Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.


The measure of angle ABC is
°.

The measure of angle BAC is
°.

The measure of angle ACB is

Answer:

22+_3 because I don't know

\(\bf{Swap \ sides \ 8x+2(x+6)=-28 }\)

\(\bf{Expand \ 2(x+6): \ \ \ \ 2x+12}\)

\(\mathrm{Set \ the \ variables \ using: \ \ \ a(b+c)=ab+ac}\)

\(a=2,\:b=x,\:c=6\)

\(=2x+2\cdot \:6\)

\(\mathrm{Multiply\:the\:numbers:}\:2\cdot \:6=12\)

\(=2x+12\)

\(8x+2x+12=-28\)

\(\mathrm{Add\:similar\:elements:\:8x+2x=10x}\)

\(10x+12=-28\)

\(\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}\)

\(10x+12-12=-28-12\)

\(\mathrm{Simplify}\)

\(10x=-40\)

\(\mathrm{Divide\:both\:sides\:by\:}10\)

\(\dfrac{10x}{10}=\dfrac{-40}{10}\)

\(\mathrm{Simplify \ \dfrac{10x}{10}: \ \ x }\)

\(\mathrm{Divide:}\:\dfrac{10}{10}=1\)

\(=x\)

\(\mathrm{Simplify \ \dfrac{-40}{10}: \ \ -4 }\)

\(\rm{Apply \ the \ properties \ of \ fractions \ to \ fractions: \ \ \dfrac{-a}{b}=-\drac{a}{b}}\)

\(=-\dfrac{40}{10}\)

\(\rm{split: \ \dfrac{40}{10}=4 }\)

\(\bf{x=-4 \ \ \to \ \ \ Answer }\)

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

You can make 14 with some ribbon left over.

Step-by-step explanation:

A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

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Therefore , the solution of the given problem of standard deviation  comes out to be the margin of error will increase if the standard deviation is 0.85 instead" is the appropriate response.

Variance is measured in statistics as a measure of difference. The average variation between the data that was gathered and the mean is calculated using the image of that figure. By comparing every number to the mean, it incorporates those points of data on their own, unlike many other legitimate measures of variability.

Here,

The claim that "If the sample size is increased to 100 returned books, the margin of error will decrease" is untrue.

Therefore, a larger sample number will result in a lower margin of error, which will also be achieved by a smaller standard deviation.

Therefore, the claim that "The margin of error will increase if the sample size is changed to 120 returned books" is also untrue.

Since a lower standard deviation will result in a lower margin of error, the assertion "The margin of error will decrease if the standard deviation is 0.95 instead" is accurate.

Therefore, "The margin of error will increase if the standard deviation is 0.85 instead" is the appropriate response.

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An equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is \(7x > -22.\)

To find an equivalent inequality, we can start by simplifying the given inequality and then make adjustments to preserve its truth.

Let's simplify the given inequality step by step:

\(-4(x + 7) < 3(x - 2)\)

Expanding both sides:

\(-4x - 28 < 3x - 6\)

Grouping like terms:

\(-4x - 3x < -6 + 28\)

Simplifying:

\(-7x < 22\)

To maintain the direction of the inequality, we need to multiply both sides by -1.

However, when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality is reversed.

Therefore, we need to flip the inequality sign:

\(7x > -22\)

Hence, an equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is

\(7x > -22.\)

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The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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Answer:

If the base and the negative exponent is in the denominator already

Step-by-step explanation:

Normally, a base with a negative exponent moves to the denominator.

Example: (2^-3 = 1 / (2)^3 = 1/8)

However, if the base and the negative exponent is already in the denominator, the base would move to the numerator and the exponent would become positive.

Example:  2 / (3)^-3 = 2 * 3^3 = 2 * 27 = 54

Answer: D) 2

Step-by-step explanation:

The standard deviation of the difference between the means of the two populations is given by:-

\(S.E.=\sqrt{\dfrac{\sigma^2_1}{n_1}+\dfrac{\sigma^2_2}{n_2}}}\)

where \(n_1\)= sample size of population 1

\(n_2\)= sample size of population 2

\(\sigma^2_1\)= variance of population 1

\(\sigma^2_2\)= variance of population 2

As per given,

\(S.E.=\sqrt{\dfrac{112.5}{45}+\dfrac{54}{36}}}\\\\=\sqrt{4}\\=2\)

Hence, the correct option is D) 2.

15

Percentages represent a proportion of a number. There are 2 ways to find a percent of a whole number.

Multiple of 10

Since 30% is a multiple of 10%, there is a shortcut we can use. We can find 10% and then multiply by 3 in order to find 30%. First, find 10% of 50. Like always, 10% of any number is that number divided by 10 (move the decimal 1 place to the left).

So, 10% of 50 is 5.0.

Then, to find 30%, multiply 5 by 3.

30% of 50 is 15.

Multiplication

The more consistent method includes multiplication, this can be used with any percentage. To use this method we need to convert 30% to a decimal. To convert any percentage to a decimal divide by 100 (move the decimal 2 places to the left).

Now, we can multiply this decimal by the whole number, 50. This will give us our desired answer.

So, this once again shows that 30% of 50 is 15.

Answer:

Step-by-step explanation

I:

Answer:

To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.

The annual depreciation amount is calculated as: $1 million / 50 years = $20,000

In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000

In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000

Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

\(1000 \div 5=200\), not \(2000\).

Answer:

1,000 is a smaller number than 2,000, while 1,000 is being divided by a positive number, it is impossible for 1,000 ÷ 5 to become 2,000. 1,000 divided by 5 is 200, and 1,000 multiplied by 2 is 2000

Step-by-step explanation:

Answer:

WN=37.8

Step-by-step explanation:

WN=18%*210

WN=0.18*210

WN=37.8

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

The margin of error for a 96% confidence interval is of 0.0114 = 1.14%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

For this problem, we have that:

\(n = 400, p = \frac{395}{400} = 0.9875\)

96% confidence level

So \(\alpha = 0.04\), z is the value of Z that has a pvalue of \(1 - \frac{0.04}{2} = 0.98\), so \(Z = 2.056\).

Calculate the margin of error for a 96% confidence interval.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 2.056\sqrt{\frac{0.9875(0.0125)}{400}}\)

\(M = 0.0114\)

The margin of error for a 96% confidence interval is of 0.0114 = 1.14%.

Answer:

38

Step-by-step explanation:

cross the numbers out

According to the described situation, we have that:

The decision rule is:

The value of the test statistic is of z = -0.866.

The claim is:

"Forty percent or more of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available"

At the null hypothesis, we consider that the claim is false, that is, the proportion is of less than 40%, hence:

\(H_0: p < 0.4\)

We have a right-tailed test, as we are testing if a proportion is less/greater than a value. Since we are working with a proportion, the z-distribution is used.

Using a z-distribution calculator, the critical value for a right-tailed test with a significance level of 0.01 is of z = 2.327, hence, the decision rule is:

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

In this problem, the parameters are:

\(p = 0.4, n = 200, \overline{p} = \frac{74}{200} = 0.37\)

Hence:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.37 - 0.4}{\sqrt{\frac{0.4(0.6)}{200}}}\)

\(z = -0.866\)

The value of the test statistic is of z = -0.866.

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Answer:

  (-∞, -3] or [-3, ∞)

Step-by-step explanation:

You want the largest domain interval(s) on which the function shown in the graph could be one-to-one.

A one-to-one function must pass the horizontal line test. That is, no horizontal line can intersect its graph in more than one place.

For that to be true of the given function, the interval on which it is defined cannot include values on both sides of x=-3, where the graph has a minimum. That is, the domain must be either x ≤ -3, or x ≥ -3, (or some subset of either of these).

The largest intervals on which the function has an inverse are ...

  (-∞, -3]  or  [-3, ∞)

<95141404393>

To make the given function one-to-one and have an inverse, we can restrict its domain to (-∞, a) or (a, ∞), where 'a' is the x-coordinate of the highest or lowest point on the graph.

To make the given function one-to-one and have an inverse, we need to restrict its domain. The largest domains, in interval notation, that can be used are: (-∞, a) or (a, ∞) where 'a' is the x-coordinate of the highest or the lowest point on the graph, depending on the function type.

If the graph has a highest point, the domain is restricted to (a, ∞), where 'a' is the x-coordinate of the highest point. If the graph has a lowest point, the domain is restricted to (-∞, a), where 'a' is the x-coordinate of the lowest point.

For example, if the graph has a highest point at (3, 5), the domain would be restricted to (3, ∞) to make the function one-to-one and have an inverse.

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Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Answer:

three more couches are needed to increase the truckload to one ton.

Step-by-step explanation:

First, let's calculate the weight of the five couches:

5 couches * 250 pounds/couch = 1250 poundsSince one ton is equal to 2000 pounds, we can subtract the weight of the couches from one ton to find out how much additional weight is needed:

2000 pounds - 1250 pounds = 750 poundsEach couch weighs 250 pounds, so we can divide the additional weight needed by the weight of each couch to determine how many more couches are needed:

750 pounds / 250 pounds/couch = 3 couches Therefore, three more couches are needed to increase the truckload to one ton.

Answer:

\(\large \boxed{\sf \ \ \dfrac{1}{2}\sqrt{(x_1^2+y_1^2)(x_2^2+y_2^2)} \ \ }\)

Step-by-step explanation:

Hello,

This is a right triangle so the area is:

\(\dfrac{1}{2} \left\{ \sqrt{x_2^2+y_2^2} \cdot \sqrt{x_1^2+y_1^2} \right\}\\\\=\dfrac{1}{2}\sqrt{(x_1^2+y_1^2)(x_2^2+y_2^2)}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

-8

Step-by-step explanation:

Yes, it is rational. It's an integer.

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Which negative angle is equivalent to an 85° angle?

A. An angle measuring -95°

B. An angle measuring -275°

D. An angle measuring -265°

-KeonLee

I hope it help

#Carry on learning

An angle measuring -275°

*view photo*

Answer:

es verdad pero 3 nomas puede ser dividido por 3 o 1

Step-by-step explanation:

The number 5.4 is greater than the number 5.04. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The number line goes from 5.0 to 6.0 with 9 labeled marks in between.

Each mark increases by point one.

There are five labeled points.

A point labeled 5.04 is between 5.0 and 5.1.

A point labeled 5.26 is between 5.2 and 5.3.

A point labeled 5.4 is at the mark labeled 5.4.

A point labeled 5.520 is between 5.5 and 5.6.

A point labeled 5.71 is between 5.7 and 5.8.

Then the ascending order of the number will be

5.04 < 5.26 < 5.4 < 5.52 < 5.71

Thus, the correct option is B.

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Answer:

B did it on collegebridge

Step-by-step explanation: