Hank can see the top of a tree in a mirror that is placed 475 cm from the tree when he stands 190 cm from the mirror. What is the height of the tree?

That is the same as writing [tex]10\sqrt{30}[/tex]

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Explanation:

The diagram shows that

That must mean DC = AC-AD = 60-50 = 10

We'll use this to help find BD as shown below

AD/BD = BD/DC

AD*DC = BD*BD .... cross multiply

(BD)^2 = AD*DC

BD = sqrt(AD*DC) ..... geometric mean formula

BD = sqrt(50*10)

BD = sqrt(500)

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Now apply the pythagorean theorem to find AB. Focus on triangle ABD.

(AD)^2 + (BD)^2 = (AB)^2

(AB)^2 = (AD)^2 + (BD)^2

(AB)^2 = (50)^2 + (sqrt(500))^2

(AB)^2 = 2500 + 500

(AB)^2 = 3000

AB = sqrt(3000)

AB = sqrt(100*30)

AB = sqrt(100)*sqrt(30)

AB = 10*sqrt(30)

Answer:

y-5 = 3/4(x+3)

Step-by-step explanation:

Answer:

y = 14x

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in 7 as y and 0.5 as x, and solve for k:

y = kx

7 = k(0.5)

14 = k

Plug this into the equation:

y = kx

y = 14x

So, the equation of variation is y = 14x

Answer:

19 is 47.5% of 40.

Step-by-step explanation:

First, you have to use the formula is/of=%/100, so since 19 is closest to the word is, 19 will go on the top left, since 47.5% is a percentage it will go on top of 100, finally, 100 always goes on the bottom and x will be the of, since there is no given number for it (19/x=47.5/100). You cross multiply (19x100) then divide it by the remaining number (47.5) then you get your answer of 40.

Answer:

x = 9

y = 9

Step-by-step explanation:

Given :

Let :

Kenyan French roast coffee = x

Cost per x = $8

Sumatran Coffee = y

Cost per y = $10

x + y = 18 - - - - (1)

8x + 10y = 9 * 18 ;

8x + 10y = 162 - - - - (2)

From (1):

x = 18 - y

Put x = 18 - y in (2)

8(18 - y) + 10y = 162

144 - 8y + 10y = 162

2y = 162 - 144

2y = 18

y = 9

x = 18 - y

x = 18 - 9

x = 9

The GPA of the student, based on the given grades, is approximately 1.93.

Use the concept of probability defined as:

Given that,

Grades provided: B (13 hours), D (16 hours), C (13 hours)

Grade equivalencies: A = 4.0, B = 3.0, C = 2.0, D = 1.0, F = 0

Credit hours associated with each grade: B (13 hours), D (16 hours), C (13 hours)

To calculate GPA,

Convert grades to their point values and calculate the weighted GPA

Point values for the given grades: B (3.0), D (1.0), C (2.0)

To calculate the GPA,

First, convert each grade to its equivalent point value.

For the given grades, we have:

B (13 hours) = 3.0

D (16 hours) = 1.0

C (13 hours) = 2.0

Now, calculate the weighted GPA by multiplying the point value of each grade by the number of credit hours and then summing them up.

In this case, it would be:

(3.0 x 13) + (1.0 x 16) + (2.0 x 13) = 81

Divide the sum of the weighted grade points (81) by the total number of credit hours (13 + 16 + 13 = 42) to get the GPA:

81 / 42 = 1.93

Hence,

Rounding to two decimal places, the GPA would be approximately 1.93.

Learn more about the probability visit:

https://brainly.com/question/13604758

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Answer:

The base is: [tex]3 \sqrt[3]{4}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{4}(\sqrt[3]{108})^x[/tex]

Required

The base

Expand 108

[tex]f(x) = \frac{1}{4}(\sqrt[3]{3^3 * 4})^x[/tex]

Rewrite the exponent as:

[tex]f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x[/tex]

Expand

[tex]f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x[/tex]

[tex]f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x[/tex]

Rewrite as:

[tex]f(x) = \frac{1}{4}(3 \sqrt[3]{4})^x[/tex]

An exponential function has the following form:

[tex]f(x)=ab^x[/tex]

Where

[tex]b \to base[/tex]

By comparison:

[tex]b =3 \sqrt[3]{4}[/tex]

So, the base is: [tex]3 \sqrt[3]{4}[/tex]

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Reason \to Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990[/tex]

[tex]Coronary\ atherosclerosis\to 1400[/tex]

[tex]Heart\ attack \to 744[/tex]

[tex]Infant\ birth\to 3800[/tex]

Solving (a): Frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the frequency (on the y-axis).

See attachment

Solving (b): Relative frequency distribution

The relative frequency is calculated as:

[tex]RF = \frac{F}{Total}[/tex]

Where

[tex]Total = 990+1400+744+3800[/tex]

[tex]Total = 6934[/tex]

So, we have:

[tex]Congestive\ heart\ failure \to \frac{990}{6934} = 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to \frac{1400}{6934} = 0.2019[/tex]

[tex]Heart\ attack \to \frac{744}{6934} = 0.1073[/tex]

[tex]Infant\ birth\to \frac{3800}{6934} = 0.5481[/tex]

So, the relative distribution is:

[tex]Reason \to Frequency \to Relative\ Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to 1400 \to 0.2019[/tex]

[tex]Heart\ attack \to 744 \to 0.1073[/tex]

[tex]Infant\ birth\to 3800 \to 0.5481[/tex]

Solving (c): Relative frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the relative frequency (on the y-axis).

See attachment

Solving (d): Relative frequency Pareto chart

First, calculate the cumulative relative frequency

This is done by adding up the previous relative frequency,

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.2019+0.1427=0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.3446+0.1073 = 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 0.5481+4519 =1[/tex]

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 1[/tex]

Next, we simply plot the reasons (on the x-axis) against the cumulative relative frequency (on the right) and the left of the Pareto chart.

See attachment

Answer:

6144π ft³ ; 19292.2 ft³

Step-by-step explanation:

The volume of the cylinder Given above :

Volume of cylinder, V = πr²h

r =Radius = 16 ; h = 24 ft

V = π * 16² * 24

V = 256 * 24 * π

V = 6144π

Using π = 3.14

V = 6144 * 3.14 = 19292.16

Answer:

I think no B

if wrong correct me pls

I HOPE IT HELPS

HAVE A GREAT DAY

[tex]#Liliflim[/tex]

Answer:

B

Step-by-step explanation:

C=7s

Answer:

Kindly check explanation

Step-by-step explanation:

Using technology on the data above, the least square regression equation obtained is ;

y = 33.4528+2.7975x

Where, slope = 2.7975 ; Intercept = 33.4528

x = chirps per second, independent variable

y = temperature, predicted variable.

The Correlation Coefficient, r = 0.71

The Coefficient of determination, r² = 0.71² = 0.5041

The percentage of variation in y due to regression is the r² value, which is about 50.41%

Hence, the percentage variation in temperature due to the regression line is 50.4, while the rest is due to other factors.

Predicted temperature, y when x = 19 ;

Put x = 19

y = 33.4528+2.7975(19)

y = 86.60°

Answer:i took the test

Step-by-step explanation: 76879686

Answer:

Repeated measures(dependent samples t-test).

Step-by-step explanation:

Repeated measures (dependent samples t-test ):-

(Repeated measures dependent sample t-test is a statistical test that is used to found A significant difference in the within-subject design when the same participants go through both the conditions and there are only two conditions. In this scenario there are only two conditions -classical music and country music and every participant is exposed to both making it a dependent sample as the score of one participant on country music corresponds to the score of his on classic music.

Since it has only two variables, ANOVA can't be performed as it is performed to compare the means of more than 2 variables).

Answer:

54

Step-by-step explanation:

16.4= 16

12.8= 13

9.6= 10

14.6=15

16 + 13 +10 +15 = 54

Answers:

x = 6

Each angle is 45 degrees

The diagram is shown below

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Explanation:

Vertical angles are always congruent

Set the two expressions equal to each other and solve for x.

5x+15 = 3x+27

5x-3x = 27-15

2x = 12

x = 12/2

x = 6

As a way to check the answer, replace x with 6 in each expression. We should get the same thing on both sides

5x+15 = 3x+27

5*6+15 = 3*6+27

30+15 = 18+27

45 = 45

Each angle is 45 degrees, so the answer is confirmed.

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The diagram is shown below. There are infinitely many ways to draw out the diagram. In the version I drew, the angles aren't vertically aligned but instead they are opposite one another in this X configuration. So the vertical angles could be vertically aligned, but they don't have to be.

In short: draw an X shape and mark any two opposite angles to form the vertical angles.

Answer: $1260

Step-by-step explanation:

Based on the information given, Abby's gross income for the month if her sales were $12500 will be:

= $1000 + (1% × $8000) + [4% × ($12500 - $8000)]

= $1000 + (0.01 × $8000) + (0.04 × $4500)

= $1000 + $80 + $180

= $1260

Her gross income is $1260

Answer:yes it is

hsyhsyxhsyxhsyhxysxys

Answer:

24/40 = 12/20 = 6/10 = 3/5 ...

so no 24/40 does not = 4/5

Step-by-step explanation:

9514 1404 393

Answer:

  b) y=(x+6)^2-32

Step-by-step explanation:

Add and subtract the square of half the x-coefficient to put into vertex form.

  f(x) = x^2 +12x +4 . . . . . given

  y = x^2 +12x +36 +4 -36 . . . . add and subtract (12/2)^2 = 36

  y = (x +6)^2 -32 . . . . . . . . . . . write in vertex form

Answer:

Step-by-step explanation:

hope it helps

Answer:

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

θ=arccot(x/o)

Answer:

18

Step-by-step explanation:

Hope this help!!!

Have a nice day!!!

Answer:

here u go

Step-by-step explanation:

i got 45

Step-by-step explanation:

The power reducing formulas are given by the following:

[tex]\sin^2 x = \dfrac{1- \cos2x}{2}[/tex]

[tex]\cos^2 x = \dfrac{1+ \cos2x}{2}[/tex]

We can then write the given expression as

[tex]\sin^25x \cos^25x[/tex]

[tex]= \left(\dfrac{1- \cos 2(5x)}{2} \right) \left(\dfrac{1+ \cos 2(5x)}{2} \right)[/tex]

[tex]= \dfrac{1}{4}(1- \cos 10x)(1+ \cos 10x)[/tex]

[tex]= \dfrac{1}{4}(1- \cos^2 10x)[/tex]

[tex]= \dfrac{1}{4} \left(\dfrac{1- \cos 20x}{2} \right)[/tex]

or

[tex]\sin^25x \cos^25x= \dfrac{1}{8}(1- \cos 20x)[/tex]

Answer:

2

Step-by-step explanation:

Solution :

It is given that :

[tex]$f'(t) = (350 \ln t)'$[/tex]

       [tex]$=350(\ln t)'$[/tex]

        [tex]$=\frac{350}{t}$[/tex]

So, [tex]f(5)=350 \ln (5) \approx 563[/tex]

     [tex]$f'(5) = \frac{350}{5}$[/tex]

              [tex]=70[/tex]

The relative change is then,

[tex]$\frac{f'(5)}{f(5)}=\frac{70}{350\ \ln(5)}$[/tex]

         [tex]$=\frac{1}{5\ \ln(5)}$[/tex]

         [tex]$\approx 0.12$[/tex]

          [tex]=12\%[/tex]

This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.

Answer:

??

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

median is the middle value.

1. arrange in numerical order

65, 74, 77, 88, 92

2. cross out all outside numbers untill you find the middle value

65, 74, 77, 88, 92

3. it's 77

Answer:

acute and isosceles

Step-by-step explanation:

Define:

Acute - All angles have a measure of less than 90 degrees

Obtuse - has an angle with a measure of more than 90 degrees

Right - has an angle with a measure of 90 degrees

Scalene - no congruent side lengths or angles

Isosceles - two congruent sides and two congruent angles

Equilateral - all congruent sides and all congruent angles

Identify:

The triangle shown has angles that measure less than 90 degrees which means that it's an acute triangle

The triangle also has two congruent sides and two congruent angles which means that it's an isosceles triangle.

So we can conclude that the triangle can be identified as an acute isosceles

Using trigonometry solve for h and d.

H :

Sin(60) = h/120

H = 120 x sin(60)

H = 103.9 = 104 feet

D:

Cos(60) = d/120

D = 120 x cos(60)

D = 60 feet

The correct answers:

A. D = 60 ft.

C. H = 104 ft

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude is the distance between the midline and the maximum/minimum. Because the midline is located at y=1, then the maximum and minimum are both 2 units apart from the midline. That is your amplitude.

Answer:

c.

0.1824

Step-by-step explanation:

The computation of the decay factor is as follows;

= (1 - decrease percentage) × (1 - decrease percentage) × (1 - decrease percentage)

= (1 - 0.2) × (1 - 0.4) × (1 - 0.62)

= (0.8) × (0.6) × (0.38)

= 0.1824

hence, the decay factor is 0.1824

Therefore the option c is correct