The Great Lakes have a water area of about 2.44 X 105 square
kilometers. One of them, Lake Huron, has a water area of about
6.0 x 104 square kilometers. What approximate fraction of the total
water area of the Great Lakes does Lake Huron represent?

It would take the two painters together eight hours to paint the house

Step-by-step explanation: Given that, One painter can paint the entire house in twelve hours. The second painter takes eight hours to paint a similarly-sized house. To find, How long would it take the two painters together to paint the house? Suppose one painter takes x hours to paint the house.

Therefore, the other painter will take x-4 hours to paint the same house. According to the question, \(1/x+1/(x-4)=1/12+1/8\) Multiply by LCM, \(8(x-4)=12x+12(x-4)8x-32=6x+484x=80x=20\)Therefore, the first painter will take 20 hours to paint the house. The second painter will take 16 hours (20-4). Together they will take, \(1/20+1/16=0.1+0.0625=0.1625\) Thus, they will take 6.1538 hours which can be rounded to 4.8 hours.

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The probability that a randomly chosen part is defective is 0.16, or 16%.

The probability that a randomly chosen part is defective, we need to use the law of total probability.

Let \($D$\) be the event that a part is defective and let \($M_i$\) be the event that the part came from machine \($i$\), for \($i = A, B, C$\).

Then we have:

\($P(D) = P(D|M_A)P(M_A) + P(D|M_B)P(M_B) + P(D|M_C)P(M_C)$\)

60% of the products come from machine A, 30% from machine B, and 10% from machine C.

Therefore:

\($P(M_A) = 0.6$\)

\($P(M_B) = 0.3$\)

\($P(M_C) = 0.1$\)

The probability of a part being defective is 10% if it comes from machine A, 30% if it comes from machine B, and 40% if it comes from machine C.

Therefore:

\($P(D|M_A) = 0.1$\)

\($P(D|M_B) = 0.3$\)

\($P(D|M_C) = 0.4$\)

Substituting these values into the law of total probability, we get:

\($P(D) = 0.1 \cdot 0.6 + 0.3 \cdot 0.3 + 0.4 \cdot 0.1 = 0.16$\)

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The line which has a gradient of 6 is A. line A

To answer the question, we need to know what the gradient of a line is.

The gradient of a line is its slope. It is given by m = Δy/Δx where

Now, to find the line that has the gradient of 6, we see that the gradient

So, for a high value of gradient, we need

Also, since 6 is positive, the gradient for the line will be positive.

The only line that meets these criteria is line A.

So, the line which has a gradient of 6 is A. line A

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The equivalent exponential decay function is given as \(m(t)=18000(0.81)^t\)

An exponential function is in the form

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let m(t) represent the value of the car after t years, hence the exponential decay is given by:

\(m(t) = 18000(0.9)^{2t}\\\\m(t)= 18000(0.9)^{2(t)}\\\\m(t)=18000(0.81)^t\)

The equivalent exponential decay function is given as \(m(t)=18000(0.81)^t\)

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Answer:

4566

Step-by-step explanation:

you you get that answer by learning and trying your best like me by

The function that best models the temperature as a function of time in hours since noon is a sinusoidal function, specifically a cosine function.

The cosine function best represents the temperature variation over time, with a range of 40°F (from 30°F to 70°F) and a period of 12 hours.

The temperature variation throughout the day follows a cyclic pattern, similar to the shape of a cosine curve. At noon, which is 6 hours after the low temperature of 30°F, the temperature is at its highest point of 70°F. As time progresses from noon, the temperature decreases following the decreasing phase of the cosine curve until it reaches its lowest point of 30°F at 6:00 am, which is 18 hours after noon. From that point, the temperature begins to increase again, following the increasing phase of the cosine curve.

The cosine function is well-suited to represent this cyclic behavior because it oscillates between the highest and lowest temperatures with a regular period of 12 hours. By using a cosine function, we can accurately model and predict the temperature at any given time since noon.

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Answer:

I believe the answer is $1702.50.

Step-by-step explanation:

If you multiply 1500 by 4.5% (0.045 as a decimal) you will get 67.5 which is $67.5 interest for one year. For three years, you have too multiply 67.5 by 3 and you get $202.5. Finally, you add the total interest to the starting amount, $1500, which results in $1702.50.

Answer:

Step-by-step explanation:

\(\pmb {sin(22)^o=\cfrac{x}{35} }\)

\(\pmb {35sin(22)=w}\)

\(\pmb {w=13.11}\)

_________________

Hope this helps!

Have a great day! :)

Answer:

numbro 4

Step-by-step explanation:

Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

Therefore, it will take Sam 8 minutes to cut another identical plank into only 3 pieces, working at the same pace.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equals sign (=). The LHS and RHS can be made up of variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the relationship between the LHS and the RHS. Equations are fundamental to many areas of mathematics, science, engineering, and everyday life.

Here,

If Sam cuts a plank of wood into 4 pieces, then he needs to make 3 cuts. Since each cut takes equally as long, he spends 12/3 = 4 minutes per cut.

To cut another identical plank of wood into 3 pieces, he needs to make 2 cuts. Since he spends 4 minutes per cut, it will take him 2 * 4 = 8 minutes to complete this task.

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The factorization can be used to reveal the zeros of the function is the group method

To determine the zeros, we need to multiply the coefficient of the x squared by the constant value.

Then, find the pair factors of the product that add up to give -11

From the information given, we have ;

-12n^2-11n+15

Now, substitute the pair factors, we get;

-12n² - 9n + 20n + 15

Group in pairs

(-12n² - 9n ) + (20n + 15)

Factor the common terms

-3n(4n + 3) + 5(4n + 3)

then, we have;

-3n + 5 = 0

n = 5/3

4n + 3 = 0

n = -3/4

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Answer:

The answer is B (4, 8) and (0, -8)

Answer:

50

Step-by-step explanation:

I got mine right I promis

Answer:

115%, 1.15, 115/100

Step-by-step explanation:

The end of the 48-inch long treadmill is raised approximately 8.36 inches.

The incline of the treadmill is given as 10 degrees.

We can use trigonometry to calculate the height of the end of the treadmill.

The height (h) can be found using the formula h = l * sin(θ), where l is the length of the treadmill and θ is the angle of inclination.

Substitute the values into the formula:

h = 48 inches * sin(10 degrees)

Calculate the sine of 10 degrees using a calculator:

sin(10 degrees) ≈ 0.1736

Multiply the length of the treadmill by the sine of the angle:

h = 48 inches * 0.1736 ≈ 8.36 inches

The end of the 48-inch long treadmill is raised approximately 8.36 inches when set at an incline of 10 degrees.

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Answer:

There are 220 students at Marie's school :)

Step-by-step explanation:

-3y=12-15x

y=12-15x/-3

y=5x-4

Answer:

y = 1/5y + 4/5

Step-by-step explanation:

15x = 3y + 12

y = 3/15y + 12/15

y = 1/5y + 4/5

Answer:

52.5

Step-by-step explanation:

A=a+b

2h=8+13

2·5=52.5

The specific gravity of the combined product is 1.22

Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.

Given,

The total quantity of portion= 50 ml

Specific gravities of the three syrups = 1.10,1.25 and 1.32

Then,

The specific gravity of the combined product= \(\frac{1.10+1.25+1.32}{3}\)

= 1.22

Hence, the specific gravity of the combined product is 1.22.

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Δy=v-0.32 and dy = -0.32 .Δy and dy are both used to represent changes in the dependent variable y based on changes in the independent variable x.

Δy represents the change in y (the dependent variable) resulting from a specific change in x (the independent variable). In this case, y = x^4 + 7, x = -2, and Δx = dx = 0.01. Therefore, we need to calculate Δy and dy based on these values.

To calculate Δy, we substitute the given values into the derivative of the function and multiply it by Δx. The derivative of y = x^4 + 7 is dy/dx = 4x^3. Plugging in x = -2, we have dy/dx = 4(-2)^3 = -32. Now, we can calculate Δy by multiplying dy/dx with Δx: Δy = dy/dx * Δx = -32 * 0.01 = -0.32.

On the other hand, dy represents an infinitesimally small change in y due to an infinitesimally small change in x. It is calculated using the derivative of the function with respect to x. In this case, dy = dy/dx * dx = 4x^3 * dx = 4(-2)^3 * 0.01 = -0.32.

Therefore, both Δy and dy in this context have the same value of -0.32. They represent the change in y corresponding to the change in x, but Δy considers a specific change (Δx), while dy represents an infinitesimally small change (dx) based on the derivative of the function.

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Answer: $1.05

Step-by-step explanation:

March has 31 days

Hence,

\(\displaystyle\\32.55:31=\\\\32\frac{55}{100}*\frac{1}{31} =\\\\32\frac{11}{20} *\frac{1}{31} =\\\\\frac{(32)(20)+11}{(20)(31)} =\\\\\frac{640+11}{620} =\\\\\frac{651}{620}=\)

$1.05

Answer:

-1

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

5×(-8)+8×4+6+1

-40+32+7

=-1

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = - 3x + 2.5

The value of the equation at x = 1 will be given as,

y = - 3 × (1) + 2.5

y = - 3 + 2.5

y = - 0.5

The value of the equation at x = - 1.5 will be given as,

y = - 3 × (-1.5) + 2.5

y = 4.5 + 2.5

y = 7

The value of the equation at x = 8.5 will be given as,

y = - 3 × (8.5) + 2.5

y = - 22.5+ 2.5

y = - 20

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

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Complete question:

Answer:

-6a\(x^{3\)b\(x^{6}\) - 8a\(x^{2}\)b\(x^{5}\)

Step-by-step explanation:

Answer:

No asymptote

Step-by-step explanation:

This equation is linear, so it will not have an astmptote.

The probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

In a probability context, an event refers to an outcome or set of outcomes of an experiment or process. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of winning the lottery can be calculated using the formula:

Probability of winning = 1 / odds

Here, the odds of winning are given as 1-in-3,598. So, the probability of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla has bought 10 lottery tickets. So, the probability of winning the $200 prize with at least one ticket can be calculated as the complement of the probability of not winning with any of the tickets. That is:

Probability of winning with at least one ticket = 1 - Probability of not winning with any ticket

The probability of not winning with a single ticket is 1 - 0.000278 = 0.999722. So, the probability of not winning with all 10 tickets is:

Probability of not winning with all 10 tickets = (0.999722)¹⁰

= 0.997247

Therefore, the probability of winning with at least one ticket is:

Probability of winning with at least one ticket = 1 - Probability of not winning with all tickets

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

So, the probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

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Shayla's probability of winning the $200 prize with 10 lottery tickets are at 0.2753%.

An event in the context of probability is a result, or series of results, of an experiment or procedure. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.

The following formula can be used to determine the likelihood of winning the lottery:

Probability of winning = 1 / odds

The odds of winning in this case are 1 in 3,598. Therefore, the likelihood of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla purchased ten lottery tickets. As a result, the likelihood that at least one ticket will win the $200 reward can be computed as the complement of the likelihood that none of the tickets will win. Which is:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

The likelihood that a single ticket won't be the winner is 1 - 0.000278 = 0.999722. Consequently, the likelihood of not winning with all ten

tickets is:

with all ten tickets, what is the likelihood of not winning = (0.999722)¹⁰

= 0.997247

Consequently, the following is the likelihood of winning with at least one ticket:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

Shayla's chances of winning the $200 prize with 10 lottery tickets are at 0.2753%.

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The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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