A researcher would like to estimate the mean weight of all adult male American alligators in the
Everglades. The mean weight of a random sample of 89 adult male American alligators from the Everglades
was found to be 520 pounds. The standard deviation of the weights of all adult male American alligators in
the Everglades is known to be 18 pounds.
Using a 98% confidence level, determine the margin of error, E, and a confidence interval for the mean
weight of all adult male American alligators in the Everglades. Report the confidence interval using interval
notation. Round solutions to two decimal places, if necessary.

Answer:

the ratio of boys to girls in Mr Hegarty's class is 5:3 (in its simplest form).

Step-by-step explanation:

For every 3 girls, there are 5 boys, which can be written as a ratio of 5:3 (boys to girls).

To simplify the ratio, we can divide both sides by the greatest common factor of 5 and 3, which is 1.

Answer: x = 50, y = 25

Step-by-step explanation:

Use your trigonometric identities. Sin = Opposite over hypotenuse. Sin(60) = [tex]25\sqrt{3}/x[/tex]. Therefore, [tex]25\sqrt{3}/sin(60) = x[/tex]. Sin(60) = 0.866, so your answer is 50.0014667312, or x = 50. Do the same for the other one, just with tan (Opposite over adjacent). Your answer is 25.  

The cell that is indicated by the arrow on the right would fall into population c of the circled areas.

We know that the scatterplot that is pictured below represents results from a normal peripheral blood sample that was analyzed using flow cytometry, the cell that is indicated by the arrow on the right would fall into population c of the circled areas.

Red blood cells are equipped with iron, which binds to oxygen molecules and enables them to be transported throughout the body. In terms of immunity, these cells break down in the presence of harmful pathogens, releasing free radicals that can help to destroy them. Leukocytes play a crucial role in fighting off disease and foreign invaders. Granulocytes, including eosinophils, basophils, and neutrophils, are responsible for battling fungi, bacteria, and parasites, as well as responding to allergic reactions. Meanwhile, the agranulocytes, which include monocytes, lymphocytes, and macrophages, differentiate into macrophages and target B cells, T cells, and natural killer cells, while also performing the important function of phagocytosis. Thrombocytes are responsible for maintaining the body's blood volume and preventing bleeding by promoting clot formation. This process is known as hemostasis. Finally, blood plasma serves as the transport medium for all of the components of peripheral blood, with carbon dioxide playing a key role in enabling the removal of waste and other excretory matter from the body.

The circulating blood of the body is known as peripheral blood. It is comprised of red blood cells, white blood cells, and platelets. These cells are suspended in plasma and circulated throughout the body.

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If 0.25 inches on the map represents 400 meters in real life, then 1 inch on the map represents 4 * 400 = 1600 meters in real life. Therefore, 4.5 inches on the map represents 4.5 * 1600 = 7200 meters in real life. So, the distance between the towns is 7200 meters.

Based on the information provided, we cannot conclude with certainty that the average pickup order has a higher amount than the average delivery order.

Based on the information given, we can conclude that there is a 95% chance that the true mean for pickup orders falls between $33 and $51, and the true mean for delivery orders falls between $21 and $41. However, we cannot conclude with certainty that the average pickup order has a higher amount than the average delivery order.

To determine if there is a significant difference between the means of the two groups, we need to perform a hypothesis test. We can set up our null hypothesis as "there is no significant difference between the means of the pickup and delivery orders" and our alternative hypothesis as "the average pickup order has a higher amount than the average delivery order."

We can use a two-sample t-test to test this hypothesis. Assuming equal variances, we would calculate the test statistic as

t = (xpickup - xdelivery) / (s / √n)

where xpickup and xdelivery are the sample means for pickup and delivery orders, s is the pooled standard deviation, and n is the sample size for each group.

If our calculated t-value is greater than the critical value at a chosen significance level (e.g. 0.05), we can reject the null hypothesis and conclude that there is a significant difference between the means of the two groups.

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Answer and Step-by-step explanation:

We want to find the measure of angle ABD (∠ABD).

We can tell by looking at this triangle that the array BD creates complementary angles (two angles who's sum equals 90°). ∠CBD is given to us, and we want to find ∠ABD. By knowing that these two angles will add up to 90°, we can create a formula to solve for ∠ABD.

90° = ∠ABD + ∠CBD

Plug in the angle for ∠CBD.

90° = ∠ABD + 45°.

Subtract 45° from both sides of the equation.

90° - 45° = ∠ABD + 45° - 45°

45° = ∠ABD

So, angle ∠ABD is 45°.

Have a great day!

Answer:

∠ABD = 45°

Step-by-step explanation:

∠ABC = 90° (right angle)

∴ ∠ABD = ∠ABC - ∠CBD

             = 90° - 45°

             = 45°

Answer:

50mm²

Step-by-step explanation:

divide it into a rectangle and triangle

rectangle = 7x5 = 35

triangle = 1/2x5x(13-7) = 1/2x5x6 = 15

35+15=50

Dayna will earn $13.43 in interest after 3 months.

Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is usually expressed as an annual percentage rate, interest expense or revenue is frequently expressed as a dollar amount.(APR).

To calculate the interest earned by Dayna after 3 months, we need to convert the interest rate to a monthly rate, since the time period given is in months.

The monthly interest rate can be calculated by dividing the annual interest rate by 12 (the number of months in a year):

monthly interest rate = 1.8% / 12 = 0.15% per month

Now we can use the formula for simple interest to calculate the interest earned:

simple interest = principal x rate x time

Where:

We know the principal is $2,978, the rate is 0.15% per month, and the time is 3 months. We can plug these values into the formula and solve for the simple interest:

simple interest = $2,978 x 0.0015 x 3

Simplifying:

simple interest = $13.43

Therefore, Dayna will earn $13.43 in interest after 3 months.

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Answer:

Step-by-step explanation:

The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side.

What is the bisector about?

A bisector is known to be a kind of straight line that cut or divide an angle or a line segment.

Note that The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side as it is the right step to take.

The correct answer to this question is letter b.There are only three steps in constructing a circle circumscribed by a triangle. He is done with the first step.  Use the compass to find the perpendicular bisector for side DF. I hope I have helped you.

For given squares, the area of the light greyed figure will be 9²-x² unit².

What are squares?

In mathematics, a square is a geometric shape with four sides of equal length and four right angles. It is also a special case of a rectangle where all sides have the same length. A square can also be defined as a regular quadrilateral, which means all its interior angles are right angles (90 degrees) and all its sides are congruent.

The area of a square can be calculated by multiplying the length of one side by itself, written as A = s², where A is the area and s is the length of a side.

Now,

side of bigger square=9

side of dark greyed square=x

as

Area of light greyed figure will be = area of bigger square - area of dark greyed square

Area(light greyed)=9²-x²

Hence,

           the area of the light greyed figure will be 9²-x² unit².

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Based on the given information, we can answer the following questions:

Therefore, the total cost of all the approved projects is 31,390 GHC.

The project with the highest cost is "Restock the computer laboratory with new computers" with a cost of 9,990 GHC.

Percentage of budget = (Cost of buying prizes / Total cost) x 100%

Percentage of budget = (5,270 / 31,390) x 100%

Percentage of budget = 0.1676 x 100%

Percentage of budget = 16.76%

Therefore, 16.76% of the total budget is allocated to buying prizes for awards.

The project with the highest cost in the budget approved by the school management committee is restocking the computer laboratory with new computers, with a cost of GHC 9,990.00.

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[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Mean = \dfrac{Sum\: of \: Observations }{No.\:of \:Observations }}\\[/tex]

As per question, we are given -

[tex] \:\:\:\:\:\:\star\:\sf Sum \:of \:observations \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 9+4+8+8+7+x \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 36+x \\[/tex]

Now that, we are given all the values which are required for solving this problem, so we can substitute the values and solve for the sixth datum -

[tex] \:\:\:\:\:\:\longrightarrow \sf Mean = \dfrac{Sum\: of \: Observation }{No.\:of \:Observation }\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 7 = \dfrac{36+x}{6}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 7\times 6 = 36+x \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 42 -36 =x\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{x = 6}\\[/tex]

Answer:

Step-by-step explanation:

Middle right = 3

Bottom left = 15t

Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

3 * ( 5t + 4 )

3 * 5t + 3 * 4

15t + 12

Using the central angle theorem, we can find that the value of the angle:

∠ BOC = 130°.

An inscribed angle is the angle formed inside the circle when two chords intersect it. It can also be defined as the angle made by two specific points at a given location on a circle. Instead, an inscribed angle is defined by two circle chords that share an endpoint.

In the given question,

O is the centre of the circle.

OC, OD, OE, OA and OB are all radius of the circle.

AC and BD are the diameters of the circle.

As BD intersects AC and the angles are given as:

∠COD = 50°

∠DOE = 60°

So, ∠ AOE = 180 - 50 - 60

= 70°

Similarly, ∠AOB = 50°.

Now, ∠ BOC = 360° - 50° - 60° - 70° - 50°

= 130°

Therefore, ∠ BOC = 130°.

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The largest possible difference between two different 3-digit numbers with the same digits in reverse order is 792.

Let's assume the two numbers are ABC and CBA. The largest possible difference is achieved when the digits A and C have the largest possible difference.

If A > C, then the difference would be (ABC - CBA) = (100A + 10B + C) - (100C + 10B + A) = 99A - 99C = 99(A - C).

If A < C, then the difference would be (CBA - ABC) = (100C + 10B + A) - (100A + 10B + C) = 99C - 99A = 99(C - A).

Since we want the largest possible difference, we want to maximize the difference between A and C. The maximum possible difference between two single-digit non-zero numbers is 9. So, we want A = 9 and C = 1.

Therefore, the two numbers are 901 and 109, and the largest possible difference is (901 - 109) = 792.

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The probability that a person did not see the ad given that they did not purchase the game is 0.146.

Let A be the event that a person has seen the advertisement, and let B be the event that a person has not purchased the game. We are asked to find the probability P(A' | B), which is the probability that a person did not see the ad given that they did not purchase the game.

We can use Bayes' theorem to calculate this probability:

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

Where

We know that 47% of the market has seen the ad, so the probability of not seeing the ad is 1 - 0.47 = 0.53. We also know that 48% of those who see the ad purchase the game, so 52% of those who see the ad do not purchase the game. Finally, we know that 86% of those who have not seen the ad have not purchased the game.

Putting all of this information together, we can calculate:

P(B | A') = 86%

P(A') = 53%

P(B) = P(B | A') * P(A') + P(B | A) * P(A) = 0.52 * 0.47 + 0.14 * 0.53 = 0.3111

Substituting these values into Bayes' theorem, we get:

P(A' | B) = (0.86 * 0.53) / 0.3111 = 0.146 (rounded to three decimal places)

Therefore, the probability that a person did not see the ad given that they did not purchase the game is 0.146.

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Answer: The probability of landing on orange is equal to the probability of landing on purple

Step-by-step explanation:

The spinner has a total of 8 equally-sized sections, and each section has a unique color. Therefore, the probability of landing on any particular section is 1/8 or 0.125.

Looking at the colors on the spinner, we can see that there are two purple sections, two yellow sections, three blue sections, and one orange section.

Therefore, the probability of landing on orange is 1/8 or 0.125, which is equal to the probability of landing on purple (sections 1 and 8). So the statement "The probability of landing on orange is equal to the probability of landing on purple" is true.

On the other hand, the probability of landing on yellow is 2/8 or 0.25, which is greater than the probability of landing on blue (sections 4, 5, and 6), which is 3/8 or 0.375. So the statement "The probability of landing on yellow is less than the probability of landing on blue" is false.

Therefore, the correct statement about probability is "The probability of landing on orange is equal to the probability of landing on purple."

"The given statement is option C."The point I is located three-fourths unit to the right and three-fourths unit up from the origin. So the ordered pair that represents point I is (3/4, 3/4).  Which shows (3/4, 3/4) as one of the options.

It is important to remember that the x-coordinate represents the horizontal distance from the origin and the y-coordinate represents the vertical distance from the origin.

The signs of the coordinates indicate the direction: positive indicates to the right or up, while negative indicates to the left or down. In this case, the x-axis starts at -2 and goes up to 2 with tick marks every one-fourth unit, and the y-axis starts at -2 and goes up to 2 with tick marks every one-fourth unit.

By following the directions given, we can determine the location of each point and its corresponding ordered pair.The point I is located to the right three-fourths unit and up three-fourths unit from the origin. Therefore, the ordered pair that represents the point labeled as I is (3/4, 3/4).

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A marketing company is testing eight different page designs for its new catalogue of clothing. The analysis is most appropriate is ANOVA

The best analysis to use to determine whether there is a noticeable difference in sales amounts between the eight various page designs in the marketing company's new clothing catalogue is Analysis of Variance. In this instance, the averages of the sales figures for each of the eight page designs were compared using the statistical technique known as an ANOVA.

If there is a statistically significant difference between the group means, then at least one of the patterns may be linked to a higher degree of revenue than the others. This can be determined using an ANOVA. The marketing firm can use this data to identify the page designs that are most successful at driving purchases and change their catalogue as necessary to maximise income.

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The required probability of the given exponential distribution with mean of 10 minutes is equal to 0.39 rounded to two decimal places.

The amount of time spent at a bank follows an exponential distribution with a mean of 10 minutes,

The probability density function (PDF) of the time spent at the bank is given by,

f(x) = (1/10)e^(-x/10), where x ≥ 0

The probability of spending less than 5 minutes at the bank,

Evaluate the cumulative distribution function (CDF) of the exponential distribution up to x=5 minutes,

P(X < 5) = [tex]\int_{0}^{5}[/tex] f(x) dx

=[tex]\int_{0}^{5}[/tex](1/10)e^(-x/10) dx

= [-e^(-x/10)][tex]|_{0}^{5}[/tex]

= -e^(-1/2) + 1

≈ 0.393

Therefore, the probability of spending less than 5 minutes at the bank is approximately 0.39, rounded to two decimal places.

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Answer:

[tex]x^{2}[/tex] + 2x

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

x^{2} + 2x

Step-by-step explanation:

The person who answered above me is correct

[tex]0, 1, 1, 2, 2, 2, 2, 3, 3, 5[/tex], minimum: [tex]0[/tex], maximum: [tex]5[/tex], mean: [tex]2.1[/tex], median: [tex]2[/tex], mode: [tex]2[/tex]. I think the data have zero skew. Its mean, median, and mode are based on [tex]2[/tex]. It shows symmetry.

The value that happens most frequently is the mode. The only averaging that is capable of having zero, one, or several values is the mode. Finding the mode is aided by first sorting the numbers.

The mode formula in statistics is used to determine the mode or mode value for a specific collection of data. It is regarded as the number that consistently appears in a particular set. In other words, the mode or mode value in a data collection is the value or quantity that occurs more frequently or with a specific rate.

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The complete question is:

A school sells boxes of cookies each year for a charity fund. The data set shows the number of boxes the 10 families living on Willow Avenue buy, on average, every year. Does this data have negative, positive, or zero skew?

{2,3,2,2,0,5,2,1,1,3}

The 11th term in the arithmetic sequence 13, 19, 25, 31 is 73.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed number called the common difference (d) to the preceding term.

To find the 11th term in the arithmetic sequence 13, 19, 25, 31, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where:

an is the nth term

a1 is the first term

n is the number of the term we want to find

d is the common difference

In this sequence, the first term (a1) is 13 and the common difference (d) is 6 (we can see that by subtracting each term from the one before it). So we can plug in the values we know:

a11 = 13 + (11 - 1)6

a11 = 13 + 60

a11 = 73

Therefore, the 11th term in the sequence 13, 19, 25, 31 is 73.

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Jacki's estimates are reasonable because they make the total of the five winning basketball scores equal to 500 points.

The correct answer is D. It is reasonable because all the scores equal 500.

First, we know that the five winning scores totaled 500 points.
Three of the scores (81, 112, and 97) are already recorded in the team log. We can add these three scores together to find out how many points we need to reach 500:

81 + 112 + 97 = 290 points.

To find the remaining points needed, we can subtract the sum of the known scores (290 points) from the total points (500 points):

500 - 290 = 210 points.
Jacki estimated that the other two scores were 100 and 110 points.

We can add these two scores together to check if they equal the remaining points needed (210 points):

100 + 110 = 210 points.

Since Jacki's estimates add up to the remaining points needed (210 points), we can conclude that her estimates are reasonable.

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Answer:

Step-by-step explanation:

112

The sixth term is -48672 * x^5.

The coefficient of the fourth term is -2880.

The third term in ascending powers of x is 540 * x^8.

To find the terms and coefficients in the expansion of (3x - 2)^10, we'll use the binomial theorem which states that:

(a + b)^n = Σ [C(n, k) * a^(n-k) * b^k] for k = 0 to n

where C(n, k) is the number of combinations (n! / (k!(n - k)!)) and Σ is the summation symbol.

Here, n = 10, a = 3x, and b = -2.

Sixth term:

To find the sixth term, we'll plug k = 5 into the formula (since the index starts from 0):

C(10, 5) * (3x)^(10 - 5) * (-2)^5 = 252 * (3x)^5 * (-32)

The sixth term is -48672 * x^5.

Coefficient of the 4th term:

To find the coefficient of the fourth term, we'll plug k = 3 into the formula:

C(10, 3) * (3x)^(10 - 3) * (-2)^3 = 120 * (3x)^7 * (-8)

The coefficient of the fourth term is -2880.

Third term in ascending powers of x:

In ascending powers of x, the third term corresponds to x^2. Here, k = 2:

C(10, 2) * (3x)^(10 - 2) * (-2)^2 = 45 * (3x)^8 * 4

The third term in ascending powers of x is 540 * x^8.

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Answer:

Number of Walks | Amount Left to Raise

0             | $594

1             | $581

2             | $568

3             | $555

4             | $542

5             | $529

Pattern Rule: The amount left to raise decreases by 13 each time the number of walks increases by 1.

Expression: Let n = the number of walks. Amount left to raise = 594 - 13n

After 2 walks, there is $568 left to raise. You know this because 2 multiplied by 13 (the number subtracted for each walk) is 26. Subtract 26 from 594 to get 568.

Andres will practice with his band for a total of 6 hours and 45 minutes over these 6 days.

To add these times, we need to find a common denominator for 2, 4, and 8, which is 8.

1[tex]\frac{1}{2}[/tex] can be written as [tex]\frac{4}{8}[/tex],

1[tex]\frac{3}{4}[/tex] can be written as [tex]\frac{7}{8}[/tex],

and 2 can be written as [tex]\frac{16}{8}[/tex].

Now we can add the times:

[tex]\frac{4}{8} +\frac{7}{8} +\frac{16}{8} =\frac{27}{8}[/tex]

So Andres will practice for [tex]\frac{27}{8}[/tex] hours this week.

Next week, he will practice for the same number of hours on each day, so he will practice for a total of [tex]\frac{27}{8}[/tex] hours over the three days.

To find the total number of hours he will practice over the 6 days

[tex]\frac{27}{8} + \frac{27}{8} = \frac{54}{8}[/tex]

Simplifying,

[tex]\frac{54}{8} = 6\frac{3}{4}[/tex]

Andres will practice with his band for a total of 6 hours and 45 minutes over these 6 days.

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18/99 simplified is 2/11 by dividing the numerator and denominator by 9.

A mathematical expression can be simplified by replacing it with an equivalent one that is easier (typically shorter), for example. In computer algebra, formulas of algebra are simplified. Boolean equation simplification is also known as logic optimization.

To simplify 18/99

We need to simplify the denominator and numerator by the greatest common factor.

In 18 and 99, 9 is the greatest common factor so, we can divide the numerator and denominator by 9 .

[tex]\frac{18}{99} = \frac{18/9}{99/9} \\\frac{18}{99} = \frac{2}{11}[/tex]

Therefore 18/99 simplified is 2/11

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