What is the covariance for the number of times a head appears for each coin? Suppose you have two unfair coins. Coin 1, denoted as C1, has a probability of landing heads with probability 2/5 and tails with probability 3/5. Coin 2, denoted as C2, has a probability of landing heads with probability 1/3 and tails with probability 2/3. Toss coin 1 first. If coin 1 lands heads, toss coin 1 again. If coin 1 lands tails, then toss coin 2.

Answer:-2048

Step-by-step explanation:

First term(a)=1

Common ratio(r)=-2/1 or 4/-2

Common ratio(r)=-2

nth term=a x r^(n-1)

12th term=1 x (-2)^(12-1)

12th term=1 x (-2)^11

12th term=(-2)^11

12th term=-2048

The 12th term of the geometric sequence 1, −2, 4, .... is equal to -2048.

In Mathematics and Geometry, the nth term of any geometric sequence can be determined by using the following formula:

[tex]a_n=a_1(r)^{n-1}[/tex]

Where:

In this context, the common ratio would be determined as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -2/1

Common ratio, r = -2

Now, we can determine the 12th term in the sequence defined by this explicit rule;

[tex]a_n=a_1(r)^{n-1}\\\\a_{12}=1(-2)^{12-1}\\\\a_{12}=(-2)^{-11}\\\\a_{12}=-2048[/tex]

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To find the p-value from the given data in Excel, populate your data in Excel sheet into various columns for each variable. Then, use the 'Regression' tool under 'Data Analysis' in the 'Data' tab, selecting the appropriate ranges for dependent and independent variables. Ensure that the 'P-Values' box is checked before clicking 'OK'. Excel will then generate the regression analysis with the p-value.

In Excel, you can perform regression analysis to deduce the p-value from this data using the following steps:

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Answer:

mean = 7.98; standard deviation = 2.52

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Answer:

The slope of the line is 2.2 or 11/5

Step-by-step explanation:

I graphed the points on the graph below and found the slope of the line.

The slope of the line is 11/ 5.

The slope is equal to the change in y over the change in x, or rise over run.

m = change in y/change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).

m = (y₂−y₁)/(x₂−x₁)

Substituting the values of x and y into the equation to find the slope.

m = (5 − ( − 6 ))/(−4−(−9))

m =11/5

Therefore, the Slope of the line is 11/ 5.

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Answer:an isosceles triangle cannot be an equilateral triangle

Step-by-step explanation:

An isosceles triangle cannot be an equilateral triangle

Final answer:

An isosceles triangle has at least 2 equal sides and an equilateral triangle has all sides equal. All equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles.

Explanation:

An isosceles triangle has at least 2 equal sides, while an equilateral triangle has all sides equal. Therefore, the sentence 'All isosceles triangles are equilateral triangles' is not true because not all isosceles triangles have all sides equal. On the other hand, the sentence 'All equilateral triangles are isosceles triangles' is true because every equilateral triangle automatically has at least 2 equal sides. Furthermore, it is possible for an equilateral triangle to not be an isosceles triangle if all three sides are not equal in length. So, the sentence 'An isosceles triangle cannot be an equilateral triangle' is not true.

Answer:

what do you need answered?

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

khan academy

Answer:

The 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

Step-by-step explanation:

The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=24\\\bar x=3.19\ \text{hours}\\s=0.2903\ \text{hours}[/tex]

Confidence level = 99%.

Compute the critical value of t for 99% confidence interval and (n - 1) degrees of freedom as follows:

[tex]t_{\alpha/2, (n-1)}=t_{0.01/2, (24-1)}=t_{0.005, 23}=2.807[/tex]

*Use a t-table.

Compute the 99% confidence interval for the true mean amount of time Americans spend social networking each day as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

     [tex]=3.19\pm 2.807\times \frac{0.2903}{\sqrt{24}}\\\\=3.19\pm 0.1663\\\\=(3.0237, 3.3563)\\\\\approx (3.02, 3.36)[/tex]

Thus, the 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

Answer:

6x+9

3(2x+3)

Step-by-step explanation:

Combine like terms

2x+9+3x+x

6x+9

We can factor out 3

3(2x+3)

Answer:

6x + 9

Step-by-step explanation:

2x + 9 + 3x + x =

6x + 9

Answer: A. Mean.

Explanation:

Mean is the only measure of central tendency that is always affected by an outlier. Mean, the average is the most popular measure of central tendency.

The mean is strongly influenced by outliers because it is the average of the scores and it is not resistant.

Answer:

A) mean

Step-by-step explanation:

Mean is a measure of central tendency, it is the sum of all data divided by the number of data. Because the mean take into consideration each of the data in its calculations, it is generally affected by outliers (extremely high or low values)

0.07 or 7 hundredths.

Answer:

[tex]z=\frac{0.503-0.48}{\sqrt{\frac{0.48(1-0.48)}{700}}}=1.218[/tex]  

Now we can calculate the p value given by:

[tex]p_v =P(z>1.218)=0.1116[/tex]  

Step-by-step explanation:

Information provided

n=700 represent the random sample selected

[tex]\hat p=0.503[/tex] estimated proportion of college enrollment

[tex]p_o=0.48[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value (variable of interest)  

System of hypothesis

we want to check if the true proportion for the college enrollment is higher thna 0.48, the system of hypothesis are:

Null hypothesis:[tex]p\leq 0.48[/tex]  

Alternative hypothesis:[tex]p > 0.48[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we have:

[tex]z=\frac{0.503-0.48}{\sqrt{\frac{0.48(1-0.48)}{700}}}=1.218[/tex]  

Now we can calculate the p value given by:

[tex]p_v =P(z>1.218)=0.1116[/tex]  

Answer:

c. 139

Step-by-step explanation:

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{1-0.95}{2} = 0.025[/tex]

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

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence?

We need a sample size of n.

n is found when [tex]M = 5, \sigma = 30[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 1.96*\frac{30}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 1.96*30[/tex]

Simplifying by 5

[tex]\sqrt{n} = 1.96*6[/tex]

[tex](\sqrt{n})^{2} = (1.96*6)^{2}[/tex]

[tex]n = 138.30[/tex]

We round up,

So the correct answer is:

c. 139

Answer:

[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]

And if we round up to the nearest integer we got n =139, and the best answer for this case is:

c. 139

Step-by-step explanation:

For this case we have this previous info:

[tex]\sigma = 30[/tex] represent the previous estimation for the population deviation

[tex]Confidence =0.95[/tex] represent the confidence level

The margin of error for the true mean is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

The desired margin of error is ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for a 95% of confidence interval given now can be founded using the normal distribution. For this case the critical value would be given by [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]

And if we round up to the nearest integer we got n =139, and the best answer for this case is:

c. 139

Answer:0.19

Step-by-step explanation:

Answer:

[tex]\sqrt[4]{10x^2}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{5x}.\sqrt[4]{2x} = \sqrt[4]{5x * 2x} = \sqrt[4]{10x^2}[/tex]

Answer:

(10x²)^¼

Or,

10^¼ × x^½

Step-by-step explanation:

(5x)^¼ × (2x)^¼

[5x × 2x]^¼

(10x²)^¼

10^¼ × (x²)^¼

10^¼ × x^½

Answer:

[tex]9^{2}[/tex]

Step-by-step explanation:

Answer:

[tex]9^{7}[/tex]

Step-by-step explanation:

There are 7 9s being multiplied together.  This can be written as 9 to the 7th power or [tex]9^{7}[/tex]

Answer:

The distribution is approximately normal.

The mean and standard deviation are 15 and 0.98 respectively.

Step-by-step explanation:

The population of the random variables X₁ and X₂ are distributed as follows:

[tex]X_{1}\sim (\mu_{1}=35, \sigma_{1}^{2}=3^{2})\\\\X_{2}\sim (\mu_{2}=20, \sigma_{2}^{2}=4^{2})[/tex]

Two independent random samples of sizes,

[tex]n_{1}=47\\\\n_{2}=54[/tex]

are selected form the two populations.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

Both the sample selected from the two populations are quite large, i.e. [tex]n_{1}=47>30\\\\n_{2}=54>30[/tex]

So, according to the central limit theorem the sampling distribution of sample means [tex]\bar X_{1}\ \text{and}\ \bar X_{2}[/tex] can be approximated by the Normal distribution.

Then, the distribution of [tex]\bar X_{1}[/tex] is:

[tex]\bar X_{1}\sim N(35,\ 0.44)[/tex]

And the distribution of [tex]\bar X_{2}[/tex] is:

[tex]\bar X_{2}\sim N(20,\ 0.54)[/tex]

If two random variables are normally distributed then their linear function is also normally distributed.

So, the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is Normal and the shape of the distribution is bell-shaped.

The mean of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:

[tex]E(\bar X_{1}\ -\ \bar X_{2})=E(\bar X_{1})-E(\bar X_{2})\\=35-20\\=15[/tex]

The standard deviation of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:

[tex]SD(\bar X_{1}-\bar X_{2})=SD(\bar X_{1})+SD(\bar X_{2})\\=0.44+0.54\\=0.98[/tex]

*X₁ and X₂ are independent.

Thus, the mean and standard deviation are 15 and 0.98 respectively.

Answer:

A, B, D

Step-by-step explanation:

The linear parent function is a straight line with equation x=y, which means that it has a slope of 1 and goes through the origin. However, it does not go through quadrants 2 and 4, only 1 and 3. Hope this helps!

Answer:

48% was sold

Step-by-step explanation:

Let the percent sold be x

x/100 * 150 = 72

(This equation basically means...what percentage of 150 bundles will give us 72 bundles remaining? and that's the answer we need)

Simplifying...

150x/100 = 72

3x/2 = 72

3x = 144

x = 48%

Answer:

144

Step-by-step explanation:

The volume of Christina's cube-shaped coin bank is calculated by cubing the length of one of its sides, which is 7 inches. The volume is therefore 7 × 7 × 7, or 343 cubic inches.

The volume of Christina's cube-shaped coin bank can be calculated using the formula for the volume of a cube, which is Volume = side × side × side. As all sides of a cube are equal and the coin bank is 7 inches wide and 7 inches tall, we can calculate the volume by multiplying 7 inches by 7 inches by 7 inches.

Calculation:

Volume = 7 in. × 7 in. × 7 in. = 343 cubic inches

Hence, the volume of Christina's coin bank is 343 cubic inches.

Final answer:

The volume of Christina's cube-shaped coin bank is calculated using the cube volume formula and is found to be 343 cubic inches.

Explanation:

To calculate the volume of Christina's coin bank, we use the formula for the volume of a cube, which is Volume = side³, where 'side' is the length of one side of the cube. Since the coin bank is 7 inches wide and 7 inches tall, each side is 7 inches. Thus, the volume of the coin bank is:

Volume = 7 in. × 7 in. × 7 in. = 343 in.³

Therefore, Christina's coin bank has a volume of 343 cubic inches.

To find the length of the band holding four pencils together, calculate the circumference of each pencil using the formula C = 2πr, where C is the circumference and r is the radius. Multiply the circumference of each pencil by 4 to find the total length of the band.

To find the length of the band holding four pencils together, you need to calculate the circumference of the pencils. The diameter of each pencil is given as 10 mm, so the radius is half of the diameter, which is 5 mm. The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference, π is a constant approximately equal to 3.14159, and r is the radius. Therefore, the circumference of each pencil is 2π(5 mm) = 10π mm. Since there are four pencils, the total length of the band is 10π mm x 4 = 40π mm. This is your answer in terms of π.

Answer:

  68.44%

Step-by-step explanation:

You compute the average the way you compute any average: add up the numbers and divide by their number.

Multiplication is a useful way to shorten the effort of repeated addition.

  (64% × 3 + 58% × 7 + 88% × 3 +33% + 100% × 2)/(3 +7 +3 + 1 + 2)

  = 1095%/16 = 68.4375%

  ≈ 68.44% . . . the average mark for the class

Answer:

20 seconds

Step-by-step explanation:

The least common multiple of 4 and 5 is 20.  So the two lights will blink at the same time every 20 seconds.

Based on the number of seconds it takes for each light to blink, they will both blink at 20 seconds.

The green light blinks every 4 seconds and the yellow, every 5 seconds.

The time that they will blink together depends on the lowest common multiple of both numbers.

Multiples of 4 = 4, 8, 12, 16, 20

Multiples of 5 = 5, 10, 15, 20

The lowest common multiple is 20 which means they will blink together after 20 seconds.

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Answer:

  2√11

Step-by-step explanation:

The square of the hypotenuse (h) of the smaller triangle is given by the Pythagorean theorem:

  h² = 6² +8² = 100

The length of x is given by that same theorem:

  h² +x² = 12²

  x² = 12² -h² = 144 -100 = 44 . . . . . subtract h², fill in its value

  x = √44 . . . . . . . . take the square root

  x = 2√11 . . . . . . . simplify the root

Answer:

Doesn’t show image

Step-by-step explanation:

Answer:

B,C

Step-by-step explanation

Pitcher 1 does not have a symmetric data set.

Pitcher 2 has a symmetric data set.

Answer:

$3,256.2

Step-by-step explanation:

First, we need to get 3% of 3,460. Find the decimal value of 3%:

3% -> [tex]\frac{3}{100}[/tex] -> 0.03

Next, lets multiply 3,460 by 0.03:

[tex]x=3,460(0.03)[/tex]

[tex]x=103.8[/tex]

Now subtract that number from 3,460:

[tex]3,460-103.8=3,356.2[/tex]

Lastly, lets take the $100 fee off of the number we just got:

[tex]3,356.2-100=3,256.2[/tex]

The new amount is $3,256.2

Answer:

3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of $3,256.2.

explanation:

Answer:

Hello,

Here is your answer:

The proper answer to this question is 87300000000000000.

Here is how:

8.73e16=87300000000000000.

Your answer is 87300000000000000.

If you need anymore help feel free to ask me! 

Hope this helps!

(P.S. REMEMBER E IS EXPONET OR ^)

1/4

Step-by-step explanation:

1/4 is the original fraction of 3/12 simplified

Final answer:

The probability of the spinner landing on an orange section is 1/4 or 0.25, meaning there is a 25% chance it will land on orange.

Explanation:

The question involves calculating the probability of a spinner landing on a specific color. If a spinner has 12 equal-sized sections and three of them are orange, to find the probability of landing on orange, we use the ratio of the number of orange sections to the total number of sections. In this case, there are 3 orange sections and 12 sections in total, so the probability (P) is:

P(orange) = Number of orange sections / Total number of sections

P(orange) = 3 / 12

P(orange) = 1 / 4

Therefore, the probability that the spinner will land on orange is 1/4 or 0.25, which means there's a 25% chance the spinner will land on an orange section.

Answer:

Was the answer possibly C)  4,671 sq.cm. ?


Explanation:
Since the expert didn't get it right from what I'm seeing.

The surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.

To calculate the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm, we follow these steps:

1. Determine the dimensions of the equilateral triangle base:
   - The diameter of the cylinder (10 cm) is equal to the side length of the equilateral triangle base.

2. Calculate the height of the equilateral triangle:
   - The height \( h \) of an equilateral triangle with side length \( a \) is given by:
     [tex]\[ h = \frac{\sqrt{3}}{2} a \] For \( a = 10 \) cm: \[ h = \frac{\sqrt{3}}{2} \times 10 \approx 8.66 \text{ cm} \][/tex]

3. Calculate the area of the equilateral triangle base:
   - The area \( A \) of an equilateral triangle with side length \( a \) is given by:
     [tex]\[ A = \frac{\sqrt{3}}{4} a^2 \] - For \( a = 10 \) cm: \[ A = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.30 \text{ cm}^2 \][/tex]

4. Calculate the lateral surface area of the prism:
   - The lateral surface area is given by the perimeter of the triangular base times the length of the prism.
   - The perimeter \( P \) of an equilateral triangle with side length \( a \) is:
     [tex]\[ P = 3a \] For \( a = 10 \) cm: \[ P = 3 \times 10 = 30 \text{ cm} \][/tex]
   - The length of the prism is 85 cm.
   - The lateral surface area \( L \) is:
     [tex]\[ L = P \times \text{length} = 30 \times 85 = 2550 \text{ cm}^2 \][/tex]

5. Calculate the total surface area of the prism:
   - The total surface area \( S \) includes the lateral surface area and the area of the two triangular bases.
   - Total surface area \( S \) is given by:
     [tex]\[ S = L + 2 \times A \] - Substitute the values: \[ S = 2550 + 2 \times 43.30 = 2550 + 86.60 = 2636.60 \text{ cm}^2 \][/tex]

6. Round the total surface area to the nearest square centimeter:
[tex]\( S \approx 2637 \text{ cm}^2 \)[/tex]

So, the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.

Answer:

10 green cubes

Step-by-step explanation:

The total number of cubes is 8+2+10 = 20

The probability of drawing a green cube when there is replacement is

P(green) = green cubes/ total

               =2/ 20

              = 1/10

Multiply the probability by the number of draws to get the total number of cubes

1/10 * 100 draws = 10 green cubes

Expect 10 green cube draws in 100 pulls, with 8 red and 10 blue cubes also present.

To calculate the expected number of times a green cube is drawn, we can use the concept of probability.

In each pull, there are 20 cubes in total (8 red + 2 green + 10 blue). So, the probability of drawing a green cube in a single pull is:

[tex]\[ P(\text{green}) = \frac{\text{number of green cubes}}{\text{total number of cubes}} = \frac{2}{20} = \frac{1}{10} \][/tex]

Since each pull is independent and the cubes are replaced after each pull, the probability of drawing a green cube remains the same for each pull.

Therefore, the expected number of times a green cube is drawn in 100 pulls is:

[tex]\[ \text{Expected number of green draws} = P(\text{green}) \times \text{Total number of pulls} = \frac{1}{10} \times 100 = 10 \][/tex]

So, you would expect them to draw a green cube about 10 times in 100 pulls.