What are the multiples of 5?

Based on the information provided the coordinates would be

To know her sequence, let's apply the rule given"Add 1, then multiply by 3"

2 + 1 = 3 x 3 = 9

3+1 = 4 x 3 =12

4 +1 = 5 x 3 =14

5 + 1 = 6x3 = 18

Let's apply the rule given "Add 2, then multiply by 2"

2+ 2 = 4x2= 8

3+2= 5x2= 10

3+3= 6x 2= 12

4+3=7x 12 = 14

Based on this, the coordinates are (2,2), (9,8), (12,10), (14,12), (18,14).

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So, Ethan gets $38 and Enoch gets $95.

We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.

Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.

So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.

Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.

And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.

So, to summarize:

Ethan gets $38

Enoch gets $95

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So, Ethan gets $38 and Enoch gets $95.

We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.

Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.

So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.

Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.

And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.

So, to summarize:

Ethan gets $38

Enoch gets $95

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Based on given ratio of 10:11:9, the share for each person is as follows:

Ratio is the relative size of one value or variable compared to another.

Ratios show how much each quantity is contained in another.

Ratios are fractional values obtained as the quotient of one value divided by another, and are depicted in fractions, decimals, or percentages.

The total shareable amount =  £300

The sharing ratio = 10:11:9

The sum of ratios = 30

Simon's share =  £100 (10/30 x  £300)

Sarah's share =  £110 (11/30 x  £300)

Matthew's share =  £90 99/30 x  £300)

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Answer:

A. and 3

Step-by-step explanation:

3x+2=8

3x=6

x=2

If the taco truck were to sell its tacos for $1, it would earn a profit of $267. However, if they were to sell their tacos for $-1, they would incur a loss of $202.

[tex]x | -7x^2 + 32x + 240[/tex]

[tex]-1 | -7(-1)^2 + 32(-1) + 240 = 6 + 32 - 240 = -202[/tex]

[tex]0 | -7(0)^2 + 32(0) + 240 = 240[/tex]

[tex]1 | -7(1)^2 + 32(1) + 240 = -5 + 32 + 240 = 267[/tex]

The optimal price that the taco truck should sell its tacos for is $0. This is because when x is equal to 0, the value of the polynomial expression is at its highest point. This means that the taco truck will earn the most profit when they sell their tacos for $0.

However, it is important to note that this is not a realistic scenario and the taco truck would need to sell its tacos for a positive whole dollar amount.

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If you flip a fair coin 10 times , then the probability of getting all tails is 1/1024 .

The outcomes in flipping a coin is = {H , T} ;

probability of getting a tail is = 1/2 ;

the number of times the coin is flipped is = 10 times .

The probability of getting a sequence of 10 independent events, each with a probability of 1/2 of occurring. The overall probability is found by multiplying the probability of each event:

⇒ (1/2) × (1/2) × (1/2) × ... × (1/2) = (1/2)¹⁰ = 1/1024 .

Therefore ,  the probability of getting "all tails" in 10 coin flips of a fair coin is 1/1024 , which means that if we flip the coin 10 times repeatedly, we  would expect to get all tails only once in approximately 1024 trials .

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The expanded logarithmic expression is 7log y + log x + 3log z.

The use of a logarithm can be utilised to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Log interpretation is not that tough. It suffices to know that an exponential equation can also be written as a logarithmic equation in order to comprehend logarithms.

Exponent and logarithm are inverses of one another. This is explained in the section below. John Napier, a mathematician, first developed logarithms as a technique to perform computations simply, and other scientists, engineers, etc. immediately embraced this idea.

The given logarithmic equation is:

log ([tex]y^{7}xz^{3}[/tex])

Now, we can use the properties of logarithms to expand this fully.

Therefore,

log ([tex]y^{7}xz^{3}[/tex]) = log ([tex]y^{7}[/tex]) + log (x) + log ([tex]z^{3}[/tex])

Therefore,

log (y⁷) = 7 log y

log (z³) = 3 log z

Therefore, the expanded logarithmic expression is 7log y + log x + 3log z.

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Answer:  5 : 18 =  10 : 36

Step-by-step explanation:

The ratio is already in lowest terms so we found an equivalent ratio by multiplying both terms by 2.

Answer:

5 to 18

Step-by-step explanation:

The phase shift of the sin function , y = -2 sin (2x - π)-3 is   =π/-3.

Amplitude: The amplitude of a wave is a maximum displacement of a particle from its rest position

Period: The ratio of wavelength to the velocity.

Phase shift: The phase shift represents the amount a wave has shifted horizontally from the the usual position.

here, we have,

The equation of a wave is

f(x) = a sin(bx - c)+d

Where

amplitude = |a|

phase shift = c/d

now,

Given equation of wave is

f(x) =-2 sin (2x - π)-3

Here a=-4, b=2, c = π, d = -3

i.e.

phase shift = c/d

                  =π/-3

Therefore, phase shift   =π/-3.

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The description of the proportional relationship on the table is given as follows:

The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

Hence the constant is given as follows:

k = 570/3 = 380/2 = 190/1 = 190 calories burned per hour.

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The solution of the initial value problem is [tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex].

Initial value issues are a specific kind of calculus issue. Calculus initial value issues include differential equations with a known beginning condition that identifies the function's value at a certain point. Finding the function that best describes the system is the goal of these puzzles, and this can be accomplished by integrating the differential equation.

There is always an unknown constant present when doing an integration with an indeterminate integral or without initial conditions. The constant of integration is what is commonly indicated by the letter C.

Given that the initial value problem is:

dy/dt= e^(y-t) sec(y)(1+t2)

This can be re written as follows:

dy/ dt = e^(y-t) (1 + t^2) / sec (y)

Separate the derivative in terms of y and t and take integration:

[tex]\int{e^{-y}cos(y)} \, dy = \int {e^{-t}(1 + t^2)} \, dt[/tex]

Integrate the following:

[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + c\\[/tex]

The initial conditions given are y(0) = 0, substitute the value of the variables as 0:

[tex]\frac{e^{0}}{2} [sin0 - cos0] = -e^{0} [0^2 + 2(0) + 3] + c\\\\\\\frac{1}{2} [-1] = 3 + c[/tex]

c = 5/2

Hence, the solution of the initial value problem is:

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#SPJ4[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex]

Answer:

Step-by-step explanation:

Jackson -

8.25 + 5p

Tim -

2.15 + 4p

8.25 - 2.15 = 6.1

5p - 4p = 1p or p

simplified expression

6.1 + p is how much more Jackson spent

(I’m sorry if it’s wrong not 100 percent sure)

The monthly Period interest rate is 1.67( nearest hundredth)

Annual percentage rate (APR) refers to the yearly interest rate you'll pay if you carry a balance on your credit card. Some credit cards have variable APRs, meaning your rate can go up or down over time.

To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.

The APR of the card holder is 19.99%

Therefore the monthly Period interest will be calculated as ;

19.99/12

= 1.67% ( nearest hundredth)

therefore the monthly periodic interest is 1.67%

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The equation of the graph is (a) [tex]\frac{2x^2-8}{x^2+x-6}[/tex]

From the question, we have the following parameters that can be used in our computation:

The graph and the list of options

Next, we test the graph with the options

On the graph, we have:

f(0) = 1.3

f(-1) = -1

From the list of options, the equation that has the above properties is option (a)

Hence, the equation is (a)

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The amount of total distance walked has walked by Eric in a man-made circular lake is 75.36 miles.

A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.

Circumference = D* π

Total distance walked four times = 4.C

= 4 * D * π

= 4 * 6 * 3.14

= 75.36 miles

So, the total distance is 75.36 miles.

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Answer:

x = (2, 0), y = (0, -10)

The cost of painting the wall is Rs.48.75 .

The square shape wall whose length is 10m has a door of length 2m and breadth 1m.   It also has a window of length 1m and breadth 0.5m.

Therefore, the cost of painting the wall can be calculated as follows:

cost of painting per meters = Rs0.5 per metre square

Therefore, the area of the wall to be painted will exclude the window and the door.

Hence,

area of wall of the wall to be painted = area of the wall - area of the window - area of the door

Therefore,

area of wall of the wall to be painted = 10² - (1 ×  0.5) - (2 × 1)

area of wall of the wall to be painted = 100 - 0.5 - 2

area of wall of the wall to be painted = 97.5 metres²

Therefore,

1 metres square = Rs0.5

97.5 metres squared = ?

cross multiply

cost to paint the wall = 0.5 × 97.5

cost to paint the wall = Rs.48.75

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Answer:

Step-by-step explanation:

1. Total number of students in class 8B: 30

2. Number of students studying both German and French: 3

3. Number of students studying only German: 12

4. Number of students studying only French: 15

Jorimiah score 680 points in the season.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Jorimiah scored 85 points in a basketball game.

That was 1/8 of the points that he scored for the season.

let Jorimiah score x points

So, 1/8 of x= 85

x= 85(8)

x= 680 points.

Hence, he score 680 points.

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The graph shows an inverse relationship between the number of baseballs produced per day and the cost of production. As the number of baseballs produced per day increases, the cost of production decreases.

1. The graph shows a downward-sloping line, which indicates an inverse relationship between the number of baseballs produced per day, q, and the daily cost of production, c.

2. As q increases, c decreases.

3. This inverse relationship means that as the number of baseballs produced per day increases, the cost of production decreases.

The graph shows an inverse relationship between the number of baseballs produced per day and the cost of production. As the number of baseballs produced per day increases, the cost of production decreases.

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The formula (y2y1)/(x2x1)  (y 2y1)/(x 2x1) can be used to determine the constant rate of change.

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For the function P = 3x + y, there is no solution present to maximize it.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given objective function -

P = 3x + y

Subjected to the constraints -

5x + 7y ≥ 35

3x + 4y ≤ 12

x ≥ 0, y ≤ 0

First consider the inequality 5x + 7y ≥ 35.

The equation of the above inequality is as follows -

5x + 7y = 35

Find two points that satisfies the above equation.

Take x = 0, then -

5(0) + 7y = 35

7y = 35

y = 5

The first point is (0,5).

Take y = 0, then -

5x + 7(0) = 35

5x = 35

x = 7

The second point is (7,0).

Substitute (x,y) = (0,0) and see the direction of the region for 5x + 7y ≥ 35.

5(0) + 7(0) ≥ 35

0 ≥ 35

This is not true.

Therefore, the region is non-origin side.

Now consider the inequality 3x + 4y ≤ 12.

The equation of the above inequality is as follows -

3x + 4y = 12

Find two points that satisfies the above equation.

Take x = 0, then -

3(0) + 4y = 12

4y = 12

y = 3

The first point is (0,3).

Take y = 0, then -

3x + 4(0) = 12

3x = 12

x = 4

The second point is (4,0).

Substitute (x,y) = (0,0) and see the direction of the region for 3x + 4y ≤ 12.

3(0) + 4(0) ≤ 12

0 ≥ 12

This is true.

Therefore, the region is origin side.

Plot the graph.

From the graph it can be seen that there are no corner points and no feasible region.

Therefore, there is no solution for the function.

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Option (A) Only Manoj is the correct answer. the correct formula for the sequence -9, -27, -81, -243 is  [tex]h(n) = -9 * 3^n[/tex],  as proposed by Manoj.

The formula for a sequence represents a pattern in the terms of the sequence. By finding an explicit formula for a sequence, we can generate any term of the sequence without having to list out all of the terms.

In this case, the sequence -9, -27, -81, -243 follows a pattern where each term is obtained by multiplying the previous term by 3. This can be represented by the formula [tex]h(n) = -9 * 3^n[/tex], where n is the index of the term in the sequence and [tex]3^n[/tex] represents 3 raised to the power of n.

In contrast, Shira's formula  [tex]h(n) = -3 * 3^n[/tex]  results in a different sequence, -3, -9, -27, -81, which does not match the given sequence.

Therefore, the correct formula for the sequence -9, -27, -81, -243 is[tex]h(n) = -9 * 3^n[/tex], as proposed by Manoj.

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Answer:

77.35

Step-by-step explanation:

I'm sorry because I don't know how to explain it...

Yes, this is true. This phenomenon is known as the Central Limit Theorem and it states that, as the sample size increases, the distribution of the sample mean converges to a normal distribution.

Yes, this is true. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample mean converges to a normal distribution. This means that, when the sample size is large enough, the histogram of sample means will appear to be close to a normal distribution. This is because the mean of a large enough sample size will be close to the population mean, regardless of the shape of the original population distribution.

The Central Limit Theorem also states that the larger the sample size, the more closely the sample distribution will resemble a normal distribution. This is why, when the sample size is large enough, a histogram of sample means will appear to be a normal distribution.

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Yes the estimated intercept B meaningful in this case

The estimated intercept, also known as the constant, is the point at which the regression line intersects the y-axis.

In this case, the meaning of the estimated intercept Bo is crucial in understanding the results of the regression analysis.

The intercept represents the expected value of the dependent variable when all independent variables are equal to zero.

In conclusion, the estimated intercept can be a meaningful and valuable tool in regression analysis, but it is important to consider the context of the data and the relationships between the variables before interpreting the results.

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The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.

The age of automobiles indicates the lifetime of the Automobiles from their manufacturing day to the present workday. For example, if the car was made in 2010 and working till 2020 then the age of the car will be 10 years.  

Odometer is a machine or instrument which is used to calculate the distance traveled by a vehicle in its lifetime. The reading of the Odometer shows the distance covered by the car in the number of milages.  

Here the more age of the automobile increases the more the distance covered by the automobile will increased hence the reading of the Odometer will increase.

As we know in mathematics, if two quantities are in relation such as one quantity is increased then the other quantity will also increase then two quantities are said to be in Direct proportion.      

So here we can conclude that the age of the automobile and the odometer reading will be in direct proportion Since both are increases both variables will have a strong positive correlation.

Therefore,

The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.

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The inverse of the function is given by x=√y-10

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here;  g(x)= (x+10)²

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

Thus y=(x+10)²

√y=x+10

x=√y-10

Hence, The inverse of the function is given by x=√y-10

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Answer:

7.5qt is the correct answer

the rule for x terms is 1.5x - 1.5 and the rule for y terms is 4.5y - 4.5.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, the ordered pairs.(0,0) (1.5,4.5) (3,9) (4.5,13.5)

For x term:

The rule for x term that is 0, 1.5, 3, 4.5

First term = 0

difference = 1.5

From the general formula of Arithmetic sequence:

an = a + (n – 1)d.

thus,

Equation = 0 + (x -1 ) d

Equation = 1.5x - 1.5

For y term:

The rule for y term that is 0, 4.5, 9, 13.5

First term = 0

difference = 4.5

From the general formula of Arithmetic sequence:

an = a + (n – 1)d.

thus,

Equation = 0 + (x -1 ) d

Equation = 4.5x - 4.5

Therefore, The x-term rule is 1.5x-1.5, while the y-term rule is 4.5y-4.5.

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