% if you need the exact percentage.)

Step-by-step explanation:

All you would need to do is add 7 + 18 + 12 which = 37, and divide 3/37, which in percentage that gives you 8.1%. (8.108% if you need exact percentage.)

Part 1

a.  In function notation, we have that R(3) > D(3)

b. In function notation, we have that R(0) - D(0) = 25

Part 2

The drone is 20 feet above the ground when the rocket hit the ground.

Part 3

a. R(t) = D(t) when the graphs intercept at t = 4.75 s

b.  It tell us that the drone and rocket are at the same height at that time.

A function notation is the representation of a statement as a mathematical equation using symbols.

Part 1

a. To write the statement at 3 seconds the toy rocket is higher than the drone in function notation.

Since

At t = 3, the toy rocket is higher than the drone.

So, in function notation, we have that R(3) > D(3)

b. To write the statement at the start the toy rocket is 25 feet above the drone.

At the start t = 0, and the toy rocket is 25 feet above the drone.

So, in function notation, we have that R(0) - D(0) = 25

Part 2.

To find the height of the drone when the rocket hit the ground,

Since

We find R(t) = 0 and find the time t, where it intercepts the height of the drone.

So, from the graph R(t) = 0 at t = 5. And at t = 5, D(t) = 20

So, the drone is 20 feet above the ground when the rocket hit the ground.

Part 3.

a. The value of t at which R(t) = D(t) is where the graphs intercept.

The graphs intercept at t = 4.75 s

b. Since R(t) = D(t) at t = 4.75 s, it tell us that the drone and rocket are at the same height at that time.

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Answer:

-16

Step-by-step explanation:

1. multiply the minus sign on both sides now we have 4x=-64

2. divide 4 on both sides

You're done! x=-16

Answer: B) 2

Step-by-step explanation:

In the image, we see a box and whisker plot. The middle line represents the median. Looking at the numbers on the side, and the placement of the middle line, we can see that the median in this situation is 2.

The transformations that compares the functions y = 1/x and y = 5/(x + 6) are

What are transformations?

Transformations are mathematical operations that are performed to change the shape or value of a graph, function or image.

Since we have the functions

We want to see how the graphs of

We proceed as folows.

Looking at the functions

We compare the transformations and see that

So, the functions compare by

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We can use the binοmial distributiοn tο mοdel this situatiοn, where each questiοn is a Bernοulli trial with a prοbability οf success (getting the cοrrect answer) οf 0.5.

A prοbability is a numerical representatiοn οf the likelihοοd οr chance that a specific event will take place. Bοth prοpοrtiοns ranging frοm 0 tο 1 and percentages ranging frοm 0% tο 100% can be used tο describe prοbabilities.

Let X be the number οf False answers in the cοmpleted exam paper.

Prοbability that all answers are False:

[tex]P(X = 4) = (0.5)^4 = 0.0625[/tex]

Prοbability that exactly three οr fοur answers are False:

P(X = 3 οr X = 4) = P(X = 3) + P(X = 4)

[tex]= 4C3(0.5)^3(0.5)^1 + (0.5)^4[/tex]

= 0.25 + 0.0625

= 0.3125

Prοbability that at least οne answer is True (which is the cοmplement οf the event that all answers are False):

P(at least οne True) = 1 - P(all False) = 1 - 0.0625 = 0.9375

Prοbability that the last answer is True:

This prοbability can be calculated using cοnditiοnal prοbability, where we find the prοbability that the last answer is True given that we knοw that at least οne answer is True:

P(last answer is True | at least οne True) = P(last answer is True and at least οne True) / P(at least οne True)

P(last answer is True and at least οne True) = P(last answer is True) = 0.5

P(at least οne True) = 0.9375 (calculated in part 3)

Sο, P(last answer is True | at least οne True) = 0.5 / 0.9375 = 0.5333 (rοunded tο fοur decimal places).

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Answer:

(x, y) = (-1/2, 5/2)

Step-by-step explanation:

To solve this system of equations using substitution, we can use the first equation to express y in terms of x, and then substitute that expression into the second equation to get an equation in terms of x alone.

Starting with the first equation, we have:

y = x + 3

We can now substitute this expression for y into the second equation:

3x + 3y = 6

3x + 3(x + 3) = 6

Simplifying the right-hand side:

3x + 3x + 9 = 6

6x = -3

x = -1/2

Now that we have solved for x, we can substitute this value back into the first equation to find y:

y = x + 3

y = -1/2 + 3

y = 5/2

Therefore, the solution to the system of equations is (x, y) = (-1/2, 5/2).

To check our solution, we can substitute these values back into both equations and verify that they hold true:

y = x + 3

5/2 = -1/2 + 3

5/2 = 5/2

This equation holds true, so the first equation is satisfied by our solution.

3x + 3y = 6

3(-1/2) + 3(5/2) = 6

-3/2 + 15/2 = 6

6 = 6

This equation also holds true, so the second equation is satisfied by our solution as well.

Therefore, we can conclude that our solution is correct.

The equations have two variables, x and y, and we can use substitution to solve for one variable in terms of the other. By substituting the expression for y into the second equation and solving for x, we get the value of x as -1/2. We can then substitute this value back into the first equation to get the value of y, which is 5/2. This means that the solution to the system of equations is (x, y) = (-1/2, 5/2) and we can check that this solution satisfies both equations.

Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]

The minimum number of children in the colony is 47 given the ratio 6 : 4 : 3

Given that

Ratio = 6 : 4 : 3

We are given the ratio of male to female to children as 6:4:3.

Let the common ratio be x, so the actual number of males, females, and children respectively will be 6x, 4x, and 3x.

Total number of members in the colony = 6x + 4x + 3x = 13x.

We are given that the minimum number of members in the colony is 200.

So,

13x = 200

x = 200/13

The actual number of children in the colony 3x is

Children =  3 * (200/13) = 46.15

Children = 46.15

However, since we cannot have a fraction of a child, we round to the nearest whole number.

Therefore, the minimum number of children in the colony is 47.

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According to the tax tables below, Melvin would have to pay in federal income taxes if filing separately $5,131 and Sylvia $6,750. The total would be $11,881

To identify how much Melvin and Sylvia have to pay in taxes, we must look carefully at the table. In this, the different incomes are classified and on the right side are shown how much the tax is depending on the condition of the citizen. These options are: single, married filling jointly, married filling separately and head of a household.

In accordance with the above, we must look at which number coincides in the row of married filling separately with the value of the income of each one of them. According to the above, Melvin has to pay 5,131 in taxes while Sylvia has to pay 6,750.

Note: This question is incomplete. Here is the complete information:

Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $35,750 last year, while Sylvia had a gross income of $41,700.

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Answer:

1. the radius is increasing at a rate of approximately 0.265 cm/s when the radius is 3 cm

2. the radius is increasing at a rate of approximately 0.159 cm/s when the circumference is 1 cm

Step-by-step explanation:

We can use the formulas for the area and circumference of a circle to solve these problems:

a. To find how fast the radius is changing when the radius is 3 cm, we can use the formula for the area of a circle:

A = πr^2

Taking the derivative of both sides with respect to time, t, we get:

dA/dt = 2πr dr/dt

where dr/dt is the rate of change of the radius.

We know that dA/dt = 5 cm²/s, and when the radius is 3 cm, we can plug in these values to solve for dr/dt:

5 = 2π(3) dr/dt

dr/dt = 5/(6π) cm/s ≈ 0.265 cm/s

Therefore, the radius is increasing at a rate of approximately 0.265 cm/s when the radius is 3 cm.

b. To find how fast the radius is changing when the circumference is 1 cm, we can use the formula for the circumference of a circle:

C = 2πr

Taking the derivative of both sides with respect to time, t, we get:

dC/dt = 2π dr/dt

where dr/dt is the rate of change of the radius.

We know that when the circumference is 1 cm, C = 1 cm, so we can plug in these values to solve for dr/dt:

1 = 2π dr/dt

dr/dt = 1/(2π) cm/s ≈ 0.159 cm/s

Therefore, the radius is increasing at a rate of approximately 0.159 cm/s when the circumference is 1 cm.

From the table, we see that Julia rolled the die 100 times, and the number of times she rolled a 3 was 45.

The best estimate of the probability of rolling a 3 can be found by dividing the number of times a 3 was rolled by the total number of rolls:

P(rolling a 3) = Number of times 3 was rolled / Total number of rolls

P(rolling a 3) = 45 / 100

P(rolling a 3) = 0.45 or 45%

Therefore, based on Julia's experimental results, the best estimate of the probability of rolling a 3 on her biased die is 0.45 or 45%.

Answer:

To prove that every bounded sequence contains a convergent subsequence, we will use the Bolzano-Weierstrass theorem.

Bolzano-Weierstrass theorem: Every bounded sequence in Euclidean space has a convergent subsequence.

Proof: Let (a_n) be a bounded sequence in Euclidean space, which means that there exists some M > 0 such that |a_n| <= M for all n. We will use the bisection method to construct a subsequence that converges to some limit L.

Step 1: Divide the interval [-M, M] into two subintervals, [-M, 0] and [0, M]. Since (a_n) is bounded, at least one of these intervals contains infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_1.

Step 2: Divide I_1 into two subintervals of equal length, and again, at least one of these subintervals must contain infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_2.

Step 3: Repeat this process for each subinterval, dividing it into two subintervals of equal length and choosing the one that contains infinitely many terms of the sequence. We obtain a sequence of nested intervals I_1 ⊃ I_2 ⊃ I_3 ⊃ ... that contain infinitely many terms of the sequence.

Step 4: Since the length of each interval is decreasing and they are nested, the intersection of all the intervals is a single point L. By construction, every term of the sequence (a_n) belongs to one of the intervals I_k, which means that there exists a subsequence (a_nk) that converges to L.

Therefore, every bounded sequence in Euclidean space has a convergent subsequence, as required.

Step-by-step explanation:

Answer:

144ft^2

Step-by-step explanation:

Answer:

144^2 feet

Step-by-step explanation:

To find the area you would multiply length x width for your answer. I hope this helps!

Answer:

0

Step-by-step explanation:

Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)

In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).

The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.

Therefore, the expected value is:

Expected Value = (1/6) x $15 + (5/6) x (-$3)

Expected Value = $2.50 - $2.50

Expected Value = $0

Starting with the angle of -270°, adding 360° gives us 90° (which is a coterminal angle with -270°).

If we rotate 180° counter-clockwise from 90°, we end up at the angle of 270°. Therefore, the new measurement of the coterminal angle is 270°.

I hope this helps :)

Answer:

7+2=3x-2+2

9/3=3x/3

3=x

Answer:

b

Step-by-step explanation:

my brain

The Tοtal number οf tickets tο play will be 15.

Mathematical expressiοns with inequalities οn bοth sides are knοwn as inequalities. In an inequality, we cοmpare twο values as οppοsed tο equatiοns. In between, the equal sign is changed tο a less than (οr less than οr equal tο), greater than (οr greater than οr equal tο), οr nοt equal tο sign.

At a schοοl fair, there are different games tο play that each require 5 tickets tο play.

Jοrdan wants a bag οf pοpcοrn that requires 26 tickets and tο use the rest οf the tickets tο play games.

Jοrdan has 101 tickets.

Fοr tickets tο play will be 101-26 = 75

Sο the Tοtal number οf tickets tο play will be 75/5 = 15.

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The equation of the hyperbola x²/36 = 1. The equation of a horizontal line passing through (±6,0).

The resulting curve of a hyperbola consists of two separate branches that are mirror images of each other, and they are characterized by their asymptotes, which are straight lines that the curve approaches but never touches. The asymptotes intersect at the center of the hyperbola, which is also the point where the two branches are closest together.

Since the foci of the hyperbola are at (0,-6) and (0,6), and the transverse axis is vertical, the center of the hyperbola is at the midpoint of the foci, which is the point (0,0).

Also, since the asymptote of the hyperbola is the line y = -x, we know that the slopes of the asymptotes are ±1, and since the transverse axis is vertical, the slope of the transverse axis is 0. Therefore, we have a hyperbola with center (0,0), vertical transverse axis, and asymptotes y = x and y = -x.

The standard form of the equation for a hyperbola with center (0,0), transverse axis of length 2a, and asymptotes y = ±(a/x) is:

x²/a² - y²/b² = 1

where b² = a² - c², where c is the distance from the center to each focus.

In this case, since the distance between the foci is 12, we have:

c = 6

Also, since the transverse axis is vertical and the distance from the center to each vertex is a, we have:

a = distance from center to vertex = 6

Therefore, we have:

b² = a² - c² = 36 - 36 = 0

So the equation of the hyperbola is:

x²/36 - y²/0 = 1

Simplifying, we get:

x²/36 = 1

or

x² = 36

This is the equation of a horizontal line passing through (±6,0).

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