How do you find slope on a coordinate plane

Answer:

1. y= -3x+4

2. y= 2/5x-1

3. y= -4

4. x= 2

5. y= 2x+7

Answer:

D: {0 ≤ x ≤ 6.25}

Step-by-step explanation:

6.25 is an approximation

The Marginal Rate of Substitution (MRS) for the given function is equal to -2/sqrt(x). To find the Marginal Rate of Substitution (MRS), we need to take the derivative of the given function with respect to x.

Given: y = 24 - 4(sqrt(x))

Step 1: Differentiate the function y with respect to x.

dy/dx = d/dx(24 - 4(sqrt(x)))

Step 2: Differentiate each term separately using the power rule and chain rule.

dy/dx = 0 - 4(1/2)(x^(-1/2))(1)

Step 3: Simplify the derivative.

dy/dx = -2(x^(-1/2))

Step 4: Rewrite the derivative in terms of MRS.

MRS = dy/dx = -2/sqrt(x)

Therefore, the Marginal Rate of Substitution (MRS) for the given function y = 24 - 4(sqrt(x)) is -2/sqrt(x).

The negative sign indicates that the MRS is inversely related to x, which means as x increases, the MRS decreases. The value of MRS represents the rate at which a consumer is willing to substitute y (the dependent variable) for an incremental change in x (the independent variable). In this case, as x increases, the consumer is willing to substitute less y for the additional units of x.

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Answer:

rational

Step-by-step explanation:

sqrt(36) = ±6

This is a rational number since we can write it as a fraction of integers

±6/1

Answer:

Rational Number.

Step-by-step explanation:

Simplify √36:

√36 = √(6 * 6) = 6

6 is a rational number (whole number), therefore, √36 is a rational number.

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Answer:

Sarah would take 35 minutes longer than Leo to type 5500 word essay

Step-by-step explanation:

Let us solve the question

∵ It took Leo 3 hours to type a 4125-word essay

→ The rate is the number of words divided by the time

∴ Leo's rate = 4125 ÷ 3 = 1375 words/hour

∵ Sarah typed her 3800-word essay in 3 hours and 10 minutes

→ Change the 10 min to the hour by divide it by 60

∵ 3 hours 10 min = 3 + \(\frac{10}{60}\) = 3 + \(\frac{1}{6}\)  = 3\(\frac{1}{6}\) hours

∴ Sarah's rate = 3800 ÷ 3\(\frac{1}{6}\)  = 1200 words/hour

∵ Leo will type a 5500-word essay

→ Divide it by his rate to find the time taken

∴ Leo takes = 5500 ÷ 1375 = 4 hours

∵ Sarah will type a 5500-word essay

→ Divide it by her rate to find the time taken

∴ Sarah takes = 5500 ÷ 1200 = 4\(\frac{7}{12}\) hours

→ Find the difference between their times

∵ The difference = 4\(\frac{7}{12}\) - 4 = \(\frac{7}{12}\) hour

→ Multiply it by 60 to change to minutes

∴ The difference = \(\frac{7}{12}\) × 60 = 35 minutes

∴ Sarah would take 35 minutes longer than Leo to type 5500 word essay

The new function after applying the sequence of transformation include: B. 1/2f(x + 5) - 11

In Mathematics and Geometry, the translation of a graph to the left means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x + N)

Conversely, the translation of a graph downward means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

Since the parent function f(x) was translated 11 units downward, 5 units to the left, and vertically compressed (making it wider) by a factor of 1/2, the equation of the image g(x), we have:

g(x) = 1/2f(x + 5) - 11

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Complete Question:

If f(x) is transformed by compressing the function vertically (making it wider) by a factor of 1/2, shifting 5 units to the left, and shifting 11 units downward, what will be the new function?

Answer: one degree of latitude is equal to 60 Minutes

Steps-  We Know that-

                                    1 min = 60 sec

                                    1 day = 24 hrs

  Additionally, The hour hand measures the clock's 360 degree arcs twice         throughout the day, i.e.

                                     2*360= 720 degree

                                     1 degree 2*360/12= 60 min

Hence proved 1 degree = 60 Minutes

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Answer:

L= 12

Step-by-step explanation:

area= L×B

108= 9×L

108= 9L

Divide both sides by 9

108/9= 9L/9

L= 12

Answer:

90

Step-by-step explanation:

90 degree angle is a perfect square

Answer:

B)  81

Step-by-step explanation:

Answer:

C. 3x + 5  = 2x -6

Step-by-step explanation:

The explanation of each of the term are defined below.

The order of each reactant is known as the reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations.

The term rate law expression in math is defined as the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power in which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.

The term overall order of the reaction is known as  the sum of orders for each reactant.

Finally value of the rate constant means the rate constant is temperature dependent.

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Answer:

17

Step-by-step explanation:

it's sufficient to set x=7

g(7)=2×7+3=14+3=17

Answer:

g(7)=2.7+3=17

Answer: you would need to buy 2 bags of popcorn and 3 bags of candies

Step-by-step explanation:

you would need to buy 2 bags of popcorn and 3 bags of candies because you would have to have a .50 at the total amount, so the answers for the bags of candy could be 5, or 3, or 1. It couldn't be 5 because it is a total of candy AND bags of popcorn, and it couldn't be 1 because 4*6= 24, so it would have to be 3 bags of candy, and 3+2=5 so there would have to be 2 bags of popcorn

The test statistic (42.19) falls between the lower and upper critical values (13.839 and 42.982) and the p-value (0.057) is greater than the significance level (0.05), we do not reject the null hypothesis.

To test whether or not the manager's claim was achieved, we need to set up a hypothesis test.

Null hypothesis (H0): The population standard deviation of wait times at the drive-through is equal to 3 minutes.
Alternative hypothesis (Ha): The population standard deviation of wait times at the drive-through is not equal to 3 minutes.

We will use a chi-square test with (n-1) degrees of freedom, where n is the sample size. At a 5% level of significance, the critical values are 12.242 (lower) and 41.337 (upper).

To calculate the test statistic, we use the formula:
χ^2 = (n-1) * s^2 / σ^2

where n is the sample size, s is the sample standard deviation, and σ is the hypothesized population standard deviation.

Plugging in the values, we get:
χ^2 = (28-1) * 3.75^2 / 3^2 = 30.1875

The corresponding p-value for this test statistic is 0.168, which is greater than 0.05. Therefore, we fail to reject the null hypothesis.

Our conclusion is: Do not reject the null hypothesis. There is insufficient evidence to support the Manager's claim.
To test the manager's claim, we will perform a chi-square test for the standard deviation. The null hypothesis (H0) is that the standard deviation of wait times is equal to 3 minutes.

First, we calculate the test statistic (rounded to 2 decimal places):

Chi-square = (n - 1) * (s^2) / σ^2
Chi-square = (28 - 1) * (3.75^2) / (3^2)
Chi-square = 27 * (14.0625) / 9
Chi-square = 42.19

Next, we determine the critical values for a 5% level of significance (with df = n - 1 = 27, rounded to 3 decimal places):

Lower critical value: 13.839
Upper critical value: 42.982

Now, we find the p-value (rounded to 3 decimal places):

p-value = P(Chi-square > 42.19) = 0.057

Since the test statistic (42.19) falls between the lower and upper critical values (13.839 and 42.982) and the p-value (0.057) is greater than the significance level (0.05), we do not reject the null hypothesis. There is insufficient evidence to support the manager's claim.

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Answer:

  10.)  -46 -38i

  11.)  12 +8i

Step-by-step explanation:

You want the products (2+6i)(-8+5i) and 4i(2-3i) expressed in standard form.

An expression containing i can be expanded or simplified by treating i the same as any other variable. All instances of i² can be replaced by -1.

  (2 +6i)(-8 +5i) = (2)(-8) +2(5i) +(6i)(-8) +(6i)(5i)

  = -16 +10i -48i +30i² . . . . . . i² = -1

  = -46 -38i

  4i(2 -3i) = (4i)(2) +(4i)(-3i) = 8i -12i²

  = 12 +8i . . . . . . . i² = -1

Answer:

divide them both by 2 to get 6/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

divide by two or a common factor

The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

What is a normal distribution?

A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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Answer:

I think it is 2.94 cm

Answer:

7.4676

Step-by-step explanation:

19.88-16.94=2.94 then convert it to cm 7.4676

The missing information for the SAS congruence theorem is given as follows:

B. SU = JL.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The congruent angles for this problem are given as follows:

<S and <J.

Hence the proportional side lengths are given as follows:

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There are 720 ways the first three positions of the order of finish can occur assuming no ties in a race with 10 horses.

To calculate the number of ways the first three positions can occur, we use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we are choosing.

In this case, we have 10 horses and we want to choose the first three positions, so we get:

10P3 = 10! / (10 - 3)! = 10! / 7! = (10 x 9 x 8) / (3 x 2 x 1) = 720

Therefore, there are 720 ways the first three positions of the order of finish can occur assuming no ties.

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Answer:

.05

Step-by-step explanation:

to get a percent, you multiply by 100. so take 5 and divide by 100 to get decimal

The above expression in terms of 8n can be written as 8(0).

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.

We are given a an expression (8-8)(8³)

Now the first bracket after simplifying we get an answer is 0.

Hence the expression can be given in the form of 8(n) as 8(0)

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Answer:

given

area of triangle = 48

height(h)=12

base(b) =‽

now,

area of triangle(a) =1/2 base×height

48=1/2 b×12

48=b×6

b=8

Answer:

4

Step-by-step explanation:

First of all, subtract the rental fee. 357 - 85 = 272. Now, simply divide 272 by 68 to find the number of hours. 272 / 68 = 4.

By the end of the 24th day of autumn, there is exactly 1,594,323 number leaf total on the ground.

So, let uscalculate the total number of leaves as follows:

A number of leaves on day 1.

A number of leaves on day 2.

A number of leaves of day 3.

A number of leaves on day 4.

A number of leaves on day 5.

A number of leaves on day 6.

A number of leaves of day 7.

A number of leaves on day 8.

A number of leaves on day 9.

A number of leaves on day 10.

A number of leaves on day 11.

A number of leaves on day 12.

A number of leaves on day 13.

Therefore, by the end of the 24th day of autumn, there is exactly 1,594,323 number leaf total on the ground.

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The given sequence is 6, 4.8, 3.6, 2.4, 1.2, ...

To find the nth term of this sequence, we can observe that each term is obtained by multiplying the previous term by 0.8. Therefore, the common ratio between the terms is 0.8.

To find the nth term, we can use the formula: an = \(a1 * r^{n-1)},\) where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

For this sequence, a1 = 6 and r = 0.8.

For the 1st term (n = 1): a1 = 6

For the 2nd term (n = 2): a2 =\(6 * 0.8^{(2-1)}\) = 4.8

For the 3rd term (n = 3): a3 =\(6 * 0.8^{(3-1)}\) = 3.84

For the 4th term (n = 4): a4 = \(6 * 0.8^{(4-1)}\)= 3.072

For the 5th term (n = 5): a5 =\(6 * 0.8^{(5-1)}\) = 2.4576

Therefore, the nth term for this sequence is an = 6 * 0.8^(n-1), and the 1525th term would be a1525 = \(6 * 0.8^{(1525-1)}.\)

The given sequence is 13, 11, 9, 7, 5, ...

To find the nth term of this sequence, we can observe that each term is obtained by subtracting 2 from the previous term. Therefore, the common difference between the terms is -2.

To find the nth term, we can use the formula: an = a1 + d * (n-1), where an is the nth term, a1 is the first term, d is the common difference, and n is the term number.

For this sequence, a1 = 13 and d = -2.

For the 1st term (n = 1): \(a1 = 13\)

For the 2nd term (n = 2): \(a2 = 13 + (-2) * (2-1) = 11\)

For the 3rd term (n = 3): \(a3 = 13 + (-2) * (3-1) = 9\)

For the 4th term (n = 4): \(a4 = 13 + (-2) * (4-1) = 7\)

For the 5th term (n = 5): \(a5 = 13 + (-2) * (5-1) = 5\)

Therefore, the nth term for this sequence is an = \(13 + (-2) * (n-1\)), and the 1525th term would be \(a1525 = 13 + (-2) * (1525-1).\)

The given explicit formula for the arithmetic sequence is nth = 65 - 100n.

To find the first five terms, we substitute n = 1, 2, 3, 4, and 5 into the formula:

For the 1st term (n = 1): \(a1 = 65 - 100 * 1 = -35\)

For the 2nd term (n = 2): \(a3 = 65 - 100 * 3 = -235\)

For the 3rd term(n = 3): \(a3 = 65 - 100 * 3 = -235\)

For the 4th term (n = 4): \(a4 = 65 - 100 * 4 = -335\)

For the 5th term (n = 5): \(a5 = 65 - 100 * 5 = -435\)

Therefore, the first five terms of this arithmetic sequence are: -35, -135, -235, -335, -435.

To find the 39th term, we substitute n = 39 into the formula:

\(a39 = 65 - 100 * 39 = 65 - 3900 = -3835\)

Therefore, the 39th term of this arithmetic sequence is -3835.

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Answer:

√34

Step-by-step explanation:

To find the distance between two points, you can use the distance formula, which is:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

We can plug in the points (3, 7) and (-2, 10) to get:

d = √[(-2 - 3)^2 + (10 - 7)^2]

We can simplify.

d = √[(-5)^2 + (3)^2]

d = √(25 + 9)

d = √(34)

d =  √34

Answer:

-52

Step-by-step explanation:

I hope this helps!

Answer: -52

Step-by-step explanation: Using PEMDAS

(2x3)+4-62

6+4-62

10-62

= -52

If the mean number of particles is exactly seven per mL, the probability that X is less than or equal to 1 is approximately 0.000911881965, or about 0.0912%.

If the mean number of particles is exactly seven per mL, we can assume that the distribution of X, the number of particles in a 1 mL sample, follows a Poisson distribution with λ = 7.

To calculate P(X ≤ 1), we need to find the cumulative probability of X taking on values less than or equal to 1.

P(X ≤ 1) = P(X = 0) + P(X = 1)

Using the Poisson probability mass function (PMF), we can calculate each term:

P(X = k) = (e^(-λ) * λ^k) / k!

Let's calculate each term:

P(X = 0) = (e^(-7) * 7^0) / 0! = e^(-7)

P(X = 1) = (e^(-7) * 7^1) / 1! = 7e^(-7)

Now, we can calculate P(X ≤ 1):

P(X ≤ 1) = e^(-7) + 7e^(-7)

Using a calculator, we can evaluate this expression:

P(X ≤ 1) ≈ 0.000911881965

Therefore, if the mean number of particles is exactly seven per mL, the probability that X is less than or equal to 1 is approximately 0.000911881965, or about 0.0912%.

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