Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.

scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80

Find the y-intercept of the line of fit and explain its meaning in the context of the data.

5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
80; a student who studies for 0 hours is predicted to earn 80% on the test

Answer:

  4/33

Step-by-step explanation:

You want to write 0.1212...(repeating) as a simplified fraction.

A repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.

Here, there are 2 repeating digits, so the basic fraction is ...

  12/99

This can be reduced by removing a factor of 3 from numerator and denominator:

  [tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]

__

Additional comment

Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.

  0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99

Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.

You can also approach this by writing the number as a continued fraction. The basic form is ...

  [tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]

where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.

A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.

Answer:

The possible coordinates of point A are (−8,1) or (8,1).

Answer: what do you mean? I need more info-

Step-by-step explanation:

I can answer it with more info :)

Therefore, the expression that would give the total number of elements in the array list is n*m.

The Student question is given below :Assume that Item is some class available to the code below and that n and m are two integer variables correctly initialized. Consider the following array declaration and initialization.

[tex]Item[][] list= new Item[n][m];[/tex]

What expression would give the total number of elements in the array list?

The expression that would give the total number of elements in the array list is n*m. The given array declaration and initialization is Item[][] list= new Item[n][m]; This declaration and initialization signify that the array list is a 2D array with n rows and m columns. The total number of elements in this array can be determined by computing the product of the total number of rows (n) and the total number of columns (m).

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Since the triangles are similar, the value of x is equal to: C. 18 units.

In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;

AC/RS = AB/RT

By substituting the given side lengths into the above equation, we have the following:

x/24 = 24/32

By cross-multiplying, we have the following;

32x = 24(24)

32x = 576

x = 576/32

x = 18 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.

Let's start by defining some variables to represent the quantities we're interested in: Let A be the number of adult tickets purchased. Let C be the number of children tickets purchased. Let T be the total number of teachers and students who go on the trip. To maximize the number of teachers and students while staying within budget, we can use linear programming. The objective function is N = T - A - C, where N is the number of teachers and students. The inequalities are 68A + 47C ≤ 12000 and T ≤ 225. Solving this linear program, we find that the school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.

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the complete question :

A middle school wants to take students and teachers on a field trip to Six Flags Great America for spring break. The school has a budget of spending at most $12,000. They can also only take no more than 225 teachers and students. The adult tickets cost $68 each, and children tickets cost $47 each. How many adults and children can the school take to Six Flags within the given budget and attendance limit?

Answer:

what's your exact question

Answer:

can u pls type the full question

Answer: 30

180 - x = 180 - 2x + 30

x = 30

Answer:

The measure of the unknown angle is 30°.

Step-by-step explanation:

Let the measure of the unknown angle be x°.

Supplementary angles are two angles whose measures sum to 180°.

Complementary angles are two angles whose measures sum to 90°.

Therefore, the supplement of x° is (180 - x)°, and its complement is (90 - x)°.

Given that the supplement is 30° more than twice its complement:

(180 - x)° = 2(90 - x)° + 30°

To find the measure of the angle, solve the equation:

⇒ (180 - x)° = (180 - 2x)° + 30°

⇒ 180° - x° = 180° - 2x° + 30°

⇒ 180° - x° = 210° - 2x°

⇒ 180° - x° + 2x° = 210° - 2x° + 2x°

⇒ 180° + x° = 210°

⇒ 180° + x° - 180° = 210° - 180°

⇒ x° = 30°

Therefore, the measure of the unknown angle is 30°.

The two planes will meet 6 hours after they start, i.e. at 3 pm.

Two planes leave at 9 am from airports that are 2700 miles apart and fly towards each other at a speed of 200 mph and 250 mph. At what time will they pass each other?

Let's assume the planes A and B leave the two airports that are 2700 miles apart at the same time. The speed of the first plane is 200 mph and the speed of the second plane is 250 mph. To find out the time at which they pass each other, we need to calculate the distance between them and divide it by the sum of their speeds.

Distance traveled by the first plane in time t1 is equal to 200t1.Distance traveled by the second plane in time t2 is equal to 250t2.The distance covered by the first plane and the second plane together will be 2700 miles.Time taken by both the planes to meet can be calculated as below:

t1 + t2 = 2700/(200+250) = 6 hoursAs both the planes start at 9 am, they will meet each other after 6 hours of their journey. Therefore, they will pass each other at 3 pm. This is the required answer. Explanation: So, the two planes will meet 6 hours after they start, i.e. at 3 pm.

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it will take approximately 22.56 years for the amount to triple.

The given information for this problem is that there is an initial investment of $600 in an account with an annual interest rate of 4%. The task is to determine after how many years the amount will triple.Using the compound interest formula, we can find the amount in the account after t years:A = P(1 + r/n)nt Where,A = final amount in the account, P = initial amount in the account r = annual interest rate ,n = number of times the interest is compounded per year ,t = time in years.

From the problem statement, we know that the initial amount, P, is $600 and the annual interest rate, r, is 4%. Let's assume that the interest is compounded annually, i.e., n = 1.Substituting these values in the formula, we get:A = $600(1 + 0.04/1)1t Simplifying this expression,A = $600(1.04)t.

Taking the ratio of the final amount to the initial amount, we get: 3P = $600 × 3 = $1800. Therefore,A/P = 3 = (1.04)t.Dividing both sides by P, we get:3 = (1.04)t ln(3) = ln(1.04)t. Using the logarithmic property, we can bring down the exponent to the front:ln(3) / ln(1.04) = t Using a calculator, we get ≈ 22.56. Therefore, it will take approximately 22.56 years for the amount to triple.

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Using the area formula for the rectangle, we can find that 2752 in² of plastic is needed to line the trough.

To determine the area a rectangle occupies within its perimeter, apply the formula for calculating a rectangle's area. Multiplying the length by the width yields the area of a rectangle (breadth).

As a result, the area of a rectangle with the length and breadth l and w, respectively, is calculated as follows. L × W = the rectangle's area. Hence, the area of a rectangle is equal to (length width).

Now in the given question,

We have 5 faces of the cuboid.

Now to find the total area of the required space we have to find the area of all the rectangles.

Area of rectangle with dimensions, l = 40inches and b = 14 inches.

Area = l × b

= 40 × 14

= 560in²

Now there are 2 rectangles with the same dimensions, so the total area = 560 + 560 = 1120in².

Now area of rectangles with dimensions, l = 14 inches and b = 24 inches.

Area = l × b

= 14 × 24

= 336in².

There are 2 rectangles with the same dimensions, so area = 336 + 336 = 672in².

Area of the final rectangle = l × b

= 40 × 24

= 960in².

So, the total required area = 1120 + 672 + 960 = 2752in².

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Answer:

it is a triangle bc it has angles of points

Step-by-step explanation:

The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is [tex]\frac{7}{12}[/tex] , where 7 and 12 are relatively prime positive integers. The answer is 7+12=19.

The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is 1 minus the probability that no diameter of the circle has two girls sitting on opposite ends of the diameter.

There are

[tex]{10\choose5}[/tex] =252

ways to seat the five girls and five boys.

There are 5 ways to choose a diameter of the circle.

Once this diameter is fixed, there are [tex]{5\choose2}[/tex] = 10 ways to choose a pair of seats on the diameter to place two girls (in the order in which they appear counterclockwise).

There are 5!=120 ways to seat the remaining 3 girls and 5 boys such that no two girls sit on the same diameter.

Hence, there are [tex]5\cdot10\cdot120[/tex] =6000 valid seatings that satisfy the condition in the question.

Thus, the desired probability is 1 - [tex]\frac{6000}{252}[/tex] = [tex]\frac{7}{12}[/tex], as stated above.

Thus, the answer is 7+12 = [tex]\boxed{19}[/tex]

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Answer:

10

Step-by-step explanation:

The mean of a set of numbers is the sum divided by the number of terms.

Answer:

x [tex]\geq[/tex]2

Step-by-step explanation:

Since the arrow is pointing to the right, we know that it is greater than two. We also know that it could be equal to 2 because the dot is filled in on the number line. So, the answer is x is greater than or equal to 2.

Strings of 6 letters of the English alphabet containing one vowel: 2,832,240, exactly two vowels: 2,233,200, at least one vowel: 10,919,736, least two vowels: 8,087,496 and number of strings of length n with exactly k vowels: nCk * 5Ck * 21^(n-k)

There are 26 letters in the English alphabet, out of which 5 are vowels (A, E, I, O, U). To find the number of strings of 6 letters of the English alphabet that contain one vowel, we can choose the position of the vowel in 6C1 ways and fill the remaining positions with any of the 21 consonants in 21C5 ways.

Therefore, the total number of such strings is 6C1 * 21C5 = 2,832,240.

To find the number of strings with exactly two vowels, we can choose the positions of the vowels in 6C2 ways and fill them with any of the 5 vowels in 5C2 ways. We can fill the remaining positions with any of the 21 consonants in 21C4 ways.

Therefore, the total number of such strings is 6C2 * 5C2 * 21C4 = 2,233,200.

To find the number of strings with at least one vowel, we can subtract the number of strings with no vowels from the total number of strings. The number of strings with no vowels is 21^6 (since there are 21 consonants and we can choose any of them for each of the 6 positions).

Therefore, the number of strings with at least one vowel is 26^6 - 21^6 = 10,919,736.

To find the number of strings with at least two vowels, we can subtract the number of strings with one vowel or no vowel from the total number of strings. The number of strings with one vowel is 2,832,240 (as we found earlier) and the number of strings with no vowels is 21^6.

Therefore, the number of strings with at least two vowels is 26^6 - 2,832,240 - 21^6 = 8,087,496.

To find the number of strings of length n with exactly k vowels, we can choose the positions of the k vowels in nCk ways and fill them with any of the 5 vowels in 5Ck ways. We can fill the remaining positions with any of the 21 consonants in 21^(n-k) ways.

Therefore, the total number of such strings is nCk * 5Ck * 21^(n-k).

Hence, the number of strings of 6 letters of the English alphabet containing one vowel is 2,832,240, while the number of strings with exactly two vowels is 2,233,200. The number of strings with at least one vowel is 10,919,736, and the number of strings with at least two vowels is 8,087,496.

Finally, the number of strings of length n with exactly k vowels is nCk * 5Ck * 21^(n-k).

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Answer:

20/52 or simplified to 5/13

Step-by-step explanation:

The Venn Diagram is provided

Let
n(A) =  number of customers who had syrup
n(B) =  number of customers who had sprinkles

n(A and B) = number of customers who had both syrup and sprinkles = 16
This would be the number in the overlapping region

n(A or B) = number of customers who had either syrup or sprinkles or both
= n(A) + n(B) - n(A and B)
= 48 + 28 - 16
= 60

Therefore number of customers who had neither topping = 80 - 60 = 20

This number is indicated outside both circles but within the rectangle

The number of customers who had only syrup is given by set difference

= No. of customers who had syrup - No. of customers who had both
= n(A) - n(A and B)
= 48 - 16
= 32

This is the figure inside the left circle

Let's consider the statement: Customers who didn't have sprinkles

This would be customers who had only syrup(32) + customers who had neither topping(20)
= 32 + 20 = 52

Number of customers who did not have either topping = 20
P(selected customer doesn't have either topping, given that they don't have sprinkles)
= 20/52
= 5/13

Step-by-step explanation:

Diameter = 10 units then radius, r = 5 inches

Cylinder's  base AREA = pi r^2 = pi (5)^2 = 25 pi = 78.54 units^2

Base area * height = volume = 25 pi * 4 = 100 pi =314.2 units^3

The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).

The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.

To express this probability as a fraction, we can use the formula:

Probability of winning = 1 / (odds + 1)

Plugging in the given odds, we get:

Probability of winning = 1 / (16 + 1)

Probability of winning = 1/17

In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.

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The following conditions must be met to conduct a two-proportion significance test:

the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.

The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.

To conduct the two-proportion significance test, the following conditions must be met:

Populations must be independent.

Sample sizes are greater than 30.

The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.

The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.

In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.


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Step-by-step explanation:

Area of circle =   pi r^2

10 inch = pi (5)^2 = 25 pi

12 inch = pi (6)^2 = 36 pi

12 inch is 11pi bigger

    percentage:  11 pi is what percentage of 25 pi ?

        11 pi / 25 pi x 100%  = 44 % bigger

The area of a pizza increases with the square of the diameter. Therefore, a 10-inch pizza has an area of [tex]π*(10/2)^2= 78.54[/tex]  square inches, and a 12-inch pizza has an area of [tex]π*(12/2)^2 = 113.10[/tex] square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%.

To explain further, the diameter of a pizza is measured from one side to the other through the center of the pizza. As the diameter of the pizza increases, the area of the pizza increases. This is because the area of a pizza is calculated as [tex]π*(d/2)^2[/tex], where d is the diameter. So, if the diameter increases, the area increases as well.

For example, if a 10-inch pizza has an area of 78.54 square inches, a 12-inch pizza would have an area of 113.10 square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%. This is because the diameter of the pizza has increased by 2 inches (10 inches to 12 inches), and the area has increased by 44.2%.

It is important to note that increasing the diameter of the pizza does not just increase the circumference of the pizza, but also the area. The increase in area is directly related to the increase in diameter, and can be calculated by taking the difference between the areas of the two pizzas.

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Answer:

x = -7, 17.

Step-by-step explanation:

I am assuming it's:

35/ x-3 = X-7/4

(x - 3)(x - 7) = 4*35

x^2 - 10x + 21 = 140

x^2 - 10x - 119 = 0

(x - 17)(x + 7) = 0

x = -7, 17.

Roll a 5: There is only one way to roll a 5 out of six possible outcomes, so the probability of rolling a 5 is 1/6.

Roll a 6: Similarly, there is only one way to roll a 6 out of six possible outcomes, so the probability of rolling a 6 is 1/6.

Roll a c or 4: There are two ways to roll a 4 (rolling a 4 or rolling a 3) and one way to roll a 3, so there are three ways to roll a 4 or c out of six possible outcomes. Therefore, the probability of rolling a 4 or c is 3/6, simplifying it to 1/2.

Roll an odd number: There are three odd numbers (1, 3, 5) out of six possible outcomes, so the probability of rolling an odd number is 3/6, simplifying to 1/2.

Roll an even number: There are three even numbers (2, 4, 6) out of six possible outcomes, so the probability of rolling an exact number is 3/6 or 1/2.

Roll a number greater than 3: There are three numbers greater than 3 (4, 5, 6) out of six possible outcomes, so the probability of rolling a number greater than 3 is 3/6, which simplifies to 1/2.

Roll an even number less than 5: There is only one number less than 5 (2) out of six possible outcomes, so the probability of rolling an actual number less than 5 is 1/6.

Roll a multiple of 2 (2, 4, 6): There are three multiples of 2 out of six possible outcomes, so the probability of rolling a multiple of 2 is 3/6, simplifying to 1/2.

Roll a factor of 6 (1, 2, 3, 6): There are four factors of 6 out of six possible outcomes, so the probability of rolling a factor of 6 is 4/6, which simplifies to 2/3.

So the probabilities for each event expressed as fractions are:

Roll a 5: 1/6

Roll a 6: 1/6

Roll a 4 or c: 1/2

Roll an odd number: 1/2

Roll an even number: 1/2

Roll a number greater than 3: 1/2

Roll an even number less than 5: 1/6

Roll a multiple of 2: 1/2

Roll a factor of 6: 2/3

The equation that represents the relationship between the number of hours needed to complete a trip, h, and the driving speed, s, is h = 5/s. This means that the number of hours needed to complete the trip is inversely proportional to the driving speed.

When the driving speed is 60 miles per hour, the number of hours needed to complete the trip is 5 (h = 5/60). If the driving speed is increased to 90 miles per hour, the number of hours needed to complete the trip is 5/90 (h = 5/90).

In general, as the driving speed increases, the number of hours needed to complete the trip decreases.

To summarize, the equation that represents the inverse relationship between the number of hours needed to complete a trip and the driving speed is h = 5/s. This equation can be used to determine the number of hours needed to complete a trip at any given speed.

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Answer:

a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds

Answer:

90 seconds

Step-by-step explanation: We know that,

A quarter of an hour= 60×1/4 =15 mins

15 minutes is equal to 15 minutes × 60 = 90 seconds.

The height RT from R to PQ is approximately 3.16 cm.

To find the area of triangle PQR, we can use the formula:

Area = 1/2 * base * height

Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.

Area of PQR = 1/2 * PQ * PS

Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:

[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]

[tex]Area of PQR = 22.5 cm^2[/tex]

Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].

To find the height RT from R to PQ, we can use the Pythagorean theorem.

Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.

Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).

Using the sine function, we can find the length of PT:

sin(69.3) = PT / 7.5

PT = 7.5 * sin(69.3)

PT ≈ 6.93 cm

Using the Pythagorean theorem, we can find the length of RT:

[tex]RT^2 + PT^2 = PR^2[/tex]

[tex]RT^2 = PR^2 - PT^2[/tex]

[tex]RT^2 = 7.5^2 - 6.93^2[/tex]

RT ≈ 3.16 cm

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Two plus x divided by twelve equals one divided by three

Case 1 :

Rewrite into numbers : 2 + x /12 = 1/3

-> x/12 = 1/3 - 2 = -5/3

-> x = -5/3 x 12 = -20

Case 2 :

Rewrite into numbers : (2 + x)/12 = 1/3

-> 2 + x = 1/3 x 12 = 4

-> x = 4 - 2 = 2

i dont know if you meant it the right way or the wrong way but ill just put them both

x=2

Step-by-step explanation:

(2+x)/12=1/3

3(2+x)=12

2+x=4

x=4-2

x=2

Answer: 16x+3x^3−8

Please mark me brainliest :)

Answer:

x = 100/9

Step-by-step explanation:

1) Square both sides.

[tex]9x=100[/tex]

2) Divide both sides by 9.

[tex]x = \frac{100}{9}[/tex]

Decimal Form: 11.111111

1) Let [tex]x = \frac{100}{9}[/tex].

[tex]3\sqrt{\frac{100}{9} } =10[/tex]

2) Simplify [tex]\sqrt{\frac{100}{9} }[/tex] to [tex]\frac{\sqrt{100} }{\sqrt{9} }[/tex].

[tex]3\times\frac{\sqrt{100} }{\sqrt{9} }=10[/tex]

3) Since 10 x 10 = 100, the square root of 100 is 10.

[tex]3\times\frac{10}{\sqrt{9} }=10[/tex]

4) Since 3 x 3 = 9, the square root of 9 is 3.

[tex]3\times\frac{10}{3} =10[/tex]

5) Cancel 3.

10 = 10