Use summation notation to write the series -1+2-4+8-16... for 12 terms

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Answer: -0.833 (repeating decimal)

Step-by-step explanation: fg(x) means plug the g(x) equation into f(x), and for gf(x) it’s vice versa:

Fg(x) = 3x^2 - 1 + 2

Gf(x) = 3(x + 2)^2 - 1

First, we should simplify gf(x) to eliminate the (x + 2)^2:

3(x^2 + 4x + 4) - 1

3x^2 + 12x + 12 - 1

3x^2 + 12x + 11

Second, simplify fg(x) by solving -1 + 2: 1

Now, we can set the two equations equal to each other and solve:

3x^2 + 1 = 3x^2 + 12x + 11 (subtract 3x^2 from each other and 1 from 11)

-10 = 12x (Divide)

-0.8333... = x

To make sure this answer is correct, plug -0.833 into the original equations and set them equal to each other:

3(-0.833)^2 + 1 = 3(-0.833)^2 + 12(-0.833] + 11

3.083 = 3.083

Answer:

friend alone could do it in 13 hours and 1/3

Step-by-step explanation:

Your rate = room/8

friends rate = room/x

combined rate = room/8 + room/x

= room(x+8)/(8x)

then

5 = room / [room(x+8)/(8x)]

5 = 8x/(x+8)

8x = 5x + 40

3x = 40

x = 40/3 = 13 1/3

friend alone could do it in 13 hours and 1/3

Answer:

2option is the correct answer

Answer:

4+3+6+2 = 15

Step-by-step explanation:

selecting a yellow marker 4/15

selecting a red marker 2/15

Answer: C

Step-by-step explanation:

Answer:

The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8.

This means that:

[tex]\mu_A = 85, s_A = \frac{9.8}{\sqrt{22}} = 2.09[/tex]

An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6.

This means that:

[tex]\mu_N = 77, s_N = \frac{10.6}{\sqrt{47}} = 1.55[/tex]

Distribution of the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.

Mean:

[tex]\mu = \mu_A - \mu_N = 85 - 77 = 8[/tex]

Standard deviation:

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{2.09^2 + 1.55^2} = 2.6[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs[/tex]

So

[tex]M = 1.645*2.6 = 4.3[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 8 - 4.3 = 3.7

The upper end of the interval is the sample mean added to M. So it is 8 + 4.3 = 12.3

The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).

Step-by-step explanation:

the circle to any point on the circle

Answer:

Radius

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Answer:

Hence the carnival game gives you better chance of winning.

Step-by-step explanation:

Let the event of win be given by 1/10 in the game of rifle then the event of loose is given by 9/10

the

Odds in favor of a game are given by  = P(Event)/ 1- P(Event)

Odds in favor of winning a rifle are given by = 1/10/ 1- 1/10

                                                                         =1/10/9/10

                                                                          =1/9

                                                                             = 0.111

The probability of winning aa rifle game is 0.111

The probability of winning the carnival game is 0.15

Comparing the two probabilities   0.111:0.15

The probability of  winning carnival game is greater than winning a rifle game

0.15>0.11

Hence the carnival game gives you better chance of winning.

Answer:

y = 10(½)^(x)

Step-by-step explanation:

In writing exponential functions passing through points, we will just substitute the x and y values in each case into y = ab^(x).

Now, for point (-1, 20), the exponential function is; 20 = ab^(-1)

20 = a/b

For the point (1, 5), the exponential function is; 5 = ab^(1)

5 = ab

From 20 = a/b, we have; a = 20b

Thus, putting 20b for a in 5 = ab, we have;

5 = 20b(b)

b² = 5/20

b² = 1/4

b = √(1/4)

b = 1/2

Since a = 20b, then;

a = 20 × 1/2

a = 10

Thus, from y = ab^(x), we have;

y = 10(½)^(x)

Answer:

60,000

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

Answer:

I think you can answer it with a chart, I guess, of course I'm not sure‍♀️

Answer:

C: The median

Step-by-step explanation:

Answer:

17 ft

Step-by-step explanation:

The triangle on the bottom left is a right triangle.

a² + b² = c²

(8 ft)² + (15 ft)² = (RQ)²

64 ft² + 225 ft² = (RQ)²

(RQ)² = 289 ft²

RQ = 17 ft

Answer:

y = 1

Step-by-step explanation:

since its a horizantal line

if u take any 2 points and find the slope, for example if we take points (1, 1) and (4, 1) the slope will be 0/3 which is zero

y = 0x + b

so there is basically no x in this case

so y = b

now plug in a point from the line, (1, 1)

y = mx + b

y = 0x + b

1 = 0(1) + b

1 = 0 + b

1 = b

b = 1

final equation:

y = 0x + 1

Answer:

the bottom left

Step-by-step explanation:

A linear function will have a constant slope so the bottom left graph is the only one with a constant slope. The y-values are all increasing by 2.

Answer: 292

Step-by-step explanation:

Given

There are 240 members in a labor union

The number increases by 5% each year

After 1 year it is

[tex]\Rightarrow 240+5\%\times 240\\\Rightarrow 240(1+0.05)[/tex]

After 2 years

[tex]\Rightarrow 240(1+0.05)+5\%\times 240(1+0.05)\\\Rightarrow 240(1+0.05)(1+0.05)=240(1+0.05)^2[/tex]

Similarly, after 4 years

[tex]\Rightarrow 240(1+0.05)^4\\\Rightarrow 291.72\approx 292[/tex]

Answer:

5.5

Step-by-step explanation:

5 + 6 =

11 / 2 =

5.5

Answer:

90,000

Step-by-step explanation:

As an estimate

200 * 450

which is 90,000

Answer:

95% Confidence Interval = (611.81 ppm, 696.51 ppm)

Step-by-step explanation:

The formula for Confidence Interval is given as:

Confidence Interval = Mean ± z × s /√n

Mean = the sample mean/average = 654.16

s = the sample standard deviation = 164.55

z = z score of 95% confidence interval = 1.96

Confidence Interval =

654.16 ± 1.96 × 164.55/√58

= 654.16 ± 42.348

Hence,

654.16 - 42.348

= 611.812

Approximately to two decimal places = 611.81 ppm

654.16 + 42.348

= 696.508

Approximately to two decimal places = 696.51 ppm

Therefore, the 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected is (611.81 ppm, 696.51 ppm).

Answer:

1/6 = 1/6 (already simplified) 1 3/8 = 11/8

Step-by-step explanation:

Answer:

[tex] \frac{8}{1} [/tex]

Step-by-step explanation:

[tex] \frac{ - 32}{ - 4} [/tex]

Reduce factor by 4

[tex] \frac{ - 8}{ - 1} [/tex]

A negative divided by a negative equal positve so

[tex] \frac{8}{1} [/tex]

the simplest form of 32/4 is 8/1

find the GCD ( or HCF) of numerator and denominator GCD of 32 4 is 4

divide both the numerator and denominator GCD

32/4 ÷ 4/4

reduce fraction: 8/1

therefore, 32/4 simplify to lowest terms is 8/1.

Answer: 3 7/20

Step-by-step explanation:

5 3/5 - 2 1/4

Find GCD.

5 12/20 - 2 5/20

3 7/20 more boxes of raspberries than strawberries

1. Use sharpie to cover up private information before throwing it away (because people can look through your trash for your info). For example: credit card information, your address, etc.

2. Secure your mail box. Get a lock to make sure that people won't steal your credit card information.

3. Never ever leave your receipts behind.

4. Don't lose your credit card!! People can steal it can spend your money!

5. Just don't give random people or friends your credit card information...

Well, I hope this helped! Be careful and stay safe!

Answer:

Solution given.

f = 5, g = 6, h = 7

<F=?

we have;

f² = g² + h² – 2gh cos F

5²-6²-7²=-2×6×7 cos F

-60/-84=cos F

F=cos-¹(5/7)=44.41°

<F=44.4° is a required answer

Answer:

-6,-2 is the answer!!

Step-by-step explanation:

The coordinate of A' would be (-6, -2)

Dilation is a transformation technique that changes the size of an object by a scale factor "k"

From the diagram shown, the measure of the coordinate point is given as (-3, -1).

If the coordinate A is dilated by a factor of 2, the resulting coordinate A' will be given as:

A' = (2(-3), 2(-1)) = (-6, -2)

Hence the  coordinate of A' would be (-6, -2)

Learn more on dilation here: https://brainly.com/question/3457976

9514 1404 393

Answer:

  no; √4 = 2

Step-by-step explanation:

If an integer is the square of another integer, its square root is rational. For example, 9 = 3², so √9 = 3, a rational number.

The square root of an integer is irrational if and only if the integer is not a perfect square.

Answer:

In order of pictures,

Picture #1: 230

Picture #2: 140

Picture #3: 9.9

Picture #4: 13.5

Picture #5: 7.07

Step-by-step explanation:

I am not entirely sure that 3 - 5 are correct, but I know that 1 and 2 are correct. I am sorry if they are incorrect.

Hope that this helps!