You need 2 jugs of orange juice for every 3 batches of punch you make. How many jugs of orange juice do you need if you make 24 batches of punch? 16​

Answer:

x = 18

Step-by-step explanation:

Alternate exterior angles are congruent.  Set the equations equal to each other and solve for x.

7x + 11 = 10x - 43  Subtract 7 x from both sides

7x - 7x + 11 = 10x - 7x - 43

11 = 3x - 43  Add 3 to both sides

11 + 43 = 3x -43 + 43

54 = 3x  Divide both sides by 3

[tex]\frac{54}{3}[/tex] = [tex]\frac{3x}{3}[/tex]

18 = x

Helping in the name of Jesus.

a) The sum of x and 4 equals 7: x + 4 = 7

b) The difference of y and 5 equals 4: y - 5 = 4

c) Two times x equals 10: 2x = 10

d) Two times y added to 3 equals 9: 2y + 3 = 9

f) If y > 3 + 2 or if 3 = y - 2 then y is smaller than y by 2

An equation is a statement in mathematics that two expressions are equivalent. It has two sides that are divided by the equals sign (=). One or more terms, such as integers, variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation, may be included on each side of the equation.

a) The sum of x and 4 equals 7:

x + 4 = 7

b) The difference of y and 5 equals 4:

y - 5 = 4

c) Two times x equals 10:

2x = 10

d) Two times y added to 3 equals 9:

2y + 3 = 9

e) If x exceeds 2 by 1, then either x = 3 or x > 2 + 1.

f) If 3 is smaller than y by 2 then either y > 3 + 2 or 3 = y - 2

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Sacramento, California's electricity demand on a scorching summer day is depicted in a function graph. The domain is 24 hours of a day.

The site is available around-the-clock.

One thousand two hundred megawatts are consumed at eight in the morning.

The hours between 4:00 and 6:00 pm saw the highest electricity use, while 4:00 am saw the lowest use.

It would be 1,900 megawatts for f (12).

From 4 am to 5 pm, usage rises, and from 5 pm to 4 am, it falls.

Because each point on the graph reflects a different megawatt usage, the graph is a function. As this graph of electricity usage illustrates, the domain would be available throughout the entire day.

At 8 a.m., these megawatts are used:

= 1, 300 - ( 200 / 2 )

equal to 1,200 megawatts

As people get ready for work and leave for work, we can observe an increase in power demand from 4 am to 5 pm, but a reduction from 5 pm to 4 am.

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Answering the presented question, we may conclude that This greater expressions scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

The difference in look between the two charts is due to the choice of the scales on the x and y-axes. In the left chart, the y-axis starts offevolved at 800 and has a range of only 200 points, whilst the x-axis starts offevolved at 1300 and has a vary of 200 points. This compressed scale makes the variations between the ratings of the three students appear larger than they absolutely are.

On the other hand, the proper chart has a y-axis that starts at zero and has a vary of 800 points, whilst the x-axis begins at 1200 and has a range of 800 points. This greater expanded scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.

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Answer: We can simplify the expression inside the absolute value first:

|(sqrt(2) + 3 - 5)|

= |(sqrt(2) - 2)|

Since sqrt(2) > 2, we know that sqrt(2) - 2 is negative. Therefore, we can rewrite the absolute value as a negative:

|sqrt(2) - 2| = -(sqrt(2) - 2)

So the expression without absolute value is:

-(sqrt(2) - 2)

Step-by-step explanation:

Answer:

The formula to calculate the amount of loan with flat rate interest is:

Amount = Principal + (Principal x Rate x Time)

Where,

Principal = the amount of loan

Rate = the interest rate per year

Time = the time period in years

Given,

Principal = K40,000.00

Rate = 9% per year

Time = 2.5 years

Substituting the values in the formula, we get:

Amount = K40,000.00 + (K40,000.00 x 0.09 x 2.5)

Amount = K40,000.00 + K9,000.00

Amount = K49,000.00

Therefore, the amount he will pay the bank is K49,000.00.

Answer:

We have two equations:

√x +2y^2 = 15 ----(1)

√4x - 4y^2=6 ----(2)

Let's solve for x:

From (1), we have:

√x = 15 - 2y^2

Squaring both sides, we get:

x = (15 - 2y^2)^2

Expanding, we get:

x = 225 - 60y^2 + 4y^4

From (2), we have:

√4x = 6 + 4y^2

Squaring both sides, we get:

4x = (6 + 4y^2)^2

Expanding, we get:

4x = 36 + 48y^2 + 16y^4

Substituting the expression for x from equation (1), we get:

4(225 - 60y^2 + 4y^4) = 36 + 48y^2 + 16y^4

Simplifying, we get:

900 - 240y^2 + 16y^4 = 9 + 12y^2 + 4y^4

Rearranging, we get:

12y^2 - 12y^4 = 891

Dividing both sides by 12y^2, we get:

1 - y^2 = 74.25/(y^2)

Multiplying both sides by y^2, we get:

y^2 - y^4 = 74.25

Let z = y^2. Substituting, we get:

z - z^2 = 74.25

Rearranging, we get:

z^2 - z + 74.25 = 0

Using the quadratic formula, we get:

z = (1 ± √(1 - 4(1)(74.25))) / 2

z = (1 ± √(-295)) / 2

Since the square root of a negative number is not real, there are no real solutions for z, which means there are no real solutions for y and x.

Therefore, the answer is "no solution".

The claims under "Regression" are as follows: 1. can be described by the l

Regression is a statistical technique that connects one or more independent (explanatory) variables to a dependent variable. If there is a relationship between changes in one or more of the explanatory factors and changes in the dependent variable, it can be shown using a regression model.

Y = mx + b is how the slope-intercept form of the equation for a straight line is expressed.

In the equation y = mx + b, m denotes the slope of the line and b its intercept. The distance between the line and the x- and y-axes is denoted by the letters x and y, respectively.

The first of the following claims, "Is used to assess the fit of a model," is true.

b) By including more factors, the result may be overstated.

called the coefficient of determination.

d.) Indicates the proportion of the variation in y that the model can account for.

e.) It is equivalent to the correlation coefficient r2 in basic linear regression.

What is Regression Analysis?

A collection of statistical procedures known as regression analysis is used to estimate the correlations between a dependent variable and one or more independent variables.

SS(res) + SS(reg) = SS, R2 1 - SS(res) / SS(tot) (tot)

R2 is defined as (SS(reg)/SS(tot) = (SS(reg)/n)/(SS(tot)/n)

Where SS(tot) = (y - y(bar)), the total sum of squares (proportional to the variance of the data), 2 • The explained sum of squares, also known as the regression sum of squares, is SS(reg) = (f(i)-y(bar)). SS(res) = (y(i) - f(i))2 = e2 is the sum of squares of residuals, often known as the residual sum of squares (i)

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The direction angle of the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0) is approximately 74.5 degrees clockwise from the positive x-axis in the xy plane.

To calculate the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0), we need to take the negative gradient of the electric potential V:

E = -∇V

where ∇ is the del operator, which is given by:

∇ = i(∂/∂x) + j(∂/∂y) + k(∂/∂z)

and i, j, k are the unit vectors in the x, y, and z directions, respectively.

To calculate the magnitude of the electric field at the point, we first need to find the partial derivatives of V with respect to x and y:

∂V/∂x = 2Axy - By^2

∂V/∂y = Ax^2 - 2Bxy

Substituting the values of A, B, x, and y, we get:

∂V/∂x = 2(5.00 V/m^3)(1.10 m)(0.400 m) - (8.00 V/m^3)(0.400 m)^2 = 0.44 V/m

∂V/∂y = (5.00 V/m^3)(1.10 m)^2 - 2(8.00 V/m^3)(1.10 m)(0.400 m) = -1.64 V/m

Next, we can calculate the magnitude of the electric field:

E = -∇V = -i(∂V/∂x) - j(∂V/∂y) - k(∂V/∂z)

= -i(0.44 V/m) + j(1.64 V/m) + 0k

= (0.44 i - 1.64 j) V/m

The magnitude of the electric field is given by:

|E| = sqrt((0.44 V/m)^2 + (-1.64 V/m)^2) = 1.70 V/m

Therefore, the magnitude of the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0) is 1.70 V/m.

To calculate the direction angle of the electric field, we need to find the angle that the electric field vector makes with the positive x-axis in the xy plane.

The angle can be found using the arctan function:

θ = arctan(Ey/Ex)

Substituting the values of Ex and Ey, we get:

θ = arctan(-1.64 V/m / 0.44 V/m) = -1.30 radians

The negative sign indicates that the direction angle is measured counter clockwise from the negative x-axis, which is equivalent to measuring clockwise from the positive x-axis.

Converting to degrees, we get:

θ = -1.30 radians * (180 degrees / pi radians) = -74.5 degrees

Therefore, the direction angle is approximately 74.5 degrees clockwise in the xy plane.

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James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.

Prοbability is a measure οf the likelihοοd οf an event οccurring. It is a numerical value between 0 and 1, where 0 means the event is impοssible and 1 means the event is certain tο οccur. Fοr example, the prοbability οf flipping a fair cοin and getting heads is 1/2 οr 0.5.

Tο calculate the tοtal cοst in Singapοre dοllars, we need tο cοnvert the US dοllars tο Singapοre dοllars using the given exchange rate, and then add the twο cοsts tοgether.

The cοst οf the item in Singapοre dοllars is:

75 USD * 1.65 SGD/USD = 123.75 SGD

The shipping and handling cοst in Singapοre dοllars is:

39 USD * 1.65 SGD/USD = 64.35 SGD

The tοtal cοst in Singapοre dοllars is the sum οf these twο cοsts:

Tοtal cοst = 123.75 SGD + 64.35 SGD = 188.10 SGD

Therefοre, James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.

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Therefore, the equation of the tangent line at (5,f(5)) is y = 18x - 65.

In mathematics, the slope of a line is a measure of its steepness or incline, usually denoted by the letter m. It describes the rate of change of a line in the vertical direction compared to the horizontal direction. The slope of a line can be positive, negative, zero, or undefined, depending on the angle it makes with the horizontal axis. The slope of a line is commonly calculated as the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points on the line.

Here,

(A) The slope of the secant line joining (2,f(2)) and (7,f(7)) is given by:

slope = (f(7) - f(2)) / (7 - 2)

We can find f(7) and f(2) by substituting 7 and 2, respectively, into the function f(x):

f(7) = 7² + 8(7) = 49 + 56 = 105

f(2) = 2² + 8(2) = 4 + 16 = 20

Substituting these values into the formula for the slope of the secant line, we get:

slope = (105 - 20) / (7 - 2) = 85 / 5 = 17

Therefore, the slope of the secant line joining (2,f(2)) and (7,f(7)) is 17.

(B) The slope of the secant line joining (5,f(5)) and (5+h,f(5+h)) is given by:

slope = (f(5+h) - f(5)) / (5+h - 5) = (f(5+h) - f(5)) / h

We can find f(5) and f(5+h) by substituting 5 and 5+h, respectively, into the function f(x):

f(5) = 5² + 8(5) = 25 + 40 = 65

f(5+h) = (5+h)² + 8(5+h) = 25 + 10h + h² + 40 + 8h = h² + 18h + 65

Substituting these values into the formula for the slope of the secant line, we get:

slope = ((h² + 18h + 65) - 65) / h = h² / h + 18h / h = h + 18

Therefore, the slope of the secant line joining (5,f(5)) and (5+h,f(5+h)) is h+18.

(C) The slope of the tangent line at (5,f(5)) is equal to the derivative of the function f(x) at x=5. We can find the derivative of f(x) as follows:

f(x) = x² + 8x

f'(x) = 2x + 8

Substituting x=5, we get:

f'(5) = 2(5) + 8 = 18

Therefore, the slope of the tangent line at (5,f(5)) is 18.

(D) The equation of the tangent line at (5,f(5)) can be written in point-slope form as:

y - f(5) = m(x - 5)

where m is the slope of the tangent line, which we found to be 18. Substituting the values of m and f(5), we get:

y - 65 = 18(x - 5)

Simplifying, we get:

y = 18x - 65

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Answer:

30 pounds

Step-by-step explanation:

Since the jumper costs 50 pounds, the decimal for the number will be:

50.

To find ten percent of the number, you move the decimal one time to the LEFT.

Therefore, 10% of 50 pounds will be 5 pounds. To find 40%, we simply will multiply the 10% amount by 4.

40% of 50 will be:

20

Therefore, the jumper will have 20 pounds off.

Since the original cost is 50 pounds, we simply will just subtract 50 - 20:

50 - 20 = 30

The jumper will cost 30 pounds with the sale deal.

The cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.

Marginal cost is the additional cost incurred by producing one additional unit of a good or service. In other words, it is the cost of producing one more unit of output.

The marginal cost (MC) equation given is MC = 2x - 100, where x is the number of units produced.

To find the cost of producing an additional 200 items due to increased demand, we need to calculate the marginal cost of producing these 200 items and then multiply that by 200.

The marginal cost of producing 200 additional items is given by:

MC(200) = 2(300 + 200) - 100

MC(200) = 2(500) - 100

MC(200) = 900

So the marginal cost of producing 200 additional items is 900. To find the total cost of producing these 200 items, we can simply multiply the marginal cost by the number of units produced, which in this case is 200:

Total cost = MC(200) × 200

Total cost = 900 × 200

Total cost = 180,000

Therefore, the cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.

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Answer:j+309=313

Step-by-step explanation:

313-309=4

J=4

The function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.

Function in mathematics is a relation between two sets, where one set is the input and the other set is the output. Functions are an important tool in mathematics and can be used to describe and model real-world phenomena. Functions take inputs, manipulate them and produce outputs. They can be used to represent relationships between two or more variables, or to represent a complex process. Functions allow us to break down complex problems into smaller, more manageable pieces and to study how changes in one variable affect other variables.

The function represented by the table is linear. It can be determined by the fact that the y-values change by the same amount every time the x-values increase by one unit. In this case, the y-values decrease by 2 each time the x-values increase by one unit. This is an example of a linear function.

Linear functions have the shape of a straight line and are characterized by having a constant rate of change. The constant rate of change is represented by the slope of the line, which in this case is -2. This means that for every one unit increase in the x-values, the y-values decrease by two.

A quadratic function is the opposite of a linear function, as it has a rate of change that is not constant. Quadratic functions are characterized by their parabolic shape and their rate of change increases as x-values increase. Exponential functions are characterized by their curved shape and increase exponentially as x-values increase.

In conclusion, the function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.

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Answer:

470.4 mm

Step-by-step explanation:

Given: the annual rainfall in 2017 in opuwo was 420 mm, the annual rainfall in 2018 was 12% more than in 2017.

First, find 12% of 420 mm:

12% of 420 mm

[tex]\frac{12}{100}[/tex] x 420 mm

1.2 x 420 mm

= 50.4 mm

Then add 50.4 mm to the previous annual rainfall of 420 mm:

50.4 mm + 420 mm

= 470.4 mm

Therefore, the annual rainfall in opuwo in 2018 is 470.4 mm.

The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.

In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.

Next, we need to find the derivative of x = √y with respect to y, which is:

dx/dy = 1/2√y

Substituting this into the formula for the surface area, we get:

Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy

Simplifying the expression inside the square root, we get:

Surface Area = 2π ∫[0,4] √(y+(1/4)) dy

We can evaluate this integral using the power rule of integration, which gives:

Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴

Simplifying further, we get:

Surface Area = 2π [2/3(17/4)^(3/2)]

Surface Area ≈ 54.33 square units

Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.

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Complete Question:

How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?

Answer:

the two numbers are 15 and 35, and their ratio is 3:7, and their difference is 20.

Step-by-step explanation:

The radioactive material has a half-life of roughly 11.8 days.

The amount of time it takes for an active component of a medication to degrade by half in your body is referred to as the half-life.

Let's apply the exponential decay formula:

N(t) = N0 e(-kt)

Let's calculate the decay constant using the information provided:

At time t=0, the number of counts per minute is N0 = 16000.

At time t=13 days, the number of counts per minute is N(13) = 1000.

When we enter these numbers into the equation, we obtain:

N(13) = N0 e(-k*13)

1000 = 16000 e(-k*13)

e(-k*13) = 1000/16000

When we take the natural logarithm of both sides, we obtain:

ln(e(-k*13)) = ln(1000/16000)

-k*13 = ln(1000/16000)

k = -ln(1000/16000)/13

k ≈ 0.0585

We may use the half-life formula now that we know the decay constant:

t1/2 = ln(2)/k

Substituting k = 0.0585, we get:

t1/2 = ln(2)/0.0585

t1/2 ≈ 11.8

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10% chance of contamination by a particular: It's not clear what random variable is being referred to here, but if it's the probability of contamination.

In general terms, a distribution refers to the way something is divided or spread out. In the context of statistics and probability theory, a distribution is a mathematical function that describes the likelihood of different possible outcomes or values that a variable can take.

There are various types of distributions, but some of the most commonly used ones include:

Normal distribution: also known as the Gaussian distribution, it is a continuous probability distribution that is symmetrical around the mean, with most of the data falling within one standard deviation of the mean.

Binomial distribution: this is a discrete probability distribution that describes the likelihood of a certain number of successes in a fixed number of trials.

Poisson distribution: another discrete probability distribution that describes the likelihood of a certain number of events occurring in a fixed interval of time or space.

Exponential distribution: a continuous probability distribution that describes the time between events occurring at a constant rate.

Distributions are essential in statistical analysis as they can help to understand and analyze data, make predictions, and draw conclusions about a population based on a sample of data.

Given by the question.

a. The wages of academician and non-academician workers in UPSI: This random variable can be approximated to a continuous distribution as wages can take on any numerical value within a range. However, it's worth noting that in practice, there may be discrete intervals or categories of wages, in which case a discrete distribution may be more appropriate.

b. The time taken to submit online quiz answer's document: This random variable can also be approximated to a continuous distribution as it can take on any numerical value within a range.

c. The prices of SAMSUNG mobile phones displayed at a phone shop: This random variable can be approximated to a continuous distribution as prices can take on any numerical value within a range.

d. The number of pumps at Shell petrol stations in Perak: This random variable can be approximated to a discrete distribution since the number of pumps can only take on integer values.

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In respοnse tο the questiοn, we may say that As a result, FHJ stοck has equatiοn highest cοefficient οf variatiοn, with a value οf arοund 4.33%.

In mathematics, an equatiοn is a statement that expresses the equality οf twο expressiοns. Equatiοn is made up οf twο sides that are jοined by the algebraic symbοl (=). Fοr example, in this argument, it is asserted that "2x + 3 = 9" denοtes that "2x plus 3" equals the number "9".

Equatiοn sοlving is the prοcess οf determining the value(s) οf the variable(s) required fοr the equatiοn tο be true. There are many different kinds οf equatiοns, such as regular and nοnlinear οnes with οne οr mοre elements. This fοrmula raises the variable x tο the secοnd pοwer: "x² + 2x - 3 = 0." Lines are used in the study οf mathematics in the fields οf algebra, calculus, and geοmetry.

The cοefficient οf variatiοn (CV) represents the standard deviatiοn as a percentage οf the mean and is a relative measure οf variability. It is cοmputed as fοllοws:

CV = (standard deviatiοn / mean) multiplied by 100%

Tο determine which οf the three stοcks has the highest cοefficient οf variatiοn, we must cοmpute the CV fοr each and cοmpare the results.

Fοr ACE inventοry:

CV = (1.5 / 37.03) x 100% ≈ 4.05%

In the case οf FHJ stοck:

CV = (2.62 / 60.55) x 100% ≈ 4.33%

In the case οf LMP stοck:

CV = (3.06 / 124.9) x 100% ≈ 2.45%

As a result, FHJ stοck has the highest cοefficient οf variatiοn, with a value οf arοund 4.33%.

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The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.

It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.

To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.

0-3 interval:

Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:

slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2

pauses [3, 5]:

Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:

slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5

[5–7] Interval:

Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:

slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1

Interval 7 and 9:

Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:

slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5

As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.

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a) The domain and the range of the function are given as follows:

The graph of the function is given by the image presented at the end of the answer.

b) The trip was 5.1875 hours long.

The function for this problem is defined as follows:

g(t) = 23 - 3.2t.

The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the volume is given as follows:

23 - 3.2t = 0

3.2t = 23

t = 23/3.2

t = 7.1875 hours.

The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].

The graph is a linear function between points (0, 23) and (7.1875, 0).

At the end of the trip there were 6.4 gallons left, hence the length of the trip is given as follows:

23 - 3.2t = 6.4

t = (23 - 6.4)/3.2

t = 5.1875 hours.

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Answer:

Let's start by setting up an equation to represent the problem. Let x be the cost of the meal:

x + 0.1x = 126.50

Simplifying the left side of the equation:

1.1x = 126.50

Dividing both sides by 1.1:

x = 115

Therefore, the cost of the meal was £115.

Answer:

[tex]\dfrac{4096\pi}{5}\approx 2573.593\; \sf (3\;d.p.)[/tex]

Step-by-step explanation:

The shell method is a calculus technique used to find the volume of a solid revolution by decomposing the solid into cylindrical shells. The volume of each cylindrical shell is the product of the surface area of the cylinder and the thickness of the cylindrical wall. The total volume of the solid is found by integrating the volumes of all the shells over a certain interval.

The volume of the solid formed by revolving a region, R, around a vertical axis, bounded by x = a and x = b, is given by:

[tex]\displaystyle 2\pi \int^b_ar(x)h(x)\;\text{d}x[/tex]

where:

[tex]\hrulefill[/tex]

We want to find the volume of the solid formed by rotating the region bounded by y = 0, y = √x, x = 0 and x = 16 about the y-axis.

As the axis of rotation is the y-axis, r(x) = x.

Therefore, in this case:

[tex]r(x)=x[/tex]

[tex]h(x)=\sqrt{x}[/tex]

[tex]a=0[/tex]

[tex]b=16[/tex]

Set up the integral:

[tex]\displaystyle 2\pi \int^{16}_0x\sqrt{x}\;\text{d}x[/tex]

Rewrite the square root of x as x to the power of 1/2:

[tex]\displaystyle 2\pi \int^{16}_0x \cdot x^{\frac{1}{2}}\;\text{d}x[/tex]

[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x[/tex]

Integrate using the power rule (increase the power by 1, then divide by the new power):

[tex]\begin{aligned}\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x&=2\pi \left[\dfrac{2}{5}x^{\frac{5}{2}}\right]^{16}_0\\\\&=2\pi \left[\dfrac{2}{5}(16)^{\frac{5}{2}}-\dfrac{2}{5}(0)^{\frac{5}{2}}\right]\\\\&=2 \pi \cdot \dfrac{2}{5}(16)^{\frac{5}{2}}\\\\&=\dfrac{4\pi}{5}\cdot 1024\\\\&=\dfrac{4096\pi}{5}\\\\&\approx 2573.593\; \sf (3\;d.p.)\end{aligned}[/tex]

Therefore, the volume of the solid is exactly 4096π/5 or approximately 2573.593 (3 d.p.).

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Power Rule of Integration}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}(+\;\text{C})$\\\end{minipage}}[/tex]

The height of the pole is approximately 17.75 meters.

The main trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. They are used to relate the angles of a right triangle to the lengths of its sides. The sine function gives the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle. The cosine function gives the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent function gives the ratio of the length of the opposite side to the length of the adjacent side.

Let's denote the height of the pole as h, and let's denote the distance between the pole and the student's original position (due west of the pole) as x.

From the student's original position, we have a right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 40°. So, we have:

tan(40°) = h/x

From the student's new position (10 m due south of the original position), we have another right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 35°. The distance between the pole and the student's new position is (x+10) meters (the student moved 10 m south). So, we have:

tan(35°) = h/(x+10)

Now we have two equations with two unknowns (h and x). We can solve for x in terms of h from the first equation:

x = h/tan(40°)

Substitute this expression for x into the second equation:

tan(35°) = h/((h/tan(40°))+10)

Simplify and solve for h:

h = (10 tan(35°) tan(40°)) / (tan(40°) - tan(35°)) ≈ 17.75 m

Therefore, the height of the pole is approximately 17.75 meters.

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Answer: 44%

Step-by-step explanation:

22 is the smallest of the two numbers, and you want that number as a percentage of the sum of the two numbers. So basically it is asking you to put 22/(22+28) as a percentage. The step by step is as follows:

1. Simplify denominator

22+28 = 50

2. Rewrite the fraction so that the numerator is out of 100

22/50 = 44/100

3. Convert this new fraction to percentage

44/100= 44%

Hope this helps!!

Exchange rate calculation.

To find out the amount in Singapore dollars that Mr Li would need to give each of his five relatives 500 RMB each, we can follow these steps:

Calculate the total amount in RMB that Mr Li needs to give:

500 RMB/relative x 5 relatives = 2500 RMB

Convert the total amount in RMB to Singapore dollars using the given exchange rate:

2500 RMB x (S$100/RMB510.20) = S$490.64 (rounded to the nearest cent)

Therefore, Mr Li would need S$490.64 to give each of his five relatives 500 RMB each, given the exchange rate of S$100 to RMB510.20.

ChatGPT

Uri paid a total of $85.47 for the landscaping service including tax and tip.

Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.

Given that company charged $74 for the service plus 5% tax.

The tax is 5%, that is:

Tax = 5% of $74 = 0.05 x $74 = $3.70

Cost after tax = $74 + $3.70 = $77.70

Now, tip is 10%:

Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77

Total cost = $77.70 + $7.77 = $85.47

Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.

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