Find each product.

29. (r-1)(7r+2)
31. x²(3x-2)(5x+1)
37. (m-n+k)(m+2n-3k)
43. (2m+3)(2m-3)
45. (4x²-5y)(4x²+5y)

Answer: 2.5, 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)

Answer:

the last one

Step-by-step explanation:

The total number of steps from the 1st floor to the 6th floor in a 10-story building with 15 steps in a flight of stairs is 60.

In a 10-story building, a flight of stairs has 15 steps.

What is the total number of steps from the 1st floor to the 6th floor.

The total number of steps from the 1st floor to the 6th floor in a 10-story building with 15 steps in a flight of stairs is as follows:

Take into consideration the following:

Given that a flight of stairs in a 10-story building has 15 steps, therefore a total number of steps on 10th floor would be;N1 = 10 * 15N1 = 150.

Similarly, the total number of steps on the 6th floor would be;

N2 = 6 * 15N2 = 90

Finally, the total number of steps from the 1st floor to the 6th floor will be;

Total number of steps = N1 – N2

Total number of steps = 150 – 90

Total number of steps = 60

For similar question on floor.

https://brainly.com/question/29425092

#SPJ11

The height of the cylinder is approximately 5.97 cm.

A cylinder is a three-dimensional geometric shape that consists of two parallel, congruent circular bases and a curved lateral surface that connects the bases. The bases are perpendicular to the lateral surface, which means that the lateral surface forms a curved rectangle.

Given;

The circumference of the cylinder is 32π.

The lateral surface area of the cylinder is 750 cm².

Lateral surface area of a cylinder = 2πrh

Circumference of a cylinder = 2πr

We can use the circumference formula to find the radius of the cylinder:

2πr = 32π

r = 16

Now we can use the lateral surface area formula to find the height of the cylinder:

750 = 2π(16)(h)

750 = 32πh

h = 750/(32π)

h ≈ 5.97

As a result, the cylinder's height is around 5.97 cm.

To know more about area, visit:

https://brainly.com/question/27683633

#SPJ1

The length of CD is given as follows:

CD = 12.686 cm.

The three trigonometric ratios are defined as follows:

Applying the Pythagorean Theorem, the length of CB is obtained as follows:

(CB)² + 6² = 12²

CB = sqrt(12² - 6²)

CB = 10.392.

As CB is the opposite side of the angle of 55º, while CD is the hypotenuse, the length of CD is obtained as follows:

sin(55º) = 10.392/CD

CD = 10.392/sine of 55 degrees

CD = 12.686 cm.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The probability that an Endure All battery selected at random will last more than 610 hours is 0.1056.

A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred . Eventsare approximately normal happen more often than information that are far the mean.

The normal distribution appears as a "bell curve" on a graph.

A probability bell curve is more properly described as the normal distribution.

In a normal distribution, the mean is 0 and the standard deviation is 1. The kurtosis is 3, and there is no skew.All  normal distributions are symmetrical.

Natural occurrences frequently resemble the usual distribution.

However, in finance, most price distributions are not fully normal.

How to solve?

Given that μ = 500, σ = 40, for x > 550

z = 550-500/40

z = 1.25

From the normal distribution table, P(z > 1.25) = 1 - P(z < 1.25) = 1 - 0.8944 = 0.1056

To learn more about the normal distribution, visit:

brainly.com/question/4079902

#SPJ4

Answer:

look at the screenshot

Step-by-step explanation:

Answer:

4.082 radians

Step-by-step explanation:

Here we want to convert 234° into radians.

To do it, we use the fact that pi radians is equal to 180°

Then we can write two equations:

x radians = 234°

3.14 radians  = 180°

Where we want to find the value of x, which is the equivalent in radians to 234°.

Now we can take the quotient of these two equations to get:

( x radians)/(3.14 radians) = (234°/180°)

Solving this for x, we get:

x radians = (234°/180°)*(3.14 radians) = 4.082 radians.

Answer:

\(x=\frac{-3d-9}{k-d}\)

Step-by-step explanation:

Step 1: Write out equation

d(-3 + x) = kx + 9

Step 2: Distribute

-3d + dx = kx + 9

Step 3: Subtract dx on both sides

-3d = kx - dx + 9

Step 4: Subtract 9 on both sides

-3d - 9 = kx - dx

Step 5: Factor

-3d - 9 = x(k - d)

Step 6: Divide both sides by k - d

\(x=\frac{-3d-9}{k-d}\)

Answer:

Step-by-step explanation:

Step 1: Write out equation

d(-3 + x) = kx + 9

Step 2: Distribute

-3d + dx = kx + 9

Step 3: Subtract dx on both sides

-3d = kx - dx + 9

Step 4: Subtract 9 on both sides

-3d - 9 = kx - dx

Step 5: Factor

-3d - 9 = x(k - d)

Step 6: Divide both sides by k - d

The reduced cost matrix for travelling salesperson problem in the given instance is shown below. The Travelling Salesperson Problem (TSP) is a classical combinatorial optimization issue that belongs to the category of NP-Hard problems.

This problem can be resolved using a branch and bound algorithm or by using dynamic programming.The reduced cost matrix for the given travelling salesperson problem instance The computation of the reduced cost matrix for travelling salesperson problem involves two steps: Identify the smallest element of each row and subtract the value from all the values in the row.

Identify the smallest element of each column and subtract the value from all the values in the column.In the given instance, the smallest element of each row is highlighted in bold. Therefore, after performing Step 1 the matrix becomes the matrix becomes Hence, the reduced cost matrix for the travelling salesperson problem is obtained.

To know more about optimization visit :

https://brainly.com/question/3589540

#SPJ11

If one of the measurements taken by a surveyor is drastically different from the other measurements, the surveyor should investigate the cause of the discrepancy and determine whether the measurement is accurate or not.

Some possible reasons for a measurement to be drastically different could be errors in equipment, human error, environmental factors, or other sources of interference.

To verify the accuracy of the measurement, the surveyor may take additional measurements and compare them to the initial measurement, or they may use alternative methods to obtain the same measurement. If the measurement is found to be inaccurate, the surveyor may need to recalibrate or replace the equipment, or take steps to eliminate or minimize the sources of interference.

It is important for the surveyor to ensure the accuracy of their measurements to ensure the reliability of their data and the validity of their conclusions.

You can learn more about survey at

https://brainly.com/question/2141789

#SPJ4

The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10

In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y

If a given number let's say Z is Y less than X then the value of Z will be

Z=X-Y

More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value

So, 3 more than 7 means 7+3 = 10

Learn more about adding:

https://brainly.com/question/3255453

#SPJ4

Answer: c = 520

Step-by-step explanation:

     f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.

Given:

    f(x) = 4x³ + 7x² - x + c

Substitute:

    578 = 4(2)³ + 7(2)² - (2) + c

Distribute:

    578 = 4 * 2³ + 7 * 2² - 2 + c

Raise to the power of 3 and 2:

    578 = 4 * 8 + 7 * 4 - 2 + c

Multiply:

    578 = 32 + 28 - 2 + c

Add:

    578 = 60 - 2 + c

Subtract:

    578 = 58 + c

Subtract 58 from both sides:

    520 = c

Reflexive property:

   c = 520

\( \huge\mathbb{ \underline{SOLUTION :}}\)

Given:

\(\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}\)

\(\longrightarrow\sf{578= 32+28 −2+ c}\)

\(\longrightarrow\sf{578 =58+ c}\)

\(\longrightarrow\sf{c = 578-58}\)

\(\huge \mathbb{ \underline{ANSWER:}}\)

\(\longrightarrow\sf{c= 520}\)

The answer is A, square root of 29

The four consecutive odd integers = 15, 17, 19, 21

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.

According to our question-

First digit: x

Second digit: x + 2

Three-digit number Equals x + 4

Fourth digit: x + 6

The difference between the opposite of the third and the first two sums up to 55.

x + x + 6 = -(x + 4) + 55

x + x+6 = (-x - 4) + 55

2x + 6 = -x + 51

assemble similar terms

2x + x = 51 - 6

3x = 45

x = 15

Therefore,

First digit: x = 15

Second digit: 15 + 2 + x = 17

Third number: 15 + 4 + 4 = 19

Fourth digit: x+6 = 15+6 = 21

The four odd numbers in a row equal 15, 17, 19, and 21.

learn more about integers click here:

https://brainly.com/question/929808

#SPJ4

Answer:

39cm²

Step-by-step explanation:

Surface area of square-based pyramid = length X width + 4(area of triangle)

= 3 X 3 + 4 (1.5 X 5)

= 9 + 4 (7.5)

= 9 + 30

= 39cm²

The average speed of the train  during the journey is 35 km/hour.

a) The train leave city A at 5 AM.

b) By 12 noon the train cover a distance of 200 km.

c) By 1 pm the train travelled 250 km.

d) The speed of the train during 1 pm and 3 pm is 100/2 = 50 km/hour

e) The average speed of the train  during the journey = 350/10

= 35 km/hour

f) The number of hours trains spend at rest is 3 hours.

Therefore, the average speed of the train  during the journey is 35 km/hour.

Learn more about the average speed here:

brainly.com/question/9834403.

#SPJ1

The statement "the first step in the sampling design process is to determine the sample size" is false because according to the text, the first step in the sampling design process is to clearly define the target population.

The first step in the sampling design process is typically to define the target population and the research objectives.

This involves specifying the characteristics of the population under study and identifying the specific research questions or objectives that the sampling will address.

Once the target population and research objectives are established, the next steps in the sampling design process typically involve determining the appropriate sampling method (such as random sampling, stratified sampling, or cluster sampling) and selecting the sampling frame (the list or source from which the sample will be drawn).

After these initial steps, researchers can then consider factors such as the desired level of precision, confidence level, and variability in the population to determine the appropriate sample size.

The determination of the sample size usually comes after clarifying the research objectives and selecting the appropriate sampling method.

To know more about sampling design refer here:

https://brainly.com/question/32283666#

#SPJ11

Answer:

4

Step-by-step explanation:

Answer:

See attached image

Step-by-step explanation:

the formula for circumference is 2πr

6983245455445

it's correct

Answer:

x= -5

Step-by-step explanation:

Isolate the variable by dividing the factors that don't contain the variable.

Hope this helps. Plz give brainliest.

Answer:

is it on edge

Step-by-step explanation:

12 penguins and 30 monkeys are in the safari park now

Let p and m represent the initial number of penguins and monkeys respectively.

Since the ratio of penguins to monkeys was 6: 7, we can write:

p/m = 6/7  --- (1)

Also, 16 monkeys were then born, and the ratio of penguins to monkeys became 2 : 5. We can write:

p/(m + 16) = 2/5  --- (2)

From (1):

p/m = 6/7

p = (6/7)m  --- (3)

Put (3) in (2) and solve for m:

p/(m + 16) = 2/5

(6/7)m/(m + 16) = 2/5

(6/7)m =2(m + 16)/5

(6/7)m = (2m + 32)/5

6m = 7(2m + 32)/5

30m = 14m + 224

30m - 14m = 224

16m = 224

m = 224/16

m = 14

put m = 14 in (3) and solve for p:

p = (6/7)m

p = (6/7) * 14

p = 12

Since no new penguins were born, we still have 12 penguins now.

But 16 new monkeys were born. Thus, we have:

number of monkeys now = m + 16 = 14 + 16 = 30

Learn more about ratio on:

https://brainly.com/question/2328454

#SPJ1

Using proportions, the horse 8 feet from the center would have to make 96 revolutions.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

A horse 24 feet from the center of a merry-go-round makes 32 revolutions. If it is 8 feet and wants the same distance, how many revolutions will it need? The rule of three is:

24 feet - 32 revolutions

8 feet - x revolutions

The measures are inverse proportional, hence:

8x = 24 x 32

x = 24 x 32/8

x = 96 revolutions.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

0.80

Step-by-step explanation:

I did the math 5 times