14) A submarine travels and evasive course trying to outrun a destroyer. It travels 1 km north, then 1 km west then 1 km north, then 1 km west, etc... until it travels a total of 41 km. How many kilometers is the sub from the at which it started ?

In order to be within a 1% margin of error at a 95% confidence level, the candidate would need to survey 9604 people in the community. The size of the sample is 9604.

We have a political candidate who wants a 1% margin of error at a 95% confidence level. To find the size of the sample, we use the formula given below;

n = [ Z (α/2) / E ]²

Where,

n = the sample size required

Z (α/2) = the value obtained from the standard normal distribution for the given level of confidence

E = the margin of error

Here, α = 1 - 0.95 = 0.05

Z (α/2) = Z (0.025), is the z-value corresponding to 0.025 in the normal distribution table. It is found to be 1.96.

Now, substituting the given values in the formula,

n = (1.96² * 0.5 * 0.5) / 0.01² ⇒ 9604

Hence, the sample size required for the poll is 9604.

However, this is not feasible, as it would be very expensive and time-consuming. Therefore, we will round the answer to the nearest whole number as we are looking for a practical solution. Thus, the candidate would need to survey 9604 people in the community (rounded to the nearest whole number).

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To model the given data points, we can use a linear function of the form y = mx + b.

First, we need to find the slope (m) of the line:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-2)) / (1 - 0)

m = -4/1

m = -4

Now, we can use the slope and one of the points to find the y-intercept (b):

y = mx + b

-2 = (-4)(0) + b

b = -2

Therefore, the linear function that models the given data is:

y = -4x - 2

Answer: B

Step-by-step explanation:

There is no alternate exterior angle corresponding to ∠8. ∠3 ∠4 ∠5 ∠6 are not an alternate exterior angle to ∠8

We know that alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal,

here, we have,

We have been given a geometrical figure as shown in the image.

Now we know that a pair of alternate exterior angles exist for a pair of parallel lines.

Hence, there is no alternate exterior angle corresponding to ∠8.

Therefore, there is no alternate exterior angle corresponding to ∠8.

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Answer:(0,-1).

Step-by-step explanation:

As the diagonals of a parallelogram bisect each other, the midpoint of AC is the same as the midpoint of BD. Therefore, the fourth vertex D is (0,-1).

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

A loan or investment's principle amount is the sole amount used to compute simple interest. Any interest that has been earned on interest that has accrued over time is not taken into account by simple interest.

Contrarily, compound interest is a sort of interest that takes into account both the original principal and any interest that has accrued over time. As a result, the interest gained during one period is added to the principle for the following month, where it continues to earn interest.

Joni is not correct, because $230 is just the interest she will earn; she will have $430 total.

The compound interest is given by the formula:

[tex]A = P (1 + r/n)^{(nt)}[/tex]

Substituting the values we have:

[tex]A = 200(1 + 0.05/1)^{(1*3)}\\A = 200(1.05)^3[/tex]

A = 200(1.157625)

A = $231.53

Hence, Joni will have a total balance of $231.53 after 3 years.

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The complete question is:

the measure of angle V is approximately 21.87 degrees. To find the measure of angle V, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:

m∠V + m∠W + m∠X = 180

where angle X is the third angle in the triangle formed by V, W, and X. We know that m∠W is (3x+4) degrees, and we can see that angle X is adjacent to angle V, so we can use the fact that the sum of adjacent angles is equal to the total angle to write:

m∠V + m∠X = (2x+2) degrees

Now we can substitute this expression for m∠X into the first equation to eliminate m∠X:

m∠V + (2x+2 - m∠V) + (3x+4) = 180

Simplifying and solving for x, we get:

5x + 6 = 180

5x = 174

x = 34.8

Now we can substitute this value of x back into our expression for m∠V + m∠X to find m∠V:

m∠V + (2(34.8)+2 - m∠V) = 71.6

Simplifying and solving for m∠V, we get:

3m∠V = 65.6

m∠V = 21.87 (rounded to two decimal places)

Therefore, the measure of angle V is approximately 21.87 degrees.

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An equation is formed of two equal expressions. The maximum height reached by a rocket, to the nearest tenth of a foot is 1542.82 feet.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

To find the maximum height through which the rocket will reach, we need to differentiate the given function, therefore, we can write,

y=-16x²+173x+140

dy/dx = -16(2x)+173

Substitute the value of dy/dx as 0, to get the value of x,

0 = -32x + 173

173 = 32x

x =5.406

Substitute the value of x in the equation to get the maximum height,

y=-16x²+173x+140

y=-16(5.406²) +173(5.406) +140

y= 467.59 + 935.23 + 140

= 1542.82 feet.

Hence, the maximum height reached by the rocket, to the nearest tenth of a foot is 1542.82 feet.

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The answer of the given question based on the histogram is option (a) IQR, because Sunny Town is symmetric and option (b) IQR, because Beach Town is skewed.

Frequency refers to the number of times a particular event or value occurs within a given dataset or sample. In statistics, frequency is often used to describe the distribution of a variable, where a frequency distribution shows the number of observations that fall into each category or interval.

The IQR (interquartile range) should be used for both sets of data to determine the location with the most consistent temperature. The IQR is a measure of spread that is not influenced by extreme values or outliers, which is helpful in comparing the consistency of temperatures in different locations. It is appropriate to use the IQR for Sunny Town because the data is roughly symmetric, and for Beach Town because although it is skewed, the IQR is more robust than the range and is not influenced by outliers.

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All three methods give the same solutions. So, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2).

An equation is a mathematical statement that shows the equality between two expressions. It consists of an equal sign between two expressions, which are usually separated by variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

Let x be the cost of a chocolate truffle and y be the cost of a caramel turtle candy. From the given information, we can write the following system of equations:

5x + 2y = C1 (Cost of Chocolate Lovers Bag)

2x + 8y = C2 (Cost of Combusting Caramel Bag)

To solve the system of equations, we can use various strategies. Here are a few:

Method 1: Substitution

We can solve for x or y in one equation and substitute the result into the other equation to eliminate one variable. For example, we can solve for x in the first equation:

5x + 2y = C1

5x = C1 - 2y

x = (C1 - 2y) / 5

Substituting this into the second equation:

2((C1 - 2y) / 5) + 8y = C2

Simplifying and solving for y:

C1/5 - 4y/5 + 8y = C2

y = (5C2 - C1) / 26

Substituting this value of y into the first equation and solving for x:

5x + 2((5C2 - C1) / 26) = C1

x = (3C1 - 10C2) / 65

Therefore, the cost of a chocolate truffle is (3C1 - 10C2) / 65 and the cost of a caramel turtle candy is (5C2 - C1) / 26.

Method 2: Elimination

We can multiply the first equation by 4 and the second equation by -1, and add them to eliminate y:

20x + 8y = 4C1

-2x - 8y = -C2

Adding these equations gives:

18x = 4C1 - C2

x = (4C1 - C2) / 18

Substituting this into the first equation and solving for y:

5((4C1 - C2) / 18) + 2y = C1

y = (9C1 - 20C2) / 36

Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.

Method 3: Matrix algebra

We can write the system of equations in matrix form:

[5 2] [x] [C1]

[2 8] [y] = [C2]

Using matrix algebra, we can solve for the variables:

[x] [C1] [8 -2] [y]

[y] = [C2] [-2 5 ] [x]

Multiplying the matrices, we get:

[x] [8x - 2y] [C1]

[y] = [-2x + 5y] * [C2]

Solving for x and y:

x = (4C1 - C2) / 18

y = (9C1 - 20C2) / 36

Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.

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Answer:

$104.11

Step-by-step explanation:

To calculate the monthly payment for a loan, we can use the following formula:

Monthly payment = (Pr(1+r)^n) / ((1+r)^n-1)

where:

P = the principal amount (the amount borrowed)

r = the monthly interest rate (annual interest rate divided by 12)

n = the number of payments (total number of years multiplied by 12)

In this case, the principal amount is $3825, the annual interest rate is 15%, and the loan term is 4 years. So we have:

P = $3825

r = 0.15/12 = 0.0125

n = 4*12 = 48

Substituting these values into the formula, we get:

Monthly payment = (38250.0125(1+0.0125)^48) / ((1+0.0125)^48-1)

Monthly payment ≈ $104.11

Therefore, the monthly payment for a $3825 loan at 15% annual interest for 4 years is approximately $104.11.

Answer:

To graph the function f(x) = 2sin(x) - 2 by hand, we can use the following steps:

Step 1: Find the amplitude

The amplitude of the function is the absolute value of the coefficient of the sine function, which is 2 in this case. Therefore, the amplitude is 2.

Step 2: Find the period

The period of the function is given by the formula 2π/b, where b is the coefficient of x in the sine function. In this case, b = 1, so the period is 2π/1 = 2π.

Step 3: Find the midline

The midline is the horizontal line that the graph oscillates around. For the sine function, the midline is the y-value of the function when there is no vertical shift. In this case, the midline is y = -2.

Step 4: Find the y-intercept

The y-intercept is the value of the function when x = 0. Plugging in x = 0, we get f(0) = 2sin(0) - 2 = -2. Therefore, the y-intercept is -2.

Step 5: Sketch the graph

Based on the amplitude, period, midline, and y-intercept we just found, we can sketch the graph of the function as follows:

- The graph oscillates between y = 2 and y = -6, with a midline at y = -2.

- The graph starts at (0, -2), then goes up to (π/2, 0), down to (π, -2), down further to (3π/2, -4), and back up to (2π, -2).

- The graph is symmetric about the midline.

Therefore, the information about the function is:

Amplitude: 2 (The distance from the midline to the maximum or minimum of the graph is 2.)

Period: 2π (The graph completes one full cycle over a horizontal distance of 2π.)

Midline: y = -2 (The horizontal line that the graph oscillates around.)

y-intercept: -2 (The value of the function when x = 0.)

The ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.

Ratio and proportion are two mathematical concepts that are closely related.

A ratio is a way of comparing two or more quantities by dividing one quantity by another. It expresses the relative size or magnitude of two quantities. Proportion, on the other hand, refers to the equality of two ratios. It states that two ratios are equal. Proportions can be used to solve problems involving unknown quantities.

To determine whether x and y are proportional, we need to check if the ratio of corresponding values of x and y is always the same.

Let's find the ratio of y to x for each corresponding value:

y/x for x=1: 7/1 = 7

y/x for x=2: 8/2 = 4

y/x for x=3: 9/3 = 3

Since the ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.

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Answer:Red

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 blue out of 15 chips

Answer:

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.

Step-by-step explanation:

In a 45°-45°-90° triangle, the two legs are congruent, which means that each leg is equal to the length of the hypotenuse divided by √2.

Let h be the length of the hypotenuse. Then we have:

leg = h/√2

Given that one of the legs is 8√8 centimeters, we can substitute this value into the equation above to solve for h:

8√8 = h/√2

Multiplying both sides by √2, we get:

8√8 x √2 = h

Simplifying, we get:

h = 8√16

h = 8 x 4

h = 32

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.

(b) The difference in sample mean is 0.544 ml. (c) Using StatKey, we find the p-value to be 0.046. (d) It is unlikely that this difference is due to random chance alone.

(a) The null hypothesis is that there is no difference in average brain size between football players with no history of concussions (FBNoConcuss) and football players with a history of concussions (FBConcuss). The alternative hypothesis is that the average brain size is larger in FBNoConcuss than in FBConcuss.

H0: μFBNoConcuss = μFBConcuss

HA: μFBNoConcuss > μFBConcuss

(b) The relevant sample statistic is the difference in sample mean between the two groups.

Therefore, the difference in sample mean is 0.544 ml.

(c) Using StatKey, we find the p-value to be 0.046.

(d) With a p-value of 0.046, which is less than the commonly used significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the average brain size is larger in FBNoConcuss than in FBConcuss. It is unlikely that this difference is due to random chance alone.

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You paid the total amount of $1257 at the end of 5 years.

Let us assume that c represents the cost per month.

So, c = $20.95

and let t represents the total number of months.

We know that there are 12 months in a year.

so, the number of months in 5 years would be:

12 × 5 = 60

So, t = 60 months

Using unitary method the total amount paid at the end of five years :

s = c × t

s = 20.95 × 60

s = $1257

Therefore, the total amount is $1257

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the orthogonal projection of a point P onto a line L can be expressed as: projection  L(P) = ((P . u) ×u)·

Orthogonal projection is a mathematical operation that involves projecting a vector or point onto another vector or line in a way that the projection is perpendicular (or orthogonal) to the vector or line.

In mathematical notation, the orthogonal projection of a point P onto a line L can be expressed as:

projection L(P) = ((P . u) × u)

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The coordinates of point C are (17, -1).

let say a line have two points A (x1,y1) and B(x2,y2)

slope of line AB = (y2 - y1) / (x2 - x1)

Now given that  points B, C, and D are collinear, then they lie on the same straight line. This means that the slope of the line passing through any two of the points will be the same as the slope of the line passing through the other two points. We can use this fact to find the value of x.

The slope which is between points B and C is:

slope of line BC = (y2 - y1) / (x2 - x1) = (-1 - 7) / (x - (-1)) = -8 / (x + 1)

The slope which is between points C and D is:

slope of line CD = (y2 - y1) / (x2 - x1) = (8 - (-1)) / (1 - x) = (9) / (1 - x)

Since B, C, and D are collinear, slope of BC = slope of CD. Therefore:

-8/(x+1) = 9/(1-x)

by solving the x, we get:

-8(1 - x) = 9(x + 1)

-8+8x=9x + 9

x = 17

So, the coordinates of point C are (17, -1).

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The likelihood of being over 67 inches tall is 0.127978, or 12.8%.

The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.At the point when this happens, we broadcast that there is plausible that the occasion will happen.

In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence.

By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.

5 feet 7 inches equals (5*12 +7) inches, or (60 +7) inches, according to our question.

(67 - 69.1)/(2.65) = -1.136 is the z-score.

The probability of having a height greater than 67 inches is 0.127978, or 12.8%.

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The probability of selecting a striped marble, not replacing it, then selecting a black marble is 4/15.

The probability of selecting a striped marble on the first draw is 6/10, since there are 6 striped marbles out of a total of 10 marbles in the bag.

After the first marble is drawn, it is not replaced, so there are now 9 marbles left in the bag. Out of these, there are 4 solid marbles and 5 striped marbles. Therefore, the probability of selecting a black marble on the second draw is 4/9.

To find the probability of both of these events occurring together, we multiply the probabilities

P(striped, then black) = P(striped) × P(black | striped not replaced)

P(striped, then black) = (6/10) × (4/9)

P(striped, then black) = 24/90

P(striped, then black) = 4/15

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The given question is incomplete, the complete question is:

There are 10 marbles in a bag (4 solid, 6 striped) .what is the probability of selecting a striped marble, not replacing it, then selecting a black marble?

Answer: You can comment if this is wrong but I don't know what an area model is entirely I might just I don't remember

|\ |\

| \ | \

|  \|  \

|___\|___\

1/4  1/5

Step-by-step explanation:

1. Draw a rectangular area model with two sections.

2. Label the left section with 1/4 and the right section with 1/5.

3. Divide the left section into 4 equal parts by drawing lines horizontally and vertically

4. Divide the right section into 5 equal parts by drawing lines horizontally and vertically.

5. Count the number of parts in the left section (4 parts) and the number of parts in the right section (5 parts).

6. Multiply the parts in the left section by the parts in the right section, which gives 4 x 5 =20.

7. The answer is 20/4 = 5.

Answer:

The correct responses are:

A) S(10)=S(5) means that there were the same number of students in 2010 as in 2005.

E) S(0) = 2,000 means that there were no students in the year 2000.

B and D are not plausible statements because they imply that there is an inverse relationship between t and S(t), meaning that the number of students decreases as t increases. Also, C is incorrect as it implies that there were fewer students in 2015 than there were in 2010, which contradicts the nature of the situation.

In addition, the image's y-coordinate would be , this indicates that we must raise the point by  to align it with the y-axis. Hence, D  is the right response.

Option A moves the point 4 units horizontally and 8 units vertically, but does not move it onto the y-axis.

Option B moves the point -4 units horizontally and 8 units vertically, but does not move it onto the y-axis.

Option C moves the point horizontally by 8 units and vertically by 4 units, but it does not move it to the y-axis.

Option D moves the point 8 units horizontally and -4 units vertically. When we apply this transformation to an x-axis point, its y-coordinate remains unchanged, so the point's image is on the y-axis. As a result, option D is the correct translation:

(x, y) → (x+8, y-4)

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Answer:

14

Step-by-step explanation:

Rewrite the equation: 4*4+3-5

Multiply: 16+3-5

Add: 19-5

Subtract: 14

Answer:

1 orange weighs 5 ounces.

Divide

35÷7 = 5

so, one orange weighs 5 ounces.

Answer:

12.9cm

Step-by-step explanation:

Trapeziums QRVW and QRSP are similar because they share the same side 5.5 cm and their angles are corresponding to each other.

We can express the ratios of sides in both trapeziums to find WV.

Since side 5.5 is the same in each trapezium,

[tex]\frac{5.5}{WV}=\frac{5.5}{12.9}[/tex]

Thus, WV = 12.9cm

Hope this helps:)

Answer:

-7/9

Step-by-step explanation:

its not a complete change to 1 but it is very close to being a 1

we get that the wheel of Kathel's car makes about 146 more revolutions than the wheel of Nguye's lorry to cover a distance of 770 m.

The circumference of a circle is the distance around the outer boundary of the circle. It is the length of the boundary or the "perimeter" of the circle. The circumference is calculated using the formula C = 2πr, where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The circumference is measured in units of length, such as meters or feet.

by the question.

To solve this problem, we need to first find the circumference of each wheel:

[tex]Circumference of Nguyon's lorry wheel = 2πr = 2 x (22/7) x 28 cm = 176[/tex]cm

Circumference of Kathel's car wheel = πd = (22/7) x 42 cm = 132 cm

Next, we can calculate how many revolutions each wheel needs to make to cover a distance of 770 m:

Number of revolutions for Nguyon's lorry wheel = distance ÷ distance covered in one revolution

= 77000 cm ÷ 176 cm ≈ 437.5 revolutions

Number of revolutions for Kathel's car wheel = distance ÷ distance covered in one revolution

= 77000 cm ÷ 132 cm ≈ 583.3 revolutions

Finally, we can find the difference in revolutions between the two wheels:

Difference in revolutions = Number of revolutions for Kathel's car wheel - Number of revolutions for Nguyon's lorry wheel

= 583.3 - 437.5 ≈ 145.8 revolutions

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