Make x the subject of the formula
6x + a = 5 ( x + t )
(don’t solve it like a normal equation and it isn’t 5t+a)

Answers

Answer 1

Answer:

y33urhrhf he ghhrhddbhdjjx


Related Questions

help..!!! Why do i ask so many questions

help..!!! Why do i ask so many questions

Answers

Answer:

Hey there!

-4/3-4/5

-20/15-12/15

-32/15

Let me know if this helps :)

11, 20, 29, ...
Find the 43rd term.

Answers

Answer:

389

Step-by-step explanation:

20 - 11 = 9

29 - 20 = 9

This is a geometric sequence with a common difference of 9.

a_1 = 11

a_2 = 11 + 9

a_3 = 11 + 2 × 9

...

a_n = 11 + (n - 1) × 9

a_43 = 11 + (43 - 1) × 9

a_43 = 11 + 42 × 9

a_43 = 389

Hence, the \(43\)rd term is \(389\).

What is the sequence?

A  sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.

Here given sequence is \(11, 20, 29, ...\)

Here,

\(a=11\\\\d=a_2-a_1\\d=20-11\\d=9\)

The general formula is

\(a_n=a+(n-1)d\)

where,

\(a_n\) is the \(n\)th term

\(a\) is the first term

\(n\) is the number of terms

\(d\) is the common difference

Substituting the values in the general formula

\(a_n=a+(n-1)d\\\\a_{43}=11+(43-1)9\\\\a_{43}=11+(42)9\\\\a_{43}=11+378\\\\a_{43}=389\)

Hence, the \(43\)rd term is \(389\).

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In the short run, a decrease in market power (or monopolization): A) will increase the price level. B) will decrease the price level. C) will not affect the price level. D) will not affect output.

Answers

In the short run, a decrease in market power (or monopolization) will decrease the price level. Hence option B is correct.

The ability of a corporation or group of enterprises to affect the price or quantity of goods or services in a market is referred to as market power. A company with market power has the ability to raise prices above the level of the market, which reduces consumer surplus and may result in inefficiencies. Market dominance can develop as a result of things like entry hurdles, brand awareness, or control over vital resources. In order to encourage competition and safeguard consumer welfare, governments may restrict or dissolve businesses that hold a large amount of market power. Market structure and performance are significantly impacted by market power, a major notion in industrial organisation.

This is because when a firm has market power, it can charge a higher price for its output due to its ability to restrict output and control the market. When this market power decreases, the firm loses the ability to control the price and must lower it to remain competitive. This decrease in price may also lead to an increase in output as the firm may seek to sell more units to make up for the lost revenue from lower prices.


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A watch company is developing packaging for its new watch. the designer uses hexagons with a base area of 25 in2 and rectangles with a length of 10 in to create a prototype for the new package. what is the volume of the prototype? 150 in3 200 in3 250 in3 300 in3

Answers

Answer:

The answer should be C. 250 in^3

Answer:

C. 250 in^3

Step-by-step explanation:

A student used this complex fraction to find a unit rate: (340 pages)/(3/4 hour.) Which quotient equals the fraction?

A. 3/4 ÷ 340
B. 4/3 ÷ 340
C. 340 ÷ 3/4

Answers

B

Step by step explanation

Yes yes I am going out of the way for now you have a good




Tell me if I’m right


Thanks again to your email I’m on my way back to the bell and I will be there in about the bell bell and I will be there in about the same time I will get it to your house and then I

Imani sells shirts packed in boxes that are each 15in. x 10in. x 2in. Imani stacked 3 boxes and wrapped them with one piece of paper. How much paper did she use, not including overlap?

Answers

Answer:

She used 600 square inches of paper.

Step-by-step explanation:

Since the box are 15 in x 10 in x 2 in and are stacked on top of each other, they form a bigger rectangular prism with 15 in x 10 in x 6 in. In order to calculate how much paper she used, we need to calculate the surface area of this prism, this is done by using the following formulla:

surface area = 2*width*length + 2*width*height + 2*length*height

surface area = 2*15*10 + 2*15*6 + 2*10*6 = 300 + 180 + 120

surface area = 600 in².

She used 600 square inches of paper.

The seventh grade students are having an end-of-year party in the school
cafeteria. There are 754 students attending the party. Each table seats 6 students.
How many tables are needed to seat all of the students?
Fill in the blanks to complete the sentences.
Determine the number of tables by dividing by .
If there is a remainder, the answer will need to be rounded .
There a remainder, so tables are needed.

Answers

The complete statement is:

Determine the number of tables by dividing 754 by 6If there is a remainder, the answer will need to be rounded.There is a remainder, so 126 tables are needed.

How to determine the number of tables?

The given parameters are:

Students = 754

Student per table = 6

The number of tables is calculated as:

Table = Students / Student per table

This gives

Table = 754/6

Evaluate the quotient

Table = 125.7

Approximate

Table = 126

Hence, the complete statement is:

Determine the number of tables by dividing 754 by 6

If there is a remainder, the answer will need to be rounded.

There is a remainder, so 126 tables are needed.

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Help me please if it right I give brainliest I promise

Help me please if it right I give brainliest I promise

Answers

Answer:

48,400 yd²

Step-by-step explanation:

(220+180)/2*260=52000

1/2(180)(60)=5400

So the total area is 52000+5400=57400

Basketball court=2400

Picnic area = 4200

Playground = 40x50 + 10x40=2400

2400+4200+2400=9000

57400-9000=48400

Answer: Hey I see someone gave you an answer already just wanted to say hi

Step-by-step explanation:

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
A) 2.3p – 10.1 = 6.4p – 4
B) 2.3p – 10.1 = 6.49p – 4
C) 230p – 1010 = 650p – 400 – p
D) 23p – 101 = 65p – 40 – p
E) 2.3p – 14.1 = 6.4p – 4

Answers

Answer: Multiplying both sides of the original equation by 100 gives the same

the solution as follows;

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

Step-by-step explanation:

When sketching a normal curve, what

value represents one standard deviation

to the right of the mean for the data set?

56, 54, 45, 52, and 48.

Answers

Answer:

The value representing one standard deviation  to the right of the mean is 55.

Step-by-step explanation:

The provided data set is:

S = {56, 54, 45, 52, and 48}

Compute the mean and standard deviation as follows:

\(\mu=\frac{1}{n}\sum X=\frac{1}{5}\times [56+54+45+52+48]=51\\\\\sigma=\sqrt{\frac{1}{n}\sum (X-\mu)^{2}}=\sqrt{\frac{1}{5}\cdot {(56-51)^{2}+...+(48-51)^{2}}}=\sqrt{\frac{1}{5}\times 80}=4\)

Compute the value representing one standard deviation  to the right of the mean as follows:

\(X=\mu+1\cdot \sigma\)

    \(=51+(1\times 4)\\=51+4\\=55\)

Thus, the value representing one standard deviation  to the right of the mean is 55.


Mr Leong just celebrated his birthday with his family recently. Mr Leong is 6m years old now. He is 3 times as old as his son. How old is Mr Leong when his son is 25 years old?

Answers

The age of Mr Leong, when his son is 25 years old, can be represented as 25 + 4m, where m represents a certain value that determines Mr Leong's age.

To find out how old Mr Leong will be when his son is 25 years old, we need to determine the age difference between them and then add that difference to Mr Leong's current age.

Given that Mr Leong is currently 6m years old and he is 3 times as old as his son, we can calculate the age of his son as follows:

Son's age = (1/3) * Mr Leong's age

Since the son's age is unknown, we can represent it as s:

s = (1/3) * 6m

s = 2m

Therefore, the son's current age is 2m.

To determine the age difference between Mr Leong and his son, we subtract their ages:

Age difference = Mr Leong's age - Son's age

Age difference = 6m - 2m

Age difference = 4m

This means that currently, Mr Leong is 4m years older than his son.

To find out Mr Leong's age when his son is 25 years old, we need to add the age difference to the son's age:

Mr Leong's age = Son's age + Age difference

Mr Leong's age = 25 + 4m

Therefore, Mr Leong will be 25 + 4m years old when his son is 25 years old.

In summary, the age of Mr Leong, when his son is 25 years old, can be represented as 25 + 4m, where m represents a certain value that determines Mr Leong's age.

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Create the B-Tree Index (m=4) after insert the following input index: (7 pts.) 12,13,10,5,6,1,2,3,7,8,9,11,4,15,19,16,14,17

Answers

The B-Tree index (m = 4) after inserting the given input index

                   [10, 13]

                  /       \

       [1, 2, 3, 4, 5, 6, 7, 8, 9]    [11, 12]    [14, 15, 16, 17, 19]

To create a B-Tree index with m = 4 after inserting the given input index, we'll follow the steps of inserting each value into the B-Tree and perform any necessary splits or reorganizations.

Here's the step-by-step process:

1. Start with an empty B-Tree index.

2. Insert the values in the given order: 12, 13, 10, 5, 6, 1, 2, 3, 7, 8, 9, 11, 4, 15, 19, 16, 14, 17.

3. Insert 12:

  - As the first value, it becomes the root node.

4. Insert 13:

  - Add 13 as a child to the root node.

5. Insert 10:

  - Add 10 as a child to the root node.

6. Insert 5:

  - Add 5 as a child to the node containing 10.

7. Insert 6:

  - Add 6 as a child to the node containing 5.

8. Insert 1:

  - Add 1 as a child to the node containing 5.

9. Insert 2:

  - Add 2 as a child to the node containing 1.

10. Insert 3:

  - Add 3 as a child to the node containing 2.

11. Insert 7:

  - Add 7 as a child to the node containing 6.

12. Insert 8:

  - Add 8 as a child to the node containing 7.

13. Insert 9:

  - Add 9 as a child to the node containing 8.

14. Insert 11:

  - Add 11 as a child to the node containing 10.

15. Insert 4:

  - Add 4 as a child to the node containing 3.

16. Insert 15:

  - Add 15 as a child to the node containing 13.

17. Insert 19:

  - Add 19 as a child to the node containing 15.

18. Insert 16:

  - Add 16 as a child to the node containing 15.

19. Insert 14:

  - Add 14 as a child to the node containing 13.

20. Insert 17:

  - Add 17 as a child to the node containing 15.

The resulting B-Tree index (m = 4) after inserting the given input index will look like this:

```

                   [10, 13]

                  /       \

       [1, 2, 3, 4, 5, 6, 7, 8, 9]    [11, 12]    [14, 15, 16, 17, 19]

```

Each node in the B-Tree is represented by its values enclosed in brackets. The children of each node are shown below it. The index values are arranged in ascending order within each node.

Please note that the B-Tree index may have different representations or organization depending on the specific rules and algorithms applied during the insertion process. The provided representation above is one possible arrangement based on the given input.

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Pls help ASAP! 20pts! What is the value of sin N? What is the value of x to the nearest tenth? What is the value of x to the nearest degree?

Pls help ASAP! 20pts! What is the value of sin N? What is the value of x to the nearest tenth? What is

Answers

Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

The range of F(x) = logo x is the set of all real numbers.
A. True
O B. False

Answers

Answer:

The range of F(x) = logo x is the set of all real numbers is True.

Step-by-step explanation:

The range of F(x) = logo x is the set of all real numbers.A. TrueO B. False

Yes, Because range of the logarithmic function is the set of ''all real numbers.'

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ f (x) = log x

Now,

The given function is a logarithmic function.

And, The range of the logarithmic function is the set of all real numbers.

Hence, The range of function F(x) = log x is the set of all real numbers.

Thus, The range of F(x) = log x is the set of ''all real numbers''.

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What is the slope of this graph?

What is the slope of this graph?

Answers

Answer:

the slope is -1/3

Step-by-step explanation:

convert this algebraic expression to English 1/4x-2=5​

Answers

Step-by-step explanation:

Hi there!

The word Question of this equation (1/4x-2=5) is:

The difference of one fourth of number and 2 is 5.

Reason:

The one fourth of number is unknown number. So, let the number be "x". The number is 1/4 X .

Then the difference of it and 2 is 5.

Which brings an algebraic expression: 1/4x-2=5.

Hope it helps!

What is the solution of the system of equations system?

Answers

The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect. To solve a system is to find all such common solutions or points of intersection.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

Calculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations. Finding the value of the variable that makes the condition of all the provided equations true is how we solve an equation system. There are several ways to solve a system of equations, including

graphical approachsubstitute techniqueElimination procedureCross-multiplication method

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Find the standard deviation for the set of data. {12,20,7,18,25,6,17,26,16}
A. 6.3
B. 6.65
C. 6.09
D. 8.22

Answers

Answer:

6.65

Step-by-step explanation:

That is approximately how far each number is from each other

What is the product of 2v3 and 4V 18 in simplest radical form?

Answers

Answer:

a x n = n √ a = n = √ a a x = n = √ a a 144 v ⋅ 3 ⋅ V = 432 v V

Step-by-step explanation:

n = √ a a Multiply 3 by 144 . 432 v V

List all of the solutions. a x n = n √

a = n = √ a

a x = n = √ a a 144 v ⋅ 3 ⋅ V = 432 v V

Answer: 24\(\sqrt{6}\)

Step-by-step explanation:

1. Identify that 4\(\sqrt{18}\) is equal to 4 times \(\sqrt{2}\) times \(\sqrt{3^2}\). \(\sqrt{3^2}=3\). Our rational numbers are now 4 and 3. 4 times 3 equals 12, and we have a remainder of \(\sqrt{2}\). Knowing \(4\sqrt{18}=12\sqrt{2}\) makes the second step much easier.

2. A fast approach for these types of problems is to multiply the rational numbers together and multiply the irrational numbers separately until the last step. 2 times 12 equals 24. \(\sqrt{3}\) times \(\sqrt{2}\) equals \(\sqrt{6}\).

3. Now we must simply multiply the whole number with the irrational number. 24 times \(\sqrt{6}\) equals 24\(\sqrt{6}\).

Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B.Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

Answers

Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.

Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.

Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.

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Correct Question:

Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B. Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

Match the plot with a possible description of the sample.60 70 80 90 100Choose the correct answer belowA.

Find the lateral area and surface area of a cone with a radius of 12 and a height of 21

Answers

Answer:

The Lateral Surface Area is 911.32 square unit and

Total Surface Area is 1361.7 square unit.

Step-by-step explanation:

For a given Cone

Radius (r) = 12

Height (h) = 21

For Lateral Surface Area

Formula:

A = πr√r² + h²

A = 3.14 × 12 × √(12)² + (21)²

A = 3.14 × 12 × √144 + 441

A = 3.14 × 12 × √585

A = 37.68 × 24.18

A = 911.32 square unit

Now,

For Total Surface Area

Formula:

A = πrl + πr²

For Slant height (l)

l² = r² + h²

l² = (12)² + (21)²

l² = 144 + 441

l² = 585

l = 24.18

So,

A = πrl + πr²

A = πr(l + r)

A = 3.14 × 12 × (24.14 + 12)

A = 3.14 × 12 × 36.14

A = 1361.7 square unit

Thus, The Lateral Surface Area is 911.32 square unit and Total Surface Area is 1361.7 square unit.

-TheUnknownScientist

Step-by-step explanation:

Hope it's helpful to you dear frnd ☺️

Find the lateral area and surface area of a cone with a radius of 12 and a height of 21

Can someone solve for x

Can someone solve for x

Answers

Answer:

x = 5, x = 26

Step-by-step explanation:

(8)

7 = \(\frac{77}{x+6}\) ( multiply both sides by x + 6 )

7(x + 6) = 77 ( divide both sides by 7 )

x + 6 = 11 ( subtract 6 from both sides )

x = 5

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

(10)

\(\frac{x}{-2}\) + 10 = - 3 ( subtract 10 from both sides )

\(\frac{x}{-2}\) = - 13 ( multiply both sides by - 2 to clear the fraction )

x = 26

Step-by-step explanation:

Hey there!

8. 7 = 77/(X+6).

Multiply 7 and (X+6)

\(7x + 42 = 77\)

Take "42" on right side and subtract it from 77.

\(7x = 77 - 42\)

\(x = \frac{35}{7} \)

Therefore, X = 5.

10.

\( \frac{x}{ - 2} + 10 = - 3\)

Shift "10" on right side.

\( \frac{x}{ - 2 } = - 3 - 10\)

Simplify it.

\(x = - 13 \times - 2\)

\(x = 26\)

Therefore, X = 26.

Hope it helps...

35 out of 50 students in a class wear glasses. What percentage of students in the class wear glasses?

Answers

Answer:

70%

Step-by-step explanation:

Percentage is out of 100

35/50 change denominator

multiply both numerator and denominator by 2

70/100= 70%

A plane is flying at a speed of 150 miles per hour. The pilot plans to fly at this speed for
the next 160 miles, plus or minus 25 miles. Write an absolute value equation to find the
minimum and maximum number of hours the plane will travel at that speed.

Answers

Maximum time = 0.914 hour , Minimum time = 1.28 hour

Speed is determined by dividing the distance traveled by the time taken to travel it. It gives the amount of time it took to travel a certain distance divided by the distance traveled.

Speed is inversely correlated with time and directly correlated with distance. Hence, Speed X  time equals distance, and

Time is calculated as Distance / Speed; as speed increases, time decreases and vice versa.

Distance = speed  x  time

Maximum speed =  150 +25

                              = 175 miles/ hour

Minimum speed = 150 - 25

                              = 125

Distance = 160 miles

Maximum time = 160/175

                              = 0.914 hour

Minimum time = 160/125

                           = 1.28 hour

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test the claim about the population mean μ at the level of significance α. assume the population is normally distributed. claim: μ>29; α=0.05; σ=1.2 sample statistics: x=29.3, n=50

Answers

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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a room has a floor dimension of 6 meters by 8 meters the height of the basement is 8 meters what is the total area of all four walls

Answers

Answer:

224 m^2

Step-by-step explanation:

The dimensions of the four walls are:

6x8, 8x8, 6x8, 8x8

The area of all of these walls is 2(6x8 + 8x8) = 224 m^2

Which point was translated 2 units down from the orange point?
B

C

D

Which point was translated 2 units down from the orange point?BCD

Answers

Answer:

Point C

Step-by-step explanation:

The orange point is at ( -4, 4)

It was translated 2 units down, which means the y decreased by 2.

So, it will be at (-4,2), and Point C is the answer!

A store sells 6 bananas for $4. Determine how much it would cost to buy 15 bananas

Answers

Answer:

$10

Step-by-step explanation:

Since 6 cost four dollars 3 would cost 2 dollars multiply 3 to get 15 bananas and 2 to get $10

Answer:

$10

Step-by-step explanation:

Make proportion:

?= cost  of bananas

6  -  4

15  -  ?

?= 15×4÷6=10

I 3) A store is holding a promotion. Every fourth customer receives a free key chain and every sixth customer receives a free magnet. Which customer will be the first to receive both a key chain and a magnet?​

Answers

Answer:

The 12th Customer

Step-by-step explanation:

The LCM of 4 and 6 is 12, as 4x3=12 and 6x2=12

a beam having a circular cross-section of diameter, D, is designed to resist a maximum bending moment of 80kNm. the maximum allowable bending stress is 500MPa what is the minimum required diameter, D, of the cross section of the beam?

Answers

To determine the minimum required diameter (D) of the cross-section of the beam, we need to consider the maximum bending moment and the maximum allowable bending stress.

The bending stress in a beam is given by the formula:

σ = (M * c) / I

Where σ is the bending stress, M is the maximum bending moment, c is the distance from the neutral axis to the outermost fiber (which is equal to half of the diameter for a circular cross-section), and I is the moment of inertia of the cross-section.

Rearranging the formula, we have:

D = (2 * M) / (σ * π)

Substituting the given values, with M = 80 kNm (converted to Nm) and σ = 500 MPa (converted to N/m²), we can calculate the minimum required diameter (D):

D = (2 * 80,000 Nm) / (500,000,000 N/m² * π)

D ≈ 0.255 meters or 255 mm

Therefore, the minimum required diameter of the cross-section of the beam is approximately 0.255 meters or 255 mm to resist the maximum bending moment of 80 kNm within the allowable bending stress of 500 MPa.

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