the driver of a car completes a trip. the graph displays data about the car's motion during the trip. which of the following statements about the car's motion is true? responses the total time for the car trip was 50 minutes. the total time for the car trip was 50 minutes. the car did not slow down during the trip. the car did not slow down during the trip. the car returned to where it had started the trip at the end of the trip. the car returned to where it had started the trip at the end of the trip. the car did not travel at a constant speed during the entire trip. the car did not travel at a constant speed during the entire trip. skip to navigation highlight previous 1, fully attempted. 2, fully attempted. 3, fully attempted. 4, unattempted. 5, unattempted. 6, unattempted. 7, unattempted. 8, unattempted. 9, unattempted. 10, unattempted.next auto saved at: 10:49:59

Answer:

To solve this problem, we need to first find the numbers that are multiples of 4 or 6 between 1 and 15, inclusive.

Multiples of 4: 4, 8, 12

Multiples of 6: 6, 12

The number 12 is a multiple of both 4 and 6, so we only count it once.

So, there are a total of 4 possible outcomes that meet the condition of being a multiple of 4 or 6.

Therefore, the probability of getting a multiple of 4 or 6 is:

P(multiple of 4 or 6) = 4/15

Answer: 4/15.

Hope This Helps!

Answer:

81 eggs

Step-by-step explanation:

already had 9 eggs

6 crates x 12 eggs in each crate

= 72 eggs

72+9=81

Answer:

x = -5

Y = -22/3

Step-by-step explanation:

Y= 2/3x - 4                     Y = -x + 1

We put -x + 1 in for y to solve for x

-x + 1 = 2/3x - 4

-5/3x + 1 = -4

-5/3x = -5

x = -5

Now put -5 in for x and solve for y

Y= 2/3(-5) - 4

Y = -10/3 - 4

Y = -22/3

So, there are only one solution x = -5 and y = -22/3

Answer: 13.51 (not in inches format)

Step-by-step explanation:

tan(x) = 4.384/12

x = tan^-1 (4.384/12)

x = 20.068°

tan(20.068) = y/(12+25)

tan(20.068) = y/37

20.068 = tan^-1 (y/37)

y = 13.51

Answer:

Step-by-step explanation:

To solve this with similar triangles - you need to set up a proportion.

I changed it all to inches.

12 ft = 144 in

4.384 ft = 51. 84 inches

12 + 25 (you need to add the base of the triangle) = 37 ft = 444 inches

set up smaller triangle in proportion to bigger triangle

51.84"/144" = x/444

cross mulitply then divide

51.84 times 444 = 23016.96

23016.96 ÷ 144 = 159.84 inches

Change back to feet by dividing by 12

159.84 ÷ 12 = 13.32 ft

The number of students who earned a score of 90 or less in class 2 is 7, and the number of students who earned less than 75 in class 1 is 3. The difference between the two is 4.

The given problem presents two box plots representing the test scores for two different classes. Class 1 has 17 students, while class 2 has 13 students. It is required to find the difference between the number of students who earned a score of 90 or less in class 2 and the number of students who earned less than 75 in class 1.

By analyzing the box plots, we can see that 7 students in class 2 earned a score of 90 or less, while only 3 students in class 1 earned less than 75. Therefore, the difference between the two is 4. It is important to understand box plots and their interpretation to solve such problems.

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Answer:

Step-by-step explanation:

The required polynomial of exact degree 5 which interpolates the four given points is equals to  p(x) = x^3/2 -4x^2 + 63x/6 -6.

Polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4).

Apply Lagrange interpolation.

Standard form of the Lagrange interpolation polynomial of degree n passing through n+1 distinct points (x0, y0), (x1, y1), ..., (xn, yn) is,

L(x) = Σ [yi × Π (x - xj) / (xi - xj)], for i = 0, 1, ..., n

where Π is the product operator and j takes all values different from i.

For the given four points, we have n = 3, so the polynomial has degree n+1 = 4.

Using the formula, we have,

L(x) = (1× (x - 2)(x - 3)(x - 4) / ((1 - 2)(1 - 3)(1 - 4)))

+ (3× (x - 1)(x - 3)(x - 4) / ((2 - 1)(2 - 3)(2 - 4)))

+ (3× (x - 1)(x - 2)(x - 4) / ((3 - 1)(3 - 2)(3 - 4)))

+ (4× (x - 1)(x - 2)(x - 3) / ((4 - 1)(4 - 2)(4 - 3)))

Simplifying this expression, we get,

⇒L(x) = (-x^3 + 9x^2 - 26x + 24)/6 + (3x^3/2 - 12x^2 + 57x/2 - 18) +(-3x^3/2 + 21x^2 /2- 21x + 12) + (2x^3/3 - 4x^2 + 22x/3 - 4)

⇒L(x) = x^3/2 -4x^2 + 63x/6 -6

Therefore, the polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4) is  p(x) = x^3/2 -4x^2 + 63x/6 -6.

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Answer: We can find the total distance of the first route by adding the individual distances:

53 + 28 + 98 = 179 miles

Similarly, we can find the total distance of the second route:

28 + 49 + 85 = 162 miles

Therefore, the second route is shorter by (179 - 162) = 17 miles.

Step-by-step explanation:

A random sample of 38 cities was asked to report their voter turnout percentages, which can be used to estimate the average voter turnout in those cities. However, caution should be taken when making generalizations about the larger population of cities, since the sample size is relatively small.

The average voter turnout during an election can be calculated by taking the percentage of registered voters who actually voted in a sample of cities and finding the mean. In this case, a random sample of 38 cities was asked to report the percent of registered voters who voted in the most recent election. To calculate the average voter turnout, follow these steps:

1. Obtain the reported voter turnout percentages from each of the 38 cities in the random sample.
2. Add up all the percentages of voter turnout from the 38 cities.
3. Divide the sum of voter turnout percentages by the number of cities (38) to find the average voter turnout.

By following these steps, you will find the average voter turnout for the most recent election, based on the random sample of 38 cities. Keep in mind that the average voter turnout can vary depending on the election and location, as factors such as political climate, awareness, and accessibility can impact voter participation. This calculated average represents an estimation of the overall turnout and may not be completely representative of the entire population, but it provides a useful measure to understand voter engagement during elections.

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The candy distributor needs to use 30 kilograms of 10% fat-content chocolate and 70 kilograms of 50% fat-content chocolate to create 100 kilograms of a 14% fat-content chocolate.

To solve this problem, we can use the method of mixture problems, which involves setting up a system of equations. Let x be the number of kilograms of the 10% fat-content chocolate and y be the number of kilograms of the 50% fat-content chocolate.

We have two equations based on the fat content and the total weight of the mixture:

0.1x + 0.5y = 0.14(100) (equation for fat content)

x + y = 100 (equation for total weight)

We can solve this system of equations using substitution or elimination. Using substitution, we can solve for x in terms of y from the second equation and substitute it into the first equation:

x = 100 - y

0.1(100 - y) + 0.5y = 0.14(100)

10 - 0.1y + 0.5y = 14

0.4y = 4

y = 10

Then we can substitute y = 10 back into the equation for x and get:

x = 100 - y = 100 - 10 = 90

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For given dilation of the figure, the distance from the center of dilation to point A' is approximately 1.414 units.

What exactly is dilation in mathematics?

In mathematics, dilation is a transformation that changes the size of a figure but not its shape. It is also known as scaling, enlargement, or reduction.

To perform a dilation, a figure is multiplied or divided by a scale factor, which is a positive number greater than zero. If the scale factor is greater than 1, the figure is enlarged, while if it is less than 1, the figure is reduced. If the scale factor is equal to 1, the figure remains the same size.

Now,

To find the distance from the center of dilation to point A', we need to use the fact that the distance between the center of dilation and any point on the preimage is multiplied by the scale factor to get the corresponding distance on the image.

First, let's find the distance from the center of dilation to point A:

distance from center to A = √((6-2)² + (-2-2)²) = √(4² + (-4)²) = √32 ≈ 5.657 units (rounded to three decimal places)

Next, we can use the fact that the scale factor is 1/4 to find the distance from the center of dilation to point A':

distance from center to A' = (scale factor) x (distance from center to A)

= (1/4) x 5.657

= 1.414 units (rounded to three decimal places)

Therefore, the distance from the center of dilation to point A' is approximately 1.414 units.

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Answer:

  use SSS

Step-by-step explanation:

Given two congruent chords AB and BC in circle O, you want to prove ∆AOB is congruent to ∆COB.

1. circle O, AB≅BC . . . . given

2. OB ≅ OB . . . . reflexive property of congruence

3. OA ≅ OC . . . . definition of a circle

4. ∆AOB ≅ ∆COB . . . . SSS postulate

__

Additional comment

Your erased statement 2 shows you know exactly how to do this.

All the radii of a circle are the same length, so it is easy to show congruence by SSS, given that AB≅BC.

Answer: 19 3/5 x 20 2/5 = 9996/25 = 399 21/25

Since AB is tangent to circle E at A, we know that angle CAB is a right angle (tangent is perpendicular to the radius at the point of tangency). Therefore, triangle ADC is a right triangle.

Let's use the Pythagorean theorem to find the length of CE:

CE^2 = AC^2 + AE^2 (using Pythagorean theorem in triangle ACE)

CE^2 = 9^2 + EA^2 (since AE = EA, by definition of radius)

CE^2 = 81 + EA^2

We still need to find EA. Let's use the fact that EA is half the length of CD:

EA = CD/2

Now we can substitute this expression into the previous equation:

CE^2 = 81 + (CD/2)^2

CE^2 = 81 + CD^2/4

Next, let's use the Pythagorean theorem in triangle ADC:

AD^2 + DC^2 = AC^2

4^2 + DC^2 = 9^2

DC^2 = 9^2 - 4^2

DC^2 = 65

Now we can substitute this expression into the previous equation:

CE^2 = 81 + 65/4

CE^2 = 99.25

Taking the square root of both sides, we get:

CE ≈ 9.96

Therefore, CD = 2CE ≈ 19.9.

Answer: CD ≈ 19.9

Angle B is approximately 53.15 degrees using trigonometry.

We can use trigonometry to solve for angle B in the right triangle BCD. We know that angle CBC is 37 degrees, and BD is 64.

First, we can use the Pythagorean theorem to find the length of BC, which is the hypotenuse of the right triangle:

[tex]BC^{2}[/tex] = [tex]BD^{2}+CD^{2}[/tex]

[tex]BC^{2}[/tex] = 64² + [tex]CD^{2}[/tex]

Since CD is opposite angle B, we can use trigonometry to relate CD to angle B. Specifically, we can use the tangent function:

tan(B) = CD/BD

Rearranging, we have:

CD = BDxtan(B)

Taking the square root of both sides, we have:

BC = 64[tex]\sqrt{(1+tan^{2}B)}[/tex]

Now we can use the fact that BC is the hypotenuse of the right triangle to relate it to angle CBC, which is 37 degrees. Specifically, we can use the sine function:

sin(CBC) = BD/BC

Substituting our expression for BC, we have:

sin(37) = 64/64√(1 + tan²(B))

Simplifying, we get:

sin(37) = 1/[tex]\sqrt{(1+tan^{2}B)}[/tex]

Squaring both sides, we have:

sin²(37) = 1/[tex](1+tan^{2}B)}[/tex]

Substituting the identity cos²(θ) + sin²(θ) = 1, we have:

cos²(37) = cos²(B)

Taking the square root of both sides, we have:

cos(37) = ±cos(B)

Since angle B is acute (it is less than 90 degrees because it is in a right triangle), we know that cos(B) is positive. Therefore, we can take the positive square root:

cos(B) = cos(37)

B = 53.15 degrees (rounded to two decimal places)

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We can solve for the time when the stone will be 698 feet above the planet's surface by setting h = 698 and solving for t in the equation h = 500 + 110t - 5.5t²:

698 = 500 + 110t - 5.5t²

Rearranging, we get:

5.5t² - 110t + 198 = 0

Dividing both sides by 5.5, we get:

t² - 20t + 36 = 0

This is a quadratic equation that we can solve using the quadratic formula:

t = (-(-20) ± sqrt((-20)² - 4(1)(36))) / (2(1))

Simplifying, we get:

t = (20 ± sqrt(64)) / 2

t = 10 ± 4

So the possible values of t are t = 14 or t = 6. We can check which value is correct by plugging each value into the original equation and seeing if it gives a height of 698:

When t = 14:

h = 500 + 110(14) - 5.5(14)²

h = 500 + 1540 - 1078

h = 962

When t = 6:

h = 500 + 110(6) - 5.5(6)²

h = 500 + 660 - 198

h = 962

So both values of t give a height of 698. Therefore, the stone will be 698 feet above the planet's surface at t = 6 seconds or t = 14 seconds.

Answer:

Yes they can.

The only time they would have to be different lengths is if it was a square

Therefore, the slope is 1/3 and the y-intercept is 0.

a. The equation is in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 4, and the y-intercept is 1. Therefore, the slope is 4 and the y-intercept is 1.

b. This equation is also in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 1, and the y-intercept is -2. Therefore, the slope is 1 and the y-intercept is -2.

c. This equation is already in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 1/3, and the y-intercept is 0 (since there is no constant term). Therefore, the slope is 1/3 and the y-intercept is 0.

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The coordinate of the segment in the ratio is (-2,-2).

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Partitions the line segment in the ratio A to B... then,

=> x-coordinate is : x1 +[tex]\frac{ A(x2-x1)}{(A+B)}[/tex]

=> y-coordinate is: y1 + [tex]\frac{A(y2-y1)}{(A+B)}[/tex]

Here A = 2 , B = 1 and [tex](x_1,y_1)=(-10,10)[/tex] , [tex](x_2,y_2)=(2,-8)[/tex] .

x-coordinate = -10+[tex]\frac{2(2+10)}{(2+1)}[/tex] =  -10 + [tex]\frac{2(12)}{3}[/tex] = -10 + 2(4) = -10+8 = -2

y-coordinate = 10+[tex]\frac{2(-8-10)}{(2+1)}=10+\frac{2(-18)}{3}[/tex] = 10+2(-6) = 10-12 = -2.

Hence the coordinate of the segment in the ratio is (-2,-2).

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The correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.

What is Exterior angles ?

In a polygon, an exterior angle is an angle formed by a side and an extension of an adjacent side. The measure of an exterior angle of a regular polygon with n sides is given by 360/n degrees.

To find the measure of each exterior angle of a regular polygon, we use the formula:

Measure of each exterior angle = 360 degrees / number of sides

In this case, the polygon is a regular 66-gon, so the number of sides is 66. Thus,

Measure of each exterior angle = 360 degrees / 66 = 5.454545...

Rounding to the nearest tenth, we get:

Measure of each exterior angle ≈ 5.5 degrees

Therefore, the correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.

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The total value of Mary's investment after two years is $233.

17-x

Because he sends more than you we subtract your value,x,from his 17,mostly because we are unaware of the number of texts you send.Which means 17 minus x will give you the amount of texts he sends more.

Answer: $4.20

Step-by-step explanation:

   To answer this question, we will find 5% of $84.

   First, a percent divided by 100 becomes a decimal.

5% / 100 = 0.05

   Next, we are finding 5% of $84. In mathematics, "of" means multiplication.

0.05 * $84 = $4.20

The inequalities that can be used to determine the possible number of bass in the pond over time are:

[tex]P > =250e^{0.048t} , P < =275e^{0.048t}.[/tex]

Rachel has a large pond on her property. The pond contains many different kinds of fish including bass. She knows that the population of bass is increasing exponentially each year at a rate of 4.8%. She also knows that there are currently between 250 and 275 basses in the pond.

Inequalities

Given:

r=4.8/100=0.048

Initial amount:

Lower end=250

Upper end=275

Using this equation to determine the inequalities

A=p×e^rt

Where:

A=Amount

P=Population

r=Growth rate

t=Time

Let's plug in the formula

Inequalities:

[tex]P > =250e^{0.048t}P < =275e^{0.048t}[/tex]

Therefore the inequalities are : [tex]P > =250e^{0.048t} , P < =275e^{0.048t}.[/tex]

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Percentage of students who were undecided is  59% of the students were undecided about their future careers.

what is Percentage?

A percentage is a fraction or ratio expressed as a fraction of 100. It is a way of expressing a part of a whole as a proportion of the whole. It is denoted by the symbol '%'. For example, if there are 100 students in a class and 20 of them are girls, then the percentage of girls in the class is 20%.

In the given question,

To solve the problem, we need to first find out the percentage of students who were undecided. We know that 25% of the students wanted to become doctors and 16% wanted to become teachers. The percentage of students who were undecided can be found by subtracting the sum of the percentages of those who wanted to become doctors and teachers from 100%:

Percentage of students who were undecided = 100% - (25% + 16%) = 59%

Therefore, 59% of the students were undecided about their future careers.

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(a) Since M is the midpoint of DE, we have ME = (1/2)b.

Also, CXE is a straight line, so C, X, and E are collinear.

Therefore, we have CX + XE = CE, or a - b + FE = b + (2a - b), which simplifies to FE = a.

(b) n = a/b - 1.

X is the point on FM such that

FX:XM =n:1,

we have FX = nX and XM = X.

Since M is the midpoint of DE, we have ME = (1/2)b,

so that  DX = DE - EX = b - (n + 1)X.

Using the fact that CXE is a straight line,

we have CX + XE = CE, or a - b + FE = b + (2a - b),

which simplifies to FE = a.

Therefore, we have FX + FE = AX, or nX + a = a + b + (n + 1)X.

Simplifying, we get b = (n + 1)X - nX = X.

We know that  DX = b - (n + 1)X = 0, so X = b/(n + 1).

Therefore, we have n/(n + 1) = FX/X = (a-b)/b.

Calculating  for n, we have  n = a/b - 1.

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To create identical donation bags, you will need 55 hats and 40 scarves. You produce the most donation bags without any extra apparel. Each donation package contains 11 hats and 8 scarves.

To make the greatest amount of donation bags with no clothing left over, we need to find the greatest common factor (GCF) of 40 and 55. We can do this by finding the prime factors of both numbers:

[tex]40 = 2 * 2 * 2 * 5[/tex]

55 = 5 x 11

The GCF is the product of the common prime factors, which is 5. This means we can make 5 identical donation bags.

To find out how many scarves and hats are in each donation bag, we can divide the total number of scarves and hats by the number of donation bags:

Number of scarves per bag = 40 / 5 = 8 scarves

Number of hats per bag = 55 / 5 = 11 hats

Therefore, each donation bag will contain 8 scarves and 11 hats.

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The geometric sequence for the value of a₁= 3 r= 1/10 n=8 is [tex]a_{8} = \frac{3}{10000000}[/tex] i.e option c is correct.

What does the term "geometric sequence" mean?

A geometric sequence is a set of integers where the ratio between each pair of succeeding terms is fixed. The geometric sequence's general ratio is the name of this constant.

We can use the following algorithm to determine the nth term (an) of a geometric sequence:

[tex]a_{n} = a_{1} * r^{n-1}[/tex]

where a1 is the first term in the series, r represents the common ratio, and n denotes the term's number.

Since a1 = 3, r = 1/10, and n = 8, we get:

[tex]a_{8} = 3 * (\frac{1}{10})^{8-1} = 3 *( \frac{1}{10})^{7}[/tex]

[tex]= 3 * \frac{1}{10^{7} }[/tex]

Now, we can condense this equation to get the solution:

a₈ = [tex]\frac{3}{10000000}[/tex]

The solution is therefore [tex]\frac{3}{10000000}[/tex] that option c.

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"Triangle CFE is congruent to triangle PTR" is true.

If Triangle CFE is congruent to triangle PTR, we can make the following statements:
The corresponding sides of the triangles are congruent:

This means that CF = PT, FE = TR, and CE = PR.
The corresponding angles of the triangles are congruent:

This means that angle CFE is congruent to angle PTR, angle FCE is congruent to angle PRT, and angle ECF is congruent to angle TPR.
The triangles are equal in area: Since the triangles are congruent, they have the same shape and size. Therefore, they will have the same area.
The triangles can be superimposed on each other: This means that we can place triangle CFE on top of triangle PTR in such a way that their corresponding sides and angles overlap.
If we know the measurements of the sides and angles of one triangle, we can find the measurements of the sides and angles of the other triangle: Since the triangles are congruent, we know that their corresponding sides and angles are equal.

Therefore, if we know the measurements of the sides and angles of one triangle, we can find the measurements of the sides and angles of the other triangle by using the congruence criteria.
In conclusion, if Triangle CFE is congruent to triangle PTR, we can make several statements about their corresponding sides and angles, their areas, and their ability to be superimposed on each other.

We can also use the congruence criteria to find the measurements of the sides and angles of one triangle if we know the measurements of the sides and angles of the other triangle.

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