Hi I need help with the questions below, thank you!

Answer:

For the first 30 minutes, we will have a line with a given steepness, this will represent the 30 minutes riding at a fast pace.

Then he stops for 20 minutes, we will represent this with a constant line.

Then he again moves for another 30 minutes, but with a slower pace than in the first 30 minutes, then this line will be less steep than the first line.

A sketch of this situation can be seen below.

By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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In the table, we can see that the highest number corresponds to the cats who failed. Then, if a comparative bar chart represents the data, the bar representing the number of cats that failed will be the tallest.

A. Cats who failed

5 years longer then Bill, 2x5=10.

10+2=12.

12-5=7

Hoang has be there for 12 years. Bill has for 7 years.

The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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A). The first term represents the total cost of the waffle irons and the second term represents the expenses.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be 350x - 1500

C). The company's profit for a 5-day week is $250.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.

A). The first term represents the total cost of the waffle irons and the second term represents the expenses. Here 25 is the number of the waffle iron and the x is the number of days.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be written as:-

350x - 1500

C). The company's profit for a 5-day week will be;-

Profit = 350x - 1500

Profit = ( 350 x 5 ) + 1500

Profit = 1750 - 1500

Profit = 250

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The correct statement regarding the graph of the function f(x) = (x + 2)(x + 6) is given by:

The function is negative for all real values of x where -6 < x < -2.

The graph of the function f(x) = (x + 2)(x + 6) is missing, and is given at the end of the answer.

We have to look at the graph of the function relative to the x-axis, as follows:

Hence, for function f(x) = (x + 2)(x + 6), we have that:

Hence the correct statement for the signal of the function is given as follows:

The function is negative for all real values of x where -6 < x < -2.

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It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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One way to construct such a graph is to take two 8-vertex periods, each with a degree sequence (3, 3, 3, 3, 3, 3, 3, 3) and connect them together at one vertex. The resulting graphs have the desired order sequence but are not isomorphic because they have different periodic structures.

A graph is said to be isomorphic to another graph if there is a one-to-one correspondence between the vertices of the two graphs preserving the edges. That is, two graphs are isomorphic if they have the same structure regardless of labeling. The degree sequence of a the graph is simply a list of the degree (number of edges) of each vertex in the graph.

This is a useful property for characterizing graphs and proving non-isomorphism. Connecting two loops at the same vertex produces two different graphs. Two cycles in a graph are connected by a "necklace" structure with a common vertex. In another graph, two cycles are connected at two different vertices to form two separate "arms".

The two graphs are not isomorphic because they have the same order sequence but different periodic structures.

The periods in the first graph have one common vertex, whereas the periods in the second graph have two separate vertices. This difference in structure prevents a one-to-one correspondence between vertices, so the graph is not isomorphic.

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Step-by-step explanation:

Let x be the number of buses for the trip.

Then (32 - x) is the number of cars for the trip.

We have 27x + 3(32 - x) = 408.

=> 27x + 96 - 3x = 408

=> 24x = 312

=> x = 13

Hence there are 13 buses and (32 - 13) = 19 cars.

Answer:

ANSWER IS B

Step-by-step explanation:

The formula for the Coulomb's law with respect to r is given by the equation r = ( Kq₁q₂ / F )^1/2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

F = Kq₁q₂ / r²

where F is the force, K is a constant, q1 and q2 are the charges on the two bodies, and r is the distance between them

On simplifying for r , we get

Multiply by r² on both sides , we get

Fr² = Kq₁q₂

Divide by F on both sides of the equation , we get

r² = ( Kq₁q₂ / F )

Taking square roots on both sides of the equation , we get

r = ( Kq₁q₂ / F )^1/2

Hence , the equation is r = ( Kq₁q₂ / F )^1/2

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The Space Shuttle Discovery traveled 22.3 million miles more distance than the Space Shuttle Atlantis.

What is distance ?

To find how many more miles the Space Shuttle Discovery traveled than the Space Shuttle Atlantis, we can subtract the distance traveled by Atlantis from the distance traveled by Discovery:

148.2 million miles - 125.9 million miles = 22.3 million miles

Therefore, the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

What is Space Shuttle ?

The Space Shuttle was a reusable spacecraft designed and operated by NASA (the National Aeronautics and Space Administration) to carry astronauts and cargo into space. It was in service from 1981 until 2011, when the final mission was completed.

The Space Shuttle consisted of several components, including the orbiter, which was the main spacecraft, and the two solid rocket boosters and external fuel tank that provided the initial propulsion during liftoff. The orbiter was designed to carry up to seven crew members and could be used to deploy satellites, conduct scientific experiments, and perform other tasks in space.

The Space Shuttle was unique in that it could land like an airplane, allowing it to be reused multiple times. After completing a mission, the orbiter would re-enter Earth's atmosphere and glide to a landing on a runway.

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Complete question is: The space shuttle discovery traveled 148.2 million miles during its mission. The space shuttle Atlantis traveled 125.9 million miles. the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

Given that the height of a object thrown within a gravitational field is given as a quadratic equation in time, t, the time at which the object is at a specified height can be found by the quadratic formula

The values of, t, for which the height of the rocket is 82 feet are;

t = 12.21 seconds or t = 0.42 seconds

Question: Parts of the question that appear missing but can be found online are (i) To find the values of the time, t, when the rocket's height is 82 feet and round answers to the nearest hundredth

The known parameters of the rocket are;

The initial upward velocity of the rocket, v = 202 ft./s

The given function representing the height, h, (in feet) after t seconds is presented as follows;

H = 202·t - 16·t²

The unknown;

The time for which the height of the rocket is 82 feet

Method;

Substitute H = 82 feet in the height function equation and solve for t as follows;

When H = 82, we get;

82 = 202·t - 16·t²

Therefore;

16·t² - 202·t + 82 = 0

Dividing the above equation by 2 gives;

(16·t² - 202·t + 82)/2 = 0/2

8·t² - 101·t + 41 = 0

By using the quadratic formula, we get;

\(\mathbf{t = \dfrac{101 \pm \sqrt{(-101)^2 - 4 \times 8 \times 41} }{2 \times 8} = \dfrac{101 \pm \sqrt{8889} }{16}}\)

Therefore, the values of t given by rounding off to the nearest hundredth are;

t = 12.21 or t = 0.42

The values of the time, t, at which the height of the rocket is 82 feet are t = 12.21 seconds or t = 0.42 seconds

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Answer:

1/6

Step-by-step explanation:

A (6,1)

B (12,2)

slope = (2-1)/(12-6)

1/6

Answer:

Surface area of cube = 6a²

Side of cube = 5/2

Surface area of cube = 6 (5/2)² = 6 (25/4)

= 37.5 unit²

Answer:A

Step-by-step explanation:

To find the rate of decay, we need to use the formula A(t) = P(0.82)^t, where A(t) is the amount after t years, P is the initial amount, and 0.82 is the decay factor.

The decay factor is equal to 1 minus the decay rate, so we can solve for the decay rate as follows:

0.82 = 1 - r

r = 1 - 0.82

r = 0.18

Therefore, the rate of decay is 18%, which corresponds to answer choice A.

Answer:

A

Step-by-step explanation:

The 95% confidence interval to estimate the proportion of students on financial aid = (0.522, 0.658)

In this question we have been given a university dean is interested in determining the proportion of students who receive some sort of financial aid.

Let p be the population proportion of students who receive some financial aid.

The dean randomly selects 200 students and finds that 118 of them are receiving financial aid.

i.e. n= 200

p{hat} = 118/200 = 0.59

We know that the critical value for 95% confidence interval : z = 1.96

The standard deviation would be,

σ = √[p{hat}(1 - p{hat})/N]

σ = √0.59(1 - 0.59)/200

σ = √(0.0012095)

σ = 0.0348

The 95% confidence interval for population proportion would be,

(0.59 ± (1.96 * 0.0348))

= (0.59 - (1.96 * 0.0348), 0.59 + (1.96 * 0.0348))

= (0.5218, 0.6582)

Therefore, the 95% confidence interval : (0.522, 0.658)

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The statements that are true with regards to the graph of the functions and the sprinter that wins and lead the race are;

The true statements are; A, B, and C

The graph of a function visually represents the rule of the function showing how the output values of the function changes as the input value varies.

The distance the two sprinter's will run = 80 meters

The speed of sprinter A = 9 meters per second

The speed of sprinter B = 9 meters per second

The head start of sprinter B = 14 meter

The analysis of the statements are as follows

A. The graph of the functions representing the speeds of the sprinters have the same slope of 9 which is the rate of change of distance with time, therefore, the graphs are parallel and will never intersect.

The statement is therefore; True

B. Sprinter B will win the race. - True

Sprinter B has a head start of 14 meters and both sprinters have the same speed, therefore, sprinter B will reach the finish line first and win the race.

C. Sprinter B is leading the race at the 4 seconds mark;- True

Sprinter A will cover a distance of 9 m/s × 4 s = 36 m at the 4 seconds mark, while sprinter B will cover a distance in the 80 m race of 9 m/s × 4 s + 14 m = 50 m at the 4 second mark, therefore, sprinter B will be leading at the 4 second mark

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Answer:

x² - 7x + 12

Step-by-step explanation:

Use FOIL method

(x - 3) (x -4) = x*x + x *(-4) + (-3)*x + (-3)*(-4)

                  = x² - 4x - 3x + 12           {Combine like terms}

                  = x² - 7x + 12

Answer:

x^2−7x+12

Step-by-step explanation:

Use the FOIL method:  (a+b)(c+d)= ac+ad+bc+bd.

x^2−4x−3x+12

Collect like terms.

x^2 +(−4x−3x)+12

Simplify.

anddthe answer is  

x^2−7x+12

Answer:

198,634

Explanation:

Substitute the given values into the formula: A = Pe^(−rt), where A represents the future value, P represents the initial (current) value, r represents the rate, and t represnts the time.

A = 400,000e^(-0.10)(7)

A = 198634.12

The value of building depreciation after seven-year is $191,318.76

What information do we have?

Value of building = $400,000

Depreciation rate = 10%

Number of year = 7 year

Value of building after depreciation = P(1-r)ⁿ

Value of building depreiciation = 400,000(1-10%)⁷

Value of building depreciation = 400,000(1-0.1)⁷

Value of building depreiciation = 400,000(0.9)⁷

Value of building depreiciation = 400,000(0.4782969)

Value of building depreciation = $191,318.76

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The shape of the cross section taken parallel to the base of a cone is frustum cone.

The form created when a solid and a plane intersect is known as a cross-section. A two-dimensional geometric shape makes up the cross-section of a three-dimensional shape. In other words, a cross-section is the shape created by slicing a solid parallel to the base.

When a cone is cut by a plane that is parallel to its base, the portion of the cone that still has its base is known as the frustum. Cones and pyramids are examples of frustums, which are also referred to as truncated shapes.

Therefore, the shape of the cross section taken parallel to the base of a cone is frustum cone.

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The range of x-values extrapolation occurs in between x < 0 and x > 6

We have given that,

On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).

The Range is the difference between the lowest and highest values.

Therefore we can conclude that the,

range of x-values extrapolation occurs in between x < 0 and x > 6.

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Answer:

32

Step-by-step explanation:

8 x 4 = 32

I'm pretty sure

Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

Answer:

The table is:

x        y

1         1

2        5

3        9

The graph B shows the relationship y=4x-3

Step-by-step explanation:

We need to fill the table using the rule:

To find y multiply x by 4 and then subtract 3.

Writing rule in mathematical form:

y=4x-3

Now for completing the table we need to put x=1,2 and 3 and find values of y

\(For x=1//y=4x-3\\ y=4(1)-3\\ y=4-3\\ y=1\\\)

\(For \ x=2\\y=4x-3\\ y=4(2)-3\\ y=8-3\\ y=5\)

\(For \ x=3\\y=4x-3\\ y=4(3)-3\\ y=12-3\\ y=9\)

So, the table is:

x        y

1         1

2        5

3        9

The graph B shows the relationship y=4x-3

Answer:

A (-1,-10) ; A (-1,14)

Step-by-step explanation:

\(\sqrt{(-1-4)^2 + (y-2)^2} = 13 \\ 25 + y^2 + 4 -4y = 169\)

y^2 -4y - 140 = 0

Δ/4 = 4 + 140 = 144

y1 = 2 + 12 = 14

y2 = 2 -12= -10

Answer:

Y=-2X + 4

Step-by-step explanation:

Follow the rise of run and to get  the  B= 4 you must answer this problem

Y+2=-2(X-3)

Answer:

C, F.

Step-by-step explanation:

All angle measures are preserved in a dilation. And if all angle measures are preserved, it makes the triangles similar by the AA similarity theorem.

The probability of the hotel purchasing no defective sets is 2/7, the probability of purchasing 1 defective set is 4/7, and the probability of purchasing 2 defective sets is 1/7.

To find the probability distribution of x, we need to consider all possible combinations of 3 sets that the hotel can purchase from the shipment of 7 sets.

The total number of ways to choose 3 sets from 7 is given by the binomial coefficient C(7, 3) = 35.

Now, let's consider the different possible values of x.

If the hotel purchases 0 defective sets, then it must choose 3 sets from the 5 non-defective sets, which can be done in C(5, 3) = 10 ways. The probability of this occurring is:

P(x=0) = C(2, 0) * C(5, 3) / C(7, 3) = 10/35 = 2/7

If the hotel purchases 1 defective set, then it must choose 2 non-defective sets and 1 defective set, which can be done in C(2, 1) * C(5, 2) = 20 ways. The probability of this occurring is:

P(x=1) = C(2, 1) * C(5, 2) / C(7, 3) = 20/35 = 4/7

If the hotel purchases 2 defective sets, then it must choose 1 non-defective set and 2 defective sets, which can be done in C(2, 2) * C(5, 1) = 5 ways. The probability of this occurring is:

P(x=2) = C(2, 2) * C(5, 1) / C(7, 3) = 5/35 = 1/7

Therefore, the probability distribution of x is:

x | 0 | 1 | 2

P(x) | 2/7 | 4/7 | 1/7

Note that the sum of these probabilities is 1, as it should be for a probability distribution.

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