A motorboat left a harbor and traveled to an island at an average rate of 10 knots. The average speed on the return trip was 10 knots. If the total trip took 4.0 hours, how far is the harbor from the island?

Answer:

Step-by-step explanation:

(a) R2 does not determine the level of correlation between two variables in statistics but rather it is used to determine the level of variance in a dependent variable that is explained by an independent variable. It is also known as coefficient of determination.

Pearson's correlation coefficient (r) will better explain a direct relationship between a country's literacy rate and life expectancy and the value obtained will better explain option a

(b) The slope of the line can predict an improvement in life expectancy but cannot guarantee this improvement. And as such, the use of the word "will" suggests a form of guarantee which is wrong in interpreting slopes.

Answer:

Option 2: [tex]\sin(30)=\frac{1}{2}[/tex]

Step-by-step explanation:

Given:

From the triangle shown below;

A triangle QRS with angle QRS = 90°, ∠QSR = 30°.

Side QR = 5, SQ = 10 and RS = 5√3

Now, we know from trigonometric ratio that,

[tex]\sin (A) = \frac{Opposite\ side}{Hypotenuse}[/tex]

Here, opposite side of angle QSR is QR and Hypotenuse is the side opposite angle QRS which is SQ. Therefore,

[tex]\sin(\angle QSR)=\dfrac{QR}{SQ}\\\\\\\sin(30)=\dfrac{5}{10}\\\\\\\sin(30)=\dfrac{5}{2\times 5}=\dfrac{1}{2}[/tex]

Therefore, the value of sine of 30° is one-half. So, second option is correct.

Answer:

B

Step-by-step explanation:

The model shown in the graph describes a piece rate. Correct option is D.

Let us take a point (3, 60) in the given graph.

The function which model this is y=kx.

Let us plug in y as 60 and x as 3.

60=3k

Divide both sides by 3:

k=20

So, y=20x.

The model is proportional function, if the x value increases then y value increases.

Similarly, if x value decreases the y value decreases.

Hence, the model shown in the graph describes a piece rate. option D is correct.

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Answer:

Hourly pay without a bonus

Step-by-step explanation:

I just took the test

Answer:

Don't worry friend! I am here to help you!

Step-by-step explanation:

I tried answering as many questions as I could, but the ones I didn't answer, I didn't know how to solve.

Please understand that I am here to help you and others on brainly!

I hope this makes you feel better!

- sincerelynini

The student asked for the calculations of probabilities concerning a football player's passes. The answers are: (a) 21.18%, (b) 90.58%, (c) 8.68%. This involves the use of probability rules and calculations carried out to two decimal places.

The subject of this question is probability, particularly in the context of repeated independent trials. The football player has a 69.4% chance of completing a pass, so we can use this information to answer the questions.

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(a) The probability that the first pass he completes is the second pass is [tex]$\frac{3099}{10000}$[/tex].

(b) The probability that the first pass he completes is the first or second pass is [tex]$\frac{3499}{5000}$[/tex].

(c) The probability that he does not complete his first two passes is [tex]$\frac{9826}{2500}$[/tex].

To solve this problem, we will use the given completion rate of 69.4% and convert it into a fraction to make the calculations easier. The completion rate is equivalent to [tex]$\frac{694}{1000}$[/tex] or [tex]$\frac{347}{500}$[/tex].

(a) To find the probability that the first pass he completes is the second pass, we need to consider two events: he must fail the first pass and then succeed on the second pass. The probability of failing the first pass is [tex]$1[/tex] - [tex]\frac{347}{500}$[/tex], and the probability of succeeding on the second pass is [tex]$\frac{347}{500}$[/tex]. Multiplying these two probabilities gives us the desired probability:

[tex]$$ \left(1 - \frac{347}{500}\right) \times \frac{347}{500} = \frac{153}{500} \times \frac{347}{500} = \frac{3099}{25000}. $$[/tex]

Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:

[tex]$$ \frac{3099}{25000} = \frac{77475}{62500} = \frac{3099}{10000}. $$[/tex]

(b) To find the probability that the first pass he completes is the first or second pass, we need to consider the probability of completing the first pass and the probability of failing the first pass but completing the second pass. We add these two probabilities because they are mutually exclusive events. The probability of completing the first pass is [tex]$\frac{347}{500}$[/tex], and the probability of failing the first pass but completing the second pass is the same as calculated in part (a), [tex]$\frac{3099}{10000}$[/tex]. Adding these probabilities gives us:

[tex]$$ \frac{347}{500} + \frac{3099}{10000} = \frac{694}{1000} + \frac{3099}{10000} = \frac{3499}{5000}. $$[/tex]

(c) To find the probability that he does not complete his first two passes, we need to consider the probability of failing both passes. The probability of failing one pass is [tex]$1[/tex]- [tex]\frac{347}{500}$[/tex], so for two consecutive failures, we square this probability:

[tex]$$ \left(1 - \frac{347}{500}\right)^2 = \left(\frac{153}{500}\right)^2 = \frac{23409}{25000}. $$[/tex]

Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:

[tex]$$ \frac{23409}{25000} = \frac{585025}{62500} = \frac{9826}{2500}. $$[/tex]

These calculations provide the probabilities for each of the specified events.

Answer: (1812.967, 1907.033)

Step-by-step explanation:

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm t_{df,\ \alpha} \dfrac{s}{\sqrt{n}}[/tex]

, where [tex]\overline{x}[/tex] = Sample mean

n= Sample size.

s = Sample standard deviation

[tex]t_{df,\ \alpha}[/tex] = Critical t-value for degree of freedom(n-1).

As per given , we have

n= 35

[tex]\overline{x}=1860[/tex]

s=102

Significance level : [tex]\alpha=0.01[/tex]

By t- distribution table , for degree of freedom 43 and [tex]\alpha=0.01[/tex] , we have

[tex]t_{df,\ \alpha}=t_{34,\ 0.005} =2.728[/tex]

Substitute all the values in the above formula , we will get

[tex]1860\pm (2.728)\dfrac{102}{\sqrt{35}}[/tex]

[tex]=1860\pm (2.728)(17.2411)[/tex]

[tex]=1860\pm47.034[/tex]

[tex]=(1860-47.033\ 1860+47.033)= (1812.967,\ 1907.033)[/tex]

Hence, the  99% confidence interval estimate of the mean of the population is  (1812.967, 1907.033).

Final answer:

To construct a 99% confidence interval for the population mean with a known standard deviation, calculate the standard error, find the appropriate z-score for 99% confidence, and apply the formula Sample mean ± z * SEM. The 99% confidence interval for the given sample data is approximately (1811.26, 1908.74).

Explanation:

A student asked how to construct a 99% confidence interval estimate for the mean of the population given that the mean of a sample of size n=35 is 1860 with a standard deviation of 102, and the population is normally distributed.

To construct a 99% confidence interval, we proceed by calculating the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size:

SEM = σ / √n = 102 / √35 ≈ 17.25

We then find the z-score that corresponds to a 99% confidence level. For a two-tailed test, which is relevant here, this value is approximately 2.576.

The confidence interval is then calculated by:

Sample mean ± z * SEM = 1860 ± 2.576 * 17.25

Lower limit: 1860 - (2.576 * 17.25) ≈ 1811.26

Upper limit: 1860 + (2.576 * 17.25) ≈ 1908.74

Hence, the 99% confidence interval estimate for the population mean is approximately (1811.26, 1908.74).

Answer:

Step-by-step explanation:

5.

y=kx

when x=4,y=5

5=4k

k=5/4

y=5/4 x

or y=1.25 x

6.

y=kx

when x=4,y=9

9=4k

k=9/4

y=9/4 x

or y=2.25 x

Answer:

0.33

Step-by-step explanation:

So we find the difference between the price of milk at 6 storms and the price of milk at 3 storms.

3.88 - 2.89= 0.99

Then we divide the difference by 3 to find the average rate of change for each storm between 3 to 6.

0.99 ÷3= 0.33

So the answer is 0.33.

The average rate of change from 3 to 6 storms is 0.33

A correlation exists as a statistical measurement that expresses the extent to which two variables are linearly related (suggesting they change together at a constant rate). It's a familiar tool for defining simple relationships without making a statement about cause and effect.

To solve this example use this rule :

Δx/Δy

x exists the amount that changed. so Δx=0,99.

The storm stands to 3 to 6 so find the difference for x: for the 3rd and 6th members of the table... 3.88-2.89=0.99

Now,

0.99/Δy

Because require to find from 3 to 6, Δy=3,

When finding both, rate of change with :

0.99/3=0.33.

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Answer:

Step-by-step explanation:

Let x represent the average speed of flight 725.

Flight 725 left New York at 10:28 a.m. flying north.

Flight 245 left from the same airport at 11:18 a.m. flying south at one hundred twenty kph less than three times the speed of flight 725. This means that the speed of flight 245 is

3x - 120

At 1:06 p.m. they are 1,030 kilometers apart. This means that total distance travelled by both planes would be 1030

Between 10:28am and 1:06pm, the number of hours would be 2hr 38 minutes = 2 + 38/60 = 2.63 hours

Distance = speed × time

Total distance travelled by flight 725 = x × 2.63 = 2.63x

Between 11:18am and 1:06pm, the number of hours would be 1hr 48 minutes = 1 + 48/60 = 1.8 hours

Distance = speed × time

Total distance travelled by flight 245 = x × 1.8 = 1.8(3x - 120)

5.4x - 216 + 2.63x = 1030

8.03x = 1030 + 216 = 1246

x = 1246/8.03 = 155 kph

Answer:

The answer to your question is 12 monitors

Step-by-step explanation:

Data

v = monitors weighing 25 lb

f = monitors weighing 40 lb

Total weight = 680 lb

Total monitors = 20

Process

1.- Write equations

         v + f = 20          ------------------ (l)

       25v + 40f = 680  -----------------(II)

2.- Solve the system by elimination

Multiply equation l by -25

       -25v -  25f  = - 500

        25v + 40f =    680

          0    + 15 f = 180

Solve for f

                       f = 180 / 15

                       f = 12

3.- Find the value of v

          v + 12 = 20

          v = 20 - 12

          v = 8

4.- Conclusion

      There are 12 monitors weighing forty lb

       There are 8 monitors weighing 25 lb

Final answer:

Carol has 10 green cubes in the box. After adding 12 more red cubes, she ends up with 32 red cubes.

Explanation:

To solve this problem, we can use the concept of ratios and equations. First, we know that the initial ratio of red to green cubes is 2:1. Let's represent the number of red cubes as 2x and green cubes as x. We then are told that Carol adds 12 more red cubes and the ratio becomes 4:5. If we let the number of green cubes remain as x, we have that the new number of red cubes is 2x + 12.

We can set up the following proportion to represent the new situation:

(2x + 12) / x = 4 / 5

By cross-multiplying, we can solve for x to find the quantity of green cubes:

5(2x + 12) = 4x

10x + 60 = 4x

6x = 60

x = 10

Therefore, there are 10 green cubes in the box (as x represents the number of green cubes).

To find out how many red cubes are there in the end, we add 12 to the initial amount of red cubes (2 times the number of green cubes):

Initial red cubes = 2x = 2(10) = 20

Final red cubes = 20 + 12 = 32 cubes

So, Carol has 32 red cubes in the end.

Answer:

yo is ya boi Nick you already know what it is yeah big daddy nick

Answer:

B)temperature during the game on Saturday

Step-by-step explanation:

Final answer:

To find out how many liters of paint are needed for one door, when 3 liters were used for 1 4/5 doors, divide the total amount of paint by the number of doors. The calculation is 3 liters divided by 9/5, which results in 1.67 liters of paint for one door.

Explanation:

Maren used 3 liters of paint to cover 1 4/5 doors which implies that the amount of paint needed for 1 door can be found by dividing the total amount of paint by the number of doors painted. To calculate this:

Therefore, 1.67 liters of paint are needed for 1 door.

Answer: 16

Step-by-step explanation:

Answer:

The height of each pyramid is 1/2 h units.

Step-by-step explanation:

did it on edg 2020

Answer: y(t) = 600(0.921)^t

Step-by-step explanation:

Given:

Percentage yearly reduction = 7.9%

Initial mass m = 600 mg

time in years = t

An exponential function with yearly decay rate to determine the final mass of the substance is given as:

y(t) = m(f)^t

y(t) = final mass in milligram

m = 600

f = final mass fraction = 1 - 0.079 = 0.921

f = 0.921

Therefore, the exponential function is given as;

y(t) = 600(0.921)^t

The probability of winning in the state lottery is 0.24%.

To calculate the probability of winning, we need to consider the total number of possible outcomes and the number of favorable outcomes. In this case, there are 10 choices for each digit, so the total number of possible outcomes is 10 x 10 x 10 x 10 = 10,000. Since any permutation of the selected integers counts as a win, we have 4! = 4 x 3 x 2 x 1 = 24 favorable outcomes.

Therefore, the probability of winning is 24/10,000 = 0.0024, or 0.24%.

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The probability of winning by selecting unique digits is 0.0024 or 24/10,000.

We first determine the total number of possible outcomes when drawing four digits. Since the digits range from 0 to 9, there are 10 possible choices for each digit.

Total outcomes = 10 choices for the first digit * 10 choices for the second digit * 10 choices for the third digit * 10 choices for the fourth digit

= 10⁴ = 10,000.

Now, if you select four specific digits, we need to consider the number of ways these digits can be arranged, which is calculated using permutations. If all selected digits are unique, the number of permutations is 4! = 24.

If you select digits with repetitions, the calculation varies. For example, if you select 1, 2, 2, and 3, the permutations would be 4! / 2! = 12.

Assuming you selected four unique digits, the probability of winning is given by the number of favorable outcomes divided by the total outcomes. Thus, the probability of winning with unique digits is:

Probability = Number of favorable outcomes / Total outcomes

= 24 / 10,000

= 0.0024.

Answer:

x=11

Step-by-step explanation:

[tex]\frac{5x}{3x-3} =\frac{44}{24} =\frac{11}{6} \\33x-33=30x\\33x-30x=33\\3x=33\\x=11[/tex]

1) you first add up all of the amount of ingredients you have

2)you the take the total and divide your total up by the 4 ingredients you currently have

3)that is your total

11+4++4+5=24

24/4=6

answer= 6

There are 880 different pizzas are possible if a pizza must have a topping, cheese, sauce and crust.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A restaurant offers a medium pizza for $8.

And, A person can choose from one of 11 toppings, one of 4 cheeses, one of 4 kinds of sauce, and one of 5 type of crust.

Now,

Since, A person can choose from one of 11 toppings, one of 4 cheeses, one of 4 kinds of sauce, and one of 5 type of crust.

So, We get;

The different ways for a pizza must have a topping, cheese, sauce. And crust = 11 x 4 x 4 x 5

        = 880

Thus, There are 880 different pizzas are possible if a pizza must have a topping, cheese, sauce and crust.

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Answer: Its True

Step-by-step explanation:

The statement is true because the Percentages are preferred and also they are easier to compare than counts.

Final answer:

After 100 days, there will be approximately 7.18 bacteria present.

Explanation:

To determine the number of bacteria that will be present after 100 days, we need to calculate the exponential growth of the bacteria. The bacteria reproduce at a rate of 4% per day, which means the population will double every 25 days (since 100 divided by 4 is 25).

To calculate the final population, we can use the formula N = N₀ * [tex](1 + r/100)^t[/tex], where N is the final population, N₀ is the initial population, r is the growth rate, and t is the time in days.

In this case, the initial population is 2 (assuming there are initially only two bacteria), the growth rate is 4%, and the time is 100 days.

Plugging in these values,

we get [tex]N = 2 * (1 + 4/100)^{100} = 2 * (1.04)^{100}[/tex]nal population of approximately 7.18 bacteria. Therefore, there will be approximately 7.18 bacteria present after 100 days.

Answer:

The amount invested at 3% is 300 &

The amount invested at 2% is 100.

Step-by-step explanation:

Total yearly interest for the two accounts is: $11

Let x be the amount invested at 3%

& y be the amount invested at 2%

From the question we can get 2 equations as;

x = 3y --------------------------Equation 1

0.03x + 0.02y = 11 ----------Equation 2

Substitute for x in Equation 2 we get;

0.03 (3y) + 0.02y = 11

0.09y + 0.02y = 11

0.11y = 11

Divide the above equation by 0.11, we get;

y = [tex]\frac{11}{0.11}[/tex]

y = 100

Let us substitute the value of y in Equation 1 we get;

x = 3(100)

x = 300

Now to check our answer let us put in the simple interest formula. If we get the sum of the two interests equal to 11 then our answers are correct:

0.03 x 300 + 0.02 x 100

= 9 + 2

= 11

Hence the amount invested at 3% is 300 and the amount invested at 2% is 100.

Answer:

48 liters

Step-by-step explanation:

You should multiply the number of containers by the number of liters in each container.

12 x 4 = 48

Pam brought 48 liters of water to the soccer game.

Answer:

[tex]a=-6[/tex]

Step-by-step explanation:

Line 1:  (1, a) and (5, −2)

slope of the   line is

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-2-a}{5-1} =\frac{-2-a}{4}[/tex]

Line 2:  (2, 8) and (−5, a + 7)

slope of the   line is

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{a+7-8}{-5-2} =\frac{a-1}{-7}[/tex]

when the lines are parallel then slopes are equal

[tex]\frac{a-1}{-7} =\frac{-2-a}{4}[/tex]

cross multiply it

[tex]4(a-1)=-7(-2-a)[/tex]

[tex]4a-4=14+7a[/tex]

subtract 4a from both sides

[tex]-4=14+3a[/tex]

[tex]-18=+3a[/tex]

divide both sides by 3

[tex]a=-6[/tex]

The solution to the given system of equations, x + 5y = 11 and x - y = 5, is x = 6, y = 1. The solution matrix for this system is therefore [6, 1].

To solve the given system of linear equations, x + 5y = 11 and x - y = 5, you can use the elimination or substitution method. Let's use the elimination method:

The solution of this system of equations is x = 6 and y = 1. For the matrix format of the solution, it would be [6,1] as the solution matrix typically formats solutions in [x, y].

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The solution matrix X is [tex]\(\begin{bmatrix} 3 \\ 2 \end{bmatrix}\)[/tex].

To find the solution matrix for the given system of equations [tex]\(x + 5y = 11\)[/tex] and [tex]\(x - y = 5\)[/tex], we can represent the system in matrix form \(AX = B\), where:

[tex]\[ A = \begin{bmatrix} 1 & 5 \\ 1 & -1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \end{bmatrix}, \quad B = \begin{bmatrix} 11 \\ 5 \end{bmatrix} \][/tex]

The solution matrix X is given by [tex]\(X = A^{-1}B\)[/tex], where [tex]\(A^{-1}\)[/tex] is the inverse of matrix A.

1. Form the matrix equation AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

2. Compute the inverse of matrix A, denoted as [tex]\(A^{-1}\).[/tex]

3. Multiply [tex]\(A^{-1}\)[/tex]by matrix B to obtain the solution matrix X.

By following these steps, you can find that the solution matrix X for the given system is [tex]\(\begin{bmatrix} 3 \\ 2 \end{bmatrix}\).[/tex]

Final answer:

Andrea's score of 76 is 2.4 standard deviations above the mean test score of 52 with a standard deviation of 10.

Explanation:

The question is how many standard deviations from the mean Andrea's score of 76 is on the mathematics test where the mean is 52 and the standard deviation is 10. To find this, you would use the formula for calculating a z-score:

Z = (X - μ) / σ

Where:

Z is the z-score

X is the value of the score

μ is the mean of the scores

σ is the standard deviation of the scores

For Andrea's score, the calculation would be:

Z = (76 - 52) / 10 = 24 / 10 = 2.4

Therefore, Andrea's score is 2.4 standard deviations above the mean. This indicates that her score was significantly higher than the average test score.

Answer:

i dont understand

Step-by-step explanation:

Answer:

side length is [tex]\frac{20\sqrt{3} }{3}[/tex] feet

Step-by-step explanation:

An equilateral triangle has a height of 10 feet.  the height of the triangle is the perpendicular bisector to the base

so it forms a two right angle triangle

the triangle formed is a 30-60-90 degree triangle

the diagram is attached below

Let x be the side if the equilateral triangle

sin(theta)=opposite by hypotenuse

[tex]sin(60)=\frac{10}{x}[/tex]

[tex]\frac{\sqrt{3}}{2} =\frac{10}{x}[/tex]

cross multiply

[tex]\sqrt{3} x=20[/tex]

[tex]x=\frac{20}{\sqrt{3} } =\frac{20\sqrt{3} }{3}[/tex]

The length of the side of an equilateral triangle with a height of 10 feet is approximately 11.54 feet. This is determined by applying the properties of a 30-60-90 triangle which is a half of an equilateral triangle.

The problem is asking to solve for the side (s) of an equilateral triangle given the height (h). An equilateral triangle can be divided into two 30-60-90 right triangles. In such a triangle, the ratio between the hypotenuse (which is the side of the equilateral triangle) and the longer leg (which is half of the height) is 2:√3. Therefore, if the height is 10 feet, then the side length would be (2/√3)*h.

Step 1: Recognize that the triangle is a 30-60-90 triangle.

Step 2: Apply the ratio between the sides in a 30-60-90 triangle, 2:√3.

Step 3: Multiply the height by 2/√3 to get the length of one side which equals about 11.5 feet.

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Answer:

$3.00

Step-by-step explanation:

If you wanna buy 2 pounds, just time it by 2! $1.50*2=$3.00!

If peanuts cost $1.50 per pound, the cost of 2 pounds of peanuts would be equal to $3.0.

Given the following data:

In order to determine the cost of 2 pounds of peanuts, we would set up a direct proportion equation as follows:

1 pounds = 1.50 dollars.

2 pounds = X dollars.

Cross-multiplying, we have:

X = 2 × 1.5

X = $3.0

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Answer: she has 16 dimes and 48 nickels

Step-by-step explanation:

The worth of a dime is 10 cents. Converting to dollars, it becomes

10/100 = $0.1

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

Let x represent the number of dimes that she has in her wallet.

Let y represent the number of nickels that she has in her wallet.

she has three times as many nickels as she does dimes. This means that

y = 3x

the total value of the coins is $4.00. This means that

0.1x + 0.05y = 4 - - - - - - - - - - - 1

Substituting y = 3x into equation 1, it becomes

0.1x + 0.05 × 3x = 4

0.1x + 0.15x = 4

x = 4/0.25 = 16

y = 3x = 3 × 16

y = 48