Which expression is equivalent to 163?

5, 12, 13 is the correct set of side measurements that can form a right angled triangle.

Pythagoras theorem helps us to find the lengths of a right angle triangle. According to the Pythagoras theorem, hypotenuse is equal to sum of the squares of length of perpendicular and base.

Mathematically can be written as,  [tex]h^{2} = p^{2} + b^{2}[/tex].

Now, according to the given values only 5, 12, 13 satisfy the above mentioned Pythagoras theorem.

Since, [tex]5^{2} + 12^{2} = 13^{2}[/tex].

which is equal to 169.

other sets like 5, 10, 20 do not satisfy the theorem as, [tex]5^{2} +10^{2} \neq 20^{2}[/tex].

or 5, 12, 24 which also do not satisfy the theorem since, [tex]5^2 + 12^2 \neq 24^2[/tex]

Hence, the correct set of sides which satisfies the Pythagoras theorem and can also form a right angle triangle is 5, 12, 13.

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

The statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.

To determine if there are any outliers in the given data set of the number of books checked out from a library during the first two weeks of the month, we can examine the values and look for extreme values that deviate significantly from the rest of the data.

The data set is as follows:

19, 10, 15, 99, 12, 18, 15, 16, 12, 13, 18, 17, 19, 13

To identify outliers, we can use different methods, such as the interquartile range (IQR) or z-scores. Let's calculate the IQR to determine if there are any outliers:

Arrange the data set in ascending order:

10, 12, 12, 13, 13, 15, 15, 16, 17, 18, 18, 19, 19, 99

Calculate the first quartile (Q1) and third quartile (Q3):

Q1 = 13 (median of the lower half)

Q3 = 18 (median of the upper half)

Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 18 - 13 = 5

Define the lower and upper boundaries for outliers:

Lower bound = Q1 - 1.5 * IQR = 13 - 1.5 * 5 = 5.5

Upper bound = Q3 + 1.5 * IQR = 18 + 1.5 * 5 = 25.5

Based on these calculations, any value below 5.5 or above 25.5 would be considered an outlier.

Looking at the data set, we can see that there is indeed one outlier, which is the value 99. It is significantly larger than the rest of the values and falls above the upper bound.

Therefore, the statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.

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Answer:

the two numbers are 20 and 1.

The correct statements are A and B, while C, D, and E are incorrect.

The correct statements are:

A: The surface area of the sphere in terms of r is 4(pi)r^2 square units. This is true. The formula for the surface area of a sphere is given by A = 4(pi)r^2, where r is the radius.

B: The surface area of the cylinder in terms of r is 4(pi)r^2 square units. This is true. The formula for the lateral surface area of a cylinder is given by A = 2(pi)rh, where r is the radius and h is the height. Since the height of the cylinder is also r, the formula simplifies to A = 2(pi)rh = 2(pi)r(r) = 2(pi)r^2. Additionally, the two circular bases of the cylinder also contribute to the surface area, each with an area of (pi)r^2. Therefore, the total surface area of the cylinder is A = 2(pi)r^2 + 2(pi)r^2 = 4(pi)r^2.

C: The surface area of the cylinder in terms of r is 6(pi)d^2 square units. This statement is incorrect. The formula provided is incorrect. The correct formula for the surface area of a cylinder is A = 2(pi)rh, not 6(pi)d^2.

D: The surface area of the cylinder and sphere are the same. This statement is incorrect. The surface areas of a cylinder and a sphere are different. The surface area of a sphere is given by A = 4(pi)r^2, while the surface area of a cylinder is given by A = 2(pi)r^2 + 2(pi)rh. The presence of the curved surface in the cylinder makes its surface area different from that of a sphere.

E: The surface area of the cylinder and sphere are NOT the same. This statement is correct. As mentioned above, the surface areas of a cylinder and a sphere are different, so they are not the same.

In summary, the correct statements are A and B, while C, D, and E are incorrect.

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Answer:

2

DNE

-3

3

Step-by-step explanation:

(1) DNE because it is not continuous

(2) DNE because it is not continuous

(3) -3 because at 4, f(x) = -3

(4) x can be any value of -5-2k (where k is a positive integer) or 3. So you can just put 3.

Answer:

n = -1/8

Step-by-step explanation:

n + 3/4 = 5/8

n = 5/8 - 3/4

n = 5/8 - 6/8

n = -1/8

So, n = -1/8

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

If mLEFD=2x -3 and mZDFG= x+12, the measure of angle LEFD (mLEFD) is 27.

To find the measure of angle LEFD (mLEFD), we need to equate it to the given expressions mLEFD = 2x - 3 and mZDFG = x + 12.

Since angle LEFD and angle ZDFG are alternate interior angles, they are congruent.

Therefore, we have:

mLEFD = mZDFG

Substituting the expressions for mLEFD and mZDFG:

2x - 3 = x + 12

Next, we solve the equation for x by isolating the variable:

2x - x = 12 + 3

x = 15

Now that we have the value of x, we can substitute it back into the expression for mLEFD to find the measure of angle LEFD:

mLEFD = 2(15) - 3

mLEFD = 30 - 3

mLEFD = 27

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If Blue Spruce Corp, was organized on January 1, 2025. The entry on June 10 is:Debit Cash 396,600, Debit Common Stock 198,300,Credit Additional Paid-in Capital 198,300.

(A) Journalize the transactions:

Jan. 10:

Debit Cash 396,600

(66,100 shares x $6)

Debit Common Stock 198,300

(66,100 shares x $3)

Credit Additional Paid-in Capital 198,300

Mar. 1:

Debit Cash 764,400

(14,700 shares x $52)

Credit Preferred Stock 764,400

(14,700 shares x $52)

May 1:

Debit Cash 972,000

(121,500 shares x $8)

Credit Common Stock 364,50

(121,500 shares x $3)

Credit Additional Paid-in Capital 607,500

Sept. 1:

Debit Cash 44,100

(6,300 shares x $7)

Credit Common Stock 18,900

(6,300 shares x $3)

Credit Additional Paid-in Capital 25,200

Nov. 1:

Debit Cash 236,500

(4,300 shares x $55)

Credit Preferred Stock 236,500

(4,300 shares x $55)

(B) Post to the stockholders equity accounts:

Preferred Stock:

Date | Explanation | Debit | Credit

Mar. 1 | Issuance | | $764,400

Nov. 1 | Issuance | | $236,500

Common Stock:

Date | Explanation | Debit | Credit

Jan. 10 | Issuance | | $198,300

May 1 | Issuance | | $364,500

Sept. 1 | Issuance | | $18,900

Additional Paid-in Capital:

Date | Explanation | Debit | Credit

Jan. 10 | Issuance | | $198,300

May 1 | Issuance | | $607,500

Sept. 1 | Issuance | | $25,200

(C) Prepare the paid-in capital portion of the stockholders equity section at December 31, 2025:

Paid-in Capital:

Preferred Stock: $1,000,900 ($764,400 + $236,500)

Common Stock: $581,700 ($198,300 + $364,500 + $18,900)

Additional Paid-in Capital: $831,000 ($198,300 + $607,500 + $25,200)

Total Paid-in Capital = ($1,000,900 + $581,700 + $831,000)

=$2,413,600

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Answer:

h(x) = -x - 4

Step-by-step explanation:

Given:

f(x) = 8x - 2

g(x) = 9x + 2

Substituting these values into the equation h(x) = f(x) - g(x)

h(x) = (8x - 2) - (9x + 2)

Simplify

h(x) = 8x - 2 - 9x - 2

Combining like terms

h(x) = (8x - 9x) - (2 + 2)

h(x) = -x - 4

Hope this helps.

The mean score of Dora's bowling for this week would be = 161.

To calculate the mean score for the week the following would be carried out as follows;

The formula that is used to calculate mean = summation of the score/ number of scores recorded.

That is;

The weeks scores = 152+170+161

= 483/3

= 161

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The measure of center that the student should give to their teacher is the median.

In statistics, the median is a measure of central tendency that represents the middle value in a dataset when it is ordered from least to greatest. It divides the dataset into two equal halves, where half the values are smaller than the median and half are larger.

The median is useful because it is not influenced by extreme values or outliers in the dataset, unlike the mean (average). It provides a representative value that indicates the central position of the data.

The median is a better measure of center in this case since the data is skewed. The value of median is not affected by skewness

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Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

The value of x, representing the length of the hypotenuse AC, is 3√2 units.

In a right triangle ABC, with angle ABC measuring 45 degrees and side AB having a length of 3 units, we can use trigonometric ratios to find the length of the hypotenuse AC, represented by x.

Since angle ABC is 45 degrees, we know that it is a special right triangle, specifically a 45-45-90 triangle.

In such a triangle, the lengths of the sides are in a specific ratio: 1:1:√2.

In this case, side AB is 3 units, which represents the length of one of the legs. By the ratio mentioned earlier, the hypotenuse AC (x) will be √2 times the length of AB.

Therefore, we have:

AC = AB [tex]\times[/tex] √2

AC = 3 [tex]\times[/tex] √2

AC = 3√2 units

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y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.

To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.

Equation: cos(y) + sin(x) = 1

Differentiating once with respect to x using the chain rule:

-sin(y) * dy/dx + cos(x) = 0

Now, differentiating again with respect to x:

Differentiating the first term:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2

Differentiating the second term:

-d/dx(cos(x)) = -(-sin(x)) = sin(x)

The equation becomes:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0

Now, let's isolate the second derivative, d^2y/dx^2:

-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)

Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):

-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)

Thus, the second derivative (y") by the equation:

y" = cos(y) * dy/dx - sin(x) + sin(y)

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The predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.

To predict the sales in Glover's Golf Emporium's eleventh business year, we can use the concept of linear growth. We have two data points: sales in the second year ($160,000) and sales in the seventh year ($335,000).

Let's first find the annual increase in sales:

Increase in sales = Sales in the seventh year - Sales in the second year

Increase in sales = $335,000 - $160,000

Increase in sales = $175,000

Next, we need to determine the rate of increase per year. Since we have a linear growth pattern, we can calculate the average annual increase by dividing the total increase in sales by the number of years:

Average annual increase = Increase in sales / Number of years

Average annual increase = $175,000 / (7 - 2) years

Average annual increase = $175,000 / 5 years

Average annual increase = $35,000 per year

Now, we can predict the sales in the eleventh business year by adding the average annual increase to the sales in the seventh year:

Predicted sales in the eleventh year = Sales in the seventh year + (Average annual increase * Number of additional years)

Predicted sales in the eleventh year = $335,000 + ($35,000 * (11 - 7))

Predicted sales in the eleventh year = $335,000 + ($35,000 * 4)

Predicted sales in the eleventh year = $335,000 + $140,000

Predicted sales in the eleventh year = $475,000

Therefore, the predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.

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The units of each product that Cane should produce to maximize profits will be 62000 units of Beta and 7600 units of

Alpha.

               Alpha Beta

Selling price 130 90

Variable cost 78 48

Contribution margin 52 42

Pound per unit 5 2

Contribution margin per pound 10.4 21

                      Pound                   Unit

Beta 62000*2 = 124000 62000

Alpha 38000 38000/5 = 7600

Total 162000

Maximum contribution margin = (38000*10.4+124000*21) = 2999200

Highest price = 10.4+5 = 15.40 per pound

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The period of the function in this problem is given as follows:

5 units.

A periodic function is a function that has the behavior repeating over intervals in the domain of the function.

Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.

Two consecutive peaks of the graph of the function in this problem are given as follows:

Input of 1 and input of 6.

Hence the period of the function is given as follows:

6 - 1 = 5 units.

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Answer:

C) -2/9

Step-by-step explanation:

[tex]\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}[/tex]

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

The table is not a function because (a) No, because one x-value corresponds to two different y-values

From the question, we have the following parameters that can be used in our computation:

The table

The table can be represented as

x  y

2  1

2  4

3  4

4  2

5  5

The above table of values is not a function

This is so because some output values have the same input values.

i.e. it would fail the vertical line test when represented on a graph

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The statement "1 is NOT in the domain" is true because for the function f(x), the expression x - 7 results in division by zero when x equals 1, which makes 1 not a valid input for the function.

To determine if a value is in the domain of a function, we need to consider any restrictions or limitations on the input values.

For the function f(x) = √(x - 7), the square root function is defined only for non-negative values.

Therefore, the expression (x - 7) inside the square root must be greater than or equal to zero. In other words, x - 7 ≥ 0.

Solving this inequality, we find x ≥ 7.

This means that any value of x that is greater than or equal to 7 is in the domain of f(x).

However, the statement is asking specifically about the value 1.

Since 1 is less than 7, it does not satisfy the inequality x ≥ 7 and is therefore not in the domain of f(x).

Similarly, for the function g(x) = 4x - 8, there are no restrictions on the domain.

Any real number can be substituted into the function, including the value 1.

Therefore, the statement "1 isn't in the domain of f(0) g" is not accurate.

It is true that 1 is not in the domain of f(x), but it is in the domain of g(x).

In summary, the correct statement is that "1 is not in the domain."

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Answer$535.50

Step-by-step explanation:

15% is equal to .15

So, multiply 600.00x .15=90

                   600.00 - 90.0=510.
                   510. 00x .05=25.50

                   510.00+25.50=535.50

                   Your answer is $535.5

The negative value indicates that the policy is providing a net benefit of approximately $9,742.21 over the 10-year period.

To calculate the net cost of insurance, we need to compare the return on investment from investing the premium elsewhere with the cash value of the policy.

First, let's calculate the amount of money you would have if you invested the $2,000 premium elsewhere for 10 years with a 5% annual yield. We can use the compound interest formula:

A = P * (1 + r)^n

Where:

A is the final amount.

P is the principal amount (premium).

r is the interest rate per period (5% or 0.05).

n is the number of periods (10 years).

Calculating the investment amount:

A = 2,000 * (1 + 0.05)^10

A ≈ 2,000 * 1.628895

A ≈ 3,257.79

Therefore, if you invested the premium elsewhere, you would have approximately $3,257.79 after 10 years.

Now, let's calculate the net cost of insurance:

Net cost of insurance = Annual premium - Cash value of the policy + Investment return

Net cost of insurance = 2,000 - 15,000 + 3,257.79

Net cost of insurance ≈ -$9,742.21

The negative value indicates that the policy is providing a net benefit of approximately $9,742.21 over the 10-year period.

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Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

The graph of the solution to the inequality is attached as image to this answer.

The piece-wise defined function h(x) represents different values of y (the output) depending on the value of x (the input). Each interval of x has a different value assigned to it.

In this particular case, the inequality statements define the intervals for x and their corresponding output values.

Let's break it down:

- For values of x that are greater than -3 and less than or equal to -2, h(x) is assigned the value of -1.

- For values of x that are greater than -2 and less than or equal to -1, h(x) is assigned the value of 0.

- For values of x that are greater than -1 and less than or equal to 0, h(x) is assigned the value of 1.

- For values of x that are greater than 0 and less than or equal to 1, h(x) is assigned the value of 2.

Any values of x outside of these intervals are not defined in this piece-wise function and are typically represented as "not a number" (NaN).

For example, if you were to evaluate h(-2.5), it falls within the first interval (-3 < x ≤ -2), so h(-2.5) would be equal to -1. Similarly, if you were to evaluate h(0.5), it falls within the fourth interval (0 < x ≤ 1), so h(0.5) would be equal to 2.

The graph of the piece-wise function h(x) consists of horizontal line segments connecting the specified values of y for each interval, resulting in a step-like pattern.

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Answer:

19, 14, 38

Step-by-step explanation:

Let x, y, and z be each number respectively:

[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]

Therefore, the three numbers are 19, 14, and 38.

In the class , each child needs to pay (n * p) / y shillings to cover the cost of the lost books.

In the given scenario, there is a class of "y" children, and "n" mathematics books were lost, each costing "p" shillings. The teacher decides to distribute the cost of the lost books equally among all the children.

To find out how much money each child needs to pay, we need to divide the total cost of the lost books by the number of children in the class.

The total cost of the lost books can be calculated by multiplying the number of lost books ("n") by the cost of each book ("p").

Total cost = n * p

To distribute the cost equally among all the children, we divide the total cost by the number of children ("y"):

Cost per child = Total cost / Number of children

Substituting the values, we get:

Cost per child = (n * p) / y

Therefore, each child in the class needs to pay (n * p) / y shillings to cover the cost of the lost books.

It's important to note that this calculation assumes that the total cost is evenly distributed among all the children, regardless of whether they were responsible for losing the books or not.

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Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4