Serena is measuring the length of beetles for a science project .One beetle measures 4/5 cm and another measure 7/10 cm. What is the difference in the beatles length

The probability that a cell phone user makes or receives less than 12 calls per day is 0.3971.

To find P(x < 12), we need to standardize the value of 12 using the formula: z = (x - μ) / σ where z = z-score, x = value of interest, μ = mean, and σ = standard deviation.

Substituting the values, we get:

z = (12 - 13.1) / 4.3

z = -0.25581

Using a calculator, we can find the probability that z is less than -0.25581, which is:

P(z < -0.25581) = 0.3971

P(z < -0.25581) = 39.71%.

Full question "Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Find P (x <12)".

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The only equation that met the condition is x² + (y + 8)² = 36

Analytic Geometry is a branch of mathematics that deals with the study of geometry using algebraic methods. It involves using coordinate systems to describe geometric figures and to express geometric properties in terms of algebraic equations.

In particular, the study of equations of circles is a fundamental topic in analytic geometry. A circle is a set of points in a plane that are equidistant from a fixed point called the center. In the coordinate plane, a circle with center (a, b) and radius r can be described by the equation:

(x - a)² + (y - b)² = r²

where x and y are the coordinates of any point on the circle.

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The number of hours without daylight will be 5.6 hours.

On June 1, 2013, the number of hours of daylight in Anchorage, Alaska was 18.4 hours.

There are 24 hours a day. Then the number of hours without daylight is calculated as,

⇒ 24 - 18.4

⇒ 5.6 hours

The number of hours without daylight is 5.6 hours.

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The circular cookie cake have an area of 200.96 in², and thus 100.48 square inches will make up its half.

The area of a circle is π multiplied by the square of the radius. The area of a circle when the radius 'r' is given is πr².

Area of circle = πr²

π = 3.14

radius = 2 m {half the diameter}

Area of the circular cookie = 3.14 × 8 in × 8 in

Area of the circular cookie = 200.96 in²

square inches to make up half the cookie = 200.96 in²/2

square inches to make up half the cookie = 100.48 in²

Therefore, the circular cookie cake have an area of 200.96 in², and thus 100.48 square inches will make up its half.

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(a) We need to find P(X ≤ 50), where X is the maximum speed of a moped. We have:

μ = 46.8 km/h

σ = 1.75 km/h

Using standardization, we get:

Z = (X - μ) / σ

Z follows a standard normal distribution. Therefore,

P(X ≤ 50) = P(Z ≤ (50 - μ) / σ)

= P(Z ≤ (50 - 46.8) / 1.75)

= P(Z ≤ 1.8286)

= 0.9641 (rounded to four decimal places)

Therefore, the probability that the maximum speed is at most 50 km/h is 0.9641.

(b) We need to find P(X ≥ 49). Using standardization, we get:

P(X ≥ 49) = P(Z ≥ (49 - μ) / σ)

= P(Z ≥ (49 - 46.8) / 1.75)

= P(Z ≥ 1.2571)

= 0.1038 (rounded to four decimal places)

Therefore, the probability that the maximum speed is at least 49 km/h is 0.1038.

(c) We need to find P(|X - μ| ≤ 1.5σ). Using standardization, we get:

P(|X - μ| ≤ 1.5σ) = P(-1.5 ≤ (X - μ) / σ ≤ 1.5)

= P(-1.5 ≤ Z ≤ 1.5)

= P(Z ≤ 1.5) - P(Z ≤ -1.5)

= 0.8664 - 0.0668

= 0.7996 (rounded to four decimal places)

Therefore, the probability that the maximum speed differs from the mean value by at most 1.5 standard deviations is 0.7996.

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The minimum weight of the middle 95% of the players is 185.4 pounds.

To find the minimum weight of the middle 95% of the players, we need to find the weight that separates the bottom 2.5% of the distribution from the top 2.5%.

We can use the z-score formula:

z = (x - μ) / σ

Where:
x = the weight we're looking for
μ = the mean weight of 205 pounds
σ = the standard deviation of 10 pounds

To find the z-score that corresponds to the bottom 2.5%, we can use a z-table or calculator and look up the z-score that has an area of 0.025 to its left. This value is -1.96.

Plugging this into the z-score formula:

-1.96 = (x - 205) / 10

Solving for x:

x = (-1.96 * 10) + 205

x = 185.4

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The yield on the corporate bond is 8.65%.

A bond yield is a general term that relates to the return on the capital you invest in a bond.  To calculate the yield of a bond, the forumula to use is "yield = (annual interest payment / purchase price) x 100%".

Data:

Face value of the bond is $1000

Fixed interest rate is 8%.

Annual interest payment = 8% x $1000

Annual interest payment = $80

The purchase price is $925.

We can substitute these values to find the yield:

= ($80 / $925) x 100%

= 0.0864864865 * 100%

= 8.65%

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True.

If A is a 5 by 5 matrix and has three pivots, then its row reduced echelon form will have three leading 1's, and the other two rows will be zero rows.

If A is a 5 by 5 matrix and has three pivots, then its row reduced echelon form will have three leading 1's, and the other two rows will be zero rows. This means that the three pivot columns of A are linearly independent, and they span a three-dimensional subspace of R^5.

Since the pivot columns of A are the columns of ColA, we can say that ColA is a subspace of R^5 that is spanned by three linearly independent vectors. Since the dimension of this subspace is three, it is a three-dimensional subspace of R^5. Geometrically, a three-dimensional subspace of R^5 is a (two-dimensional) plane, sincsincesincsinceee it is the intersection of two three-dimensional spaces. Therefore, we can conclude that ColA is a (two-dimensional) plane in R^5.

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The minimum score an applicant must achieve in order to receive consideration for admission to the university is 678.

To solve this problem, we need to find the score x such that the area to the right of x under the standard normal curve is 0.1 (since the 90th percentile corresponds to the top 10% of scores).

Using a standard normal table (also known as a Z-table), we can find the z-score that corresponds to the area of 0.1. The closest value we can find in the table is 1.28. This means that 10% of the scores fall above a z-score of 1.28.

Now we can use the formula for converting a z-score to an x-score:

z = (x - mu) / sigma

where mu is the mean and sigma is the standard deviation of the distribution. Substituting the given values, we have:

1.28 = (x - 550) / 100

Solving for x, we get:

x = 100(1.28) + 550 = 678

Therefore, the minimum score an applicant must achieve in order to receive consideration for admission to the university is 678.

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To compute the variance of a geometric distribution with parameter p, we first need to understand the geometric distribution itself.

The geometric distribution represents the number of trials required for the first success in a sequence of Bernoulli trials, where each trial has a success probability of p.

The variance of a geometric distribution with parameter p can be calculated using the formula:

Variance = (1 - p) / p^2

Please note that the Taylor expansion "=1+r+ ir -1" you mentioned does not seem to be relevant to the calculation of the variance of a geometric distribution. The correct formula for the variance is provided above.

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The correct choice is A: (2,2,4) | 10x dx + 18y dy + 8z dz = 21 (0,0,0)

To check whether the differential form is exact, we need to calculate its curl:

curl(F) = (∂Q/∂y - ∂P/∂z)i + (∂R/∂z - ∂Q/∂x)j + (∂P/∂x - ∂R/∂y)k

Here, P = 10x, Q = 18y, and R = 8z. Substituting these values, we get:

curl(F) = (0 - 0)i + (0 - 0)j + (0 - 0)k = 0

Since the curl of F is zero, the differential form is exact. We can find a potential function f such that F = ∇f.

To find f, we integrate the differential form along any path from (0,0,0) to (2,2,4)

f(2,2,4) - f(0,0,0) = ∫CF · dr

where CF is the given differential form and the integral is taken along the path C. We can choose a simple path, such as a straight line from (0,0,0) to (2,2,4):

r(t) = ti + tj + 2tk, 0 ≤ t ≤ 1

Then CF · dr = 10x dx + 18y dy + 8z dz = (10t)i + (18t)j + (16t)k dt

Substituting for x, y, and z in terms of t, we get:

CF · dr = 10ti dt + 18tj dt + 16tk dt = d(5t^2 + 9t^2 + 8t^2/2)

Therefore, f(2,2,4) - f(0,0,0) = (5(1)^2 + 9(1)^2 + 8(1)^2/2) - (5(0)^2 + 9(0)^2 + 8(0)^2/2) = 21

Hence, the value of the integral is:

∫CF · dr = f(2,2,4) - f(0,0,0) = 21

Therefore, the correct choice is A: (2,2,4) | 10x dx + 18y dy + 8z dz = 21 (0,0,0)

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D) Median and interquartile rangemedian and interquartile range

Symmetrical data has an approximate line of symmetry.

When describing a distribution, it's important to use applicable measures of center and spread that reflect the shape and nature of the data. For symmetrical data, the mean and standard  divagation are  generally used as measures of center and spread, independently. still, when the data is disposed or contains outliers, these measures may not be applicable.

 In  similar cases, the standard and interquartile range( IQR) are more robust measures of center and spread. The standard is the value that separates the lower 50 of the data from the upper 50, and is  thus  innocent by outliers. The IQR is the difference between the 75th percentile and the 25th percentile, and represents the range of the middle 50 of the data. It's also less sensitive to outliers than the range or standard  divagation.

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The best probability distribution to use for simulating the outcome of flipping a single coin is the binomial distribution. The binomial distribution is used to model the number of successes in a fixed number of independent trials, where each trial has the same probability of success (in this case, 0.5 for heads or tails).

It is a discrete distribution and is often used in situations where there are only two possible outcomes. The other distributions mentioned (uniform, exponential, normal, and Poisson) are not appropriate for this scenario.

The best probability distribution to use for simulating the outcome of flipping a single coin is the binomial distribution. The binomial distribution is appropriate because it models the number of successes (e.g., heads).

In a fixed number of independent Bernoulli trials (e.g., coin flips) with the same probability of success on each trial. In this case, there are two possible outcomes (heads or tails) and each flip is independent with an equal probability of success (0.5).

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The equation of line passing through points  (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The slope of line passing through  (-3,6 )  and (-2,9 )

m=9-6/-2+3

=3

Point slope form equation is y-y₁=m(x-x₁)

y-6=3(x-(-3))

y-6=3(x+3)

Hence, the equation of line passing through points  (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)

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Kyree would score 165 goals if Anthony scored 60 goals, given that for every 4 goals Anthony scores, Kyree scores 11 goals. This means Kyree scores at a faster rate than Anthony.

If Anthony scored 60 goals and for every 4 goals Anthony scored, Kyree scored 11 goals, we can set up a proportion to find out how many goals Kyree scored. We can use the fact that the ratio of goals scored by Anthony and Kyree is the same as the ratio of 4 to 11. We can express this as:

4/11 = 60/x

Solving for x, we can cross-multiply to get:

4x = 11 * 60

Dividing both sides by 4, we get:

x = 165

Therefore, Kyree would have scored 165 goals if Anthony scored 60 goals. This means that Kyree scores at a faster rate than Anthony, since for every 4 goals Anthony scores, Kyree scores 11 goals.

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8 is closest to the maximum number of list elements that can be examined when performing a binary search for the value in the list.Therefore option B is correct.

To find the maximum number of list elements:

When performing a binary search on a sorted list of 128 elements, you would repeatedly divide the list in half until you find the target value or the list cannot be divided further.

In this case, you can divide the list a maximum of 7 times (2^7 = 128) before you reach a single element.

However, since the options provided do not include 7, the closest option is 8 (option B).

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1. The company should use a t-test for the population mean, as we are comparing the mean test score for the sample of applicants supplied by the recruiting firm to the historical mean of 75.2.

2. The set of hypotheses the company should use to answer the research question is: D. H0: μ = 75.2 vs. H1: μ > 75.2

1. The appropriate inference procedure for this scenario is the t-test for a population mean. This is because we are comparing a sample mean (76.85) to a known population mean (75.2) with a known sample standard deviation (9.3). So the correct answer is:

E. t-test for a population mean

2. The company wants to determine if the mean test score for applicants provided by the recruiting firm is higher than the historical mean of 75.2. Therefore, the null hypothesis (H0) should be that the mean test score is equal to 75.2, and the alternative hypothesis (H1) should be that the mean test score is greater than 75.2. The correct set of hypotheses is:

H0: μ = 75.2 (the historical mean)

Ha: μ > 75.2 (the mean for the sample of applicants supplied by the recruiting firm is higher).

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x < -1/2 is the solution of the inequality -2x+7>8

The given inequality is  -2x+7>8

We have to find the solution

Subtract seven from both sides

-2x>8-7

-2x>1

Divide both sides by 2

-x>1/2

so x<-1/2 is the solution

Hence, x < -1/2 is the solution of the inequality -2x+7>8

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What is solution of inequality -2x+7>8?

The interquartile range for the data is 7.

We have

Data: 65,67,67,84,96,98,98

First Quartile,

Q1 = (n+1)/4

    = (7+1)/4

    = 8/4 th term

    = 2nd term

    = 27

Third quartile,

Q3 = 3(n+1)/4

     = 3 x 2

    = 6 th term

    = 98

So, Interquartile range

= Q3- Q1

= 98- 67

= 7

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Answer: If Chloe wants to minimize the amount of material used for the outer edges of the sandbox, she should make the sandbox a square shape.

Here's why:

- The area of a rectangle is given by the formula A = l x w, where A is the area, l is the length, and w is the width.

- For a square, the length and width are equal, so we can write A = s^2, where s is the length of a side.

- We know that the area of Chloe's sandbox is 36 square units, so we can write s^2 = 36.

- Solving for s, we get s = 6.

- Therefore, Chloe should make the sandbox a square with sides of length 6 units.

- This will minimize the amount of material used for the outer edges of the sandbox, since all sides will be the same length.

Step-by-step explanation:

Answer:

C. 54cm²

Step-by-step explanation:

Split the figure into 2. A=LW. the top shape is easy, 8x5 = 40

As for the bottom one, we need to figure out the height. The whole left side is 12cm, and the part in the top shape is 5cm since it is across from the labeled side, and is a rectangle. 12-5= 7, the height of the smaller shape.

From there, we use LW to figure that out. 7x2 = 14

Now we know the area of both shapes, so we must add them together. Think of it as finding the area of each shape seperately, which is what we did. 40 + 14 = 54 and don't forget the label!

The area of the figure is 47.67 [tex]cm^2[/tex] round to the nearest hundredth.

We can find the area of the half circle with a diameter of 11 cm.

The formula for the area of a circle is A = πr^2, where r is the radius.

Since the diameter is 11 cm, the radius is half of that, which is 5.5 cm.

Substituting the value of r, we get:

A = π(5.5)^2

A = 30.25π

The area of figure is half of the area of the full circle, so we divide by 2:

A = 15.125π

Rounding to the nearest hundredth, we get:

A ≈ 47.67 [tex]cm^2[/tex]

Thus, the answer is 47.67 [tex]cm^2[/tex].

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The two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

The given two equations are y=x²+6x+8 and y=(x+2)(x+4)

We have to check whether the two equations are equal or not

y=x²+6x+8 ----(1)

y=(x+2)(x+4) ---(2)

y=x² + 4x+2x+8

y=x² + 6x+8 ....(2)

From equation (1) and (2), y=x²+6x+8 and y=(x+2)(x+4) are equal.

Hence, the two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

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Answer:

Step-by-step explanation:

2 and 1/2

Answer:

2 1/2 or 2.5

Step-by-step explanation:

1. Rewrite:

1 1/2 + x = 4

2. Subtract 1 1/2 from both sides:

4 - 1 1/2 = 2 1/2

x = 2 1/2 or 2.5

a. No, a 95% confidence interval using the smaller sample size does not allow us to predict the winner., b) We cannot use the confidence interval to predict the winner with certainty, but we can say that there is a higher probability of the Republican candidate winning since the lower bound of the interval is 0.407.

The 95% confidence interval for the proportion of all voters voting for the Republican candidate with n=149 and counts of 68 and 81 is (0.407,0.573). This interval is wider than the interval with n=1490, which makes sense since a smaller sample size leads to more variability in the estimates.

b. We cannot use the confidence interval to predict the winner with certainty, but we can say that there is a higher probability of the Republican candidate winning since the lower bound of the interval is 0.407, which is higher than the proportion of Democratic voters. However, there is still a possibility that the Democratic candidate may win since the upper bound of the interval is 0.573.

a. To determine whether a 95% confidence interval using the smaller sample size (n=149) allows you to predict the winner, we first need to calculate the confidence interval.

Here, we have 68 voters for the Democratic candidate and 81 voters for the Republican candidate.

1. Calculate the sample proportion for the Republican candidate (p):
p = 81/149 = 0.543

2. Calculate the standard error (SE) for the sample proportion:
SE = √(p(1-p)/n) = √(0.543(1-0.543)/149) = 0.040

3. Find the margin of error (ME) for a 95% confidence interval using a Z-score of 1.96:
ME = 1.96 × SE = 1.96 × 0.040 = 0.078

4. Calculate the 95% confidence interval (CI) for the proportion of all voters voting for the Republican candidate:
CI = (p - ME, p + ME) = (0.543 - 0.078, 0.543 + 0.078) = (0.465, 0.621)

The 95% confidence interval for the proportion of all voters voting for the Republican candidate is (0.465, 0.621).

Since this interval includes values both below and above 0.5, we cannot predict the winner with 95% confidence using the smaller sample size. The interval shows that the proportion of voters supporting the Republican candidate could range from 46.5% to 62.1%, making it unclear whether the Republican or Democratic candidate would win.

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f = h - 6 and 5f = 8h + 7 are the system of equations to find f and h

We have to form a system of equations

Let F be no of pages in each science fiction comic book

Let h h be the no of pages in each super hero comic

To find f,

5f = 8h + 7

this is because no of pages in all science fiction is 7 times more than total in super hero bopks

Then f = h - 6

this is because  the science fiction has fewer pages than 6 compared to supoer heroes

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We can see from the graph that the parabola intersects the x-axis at -4 (where the vertex touches the x-axis).

Since the equation is in the form of ax^2 + bx + c = 0, we can identify that a = 1, b = 8, and c = 16.

Using the quadratic formula, we get:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

x = (-8 ± sqrt(8^2 - 4(1)(16))) / 2(1)

x = (-8 ± sqrt(0)) / 2

x = -4

Therefore, the only solution is x = -4.

Answer: 27

Step-by-step explanation:

This is a cube so all of the lengths have the same lengths.

3x3x3=27

3x3=9

9x3=27

The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

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Answer: yield = ($70 / $875) x 100% = 8% (rounded to the nearest hundredth)

Step-by-step explanation:

To calculate the yield on a corporate bond, we need to use the following formula:

yield = (annual coupon payment / bond price) x 100%

In this case, the bond has a face value of $1000 and pays a fixed interest rate of 7%. The bond was purchased at a discount price of $875. The annual coupon payment can be calculated as:

annual coupon payment = face value x coupon rate = $1000 x 7% = $70

Using the formula above, we can calculate the yield as:

yield = ($70 / $875) x 100% = 8%

Therefore, the yield on this corporate bond is 8% rounded to the nearest hundredth.