Two boats left the harbour at the same time. One travelled at 10km/h on a bearing N47degreeE. The other traveled at 8km/h on a bearing of N79degreeE. How far apart are the boats after 45min? Round the distance to nearest tenth of a km.

A randomly selected subject has a 0.40 probability of completing more tasks than expected in 5 minutes while listening to relaxing music.

The Probability distribution is:

    X                     1                    2                3              4          

   P(x)             0.20          0.40      0.30             0.10

If listening to soothing music, the expected number of puzzles in 5 minutes can be calculated as follows:

            E(x) = ∑x p(x)

       ⇒ E(x) = 1 ×(0.20) + 2× 0.40 + 3 × 0.30 + 4× 0.1

       ⇒ E(x) = 0.20 + 0.8 + 0.9 + 0.4

       ⇒ E(x) = 2.3

Thus, a randomly selected subject could solve 5 puzzles while listening to soothing music. The probability of solving more tasks than expected in a minute is calculated as:

    P( X > 2.3) = P(X = 3) + P(X = 4)

                      = 0.30 + 0.10

                      = 0.40

Explanation for other  option:

(a) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music does not equal 0.1.

(c) 5 randomly selected participants. The probability of completing more tasks than expected in a minute of listening to relaxation music does not equal 0.8.

(d) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music is not equal to 1.

(e) The likelihood of randomly selected participants completing more tasks than expected in 5 minutes while listening to relaxing music cannot be determined.

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The transformation is a vertical stretch

From the question, we have

f(x) = -|x| + 1

g(x) = -8|x| + 8

The transformation from the graph of f(x) = -|x| + 1 to the graph of g(x) = -8|x| + 8 is a vertical stretching by a factor of 8.

The transformation results in the graph of g(x) being 8 times taller than the graph of f(x).

Mathmatically, this is

g(x) = 8f(x)

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If you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).

To calculate the answer to this question, we need to consider what the words “exclusive” and “inclusive” mean. Exclusive means that one option is required and the other is not, while inclusive means that both options are available. In the case of the question a, the answer is exclusive because you must take either chemistry or physics to graduate. In the case of question b, the answer is inclusive because you can have either a complimentary coffee or tea.

To illustrate the difference between exclusive and inclusive with a formula, we can use the following:

Exclusive: A + B = A

Inclusive: A + B = A + B

This formula demonstrates that if you have two options, A and B, exclusive means only one option is required (A or B) while inclusive means both options are available (A and B).

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Answer:

There are 6 workers in the team.

Step-by-step explanation:

Let's call the number of workers "n".

We know that the team of workers could have completed the job in 24 hours if they had worked together. We also know that the resulting work time would have been reduced by 6 hours if all but 5 workers had worked together from the start.

So, if n workers worked together from the start, the work time would be 24 - 6 = 18 hours.

We also know that the workers joined one by one, starting with 1 worker and ending with n workers working together.

The total work time can be calculated using the arithmetic series formula:

work time = n/2 * (1 + n)

So, if we set the work time to 18 hours:

18 = n/2 * (1 + n)

We can solve this equation for n:

18 = n/2 * (n+1)

36 = n^2 + n

n^2 + n - 36 = 0

We can solve this quadratic equation by factoring it.

(n-6)(n+6) = 0

So the solutions are n = 6 and n = -6.

But the number of workers can not be negative, so the answer is n=6.

If to the nearest whole number, then 2. If to the nearest tenth, then 1.5.

0.579 + .94 is 1.519.

When rounding to the nearest whole number, if the first number after the decimal point is 5 or higher, round up. If 4 or lower, then round down.

Giovanna's error is that she should have added the fractions instead of adding the whole numbers and the fraction. The correct calculation is 14 7/8 inches.

2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8 + 2 5/8

= (2 + 2 + 2 + 2 + 2 + 2 + 2) + (5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8)

= 14 + (5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8)

= 14 + (7/8)

= 14 7/8

Giovanna made an error when calculating the height of a stack of 7 books that are each 2 5/8 inches thick. The correct calculation was 14 7/8 inches, however, she calculated 14 + 5/8 inches. This is incorrect because it is necessary to add the fractions together in order to get the correct answer. To calculate the height of the stack of books, we need to add each book's thickness together. Since each book is 2 5/8 inches thick, we start by adding the whole numbers: 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14. Then, we add the fractions: 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 + 5/8 = 7/8. Adding these together gives us 14 + 7/8 = 14 7/8. Thus, the correct answer is 14 7/8 inches.

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According to the separable differential equation, the family of implicit solution is  1/2 (x² - y²)

The term separable differential equation is defined as in which the variables can be separated from each other are called separable differential equations.

As per the definition the general form to write separable differential equations is dy/dx = f(x) g(y), where the variables x and y can be separated from each other.

Here we have given that (dy/dx) = (x/y)

When we cross multiply the terms, then we get,

=> y dy = x dx

When we differentiate the terms, then we get the following,

=> ∫y dy = ∫x dx

The solution of this integral can be written as,

=> y²/2 + C = x²/2 + C

When we simplify this one then we get the resulting expression as,

=> x²/2 - y²/2 = 0

=> 1/2 (x² - y²)

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Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).

Each point in the plane that is a certain distance from some other point forms a circle (center). Thus, it is an arc composed of points that also are spaced apart from one another in the plane. Additionally, at every angle, it is radial symmetric about the center. In the closed, two-dimensional plane of a circle, every pair of endpoints is uniformly separated from the "center." By drawing lines through the circle, one can create a line of circular symmetry. Additionally, it rotates equally at all angles about the center.

Here,

This is what we get when we use the parametric values in both r2 and r1 as functions of t:

Curve 1: x1(t), y(t), and z(t) = 48-12

Figure 2: Curve 2:

x2(t)=8-t, y2(t)=t-3, 22(t) = 12

Where they meet, they are equal, so:

x1(t) Equals x2(t),

where t=8-t 2t8 and t=4

(x(t), y(t), z(t)) = using curve 1 (t,5-t,48-12)

Following that,

(x(4), y(4), 2(4)) = (4,5-4, 48-42) = (4,1,32)

They get together at point (4, 1, 32).

Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).

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In mathematics, the symbol ∆ (delta) is often used to indicate a change or difference in a quantity.

When used in the context of Calculus, ∆x (delta x) is a notation that represents the change in the independent variable x, often used in the study of limits, derivatives and integrals. It is defined as the difference between two nearby values of x, for example x2 - x1.

Also, In physics and engineering, the notation ∆x is used to refer to the change in position or displacement of an object. It is defined as the final position minus the initial position of an object.

In general, ∆x is used to represent a small change or difference in a variable, usually used in the context of calculus and physics.

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The equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

What is point slope form of line?

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.

One of the formulas used to determine a line's equation is the point slope formula. According to the point slope formula, y - y1 = m (x - x1) is the equation for a line with slope "m" and the points (x, y1) on it.

We have to find the equation of line that passes through the points (6, 5) and (0, -7).

First to find the slope of the line,

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{-7-5}{0-6}= \frac{-12}{-6} = 2[/tex]

Now, consider the point slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 2, (x_1, y_1) = (0, -7)[/tex]

⇒

[tex]y-(-7)=2(x-0)\\y+7=2x\\y=2x-7[/tex]

Hence, the equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

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The volume of coal is 42.41 cubic meters when a pile of coal is stored in a barrel-shaped bin whose base has a radius of 3 meters, and the height of the pile measures 1.5 meters.

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another.

The volume of a cylinder V= b*h

where b is the area of the base

h is the height of the cylinder.

And since the area of a circle is πr², we have this equation for the volume of a cylinder  

V = π×r²×h    

Now substitute, the known values for r and h, then calculate the result:  

V = π×r²×h  

V = 3.14159×3²×1.5  

V = 3.14159×9×1.5  

V = 42.411465  

V = 42.41  

So the volume of the coal pile is 42.41 cubic meters.

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x² - 10 = 36

x² = 46

x = +- sqrt(46)

Answer:

-7.9n+9.8

Step-by-step explanation:

add em

Answer:

9.8 - 7.9n

Step-by-step explanation:

To simplify, we need to have the least amount of terms possible. To do this here, we need to group like terms. We will start by rearranging our equation to group our like terms, like this:

3.8 + 6 - 4.9n - 3n

Then, we will combine our liker terms, giving us:

9.8 - 7.9n

That is the most simplified we can get. So our simplified equation is

9.8 - 7.9n.

Hope this Helped!

About 96.17% of the students who took the test earned a 70 points or higher

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The z score of a normal distribution is given by:

z = (raw score - mean)/standard deviation

The average test score from the last year's class was 85 points with a standard deviation of 9. Hence:

Mean = 85, standard deviation = 9

For a score of 70 points or higher:

z = (70 - 85) / 9 = -1.67

P(z > -1.67) = 1 - P(z < -1.67) = 1 - 0.0383 = 0.9617 = 96.17%

96.17% of the students earned a 70 points or higher

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Answer: 1/11

Step-by-step explanation:

16 is close to 20

217 is close to 220

20/220=2/22=1/11

C(m) = 850 + 65m is the formula for the total cumulative cost (C) per month (m).

Linear equations are equations that has a leading degree of 1. An example of a linear equation is y = mx + b

where:

According to the given question, Janine is getting a new phone. She needs to purchase her phone, which is $850.

Amount paid monthly = $65

If she completes the payment in 'm' months, the equation for total cumulative cost (C) per month (m) is C(m) = 850 + 65m

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Answer:

1 is a common factor of all numbers and every number is a factor of itself.

Step-by-step explanation:

so yes it can be a common factor

Answer:

Domain: ℝ or (-∞, ∞)

Range: ℝ or (-∞, ∞)

Step-by-step explanation:

Domain is the set of valid x-values that will result in a real output when plugged into a function. On this graph, we can see that the line continues left past x = 0 and right past x = 14. So, we have to assume that the line continues on forever, and thus its domain is all real numbers (represented by ℝ). In the context of this problem, it means that there are infinite points in time where the falling object will exist at some height.

Range is the set of valid y-values that will result in a real output when plugged into the equation of a line. On this graph, the line continues upwards past y = 7 and downwards past y = 0. So, we have to assume that the line continues on forever, and thus its domain is all real numbers. In the context of this problem, that means that there are infinite heights which the falling object can be at.

The lateral surface area is 1562.5  If the floor of a cuboidal hall has a perimeter of 225m and height 25m.

What is volume of Cuboid ?

volume of cuboid can be defined as the product of length , breadth and height.

Given,

If the floor of a cuboidal hall has a perimeter of 225m and height 25m

Lateral Surface area = 2h(l+b)

Given perimeter is 225m

so,

perimeter = 4 (l+b+h)

225 = 4 (l+b+25)

Given h = 25

225 = 4(l+b) + 100

4(l+b) = 225-100

4(l+b) = 125

l+b = 125/ 4

So,

Lateral surface area = 2h (l+b)

= 2 * 25 * ( l+b)

= 50*125/4

= 1562.5

Hence , The lateral surface area is 1562.5  If the floor of a cuboidal hall has a perimeter of 225m and height 25m.

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Using proportions, it is found that Product A sold 345600 units.

In this problem, we have that Product B sold 70% less, that is, 30% of Product C, which sold 39,000 units, hence:

B = 0.3 x 33000 = 9900.

Product A sold 3.5 times more than Product B. So, the number of units sold by Product A is given by:

A = 3.5 x 9900 = 346500.

Therefore, Product A sold 345600 units.

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Answer:

1,666,667

Step-by-step explanation:

1000 milligrams is equal to one gram.

First, convert the mass of the grain of salt in milligrams to grams by dividing the mass in milligrams by 1000:

[tex]\implies \dfrac{0.06}{1000}=0.00006\; \rm g[/tex]

To calculate how many grains of salt would be in 100 grams of sand, divide 100 g by 0.00006 g:

[tex]\implies \dfrac{100}{0.00006}=1,666,666.6666...[/tex]

Therefore, there are 1,666,667 grains of salt in 100 grams of sand (to the nearest whole number).

Answer is c. 2.5, 4, 5

Step-by-step explanation:

To find the dimensions of the new triangle,

we need to apply the scale factor of 0.5 to the original triangle's dimensions.

This means we need to multiply each dimension by 0.5.

Original Dimensions: 5, 8, 10

New Dimensions:

5 x 0.5 = 2.5,

8 x 0.5 = 4

10 x 0.5 = 5

Therefore, the dimensions of the new triangle are 2.5, 4, 5.

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The inequality that represents the numbers of large, and small, boxes that can be loaded in the trailer is 2x + y ≤ 60

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, One large box and two small boxes weigh a total of 100 pounds. One large box and four small boxes weigh a total of 150 pounds.

Let the weights of large and small boxes be x and y respectively.

x + 2y = 100

x = 100-2y...(i)

x + 4y = 150

x = 150-4y...(ii)

Solving eq(i) and eq(ii)

100 - 2y = 150 - 4y

2y = 50

y = 25

Put y = 25 in eq(i)

x = 100-50

x = 50

Therefore, weights of large and small boxes are 50 and 25 pounds respectively.

Now,

Since, weight limit of a trailer is 1500 pounds

Establishing the inequality,

50x + 25y ≤ 1500

or,

2x + y ≤ 60

Hence, the inequality that represents the numbers of large, and small, boxes that can be loaded in the trailer is 2x + y ≤ 60

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The algebraic expression that shows the amount Ms. Jackson wants to rent a van for a week is T=320+0.50m

In order to calculate the total amount that Ms. Jackson will need to pay for renting we need to multiply the number of miles that she will drive by the price per mile driven.

Once we have that product we can simply add the weekly fee (w) to it which will give us the total (T) amount that Ms. Jackson will have to pay for her trip. This can all be combined into the following formula.

T = w + 0.50m

As per the mentioned table, a van containing ret for a week is 320, which is equal to the W value, then substitute the value in the equation we get:

T=320+0.50m

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8 percentage of the buttons were large. The solution has been obtained using arithmetic operations.

What are arithmetic operations?

There are four fundamental operations that all real numbers in mathematics must comprehend:

1. Adding the numbers together to get their total (with a "+").

2. Using the "-" sign to subtract two numbers yields the difference between the values.

3. Multiplication('×') is used to create the numbers' product.

4. The division('÷') procedure, which determines the numbers' quotient.

We are given that Victoria bought a bag of mixed buttons and she got 12 large buttons and 138 small buttons.

So, the total number of buttons = 138 + 12 = 150

Out of 150, she got 12 large buttons.

So, percentage of large buttons = 12*100/150 = 8%

Hence, 8 percentage of the buttons were large.

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The shaded region is made up of the area of a rectangle minus the areas of the semicircles. The semicircles have a diameter of 2 inches, so the radius of each semicircle is 1 inch.

The area of each semicircle can be found using the formula pir^2, where r is the radius. So the area of each semicircle is pi1^2 = pi square inches.

The area of the rectangle is found by multiplying the length by the width: 1 foot * 12 inches/feet = 12 square inches.

The shaded region is the area of the rectangle minus the area of the semicircles. So the area of the shaded region is 12 square inches - 2* pi square inches = 12 - 2* pi square inches.

It's important to note that the length of the shaded region is given in feet (1-foot) but the area of the semicircles and the rectangle is given in square inches.

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A value of about 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.

Interest is often expressed as an annual percentage of the borrowed amount. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in an account savings account.

The initial deposit into the personal savings account is denoted by P, and the yearly interest rate is denoted by r. The following formula determines the account balance after t years:

A = Pe^(rt)

P = $1,000, r equals 5.8%, as Well as a is $3,317 in this scenario. To determine how many years it will be for such balance to reach $3,317, apply the following formula:

3,317 = 1,000e^(5.8% * t)

You must isolate t over one portion of the equation to find the solution:

t = ln(3,317 / 1,000) / (5.8% / 100)

That amounts to:

t = ln(3.317) / 0.058

Calculating this yields a result of around 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.

Therefore, 33 years are needed to complete the process.

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Answer: 20 inches

Step-by-step explanation:

The midsection is 1/2(base #1 + base #2)

27 = 0.5(34+x)

34+x = 54
x = 20

Answer:

y=13(7)^x

Step-by-step explanation:

x = 0, y = 13, so we know that a = 13.

13b^2 = 637  ==> x=2 and y=637

b^2 = 49  ==> divide both sides by 13

b = 7  ==> take the square root on both sides

y = 13 * 7^x  ==> plug in 7 for b in y = 13b^x

Answer: y=13(7)^x