What is the sum of the infinite geometric series represented by


A. 240
B. 135
C. 360
D. 720

Answer:

Acute

Step-by-step explanation:

7² + 9² ? 11²

49 + 81 ? 121

130 is greater than 121, so it is an acute triangle

Answer:

The sum of the first 100 terms is 60400

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

 between each two consecutive terms n is the position of the

 number

- The sum of first n terms of an Arithmetic sequence is calculate from

 Sn = n/2[a + l], where a is the first term and l is the last term

* Now lets solve the problem

- We will use method (1)

- From the table the terms of the sequence are:

 10 , 22 , 34 , 46 , 58 , 82 , 94 , ............., where 10 is the first term

∵ an = a1 + (n - 1) d ⇒ explicit formula

∵ a1 = 10 and a2 = 22

∵ d = a2 - a1

∴ d = 22 - 10 = 12

- The 100th term means the term of n = 100

∴ a100 = 10 + (100 - 1) 12

∴ a100 = 10 + 99 × 12 = 10 + 1188 = 1198

∴ The 100th term is 1198

- Lets find the sum of the first 100 terms of the sequence

∵ Sn = n/2[a1 + an]

∵ n = 100 , a = 10 , a100 = 1198

∴ S100 = 100/2[10 + 1198] = 50[1208] = 60400

* The sum of the first 100 terms is 60400

Answer:

The answer is below

Step-by-step explanation:

Answer:

The residual e=2 when x = 5.

Step-by-step explanation:

A scatter plot containing the point (5, 29), it means the observed value at x=5 it 29.

The given regression equation is

[tex]\hat{y}=5x+2[/tex]

Substitute x=5 in the above regression equation, to find the predicted value at x=-5.

[tex]\hat{y}=5(5)+2=25+2=27[/tex]

The formula to find the residual value e is

e = Observed value - Predicted value

[tex]e=29-27[/tex]

[tex]e=2[/tex]

Therefore the residual e=2 when x = 5.

Answer:

  1

Step-by-step explanation:

"Complementary events" by definition have probabilities that total 1. An event is complementary to another if it occurs when the other one doesn't, and vice versa. That is, the outcome is always one or the other of the complementary outcomes--never both, never neither.

The sum of the probabilities of two complementary events is equal to 1.

In probability theory, mutually exclusive events are events that cannot occur simultaneously. The sum of the probabilities of two complementary events is equal to 1. If events A and B are mutually exclusive, then the probability that at least one occurs (A or B) is equal to the sum of their individual probabilities (PA + PB).

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Answer:

  [tex]\text{D.}\quad d=\dfrac{206-8(10)}{7}[/tex]

Step-by-step explanation:

The total length of the space between rungs is the overall length less the width of 8 rungs, so is 206 -8(10). That space is divided into 7 equal parts, as shown by the equation in choice D.

_____

Choice A looks similar, but is not. In that equation, only the term 8(10) is divided by 7. You want the difference to be divided by 7, so must have a grouping symbol of some kind. Choice D uses the division bar to group the terms of the numerator. Parentheses would work, too, as in ...

  d = (206 -8(10))÷7

but without them, the equation is incorrect.

Answer:

(3.01%, 14.77%)

Step-by-step explanation:

The confidence interval of a proportion is:

CI = p ± SE × CV,

where p is the proportion, SE is the standard error, and CV is the critical value (either a t-score or a z-score).

We already know the proportion: 8/90.  But we need to find the standard error and the critical value.

The standard error is:

SE = √(p (1-p) / n)

SE = √((8/90) * (82/90) / 90)

SE = 0.03

To find the critical value, we must first find the alpha level and the degrees of freedom.

The alpha level for a 95% confidence interval is:

α = (1 - 0.95) / 2 = 0.025

The degrees of freedom is one less than the sample size:

df = n - 1 = 90 - 1 = 89

Since df > 30, we can approximate this with a normal distribution.

If we look up the alpha level in a z score table, we find the z-score is 1.96.  That's our critical value.  CV = 1.96.

Now we can find the confidence interval:

CI = 8/90 ± 0.03 * 1.96

CI = 0.0889 ± 0.0588

CI = (0.0301, 0.1477)

So we are 95% confident that the percent of patients who had their teeth whitened is between 3.01% and 14.77%.

Answer:

[tex]\large\boxed{b.\ x=\dfrac{14}{27}\ \text{and}\ c.\ x=2}[/tex]

Step-by-step explanation:

[tex]4|5-5x|=7x+6\\4|-5(x-1)|=7x+6\\4|-5||x-1|=7x+6\\(4)(5)|x-1|=7x+6\\20|x-1|=7x+6\\\\\text{First step:}\\\text{Based on the de}\text{finition of the absolute value}\\\\|x-1|=\left\{\begin{array}{ccc}x-1&\text{for}\ x\geq1\\1-x&\text{for}\ x<1\end{array}\right\\\\\text{Let}\ x<1\to x\in(-\infty,\ 1).\ \text{Then}\ |x-1|=1-x:\\\\20(1-x)=7x+6\qquad\text{use the distributive property}\\20-20x=7x+6\qquad\text{subtract 20 from both sides}\\-20x=7x-14\qquad\text{subtract}\ 7x\ \text{from both sides}\\-27x=-14\qquad\text{divide both sides by (-27)}\\x=\dfrac{14}{27}<1\qquad \bold{:)}[/tex]

[tex]\text{Let}\ x\geq0\to x\in\left<1,\ \infty\right).\ \text{Then}\ |x-1|=x-1:\\\\20(x-1)=7x+6\qquad\text{use the distributive property}\\20x-20=7x+6\qquad\text{add 20 to both sides}\\20x=7x+26\qquad\text{subtract}\ 7x\ \text{from both sides}\\13x=26\qquad\text{divide both sides by 13}\\x=2\geq1\qquad \bold{:)}[/tex]

Answer:

A)

15 hours

B)

108 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.

A)

In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;

(24/360) = (x/225)

solving for x;

x = (24/360) * 225 = 15 hours

B)

In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;

(24/2π radians) = (x/9π radians)

Solving for x;

x = (24/2π radians)*9π radians = 108 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

Answer:

Step-by-step explanation:

9x⁴ – 2x² – 7 = 0

Let's say that u = x²:

9u² – 2u – 7 = 0

Factor:

(u – 1) (9u + 7) = 0

u = 1, -7/9

Since u = x²:

x² = 1, -7/9

x = ±1, ±i √(7/9)

By using the substitution method, the solutions of this equation (polynomial) is equal to C. x = ±1 and ±i√(7/9).

In order to determine the solutions of this equation (polynomial), we would let "u" be equal to x² and then substitute this value into the equation as follows:

9x⁴ - 2x² - 7 = 0

Substituting the value of "u" into the equation (polynomial), we have:

9u² - 2u - 7 = 0

Factorizing the equation (polynomial), we have:

(9u + 7)(u - 1) = 0

u = 1 and -7/9

Since, u = x²:

x² = 1 and -7/9

x = ±√(1 and -7/9)

x = ±1 and ±i√(7/9).

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3:7

Taxes are 30c and one dollar is 100c then the net income is 70c, making the income 30:70. this can be simplified to 3:7.

Answer:

$3735

Step-by-step explanation:

The formula for simple interest is I = Prt, where I is the interest earned, P is the initial investment, r is the interest rate in decimal form, and t is the time in years.  We have everything we need to find the interest, which is the amount your investment earned while it sat there for 7 years.  Once we find that interest amount, we will add it to the intial investment to find the total amount after 7 years that your money has grown to.

I = 3000(.035)(7) so

I = 735

3000 + 735 = 3735

Answer:

$3,630

Step-by-step explanation:

You invest $3,000 in an account at 3.5% per year simple interest.

We have to calculate the amount in the account at the beginning of the 7th year. This means we have to calculate the interest for completed 6 years.

Formula for simple interest

A = P(1+rt)

A = Amount after maturity

P = Principal amount ( 3,000)

r = rate of interest in decimal ( 0.035)

t = time in years ( 6 )

Now we put the values in to formula

A = 3,000(1 + 0.035 × 6)

A = 3,000 ( 1 + 0.021 )

A = 3,000 × 1.21

A = $3,630

The amount would be $3,630 at the beginning of the 7th year.

Answer:

35

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

nCk = n!/(k!(n -k)!)

7C3 = 7!/(3!(7-3)!) = 7·6·5/(3·2·1) = 7·5 = 35

_____

It is convenient to use the largest of the factorials in the denominator to cancel as many factors as you can from the numerator, then cancel factors from the remaining numbers. Here after canceling 4! = 4·3·2·1 from the numerator, we are left with 7·6·5 divided by 3! = 3·2·1 = 6. Obviously, this will cancel the 6 in the numerator product, leaving only 7·5 = 35.

Some graphing and/or scientific calculators will have this function built in.

Final answer:

The standard deviation of the data set is 2.98, calculated by finding the mean, squaring the differences, averaging them, and taking the square root. One standard deviation below the mean is 2.52.

Explanation:

To find the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3, follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data point and square the result.

Calculate the average of these squared differences.

Take the square root of the average to find the standard deviation.

Using a calculator or computer:

The mean of the data set is 5.5

The squared differences would be (8.2-5.5)^2, (10.1-5.5)^2, etc.

The average of these squared differences is approximately 8.86.

The square root of 8.86 gives us the standard deviation of approximately 2.98.

Therefore, the standard deviation of the data set, rounded to the nearest hundredth, is 2.98.

To find the value that is one standard deviation below the mean, you subtract the standard deviation from the mean:

5.5 - 2.98 = 2.52.

Answer:

The mean is equal to the median, so the data is symmetrical

Step-by-step explanation:

Here is the data.

10 5 8 10 12 6

8 10 15 6 12 18

The given data:   10   5   8   10   12   6   8   10   15   6   12   18

For finding the Mean, we will have to add all numbers together and divide it by total number. i.e sum of terms divided by number of terms  

Mean= 10+5+8+10+12+6+8+10+15+6+12+18  ÷ 12

Mean = 120 ÷ 12 = 10        

For finding the Median, first we need to rearrange the data in ascending order

5   6   6   8   8   10   10   10   12   12   15   18

We can see that the middle values are 10 and 10. So, the median will be the average of those two middle values.

Median = 10+10 ÷ 2

Median = 20 ÷ 2 = 10

From the calculation, we can see that both the median and mean are equal so, the data is symmetrical  

Answer: 0 ≤ t ≤ 40

Step-by-step explanation:

0 and 40 are included in all 3 number lines.

Answer:

C and E

Step-by-step explanation:

Let's factor this the "old fashioned" way.  The standard form of a quadratic is

[tex]y=ax^2+bx+c[/tex]

If you're familiar with the quadratic formula I'd say throw it into that, but if not, again, let's do it the "old fashioned" way.  

We need to find the product of our a and c.  Our a = 2 and our c = -3.  So that gives us a -6.  Now we have to find the factors of 6 (the negative right now doesn't matter so much).  The factors of 6 are 1, 6  and 2, 3.  Both of those possibilities will work to give us a +5, which is the linear term.  Puttng in the 2, 3 first:

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

Now group the terms together into groups of 2:

[tex]0=(2x^2+3x)+(2x-3)[/tex]

The idea is to factor out something common in each term so that what's left over in the parenthesis in both terms is exactly the same.  In the first term we can factor out a common x, and in the second term, the only thing common is a 1.  So that looks like this:

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

What's inside those parenthesis are not actually identical, so 2 and 3 won't work.  Lets try 1 and 6.  For those 2 numbers to equal a +5, the 6 is positive and the 1 is negative.  So let's try that:

[tex](2x^2+6x)+(-x-3)[/tex]

In the first term we can factor out the common 2x and in the second term we can factor out the common -1:

2x(x + 3) - 1(x + 3)

Now what's common is (x + 3), so we can factor THAT out and what is left over is 2x - 1:

(x + 3)(2x - 1) = 0

If x + 3 = 0, then x = -3

and if 2x - 1 = 0, then 2x = 1 and x = 1/2

You can solve this by using trial and error. When doing so I came with a conclusion of 8,4, and 2.

The dimensions of a rectangular prism with a volume of 64 cubic inches can be any combination of length, width, and height whose multiplication result is 64, including possibilities of 1x1x64, 2x2x16, 4x4x4 and many more.

The volume of a rectangular prism is calculated by multiplying the length, width, and height of the prism (Volume = Length x Width x Height).

If we know that the volume of the prism is 64 cubic inches, there can be several possible dimensions for the rectangular prism. To find these, we would look for different combinations of length, width and height that when multiplied, equal 64. Here are a few examples:

Length = 1 inch, Width = 1 inch, Height = 64

Length = 2 inches, Width = 2 inches, Height = 16 inches

Length = 4 inches, Width = 4 inches, Height = 4 inches

There can be many more possible dimensions, including fractions as well.

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Answer:

I got  65

Step-by-step explanation:

The profit will be given as:

P=$15x−$225  

(where we subtracted the cost of the mower) so that  P=$750

x will be the required number of needed lawns.

We need to solve:

$750=$15x−$225  

rearranging:

x=$750+$225 /  $15  =65  lawns

Define a variable and write an inequality to represent earning a specific profit in a lawn-mowing business.

Define variable:

Let x represent the number of lawns mowed.

Write inequality:

The inequality is 15x - 225 ≥ 750, where 15x is the amount earned, 225 is the cost of the lawnmower, and 750 is the desired profit.

Answer:

Dividend

Step-by-step explanation:

If you take a simple division problem like A = B / C

A is the quotient (result)

B is the dividend

C is the divisor

So, a number by which another number is to be divided is called a dividend, like A in the example above.

If C doesn't divide B in an exact manner (like in the case of 7 / 2), there's a remainder for the operation.

A divisor is a number by which another number, the dividend, is divided. In scientific notation, division involves dividing the coefficients and subtracting the exponents of the divisor from the dividend. Division is fundamentally related to multiplication, as it can be represented by multiplying by a reciprocal.

For this case we have that by definition:

[tex](a + b) (c + d)[/tex] is equal to:

[tex]ac + ad + bc + bd[/tex]

Applying the distributive property.

Then, it can be seen that the given binomials were multiplied correctly.

ANswer:

There is no error; the binomials were correctly multiplied together.

The answer is D 3/5

if you can pick 4 and odd it will be 1,3,4,5,7,9

that is 6 numbers, 3/5 5*2 is 10 so 3*2 is 6

3/5

Answer: m<c, m<b + m<d

Step-by-step explanation: If you use the given information, you can find that

m<a = 60

m<b = 30

m<c = 60

m<d = 30

The angles that will produce an acute angle in the given diagram are;  m<c, and m<b + m<d.

Acute angles are angles that measure less than 90 degrees.

From the image we observe the following;

m<a = 60

m<b = 30

m<c = 60

m<d = 30

Thus, the angles that will produce an acute angle in the given diagram are;  m<c, and m<b + m<d.

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Answer:

[tex]y=\tan x[/tex]

Step-by-step explanation:

The trigonometric function that needs a domain restriction of [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex] to make it invertible is [tex]y=\tan x[/tex].

The function [tex]y=\tan x[/tex] will pass the horizontal line test on this interval therefore making it an invertible function on this interval.

This explains why the inverse tangent function, [tex]y=\tan^{-1} x[/tex] has range [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex].

Answer:

A) [tex]f(x)=sin x[/tex]

Step-by-step explanation:

I just did the test and this was the correct answer.  

Answer:

• linear angles

• supplementary angles (all linear angles are supplementary)

Step-by-step explanation:

If the angles share a side and are measured in opposite directions from that side, the non-common edges of these angles form a straight line, so these angles are sometimes called "linear" angles.

Since their sum is 180°, they are always "supplementary" angles. (Supplementary angles need not share a vertex or a side.)

Answer:

1,800 bricks are needed

Step-by-step explanation:

First convert the Length and width of the sidewalk into inches

Entire Sidewalk: L= 100x12 =1200in and W= 4 x 12 = 48in

Then we know Area = LxW, so we will do this for both the sidewalk and the brick.

Area of sidewalk: 1200 x 48 = 57600

Bricks ( no need to convert since the measurements are already in inches): 8 x 4 = 32

Now we will divide the area of the entire sidewalk by the area of a single brick to find out how many bricks you need to complete the whole sidewalk:

57600/32= 1,800 bricks

Answer:

  8√2

Step-by-step explanation:

The hypotenuse of a right triangle is √2 times the leg length, so you have ...

  [tex]x\sqrt{2}=16[/tex]

Dividing by the coefficient of x gives ...

  [tex]x=\dfrac{16}{\sqrt{2}}=\dfrac{16\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=8\sqrt{2}[/tex]

Each leg has length 8√2.

I don’t know what the answer is I wish I could help

Answer: 30.01 feet.

Step-by-step explanation:

You need to remember this identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

Observe the figure attached, where [tex]h_t[/tex] is the height in feet of the tree.

You need to calculate [tex]h_1[/tex] of the Triangle 1, where:

[tex]\alpha= \alpha_1=42\°\\opposite=h_1\\adjacent=20[/tex]

Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_1[/tex]:

[tex]tan(42\°)=\frac{h_1}{20}\\\\h_1=20*tan(42\°)\\h_1=18[/tex]

Now you need to calculate [tex]h_2[/tex] of the Triangle 2, where:

[tex]\alpha= \alpha_2=31\°\\opposite=h_2\\adjacent=20[/tex]

Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_2[/tex]:

[tex]tan(31\°)=\frac{h_2}{20}\\\\h_2=20*tan(31\°)\\h_2=12.01[/tex]

Then the height in feet of the tree is:

[tex]h_t=h_1+h_2\\h_t=(18+12.01)ft\\h_t=30.01ft[/tex]

The height of the tree can be determined by the trigonometric ratio of tan angle.

The height of the tree is 30 feet.

Given that,

Mariela is standing in a building and looking out a window at a tree.

The tree is 20 feet away from Mariela,

Mariela's line of sight creates a 42-degree angle of elevation, and her line of sight creates a 31 degree of depression.

We have to determine,

What is the height, in feet, of the tree?

According to the question,

Let, the height of the tree be h

The tree is 20 feet away from Mariela,

First, we have to calculate the length of BD which is x,

Then,

The length of BD is given by,

[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{BD}{AD}\\\\Tan42 = \dfrac{x}{20}\\\\x = tan42 \times 20\\\\x = 0.9 \times 20\\\\x = 18[/tex]

The measurement of x is 18 feet.

Again we have to calculate the length of y,

Then,

The length of DC is given by,

[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{DC}{AD}\\\\Tan31 = \dfrac{Y}{20}\\\\y = tan31 \times 20\\\\x =0.6 \times 20\\\\y = 12[/tex]

The measurement of y is 12 feet.

Therefore,

The height of the tree is given by,

[tex]\rm h= x +y\\\\h = 18+12\\\\h = 30 \ feet[/tex]

Hence, The height of the tree is 30 feet.

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Answer:

17 ft

Step-by-step explanation:

I don't think you meant to put pi over 3t ... I think you meant to put pi just over 3

Just plug in 5 assuming t is time in hours.  

Evaluate 4 *cos(pi/3 *5)+15

which is  17 ft

The height of tower after 5 hours is 17.68 feet.

The graph of the cosine function looks like this: The domain of the function y=cos(x) is all real numbers (cosine is defined for any angle measure), the range is −1≤y≤1 .

The Cosine function :  f(t) = 4 cos(π/3t) + 15

and,  f(t) = 4 cos(2kπ + π/3t) + 15

where k= 0,1,2,3....

The range of cosine function is : Maximum= +1 and minimum= -1

At t=0,

For maximum, f(t)= 4 x1 +15

   = 19 feet

For minimum, f(t) =  4 x(-1)+15

                            = 11 feet

After , 6 hours ,the tide function is: 6 n=5

                                                          n= 6/5

f(t) = 4 cos ( 2* [tex]\frac{5* \pi}{6}[/tex] + [tex]\frac{\pi}{3*5}[/tex] ) +15

    = 4 cos (26 π/15) + 15

    = 4 cos[tex]312^{0}[/tex] + 15

   = [tex]4 cos 48^{0}+ 15[/tex]

   = 4 x 0.6691 +15

  = 17.68 feet.

Thus, the height of tower after 5 hours is 17.68 feet

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Answer:

The test statistic supports the claim

Step-by-step explanation:

413 out of 1588 people says that they smoked.

So, we can find that that is 413/1588 ≈ 0.26 = 26%.

This proves that the test statistic is supporting the claim, since the two are similar.