Find the height of the building to the nearest foot in the diagram below. Show work.

Answer:

  a. a[1] = 3; a[n] = 2a[n-1]

  b. a[n] = 3·2^(n-1)

  c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

The recursive rule is ...

  a[1] = 3

  a[n] = 2×a[n-1]

__

The explicit rule is ...

  a[n] = a[1]×r^(n-1)

  a[n] = 3×2^(n-1)

__

The 15th term is ...

  a[15] = 3×2^(15-1) = 3×2^14

  a[15] = 49,152

Answer:

x = 0

Step-by-step explanation:

5^0 is 1, meaning that x must equal to 0 for the answer to be 5^0.

Answer:

I think it's the fourth one.

Answer:

2

Step-by-step explanation:

Factorization of the following.

6=3×2×1

8=2×2×8×1

Since, The common factor is 2.This implies that

H.C.F=2

Q: Where do you put a smart hot dog? A: On the honor roll.

The solution is, the final answer is 78.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

The parts of the final expression are ...

 6 walker = 150

 walker = 150/6 = 25

 yoda^4 = 81

 yoda = 81^(1/4) = 3

2 Rtwo +100 = 120

Rtwo = (120 -100)/2 = 10

 luke + yoda × Rtwo + walker × Rtwo = 285

 luke + 3×10 + 25×10 = 285

 luke = 285 -280 = 5

And the grand finale:

 luke ^ yoda - Rtwo(walker / luke) + yoda

= 5^3 -10(25/5) +3 = 125 -50 +3

= 78

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Complete question:

May the fourth be with you math riddle.

picture is attached.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order to solve this problem, you need to add their similar elements together.

First, add similar to elements.

[tex]\sf{a+a=\boxed{\sf{2a}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

a - 8

Step-by-step explanation:

1/2 a - 4

if we scale both numbers by the same factor, we will be creating an equivalent expression.

So, let's say we multiply the equation by 2.

1/2 a (2) = 1 a = a

-4 (2) = -8

One equivalent expression would be

a - 8

[If you want to test this out, try plugging in any number for a. For example, if you plug in 10...

1/2 of 10 = 5, 5 - 4 = 1

1 times 10 = 10, 10 - 8 = 2

These answers are the same scaled as the original equation, the answer for the first expression is multiplied by 2 to get the second expression]

Answer:

exponential

Step-by-step explanation:

it is an exponential function

+7

+10

+15

+21

+30

Answer:

6 in.

Step-by-step explanation:

5 inches is the width. Length is 6 in.

Answer:

the right answer is F (exterior angle of triangle is equal to its sum of opposite interior angle of a traingle)

Answer: W = 40 degrees.

Step-by-step explanation: When you're finding a missing interior angle, all you need is the angle measurements of the other two angles.  According to the picture, we have two 70's given, which both add up to 140.  All the interior angles of a triangle need to add up to 180, and we have 140 so far.  That's where the missing angle comes in.  When you subtract 140 from 180, you get 40, which is your missing angle.

Let me know if this is right! :)

Answer:

16.4 units to the nearest tenth.

Step-by-step explanation:

sin 66 = 15 / x

x *  sin 66 = 15

x = 15 / sin 66

= 16.4196

Done!

Answer:

  £102,000

Step-by-step explanation:

A growth rate of 1.6% corresponds to an annual growth factor of ...

  1 +1.6% = 1.016

The house value is multiplied by this factor each year for 4 years, so the final value is ...

  £96000 × 1.016⁴ ≈ £102,293

To 3 significant figures, the house value after 4 years is £102,000.

Answer:

answer : 102293.04

3 significant figures : 102000

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because we dont know what she started with.

Answer:

b) I guess

Step-by-step explanation:

she has n. she spends $17.50 (-). she has $6.21 left

n                -                      17.50               =$6.21

n-17.50=$6.21

Demarcus should calculate the total surface area of the rectangular prism and the measurement is 1,048 in²

Total surface area = 2(lw + hw + lh)

= 2(20×8 + 13×8 + 20×13)

= 2(160 + 104 + 260)

= 2(524)

= 1,048 in²

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Answer:

answer "Less than"

Step-by-step explanation:

a) 1 2/3 = 5/3 = 1.666 ...

b) 1 5/6 = 11/6 = 1.833 ...

a < b

Answer:

1 5/6 > 1 2/3

Step-by-step explanation:

=>        1 5/6 = (1*6)+5/6

=>        1 5/6 = 6+5/6

=>        1 5/6 = 11/6

so like that, 1 2/3 = 5/3

now the denominators should be the same

for that,

5*2/3*2 = 10/6

11/6 and 10/6

=>          11/6 > 10/6

=>          1 5/6 > 1 2/3

Answer:

64% hope this helps

Step-by-step explanation:

I'm just smart

Answer:

The answer is 64%

Step-by-step explanation:

5= 10% multiply 5 by 6 and you get 30. the 2 equals 4 percent so the percent is 64%. I hope this helps.

Using the normal distribution and the central limit theorem, it is found that there is a 0.9279 = 92.79% probability that less than 70% of the 51 recent graduates have an annual salary exceeding $40000.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we have that:

The mean and the standard error are given by:

[tex]\mu = p = 0.6[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.6(0.4)}{51}} = 0.0686[/tex]

The probability that less than 70% of the 51 recent graduates have an annual salary exceeding $40000 is the p-value of Z when X = 0.7, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.7 - 0.6}{0.0686}[/tex]

[tex]Z = 1.46[/tex]

[tex]Z = 1.46[/tex] has a p-value of 0.9279.

0.9279 = 92.79% probability that less than 70% of the 51 recent graduates have an annual salary exceeding $40000.

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Answer:

8551

Step-by-step explanation:

Answer:

I don't see any thing there

Step-by-step explanation:

u need to include the picture

Answer:

no

Step-by-step explanation:

0.06 = [tex]\frac{6}{100}[/tex] ← that is 6 books out of 100

she requires to have 60 out of 100 , that is

[tex]\frac{60}{100}[/tex] = 0.6

[tex]135 = \frac{22 + 8}{2} \times h \\ 135 = \frac{30}{2} \times h \\ 135 = 15 \times h \\ h = \frac{135}{15} \\ h = \frac{27}{3} = 9cm[/tex]

Answer:

Area of a trapezoid :

[tex]area = \frac{a + b}{2} h[/tex]

The measures given are trapezoid

Area = 135

base 1 = 22

base 2 = 8

[tex]135 = \frac{22 + 8}{2} h \\ \\135 = \frac{30}{2} h \\ 2(135) = ( 2)\frac{30}{2} h \\ 270 = 30h \\ \frac{270}{30 } = \frac{30h}{30} \\ 9 = h[/tex]

Step-by-step explanation:

We can check if the answer is right

[tex] \frac{22 + 8}{2} \times 9 \\ \frac{30}{2} \times 9 \\ 15 \times 9 = 135[/tex]

Answer: A

Step-by-step explanation:

2 2/5 is a larger number than 1 4/5.

The easiest way to know this is to look at the first number. 2 is larger than 1.

Hope this helps!

Answer:

A.

Step-by-step explanation:

2 2/5 is a bigger number than 1 4/5, so  you would us greater than sign

Answer:

[tex] \frac{7}{20} [/tex]

Step-by-step explanation:

Red marbles = 33

Blue marbles = 72

Probability of selecting red or blue marbles:

[tex]33 + 72 = 105 \\ \frac{105}{300} = \frac{7}{20} [/tex]

Answer:

the answer will be 14

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may God bless you:)

Answer:

The mean is 14

Step-by-step explanation:

Mean = The sum of all Numbers Divided by the count of Numbers

In this case there are 5 numbers and adding them together = 69

69/5 = 13.8

Rounding up because it ends in above 5

= 14

Answer:

21.42

Step-by-step explanation:

Imagine it as a full circle. 3 x 4 will give you the diameter of a full circle, which is 12. circumference = pi x diameter. so 12 pi (we can work that out later). now for the quater circle, divide it by 4, so 3 pi. Then you have the 2 extra edges which are both 2r, so 6 each. finally, you have 3 pi plus 12 which = 21.42

Yes julia is correct the run of the scond similar triangle will be b2=25.

The similar triangle are those whose three sides or one angle or two sides or two angles one side are equal.

In the given:

Height of first triangle h=3

Base of first traingle =10

Height of second triangle =7.5

The base of second triangle b2 = ?

From the triangle similarity

[tex]\dfrac{h_1}{b_1}=\dfrac{h_2}{b_2}[/tex]

[tex]\dfrac{3}{10}=\dfrac{7.5}{b_2}[/tex]

[tex]b_2=\dfrac{7.5\times 10}{3}[/tex]

[tex]b_2=25[/tex]

Thus julia is correct the run of the scond similar triangle will be b2=25.

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Answer:

P (n,r)= [tex]\frac{n!}{(n-r)!}[/tex]

Step-by-step explanation:

P (n,r)= ?

complete formula for permutation of objects in a set:

P (n,r) = [tex]\frac{n!}{(n-r)!}[/tex]

Applying the tangent ratio, the distance across the suspension bridge is: 499.2 ft.

Where we are given a right triangle, the tangent ratio is determined using the formula, tan ∅ = opposite side/adjacent side.

The diagram atatched beow whos the distance across the suspension bridge which consists of 6 identical right triangles.

Find the adjacent side of each right triangle using the tangent ratio:

∅ = 32

Opposite side = 52 ft

Adjacent side = x

Plug in the values into the tangent ratio:

tan 32 = 52/x

x = 52/tan 32

x = 83.2 ft.

Distance across the suspension bridge = 6(83.2) = 499.2 ft.

Therefore, applying the tangent ratio, the distance across the suspension bridge is: 499.2 ft.

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