11. Morty scored an 80, 60, 20, and an 20 on his first four math
tests. What does he need to score on his fifth math test to
average an 50 overall?

To prove that for real numbers a, b, and c, if a > b and b > c, then a > c, we can use the transitive property of inequalities. Similarly, to prove that for a real number a > 1, a^2 > a, we can utilize the axiom that states if a > b > 0, then a^2 > b^2.

In the given problem, we have three real numbers: a, b, and c, with a > b and b > c. We want to prove that a > c. By the transitive property of inequalities, if a > b and b > c, then we can conclude that a > c. This property states that if a > b and b > c, then a > c. Therefore, we have justified the step.

For the second problem, we are given a real number a > 1, and we need to prove that a^2 > a. We can use the axiom that states if a > b > 0, then a^2 > b^2. In this case, a > 1 > 0, so we can apply the axiom. By substituting a for b, we get a^2 > 1^2, which simplifies to a^2 > 1. Since a > 1, we can conclude that a^2 > a. This step is justified by the aforementioned axiom.

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To solve for x using the quadratic formula, we need to have an equation in the form of ax^2 + bx + c = 0. Then, we can substitute the values of a, b, and c into the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a

where the ± symbol means that we need to take both the positive and negative values of the square root. The solutions will be the values of x that make the equation true.The quadratic formula is a powerful tool for solving quadratic equations that cannot be easily factored. Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The quadratic formula gives us a way to solve for x in terms of a, b, and c. To use the quadratic formula, we need to first identify the values of a, b, and c in the given equation. Then, we can substitute those values into the formula and simplify to find the solutions. It's important to note that the quadratic formula always gives us two solutions, unless the discriminant (b^2 - 4ac) is negative, in which case there are no real solutions.

When we have the solutions, we should always check them by substituting them back into the original equation to make sure they make the equation true. If there are more than one solution, we separate them with commas.

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Answer:

Step-by-step explanation: i bet your ray r stands for g

Answer:

4:7

Step-by-step explanation:

We know that

Area of square = s²

For square 1

16 = s²

√16 = s

4 = s

For square 2

49 = s²

√49 = s

7 = s

Scale factor = 4:7

Answer:

Step-by-step explanation:

The answer of 1 question is 9 because square of 9 is 81 and 9 x 9 times is 81

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

y = 7x - 8 → (1)

y = 5x - 2 → (2)

A

Solving by substitution

Substitute y = 7x - 8 into (1)

7x - 8 = 5x - 2 ( subtract 5x from both sides )

2x - 8 = - 2 ( add 8 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Substitute x = 3 into either of the 2 equations and evaluate for y

Substituting into (1)

y = 7(3) - 8 = 21 - 8 = 13

Solution is (3, 13 )

B

The point of intersection of the graph of the 2 equations is the solution to the above equations.

That is point of intersection = (3, 13 )

Answer:

Step-by-step explanation:

The complement of event E, E°, is {14, 15, 16, 17}. The probability of event E° is 1/3, as all outcomes in the sample space are equally likely, with a probability of 1/12.

E° is the complement of event E. It is the set of all outcomes that are not in event E and can be expressed as E° = {14, 15, 16, 17}.The probability of event E° is calculated by summing the probabilities of all outcomes in the event, P(E°) = P(14) + P(15) + P(16) + P(17). Since all outcomes in the sample space are equally likely, the probability of each outcome is 1/12. This means that the probability of event E° is calculated as follows:

P(E°) = 1/12 + 1/12 + 1/12 + 1/12 = 4/12 = 1/3.

Therefore, The complement of event E, E°, is {14, 15, 16, 17}. The probability of event E° is 1/3, as all outcomes in the sample space are equally likely, with a probability of 1/12.

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Answer:

The important thing to keep in mind is that 1 kg = 2.2046 lbs. So if you wish to convert kilograms to pounds, all you have to do is multiply the value in kilograms by 2.2046.

1 kilogram (kg) is equal to 2.20462 pounds (lb). To convert 1 kg to lb, multiply 1 by 2.20462.

Kilograms and pounds are units of measurement used for weighing objects. Kilograms are part of the metric system and are used in most countries around the world, while pounds are part of the imperial system and are primarily used in the United States.

To convert kilograms to pounds, one can use the conversion factor of 2.20462, which states that 1 kilogram is equal to 2.20462 pounds. To convert a weight in kilograms to pounds, simply multiply the weight in kilograms by the conversion factor.

For example, to convert 1 kilogram to pounds, one would multiply 1 by 2.20462, which results in a weight of 2.20462 pounds.

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It should be noted that since sunset is at 8:09 PM, you have approximately 3.5 hours until you face possible dangers.

In order to use a flagpole and measuring tape as a makeshift sundial, you first need to find the angle of the sun. You can do this by measuring the angle between the shadow of the flagpole and the ground. In your case, the angle of the sun is 56°.

Once you have the angle of the sun, you can use the following formula to calculate the time of day:

time = (12 - angle) / 2

In your case, the time of day is:

time = (12 - 5) / 2

= 3.5 hours

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To find the initial number of pears at the grocery store, you need to consider that 455 pears represent 70% (100% - 30%) of the total number of pears. The grocery store started with 1517 pears.

We know that the grocery store sold 30% of its pears, which means they have 70% of the pears remaining. We can use a proportion to figure out how many pears they started with:

30/100 = x/total pears

We can simplify this to:

0.3 = x/total pears

Now we need to solve for total pears. We can start by cross-multiplying:

0.3 * total pears = x

Next, we can substitute the information we were given:

0.3 * total pears = 455

Now we can solve for total pears:

total pears = 455 / 0.3

total pears = 1516.67 (rounded to the nearest whole number)

So the grocery store started with approximately 1517 pears.

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Answer:

Step-by-step explanation:

Hypotenus=6

Adjacent=4

H and A

Cos x degrees=  A divided by H

4 divided by 6=0.666666666

cos inverse(0.6666666666666666)

=48.2

=48

Answer:

Graph A

Step-by-step explanation:

Answer:

its graph A

Step-by-step explanation:

The shortest distance between Caroline's and Mattie's houses can be found using the Pythagorean theorem.

By considering Caroline's northward walk of 6 blocks and then eastward walk of 8 blocks, the shortest distance can be calculated as 10 blocks.

To find the shortest distance between Caroline's and Mattie's houses, we can visualize their movements as forming a right triangle. Caroline walks north for 6 blocks and then turns east for 8 blocks, creating a right-angled triangle.

According to the Pythagorean theorem, the square of the hypotenuse (shortest distance) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we can calculate the shortest distance as follows: sqrt((6^2) + (8^2)) = sqrt(36 + 64) = sqrt(100) = 10 blocks. Therefore, the shortest distance between Caroline's and Mattie's houses is 10 blocks.

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Answer:

30%

Step-by-step explanation:

The level of decay is determined by the number raised to the power.

y = 0.4(0.7)^t

If you had 1^t, there would be no decay or growth since 1^t is always 1.

Instead, you have 0.7^t

As t increases, 07^t decreases. That is where the decay comes from.

Now look at 0.7

In the general decay equation, you have

y = a(1 - r)^t

r is the rate of decay.

Here we have 0.7

0.7 = 1 - 0.3

the rate of decay is 0.3 or 30%

Answer:

The equation y = 0.4(0.7)^t represents an exponential decay of 30%. The decay rate is determined by the value in the parentheses, which in this case is 0.7. To calculate the decay rate, you can subtract this value from 1, giving you 1 - 0.7 = 0.3, or 30%.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

if you add 2 and 3 you get 5 then you would add 5 and 5 and get 10 then 10 and 7 to get 17

Answer:The answer is 17

Step-by-step explanation:

If a wave forms in water with a depth of 6.8 feet, then the velocity is 15 units.

Velocity is nothing but a speed with a certain direction.

The depth d of the water (in feet) is given by d

The velocity of the wave are related by the equation v=√32d.

Here v is the velocity.

From given we know that a wave is  formed in water with a depth of 6.8 feet.

We need to find the velocity at depth of 6.8 feet.

As given v=√32d.

d is depth which is 6.8

Substitute d value in v.

v=√32×6.8

v=√217.6=14.7

Which is nearly 15

Hence,  If a wave forms in water with a depth of 6.8 feet, then the velocity is 15 units.

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(a) The matrix A=[2 -2; -1 1; 0 5] is invertible if a ≠ 3. This is because for a matrix to be invertible, its determinant must be non-zero. The determinant of matrix A is given by det(A) = (2 * 1) - (-2 * (-1)) = 2 - 2 = 0. Therefore, the matrix A is not invertible when the determinant is zero, which occurs when a = 3. Hence, the correct answer is (a) a ≠ 3.

(b) If A is a 4×4 matrix and det(A) = 2, then det(3A) is equal to 162. The determinant of a scalar multiple of a matrix can be obtained by raising the determinant of the original matrix to the power of the scalar. In this case, det(3A) = (3^4) * det(A) = 81 * 2 = 162. Therefore, the correct answer is (b) 162.

To understand the explanation for each question, let's go through them one by one:

For a matrix to be invertible, its determinant must be non-zero. In matrix A, the determinant is given by det(A) = (2 * 1) - (-2 * (-1)) = 2 - 2 = 0. Therefore, the matrix A is not invertible when the determinant is zero, which occurs when a = 3. Hence, the correct answer is (a) a ≠ 3.

If A is a 4×4 matrix and det(A) = 2, then det(3A) is equal to 162. The determinant of a scalar multiple of a matrix can be obtained by raising the determinant of the original matrix to the power of the scalar. In this case, det(3A) = (3^4) * det(A) = 81 * 2 = 162. Therefore, the correct answer is (b) 162.

The statement (a) M^2 - N^2 = (M + N)(M - N) is not true in general. Matrix multiplication is not commutative, so squaring two matrices and subtracting them is not equivalent to multiplying the sum and difference of the matrices. Therefore, option (a) is false.

The statement (b) MT + NT = (M + N)T is true. The transpose of the sum of two matrices is equal to the sum of their transposes. Therefore, (MT + NT) = (M + N)T. Hence, option (b) is true.

In summary, the correct answer is (b) MT + NT = (M + N)T.

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The likelihood of finding that the sample mean is between 59,050 and 60,950 miles can be determined by calculating the probability using the normal distribution with a sample size of 90, a population mean of 60,000 miles, and a population standard deviation of 4,000 miles.

To find out the probability of getting a sample mean between 59,050 and 60,950, a simulator is used to determine the tread life of tires mounted on light-duty trucks that follows a normal probability distribution.

Here, the population mean is 60,000 miles and the standard deviation is 4,000 miles. The given sample size is 90.

We can use the formula for standardizing the score. The standardized score for the lower limit of 59,050 is -2.78, and that of the upper limit of 60,950 is 2.78. Now, we need to find the probability of getting the mean value between -2.78 and 2.78.

We can use the standard normal distribution table to find the value, which is 0.9950 for z = 2.78 and 0.0050 for z = -2.78. Hence, the required probability is 0.9900.

Therefore, the likelihood of finding that the sample mean is between 59,050 and 60,950, for a sample size of 90 tires, is 0.9900.

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In the context of the car wash, the slope represents the rate at which the amount of money raised changes with respect to the number of cars washed. The slope in this situation is $4.50 per small car and $8 per large car or SUV.

The slope of a linear equation represents the rate of change or the ratio between the change in the dependent variable (amount of money raised) and the change in the independent variable (number of cars washed). In this case, the slope indicates how the amount of money raised changes as the number of cars washed increases. Given that they raised $420, we can assume the dependent variable (amount of money raised) is represented by "y" and the independent variable (number of cars washed) is represented by "x." The equation representing this situation is y = 4.50x + 8y, where "4.50x" represents the amount raised from small cars and "8y" represents the amount raised from large cars or SUVs. The slope of the equation is 4.50, indicating that for every small car washed, the amount raised increases by $4.50. Similarly, for every large car or SUV washed, the amount raised increases by $8. Therefore, the slope in this situation represents the rate at which the amount of money raised changes per car washed, allowing us to understand how different car sizes contribute to the overall funds raised at the car wash.

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Answer:

  F = 9/5C +32

Step-by-step explanation:

You want to rearrange C = 5/9(F-32) to make F the subject.

You can solve for F the same way you solve any similar 2-step equation:

  C = 5/9(F -32) . . . . . . given

  9/5C = F -32 . . . . . . . multiply by 9/5 (multiplication property of equality)

  9/5C +32 = F . . . . . . add 32 (addition property of equality)

The equation Josh can use to convert to °F is ...

  F = 9/5C +32

Answer:

The answer is 2990.8

Step-by-step explanation:

Answer:

volume = 980π = 3078.790801  

Step-by-step explanation:

14 ÷ 2 = 7 = radius

π x \(r^{2}\)=  = 49π = area

area x 20 = volume

volume = 980π = 3078.790801  

Answer:

36

Step-by-step explanation:

2(10)+4^2

20+4^2

20+16

36

Answer: The result of the math formula =2*10+4^2 is 28.

To calculate this formula, you first need to perform the exponentiation operation of 4^2, which is 16. Then, you multiply 2 by 10, which gives you 20. Finally, you add 20 to 16, which gives you the final answer of 28.

The average age of all students in the college is a parameter. A parameter describes the whole populations.

Tha value of parameter or statistic can be average, percentage, and others.

A college reports that the average age of their students is 28 years old.

Is this a statistic of parameter?

The college would have access to data on all students. The data of all students in the college or the entire students is called population. So, this is a parameter.

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Answer:

85°

Step-by-step explanation:

the two lines that have red arrows on them are parallel and are cut by a transversal so angle 6 and the 95° angle are same side interior angles so they are supplementary angles so they need to add to 180°

∡ 6 = 180-95 = 85°

The probability that a student is a graduate student, given that they are a history major, is given as follows:

0.1577 = 15.77%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

There are 463 history students, and of those, 73 are graduate students, hence the probability is given as follows:

73/463 = 0.1577 = 15.77%.

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