What is the surface area of the triangular prism shown

LUMBERJACKS: 4,989,600 arrangements. HIGHLIGHT: 362,880 arrangements. COOKBOOK: 10,080 arrangements. [tex]\( \frac{{88!}}{{86!}} = 7656 \).[/tex]

To find the number of unique arrangements for each word:

1. LUMBERJACKS:

  - Total letters: 11

  - Since there are repeated letters (U, B, E), we need to account for that.

  - The formula for permutations of a word with repeated letters is [tex]\( \frac{{n!}}{{n_1! \times n_2! \times \ldots \times n_k!}} \), where \( n \) is the total number of letters and \( n_1, n_2, \ldots, n_k \)[/tex] are the counts of each distinct letter.

  - For LUMBERJACKS, we have:

    - 2 L's

    - 2 M's

    - 2 B's

  - So, the number of unique arrangements is[tex]\( \frac{{11!}}{{2! \times 2! \times 2!}} \).[/tex]

2. HIGHLIGHT:

  - Total letters: 9

  - There are no repeated letters.

  - So, the number of unique arrangements is simply [tex]\( 9! \).[/tex]

3. COOKBOOK:

  - Total letters: 8

  - There are repeated letters (O, K).

  - For COOKBOOK, we have:

    - 2 O's

    - 2 K's

  - So, the number of unique arrangements is [tex]\( \frac{{8!}}{{2! \times 2!}} \).[/tex]

4. [tex]\( \frac{{88!}}{{86!}} \)[/tex]:

  - This expression simplifies to [tex]\( 88 \times 87 \), as \( 86! \) cancels out. - So, \( 88! \) divided by \( 86! \) equals \( 88 \times 87 \).[/tex]

Let's compute these:

1. For LUMBERJACKS:

[tex]\[ \frac{{11!}}{{2! \times 2! \times 2!}} = \frac{{39916800}}{{8}} = 4989600 \][/tex]

2. For HIGHLIGHT:

[tex]\[ 9! = 362880 \][/tex]

3. For COOKBOOK:

[tex]\[ \frac{{8!}}{{2! \times 2!}} = \frac{{40320}}{{4}} = 10080 \][/tex]

[tex]4. For \( \frac{{88!}}{{86!}} \):[/tex]

[tex]\[ 88 \times 87 = 7656 \][/tex]

Answer:

m Arc AD = 43°

Step-by-step explanation:

The question is missing a diagram. Find attached the diagram of the question.

Given:

AB is a diameter of circle P

Solution:

From the diagram,

∠ADP = 7x+1

∠BPC = 9x-7

∠CPD = 90° (the symbol of right angle is drawn)

∠m Arc APB = 180° (sum of angles on a straight line or sum of angle in a semi circle)

∠APD + ∠CPD + ∠BPC = 180°

(7x+1)° + 90° + (9x-7)° = 180°

7x+1 + 90 + 9x-7 = 180

Collect like terms

7x+9x = 180 - 90 + 7 -1

16x = 96

x = 96/16

x = 6

Insert the value color x in ∠APD

∠APD = 7(6) + 1

∠APD = 43°

m Arc AD = ∠ APD

m Arc AD = 43°

Therefore arc measure of AD in degrees = 43°

Answer:

36.58% probability that one of the devices fail

Step-by-step explanation:

For each device, there are only two possible outcomes. Either it fails, or it does not fail. The probability of a device failling is independent of other devices. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A total of 15 devices will be used.

This means that [tex]n = 15[/tex]

Assume that each device has a probability of 0.05 of failure during the course of the monitoring period.

This means that [tex]p = 0.05[/tex]

What is the probability that one of the devices fail?

This is [tex]P(X = 1)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{15,1}.(0.05)^{1}.(0.95)^{14} = 0.3658[/tex]

36.58% probability that one of the devices fail

Answer:

See explaination

Step-by-step explanation:

See attachment for diagram

The r value is 0.373 (low). This implies a weak correlation between the dependent and independent variables for this sample.

The overall p- value for the regression model is 0.0017. This implies that at least one of the two independent variables (x1 or x2) in the model is significant predictor of the dependent variable y.

p- values for the both "Fact" and "Star" are < 0.05. This means both the independent variables are significant predictors of the "Rating" at 95% confidence level. The variable "Fact" is significant at 99% level of confidence also. This means the rating viewers award to a movie depends upon both the storyline (fact or Fiction) and the presence or absence of stars.

Expected rating for a fact based movie with no stars = 1.7991(1) + 1.2586(0) + 12.5685 = 14.37

Expected rating for a fiction based movie with a star = 1.7991(0) + 1.2586(1) + 12.5685 = 13.83

So, one may expect a fact based movie without any stars to get better ratings than a fiction based movie with one star.

Answer:

  55.2 gallons/day

Step-by-step explanation:

There are 2.4 ten-hour periods in one day, so the total number of gallons per day is ...

  (2.4 periods/day)(23 gallons/period) = 55.2 gallons/day

Answer:

170.5

Step-by-step explanation:

2.75x62=170.5 hope this helps

Answer:

y = 15x

Step-by-step explanation:

The biggest giveaway here is the other answers have + a whole number at the end of the equation. We would see this + as a y-intercept on the graph.

Since our line had no y-intercept and starts from zero, y =15x can be used to represent the graph shown

Another way to know this is to look at the points marked on the line. There is a point at (2, 30). By plugging these co-ordinated into y = 15x we get 30 = 30, which makes sense

Answer:

y=15x

Step-by-step explanation:

because the y-intercept is 0, y=15x is the only choice that has y intercept 0

Answer:

We conclude that less than 90% of all orders are mailed within 72 hours after they are received.

Step-by-step explanation:

We are given that the company claims that at least 90% of all orders are mailed within 72 hours after they are received.

A recently taken sample of 150 orders showed that 115 of them were mailed within 72 hours.

Let p = proportion of orders that are mailed within 72 hours after they are received.

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 90%      {means that at least 90% of all orders are mailed within 72 hours after they are received}

Alternate Hypothesis, [tex]H_A[/tex] : p < 90%      {means that less than 90% of all orders are mailed within 72 hours after they are received}

The test statistics that would be used here One-sample z proportion statistics;

                    T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of orders that were mailed within 72 hours = [tex]\frac{115}{150}[/tex] = 0.767

           n = sample of orders = 150

So, test statistics  =  [tex]\frac{0.767-0.90}{\sqrt{\frac{0.767(1-0.767)}{150} } }[/tex]  

                              =  -3.853

The value of z test statistics is -3.853.

Now, at 2.5% significance level the z table gives critical value of -1.96 for left-tailed test. Since our test statistics is less than the critical values of z as -3.853 < -1.96, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that less than 90% of all orders are mailed within 72 hours after they are received.

Answer:

Scott will read 77 pages in 7 days.

Step-by-step explanation:

7x11=77

Final answer:

The sample evidence does not support the inspection​ station's claim that the wait time is less than 8 minutes.

Explanation:

To test the claim that the wait time at the vehicle emission inspection station is less than 8 minutes, we can conduct a hypothesis test using the sample data provided. The null hypothesis (H0) is that the mean wait time is greater than or equal to 8 minutes, and the alternative hypothesis (Ha) is that the mean wait time is less than 8 minutes.

We need to calculate the test statistic, which is the t-value. The formula to calculate the t-value is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Using the given data, we can plug in the values:

t = (7.43 - 8) / (3.6 / sqrt(64))

Calculating this gives us a t-value of -1.248.

Next, we need to determine the critical value at a significance level of 0.005. Since the alternative hypothesis is that the mean wait time is less than 8 minutes, we will use a one-tailed test and find the critical value from the t-distribution table. At a significance level of 0.005 and 63 degrees of freedom (64 - 1), the critical value is -2.650.

Finally, we compare the test statistic to the critical value. If the test statistic is less than the critical value, we reject the null hypothesis. In this case, -1.248 is greater than -2.650, so we fail to reject the null hypothesis. This means that the sample evidence does not support the inspection station's claim that the wait time is less than 8 minutes at a significance level of 0.005.

Answer:

A wide variety of life exists in Florida Panhandle

Step-by-step explanation:

A habitat is the natural environment in which organisms lives. We have three types of habitat which include aquatic, terrestrial and arboreal. These habitats contains different organisms.

Florida Panhandle having almost sixty different types of habitats means more organisms living in this place. This translates to a wide variety of life existing in Florida Panhandle.

The statement that best describes the Florida Panhandle based on the fact that it has almost 60 different types of habitats is that it is a region with high biodiversity and a variety of ecosystems.

The presence of nearly 60 distinct habitats in the Florida Panhandle indicates a rich tapestry of ecological systems. Biodiversity refers to the variety of life in the world or in a particular habitat or ecosystem. This includes the different species of plants, animals, and microorganisms, the genetic differences among them, and the ecosystems in which they occur. A high number of habitats suggests that the area supports a wide range of species that have adapted to the different environmental conditions present in these habitats.

Ecosystems are communities of living organisms in conjunction with the nonliving components of their environment (things like air, water, and soil), interacting as a system. These ecosystems can range from coastal marshes and estuaries to longleaf pine forests and freshwater springs. Each habitat type provides unique resources and living conditions, which in turn support different types of organisms.

The Florida Panhandle's diverse habitats likely result from its geography, climate, and history. The region may include coastal areas, wetlands, forests, and other landscapes, each with its own set of habitats. This diversity is crucial for the overall health of the environment, as it allows for a greater number of species to thrive and for ecological processes to function effectively. It also provides opportunities for recreation, research, and education, and it underscores the importance of conservation efforts to protect these valuable natural resources.

In summary, the high number of habitats in the Florida Panhandle is indicative of its ecological richness and the importance of conserving this diversity for environmental health and human enjoyment."

Answer:

Dependent

Step-by-step explanation:

Because you and your friend are in the same race, the lane number your friend will get is affected by your random draw.

Lane number for the same race is a dependent Event.

An easy way to think of independent and dependent variables is, when you're performing an experiment, the independent variable is what you change, and the dependent variable is what changes because of that. The independent variable can alternatively be viewed as the cause, and the dependent variable as the result.

We have,

A lane number for a 100-meter race.

Here, Lane number for same race is dependent Quantity.

As, You and a friend are competing in the same race.

Then, your random draw will determine which lane number your friend will receive.

Learn more Independent and Dependent variable here:

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Answer:

7

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

(9/3)+24-28

(3)+(-4)

-1

Answer:

i) The sketch of the area under the normal distribution curve is attached to this solution of the question.

ii) The minimum number of seconds we could expect the longest 20% of customers to wait in line = 162 seconds.

Step-by-step explanation:

This is is a normal distribution problem with

Mean = μ = 138 seconds

Standard deviation = σ = 29 seconds

i) Which of the following illustrates the shaded area under the normal distribution for the top 20%?

We first obtain the z-score that corresponds to the lower limit of the top 20% of the distribution of waiting times.

Let that z-score be z'

P(z > z') = 0.20

P(z > z') = 1 - P(z ≤ z') = 0.20

P(z ≤ z') = 1 - 0.20 = 0.80

P(z ≤ z') = 0.80

So, checking the normal distribution table,

z' = 0.842

we can then go ahead and obtain the waiting time that corresponds to this z-score.

Let the waiting time that corresponds to this z-score be x'

z' = (x' - μ)/σ

0.842 = (x' - 138)/29

x' = 162.42 seconds

Since, the options for the shaded area under the normal curve isn't presented with this question, the graph of the shaded area under the normal curve that corresponds to the top 20% waiting times is attached to this solution.

ii) What is the minimum number of seconds we could expect the longest 20% of customers to wait in line?

The minimum number of seconds we could expect the longest 20% of customers to wait in line corresponds to the lower limit of the top 20% waiting times obtained in (i) above.

The minimum number of seconds we could expect the longest 20% of customers to wait in line = 162.42 seconds = 162 seconds to the nearest second

Hope this Helps!!!

Answer:

  {-5, -4, -2, 0, 1}

Step-by-step explanation:

The domain is the list of first numbers of the ordered pairs. That list is shown above.

To find the two consecutive natural numbers that sum up to 13, we set up an equation: x + (x+1) = 13. Solving this, we find that x = 6, and the next number is x + 1 = 7. Therefore, the numbers are 6 and 7.

Let's call the natural number x. According to the problem, the sum of x and the next number (x+1) is 13. To find the values of these numbers, we can set up the following equation:

x + (x + 1) = 13

Simplifying the equation, we combine like terms to get:

2x + 1 = 13

Subtract 1 from both sides:

2x = 12

Divide both sides by 2:

x = 6

Now that we have the value of x, we can find the next number:

x + 1 = 6 + 1 = 7

So the two consecutive natural numbers that sum up to 13 are 6 and 7.

Answer: according to my calculations the answer is (3,-2) if im wrong im sorry but thats what i got  

Step-by-step explanation:

The solution in the attached below that is point (2, 1).

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. A set of such values is called a solution set to the considered equation or inequality.

we have given that the linear inequality y < Negative one-half + 2

y < - 1x/2 + 2

The solution of the inequality is the shaded area below the dashed line;

y = - 1x/2 + 2

The slope of the dashed line is negative 1/2.

The y-intercept of the dashed line is the point (0,2) and the x-intercept of the dashed line is the point (4,0).

The solution is attached below.

Noted that Any point that lies on the shaded area is a solution to the inequality and if a point is a solution to the linear inequality, then the point must satisfy the inequality.

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Answer:

There is not enough evidence to reject the null hypothesis.

Step-by-step explanation:

(a)

The hypothesis can be defined as follows:  

H₀: p₁ - p₂ ≤ 0 vs. Hₐ: p₁ - p₂ > 0.  

(b)

The test statistic is defined as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

The information provided is:

n₁ = 244

n₂ = 311

x₁ = 122

x₂ = 137

Compute the sample proportions and total proportions as follows:

[tex]\hat p_{1}=\frac{x_{1}}{n_{1}}=\frac{122}{244}=0.50\\\\\hat p_{2}=\frac{x_{2}}{n_{2}}=\frac{137}{311}=0.44\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{122+137}{244+311}=0.47[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

    [tex]=\frac{0.50-0.44}{\sqrt{0.47(1-0.47)[\frac{1}{244}+\frac{1}{311}]}}\\\\=1.41[/tex]

The test statistic value is 1.41.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level α = 0.05.

Compute the p-value as follows:

 [tex]p-value=P(Z>1.41)\\=1-P(Z<1.41)\\=1-0.92073\\=0.07927\\\approx 0.08[/tex]

*Use a z-table.

The p-value of the test is 0.08.

p-value = 0.08 > α = 0.05

The null hypothesis will not be rejected at 5% significance level.

Thus, there is not enough evidence to reject the null hypothesis.

Answer:

A) The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.

Step-by-step explanation:

Edg 2020

It follows from the task content that the transformation required to produce the graph is; The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.

It follows from the task content that initial equation is; y = (x-1)² - 3 while the transformation produced; y = (1/2)(x+4)².

It therefore follows that upon translation leftwards by 5 units, the (x-1) term becomes (x+4).

And finally, upon compression vertically by a factor of One-half, and translation upwards 3 units. The transformed form of the graph is obtained.

On this note, the required transformations are as indicated above.

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Answer:

3/4

Step-by-step explanation:

We know a geometric sequence has the formula:  a_n = a_1 * r^(n-1)

a_2 = 20

a_4 = (45/4)

so...    a_2 = a_1* r^(2-1) =  20

and    a_4 = a_1* r^(4-1) = (45/4)

a_1 * r = 20

a_1* r^3 = (45/4)

a_1 = 20/r

(20/r) * r^3 = (45/4)

20 * r*r = 45/4

r*r = 45/80 =  9/16

r =  3/4   or  r = -3/4   it must be positive.

common ratio is r = 3/4

Answer:

B. 9

Step-by-step explanation:

We know that a full circle should equal 360°, that'll help!

Since the 140°+3x+13 should equal to 180, because that makes the half of the circle it covers, we know how to set up our equation!

It should look like this:

3x+13=40

ISOLATE YOUR VARIABLE:

- Subtract 13 from both sides

NEXT, CONTINUE ISOLATING:

3x=27

- Divide by 3 from both sides.

FINALLY:

You will get X=9!

Answer:

The centre is the point (-4,6).

The length of the radius is 14.

Step-by-step explanation:

The equation of a circle has the following format:

[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]

In which r is the radius and the centre is the point [tex](x_{0}, y_{0})[/tex]

In this question:

We have to complete the squares, to place the equation in the general format:

So

[tex]x^{2} + 8x + y^{2} - 12y = 144[/tex]

To complete the quares, we divide each first order term(8 and -12) by two, having two new terms(4 and -6). With this, we write as the square of (x+4) and (y-6). To compensate, we have to find the square of 4 and -6 on the other side of the equality.

[tex](x+4)^{2} + (y-6)^{2} = 144 + (4)^{2} + (-6)^{2}[/tex]

[tex](x+4)^{2} + (y-6)^{2} = 196[/tex]

The centre is the point (-4,6).

The length of the radius is [tex]\sqrt{196} = 14[/tex]

The center and the length of the radius of the circle is (-4, 6) and 14units respectively

The standard equation of a circle is expressed as:

x^2+y^2+2gx+2fy+c = 0

where:

C = (-g, -f)

r = √g²+f²-c

Given the equation of a circle expressed as:

x^2 + 8x + y^2 - 12y = 144.

Compare both equations

2gx = 8x
g = 4

2fy = -12y

y = -6

The centre of the circle will be at (-4, 6)

Determine the radius

r = √4²+6²+144
r = 14

Hence the center and the length of the radius of the circle is (-4, 6) and 14units respectively

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Final answer:

To find the length of the shadow cast by the tree, calculate the scale factor between the pole and its shadow, then multiply this factor by the height of the tree to get the length of the tree's shadow.

Explanation:

To find the length of the shadow cast by the tree:

Calculate the scale factor between the pole and its shadow: 12 feet pole casts a 9 feet shadow, so the scale factor is 12/9 = 4/3.

Multiply this scale factor by the height of the tree: 45 feet x 4/3 = 60 feet shadow cast by the 45 feet tall tree.

Answer: Option D, (40 minutes) is the correct answer.

Step-by-step explanation: Time she has to complete 3 assignments = 2 hours.

Let the time taken to complete each assignment be 'x'

→ 2 hours = 120min

∴ The amount spend for each assignment is the same.

∴ Time taken for each assignment = 120/3 = 40min

∴ It takes 40 min to complete each assignment, Option D.

Answer:

x=1

Step-by-step explanation:

6^2x- 3 = 6^-2x+1

Since the bases are the same, the exponents are the same

2x-3 = -2x+1

Add 2x to each side

2x-3+2x = -2x+1+2x

4x-3 = 1

Add 3 to each side

4x-3+3 = 1+3

4x = 4

Divide each side by 4

4x/4 = 4/4

x=1

Answer: C. x = 1

Explanation: E21

Answer:

35 units^2.

Step-by-step explanation:

Area = base * altitude

= 7 * 5.

Answer:

35 sq. un.

Step-by-step explanation:

The Intuition for why the area of a parallelogram is A=bh (area = base x height)

The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

Have a great day!

Answer:

[tex]Percentage\hspace{3}error\approx 1.96\%[/tex]

Step-by-step explanation:

The error percentage is a measure of how inaccurate a measurement is, standardized based on the size of the measurement. It can be easily calculated using the following formula:

[tex]Percentage\hspace{3}error=|\frac{v_A-v_E}{v_E} | \times 100[/tex]

Where:

[tex]v_A=Approximate\hspace{3}value\\v_E=Exact\hspace{3}value[/tex]

Therefore, according to the data provided by the problem:

[tex]v_A=15.6\\v_E=15.3[/tex]

The percentage error is:

[tex]Percentage\hspace{3}error=|\frac{15.6-15.3}{15.3}| \times 100 = 1.960784314\%\approx 1.96\%[/tex]

Answer:

1165.73 sq.cm. of newspaper are  needed to cover the lateral areas of all five sculptures

Step-by-step explanation:

Diameter of 1 sculpture = 9 cm

Radius of 1 sculpture =[tex]\frac{9}{2}=4.5 cm[/tex]

Slant height of sculpture = l = 16.5 cm

Lateral surface area of each sculpture = [tex]\pi r l = \frac{22}{7} \times 4.5 \times 16.5 =233.3571 cm^2[/tex]

Lateral surface area of 5 sculptures =[tex]233.3571 \times 5 =1165.73 cm^2[/tex]

Hence 1165.73 sq.cm. of newspaper are  needed to cover the lateral areas of all five sculptures

Answer:

1,165.73 cm^2

Step-by-step explanation: