You are on a fishing boat that leaves its pier and heads east. After traveling for 29 miles, there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of S35​°W for 14.6 miles.

a. At this​ time, how far are you from the​ boat's pier?
b. What bearing could the boat have originally taken to arrive at this​ spot?

c) Population [tex]\sigma = 48[/tex]

Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]

Z-score= 1.3333

According to the question , sample size n=64 , mean M = 68 , population mean [tex]\mu= 60[/tex]

Z = [tex]\frac{M-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]

where M = Sample Mean

[tex]\mu[/tex] = Population Mean

[tex]\sigma[/tex] = Population Standard Deviation

n = Sample Size

a) Population [tex]\sigma[/tex] = 16

Z = [tex]\frac{68-60 }{\frac{16 }{\sqrt{64}}}[/tex]

Z-score = 4

b) Population [tex]\sigma[/tex] = 32

Z = [tex]\frac{68-60 }{\frac{32 }{\sqrt{64}}}[/tex]

Z-score = 2

c) Population [tex]\sigma[/tex]= 48

Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]

Z-score= 1.3333

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Answer: ∠EFB, ∠DFE, and ∠CFB

Step-by-step explanation:

Starting Angle: ∠CFD

Since its in an X formation: ∠EFB, ∠DFE, and ∠CFB would all work.

Answer:

incomplete question bru

Based on the above, about  174 people out of the sample of 600 people indicated Bluetooth capability.

To know the number of individuals who shown Bluetooth capability, we have to to begin with calculate the division of individuals who chose this choice from the circle chart.

Note that:

People who Bluetooth capability =29%

Number of people = Percentage × Total sample size

= 0.29 × 600

= 174

So,  174 individuals shows that the Bluetooth capability is their favored option for the family trip.

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The area of the figure composed of two rectangles is 99 mi²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

For the first rectangle:

Area = 11 mile * 5 mile = 55 mi²

For the second rectangle:

Area = 11 mile * 4 mile = 44 mi²

The area of figure = 55 mi² + 44 mi² = 99 mi²

The area of the figure is 99 mi²

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The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

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Answer:

According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces

Step-by-step explanation:

If the burn rate is believed to be constant, determine the average burn rate for the eight candles as the ratio of weight loss per hour.

ounces lost over three hours

0.5+0.6+0.5÷0.7÷0.7÷0.5÷0.5÷0.6

8

* 0.575

0.575

ounces lost per hour on average

= 0.19

For 0 hours, the weight of each candle is 16 ounces. Therefore, w 16 - 0.19h.

This model can be used to predict the weight of the candle when h, the number of hours of burning, is 5.

W * 16 - 0.19(5)

W = 16 - 0.95

W = 15.05

According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces.

The volume of the triangular base prism is  120 inches³.

The prism above is a triangular base prism. The volume of the triangular base prism can be calculated as follows:

volume of the prism = base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 8 × 10

base area = 80 / 2

base area = 40 inches²

Therefore,

volume of the prism = 40 × 3

volume of the prism = 120 inches³

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Answer:

Second number line

Step-by-step explanation:

(h-3)^2 <= 25

h^2 - 6h + 9 <= 25

h^2 - 6h - 16 <= 0

(h-8)(h+2) <=0

Using the graph of (x-8)(x+2),

-2 <= h <= 8

Hence, the answer is the second one (as it has shaded circles)

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All the correct values are,

⇒ ∠ABD = 60°

⇒ ∠ADB = 90°

⇒ ∠BAD = 30°

⇒ ∠CAD = 30°

⇒ BD = 3

⇒ AD = √27

⇒ The value of area of triangle ABC is, 3√27

Given that;

In the diagram shown, ABC is equilateral. AD is an altitude.

Hence, We get;

All the angles of a equilateral triangle are,

⇒ 60°

Thus, We get;

⇒ ∠ABD = 60°

Since, AD is an altitude.

⇒ ∠ADB = 90°

And,

⇒ ∠BAD = 60 / 2 = 30°

⇒ ∠CAD = 60/2 = 30°

By Pythagoras theorem;

AB² = AD² + BD²

6² = AD² + 3²

36 = AD² + 9

AD² = 27

AD = √27

Thus, The value of area of triangle ABC is,

⇒ 1/2 × AD × BC

⇒ 1/2 × √27 × 6

⇒ 3√27

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The value of k include the following: B. k is equal to one third.

In Mathematics, the vertex form of a quadratic function can be modeled by this formula:

y = a(x - h)² + k

Where:

Based on the information provided about the quadratic function f(x), we can logically deduce that its vertex is at (0, 0);

f(x) = a(x - h)² + k

2 = a(1 - 0)² + 0

2 = a

f(x) = 2(x - 0)² + 0

f(x) = 2x²

For the quadratic function g(x), we have;

g(x) = f(kx)

g(x) = 2(kx)²

g(x) = 2k²x²

By using the point (3, 2) from the table, we have:

2 = 2k²3²

1 = k²9

k² = 1/9

k = √(1/9)

k = 1/3 i.e one third.

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Answer: Well that wouldn't work quite as well.

Step-by-step explanation:

a. The basketball player is 19.50 cm tall. (Assuming you meant to write

195 cm instead of 1950 cm)

b. A new piece of chalk is about 81.00 cm long.

c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

By placing a decimal point in the appropriate location, we can make the numbers more reasonable.

a. The basketball player cannot be 1950 cm tall, as that is almost 20 meters or over 65 feet.

The average height of a basketball player in the NBA is around 6'7'' (or about 2 meters).

Therefore, we can assume that the correct height of the basketball player is 195 cm, or about 6'5''.

b. A piece of chalk that is 8100 cm long is over 80 meters long, which is clearly too long for a piece of chalk.

Therefore, we can assume that the correct length of the chalk is 81.00 cm or about 32 inches.

c. A speed limit of 400 km/hr is unreasonably high, as it is equivalent to over 248 miles per hour.

The highest speed limits in the world are typically around 80-85 mph (130-140 km/hr), so 400 km/hr is clearly incorrect.

Therefore, we can assume that the correct speed limit is 40.0 km/hr, which is a more reasonable speed limit for a town or residential area.

Hence,

a. The basketball player is 19.50 cm tall. (Assuming you meant to write

195 cm instead of 1950 cm)

b. A new piece of chalk is about 81.00 cm long.

c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).

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10x² + 13x + 11 is the sum of linear equation .

What is a linear equation in mathematics?

The algebraic equation y=mx+b is known as a linear equation. All of its terms are constant, first-order linear ones. where m denotes the slope and b the y-intercept.

                             The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are variables. One or more variables may be present in a linear equation. The term "bivariate linear equation" refers to a linear equation with two variables.

two equations are  10x² + 7x + 6 and 6x + 5.

now add both equations

= (10x² + 7x + 6 )+ (6x + 5)

=  10x² + 7x + 6 + 6x + 5

= 10x² + 13x + 11

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The graph of y=|x| is a v-shaped graph that starts at the origin and continues infinitely in both the positive and negative x-directions. The graph of y=|x|+2 is the same v-shaped graph, but it has been shifted up two units so that it no longer intersects the x-axis. Finally, the graph of y=|x|-1 is a v-shaped graph that has been shifted down one unit so that it intersects the x-axis at (1,0) and (-1,0). All three graphs are symmetric with respect to the y-axis.

Answer: D 36л

Step-by-step explanation:

s = θr

where r is the radius of the circle.  given that the arc length is 6, and the central angle is π/3 radians r:

6 = (π/3)r

r = 6/(π/3) = 18/π

the circumference of the circle is given by:

C = 2πr

Substituting r = 18/π, we get:C = 2π(18/π) = 36

The equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3) is f(x) = 4.366*log10(x+4)

To find the equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3), we need to determine the values of a, b, h, and k.

First, we know that the function passes through (1,0), so we can substitute x=1 and y=0 in the general equation of the transformed logarithmic function to get:

0 = a x log b(1-h) + k

Since log b(1-h) = 0 for any base b and any value of h, we can simplify the equation to:

0 = k

Therefore, k=0 and the equation becomes:

f(x) = a x log b(x-h)

Now, we have two equations with two unknowns (a and h), which we can solve by substitution or elimination. For simplicity, we can substitute b=10 (base 10 logarithm) since it is a common base and the values of a and h do not depend on the base of the logarithm. We get:

10⁶/ᵃ = 3-h

Since h is the horizontal shift of the graph, we can choose any value of h that makes the expression inside the logarithm positive. For example, we can choose h=-4, which makes x-h=-3-(-4)=1, the same as the x-coordinate of the point (1,0).

Taking the logarithm of both sides with base 10, we get:

log(4) = (6/a)*log(10)

Solving for a, we get:

a = 6/(log(4)*log(10)) ≈ 4.366

Now, we can substitute the values of a and h in the equation of the transformed logarithmic function to get:

f(x) = 4.366*log10(x+4)

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It should be noted that to find the equation of a line, two pieces of information are necessary: the slope and coordinates of a point on the line.

Also, to acquire this, one can leverage either the point-slope form or the slope-intercept form to compose it.

If both the slope (m) and coordinates of the point  (x1, y1) on the line are known, then one can express the equation in its point-slope style as follows:

y - y1 = m(x - x1)

Or, if only the slope (m) and the y-intercept (b), which is the value of y where the line crosses the y-axis, are accessible, then the equation can be expressed via the slope-intercept form with: y = mx + b

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Answer:

150

Step-by-step explanation:

divide the percentage by 100 to make it decimal form,
75/100= .75

The multiple .75 by the total amount to find the 75%,

200 x .75 = 150

Which means 75% of 200 is 150

The weighted mean of the deliveries each week can be found to be 5. 38 .

The weighted mean is a type of mean that takes into account, the weight of the various items in question.

First, find the total frequency :

= 1 + 5 + 4 + 3

= 13

The weighted mean would then be:

= ∑ ( weight of delivery x number of deliveries )

= ( 1 / 13 x 2 ) + ( 5 / 13 x 4 ) + ( 4 / 13 x 6 ) + ( 3 / 13 x 8 )

= 0. 15  + 1. 54 + 1. 84 + 1. 85

= 5. 38

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Answer:

1.  CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.

2.  SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.

3.  R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.

Hope this helps!

Answer:

1.  CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.

2.  SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.

3.  R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.

Hope this helps!

The cost for wall-to-wall carpeting is equal to $ 318.

In this problem we need to compute the cost for wall-to-wall carpeting, that is, the cost of covering the floor of the entire room. This can be done by using the following formula:

C = (1 / 9) · c · w · l

Where:

If we know that c = 13.25, w = 12 and l = 18, then the cost of the wall-to-wall carpeting is:

C = (1 / 9) · 13.12 · 12 · 18

C = 318

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The answer of the given question based on the experimental probability is the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.

Experimental probability is  ratio of number of times  event occurs to the total number of trials or observations conducted in  experiment or real-life situation. It is based on actual observations or data and is also known as empirical probability.

Experimental probability is used when it is not possible or feasible to determine the theoretical probability of an event, or when the theoretical probability does not match the actual outcomes observed in a given situation. In such cases, experimental probability provides an estimate of the likelihood of an event occurring based on real-life data.

The experimental probability that the next pizza sold will have pepperoni is the ratio of the number of pepperoni pizzas sold to the total number of pizzas sold in the recent past.

According to the problem, 4 of the last 6 pizzas sold had pepperoni. So, the experimental probability of the next pizza sold having pepperoni is:

experimental probability = number of pepperoni pizzas sold / total number of pizzas sold

experimental probability = 4 / 6

experimental probability = 2 / 3

Therefore, the experimental probability that the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.

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Answer:

8a^2 + 6ats - 2t^2s^2

Step-by-step explanation:

(4a-ts)(2a+2ts)

4a(2a+2ts) -ts(2a+2ts)

8a^2 + 8ats - 2ts - 2t^2s^2

= 8a^2 + 6ats - 2t^2s^2

Answer:

To determine the scale factor used, we need to find the ratio of corresponding side lengths in both triangles.

Let's compare the length of the first side in both triangles:

x/3.8 = 2/4.8

Cross-multiplying, we get:

4.8x = 7.6

Dividing both sides by 4.8, we get:

x = 1.58

Now, let's compare the length of the second side in both triangles:

2.4/4.2 = 0.57

Finally, let's compare the length of the third side in both triangles:

2.1/4.8 = 0.44

Since the scale factor is the same for all corresponding side lengths, we can take the average of the ratios:

(scale factor) = (1.58/3.8 + 0.57 + 0.44)/3

(scale factor) = 1.01

Therefore, the scale factor used is approximately 1.

There are four possible outcomes in this game: winning $1, winning $5, winning $10, or winning $0.

The probability of winning $1is the probability of drawing one of the 11 hearts that are not the ace of hearts. There are 52 cards in the deck, so the probability of drawing any one of them is 1/52. However, there are 11 hearts that win $1, so the probability of winning $1 is:

P(W = $1 ) = 11/52

The probability of winning $5 is the probability of drawing the ace of hearts, which is 1/52.

P(W = $5) = 1/52

The probability of winning $10 is the probability of drawing the king of spades, which is also 1/52.

P(W = $10) = 1/52

The probability of winning $0 is the probability of drawing any other card, which is 39/52.

P(W = $0) = 39/52

Answer: The 290 millimeters long is the ribbon.

Step-by-step explanation:

To convert centimeters to millimeters

1 cm =10 millimeters

therefore,

29cm= 290 millimeters

Therefore, the ribbon is 290 millimeters long.

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a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:

Obtain the data for the medal winnings of the Top 10 NOCs

Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)

Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option

Add a title and labels to the chart to show the NOCs and their corresponding medal winnings

b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:

Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.

Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.

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