what is the slope of a line that passes through points (2,4) and (3,8)

Main Answer:The difference quotient for the function f(x) = x^2 - 5 is 2x + h.

Supporting Question and Answer:

How do we calculate the difference quotient for a given function?

To calculate the difference quotient for a function, we need to evaluate the expression (f(x + h) - f(x)) / h, where f(x) represents the given function and h is a non-zero value.

Body of the Solution:To find the difference quotient for the function f(x) = x^2 - 5, we need to evaluate the expression (f(x + h) - f(x)) / h.

First, let's find f(x + h):

f(x + h) = (x + h)^2 - 5

= x^2 + 2hx + h^2 - 5.

Now, let's subtract f(x) from f(x + h):

f(x + h) - f(x) = (x^2 + 2hx + h^2 - 5) - (x^2 - 5)

= x^2 + 2hx + h^2 - 5 - x^2 + 5

= 2hx + h^2.

Finally, divide the result by h: (f(x + h) - f(x)) / h = (2hx + h^2) / h = 2x + h.

Final Answer: So, the simplified difference quotient for the function f(x) = x^2 - 5 is 2x + h.

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The difference quotient for the function f(x) = x^2 - 5 is 2x + h.

To calculate the difference quotient for a function, we need to evaluate the expression (f(x + h) - f(x)) / h, where f(x) represents the given function and h is a non-zero value.

To find the difference quotient for the function f(x) = x^2 - 5, we need to evaluate the expression (f(x + h) - f(x)) / h.

First, let's find f(x + h):

f(x + h) = (x + h)^2 - 5

= x^2 + 2hx + h^2 - 5.

Now, let's subtract f(x) from f(x + h):

f(x + h) - f(x) = (x^2 + 2hx + h^2 - 5) - (x^2 - 5)

= x^2 + 2hx + h^2 - 5 - x^2 + 5

= 2hx + h^2.

Finally, divide the result by h: (f(x + h) - f(x)) / h = (2hx + h^2) / h = 2x + h.

So, the simplified difference quotient for the function f(x) = x^2 - 5 is 2x + h.

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Answer:

A. Independent

Step-by-step explanation:

The required probability is 0.132 .

What is normal approximation?

The sampling distribution of averages or proportions from a large number of independent trials approximately and the expectation of a sample proportion or average is the corresponding population value.

On solving using mean sampling method, we get

P(E) = 0.132

Hence, the required probability is 0.132 .

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Answer:

35% because 4 would be 50% so its prob around 35 or 40

Answer:

35% because 4 would be 50%

Step-by-step explanation:

Comparingthe F-ratio of 4.60 to these critical values, we see that it is greater than the value for α = .05, but less than the value for α = .01. Therefore, the correct statistical decision is to reject the null hypothesis with α = .05, but not with α = .01. Option a) is the correct answer.

An independent-measures analysis of variance (ANOVA) is a statistical test used to evaluate the mean differences between two or more groups. In this case, we are comparing four treatments, each with a separate sample of n = 8.

The null hypothesis for an ANOVA is that there are no significant differences between the means of the groups being compared. The alternative hypothesis is that at least one of the means is different from the others.

To test this hypothesis, we use an F-ratio, which is the ratio of the variance between groups to the variance within groups. If the F-ratio is large enough, we can reject the null hypothesis and conclude that there are significant differences between the means.

In this case, the data produce an F-ratio of F = 4.60. To make a statistical decision, we need to compare this value to a critical value from an F-distribution table. The critical value depends on the degrees of freedom for the numerator and denominator of the F-ratio, as well as the level of significance (α) chosen for the test.

Since we have four groups, the numerator degrees of freedom are k-1 = 3, where k is the number of groups. The denominator degrees of freedom are (k-1)(n-1) = 21, where n is the sample size for each group.

For a two-tailed test with α = .05, the critical F-value for these degrees of freedom is 3.10. For α = .01, the critical value is 5.10.

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Answer:

Step-by-step explanation:

\(45.60 \times 15\% \\ 45.60 \times \frac{15}{100} \\ \frac{684}{100} \\ 6.84\)

Answer:

I think it is the first one as you add the 4 like from the other

Answer:

Step-by-step explanation:

\(f(x)=3x-11\)

\(f(-x)=3(-x)-11=-3x-11\)

I hope this is what you are asking for...apologies if not.

To find the indicated probabilities, we need to calculate the area under the normal distribution curve.

For the first problem:

μ = 22

σ = 3.4

We want to find P(x ≥ 30), which is the probability that x is greater than or equal to 30.

To find this probability, we can calculate the z-score using the formula:

z = (x - μ) / σ

Substituting the values:

z = (30 - 22) / 3.4

z = 8 / 3.4

z ≈ 2.35

Now, we can use a standard normal distribution table or a calculator to find the corresponding cumulative probability.

P(x ≥ 30) = P(z ≥ 2.35)

Looking up the value in a standard normal distribution table or using a calculator, we find that P(z ≥ 2.35) is approximately 0.0094.

Therefore, P(x ≥ 30) ≈ 0.0094.

For the second problem:

μ = 4

σ = 2

We want to find P(3 ≤ x ≤ 6), which is the probability that x is between 3 and 6 (inclusive).

To find this probability, we can calculate the z-scores for the lower and upper bounds using the formula:

z = (x - μ) / σ

For the lower bound:

z1 = (3 - 4) / 2

z1 = -1 / 2

z1 = -0.5

For the upper bound:

z2 = (6 - 4) / 2

z2 = 2 / 2

z2 = 1

Now, we can use a standard normal distribution table or a calculator to find the corresponding cumulative probabilities.

P(3 ≤ x ≤ 6) = P(-0.5 ≤ z ≤ 1)

Using a standard normal distribution table or a calculator, we find that P(-0.5 ≤ z ≤ 1) is approximately 0.3830.

Therefore, P(3 ≤ x ≤ 6) ≈ 0.3830.

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Answer:

a)1280 bacteria

Step-by-step explanation:

We find the function in t hours first

Bacteria in a petri dish doubles every 10 minutes. (Express in exponential function)

a) If there are 10 bacteria initially, how many are there after 120 minutes?

b) If there are 10 bacteria initially, when would there be a million bacteria?

The formula to use is given as

y = Ab^t

Where

y = Total Population of bacteria

B= initial population of the bacteria

r =

t = time in hours

The bacteria doubles in the petri dish every 10 minutes, we have 10 bacteria

10 minutes in hours = 10/60= 1/6 hours

10 × 2 = 10b^10/60

20 = 10b ^1/6

2 = b^1/6

Multiply both sides by Power of 6

2^6 = b

b = 64

Hence, y = 10×(64)^t

a) If there are 10 bacteria initially, how many are there after 120 minutes?

120 minutes in hours = 2

y = 10(64)²

y = 1280

There would be 1280 bacteria after 120 minutes

b) If there are 10 bacteria initially, when would there be a million bacteria?

y= 1,000,000

A = 10 bacteria

b = 64

t = ???

1000000 = 10 × (64)^t

Divide both sides by 10

100000 = (64)^t

The absolute maximum value of the function f(x) = 5x - 10 cos(x) on the interval [-2, 0] is approximately 4.13.

To find the absolute maximum and minimum values of the function f(x) = 5x - 10 cos(x) on the interval [-2, 0], we can use calculus. First, we need to find the critical points by taking the derivative of the function and setting it equal to zero. The derivative of f(x) is f'(x) = 5 + 10 sin(x). Setting f'(x) = 0, we get 5 + 10 sin(x) = 0, which gives sin(x) = -1/2. Solving for x, we find x = 7π/6 and x = 11π/6 as the critical points.

Next, we evaluate the function f(x) at the critical points and the endpoints of the interval [-2, 0]. We have f(-2) ≈ -10.96, f(0) = 0, f(7π/6) ≈ 2.66, and f(11π/6) ≈ -8.32. Therefore, the absolute maximum value of f(x) on the interval is approximately 4.13, which occurs at x ≈ 7π/6.

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Answer:

unoriginal presidential play insisting that the president is a little more aggressive and more aggressive 6PM to the

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Given:

A roofer earns ​$25 per hour for regular hours worked and ​$30 per hour for overtime hours worked. He puts in 40 hours of regular time during a certain week and he wishes to earn ​$1140​.

Required:

To find how many hours of overtime should he​ work.

Explanation:

Let he should work x hours overtime.

Then the equation becomes:

He should work approximately 5 hours.

Final Answer:

He should work approximately 5 hours overtime.

Answer:

you got it right

Step-by-step explanation:

The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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Answer:

Step-by-step explanation:

you have a right triangle,

a^2+b^2=c^2

10^2=4^2+b^2

100=16+b^2

100-16=b^2

84=b^2

b=9.16

This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Answer:

60

Step-by-step explanation:

Plug in 4 for y

3(4)² + (4) + 8

3(16) + 4 + 8

48 + 12

60

Answer:

I think it is C sorry if it wrong

Step-by-step explanation:

Answer:

I got A

Step-by-step explanation:

It was on Plato

A transition mutation is a point mutation that transforms one nucleotide from one type of purine to another (A to G) or from one type of pyrimidine to another (C to T). G and C are substituted for A and T, respectively, and G is a different purine and C is a different pyrimidine.

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Answer:

The absolute value is the distance between a number and zero. The distance between −13 - 13 and 0 0 is 13 13 . −1⋅13 - 1 ⋅ 13. Multiply −1 - 1 by 13 13 .

Step-by-step explanation:

Happy to Help   13

The Prove of sinMm=sinPp are:

A triangle that is known to have only one of its interior angles to be 90° is known to be a right triangle.

Note that  sinMm=sinPp is said to be a right triangle as it has its longest side to be the right triangle and it follows the Substitution property of equality and Division property of Equality.

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Answer:

9 1/3

Step-by-step explanation:

1. Make 4 2/3 into a improper fraction

4 2/3= 14/3

2. Keep, change, flip

14/3 x 2/1

3. Multiply

14/3 x 2/1= 28/3

4. Simplify

28/3= 9 1/3

(btw keep, change, flip basically means to keep the first fraction the way it is, change the division sign to a multiplication sign, then flip the second fraction so the original denominator is the new numerator, and vise versa.)

Answer:

28/3

Step-by-step explanation:

4 2/3 ÷ 1/2

14/3 ÷ 1/2

6(14/3 ÷ 1/2)

28 ÷ 3

28/3

Answer: c=-6

Step-by-step explanation:

First let's subtract 4 from both sides

\(5c+4-4=-26-4\\5c=-30\)

Now we can divide 5 on both sides

\(\frac{5c}{5} =\frac{-30}{5} \\c=-6\)

We can sub -6 back in to the original equation to check the answer

\(5(-6)+4=-26\\-30+4=-26\\-26=-26\)

It checks out!

Answer:

D is the correct option.

All the best!

Answer:

rational

Step-by-step explanation: