On the math exam,5 tasks were given. 25% of students solved at least two tasks. Prove that there was at least one task that no more than 12 students solved if 32 students wrote that test

The equation of the line is written in the different forms

Calculate the slope (m) using the formula:

m = (0 - 6) / (8 - 0)

m = -6 / 8

m = -3/4

Plug in the slope (m) and one of the given points (x1, y1) into the slope-intercept form to find the y-intercept (b):

y = mx + b

6 = (-3/4)(0) + b

6 = b

Substitute the y-intercept (b) into the equation:

y = (-3/4)x + 6

In point-slope form:

y - y1 = m(x - x1)

Using the point (0, 6):

y - 6 = (-3/4)(x - 0)

y - 6 = (-3/4)x

In standard form:

To convert the equation to standard form, we can manipulate the equation to have the form Ax + By = C, where A, B, and C are constants.

y - 6 = (-3/4)x

Multiply both sides by 4 to eliminate the fraction:

4(y - 6) = -3x

4y - 24 = -3x

Rearrange the equation to have x and y on the same side and a constant on the other side:

3x + 4y = 24

This is the equation in standard form.

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Answer:  18

Step-by-step explanation:  the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.

B) ∅ (empty set); The composition T ∘ S is an empty set (∅) because there are no ordered pairs that satisfy both the conditions of the relations T and S.

To find the composition T ∘ S, we need to determine the set of ordered pairs that satisfy both relations S and T. Let's analyze the definitions of S and T:

S = {(x, y) ∣ x < y}

T = {(x, y) ∣ x > y}

To find T ∘ S, we need to check if there exists an element z such that (x, z) is in T and (z, y) is in S for any (x, y) in the given relations. However, if we observe the definitions of S and T, we can see that there is no common element that satisfies both relations.

For any (x, y) in S, we have x < y, but in T, the relation is defined as x > y. Therefore, there are no elements that satisfy both conditions simultaneously.

As a result, T ∘ S will be an empty set (∅) because there are no ordered pairs that satisfy the composition of the two relations.

The composition T ∘ S is an empty set (∅) because there are no ordered pairs that satisfy both the conditions of the relations T and S.

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Answer:

x = 10

Step-by-step explanation:

\(6^{2} + 8^2 = x ^2\)

Solve for x and you get x = 10

Answer:

x=14

Step-by-step explanation:

I can simplify the math terms ;)

So basically 6 and 8 are the lengths of the shorter sides of the triangle, the triangle has three sides and the longest side is always called the hypotenuse, the hypotenuse is the sum of the lengths of the shorter sides. So 6+8=x

6+8=14 <-- That's your answer :)

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The probability that a pupil uses neither pool nor gym is 11/70

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.

Number of pupil that can use pool and gym = 28

Number of people that can use pool = 48

Number of people that can use gym = 39

Number of people that can use pool only = 48 - 28 which is 20

Number of people that can use gym only = 39 - 28 = 11

Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59

Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.

Probability = required outcome / possible outcome

Required outcome = 11

possible outcome = 70

Probability = 11/70

In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70

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Answer:

The weight in kilograms of a 150 pound person is 68.039 kg

Step-by-step explanation:

Weight = 150 pounds.

We need to convert this to kg,

Now, 1 pound = 0.453592 kg.

Then, 150 pounds will be,

150 pounds = 150(0.453592) kg

So, 150 pounds = 68.039 kg

The weight of a 150 pound person is approximately 68.04 kilograms.

To convert the weight of a person from pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms.

Given that the person weighs 150 pounds, we can multiply this value by the conversion factor to find the weight in kilograms:

Weight in kilograms = 150 pounds * 0.4536 kilograms/pound

Weight in kilograms = 68.04 kilograms

Therefore, the weight of a 150 pound person is approximately 68.04 kilograms.

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Given:

The equation of a circle is

\(10y+x^2=-18+5x-y^2\)

To find:

The center and radius of the given equation by completing the square.

Solution:

The standard form of a circle is

\((x-h)^2+(y-k)^2=r^2\)            ...(i)

where, (h,k) is center and r is radius of the circle.

We have,

\(10y+x^2=-18+5x-y^2\)

It can be written as

\((x^2-5x)+(y^2+10y)=-18\)

\(\left(x^2-5x+\left(\dfrac{5}{2}\right)^2\right)+\left(y^2+10y+\left(\dfrac{10}{2}\right)^2\right)=-18+\left(\dfrac{5}{2}\right)^2+\left(\dfrac{10}{2}\right)^2\)

\(\left(x-\dfrac{5}{2}\right)^2+\left(y^2+10y+5^2\right)=-18+\dfrac{25}{4}+5^2\)

\(\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=-18+\dfrac{25}{4}+25\)

\(\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{-72+25+100}{4}\)

\(\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{53}{4}\)

\(\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\left(\dfrac{\sqrt{53}}{2}\right)^2\)          ...(ii)

On comparing (i) and (ii), we get

\(h=\dfrac{5}{2},k=-5,r=\dfrac{\sqrt{53}}{2}\)

Therefore, the center is \(\left(\dfrac{5}{2},-5\right)\) and the radius is \(\dfrac{\sqrt{53}}{2}\) units.

Answer:

The temperature had risen 20 degrees.

Step-by-step explanation:

Answer:

20 degrees

Step-by-step explanation:

Answer:

g = 7/5 + 3r/10

Step-by-step explanation:

Brainlest plss

Answer:

i believe jack will be 13

Step-by-step explanation:

13 times 2 will be 27 plus 7 equals 34

Answer:

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

Answer:

Angle L= 53 degrees. Side ML = 4.521 and Side NL= 7.513

Step-by-step explanation:

Answer: Total cost of their meal is $78

Step-by-step explanation: 20% of 65 is a 13 dollars tip adding up to a total of $78

65*0.2 = 13

65+13=78

The margin of error for the 95% confidence level is 0.66. Then the correct option is D.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

The times it took for 35 loggerhead sea turtle eggs to hatch in a simple random sample are normally distributed, with a mean of 50 days and a standard deviation of 2 days. assuming a 95% confidence level (95% confidence level = z-score of 1.96)

The margin of error is given by

\(\rm Margin \ of \ error = z \times \dfrac{\sigma}{\sqrt{n}}\\\\Margin \ of \ error = 1.96 \times \dfrac{2}{\sqrt{35}}\\\\Margin \ of \ error = 0.6626 \approx 0.66\)

The margin of error for the 95% confidence level is 0.66. Then the correct option is D.

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Answer:

D

Step-by-step explanation:

on edge

Answer:  There are 11,880 ways to assign these four positions among the 12 members of the board of directors.

Step-by-step explanation:

The first position, the president, can be assigned in 12 ways, as any of the 12 members can be selected for this role. The second position, the vice president, can then be assigned in 11 ways, as one member has already been assigned as the president. The third position, the secretary, can be assigned in 10 ways, as two members have already been assigned. Finally, the treasurer can be assigned in 9 ways, as three members have already been assigned.

Therefore, the total number of ways these positions can be assigned is:

12 x 11 x 10 x 9 = 11,880

So, there are 11,880 ways to assign these four positions among the 12 members of the board of directors.

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Answer:

The measure of angle x is 122.5 degrees.

The measure of angle y is 57.5 degrees

Step-by-step explanation:

180=y+x

y=x-65

180= (x-65)+x

180=2x-65

245=2x

x=122.5

y=122.5-65= 57.5

Answer:

The correct answer is A.) The measure of angle x is 122.5 degrees. The measure of angle y is 57.5 degrees.

Step-by-step explanation:

I just did the test on edge 2021 and got it right!

Answer:

(9/5, 8/5)

Step-by-step explanation:

First you want to find the equations of the lines. One line is y = 2x - 2 and the other line is y = 1/3x + 1. Then you want to find the x and y that both work in the two equations.

y = 2x - 2

y = 1/3x + 1

Then you do 2x - 2 = 1/3x + 1

Then you do some maths and you get 9/5, and 8/5

Answer:

x=2

Step-by-step explanation:

Answer:

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite so just move it over to the opposite side

Step-by-step explanation:

The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution \(y = 0.7979e^-(x-5.4)^2/0.5\), where x is the number of hours.

The normal distribution is a bell-shaped curve that is often used to model real-world data. In this case, the normal distribution is used to model the amount of time that students spend at the math-tutoring center. The peak of the bell-shaped curve represents the average amount of time that students spend at the center, which is 5.4 hours per week. The tails of the bell-shaped curve represent the amount of time that students spend at the center that is less than or greater than the average amount of time.

The standard deviation of the normal distribution is 0.5 hours. This means that about 68% of the students spend between 4.9 and 6 hours at the center per week. About 16% of the students spend less than 4.9 hours at the center per week, and about 16% of the students spend more than 6 hours at the center per week.

The normal distribution is a useful tool for understanding the amount of time that students spend at the math-tutoring center. It can be used to estimate the average amount of time that students spend at the center, and it can be used to determine the amount of time that students spend at the center that is less than or greater than the average amount of time.

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Answer:

40

Step-by-step explanation:

8+1=9

16+2=18

24+3=27

32+4=36

40+ 5=45

A man wanted to investigate the linear relationship between how many miles he ran and his heart rate in beats per minute. After recording how many miles he ran and his heart rate for 12 different days, he created this 95% confidence interval for 3 miles (160,180). The twelve different days could be considered a random sample of all of his run days. The best interpretation of the confidence interval is Option a) It can be stated with 95% confidence that his average heart rate after running 3 miles is between 160 and 180 beats per minute.

Given that the 12 different days could be considered a random sample of all of his run days, the sample statistics of the study can be used to make inferences about the population parameters. Therefore, the 95% confidence interval for 3 miles of (160,180) can be interpreted as There is a 95% chance that the true population average heart rate after running 3 miles is between 160 and 180 beats per minute. Or It can be stated with 95% confidence that his average heart rate after running 3 miles is between 160 and 180 beats per minute.

Option a. It can be stated with 95% confidence that his average heart rate after running 3 miles is between 160 and 180 beats per minute is the best interpretation of the confidence interval.

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Answer:

I believe the answer is 45.

Step-by-step explanation:

a 90 degree angle is represented by a square on the corner.

So half of 90 is:

90 ÷ 2 = 45

the angle next to the letter M is 90 degreess, so the other side of the line is also 90 degrees.

45 + 90 = 135

and 180 - 135 = 45

(You subtract 135 from 180 since " the sum of angles of a triangle equals the straight angle", which is 180 degrees.

So, the length of JL is equal to 45 degrees.

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Answer:

It is not linear. It is cubic since the highest exponent is 3.

Answer:

No it is not a collection of well defined and distinct objects

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Answer:

width of each tile are equal to x cm.

SW = (number of squares on one side)^2

SW = x^2

But we also know that the area of each tile is equal to x^2 square cm. Therefore, the area of the wall can be expressed as:

SW = A/x^2

Where A is the total area of the wall.

SW × x^2 = A

SW = A/x^2

So the equation for the number of squares on the wall, SW, in terms of c, is:

SW = A/c^2

where c is the length and width of each tile in centimeters.

To find the actual number of squares on the wall, we would need to know the value of A and c.

Answer:

1364 is the number of possibilities for positive integers less than 1,00,000.

Step-by-step explanation:

1. 5 digit numbers:

We have 5 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 5 digit numbers:

\(4 \times 4 \times 4 \times 4 \times 4\\ \Rightarrow 1024\)

2. 4 digit numbers:

We have 4 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 4 digit numbers:

\(4 \times 4 \times 4 \times 4 \\ \Rightarrow 256\)

3. 3 digit numbers:

We have 3 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 3 digit numbers:

\(4 \times 4 \times 4 \\ \Rightarrow 64\)

4. 2 digit numbers:

We have 2 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 2 digit numbers:

\(4 \times 4 \\ \Rightarrow 16\)

5. 1 digit numbers:

We have 1 place here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 1 digit numbers:

\(4\)

We can add all the above possibilities to find the total.

So,  number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4 = 1024 + 256 + 64 + 16 + 4 = 1364

Answer:

This is a waste of time. I'm sorry you have to do this, this is pointless. I did it too. I'll spare you the calculations — it's 1364.

Answer: the slope of the line is 4

Step-by-step explanation:

We only need two ordered pairs to find the slope

(-2,-10), (-1,-6)

the slope formula is y2-y1/x2-x1

-6-(-10)/-1-(-2)

-6+10/-1+2

4/1

4

the slope of the line is 4

Answer:

4

Step-by-step explanation:

Knowledge Needed

The slope is the amount the y-value changes on a line when the x-value changes by 1.

Slope Formula: \(\frac{y_2-y_1}{x_2-x_1}\)

Question:

We have the points:

(-2,-10)

(-1,-6)

(0,-2)

(1,2)

We only need 2 points to plug into the slope formula. I'll use the first 2.

(-2,-10) ; (-1,-6)

\(\frac{-6--10}{-1--2}\)

\(\frac{4}{1}\)

4

By converting the mixed number, we can clearly see the relationship between the numerator and denominator and express the quantity as a single fraction

To turn a mixed number into an improper fraction, we follow the following procedure:

Step 1: Multiply the whole number by the denominator of the fraction.

Step 2: Add the result to the numerator of the fraction.

Step 3: Write the sum obtained in Step 2 as the numerator of the improper fraction.

Step 4: Keep the denominator unchanged.

Let's use the example 35 6 to illustrate the procedure:

Step 1: Multiply the whole number (35) by the denominator (6):

35 * 6 = 210

Step 2: Add the result to the numerator (6):

210 + 6 = 216

Step 3: Write the sum obtained as the numerator of the improper fraction: 216/6

Step 4: Keep the denominator unchanged: 216/6

Therefore, the mixed number 35 6 can be written as the improper fraction 216/6.

Now, let's explain the logic behind this procedure using math drawings:

Consider a rectangle divided into equal parts, where each part represents one unit of the denominator. In the case of our example, the rectangle is divided into six equal parts.

Now, the whole number (35) represents 35 complete rectangles, each containing six equal parts.

The numerator (6) represents an additional 6 parts of a rectangle.

To convert the mixed number into an improper fraction, we need to combine the total number of parts. The total number of parts can be found by multiplying the whole number by the number of parts in each rectangle \((35 * 6 = 210)\) and adding the additional numerator parts (6).

So, we have a total of 216 parts. Since each part represents one unit of the denominator (6), we can write the improper fraction as 216/6.

The procedure of turning a mixed number into an improper fraction makes sense because it allows us to represent the entire quantity in terms of the denominator. By converting the mixed number, we can clearly see the relationship between the numerator and denominator and express the quantity as a single fraction. This procedure helps in mathematical operations, comparisons, and simplifications involving fractions.

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For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

What exactly are quadratic equations?

A quadratic equation is a second-degree polynomial equation of the form:

ax²+ bx + c = 0

where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.

Now,

We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.

We want to find when the company had a profit of 7 million dollars.

So, we can set y = 7 in the equation:

7 = x² - 16x + 67

Rearranging and simplifying:

x² - 16x + 60 = 0

Now, we can solve for x using the quadratic formula:

x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)

x = (16 ± √(16)) / 2

x = 8 ± 2

Therefore, the solutions are x = 10 or x = 6.

This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

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