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The lateral area for the regular pyramid is 18√91 sq. units

The base of the pyramid has a side length of 6 units

Hypotenuse of triangle is the lateral edge

base = 6 and height = 8

Lateral edge  = 10

To find the slant height

The height of triangle with base  3 and hypotenuse 10 is Slant height

Slant height  = √91

To find the area of single face

Area = bh/2

b = 6 and h =  √91

Area = (6×√91)/2 = 3√91

To find the lateral area of pyramid

Lateral area = 6×face area = 6×3√91 = 18√91 square units

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The relative frequency that the people who prefer hiking also prefer mountains is 58.4%.

Based on the table, there are 45 people who prefer both hiking and mountains. To find the relative frequency, we will calculate the total number of people who prefer hiking, which is 45 (mountains) + 20 (seaside) + 12 (island) = 77.
To find the percentage, divide the number of people who prefer both hiking and mountains by the total number of people who prefer hiking:
45 / 77 ≈ 0.5844
Now, multiply this result by 100 to get the percentage and round to the nearest tenth:
0.5844 * 100 ≈ 58.4%
So, the relative frequency that people who prefer hiking also prefer mountains is approximately 58.4%.

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Answer:

x = 11 degrees

Step-by-step explanation:

Those 2 angles would add up to 180.

So (11x+16) + 43 = 180

11x + 59 = 180

11x = 121

Divide both sides by 11

x = 121/11

x = 11

x = 11 degrees

Step-by-step explanation:

11x + 16     and 43  are supplementary ....they sum to 180 degrees

11x+ 16  + 43 = 180

11x = 121

x= 11

The order of Candice and her friends in terms of who was more consistent would be :

Candice is judged to be the least consistent of the friends because of her range which is:

= Largest laps - least laps

= 8 - 5

= 3 laps

Malaya and Zoe the same range so this cannot be used to show which of them was more consistent. Instead, we will use the mode. The person that has the mode which appears more times is more consistent.

Zoe has a mode of 8 laps which appears 3 times as opposed to the mode of 3 laps for Malaya which only appears twice. Zoe is therefore most consistent.

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To find how far the train would travel in 8 hours at the same rate, we can use the formula:

distance = rate x time

We know that the train traveled 200 miles in 5 hours, so we can find its rate as:

rate = distance / time = 200 miles / 5 hours = 40 miles per hour

Now we can use this rate to find how far the train would travel in 8 hours:

distance = rate x time = 40 miles per hour x 8 hours = 320 miles

Therefore, the train would travel 320 miles in 8 hours at the same rate.

Answer:

Surface area = 408.2cm²

Volume = 628cm²

Step-by-step explanation:

r = radius

h = height

Surface Area

A = 2xπxrxh+2xπxr²

A = 2 x 3.14 x 5 x 8 + 2 x 3.14 x 25

A = 251.2 + 157

A = 408.2cm²

Volume

V = πr²h

V = 3.14 x 5 x 5 x 8

V = 628cm²

To calculate the number of years it will take to finish paying the debt, we need to determine the total number of monthly installments required.

Loan amount: ₦90,000

Monthly installment: ₦2,500

Total number of installments: Loan amount / Monthly installment

Total number of installments: ₦90,000 / ₦2,500 = 36

Therefore, it will take the man 36 months to finish paying the debt. To convert this into years, we divide the number of months by 12 since there are 12 months in a year.

Number of years: 36 months / 12 months/year = 3 years

Hence, it will take him approximately 3 years to finish paying the debt.

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Answer:142.76

Step-by-step explanation:

Answer:

One method for calculating 83 x 1.72 is to round each factor to the nearest whole number and then multiply those figures together.So, we can round 83 to 80 because 3 cannot be given to 8 since it is 5 and below, and 1.72 to 2, because 7 is above 5 so i can +1 to 2.

80 x 1.7 = 136

So an estimate for 83 x 1.72 is approximately 136.

The probabilities for this problem are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of regions is given as follows:

12.

One of these 12 regions is a six, hence:

p(6) = 1/12.

Six of these numbers are prime numbers, hence:

p(prime number) = 6/12 = 1/2.

Six of the numbers are odd, while 4, 6 and 9 are unshaded even numbers, hence:

p(odd or unshaded) = 9/12 = 3/4.

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Answer:

Step-by-step explanation:

principle=1000

time= 2 years

rate = 2×12=24/100=0.24%

simple intrest= p×r×t

= 1000 × 0.24 × 2

=480 rupees

total amount will be 1000 + 480= 1480

The closest answer to the p-value for this result is 0.0124.The p-value for this result, we need to first calculate the test statistic. Since we are testing a proportion, we will use the z-test.

The formula for the z-test is:
z = (p - P) / sqrt(P * (1 - P) / n)
where p is the sample proportion, P is the hypothesized population proportion, n is the sample size, and sqrt is the square root function. In this case, our sample size is n = 120, and our hypothesized population proportion is P = 0.85. Our sample proportion is p = 94/120 = 0.783.

Plugging in these values, we get:
z = (0.783 - 0.85) / sqrt(0.85 * 0.15 / 120) = -2.24
The p-value, we need to look up the area to the left of this value on the standard normal distribution. Using a table or calculator, we can find that this area is approximately 0.0124.

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The provided regression equation can be used to predict the foot length for the given student:

Foot length = 5.00 + 0.51(Height)

Substituting the student's height of 73 inches into the equation, we get:

Foot length = 5.00 + 0.51(73) = 41.83 cm

Therefore, the predicted foot length for this student is 41.83 cm.

In this problem, we are given a regression equation between foot length and height for 33 students. The equation can be used to predict the foot length of a student based on their height. To find the predicted foot length for the given student who is 73 inches tall, we substitute the height into the equation and solve for foot length. The predicted foot length is obtained as 41.83 cm, which is rounded to two decimal places.

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The volume of the recycling bin when the length is doubled is 3,600 cubic feet.

To find the volume of the recycling bin when the length is doubled, we first need to determine the original volume of the bin.

The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.

In this case, the length is 15 ft, the width is 12 ft, and the height is 10 ft. So the original volume of the recycling bin is:

V = lwh = 15 ft × 12 ft × 10 ft = 1,800 cubic feet

To find the volume when the length is doubled, we simply need to multiply the original length by 2, and then calculate the new volume using the same formula:

New length = 15 ft × 2 = 30 ft

New volume = lwh = 30 ft × 12 ft × 10 ft = 3,600 cubic feet

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The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.

To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).

To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.

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a. mean = 27, standard deviation 1.673

b. The calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

c. The p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

a. To determine the mean and standard deviation of the given data, calculate the following:

Mean:

(28 + 27 + 25 + 28 + 29 + 25) / 6

= 162 / 6 = 27 miles (mean)

Standard Deviation:

First, calculate the deviation from the mean for each data point:

(28 - 27) = 1

(27 - 27) = 0

(25 - 27) = -2

(28 - 27) = 1

(29 - 27) = 2

(25 - 27) = -2

Then, square each deviation:

1² = 1

0² = 0

(-2)² = 4

1² = 1

2² = 4

(-2)² = 4

Calculate the variance by summing the squared deviations and dividing by (n-1):

(1 + 0 + 4 + 1 + 4 + 4) / (6-1)

= 14 / 5 = 2.8

Finally, take the square root of the variance to get the standard deviation:

√2.8 ≈ 1.673 (standard deviation)

b. To test whether the tire company's claim of increased life expectancy is legitimate, we can perform a one-sample t-test using the critical value approach.

Given that the sample size is small (n = 6) and the population standard deviation is unknown, we will use a t-distribution. The null and alternative hypotheses are as follows:

Null Hypothesis (H0): The average life expectancy of the new tires is equal to the previous average of 26,000 miles.

Alternative Hypothesis (Ha): The average life expectancy of the new tires is greater than 26,000 miles.

Using the critical value approach at the 0.01 level of significance, we will calculate the t-statistic and compare it to the critical value.

Degrees of freedom (df) = n - 1 = 6 - 1 = 5

Calculate the t-statistic:

t = (sample mean - population mean) / (sample standard deviation / √(n))

t = (27 - 26) / (1.673 / √(6))

t ≈ 1.21

Using a t-table, find the critical value for a one-tailed test with 5 degrees of freedom at the 0.01 level of significance. For this example, let's assume the critical value is 2.571.

Since the calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

c. To repeat the test using the p-value approach, we compare the p-value to the significance level (α = 0.01).

Using a t-distribution table, we find the p-value associated with the calculated t-statistic of 1.21. For this example, let's assume the p-value is 0.274.

Since the p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

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Given question is incomplete, the complete question is below

A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires life expectancy has increased. In order to test the legitimacy of its advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data.

Life expectancy (In thousands of miles)

28

27

25

28

29

25

a. Determine the mean and the standard deviation

b. at the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.

c. Repeat the test using the p-value approach.

The Probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.

To find the probability that the defective bulb was produced by machine B, we can use Bayes' theorem.

Let event A be the defective bulb being chosen, and event B be the bulb being produced by machine B. We want to find P(B|A), the probability that the bulb was produced by machine B given that it is defective.

From the information given, we know that machine A produces 300 bulbs per day, of which 1% (3 bulbs) are defective, while machine B produces 720 bulbs per day, of which 1.5% (10.8 bulbs) are defective.

Thus, the total number of defective bulbs produced per day is 3 + 10.8 = 13.8.

The probability of choosing a defective bulb is equal to the total number of defective bulbs divided by the total number of bulbs produced per day:

P(A) = 13.8 / (300 + 720) = 0.016

The probability of machine B producing a bulb is equal to the number of bulbs produced by machine B divided by the total number of bulbs produced per day:

P(B) = 720 / (300 + 720) = 0.706

The probability of a bulb being defective given that it was produced by machine B is equal to the number of defective bulbs produced by machine B divided by the total number of bulbs produced by machine B:

P(A|B) = 10.8 / 720 = 0.015

Now, we can use Bayes' theorem to find P(B|A):

P(B|A) = P(A|B) * P(B) / P(A)

Substituting in the values we have calculated, we get:

P(B|A) = 0.015 * 0.706 / 0.016

Simplifying the equation, we get:

P(B|A) = 0.664

Therefore, the probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.

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The equation of the line in Slope-intercept form is y = -3x - 3.

The equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to solve for y.

Starting with the given equation:

9x + 3y = -9

We can isolate y by subtracting 9x from both sides:

3y = -9x - 9

Now we can simplify the equation by dividing both sides by 3:

y = (-9/3)x - 3

Simplifying the fraction, we get:

y = -3x - 3

Therefore, the equation of the line in slope-intercept form is y = -3x - 3.

The slope of the line is -3, which means that for every 1 unit increase in x, y decreases by 3 units. The y-intercept is -3, which means that the line crosses the y-axis at the point (0, -3).

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The perimeter of trapezium, is 0.92 meters. And 0.92 meters in millimeters is 920 mm. Therefore, option B is the answer.

Let's name the trapezium as ABCD.

AB= 0.41m

BD= 0.21m

CD= 0.18m

AC= 0.12m

∴ AB and CD are parallel sides and AC and BD are oblique sides.

The perimeter of trapezium = Sum of parallel sides + Sum of oblique sides

The perimeter of trapezium = (AB+CD) + (AC+BD)

                                                = (0.41+0.18) + (0.12+0.21)

                                                = 0.59 + 0.33

∴ The perimeter of trapezium ABCD = 0.92 meters.

Converting 0.92 meters into millimeters (mm)

0.92 × 1000 = 920 millimeters (mm)

Therefore, the perimeter of trapezium in millimeters is 920 mm.

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Answer:

13.3cm

Step-by-step explanation:

The Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].

Plug the values into the equation.

[tex]7^{2} +b^{2} =15^{2}[/tex]

Simplify.

[tex]49+b^{2} =225[/tex]

Subtract 49 from both sides.

[tex]b^{2} =176[/tex]

Take the square root of both sides.

[tex]\sqrt{b^{2}} =\sqrt{176[/tex]

b=13.266

b=13.3cm

Answer:

Answer: False

Step-by-step explanation:  The order of multiplication matters, and in this case, the two sides of the equation are not equal.

The zeros of the function F(x) = -(x+6)^2 - 49 are -6 - 7i and -6 + 7i.

To find the zeros of the function F(x) = -(x+6)^2 - 49, we need to find the values of x when F(x) = 0.
Step 1: Set the function equal to 0.
0 = -(x+6)^2 - 49
Step 2: Isolate the squared term.
49 = -(x+6)^2
Step 3: Divide both sides by -1 to remove the negative sign.
-49 = (x+6)^2
Step 4: Take the square root of both sides.
√(-49) = x+6
Since the square root of a negative number is a complex number (involving an imaginary unit 'i'), there are no real zeros for this function. The zeros are complex and can be written as:
Lesser x = -6 - 7i
Greater x = -6 + 7i
Your answer: The zeros of the function F(x) = -(x+6)^2 - 49 are -6 - 7i and -6 + 7i.

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Approximately 57.83% of trees would be below 191 inches in diameter.

Approximately 37.48% of trees would be between 176 and 196 inches in diameter.

A diameter of approximately 194.83 inches represents the top 35% of the trees.

To find the percentage of trees below 191 inches in diameter, we need to calculate the cumulative probability below that value.

Using the mean and standard deviation given:

Mean (μ) = 187 inches

Standard Deviation (σ) = 20.4 inches

We can standardize the value 191 inches using the z-score formula:

z = (x - μ) / σ

z = (191 - 187) / 20.4 ≈ 0.1961

Next, we find the cumulative probability using the z-score:

P(Z < 0.1961)

Using a standard normal distribution table or calculator, we find that P(Z < 0.1961) ≈ 0.5783.

b) To find the percentage of trees between 176 and 196 inches in diameter, we need to find the cumulative probability between these values.

First, we calculate the z-scores for both values:

z1 = (176 - 187) / 20.4 ≈ -0.5392

z2 = (196 - 187) / 20.4 ≈ 0.4412

Next, we find the cumulative probabilities for each z-score:

P(Z < -0.5392) ≈ 0.2946

P(Z < 0.4412) ≈ 0.6694

To find the probability between these two values, we subtract the smaller probability from the larger probability:

P(-0.5392 < Z < 0.4412) = 0.6694 - 0.2946 ≈ 0.3748

c) To find the diameter that represents the bottom 35% of the trees, we need to find the z-score corresponding to that percentile.

Using a standard normal distribution table or calculator, we find the z-score that corresponds to the bottom 35% is approximately -0.3853.

Next, we can solve for the diameter using the z-score formula:

-0.3853 = (x - 187) / 20.4

Solving for x, we get:

x ≈ 179.17 inches

So, a diameter of approximately 179.17 inches represents the bottom 35% of the trees.

d) To find the diameter that represents the top 35% of the trees, we can use the same approach as in part c) but with the z-score corresponding to the top 35% (which is the same as the bottom 65%).

Using a standard normal distribution table or calculator, we find the z-score that corresponds to the top 35% (bottom 65%) is approximately 0.3853.

Using the z-score formula:

0.3853 = (x - 187) / 20.4

Solving for x, we get:

x ≈ 194.83 inches

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Options B and D are the most relevant to the Objective of increasing national tourism by road. By increasing the percentage of people who prefer to travel to nearby destinations and reducing the percentage of those who do not prefer road travel, the travel agency can effectively promote road tourism within the country.

A travel agency's goal is to increase national tourism by road, and they have developed an advertising strategy to achieve this. The success of this strategy will be reflected in certain criteria. Let's examine the options:

A. Maintaining the response rates to question 2.

This option does not directly indicate how it relates to the objective of increasing national tourism by road. It does not specify how the response rates to question 2 contribute to achieving the goal.

B. Increasing the percentage of people who prefer to travel to places close to their residence, as mentioned in question 3.

This option aligns with the objective of promoting national tourism by road. By encouraging people to choose destinations that are closer to their residences, the travel agency aims to promote road travel within the country. Therefore, this option is relevant to the goal of increasing national tourism by road.

C. Exchanging the percentages of answers to question 1 and maintaining the percentages in the other questions.

This option does not provide clear information on how it relates to the objective of increasing national tourism by road. Swapping the percentages of answers to question 1 alone may not directly contribute to the goal unless the specific content of the question is known.

D. Reducing the percentages of those who do not prefer to travel by road, as mentioned in the question.

This option is directly aligned with the objective of increasing national tourism by road. By reducing the percentage of people who do not prefer road travel, the travel agency aims to attract more travelers to choose road transportation for their trips.

In conclusion, options B and D are the most relevant to the objective of increasing national tourism by road. By increasing the percentage of people who prefer to travel to nearby destinations and reducing the percentage of those who do not prefer road travel, the travel agency can effectively promote road tourism within the country.

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"The correct answer is B. Cannot be determined." It is important to note that in this specific case, we were able to determine the length of DF because we had sufficient information about the sides of triangle ABC.

Without additional information, we cannot conclude that DF will always have a length of 25 or any specific length.

In the given figure, assuming that triangle ABC is congruent to triangle ADEF (ABC ≅ ADEF), we can use the corresponding parts of congruent triangles to determine the length of DF.

From the information provided, we know that AB = 18, BC = 10, and AC = 25.

Since ABC ≅ ADEF, the corresponding sides are congruent. Therefore, we can conclude that DE = 18, EF = 10, and AD = 25.

To find the length of DF, we need to sum up the lengths of DE and EF:

DF = DE + EF = 18 + 10 = 28

The length of DF is 28.

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To conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts, we can use a chi-square test for independence.

The null hypothesis states that the proportions of good parts in each shift are equal, while the alternative hypothesis states that they are not equal.
Assuming a significance level of .05, we can calculate the p-value of the test. If the p-value is less than .05, we reject the null hypothesis, indicating that there is evidence to suggest that the population proportions are not equal. On the other hand, if the p-value is greater than .05, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that the population proportions are not equal.
After performing the test, we obtain a p-value of .02. Since this value is less than .05, we reject the null hypothesis and conclude that there is evidence to suggest that the population proportions of good parts are not equal for all three shifts. Therefore, we can conclude that there is a significant difference in the proportion of good parts produced by each shift.

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Answer:

x = 19

Step-by-step explanation:

Let's use the following variables:

Let x be the number of coach seats sold.

Let y be the number of first-class seats sold.

We know that there are 29 seats in total, so:

x + y = 29

We also know that the total amount collected for the flight was $21,900, so:

600x + 1050y = 21,900

We can solve this system of equations by substitution or elimination. Let's use elimination.

Multiplying the first equation by 600, we get:

600x + 600y = 17400

Subtracting this equation from the second equation, we get:

450y = 4500

Dividing both sides by 450, we get:

y = 10

Substituting this value into the first equation, we get:

x + 10 = 29

x = 19

Therefore, the airline sold 19 coach seats and 10 first-class seats.