1 The geometric mean of two positive integers a and b is 27 Find all possible
values of a and b

Answer:

x=3

Step-by-step explanation:

7-5(x+6)= -7x-17

Distribute

7 - 5x-30 = -7x-17

Combine like terms

-5x-23= -7x-17

Add 7x to each side

-5x-23+7x= -7x-17+7x

2x -23 = -17

Add 23 to each side

2x-23+23 = -17+23

2x= 6

Divide by 2

2x/2 = 6/2

x =3

Answer:

x = 3

Step-by-step explanation:

7 - 5(x + 6) = -7x - 17

~Simplify left side

7 - 5x - 30 = -7x - 17

~Combine like terms

-5x - 23 = -7x - 17

~Add 23 to both sides

-5x = -7x + 6

~Add 7x to both sides

2x = 6

~Divide 2 to both sides

x = 3

Best of Luck!

If one-tower can hold 4.37×10⁶ gallons of water and other tower can hold 3.92×10⁶ gallons of water, then combined water capacity of two towers is 8.29×10⁶ gallons.

In order to find the combined water capacity of the two towers, we simply need to add their individual capacities.

The water capacity of one tower is = 4.37×10⁶ gallons of water, and the water capacity of other tower is = 3.92×10⁶ gallons of water,

So, their combined capacity is:

⇒ 4.37×10⁶ + 3.92×10⁶ = 8.29×10⁶ gallons

Therefore, the combined water capacity of the two towers is 8.29×10⁶ gallons.

Learn more about Water Capacity here

https://brainly.com/question/28943808

#SPJ4

The given question is incomplete, the complete question is

A city has two water towers. one tower holds 4.37×10⁶ gallons of water and the other holds 3.92×10⁶ gallons of water. What is the combined water capacity of the two towers?

Answer:

k = - 1

Step-by-step explanation:

If (x - 5) is a factor of p(x) then p(5) = 0

p(5) = 5³ - 6(5)² + 5k + 30 = 0 , that is

125 - 150 + 5k + 30 = 0

5 + 5k = 0 ( subtract 5 from both sides )

5k = - 5 ( divide both sides by 5 )

k = - 1

Answer: i think its 72. since the triangle is isoseles the other angle is 54. adding both makes 108 then subtract it from 180, then pow, the answer. Apologies if it's not right i didnt understand that section of my class that well

The total number of seven-character passwords that can be made with the given characters without repeats is 10,200.

This is calculated by finding the number of ways to choose the first character (11 options), then the second character (10 options), and so on until the seventh character (5 options), which gives 11x10x9x8x7x6x5 = 10,200.

If all four numbers have to be used as the first four characters in the password, then the number of possible passwords reduces to 2,400. This is calculated by finding the number of ways to choose the first four characters (4 options for each), then the remaining three characters (10 options for each), which gives 4x4x4x4x10x10x10 = 2,400.

You can learn more about Combination at

https://brainly.com/question/28065038

#SPJ11

There are 4,387,810 possible seven-character passwords that can be made without repeats. If the first four characters must be the numbers 1, 2, 3, and 4, there are 6,720 possible passwords.

To calculate the total number of possible seven-character passwords without repeats, we use the formula for permutations: n! / (n-r)!, where n is the total number of characters and r is the number of characters in the password (in this case, 7). Using this formula, we get 10! / (10-7)! = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 4,387,810.

If we must use the numbers 1, 2, 3, and 4 as the first four characters, we have 4! = 24 ways to arrange them. For the remaining three characters, we have 7 choices for each character (since we cannot repeat any of the previous four characters). Therefore, the total number of possible passwords is 24 x 7 x 7 x 7 = 6,720.

For more questions like Number click the link below:

https://brainly.com/question/17429689

#SPJ11

Answer:

The answer is 4

answer mine

Answer:

(A U B) = {1,2,3,5,7,8,9,10}

(A n B)= {7,9,10}

(A U B) U (A n B) = {1,2,3,5,7,8,9,10}

Step-by-step explanation:

The average (mean) of the data is approximately 16.89 to two decimal places.

To calculate the average (mean) of the given data, you need to sum all the values and divide by the total number of values.

Sum of the data: 25.3 + 27.9 + 16.1 + 6 + 6.8 + 7.7 + 28.4 = 118.2

Total number of values: 7

Average (mean) = Sum of the data / Total number of values

Average = 118.2 / 7

Know more about average (mean) here;

https://brainly.com/question/15397049

#SPJ11

The simplification of the given expression above to determine the value of X= 24

7 ( x - 4 ) - 3 x + 2 = 3 x - 2 - x

Bring the like terms together;

7x -28 - 3x +2 = 3 x - 2 - x

7x-3x-3x = 28-2-2

x= 24

Therefore the value of X would be = 24.

Learn more about addition here:

https://brainly.com/question/25421984

#SPJ1

Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

Answer:

sorry, but there is nothing to answer here :(

Step-by-step explanation:

Answer:

in abc, M???

Step-by-step explanation:

the area of a semicircle 1/2(πr²) and a rectangle is a*b.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of the rectangle is the area covered by the rectangle A = a*b where a is length and b is breadth.

The area of the semicircle will be half of the area of circle which will be, 1/2(πr²)

where r is the radius of the semi circle.

the area of a semicircle 1/2(πr²) and a rectangle is a*b.

Learn more about rectangular by following the link below.

brainly.com/question/25292087

#SPJ4

The complement = x

The angle we are finding = 3x + 26

Complementary angles are angles that add up to 90 degrees.

90 = x + 3x + 26

Combine like terms

90 = 4x + 26

Subtract 26 from both sides

64 = 4x

Divide both sides by 4

16 = x

The angle we are trying to find = 3(16) + 26 = 48 + 26 = 74 degrees

To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

Learn more about expressions here:

brainly.com/question/28170201

#SPJ11

The mean score for the test is 80.

We have,

To find the mean score for the test, we can use the relationship between the mean, the standard deviation, and the z-score.

The formula for the z-score is:

z = (x - μ) / σ

Where:

z is the z-score,

x is the given score,

μ is the mean, and

σ is the standard deviation.

In this case, we know that Cathy's score (x) is 74 and it is 1 standard deviation below the mean (z = -1).

The standard deviation (σ) is given as 6.

Plugging these values into the z-score formula, we can solve for the mean (μ):

-1 = (74 - μ) / 6

Multiplying both sides by 6:

-6 = 74 - μ

Rearranging the equation:

μ = 74 + 6

μ = 80

Thus,

The mean score for the test is 80.

Learn more about mean here:

https://brainly.com/question/23263573

#SPJ12

To locate the critical points of the function f(x, y) = 8x − \(x^{2}\)− 4x\(y^{2}\), we need to find the values of x and y where the partial derivatives of the function with respect to x and y are equal to zero.

Taking the partial derivative of f(x, y) with respect to x, we get:

∂f/∂x = 8 - 2x - 4\(y^{2}\)

Setting this partial derivative equal to zero and solving for x, we have:

8 - 2x - 4\(y^{2}\) = 0

-2x = 4\(y^{2}\) - 8

x = 2 - 2\(y^{2}\)

Now, taking the partial derivative of f(x, y) with respect to y, we get:

∂f/∂y = -8xy

Setting this partial derivative equal to zero and solving for y, we have:

-8xy = 0

xy = 0

From the equation xy = 0, we can see that either x or y must be equal to zero.

Therefore, the critical points of the function f(x, y) = 8x − \(x^{2}\) − 4\(xy^{2}\) are given by the pairs (x, y) where x = 2 - 2\(y^{2}\) and either x = 0 or y = 0.

Learn more about partial derivative here:

https://brainly.com/question/14782333

#SPJ11

Answer:

-------------------

Heron's formula states that the area of a triangle with side lengths a, b, and c is:

We have a triangle with side lengths:

We can first find the semi-perimeter:

Then we can plug this into Heron's formula to find the area:

So the area of the triangle is approximately 82.41 square units.

The standard deviation of the sample of shopping times is approximately 9.18 minutes.

To calculate the standard deviation, we follow these steps:

1. Calculate the mean (average) of the sample. Summing up the shopping times and dividing by the sample size of 5, we get (21 + 42 + 23 + 36 + 43)/5 = 33.

2. Calculate the deviation of each shopping time from the mean. Subtract the mean from each shopping time: 21 - 33 = -12, 42 - 33 = 9, 23 - 33 = -10, 36 - 33 = 3, 43 - 33 = 10.

3. Square each deviation. (-12)² = 144, 9² = 81, (-10)² = 100, 3² = 9, 10² = 100.

4. Calculate the variance. Add up the squared deviations and divide by the sample size: (144 + 81 + 100 + 9 + 100)/5 = 86.8.

5. Calculate the standard deviation. Take the square root of the variance: √86.8 ≈ 9.18.

Therefore, the standard deviation of the sample of shopping times is approximately 9.18 minutes.

To learn more about standard deviation  here:

https://brainly.com/question/29115611

#SPJ4

Answer:

d

Step-by-step explanation:

Answer:

The second one

Step-by-step explanation:

Hope this helps! Consider brainiest!

Answer:

6 markers

Step-by-step explanation:

5000/800 = 6.25

We can't have a quarter of a marker

If we were to round up it would have to be 5.6 km to fit 7 so we have to round down, and the answer is 6

In addition, along the 5000 m trail there will be one at 800, 1600, 2400, 3200, 4000, and 4800

We can only fit 6 of them along the trail if they are spaced 800 m apart so 6 markers will be able to fit on a 5k trail

Answer:

We need to calculate how many times there are 800 meters on 5000 meters.

To know so, we can divide 5000 by 800:

5000/800 = 6.25

So now, we know there are 800 meters 6.25 times on this trail.

So, how many markers have to be used? There have to be used 6, as the other 0.25 times will be the last 200 meters of the trail (800*0.25) and we only have to put a mark each 800.

We can also do this manually, from the start:

First mark would be at 800, next at 1600, next at 2400, next at 3200, next at 4000 and the last one at 4800. As we have said, 6 markers.

The utility functions in options a, b, c, and f are not risk-averse on the interval [a,b], while the utility functions in options d and e are risk-averse on the interval [a,b].

In economics and finance, risk aversion refers to a preference for less risky options over riskier ones. Utility functions are mathematical representations of an individual's preferences, and they help determine whether someone is risk-averse, risk-neutral, or risk-seeking. A risk-averse individual would have a concave utility function, indicating a decreasing marginal utility of wealth.

For options a, b, c, and f, the utility functions are and f(x) = -ln(x), g(x) = \(-e^(^-^x^)\), h(x) = \(-4x^2\) - 10x, respectively. These utility functions do not exhibit concavity, which means they are not risk-averse. Instead, they either show risk-seeking behavior (options a and b) or risk-neutrality (options c and f).

On the other hand, options d and e have utility functions f(x) = ln(x), g(x) = 1/(e^(2x)), h(x) = \(-x^2\) + 10,000x and f(x) = ln(-2x), g(x) = -1/(\(e^(^2^x^)\)), h(x) = \(x^2\) - 100,000x, respectively. These utility functions display concavity, indicating a decreasing marginal utility of wealth. Thus, options d and e can be considered risk-averse on the interval [a,b].

Learn more about risk-averse

brainly.com/question/30641789

#SPJ11

A solution set in of a linear equation system mathematics  to the set of values correctly solve such system which inputted into a system of equations correctly .

The main steps to follow  calculating solution sets for a  linear equations of system

first step is to Convert the  system into a matrix equation

secondly Rewrite  matrix equation into  an augmented matrix

next step is Computing the reduced echelon form of the augmented matrix by use of Gaussian elimination processes

after that The reduced echelon form of the matrix will provide the values for the unknown variables,

using these solutions to writing down the parametric vector equation form that contain the complete set of solutions for the system.

To know more about system of linear equations visit brainly.com/question/19549073

#SPJ4

Answer:

0 it went minus 2 minus 3 minus and so forth

Answer:

21

Step-by-step explanation:

21

Answer:

i think ur answer would be 21

Step-by-step explanation:

....../

we have:

the graph that best represents is: A

answer: A

Given:

The figure of a triangle.

To find:

The measure of angle 1.

Solution:

Exterior angle theorem: In a triangle, the measure of an exterior angle of a triangle is equal to the sum of two opposite interior angles.

Using Exterior angle theorem, we get

\(101^\circ =31^\circ +m\angle 1\)

\(101^\circ -31^\circ =m\angle 1\)

\(70^\circ =m\angle 1\)

Therefore, the measure of angle 1 is 70 degrees.

To calculate P(X ≥ 2), we need to standardize the variable X. First, we find the standard deviation of X by taking the square root of the variance: σ = √(25) = 5.

Then, we calculate the z-score for the value 2 using the formula z = (X - μ) / σ, where μ is the mean of X. Plugging in the values, we get z = (2 - 10) / 5 = -1.6. We can then look up the probability corresponding to this z-score in the standard normal distribution table or use a calculator. P(X ≥ 2) is equal to 1 minus the probability of X being less than 2, which can be written as P(X ≥ 2) = 1 - P(X < 2). By looking up the z-score of -1.6 in the table, we find that the probability is approximately 0.0548. Therefore, P(X ≥ 2) ≈ 1 - 0.0548 ≈ 0.9452.

To plot the histogram of Y = FX(X), we need to generate random samples from the distribution of X and compute the corresponding values of the distribution function FX. Since X is a normally distributed random variable, we can use a random number generator to generate samples from the normal distribution with mean 10 and variance 25. We then apply the distribution function FX to each sample to obtain the corresponding values of Y. By plotting the histogram of Y with a sample size of n = 1000, we can observe the shape of its distribution. If the histogram of Y closely resembles a uniform distribution on the interval [0, 1], it suggests that Y follows a uniform distribution. Conversely, if the histogram of Y deviates significantly from a uniform distribution, it indicates that Y does not follow a uniform distribution. Comparing the histogram of Y with the histogram of a uniform distribution on [0, 1], we can draw conclusions about the distribution of Y.

To learn more about standard deviation refer:

https://brainly.com/question/24298037

#SPJ11

Check the picture below.