1) 5k = 27
Solve equation and proportion

Answer:

1st option

Step-by-step explanation:

since one pair of opposite sides 10 in , then

x + 2 = 10 ( subtract 2 from both sides )

x = 8

Then

x + 5 = 8 + 5 = 13 in

2x - 5 = 2(8) - 5 = 16 - 5 = 13 in

The opposite sides of a parallelogram are parallel and congruent.

So the quadrilateral could be a parallelogram

Answer: A) Yes, one pair of opposite sides could measure

10 in., and the other pair could measure 13 in.

Step-by-step explanation:

just did it on edu 2023

The equation used to solve this problem is x + y + z = 100000,  0.04x + 0.06y + 0.08z = 6700 and y = z

An equation is an expression showing the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 4% (short term), y represent the amount of money invested at 6% (intermediate term) and z represent the amount of money invested at 8% (long term)

Since an investor has $100,000 to invest, hence:

x + y + z = 100000    (1)

Also, the investor wishes to have a return of $6700, hence:

0.04x + 0.06y + 0.08z = 6700   (2)

Equal amounts invested in intermediate and long term bonds. This gives:

y = z     (3)

The third equation used to solve this problem is y = z

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Answer:

3

Step-by-step explanation:

a ÷ (b + c)

51 ÷ (15 + 2)

51 ÷ (17)

51 ÷ 17

3

Answer:

51÷{15+2}

51÷{17}

51÷17

=3

The equation of a circle with the center at the origin and radius 10 can be determined by using the standard form of the equation of a circle, which is given by the equation x² + y² = r², where (x, y) are the coordinates of any point on the circle, and r is the radius of the circle. If the center of the circle is at the origin,

then the coordinates of the center are (0, 0), and the equation can be written as x² + y² = 10². This equation represents a circle with center at the origin and radius 10. This equation can be used to graph the circle by plotting the points that satisfy the equation.

The circle will be a perfect circle with a radius of 10 units and centered at the origin. It will pass through the points (-10, 0), (0, -10), (10, 0), and (0, 10). These points can be found by solving the equation for x and y. When x = -10, 0, and 10, y will be equal to 0, and when y = -10, 0, and 10, x will be equal to 0. This is how the circle can be graphed using the equation.

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Please find attached photograph for your answer.

Hope it helps

ray4918 here to help.

Answer:

B

Step-by-step explanation:

You can try to solve each:

A. \(2x - 31 = 2x - 31\\\)

add 31 to both sides

\(2x = 2x\)

subtract 2x from both sides

\(0 = 0\)

This means infinite solutions

B. \(2x-31 = -2x-31\)

add 31 to both sides

\(2x = -2x\)

add 2x to both sides

\(4x = 0\)

divide both sides by 4

\(x = 0\)

This does have one solution

C. \(2x + 31 = 2x-31\)

subtract 31 from both sides

\(2x = 2x-62\)

subtract 2x from both sides

\(0 = -62\)

This is not true, so no solutions

D. \(2x -2 = 2x -31\)

add 2 to both sides

\(2x = 2x - 29\)

subtract 2x from both sides

0 = -29

not true, so b is the answer.

Answer:

Step-by-step explanation:

3b - 4 = 11

3b = 15

b = 5

Answer:

It is 8ft.

Step-by-step explanation:

To solve this, you just need to set up a ratio.

\(\frac{3in}{4ft} = \frac{6in}{x}\)

---------------------------

You can now cross multiply.

6 * 4 =24

24/3 = 8

----------------------------

That concludes that the actual ping pong table is 8ft!

Good Luck!!

Answer:

8 ft

Step-by-step explanation:

Answer:

6 miles per hour!

Step-by-step explanation:

If both the functions f(x) and g(x) are equal. Then the value of the variable will be 3.

The term f(x) is used to represent a function of x i.e. a function with only one independent variable ' x '.

The functions are given below.

f(x) = x³ - 3x² + 2 and g(x) = x² - 6x + 11

If both the functions f(x) and g(x) are equal.

f(x) = g(x)

x³ - 3x² + 2 = x² - 6x + 11

Simplify the equation, then we have

x³ - 4x² + 6x - 9 = 0

Then the equation is solved by the calculator, then we have

x = 3

Then the value of the variable will be 3.

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Answer:

Result = 9b/25 or 36b/100

Step-by-step explanation:

The number is b

step 1

b is decreased by 40%

value of 40% of b = 40/100 *b = 4b/10

New value after this change = b - 40% decreased value of b = b -4b/10

= (10b-4b)/10 = 6b/10

Step 2 The new value obtained is again decreased by 40%

value of 40%  number found in step 1 =  40% of value found in step 1

value of 40%  number found in step 1 =  40/100 * 6b/10 = 24b/100

This value (24b/100) is subtracted from value found in step 1(6b/10) as given that  value obtained is decreased by 40%

new value found after 40% decrease = 6b/10 - 24b/100

new value found after 40% decrease = 60b/100 - 24b/100= 36b/100

new value found after 40% decrease =  36b/100 = 9b/25

Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25

*remember to always be nice!

Have an outstanding day

The final Result is 36x/25

Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division.

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/). An example of an algebraic expression is 5x + 6. Here 5 and 6 are fixed numbers and x is a variable.

Given:

let the number be x

x is decreased by 40%

40% of x = 40/100 * x = 4x/10

After decreasing

= x- 4x/10

=6x/10

Again decreasing 40%

Then , the value will be

= 6x/10- 0.4*6x/10

=6x/10- 02.4x/10

= 3.6x/10

= 36x / 100

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The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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Answer:

x= 15

Step-by-step explanation:

first you subtract 1 then you multiply everything by 5 then  you divide by 2

hope this helps

The approximate English system equivalent for a gas tank that holds 76 liters is about 20 gallons.

To convert liters to gallons, we can use the conversion factor that 1 liter is approximately equal to 0.264172 gallons.

76 liters * 0.264172 gallons/liter ≈ 20.064192 gallons

Rounding to the nearest whole number, we get approximately 20 gallons.

Therefore, the approximate English system equivalent for a gas tank that holds 76 liters is about 20 gallons.

The gas tank in the new car, which holds 76 liters, is approximately equivalent to 20 gallons in the English system. This conversion is based on the approximate conversion factor of 1 liter being approximately equal to 0.264172 gallons.

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To prove that two triangles are similar using the AA similarity theorem, you need to know that both triangles have two angles that are congruent.

The order of the angles doesn't matter, so you could have the corresponding angles of one triangle be the first and third angles, and the corresponding angles of the other triangle be the second and third angles. This is because if two angles of one triangle are congruent to two angles of another triangle, then the third angles must also be congruent, and the triangles are similar.

The AA similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. More specifically, the theorem states that if the measure of two angles in one triangle are equal to the measure of two angles in another triangle, then the two triangles are similar.

This means that the corresponding sides of the two triangles are proportional in length, which allows us to establish the relationship between their corresponding angles and sides, without measuring them directly. The AA similarity theorem is one of the ways to prove that two triangles are similar.

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Answer:

y=-1/2x+17

Step-by-step explanation:

y=-1/2x+17

a. The probability that a patient experiences relief is 0.9.

b. The probability that at least 10 patients experience relief is 0.9988 (rounded to four decimal places)

c. The probability that at most 7 experience relief is 0.0007 (rounded to four decimal places)

d. The average number of patients who experience relief is 1.14 (rounded to two decimal places)

e. The probability that none of the 15 patients experience relief is 1.0E-15 (rounded to scientific notation)

a. The probability that a patient experiences relief is 0.9. The probability that all 15 experience relief is given by:

P(all 15 experience relief) = (0.9)^15 = 0.2059 (rounded to four decimal places)

b. The probability that at least 10 patients experience relief can be calculated by adding the probabilities of 10, 11, 12, 13, 14, and 15 patients experiencing relief:

P(at least 10 experience relief) = P(10) + P(11) + P(12) + P(13) + P(14) + P(15)

where P(k) represents the probability that k patients experience relief. Each P(k) can be calculated using the binomial probability formula:

P(k) = (15 choose k) * 0.9^k * 0.1^(15-k)

Using a calculator or software, we can find:

P(at least 10 experience relief) = 0.9988 (rounded to four decimal places)

c. The probability that at most 7 patients experience relief is the same as the probability that 8 or fewer patients experience relief. We can use the complement rule to calculate this probability:

P(at most 7 experience relief) = 1 - P(more than 7 experience relief)

To find P(more than 7 experience relief), we can add the probabilities of 8, 9, ..., 15 patients experiencing relief:

P(more than 7 experience relief) = P(8) + P(9) + ... + P(15)

Again, each P(k) can be calculated using the binomial probability formula. Using a calculator or software, we can find:

P(at most 7 experience relief) = 0.0007 (rounded to four decimal places)

d. The average number of patients who experience relief is given by the expected value of a binomial distribution:

E(X) = np

where X is the number of patients who experience relief, n is the sample size (15), and p is the probability of success (0.9). Thus,

E(X) = 15 * 0.9 = 13.5

The standard deviation of a binomial distribution is given by the square root of the variance:

s = sqrt(np*(1-p))

Thus,

s = sqrt(150.90.1) = 1.14 (rounded to two decimal places)

e. The probability that none of the 15 patients experience relief is given by:

P(none experience relief) = 0.1^15 = 1.0E-15 (rounded to scientific notation)

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The conditional proportions of people using their phones in the afternoon and the evening can be summarized as follows: A significant proportion of individuals use their phones both in the afternoon and evening, indicating a consistent pattern of phone usage throughout the day.

In the afternoon, many people rely on their phones for various purposes such as work, communication, entertainment, and staying connected to social media. With the advancements in technology and increased accessibility to smartphones, it has become common for individuals to utilize their phones during this time. Whether it's checking emails, browsing the internet, or engaging in social media activities, the afternoon serves as a convenient time for phone usage.

Moving on to the evening, phone usage remains prevalent as individuals unwind and engage in leisure activities. During this time, people often use their phones for entertainment purposes, such as streaming videos, playing games, or engaging in social interactions through messaging apps or social media platforms. The evening also offers a time for catching up on news, reading, or engaging in personal hobbies, which may involve the use of mobile devices.

Overall, the conditional proportions reveal that phone usage is not limited to a specific time of day but rather extends throughout the afternoon and evening. This emphasizes the significant role that smartphones play in our daily lives, providing us with a range of functionalities and opportunities for connectivity and entertainment.

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The mixed number would be \(10\frac{31}{100}\).

What is a mixed number?

A mixed number is a number that is made up of a whole number and a fraction. It is a combination of a whole number and a fraction that represents a value between two whole numbers. For example, 3 1/2 is a mixed number, with 3 as the whole number and 1/2 as the fraction.

To express 10.31 as a mixed number:

The whole number part is 10.

To find the fractional part, subtract the whole number from the decimal: 0.31

To express the fractional part as a fraction, we will have to divide it by 1 and write the decimal as a fraction, in this case 0.31= 31/100

Now we can express 10.31 as a mixed number, that is 10 31/100

Hence, the mixed number would be \(10\frac{31}{100}\).

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The parallel linear functions are given as follows:

1) y = x + b, b ≠ 17.

4) y = b, b ≠ -3.

5) y = b, b ≠ 19.

6) x = b, b ≠ 19.

The definition of a linear function, in slope-intercept format, is given as follows:

y = mx + b.

In which the coefficients of the function are given as follows:

When two linear functions are parallel, they have the same slope, along with different intercepts.

Hence, the parallel functions are given as follows:

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Hi,

Answer:

k = \(\frac{23}{2}\)

Step-by-step explanation:

Subtract 4k from both sides

6k - 4k = 2k

2k - 8 = 15

Add 8 on both sides (you want to get rid of the 8 in order to leave the k alone)

2k = 23

k = 23/2

Have a good day!

Answer:

\(k=23/2=11.5\)

Step-by-step explanation:

So we have the equation:

\(6k-8=4k+15\)

Add 8 to both sides. The left side cancels:

\(6k=4k+23\)

Subtract 4k from both sides. The right side cancels:

\(2k=23\)

Divide both sides by 2:

\(k=23/2=11.5\)

And we're done!

f(x, y) = e²y² is a function of two variables, x and y. The partial derivative of f with respect to y, denoted by f₂, is the derivative of f with respect to y, holding x constant.

To find f₂ (0, -2), we first find f₂ (x, y). This is given by:

f₂ (x, y) = 2ye²y²

Substituting x = 0 and y = -2, we get:

f₂ (0, -2) = 2(-2)e²(-2)² = -8

Therefore, the answer is E. -8.

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Step-by-step explanation:

y = kx, where k is a real constant.

When x = 12, y = 60.

=> (60) = (12)k, k = 5.

Therefore when x = 20,

y = kx = (5)(20) = 100.

Answer:

Option b

Step-by-step explanation:

To represent this proportion using fractions, let the numerators be the number of waffles sold and denominator, the number of sugar cones.

Thus, the proportion that can be used to represent the cone sales is

14/6 = 7/3

Answer:

BBBBBB

Step-by-step explanation:

Answer:

5143e2ee

Step-by-step explanation:

Answer:

f(x) = 2x + 2^4 is a function.

Answer:

4 cm

Step-by-step explanation:

Given 2 similar figures with sides in ratio a : b , then

ratio of areas = a² : b²

let n be the length of the smaller one , then

ratio of sides = n : 10

ratio of areas = n² : 10² = n² : 100

Using proportion

( \(\frac{ratio}{area}\) )

\(\frac{n^2}{24}\) = \(\frac{100}{150}\) = \(\frac{2}{3}\) ( cross- multiply )

3n² = 48 ( divide both sides by 3 )

n² = 16 ( take the square root of both sides )

n = \(\sqrt{16}\) = 4

length of the smaller one is 4 cm

The polynomial written in standard from is -7xy³ - 3x³y + 8x²y² + 4x².

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

In other words the terms are arranged by decreasing order of degrees.

The degree of a polynomial is the exponential value of the variables.

Therefore, the polynomial written in standard from in the options is as follows:

-7xy³ - 3x³y + 8x²y² + 4x²

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Answer:

35%

Step-by-step explanation:

40%+25%=65%

100%-65%=35%