Determine whether the equation represents a direct variation. If it does, find the constant of variation.
3y=2x-5

Answer:Red

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 blue out of 15 chips

Answer:36ab

Step-by-step explanation:

When the equation is given i.e. (6a) (6b) so the answer is to be considered as the 36 ab.

Since the equation is (6a) (6b)

So here we basically do multiplication by each other so it comes 36 ab.

Hence, we can conclude that When the equation is given i.e. (6a) (6b) so the answer is to be considered as the 36 ab.

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Answer:

x=−1 and y=−1

Step-by-step explanation:

Solve by substitution

x−y=0;2x+3y=−5

Step: Solve x−y=0 for x:

x−y+y=0+y(Add y to both sides)

x=y

Step: Substitute yfor x in 2x+3y=−5:

2x+3y=−5

2y+3y=−5

5y=−5(Simplify both sides of the equation)

5y/5=−5/5 (Divide both sides by 5)

y=−1

Step: Substitute−1 for y in x=y:

x=y

x=−1

Answer:

x=−1 and y=−1

The solution to the system is x = -1.8 and y = -1.8.

A group of two or more equations that must be solved simultaneously make up a system of equations. There are many unknown variables in a system of equations, and each equation in the system depicts the relationship between those variables.

A set of variable values that satisfy every equation in a system of equations is the solution to the system of equations.

To solve this system of equations graphically, we can plot the two equations on a coordinate plane and find the point where they intersect, which represents the solution to the system.

a) To plot the equation x - y = 0, we can rearrange it to y = x and plot the line passing through the origin and the point (1, 1), as shown below:

Graph of the line y = x passing through the origin and the point (1, 1).

To plot the equation 2x + 3y = -5, we can rearrange it to y = (-2/3)x - 5/3 and plot the line passing through the points (-2, 1) and (1/3, -5/3), as shown below:

Graph of the line y = (-2/3)x - 5/3 passing through the points (-2, 1) and (1/3, -5/3).

b) The point where the two lines intersect is the solution to the system. From the graph, we can see that this point is approximately (-1.8, -1.8).

Therefore, the solution to the system is x = -1.8 and y = -1.8.

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The ability of the normal distribution to approximate the binomial distribution under appropriate conditions justifies the use of the normal distribution for the sampling distribution of the proportion.

A sampling distribution is a statistical probability distribution derived from a larger number of samples gathered from a certain population. The sampling distribution of a particular population is the distribution of frequencies of a range of possible outcomes for a population statistic.

A population is the whole pool from which a statistical sample is selected in statistics. A population can be defined as a large group of people, things, events, medical visits, or measures. A population can thus be defined as an aggregate observation of persons linked by a common trait.

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Answer:

Step-by-step explanation:

2x = 6 + 3y

2x - 6 = 3y

Find the y-intercept when x = 0:

0 - 6 = 3y

-6 = 3y

-2 = y

Find the x-intercept when y = 0:

2x - 6 = 0

2x = 6

x = 3

Answer:

75

Step-by-step explanation

5+3=8

120/8=15

15(5)=75

If there are a total of 120 donuts served 45 will be chocolate donuts.

A ratio is a comparison between two similar quantities in simplest form.

A ratio a : b can be written as a/b.

Given, A donut shop serves plain and chocolate donuts at a ratio of 5 to 3.

∴ Plain donuts : Chocolate donuts = 3 : 5.

If there are a total of 120 donuts served chocolate donuts will be,

= 3/(5 + 3)×120.

= (3/8)×120.

= 45 chocolate donuts.

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First replace x with -2 in the g(x) equation and solve:

G(x) = x + 4 = -2 + 4 = 2

Now replace x in the f(x) equation with the solution of g(x).

F(x) = 1-3(2) = 1-6 = -5

Fg(-2) = -5

Answer:

Step-by-step explanation:

Let's do an example.

60:90:100

100 plus 90 plus 60 is 250

ben gets 90 of that 250

or 9/25.

Answer:

They need five weeks to make all their travels.

Step-by-step explanation:

Given that Cesar and Jocelyn are planning their trips to three countries next year.

One trip will be one week long, another two days, and the other two weeks.

In conclusion, they need five weeks to make this travel.

Answer:

2.3 + w > 18

Step-by-step explanation:

Answer:

we 1st can get the weight of rat by

1 rat and 1 cat + 1 dog and rat = 30

2 rat + 1 cat + 1 dog = 30

Then 1 rat and cat measure 24 so

2 rat + 24 =30

2 rat + 24 =30 1 rat = 3 kg

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 10

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 10

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg

2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg 1 dog = 17kg

so we get the weight of each now we r going to sum them 1 rat + 1 cat + 1 dog = x

1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x

1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x 27 kg = x ..... is the mass of 3 of them

The domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}. (Option A).

Now,

In the given function {(-3,4),(0,6),(2,-2),(1,-3),(6,-7),(3,2)},

Thus, According to the definition of domain and range,

Hence, Option A is correct, i.e., the domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}.

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Answer:

X= -1

Step-by-step explanation:

2x+5=1(x+4)

2x+5=1x+4

2x-1x=-5+4

x=-1

Answer: (j-1)(7j-3)

Step-by-step explanation:

Answer:

Final result :

(j - 1) • (7j - 3)

Step-by-step explanation:

Step by Step Solution

STEP1:

Equation at the end of step 1

(7j2 - 10j) + 3

STEP2:

Trying to factor by splitting the middle term

2.1 Factoring 7j2-10j+3

The first term is, 7j2 its coefficient is 7 .

The middle term is, -10j its coefficient is -10 .

The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 7 • 3 = 21

Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is -10 .

-21 + -1 = -22

-7 + -3 = -10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -3

7j2 - 7j - 3j - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

7j • (j-1)

Add up the last 2 terms, pulling out common factors :

3 • (j-1)

Step-5 : Add up the four terms of step 4 :

(7j-3) • (j-1)

Which is the desired factorization

Final result :

(j - 1) • (7j - 3)

Numbers that include a decimal point are known as real numbers, as it encompasses numbers with decimal points and includes both integers and non-integers. Correct answer is option (d) real numbers.

Real numbers are a broad category that encompasses both rational and irrational numbers. They include numbers with exact values, as well as numbers that extend infinitely without repeating patterns.

Integers, on the other hand, are a subset of real numbers and represent whole numbers without fractional or decimal parts. Integers include positive numbers, negative numbers, and zero.

While real numbers can include integers, they also include non-integer values that have decimal representations. These decimal numbers can be finite, such as 0.5 or 3.14, or they can be infinite and non-repeating, such as the square root of 2 (approximately 1.41421356).

Therefore, the correct answer is real numbers, as it encompasses numbers with decimal points and includes both integers and non-integers.

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To find the determinant of a matrix using row reduction to echelon form, you can follow these steps:

1. Start with the given matrix.

2. Apply row operations to convert the matrix into echelon form. Row operations include multiplying a row by a nonzero scalar, adding a multiple of one row to another, and swapping two rows.

3. Continue performing row operations until you reach the echelon form, where all leading coefficients (the leftmost nonzero entry in each row) are 1 and the entries below leading coefficients are all zeros.

4. Once you have the matrix in echelon form, the determinant can be calculated by multiplying the leading coefficients of each row.

5. If you perform any row swaps during the row reduction process, keep track of the number of swaps. If the number of swaps is odd, multiply the determinant by -1.

Let's look at an example to illustrate these steps. Suppose we have the following 3x3 matrix:

| 2  1  3 |
| 1 -2 -4 |
| 3  0  1 |

Step 1: Start with the given matrix.

Step 2: Apply row operations to convert the matrix into echelon form.

First, we can multiply the first row by -1/2 and add it to the second row, resulting in:

| 2   1   3  |
| 0  -5/2 -5/2|
| 3   0    1  |

Next, multiply the first row by -3/2 and add it to the third row, giving us:

| 2   1   3  |
| 0  -5/2 -5/2|
| 0  -3/2 -8/2|

Finally, multiply the second row by -2/5 to get a leading coefficient of 1:

| 2   1   3  |
| 0   1    1 |
| 0  -3/2 -8/2|

Step 3: The matrix is now in echelon form.

Step 4: Calculate the determinant by multiplying the leading coefficients of each row:

2 * 1 * (-8/2) = -8

Step 5: Since no row swaps were performed, we don't need to multiply the determinant by -1.

Therefore, the determinant of the given matrix is -8.

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Answer:

- 2 < x < 6

Step-by-step explanation:

- 6 < x - 4 < 2 ( add 4 to each interval )

- 2 < x < 6

Answer:

Below

Step-by-step explanation:

Part A: -1 and 2.5

Part B: The vertex is a minimum

Part C: tbh, I'm not quite sure about this part but just use parts A and B to answer :)

(you can also use the website desmos. com/calculator as a graphing calculator)

Answer:

answer is for x value 2/3

A countable set is the union of two countable sets. for each kN. Now that AB=cn:nN, it may be counted because it is an infinite set.

A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.

In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.

No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.

One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.

Hence, A countable set is the union of two countable sets. for each kN. Now that AB=cn:nN, it may be counted because it is an infinite set.

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Answer: 44 possible outcomes

Step-by-step explanation:

Multiply the number of games by the number of outcomes to find how many possibilities.

22 games * 2 outcomes = 44 possibilities

Interpreting the situation, it is found that there are 23 possible outcomes for the season record.

For each game, there are two possible outcomes.

In this problem, there are 22 games, hence 23 possible outcomes.

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Increasing marginal productivity infers that extra units of capital and labor contribute more to yield, driving productive asset allotment. ∝ and ß < 1 expect reducing returns, adjusting with reality.

To appear that the generation work has to expand the marginal productivity of capital (in case ∝ > 1) and labor (on the off chance that ß > 1), we ought to take fractional subsidiaries with regard to each input calculation. For capital (K), the fractional subsidiary of the generation work is:

\(\dfrac{dy}{dK }= \alpha AK^{(\alpha-1)}L^\beta\)

Since ∝ > 1, (∝ - 1) is positive, which implies that the fractional subordinate \(\dfrac{dy}{dK}\) is positive. This shows that an increment in capital input (K) leads to an increment in yield (y), appearing to expand the marginal efficiency of capital.

Additionally, for labor (L), the fractional subordinate of the generation work is:

\(\dfrac{dy}{dL} = \beta AK^{\alpha}L^{(\beta-1)}\)

Since \(\mathbf{\beta > 1, (\beta-1)}\) it is positive, which implies that the halfway subordinate \(\dfrac{dy}{dL}\) is positive. This demonstrates that an increment in labor input (L) leads to an increment in yield (y), appearing to increase the marginal productivity

The economic importance of increasing marginal productivity is that extra units of capital and labor contribute more to yield as their amounts increment.  This suggests that the more capital and labor a firm employments, the higher the rate of increment in yield. This relationship is vital for deciding the ideal assignment of assets and maximizing generation effectiveness.

In most generation capacities, it is accepted that ∝ and ß are less than 1. This presumption adjusts with experimental perceptions and financial hypotheses.

In case ∝ or ß were more prominent than 1, it would suggest that the marginal efficiency of the respective factor increments without bound as the calculated input increments.

In any case, there are decreasing returns to scale, which suggests that as calculated inputs increment, the Marginal efficiency tends to diminish. Therefore, accepting ∝ and ß are less than 1 permits for more reasonable modeling of generation forms and adjusts with the concept of diminishing marginal returns.

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Angle in a semi-circle is a right angle then, angle x is 90°, Z is 100° and y is 53° (refer below figure)

The six trigonometric functions of an angle in a right-angled triangle are connected by a set of fundamental identities known as the "Circle identities" in trigonometry.

In a semicircle AGE, angle at the circumference is 90 degree.

then, angle x = 90°

and arc Z° from the center of circle is a triangle AOB, see below figure,

40° + Z° + 40° = 180°

Then, Z° = 100°

Similarly, arc 74° from center of circle is a triangle EOG;

74°+ y° + y° = 180°

Then, y° = 53°

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Answer:

F and D

Step-by-step explanation:

there 2 out of the other lead

a. The two sample means are: Sample 1 mean = 9 and Sample 2 mean = 7.

b. The two sample standard deviations are: Sample 1 standard deviation = 2.74 and Sample 2 standard deviation = 1.63.

c. The point estimate of the difference between the two population means is 2.

d. The confidence interval estimate of the difference between the two population means is (-2.36, 6.36).

To calculate the sample mean, you add up all the values in each sample and divide by the number of observations. In Sample 1, the sum of the values is:

= 10 + 7 + 13 + 7 + 9 + 8

= 54

And since there are 6 observations, the mean is 54/6 = 9.

Similarly, in Sample 2, the sum of the values is:

= 8 + 7 + 8 + 4 + 6 + 9

= 42

And since there are 6 observations, the mean is 42/6 = 7.

To calculate the sample standard deviation, you first calculate the variance by finding the average of the squared differences from the mean, and then take the square root of the variance. For Sample 1, the variance is:

=\(\frac{{(10-9)^2 + (7-9)^2 + (13-9)^2 + (7-9)^2 + (9-9)^2 + (8-9)^2}}{6}\)

= 7.2

And therefore the standard deviation is the square root of 7.2, which is approximately 2.74. Similarly, for Sample 2, the variance is:

= \(\(\frac{{(8-7)^2 + (7-7)^2 + (8-7)^2 + (4-7)^2 + (6-7)^2 + (9-7)^2}}{6}\)\)

= 3.2

And therefore the standard deviation is the square root of 3.2, which is approximately 1.63.

The point estimate of the difference between the two population means is simply the difference between the sample means. In this case, the sample mean of Sample 1 is 9 and the sample mean of Sample 2 is 7, so the point estimate of the difference is:

= 9 - 7

= 2

To calculate the confidence interval estimate of the difference between the two population means, we need to determine the margin of error and then construct the interval around the point estimate. Using a 95% confidence level, the margin of error can be calculated using the formula:

margin of error = critical value x standard error

The critical value for a 95% confidence level with two independent samples is approximately 1.96. The standard error is calculated by taking the square root of [(standard deviation of Sample 1)^2 / (sample size of Sample 1) + (standard deviation of Sample 2)^2 / (sample size of Sample 2)]. In this case, the margin of error is approximately 2.36, and thus the confidence interval estimate is:

2 - 2.36 to 2 + 2.36

This is gives us (-0.36, 4.36).

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Answer:

U = 16206 + 22.2x

Step-by-step explanation:

This year, water usage has increased by 20% for both regular days and special events.. Write an equation for the total water usage, U, at the park this year in terms of x, the number of special events the park has hosted

Solution:

Last year regular usage of water was 13505 gallons, where as it was 18.5 gallons per special event. Let us assume that there were x special invents, hence:

The total usage for last year = 13505 + 18.5x

This year, the total usage (U) increased by 20%, hence:

Total usage for this year (U) = total usage for last year + 20% of total usage for last year

U = (13505 + 18.5x) + 0.2(13505 + 18.5x)

U = 13505 + 18.5x + 2701 + 3.7x

U = 16206 + 22.2x