Mac is 5 feet tall and casts a 4 foot 6 inch shadow. At the same time, a nearby tree casts a 20
foot shadow
Which is the closest to the height of the tree?

Answer:

V=301.59 M^3

Step-by-step explanation:

The volume of a cylinder is 3.14r^2h

3.14(4^2)6=V

3.14(16)6=V

50.24(6)=301.59

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-5}{ k})\qquad \qquad radius=\stackrel{4}{ r}\\[2em] [x-3]^2+[y-(-5)]^2=4^2\implies (x-3)^2+(y+5)^2=16[/tex]

Answer:

The tower is approximately 381 feet high.

Step-by-step explanation:

Refer to the sketch attached. The height of the tower can be found in two parts:

Each part can be seen as a leg of a right triangle. The other leg is the distance between the building and the tower and is 300-feet long. The angle opposite to the leg is given.

The height of the tower is the sum of the two parts:

[tex]300\cdot \sin{42^{\circ}} + 300\cdot \sin{37^{\circ}} = 300(\sin{42^{\circ}}+\sin{37^{\circ}}) = 381[/tex] feet.

To calculate the height the radio tower, trigonometry is used. The 'tangent' function is employed twice, once each for the angle of elevation and the angle of depression, to find out the distances to the top and bottom of the tower respectively, which are added together to get the total height.

There are two triangles formed in this problem, one from the observer's line of sight upwards to the top of the radio tower and one downwards to the bottom of the tower. The radio tower is the side that the two triangles share.

We can find the distance to the top and to the bottom of the tower separately using trigonometry, which is based on understanding of angle of elevation and angle of depression.

The height to the top of the tower can be found using the tangent of the angle of elevation (42°), which is the opposite side (height of the tower) divided by the adjacent side (distance from the tower):
height_to_top = tan(42°) * 300 feet.

The height to the bottom of the tower can be found using the tangent of the angle of depression (37°):
height_to_bottom = tan(37°) * 300 feet.

So, the overall height of the radio tower is the sum of these two heights.

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Answer:

Coach Johnson will save $1.50

Step-by-step explanation:

1. The first step is to calculate the unit price for each of the packages, ie. how much a single shin guard costs.

If we look at the package of 10 shin guards for $14.50, we can calculate the unit price by dividing the package price ($14.50) by the number of shin guards (10). Thus we get:

14.50/10 = $1.45

Now, if we do the same for the package of 15 shin guards for $22.50, we get:

22.50/15 = $1.50

2. Now we can see that the lowest unit price is $1.45 (package of 10 shin guards) and the highest unit price is $1.50 (package of 15 shin guards).

3. There are two ways to see how much he would save, so I will show both here.

1) First calculate how much the coach will have to pay for a pack of 30 shin guards for each of the packages:

3 packages of 10 shin guards for $14.50 = 3*14.5 = $43.50

2 packages of 15 shin guards for $22.50 = 2*22.5 = $45.00

Now subtract the second value from the first: 45-43.5 = 1.5

Therefor, he will save $1.50.

2) The second method is perhaps what I would personally use as it is a little quicker; so we already know that the unit price for the pack of 10 is $1.45 and the unit price for the pack of 15 is $1.50 - thus, we can say that there is a difference of $0.05 per shin guard in price. Now if we were going to calculate how much the coach would save in buying 30 shin guards, we could simply multiply how much he saves on a single shin guard by 30. Thus, we get:

0.05*30 = 1.5

Therefor, again we get the same answer that Coach Johnson would save $1.50.

Hope that helps :)

Answer:

P (over 6 feet tall or good aim) = 5/9

Step-by-step explanation:

We are given that there are a total of 27 players who are trying out for the school basketball team.

8 of them are more than 6 feet tall while 7 of them have good aim.

We are to find the probability that the coach would randomly pick a player over 6 feet tall or a player with a good aim, considering that no players over 6 feet tall have good aim.

P (more than 6 feet tall) = [tex]\frac{8}{27}[/tex]

P (good aim) = [tex]\frac{7}{27}[/tex]

P (over 6 feet tall or good aim) = [tex]\frac{8}{27} + [/tex] [tex]\frac{7}{27}[/tex] = 5/9

Answer:

5/9

Step-by-step explanation:

just did test

Answer:

Approximately 1130 cubic feet.

Step-by-step explanation:

The volume of a cylinder is the area of its base times its height.

The height of this cylinder is given to be 10 feet. What's the area of its base?

The base of a cylinder is a circle. The area of a circle with radius [tex]r[/tex] is equal to [tex]\pi \cdot r^{2}[/tex]. For the base of this cylinder, [tex]r = 6[/tex] feet. The question also dictates that [tex]\pi = 3.14[/tex]. The area of each circular base will thus be:

[tex]\text{Base} = \pi\cdot r^{2} = 3.14 \times 6^{2} = 113.04[/tex] square feet.

The volume of this cylinder will be

[tex]\text{Volume} = \text{Base}\times \text{Height} = 113.04\times 10 \approx 1130[/tex] cubic feet.

The solution to the equation is:

x = -0.8404

How to solve the equation?

The equation is given as:

[tex]\frac{3}{(x - 2)}[/tex] + 6 = √(x - 2) + 8

Subtract 8 from both sides to get:

[tex]\frac{3}{(x - 2)}[/tex] - 2 = √(x - 2)

Square both sides to get:

[tex]\frac{9}{(x - 2)^{2} }[/tex] - [tex]\frac{12}{(x - 2)}[/tex] = (x - 2)

 [tex]\frac{9 - 12(x - 2)}{(x - 2)^{2} }[/tex] = (x - 2)

Multiply both sides by (x - 2)² to get:

9 - 12x + 24 = (x - 2)³

33 - 12x = x³ - 6x² + 12x - 8

x³ - 6x² + 24x + 25 = 0

Let us try x = -0.8404 to get;

(-0.8404)³ - 6(-0.8404)² + 24(-0.8404) + 25(-0.8404) ≈ 0

Thus, - 0.8404 is a root of the polynomial.

Answer:

[tex]\frac{1}{12y}[/tex]

Step-by-step explanation:

This is a multiplication problem.

We want to multiply [tex]\frac{9z^3}{16xy}\cdot \frac{4x}{27z^3}[/tex]

We factor to get:

[tex]\frac{9z^3}{4\times 4xy}\cdot \frac{4x}{9\times 3z^3}[/tex]

We now cancel out the common factors to get:

[tex]\frac{1}{4\times y}\cdot \frac{1}{1\times 3}[/tex]

We now multiply the numerators and the denominators separately to get.

This simplifies to [tex]\frac{1}{12y}[/tex]

Therefore the simplified expression is [tex]\frac{1}{12y}[/tex]

Answer:

she is wrong, LMN is not a right triangle.

Answer:

lydias assertion is not correct

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

It is given that,  triangle LMN at the coordinates L (0, 0), M(2, 2) and N(2, -1).

To find the side lengths of triangle LMN

By using distance formula,

LM = √[(2 - 0)² + (2 - 0)²]

 =√[4 + 4]

 = √8

MN = √[(2 - 2)² + (-1 - 2)²]

 =√[0 + 9]

 = √9 = 3

LN = √[(2 - 0)² + (-1 - 0)²]

 =√[4 + 1]

 = √5

To check ΔLMN is right triangle

LN < LM <MN

LN² + LM² = (√5)² + (√8)² = 13

MN² = 3² = 9

Therefore LN² + LM²  ≠ MN²

lydias assertion is not correct

35/14

or

5/2

keep switch flip

Answer:

Step-by-step explanation:

57÷27=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

57×72=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

5×77×2=3514

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 35 and 14 using

GCF(35,14) = 7

35÷714÷7=52

The fraction

52

is the same as

5÷2

Convert to a mixed number using

long division for 5 ÷ 2 = 2R1, so

52=212

Therefore:

57÷27=21/2

Answer:

[tex](\frac{x}{9})[/tex]¹²

Step-by-step explanation:

The given function is f(x) = 9x⁻¹²

To find the inverse of f(x) we will write the function in a equation form y = 9x⁻¹²

Now we will replace x from y and y from x

x = 9y⁻¹²

Then we will find the value of y

y⁻¹² = [tex]\frac{x}{9}[/tex]

y = [tex](\frac{x}{9})[/tex]¹²

Now y will be replaced by f⁻¹(x)

f⁻¹(x) = [tex](\frac{x}{9})[/tex]¹²

Therefore inverse of the function f(x) is f⁻¹(x) = [tex](\frac{x}{9})[/tex]¹²

Answer:

see explanation

Step-by-step explanation:

Since the denominators of both fractions are common

Add the numerators leaving the denominator

= [tex]\frac{8g^2+8-4g^2-2}{h^2-3}[/tex]

= [tex]\frac{4g^2+6}{h^2-3}[/tex]

Answer:

Let us assume that the pay rate per hour = x

no. of hours worked = n

Gross earnings = x*n

Federal taxes = 18% of gross earnings

= 0.18(x*n)

State taxes = 4% of gross earnings

= 0.04(x*n)

Social security deduction = 7.05% of gross earnings

= 0.0705(x*n)

Total deductions = Federal taxes + State taxes +SSD

= 0.18(x*n) + 0.04(x*n) + 0.0705(x*n)

= 0.2905(x*n)

Net pay = Gross earnings - Total Deduction

Net pay = x*n - 0.2905(x*n)

Net pay = 0.7095(x*n)

The gross earnings are $800. Deductions total $232.40, resulting in a net pay of $567.60 after federal, state taxes, and social security deductions.

Let's calculate various components of a paycheck, starting with the given pay rate and hours worked. Suppose the pay rate is $20 per hour and the employee works 40 hours per week.

1. Gross Earnings:

Gross Earnings = Pay Rate × Hours Worked

Gross Earnings = $20/hour × 40 hours

Gross Earnings = $800

2. Federal Taxes:

Federal Taxes = 18% of Gross Earnings

Federal Taxes = 0.18 × $800

Federal Taxes = $144

3. State Taxes:

State Taxes = 4% of Gross Earnings

State Taxes = 0.04 × $800

State Taxes = $32

4. Social Security Deduction:

Social Security Deduction = 7.05% of Gross Earnings

Social Security Deduction = 0.0705 × $800

Social Security Deduction = $56.40

5. Total Deductions:

Total Deductions = Federal Taxes + State Taxes + Social Security Deduction

Total Deductions = $144 + $32 + $56.40

Total Deductions = $232.40

6. Net Pay:

Net Pay = Gross Earnings - Total Deductions

Net Pay = $800 - $232.40

Net Pay = $567.60

Therefore, the gross earnings are $800, and after accounting for $232.40 in deductions for federal and state taxes along with social security, the net pay is $567.60.

To solve the equation (−6/11) + m = −9/2, you need to isolate the variable m. The solution to the equation is m = −33/22.

To solve the equation (−6/11) + m = −9/2, we need to isolate the variable m.

First, we can start by subtracting (−6/11) from both sides of the equation: m = −9/2 - (−6/11)

Simplify the equation by finding a common denominator: m = −9/2 + 33/11

Combine the fractions: m = −99/22 + 66/22

Finally, add the numerators and keep the common denominator: m = −33/22

Therefore, the solution to the equation is m = −33/22.

Learn more about equations here:

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9x-7= 29

9x-7+7= 29+7

9x= 36

Divide by 9 for 9x and 36

9x/9= 36/9

x= 4

Check answer by using substitution method

9x-7= 29

9(4)-7=29

36-7= 29

29= 29

Answer is x=4 (second choice)

Answer:

38/9

Step-by-step explanation:

9x - 7 = 29⁰

9x = 38

x = 38/9

Answer:

y = -3 + 6ˣ

Step-by-step explanation:

-3 is the lowest it goes, and the more you increase the base, the more it its stretch will become. Now, although it passes through -2, we are not dealing with y-intercept here because this is NOT a linear function. This is called a horizontal asymptote. This is an exponential function, from the parent function of y = abˣ, if I can recall correctly. Anyway, you understand?

Answer:

Four(4)

Step-by-step explanation:

The given algebraic expression is:

[tex]3x^3y+5x^2+y+9[/tex]

The variables in this expression are [tex]x[/tex] and/or [tex]y[/tex].

The variable terms in this expression are terms containing [tex]x[/tex] and [tex]y[/tex].

These terms are:

[tex]3x^3y[/tex]

[tex]5x^2[/tex]

and

[tex]y[/tex]

Therefore there are 4 variable terms.

Answer:

A. (3x^2 + 1)(x + 3)

Step-by-step explanation:

3x3 + 9x2 + x + 3

I will factor by grouping

Factor out a 3x^2 from the first two terms

3x^2 (x+3) + (x+3)

Then factor out an x+3

(x+3)(3x^2+1)

Answer:

a or d

Step-by-step explanation:

Answer:

A survey shows that the probability that an employee gets placed in a suitable job is 0.65.

So, the probability he is in the wrong job is 0.35.

The test has an accuracy rate of 70%.

So, the probability that the test is inaccurate is 0.3. 

Thus, the probability that someone is in the right job and the test predicts it wrong is [tex]0.65\times0.3=0.195[/tex]

The probability that someone is in the wrong job and the test is right is [tex]0.35\times0.7=0.245[/tex]

Answer:

.105

Step-by-step explanation:

The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3.  Thus, the probability that someone is in the right job and the test is then wrong is 0.65*0.3=.195, and the probability that someone is in the wrong job and the test is wrong is 0.35*.3=.105.

Answer:

The diagonal of this rectangle is 41 units.

Step-by-step explanation:

The relationship between the length and width of a rectangle and the diagonal is given by the Pythagorean identity:

[tex]d=\sqrt{l^2+w^2}[/tex]

From, the given question, the rectangle has a width of 9 units and a length of 40 units.

We substitute the width and length of the rectangle into the equation to get:

[tex]d=\sqrt{40^2+9^2}[/tex]

[tex]d=\sqrt{1600+81}[/tex]

[tex]d=\sqrt{1681}[/tex]

[tex]d=41[/tex] units.

Answer:

41

Step-by-step explanation:

Answer:

x = 7/2 ± 3/2*(i√3)

Step-by-step explanation:

The equation is

(x - 5)^2 + 3(x - 5) + 9 =0

Let A = (x-5)

The equation becomes now

(A)^2 + 3(A) + 9 =0

We then apply the quadratic formula

A = [-(3) ± √((3)^2-4(1)(9)) ]/ (2(1))

A = -3/2 ± 3/2*(i√3)

Now, we revert the substitution

(x-5) = -3/2 ± 3/2*(i√3)

x = 7/2 ± 3/2*(i√3)

Answer:

Part A: X=0

Part B: x=0

Step-by-step explanation:

Part A

(6^2)^X = 1

Applying the exponent rule: [tex](a^b)^c = a^{bc}[/tex]

So, our equation will become:

[tex]6^{2X} = 1[/tex]

We know if f(x) = g(x) then ln(f(x))= ln(g(x))

SO, taking natural logarithm ln on both sides and solving.

[tex]ln(6^{2X}) =ln(1)[/tex]

We know,[tex]log(a^b) = b.loga[/tex] Applying the rule,

[tex]2Xln6 =ln(1)\\We\,\,know\,\,ln(1)=0\\2Xln6 =0\\Solving:\\X=0[/tex]

Part B

(6^9)^x = 1

Applying the exponent rule: [tex](a^b)^c = a^{bc}[/tex]

So, our equation will become:

[tex]6^{9x} = 1[/tex]

We know if f(x) = g(x) then ln(f(x))= ln(g(x))

SO, taking natural logarithm ln on both sides and solving.

[tex]ln(6^{9x}) =ln(1)[/tex]

We know,[tex]ln(a^b) = b.lna[/tex] Applying the rule,

[tex]9xln6 =ln(1)\\We\,\,know\,\,ln(1)=0\\9xln6 =0\\Solving:\\x=0[/tex]

Answer:

Step-by-step explanation:

The volume is increased by a fator of 8.  (unit³)

Then the length of all edges is increased by factor ∛8 = 2. (unit)

Therefore the surface area is increased by a factor 2² = 4. (unit²)

Answer:

A) 6 tan θ

Step-by-step explanation:

Given Expression:

6 sin θ sec θ

= 6 sin θ (1/cosθ)

= 6 sin θ/cos θ

= 6 tan θ

In the second step, we substituted 1/cos in place of sec because cos and sec are reciprocals of each other.

In the last step, we know used the formula:

sinθ/cosθ  =  tanθ

Answer:

A.

Step-by-step explanation:

sec(x)=1/cos(x)

So you have 6sin(x)*1/cos(x) which gives you 6*sin(x)/cos(x)

Since sin(x)/cos(x)=tan(x)

then you can rewrite this as 6tan(x)

Answer:

see explanation

Step-by-step explanation:

Given

6a² - a - 5 = 0

Consider the factors of the product of the a² term and the constant term which sum to give the coefficient of the a- term.

product = 6 × - 5 = - 30 and sum = - 1

The factors are - 6 and + 5

Use these factors to split the a- term

6a² - 6a + 5a - 5 = 0 ( factor the first/second and third/fourth terms )

6a(a - 1) + 5(a - 1) = 0 ← factor out (a - 1) from each term

(a - 1)(6a + 5) = 0

Equate each factor to zero and solve for a

a - 1 = 0 ⇒ a = 1

6a + 5 = 0 ⇒ 6a = - 5 ⇒ a = - [tex]\frac{5}{6}[/tex]

Solution set = { 1, - [tex]\frac{5}{6}[/tex] }

Answer:  The solution set of the given quadratic equation is  [tex]\{1,-\dfrac{5}{6}\}.[/tex]

Step-by-step explanation:  We are given to find the solution set of the following quadratic equation :

[tex]6a^2-a-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be solving the given quadratic equation by the method of FACTORIZATION.

To factorize the expression on the L.H.S. of equation (i), we need two integers with sum -1 and product -30. Those two integers are -6 and 5.

The solution of equation (i) is as follows :

[tex]6a^2-a-5=0\\\\\Rightarrow 6a^2-6a+5a-5=0\\\\\Rightarrow 6a(a-1)+5(a-1)=0\\\\\Rightarrow (a-1)(6a+5)=0\\\\\Rightarrow a-1=0,~~~~~~6a+5=0\\\\\Rightarrow a=1,~-\dfrac{5}{6}.[/tex]

Thus, the solution set of the given quadratic equation is  [tex]\{1,-\dfrac{5}{6}\}.[/tex]

Answer:

The answer is 7/17

Step-by-step explanation:

Answer: THE ANSWER IS (B)

Step-by-step explanation:

Answer:

X=6

Step-by-step explanation:

You need to cross multiply 2 by x+6. this Equals 2x+12. Then you cross multiply 8 by three which is 24. leading to the equation 2x+12=24 . Subtract 12 on both sides to get 2x=12. Divide by two to get 6 as your answer.

Answer:

16:9

Step-by-step explanation:

If the linear ratio is 4:3, the area ratio will be the square of that.

(4/3)² = 16/9

Answer:

16/9

Step-by-step explanation:

we know that R1/R2= 4/3 and L1/L2= 4/3. where R1 and L1 are cone dimensions 1 and R2 and L2 are cone dimensions 2.

We also know that the cone sourface is S=pi x R x L .

So that S1/S2= (pi R1 L1)/(pi R2 L2)

replacing and operating mathematically

S1/S2=R1 L1/R2 L2 = R1/R2 L1/L2=4/3 4/3=  16/9

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{2}{5}[/tex], hence

y = [tex]\frac{2}{5}[/tex] x + c ← is the partial equation

To find c substitute (- 3, - 1) into the partial equation

- 1 = - [tex]\frac{6}{5}[/tex] + c ⇒ c = - 1 + [tex]\frac{6}{5}[/tex] = [tex]\frac{1}{5}[/tex]

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{5}[/tex] ← in slope- intercept form