3. What are the factors in the expression 4(5 + x)?

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

Find out more information about difference quotient here:

https://brainly.com/question/18270597

#SPJ4

To compute the effect size, we can use the formula:

ES = (|Ž - X|) / SD

where Ž is the mean for Group 1, X is the mean for Group 2, and SD is the standard deviation from either group as the given question.

Using the given values, we have:

Experiment 1: ES = (|78.6 - 73.4|) / 2 = 2.6

Experiment 2: ES = (|78.6 - 73.4|) / 4 = 1.3

Experiment 3: ES = (|78.6 - 73.4|) / 8 = 0.65

From the experiments 1, 2, 3, we can see that the standard deviation increases, the effect size decreases.

It means that the larger SD makes it harder to detect a meaningful difference between the two groups.

To know more about standard deviation, visit: https://brainly.com/question/475676

#SPJ1

Answer:

heat map is the answer

Answer:

uh

Step-by-step explanation:

i dont know

According to the given statement The faster computer will take 2 minutes to send out the company's email on its own.

To solve this problem, let's assign variables to the given information. Let "x" represent the time it takes the slower computer to send out the company's email on its own, and let "y" represent the time it takes both computers working together to send out the email.

According to the problem, it takes two computers "y" minutes to send out the email, and it takes the slower computer "x" minutes to do the job on its own.

Since the two computers are working together, we can set up the following equation: 1/x + 1/y = 1/t, where "t" represents the time it takes the faster computer to do the job on its own.

Substituting the given values into the equation, we have: 1/x + 1/y = 1/2y

To find the value of "t", we need to solve for "y" in terms of "x". Multiply both sides of the equation by 2xy to eliminate the denominators:

2y + 2x = xy

Rearranging the equation, we get:

xy - 2y - 2x = 0

Now, let's factor the equation:

y(x - 2) - 2(x - 2) = 0

Simplifying further:

(x - 2)(y - 2) = 0

Since we are looking for the time it takes the faster computer to do the job on its own, we disregard the solution (y - 2) = 0, which gives us y = 2.

Therefore, the faster computer will take 2 minutes to send out the company's email on its own.

To know more about company's  visit:

https://brainly.com/question/30532251

#SPJ11

Step-by-step explanation:

For y = x^3 - 4 when x = 0, y = -4.

For y = x^2 + 3 when x = 0, y = 3.

Looking at the graph, the y-intercept of the function is below 0. Hence the bottom part is from x^3 - 4 and the top is from x^2 + 3.

The bottom part has a dark circle, which means when x = 1 it belongs to x^3 - 4.

Hence the answer is D.

Answer:

r = -19

Step-by-step explanation:

To find the value of r, we can use the slope formula and the two given points:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (3, r) and (x2, y2) = (1, -7).

Substituting these values, we get:

6 = (-7 - r) / (1 - 3)

Simplifying and solving for r, we get:

6 = (-7 - r) / (-2)

Multiplying both sides by -2, we get:

-12 = 7 + r

Subtracting 7 from both sides, we get:

r = -19

Therefore, the value of r is -19.

The option D "64/25, because probability values cannot be greater than 1" and option F "-1.5, because probability values cannot be less than 0" could not be used to represent the probability of an event.

In the given question, we have to determine which numbers could not be used to represent the probability of an event.

Let P be the probability.

It can accept any value [0,1] (inclusive of 0, 1), as well as [0%, 100%] (inclusive of 0% and 100%).

It is unable to accept negative values.

Because probability values cannot be larger than one or less than one, 64/25 and -1.5, respectively, cannot be used to indicate the likelihood of an evens.

So, the option D "64/25, because probability values cannot be greater than 1" and option F "-1.5, because probability values cannot be less than 0" could not be used to represent the probability of an event.

To learn more about probability link is here

brainly.com/question/30034780

#SPJ4

The survey mode that is not mentioned in the text is "puter-administered." The correct option is b: puter-administered.

The following is not a survey mode mentioned in the text: a.person-administered. b: puter-administered. c.self-administered. d.mixed-mode.

Know more about the survey

https://brainly.com/question/19637329

#SPJ11

To go from the first town to the second town, you must drive 137.5 miles.

What is an proportion?

A proportion is a mathematical equation that compares two ratios. It is usually written as two equal fractions or ratios, one on each side of the equation. A proportion can be used to compare the relationship between different quantities, such as measurements, rates, or even time.

We can use proportion to solve this problem. The proportion relates the map scale to the actual distance:

0.75 inch / 50 miles = x / distance

where x is the actual distance we want to find.

We can cross-multiply and solve for x:

0.75 inch * distance = 2.75 inches * 50 miles

x = (2.75 inches * 50 miles) / 0.75 inch

x = (137.5 miles)

To go from the first town to the second town, you must drive 137.5 miles.

To learn more about proportion, Visit

https://brainly.com/question/1496357

#SPJ1

Answer:

Step-by-step explanation:

The first one is equal to.  203/203 is equal to 1.  1 times any number is itself.

The second on is less than.  9/37 is a proper fraction and when a number is multiplied by a proper fraction, it gets smaller.

There are a total of 212 pounds of berries, and the number of friends sharing the berries is equal to 4.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

The total amount of berries = 212 pounds

The number of berries received by each one = 54 pounds

Then, the number of friends sharing the berries is:

212/54 = 3.92 ≈ 4 friends.

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ1

Given:

The sides of the right triangular base measures 9 cm, 12 cm and 15 cm.

The height of the prism is 20 cm.

To find:

The surface area of a triangular prism.

Solution:

We know that, the area of a triangular prism is

\(A=P\times h\)

Where, P is the perimeter of the triangular base and h is the height of the prism.

The sides of the right triangular base measures 9 cm, 12 cm and 15 cm. So, the perimeter of the right triangular base is

\(P=9+12+15\)

\(P=36\)

Now, the area of the triangular prism is

\(A=36\times 20\)

\(A=720\)

Therefore, the surface area of a triangular prism is 720 square centimetres.

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Answer: D

Step-by-step explanation:

plugged it into desmos

After 5 years, the amount in the account is $118,301, and the interest earned is $10,781. To calculate the amount in the account after 5 years, we can use the formula for the future value of an ordinary annuity:

A = PMT * ((1 + r)^n - 1) / r

Where:

A = Amount in the account after the specified time period

PMT = Monthly deposit

r = Monthly interest rate (annual interest rate divided by 12)

n = Total number of monthly deposits (time period in years multiplied by 12)

Given:

Monthly deposit (PMT) = $1,728

Annual interest rate = 6.6%

Time period = 5 years

First, we need to calculate the monthly interest rate (r) and the total number of monthly deposits (n):

r = 6.6% / 100 / 12 = 0.0055 (decimal)

n = 5 years * 12 = 60 months

Now we can plug these values into the formula to find the amount in the account after 5 years (A):

A = 1,728 * ((1 + 0.0055)^60 - 1) / 0.0055

Using a calculator, the amount in the account after 5 years comes out to be approximately $118,301 (rounded to the nearest dollar).

To calculate the amount of interest earned, we can subtract the total deposits made from the amount in the account:

Interest = A - (PMT * n)

Interest = 118,301 - (1,728 * 60)

Using a calculator, the interest earned comes out to be approximately $10,781 (rounded to the nearest dollar).

Therefore, after 5 years, the amount in the account is $118,301, and the interest earned is $10,781.

Learn more about future value here:

https://brainly.com/question/30787954

#SPJ11

Answer:

y=-2x+2

Step-by-step explanation:

it has a positive slope

the line should point like this on the graph: picture above

Answer:

$42.00

Step-by-step explanation:

So, something hasn't been subtracted from your bottom line. The bank is saying you only have $26.33. You think you have $68.33.

Let's look for the difference. This is one of those great times when the word in english and the word in math have the same meaning. Difference is telling us to subtract.

68.33 - 26.33

= 42.00

Check:

If you subtract the missing entry, $42.00 from your total,

68.33 - 42.00

you get $26.33, exactly the balance the bank says you have. Now your account is balanced!

Slope of the line passing through (-5,-4)  and (-1,3)is 1.75

The slope formula

slope = (y₂ - y₁) / (x₂ - x₁)

Notice that the slope of a line is easily calculated by hand using small, whole number coordinates. The formula becomes increasingly useful as the coordinates take on larger values or decimal values.

The  points belong to an increasing, linear function.

Equation: y = 1.75x + 4.75.

m=7/4=1.75.

Learn more about slope of straight line here:

https://brainly.com/question/3605446

#SPJ9

One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).

By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.

This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.

Option B holds true.

Learn more about frequency distribution: https://brainly.com/question/27820465

#SPJ11

Answer:

Step-by-step explanation:

a)  4.5m = 4.5×100 = 450 cm

b)  7.6km = 7.6×1000 = 7600 m

c)  68mm = 68÷10 = 6.8 cm

d) 190cm = 190÷100 = 1.9 m

...

Answer:

4,102,0004 comma 102 comma 000

Step-by-step explanation:

If it makes 292,827 candies in a day, to find the approximate value of candies produced in 2 weeks, you have to multiply 292,827 by 14, being 14 days in 2 weeks. But since this is just rounding, the easiest option is just to find the actual answer and see which one is closest.

Answer:

Base, 8 cm; height, 4 cm i think

Step-by-step explanation:

The Pythagorean triple formed is (16, 63, 65)

Any three positive numbers that fully satisfy the Pythagorean theorem are known as Pythagorean triples. According to the theorem, the square of any right triangle's hypotenuse is equal to the sum of the squares of its other two legs. The Pythagorean triples are made up of these three right triangle sides.

A three of positive numbers known as a Pythagorean triple fits into the Pythagoras theorem's formula, which is written as a2 + b2 = c2, where a, b, and c are all positive integers. Here, "a" and "b" make up the other two legs of the right-angled triangle, and "c" serves as the triangle's "hypotenuse," or longest side. In terms of the Pythagorean triples (a,b, c). The most widely used illustration of Pythagorean triples is (3, 4, 5). We can confirm that the numbers 3, 4, and 5 satisfy the formula a2 + b2 = c2.

By evaluating we get:

32 + 42 = 52

9+16 = 25

Hence, 3,4 and 5 are the Pythagorean triples

How to Form Pythagorean Triples?

You can say “triplets,” but “triples” are the favoured term. Let’s start this topic by an introduction of Pythagoras theorem.

The number may be even or odd, as we are all aware. Let's talk about how to make Pythagorean triples now.

If the number is odd, case 1:

Assume that "x" is the number.

The Pythagorean triple equals x, (x2/2) - 0.5, (x2/2) + 0.5 if "x" is an odd number.

As an illustration (7, 24, 25). Let's now talk about how to construct this Pythagorean triple.

X equals 7, making it an odd number.

(x2/2) – 0.5 = (49/2) – 0.5 = 24.5 – 0.5 = 24

(x2/2) + 0.5 = (49/2) + 0.5 = 24.5 + 0.5 = 25

Consequently, the triple generated by Pythagoras is (7, 24, 25).

Case 2: In an even number:

The Pythagorean triple is equal to x, (x/2)2-1, and (x/2)2+1 if "x" is even.Let us assume an example, (16, 63, 65). Now, we will check how to form the Pythagorean triple.

Here, x = 16, which is an even number.

(x/2)2 -1 = (16/2)2 – 1 = 82 – 1 = 64 – 1 = 63

(x/2)2 +1 = (16/2)2 +1 = 82 + 1 = 64 + 1 = 65.

Thus, the Pythagorean triple formed is (16, 63, 65)

To know more about Pythagorean triples visit : brainly.com/question/15190643

#SPJ4

Explanation:

Pick any two negative numbers to represent the x and y intercepts. Let's say we go for -2 and -3 as the x and y intercepts.

That leads to the locations (-2,0) and (0,-3)

Find the slope through these two points.

m = (y2-y1)/(x2-x1)

m = (-3-0)/(0-(-2))

m = (-3-0)/(0+2)

m = -3/2

m = -1.5

We get a negative slope. The line moves downhill as we move to the right.

Answer:

Step-by-step explanation:

3/4 * 24 = (3*24)/4

18 = 72 : 4

18 = 18

Answer: Percentage of half board students in college is 60%

Step-by-step explanation:

We know that percentage of desired quantity is:

n% = ( number of desired quantity / total number of quantity ) * 100

n% = ( n / N ) * 100  .......... (i)

where n% = percentage of desired quantity.

N = total number of quantity.

n = number of desired quantity.

Now, as per the question:

Half board students in college = 372

Total students in college = 620

percentage of Half board students in college = (372/620) * 100

n% = (372/620)*100

n% = 60%

Therefore, at 372 half board students in college , percentage of half board students in college is 60%.

Read more about Percentage:

https://brainly.com/question/24877689

\(3x - 4 < - 19\)

\( = x < - 5\)

\(3x -4 < -19 \\\\\implies 3x < -19 +4 \\\\\implies 3x< -15\\\\\implies x < -\dfrac{15}3\\\\\implies x< -5\\\\\text{Interval,}~ (-\infty, -5)\)

Approximately 95% of scores lie between -1.96 and 1.96 z-scores. This is because the area under the standard normal distribution curve between these two values is approximately 0.95.

To calculate this, first calculate the area under the standard normal distribution curve between -1.96 and 1.96. This can be done by using a Z-score table, which provides the area under the curve to the left of a given value. To calculate the area between -1.96 and 1.96, subtract the area to the left of -1.96 from the area to the left of 1.96. This is approximately 0.95.

Since the total area under the curve is 1, this implies that approximately 95% of scores lie between -1.96 and 1.96 z-scores. This is commonly known as the "95% Rule," and it is a useful way to quickly estimate the amount of scores that are within a certain range.

It is important to note that this calculation is only an approximation, as the exact value depends on the actual values that are used. Therefore, it is important to use a Z-score table with more accurate values if more precision is needed.

See more about normal distribution at: https://brainly.com/question/14243195

#SPJ11