Select the correct vectors.
A ship moves through the water at 30 miles/hour at an angle of 30° south of east. The water is moving 5 miles/hour at an angle of 20° east of north. Identify the ship's vector, the water current's vector, and the vector representing the ship's actual motion.

Please select the correct answers from the image, thanks and godbless!

Payment Every Month =  $2,514.58

Total of 1 Payments =  $2,514.58

Total Interest               =  $14.58

What is simple intertest ?

Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accumulated.

Solution:

Principal value = $2500

Interest rate = 7%

Time = One month

Formula for simple interest calculation:

                                                                [tex]=\frac{Principalamount*rate *time}{100} \\=\frac{2500*7*(\frac{1}{12}) }{100}\\ =14.588[/tex]

Total Simple interest on $2500 for month $14.588.

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The equation of the new function is f'(x) = -|x|

The function is given as:

f(x) = |x|

The rule of flipping the graph over the x-axis

(x, y) = (x, -y)

So, we have:

f'(x) = -f(x)

Substitute f(x) = |x|

f'(x) = -|x|

Hence, the equation of the new function is f'(x) = -|x|

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Answer:

2^-6

Step-by-step explanation:

(1/8)^2 = (2^-3)^2 = 2^-6

The surface area of the cone is: A. 184π units².

Surface area of a cone = πr(l + r), where r is the radius and l is the slant height.

Given the following:

Surface area of a cone = π8(15 + 8)

Surface area of a cone = 184π units²

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Answer:

m = [tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{1-7}{10-1}[/tex]

m = [tex]\frac{-6}{9}[/tex]

m = [tex]-\frac{2}{3}[/tex]

Answer:

-2/3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(10 - 1)

slope = -6/9

slope = -2/3

Answer:

60

Step-by-step explanation:

The yellow and green angles form a right angle, so the measures of those combined will be 90 degrees.

90 - 30 = 60

Answer:

20 because Brendan is 30

Using the sine ratio, the length of the missing side is: 11.8.

The sine ratio is, sin ∅ = opposite/hypotenuse.

Given the following:

∅ = 24°

Opposite = x

Hypotenuse = 29

sin 24 = x/29

x = (sin 24)(29)

x = 11.8

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Simplifying equation is done by either reducing the complexity or the components parts of an equation for better understanding.

This means to make simpler, either by reducing in complexity, reducing to component parts, or making easier to understand.

Simplification is an act of simplifying an equation or expression.

For instance,

Simplify 4(3x + 2) - 4(2x)

= 12x + 8 - 8x

= 12x - 8x + 8

= 4x + 8

Simplify 1/2 + 2/3

= (3+4) / 6

= 7/6

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Answer:

18

Step-by-step explanation:

3*3*3 = 27, assuming all 3 digits can occupy each space

However, 0 cannot start a number, so it becomes:

3*3*2, which is 18.

The word problem can be:

"let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?"

And the solution is N = 12.

We want a problem that can be described by 3 divided by 1/4.

So, let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?

The solution to that question is given by:

[tex]N = \frac{3}{1/4}[/tex]

2) To solve this, we can use a really simple model.

In one unit, we have 4 fourts.

Then in 3 units, we have 3*4 = 12 fourts.

Then the answer is 12.

3) How to use multiplication?

Remember that dividing by a fraction is equivalent to multiplying by the inverse of said fraction, then:

[tex]N = \frac{3}{1/4} = 3*(4/1) = 12[/tex]

We got the same thing as above.

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Answer:

109.36 yards  to nearest hundredth

Step-by-step explanation:

1 meter =  1.09361 yards

So 100 m = 109.361 yards

Answer:

Step-by-step explanation:

−6m2 18m − 36

= -6(m2 - 3m + 6)

the statement which defines a translation is option A that is  "A translation proportionally stretches or compresses an object based on a given scale factor".

What is Translation ?

"Translation" moves points the same distance along lines that are parallel to each other.

Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.

Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points.

There, the statement which defines a translation is option A that is  "A translation proportionally stretches or compresses an object based on a given scale factor".

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Answer:

The correct answer is:  A translation moves points a specified distance along a line parallel to a specified line

Step-by-step explanation: I got it right on plato.

The approximate length of side AB is 14.0. The correct option is B. 14.0 units

From the question, we are to determine the measure of side AB

First, we will determine the measure of angle A

A + B + C = 180° (Sum of angles in a triangle)

A + 65° + 35° = 180°

A = 180° - 65° - 35°

A = 80°

Now, using the law of sines

c/sinC = a/sinA

c = AB

a = BC =  24

Thus,

c/sin35° = 24/sin80°

c = (24×sin35°)/sin80°

c = 13.978

c ≈ 14.0

∴ AB = 14.0

Hence, the approximate length of side AB is 14.0. The correct option is B. 14.0 units

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Answer:

[tex]y=3\sqrt{x-1}-7[/tex]

Step-by-step explanation:

We are given the function [tex]y=\sqrt{x}[/tex]. Let's apply each transformation separately and see what we get. First, let's apply the vertical shift. We are told that the graph shifts downwards by 7 units. In other words, when x is 0, y should be -7 instead of 0. We can accomplish that by changing the y-intercept of the graph and subtracting our function by 7: [tex]y=\sqrt{x} -7[/tex]. Notice that the -7 is outside the square root.

Next, we can apply the horizontal transformation. We are told that the graph shifts to the right 1 unit. This means that, for [tex]y=\sqrt{x}[/tex], if y is 0, x should be 1. We can accomplish this by doing [tex]y=\sqrt{x-1}[/tex] (if x = 1, y will be 0). Now, we can combine the two transformations we have done so far: [tex]y=\sqrt{x-1}-7[/tex].

Lastly, we need to vertically stretch the function by a factor of 3. All we have to do here is multiply sqrt(x) by 3 (this way, if x is equal to 1, y should be 3 instead of 1 (3 times x)). So, we get something like this: [tex]y=3\sqrt{x}[/tex]. Now, we can combine all of the transformations we did to get our final answer:

[tex]y=3\sqrt{x-1}-7[/tex]

The length of the arc is 15.70 km

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

The formula is given by

s = ϴ × r,

where

s is the arc length

r is the radius of the circle

θ is the central angle of the arc in radians

Given :- Radius = 10km

             Angle = 90 ° = [tex]\pi[/tex]/2 radians          (1 radian = 180°/[tex]\pi[/tex])

By using formula we get

Length of arc = 10 x[tex]\pi[/tex]/2 = 5[tex]\pi[/tex] km           ([tex]\pi[/tex] = 3.14)

                     = 15.70 km

Thus the length of the arc is 15.70 km

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The explicit function that defines the sequence is 15/2 - 9n/2

The sequence is given as:

3, -3/2, -6, -21/2

The above sequence is an arithmetic sequence, with the following parameters

The explicit formula is then calculated as:

T(n) = a + (n -1) * d

This gives

T(n) = 3 +(n -1) * -9/2

Expand

T(n) = 3 + 9/2 - 9n/2

Evaluate

T(n) = 15/2 - 9n/2

Hence, the explicit function that defines the sequence is 15/2 - 9n/2

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Answer:171x+8

Step-by-step explanation:

3x^3+12x^2x+8

=27x+144x+8

=171x+8

Let f(x) = x² + 6x²-x+ 5 then ,

number to be added be P

then,

f(x) = x² + 6x²-x+ 5 +P

According to the qn,

(x+3) is exactly divisible by zero then,

R=0

comparing .. we get a= -3

now by remainder theorm

R=f(a)

0=f(-3)

0=(-3)² + 6(-3)²-(-3)+ 5 + P

0= 9 + 54 + 3 + 5 + P

-71=P

therefore, -71 should be added.

Hope you understand

The stores that will be in the sample are - 00, 02, 05, 08, 11, 14, 17, 20, 23.

What comprises the sample?

An analytical subset of a larger population is referred to as a sample in statistics. A sample are used in research so that it can be done quickly and with more manageable data. However, obtaining such a sample may be costly and time-consuming. Randomly generated samples do not have significant bias if they are large enough.

Stores in the Sample

Since it is given that the sample is made up of every third store, starting from the first retail store. The stores have been numbered systematically from 00 to 23.  Since a systematic sampling is done, after picking the first store, the third store will be picked, that is, 02, and then 05, and so on till 23.

Thus, the following retail stores will be present in the sample,

00, 02, 05, 08, 11, 14, 17, 20, 23

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The point estimate here is 0.

Calculating the Mean of Each Set

The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}

The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}

The mean of set S1 = (20+25+27+23+22+20+17)/7

= 154/7

= 22

The mean of set S2 = (22+23+37+20+25+19+18)/7

= 154/7

=22

Calculating the Point Estimate

The formula for point estimate is given as,

Point Estimate  = The mean of set S1 - The mean of set S2

Point Estimate = 22-22

Point Estimate = 0

Therefore, the point estimate for the difference between the means of the two populations or sets is 0

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The computation shows that the average monthly amount is 61.64.

The amount that's left will be:

= 3314.85 + (2 × 926.65) - (1800 × 2) - 1075

= 3314.85 + 1853.3 - 3600 - 1075

= 493.15

The average monthly amount will be:

= 493.15/8

= $61.64

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It looks like the limit you want to compute is

[tex]\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}[/tex]

Since [tex]g(4)=4[/tex], this limit corresponds exactly to the derivative of [tex](f\circ g)(x) = f(g(x))[/tex] at [tex]x=4[/tex]. Recall that

[tex]f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}[/tex]

By the chain rule,

[tex](f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}[/tex]

Since [tex]g'(4)[/tex] exists, [tex]g[/tex] is differentiable at [tex]x=4[/tex] so it must be continuous.

Answer:

[tex] {75ft}^{2} [/tex]

Step-by-step explanation:

[tex]a = \pi{r}^{2} = 3 {r}^{2} \\ a =3 ({ \frac{10}{2} })^{2} = 3 \times {5}^{2} \\ a = 3 \times 25 = 75[/tex]

To start solving this exercise, we obtain as data:

To find the area of the circle. We apply the following formula: A =π r², where

We substitute our data in the formula and solve:

Substituting values into the equation:

Taking the square root:

Multiplying

Therefore, the area of the circle is 300 ft².

The computed value must closely match the real value for a model to be considered valid. If the percentage of pleased or very satisfied students remains close to 75% after Mateo surveys additional students, Mateo's model is still viable. The model is faulty if the opposite is true.

In general, a valid model is one whose estimated value is close to the real value. This kind of model is considered to be accurate. It must be somewhat near to the real value if it doesn't resemble the real value.

If the findings of the survey are sufficiently similar to one another, then the model may be considered valid.

P1 equals 75%, which is the real assessment of the number of happy pupils

P2 is 70 percent; this represents the second assessment of happy pupils

In conclusion,  The estimated value of a model has to be somewhat close to the real value for the model to be considered valid. If the number of students who are either pleased or extremely satisfied remains close to 75 percent following Mateo's survey of more students, then Mateo's model is likely accurate. In any other scenario, the model cannot be trusted.

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The total amount of Chandra's investments after 8 years is $110.03

The formula for calculating the compound interest is expressed as;

A = P(1+r/n)^nt

where

P is the amount invested = $75

r is the rate. = 0.048

t is the time =8years

n = 12 (monthly)

Substitute

A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03

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The height & speed are mathematically given as

t = 0.2 s

u = 4 m/s

Generally, the equation for height is  mathematically given as

h = 0.2gt^2

Therefore

0.2 = 0.5 * 9.8 *[tex]t^2[/tex]

0.2 = 4.9 *[tex]t^2[/tex]

t = 0.2 s

b)

In conclusion, the initial speed is

s = ut

Therefore

u = 0.8 / 0.2

u = 4 m/s

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Answer:

a = -22/13.

Step-by-step explanation:

By the Remainder Theorem

p(3) = remainder    when p(x) is divided by x-3.

q(3)  is equal to the same remainder.

So we have:

p(3) = q(3) , so

a(3)^3 + 4(3)^2 + 3(3) - 4 = 3^2 - 4(3) + a

27a + 36 + 9 - 4 = 9 - 12 + a

27a - a = 9 - 12 - 36 - 9 + 4

26a = -12 - 36 + 4

26a = -44

a = -44/26

a = -22/13.