John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33o . How tall is the tree?

Answer:

[tex]6z^{4}[/tex]

Step-by-step explanation:

Given in the question an expression,

[tex]\frac{ (2z^5)(12z^3)}{4z^4}[/tex]

Step 1

Apply exponential "product rule"

[tex]x^{m}x^{n}=x^{m+n}[/tex]

[tex]\frac{ 12(2)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ (24)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ 24(z^{(5+3)})}{4z^4}[/tex]

[tex]\frac{ 24(z^{8})}{4z^4}[/tex]

Step 2

Apply exponential " divide rule"

[tex]\frac{x^{m}}{x^{n}}=x^{m-n}[/tex]

[tex]\frac{24/4(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8-4})}{1}[/tex]

[tex]6z^{4}[/tex]

The given data set is:

37, 4, 53, 79, 25, 48, 78, 65, 5, 6, 42, 61

We arrange the data set in ascending order of magnitude {4,5,6,25,37,42,48,53,61,65,78,79}

The median is 45.

The lower half of the data set is

{4,5,6,25,37,42}

The first quartile is the median of the lower half set;

[tex]Q_1=15.5[/tex]

The upper half of the data set is:

{48,53,61,65,78,79}

The median of the upper half is [tex]Q_3=63[/tex].

The inter-quartile range  [tex]Q_3-Q_1=63-15.5=47.5[/tex]

8. The given data set is 112, 149, 112, 148, 139, 121, 116, 134, 148.

The mean of the data set is [tex]\bar X =\frac{\sum x}{n}[/tex]

[tex]\bar X =\frac{112+149+112+148+139+121+116+134+148}{9}[/tex]

[tex]\bar X =\frac{179}{9}=131[/tex]

The standard deviation is given by:

[tex]s=\sqrt{\frac{\sum (x-\bar X)^2}{n} }[/tex]

[tex]s=\sqrt{\frac{(-19)^2+(18)^2+(-19)^2+(17)^2+(8)^2+(-10)^2+(-15)^2+(3)^2+(18)^2}{9} }[/tex]

[tex]s={\frac{\sqrt{2022}}{3}=14.98888477[/tex]

The standard deviation is 15.0 to the nearest tenth.

QUESTION 11

Given : [tex]\ln(3x-8)=\ln(x+6)[/tex]

We take antilogarithm of both sides to get:

[tex]3x-8=x+6[/tex]

Group similar terms to get:

[tex]3x-x=6+8[/tex]

Simplify both sides to get:

[tex]2x=14[/tex]

Divide both sides by 2 to obtain:

[tex]x=7[/tex]

12.  Given; [tex]\log_3(9x-2)=\log_3(4x+3)[/tex]

We take antilogarithm to obtain:

[tex](9x-2)=(4x+3)[/tex]

Group similar terms to get:

[tex]9x-4x=3+2[/tex]

[tex]5x=5[/tex]

We divide both sides by 5 to get:

[tex]x=1[/tex]

13.  [tex]\log(4x+1)=\log25[/tex]

We take antilogarithm to get:

[tex](4x+1)=25[/tex]

Group similar terms

[tex]4x=25-1[/tex]

[tex]4x=24[/tex]

Divide both sides by 4

[tex]x=6[/tex]

14. Given ; [tex]\log_6(5x+4)=2[/tex]

We take antilogarithm to get:

[tex](5x+4)=6^2[/tex]

Simplify:

[tex](5x+4)=36[/tex]

[tex]5x=36-4[/tex]

[tex]5x=32[/tex]

Divide both sides by 5

[tex]x=\frac{32}{5}[/tex]

Or

[tex]x=6\frac{2}{5}[/tex]

15. Given: [tex]\log(10x-7)=3[/tex]

We rewrite in the exponential form to get:

[tex](10x-7)=10^3[/tex]

[tex](10x-7)=1000[/tex]

[tex]10x=1000+7[/tex]

[tex]10x=1007[/tex]

Divide both sides by 10

[tex]x=\frac{1007}{10}[/tex]

16. Given:   [tex]\log_3(4x+2)=\log_3(6x)[/tex]

We take antilogarithm to obtain:

[tex](4x+2)=(6x)[/tex]

[tex]2=6x-4x[/tex]

Simplify

[tex]2=2x[/tex]

Divide both sides by 2

[tex]1=x[/tex]

17. Given [tex]\log_2(3x+12)=4[/tex].

We rewrite in exponential form:

[tex](3x+12)=2^4[/tex]

[tex](3x+12)=16[/tex]

[tex]3x=16-12[/tex]

[tex]3x=4[/tex]

Divide both sides by 3

[tex]x=\frac{4}{3}[/tex]

18. Given [tex]\log_3(3x+7)=\log_3(10x)[/tex]

We take antilogarithm to get:

[tex](3x+7)=(10x)[/tex]

Group similar terms:

[tex]7=10x-3x[/tex]

[tex]7=7x[/tex]

We divide both sides by 7

[tex]x=1[/tex]

19.  Given: [tex]\log_2x+\log_2(x-3)=2[/tex]

Apply the product rule to simplify the left hand side

[tex]\log_2x(x-3)=2[/tex]

We take antilogarithm to obtain:

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

[tex]x^2-3x=4[/tex]

[tex]x^2-3x-4=0[/tex]

[tex](x-4)(x+1)=0[/tex]

x=-1 or x=4

But x>0, therefore x=4

20. Given  [tex]\ln x+ \ln (x+4)=3[/tex]

Apply product rule to the LHS

[tex]\ln x(x+4)=3[/tex]

Rewrite in the exponential form to get:

[tex]x(x+4)=e^3[/tex]

[tex]x^2+4x=e^3[/tex]

[tex]x^2+4x-e^3=0[/tex]

This implies that:

[tex]x=-6.91[/tex] or [tex]x=2.91[/tex]

Answer: 1  5/12

Step-by-step explanation: You need to find a common denominator 3 and 4 are the denominators you can do 3 times 4 is 12 and 4 times 3 is 12, but whatever you do to the denominator needs to be done to the numerator so 2 times 4 is 8 and 1 times 4 is 4 then you have the fractions 8/12 and 3/12 then you just subtract and you get 1  5/12.

*Hard to explain*

For this case we have that the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

By clearing the radio we have:

[tex]r = \pm \sqrt {\frac {A} {\pi}}[/tex]

We take the positive value:

[tex]r = \sqrt {\frac {A} {\pi}}\\r = \sqrt {\frac {95.03} {\pi}}\\r = 5.50 \ ft[/tex]

The diameter is twice the radius:

[tex]d = 11[/tex]

Answer:

[tex]11 \ ft[/tex]

Answer:

11 feet

Step-by-step explanation:

We are given the area of a circle and we are to find the diameter of this circle.

We know that the area of a circle is given by [tex]\pi r^2[/tex] so equating its given value to get:

[tex]\pi \times r^2 = 95.03[/tex]

[tex] r ^ 2 = \frac {95.03} {\pi } [/tex] [tex] r = \sqrt {30.25} [/tex]

[tex] r = 5 . 5 [/tex]

Therefore, our required diameter will be [tex]5.5 \times 2[/tex] = 11 feet

I’ll help you, but what’s “Number 9”?

The initial hight was 5

Approximately after 2second the disc with hit the ground

The computer is worth approximately $599.83 in 2009.

To find out how much the computer is worth in 2009, we need to determine the value after each year's decline. The computer's value declines by 7% each year, so we can calculate the worth of the computer in 2009 by multiplying the original value by (1 - 0.07) four times since there are four years between 2005 and 2009.

Year 1: $800 * (1 - 0.07) = $800 * 0.93 = $744

Year 2: $744 * (1 - 0.07) = $744 * 0.93 = $692.64

Year 3: $692.64 * (1 - 0.07) = $692.64 * 0.93 = $644.86

Year 4 (2009): $644.86 * (1 - 0.07) = $644.86 * 0.93 = $599.83

Therefore, the computer is worth approximately $599.83 in 2009.

Final answer:

To find the value of a computer in 2009 that Sally bought for $800 in 2005 with a 7% annual decline, we use the exponential decay formula. The computer would be worth approximately $598.48 in 2009.

Explanation:

The question asks to calculate the value of a computer after a specific period of time, considering a yearly depreciation. Sally bought a computer for $800 in 2005, and its value declines by 7% yearly. To find its value in 2009, we can use the formula for exponential decay:

Value = Initial Value × [tex](1 - Decline \ Rate)^{Years}[/tex]

Plugging in the values:

Value = $800 × [tex](1 - 0.07)^4[/tex]

Value = $800 ×  [tex](0.93)^4[/tex]

Value = $800 × 0.7481

Value = $598.48

Therefore, the value of the computer in 2009 is approximately $598.48.

Given.

Radius of the Half sphere is 3 inches.

From the figure;

Radius of half sphere= Radius of cylinder= Radius of cone=3inches

Height of cone= 4inches.

Height of cylinder=6inches.

Volume of cone=(πr²h)/3

=(π3²×4)/3

=(12π) inch³

volume of cylinder= πr²h=π3²6=54π inch³

Volume of half sphere= (4/3) π r³=π(4×3³)/3 (1/2)=π×4×9/2=18π inch³

Total area of Composite figure=(12π +54π +18π) inch³

=84π inch³

=(84)× 22/7inch³

=12×22 inch³

=264inch³

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

The volume of the composite figure is 84π ≅ 263.89 inches³

Step-by-step explanation:

Lets revise the rules of the volume of some figures

- The composite figure consists of :

# Half sphere with radius 3 inches

# Cylinder with radius 3 inches and height 6 inches

# Cone with radius 3 inches and height 4 inches

- The volume of the sphere is 4/3 π r³

∴ The volume of the half sphere = 1/2 × 4/3 π r³ = 2/3 π r³

- The volume of the cylinder is π r² h

- The volume of the cone is 1/3 π r² h

* Now lets solve the problem

- The volume of the half sphere

∵ The radius of the half sphere = 3 inches

∵ The volume of it = 2/3 π r³

∴ The volume = 2/3 × π × (3)³ = 18π inches³

- The volume of the cylinder

∵ The radius of the cylinder = 3 inches

∵ The height of the cylinder = 6 inches

∵ The volume of it = π r² h

∴ Its volume = π × (3)² × 6 = 54π inches³

- The volume of the cone

∵ The radius of the cone = 3 inches

∵ The height of the cone = 4 inches

∵ The volume of it = 1/3 π r² h

∴ Its volume = 1/3 π × (3)² × 4 = 12π inches³

- Add all the volumes to find the volume of the composite figure

∴ The volume = 18π + 54π + 12π = 84π = 263.89 inches³

* The volume of the composite figure is 84π ≅ 263.89 inches³

One way is to find the area of the shape as if it was a whole square instead of an H shape.

That is (125+75+125) x (345), which is 112125 ft^2.

From this, let's subtract the areas of the cut-outs.

The cutouts are squares and both the same size. One side of it is 112 feet, so the area of one is 112x112=12544. So, the two squares have an area of 25088.

Now subtract that from the original total. 112125-25088=87037. <<that is the area.

You might want to double check my work.

Check the picture below.

so the net once folded up, will look more or less like the box there on the bottom-right.

Length = 2, Width = 10, Height = 6.

volume is then 2*10*6 = 120.

Answer:10,126,272 units

Step-by-step explanation:

184*184*184=6,229,504

120*120*120=1,728,000

124*124*124=1,906,624

64*64*64=262,144

6,229,504+1,728,000+1,906,624+262,144=10,126,272

The function rule for the situation is none of the given options

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

Membership = $20

Payment each time = $300 per visit

using the above as a guide, we have the following:

f(x) = Membership + Payment each time * x

substitute the known values in the above equation, so, we have the following representation

f(x) = 20 + 300* x

Evaluate

f(x) = 20 + 300x

Hence, the expression is f(x) = 20 + 300x

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none of the given options

None of the provided options in the question are correct.

The function rule that correctly represents Rex's situation, given that he paid a $20 membership fee and pays $300 each time he goes to the pool, would be a linear equation that includes a one-time fee (membership) and a per-visit cost. Let's define x as the number of times Rex goes to the pool and y as the total cost. Therefore, the equation should include the initial membership fee and the per-visit cost multiplied by the number of visits.

The correct function rule is y = 20 + 300x, where 20 represents the one-time membership fee and 300 represents the cost per pool visit. None of the provided options are correct. The equation signifies that for every visit to the pool, the total cost increases by $300, and the initial membership cost is $20.

I believe I am correct.

Multiply the side values together to get the volume of the prism.

1 x 2 2/3x 2/3 = 1.7(repeating)

Then divide 1.7(repeating) by 1/3 and you end up with 5 1/3.

Hope this helps!

Answer:

81

Step-by-step explanation:

Assuming the pigeons are either male or female, the 45% of them that are not female are male. Of those, there are 40% that are not white, so 60% are white. Then the number of white male pigeons is ...

60% of 45% of 300 = 0.60 · 0.45 · 300 = 81

Answer: 8nⁿ⁴

Step-by-step explanation:

Because we use the Qualinto formula (Taught in 4th grade) to get 6. After that multiply 6 by 8^(9n + 0) to get 48n^ + 54. After this, use the squint formula (Taught in 6th grade). To get 8n + 54. Once this step is completed, use extramath/56's equivalent formula to finally get your answer: 8nⁿ⁴

For this case we must solve the following equation:

[tex]-17+ \frac {n} {5} = 33[/tex]

Adding 17 to both sides of the equation we have:

[tex]\frac {n} {5} = 33 + 17\\\frac {n} {5} = 50[/tex]

Multiplying by 5 on both sides of the equation:

[tex]n = 50 * 5\\n = 250[/tex]

Thus, the value of n is 250

ANswer:

[tex]n = 250[/tex]

The solution to the equation -17 + n/5 = 33 is n = 250.

We have,

To solve the equation, we can start by isolating the variable term.

Here's the step-by-step solution:

-17 + n/5 = 33

First, let's get rid of the constant term (-17) by adding 17 to both sides of the equation:

-17 + 17 + n/5 = 33 + 17

Simplifying, we have:

n/5 = 50

To isolate n, we can multiply both sides of the equation by 5:

5 * (n/5) = 5 * 50

This simplifies to:

n = 250

Therefore,

The solution to the equation -17 + n/5 = 33 is n = 250.

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Answer: [tex]47,916\pi \ cm3[/tex]

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere. This is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where "r" is the radius.

You know that the radius of the exercise ball is 33 centimeters, then, you must substitute the valueof this radius into the formula  [tex]V=\frac{4}{3}\pi r^3[/tex].

Therefore, the volume of the exercise ball is:

[tex]V=\frac{4}{3}\pi (33cm)^3[/tex]

[tex]V=47,916\pi \ cm3[/tex]

Answer

a. [tex]\frac{1}{m}(6)+\frac{1}{12} (6)+\frac{1}{15} (6) =1[/tex]

b. 60hrs

Step-by-step explanation:

Let the time Molli will take to pint the room to be = t

Thus the amount of room that Molli can paint in 1 hour= 1/m

The amount of room John can paint is 1 hour= 1/12

The amount of room Rick can paint in 1 hour = 1/15

The equation for working together at a rate x time per work done will be;

[tex]\frac{1}{m} *6+\frac{1}{12} *6+\frac{1}{15} *6=1[/tex]

You multiply by 6 in the three terms of the equation because it takes 6 hours for John, Rick and Molli to complete painting.

[tex]\frac{6}{m} +\frac{1}{2} +\frac{2}{5} =1[/tex]

multiply by 10m in every part of the expression because 10m is the Least Common Multiple(LCM) is this case

Collect like terms and find value of m

[tex]60+5m+4m=10m\\\\60+9m=10m\\\\60=10m-9m\\\\60=m[/tex]

Molli will take 60 hours to paint the room if working alone

A two-dimensional shape with less than four sides and all straight sides is a triangle. Triangles are basic geometric shapes with three edges and three vertices.

If you are a two-dimensional shape with less than four sides and all your sides are straight, the shape you are describing is a triangle. A triangle is a simple polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with all three sides of equal length is an equilateral triangle, if only two sides are equal it's called an isosceles triangle, and if all sides are of different lengths, it is called a scalene triangle.

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Answer: answer is d

Step-by-step explanation: input in calculator or set both equal to y and then set them equal to each other

Answer:

(2/5, 9/6)

Step-by-step explanation:

6y = 10x + 5 | 6y = 5x + 7

Set them equal to each other because 6y = 6y.

10x +5 = 5x + 7

5x = 2

x = 2/5

6y = 5*2/5 + 7

6y = 2 + 7

y = 9/6

Answer:

Volume=943 cm^3 Cross section area=79 cm^2

Step-by-step explanation:

volume of a cylinder is [tex]\pi r^{2} h[/tex]

so 10/2=5 5^2=25*12=300*pi is about 942.477 or 943 cm^3

to find the area of the cross section, on just needs to find the area of the face of the cylinder. so pi times 5^2=pi times 25=78.540 or 79 cm^2

It’s the fourth one

Answer:

None of these

Step-by-step explanation:

This is because the answer can't have anything to do with perpendicular because you don't know if any of the angles are 90 degrees (and honestly none of them look right anyways... pun intended) and the only answer that isn't perpendicular is wrong because the lines are intersececting.

Answer:

[tex]g(3x-2) = (3x-2)^{2}[/tex]

Step-by-step explanation:

[tex]g(x)=x^{2}[/tex]

To do this, you must substitute [tex]3x-2[/tex] for x in the equation g(x)

[tex]g(3x-2) = (3x-2)^{2}[/tex]

Simplified this would be

[tex]9x^{2} -12x+4[/tex]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope m = -2 and the y-intercept b = 8. Substitute:

[tex]y=-2x+8[/tex]

The general form of an equation of a line:

[tex]Ax+By+C=0[/tex]

Convert:

[tex]y=-2x+8[/tex]              add 2x to both sides

[tex]2x+y=8[/tex]              subtract 8 from both sides

[tex]2x+y-8=0[/tex]

Answer:

9

Step-by-step explanation:

2-2+5+5+5+5+5+5-6

the answer is 9. ——-

Answer:

1. Given

2, Exterior sides on opposite rays

3. Definition of supplementary angles

4. If lines are ||, corresponding angles are equal

5. Substitution

Step-by-step explanation:

For the first one, it is given as shown in the problem. Also in the figure you can see that line s is parallel to line t.

2. ∠5 and ∠7 are adjacent, they share a common side. Their non-common side are rays that go in a direction opposite of each other. Also you can see that they form a straight line, which means that they are supplementary.

3. Supplementary angles simply put are angles that sum up to 180°. You know this for sure because of proof 2, specifically the part that they form a straight line. The measure of a straight line is 180°.

4. Corresponding angles are congruent. These are angles that have the same relative position when a line is intersected by parallel lines. You have other example in the figure like ∠2 and ∠6; ∠3 and ∠7.

5. This is substitution because ∠1 substituted ∠5 in this case. Since ∠1 is equal to ∠5, then it can substitute it in the equation given in step 3. This means that ∠1 and ∠7 are supplementary as well.

Check the picture below.

Answer:

[tex]\large\boxed{A.\ 2^0}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}:\\\\\dfrac{2^6}{2^6}=2^{6-6}=2^0=1[/tex]

First make a table of values of the function’s coordinates, and try to avoid coordinates that include decimals.

Second, find the first differences from the table you constructed. ( it should be 1)

There should be a 2 point gap in the x column if you chose the points (2,-4)(4,-3)(6,-2) (8,-2) and that is your denominator

Last, the y intercept (-5) is your b variable (y=mx +b)

The equation is

Y= x/2 -5

Sorry about my English

Answer:

The Great Barrier Reef is located in Australia.

The Great Barrier Reef is located off the northeastern coast of Australia.

It stretches for approximately 1,600 miles and is home to a diverse range of sea creatures and fish, attracting millions of tourists, scuba divers, and water enthusiasts each year.

This natural wonder is a significant tourist attraction and plays an important role in the Australian economy.

Additionally, the Great Barrier Reef has been designated as a United Nations World Heritage Site due to its ecological importance.