The top of a tree broken by the wind made an angle of 45° with the ground. If the distance of the point where the top touched the ground from the foot of the tree is 30 ft, find the height of the tree before it was broken. Ans: 72.43 ft ​

The pair of figures is similar by SSS

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Triangles BDC and FGC

When the side lengths of the triangle are compared, we have:

Side lengths of FGC are 5/3 multiplied by the side lengths of BDC

This means that the triangles are similar

And the similarity statement is SSS

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The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11

From the question, we have the following parameters that can be used in our computation:

The graphs

The lines are absolute function graphs, and they can be represented as

y = a|x - h| + k

Where

Vertex = (h, k)

For the blue line, we have

(h, k) = (2, -5) and (x, y) = (0, -4)

So, we have

-4 = a|0 - 2| - 5

2a = 1

a = 1/2

So, the equation is y = 1/2|x - 2| + 5

For the red line, we have

(h, k) = (-2, 3) and (x, y) = (0, -11)

So, we have

-11 = a|0 + 2| + 3

2a = -14

a = -7

So, the equation is y = -7|x + 2| - 11

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If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.

In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.

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the boat will coast for a distance of 400 ln(2) ft, which is approximately 277.3 ft.

To find how far the boat will coast, we need to use the concept of differential equations. The equation that describes the velocity of the boat at any time "t" after its motor quits is given by:

dv/dt = -k*v

where "v" is the velocity of the boat at time "t", "k" is the proportionality constant, and the negative sign indicates that the velocity is decreasing with time.

We can solve this differential equation to obtain the velocity of the boat as a function of time:

v(t) = v(0) * e^(-k*t)

where "v(0)" is the initial velocity of the boat (40 ft/sec).

Using the given information, we can set up two equations:

v(10) = 20 (velocity after 10 sec)

v(0) = 40 (initial velocity)

Plugging these values into the equation, we get:

20 = 40 * e^(-10k)

Solving for "k", we get:

k = ln(2)/10

Now, we can integrate the velocity equation to find the distance the boat travels during the coasting period:

d = [tex]\int\limits^{\infty}_{10} {v(t)} \, dt[/tex]

Plugging in the values, we get:

d = (40/k) * [e^(-k*10) - 0] = 400 ln(2) ft

To explain the solution, we used the concept of differential equations to model the motion of the boat as it coasts after its motor quits. We used the given information to solve for the proportionality constant "k", which allowed us to find the velocity of the boat at any time.

Finally, we integrated the velocity equation to find the distance the boat travels during the coasting period. The key to this problem was using the concept of differential equations to model the motion of the boat and setting up the appropriate equations to solve for the unknowns.

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Complete question is:

Suppose that a motorboat is moving at 40 ft/sec when its motor suddenly quits, and then 10 sec later the boat has slowed to 20 ft/sec. Assume, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?

The average rate of change over the interval [3,4] is given as follows:

3.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The numeric values for the ends of the interval are given as follows:

Then the change in the output is of:

32 - 29 = 3.

The change in the input is of:

4 - 3 = 1.

Hence the rate is of:

r = 3/1

r = 3.

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Answer:

Step-by-step explanation:

The equation connects m and n.

Suppose n=1,

m=3/1=3.

If n=2,

m=3/2=1.5

If n=3,

m=3/3=1. This shows that as n increases, m decreases.

If m was equal to 1,

1=3/n

Thus n=3.

If m=2,

2=3/n

n=1.5

If m=3,

3=3/n

n=1.

This also shows that as m increases, n decreases.

Hope this helps :)

Answer:

When I increased n, m decreased.

When I increase m, n decreases

Step-by-step explanation:

Let's say that m is one and n is 3

1 = [tex]\frac{3}{3}[/tex]  Us this as our base to compare increasing m and n.

Increase n to 6

[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]

When I increased n, m decreased.

Increase m to 3

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

When I increase m, n decreases

The values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

A + B + C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B = 180° - 139°

B = 41°

sin49 = a/12.7 {opposite/hypotenuse}

a = 12.7 × sin49 {cross multiplication}

a = 9.5848

cos49 = b/12.7 {adjacent/hypotenuse}

b = 12.7 × cos49 {cross multiplication}

b = 8.3319

Therefore, the values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°..

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The radius of the circle is 2.8feet (nearest tenth)

Arc length is the distance between two points along a section of a curve.

The length of an arc is expressed as ;

L = (tetha) / 360 × 2πr

L is the length of the arc

tetha is the angle made by the two radii and the arc.

In radian 360° = 2π

therefore ;

8 = 2.9/ 2π × 2πr

8 = 2.9 r

r = 8/2.9

r = 2.76 ft

therefore the radius of the circle is 2.8 feet( nearest tenth) .

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This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).

A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.

A linear equation is so named because plotting the graph of a given linear model yields a straight line.

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the probability of getting (a, b), i.e. the first card is a and the second card is b is 2/3 by conditional probability.

The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is computed by dividing the likelihood of the earlier occurrence by the likelihood of the subsequent, or conditional, event.

This is where the independent event and dependent event notion is used. Consider a student who misses class twice each week, omitting Sunday. What are the possibilities that he will take a leave of absence on Saturday of the same week if it is known that he will be absent from school on Tuesday? It has been noted that situations where the outcome of one event influences the outcome of a subsequent event are termed as conditional probability

We can work this out directly from the definition of conditional probability,

[tex]P(G_1|G_2)=P(G_1nG_2)/(P(G_1)[/tex]

Exactly one of the three cards has sides, so

P(G1∩G2)=1/3

and P(G1)=1/2

THEN

the probability of getting (a, b), i.e. the first card is a and the second card is b IS = 1/3÷1/2 = 2/3

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On solving the provided question we can say that from the graphs,

y = f(x) = |x| and g(x) = |x-h| + k

Mathematicians use diagrams to logically bring facts or values ​​using visual representations or charts. A graph point usually reflects a contact between two or more things. Nodes or vertices and corner form a graph, which is a nonlinear data construction. We often glue knots together called vertices. This graph has vertices V=1, 2, 3, 5 and edges E=1, 2, 1, 3, 2, 4 and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) are graphical representations of expanding growth. Logarithmic graph in the format of a triangle 

from the graphs,

y = f(x) = |x|

y = f(x) + k

y = f(x+h)

g(x) = |x-h| + k

now, it will be

k>0 and h<0

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Answer:

The graph of the function will shift vertically up by $5.

Step-by-step explanation:

The original function is m(x) = 2x + 15, where x is the number of people in the car. If the per car charge is changed to $20 per car, the new function becomes m(x) = 2x + 20, because the charge per car has increased by $5.

This means that the y-intercept of the new function is 20 instead of 15, which represents the minimum cost for a car, regardless of the number of people inside. So the graph of the new function will be shifted vertically up by $5 from the graph of the original function.

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(a) The probability that all the student pilots successfully land the plane using the simulator is 43%

(b) The probability that none of the student pilots successfully lands the plane using the simulator is 0.0026%

(c) The probability that exactly eight of the student pilots successfully land the plane using the simulator is 30.1%

Probability is a measure of the likelihood of an event occurring.

(a) What is the probability that all the student pilots successfully land the plane using the simulator?

Probability of all pilots successfully landing

=> 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = 0.43 or 43%

So, the probability that all the student pilots successfully land the plane using the simulator is 0.43 or 43%.

(b) What is the probability that none of the student pilots successfully land the plane using the simulator?

The probability of each pilot failing to land the plane is 0.20. We can use the multiplication rule again to calculate the probability of none of the pilots successfully landing the plane.

Probability of all pilots failing to land = 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 = 0.000026 or 0.0026%

So, the probability that none of the student pilots successfully land the plane using the simulator is 0.0026% or 0.000026.

(c) What is the probability that exactly eight of the student pilots successfully land the plane using the simulator?

where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success in one trial, and nCk is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.

In this case, we have n=9, k=8, p=0.80, and (1-p)=0.20. So, the probability of exactly eight pilots successfully landing the plane is:

P(X=8) = 9C8 * 0.80^8 * 0.20^(9-8) = 0.301 or 30.1%

So, the probability that exactly eight of the student pilots successfully land the plane using the simulator is 0.301 or 30.1%.

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Answer:

(x-1)(x+1)(x+3)

Step-by-step explanation:

[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]

Answer:

Let's call the length of side 1 "x". Then, the length of side 2 is 2x, and the length of side 3 is x + 4. So, the expression for the three sides of the triangle can be represented as:

x + 2x + (x + 4) = 3x + 4

This expression represents the sum of the lengths of all three sides of the triangle.

Step-by-step explanation:

Answer: x+2x+(4+x)

Step-by-step explanation:

since side one is unknown, we can substitute it with variable x, and side two is twice as much as side one so we do 2x, and side three is four cm longer than side one so we do 4+x at the end

1) The mean of the data is 4.45.

2) The mode of the data is 11.

3) The median of the data is 4.

The mean of the data is the ratio of the sum of the given data and the number of the count of the data.

The mode of the data is the number that is repeated maximum number of times. The median of the data is when the data is arranged in an increasing order then the middle most value will be the median of the data.

Given data is 6 11 5 11 4 0 2 0 1.

The mean of the data is,

Mean =  ( 6 + 11 + 5 + 11 + 4 + 0 + 2 + 0 + 1 ) / 9

Mena = 4.45

Mode = 11

Median:- 0,0,1,2,4,5,6,11,11

Median = 4

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Step-by-step explanation:

Answer:a is 3:9 B is 6:9

Step-by-step explanation:

10:40 am

63 mile distance and 27 mph. starting from 8 am

63/27 => 2 (2/3) hours. 2/3 of an hour is also, 40 minutes.

so 8 am plus 2 hours and 40 minutes means 10:40 am

Answer:

A

Step-by-step explanation:

A is correct because 3+4 = 7

B is incorrect because 9/3=3 ,not 3/9

There is no x in C

D is incorrect because 8×3=24

E is incorrect because 3-10= -7 (negative)

hope this helped :)

Uncle Harry rented 4 games, and using  that he also rented 8 movies.Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.

What is word problem?

A word problem is a type of mathematical problem that is presented using words instead of or in addition to mathematical symbols and equations. Word problems often describe a real-world scenario or situation, and they require the solver to use math skills and critical thinking to identify the relevant information, determine the mathematical operation or operations required, and arrive at a solution to the problem.

Let's assume that the number of movies Uncle Harry rented is "m" and the number of games is "g". We want to find the values of "m" and "g".

From the problem statement, we know that:

The total number of movies and games rented is 12: m + g = 12

The cost of each movie is $3.99: 3.99m

The cost of each game is $4.50: 4.5g

The total cost before tax is $49.92: 3.99m + 4.5g = 49.92

We can use the first equation to express "m" in terms of "g":

m = 12 - g

Substituting this expression for "m" in the second equation, we get:

3.99(12 - g) + 4.5g = 49.92

Expanding the brackets and simplifying, we get:

47.88 - 3.99g + 4.5g = 49.92

0.51g = 2.04

g = 4

So Uncle Harry rented 4 games, and using the first equation, we find that he also rented 8 movies.

Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.

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Answer: -1/3

Step-by-step explanation:

Slope = Rise/Run

An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. The restocking fee for an item priced at $180 is $10.

To solve this problem, we need to use a proportion to relate the item price to the restocking fee. The problem provides two pairs of corresponding item prices and restocking fees: $200 and $12, and $150 and $9. We can set up a proportion using these pairs:

$200/$12 = $150/$9

We can simplify this proportion by dividing both sides by 3:

$200/$4 = $150/$3

Now we can use the simplified proportion to find the restocking fee for an item priced at $180. We'll use cross-multiplication:

$200 x $3 = $150 x $4

$600 = $600

This tells us that the ratios are equivalent, and the restocking fee for an item priced at $180 is $10.

In other words, the restocking fee is proportional to the item price, and we can use the given pairs of prices and fees to find the fee for any given price using a proportion.

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Gwen has £0.75 money left over, as per linear equation if a litre of cola costs £1.25.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

It is given that Gwen has a £5 note and a £2 coin.

Therefore, she has a total of £(5 + 2) = £7

A liter of cola costs £1.25.

Therefore, (7 ÷ 1.25) = 5.6

Therefore, Gwen can buy a total of 5 liters of cola.

Now, Gwen has left money of £[7 - (5 × 1.25)] = £0.75

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Complete question is:

Gwen has a £5 note and a £2 coin

a litre of cola cost £1.25

gwen buys as many liter bottles of cola as she can

how much money will she have left over