Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 46 days and a standard deviation of 10.5 days. Find the probability that a simple random sample of 49 protozoa will have a mean life expectancy of 47 or more days.
a) 0.7475
b) 0.5379
c) 0.4525
d) 0.2525
e) 0.5050

Answer:

x = 5;

[tex]y = \frac{5 \sqrt{2} }{2} [/tex]

Step-by-step explanation:

Use trigonometry:

[tex]y = \tan(45°) = \frac{ \frac{5 \sqrt{2} }{2} }{y} [/tex]

Use the property of proportion to find y:

[tex]y = \frac{ \frac{5 \sqrt{2} }{2} }{ \tan(45°) } = \frac{ \frac{5 \sqrt{2} }{2} }{1} = \frac{5 \sqrt{2} }{2} [/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + { (\frac{5 \sqrt{2} }{2}) }^{2} [/tex]

[tex] {x}^{2} = {( \frac{5 \sqrt{2} }{2}) }^{2} + { (\frac{5 \sqrt{2} }{2}) }^{2} = \frac{25 \times 2}{4} + \frac{25 \times 2}{4} = \frac{50}{4} + \frac{50}{4} = \frac{100}{4} = 25[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{25} = 5[/tex]

The Greatest Common Factor of 7x^4y^3 - 15x^3y^5 is 27x^3y^3.

Answer: its A

Step-by-step explanation:

i did the test

When p = 0. 1, the mean of the sampling distribution would be 65. 5 and the standard deviation would be 7.6769.

When p = 0.5, the mean of the sampling distribution would be 327.5 and the standard deviation would be 12.7984 .

To find the mean and standard deviation of the sampling distribution of the sample proportion, we can use the following formulas:

p = 0.1

Mean:

μ p = n x p = 655 x 0.1 = 65.5

Standard Deviation:

σ_p = √(n x p x  (1 - p)) = √(655 x 0.1 x (1 - 0.1)) = √(655 x 0.1 x 0.9) = √(58.95)

σp = 7.6769

When p = 0.5

Mean:

μ p = n x p = 655 x 0.5 = 327.5

Standard Deviation:

σ p = √(n x p x (1 - p)) = √(655 x 0.5 x (1 - 0.5)) = √(655 x 0.5 x 0.5) = √(163.75)

σp = 12.7984

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0.20 is percent of observations fall between 0.7 and 0.9.

What use does percentage serve?

The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100. Consider that we are curious about the proportion of employed women who are female. If this proportion is equal to 1/2, then generally speaking, there is one employed woman for every two men.

Density curve consists of two line segments .

   first line goes from the point (0,1) to the points (0.7 , 1) . second line goes from (0.7 , 1) to (0.9 , 2 ) in the xy plane .

   then percentage of observation fall below 0.20 and is 0.20.

        percentage = 20% = 0.20

area of rectangle = ab

                        = 0.2 * 1

                        = 0.20

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Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.

Pricing strategies refer to the methods and techniques used by businesses or companies to set the prices of their products or services.

Let's first calculate the hourly rate Jasmine charges for cleaning a house with 2 bathrooms:

She charges $50 for a house with 3 bedrooms and 2 bathrooms, and it takes her 3 hours to clean it, so her hourly rate is:

⇒ $50 ÷ 3 hours = $16.67/hour

Now let's calculate the hourly rate she charges for cleaning a house with 3 or 4 bathrooms:

She charges $75 for a house with 3 to 4 bathrooms, and it takes her 4 hours to clean it, so her hourly rate is:

⇒ $75 ÷ 4 hours = $18.75/hour

Therefore, Jasmine makes $18.75/hour cleaning a larger house compared to $16.67/hour cleaning a smaller house.

To find out how much more Jasmine makes per hour cleaning a larger house compared to a smaller house, we can subtract the hourly rate for a smaller house from the hourly rate for a larger house:

⇒ $18.75/hour - $16.67/hour = $2.08/hour

So, Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.

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Answer:

5cm^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sorry, i can't "add up to five attachments" because i say only answer.

1.(−24,8)

2.[−3,1]

3.[−3,4]

4. (−3,5)

5 and 6 no answer (check my attachments)

7. (−∞,−8)v(4,+∞)

8 (−∞,1)v(7,+∞)

9. (−∞,−3]v[6,+∞)

10. (−∞,−3]v[2,+∞)

11. (−∞,∞)

12. (−∞,∞)

13. (−∞,−[tex]\frac{21}{4}[/tex]]v[[tex]\frac{15}{4}[/tex],+∞)

14.[-[tex]\frac{4}{5}[/tex],[tex]\frac{8}{5}[/tex]]

15. (-[tex]\frac{17}{3}[/tex];5)

16. (−∞,−14]v[22,+∞)

17. no answer (how 5 and 6)

18. (−∞,∞)

19. (−2,[tex]\frac{2}{3}[/tex])

20. (−∞,−4)v(−[tex]\frac{2}{3}[/tex],+∞)

Answer: Let's denote the length, width, and height of the cuboid as l, w, and h, respectively. We know that the shaded face is a square, which means that two of its dimensions are the same. Without loss of generality, let's assume that the dimensions of the square face are l and w.

Since the volume of the cuboid is 4900 cm³, we have:

lwh = 4900

Substituting l = 25 - w (since the length of the cuboid is 25 cm) and simplifying, we get:

(25 - w)w h = 4900

Now, we use the fact that the shaded face is a square. Since two of its dimensions are the same, we have:

l = w

Substituting this into the equation above, we get:

(25 - l)l h = 4900

Simplifying further, we have:

25l^2 - 4900 = 0

Solving for l using the quadratic formula, we get:

l = 14 or -14/5

Since the length of the cuboid cannot be negative, we have l = 14. Therefore, the length of one side of the square face is 14 cm.

Step-by-step explanation:

In the proportion, Gear A makes 120 turns when Gear B makes 90 turns.

What is Proportion?

A proportion is a statement that two ratios or fractions are equal. It shows the relationship between two or more quantities that are proportional to each other.

The gears have a fixed ratio of rotations, which is determined by the number of teeth on each gear.

To find out how many turns Gear A makes when Gear B makes 90 turns, we can set up a proportion:

=> [tex]\frac{36}{27} =\frac{ x}{90}[/tex]

where x is the number of turns Gear A makes.

To solve for x, we can cross-multiply:

=> 36 × 90 = 27 × x

=> 3240 = 27x

=> x = 120

Therefore, Gear A makes 120 turns when Gear B makes 90 turns.

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The possible range of scores is given as follows:

Anything from 21% to 59%.

The percentage that is typically assigned is given as follows:

40%.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The parameters for this problem are given as follows:

[tex]\pi = 0.4, n = 25[/tex]

Then the lower bound of the confidence interval is given as follows:

0.4 - 1.96 x sqrt(0.4 x 0.6/25) = 0.21.

The upper bound of the confidence interval is given as follows:

0.4 + 1.96 x sqrt(0.4 x 0.6/25) = 0.59.

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Scatterplots and correlation never prove causation. Causation may only be determined by well-designed experiments.

A scatterplot is a type of graph commonly used to observe and visually represent the relationships between variables. Variable values ​​are represented by dots. The position of the points on the vertical and horizontal axes indicates the value of each data point. Therefore, scatterplots use Cartesian coordinates to display the values ​​of the variables in the dataset. A scatterplot is also called a scatter graphs, scatter charts, or scattergrams.

Correlation means association, and more specifically, it measures how well two variables are related. Correlation analysis have three possible outcomes: Positive correlation, negative correlation, no correlation.

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Answer:

277.5

Step-by-step explanation:

first you multiply 37 * 90 then you get 3330 then you divide it by 12 and you get 277.5

Based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.

In statistics, a dataset is a collection of data that is organized in a specific way. Typically, a dataset consists of multiple data points, where each data point represents an observation or measurement of a particular variable or set of variables.

We can make some general observations to match the data sets to the appropriate MAD value without actually calculating them:

The MAD measures the average distance between each data point and the median of the data set.

Therefore, the larger the MAD value, the more spread out the data set is.

Data set 1 will have the smallest MAD value, since it is the most tightly clustered around the median.

Data set 3 will have the largest MAD value, since it is the most spread out around the median.

Data set 2 will have a MAD value between those of data sets 1 and 3.

Based on these observations, we can match the data sets to the appropriate MAD value as follows:

Data set 1 has the smallest MAD value (7).

Data set 2 has a medium MAD value (9).

Data set 3 has the largest MAD value (11).

Of course, without actually calculating the MAD values, we can't say for certain whether these matches are correct.

Therefore, based on the general properties of the MAD and the characteristics of the data sets, these matches seem reasonable.

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Answer: The pool is 40 feet long.

Step-by-step explanation:  60ft) = 2 x 100ft = 200ft. Answer. The pool is    40 feet long.

2091 square meters represents the total area of the figure.

What is the example polygon?

A polygon is any two-dimensional shape formed by straight lines. Triangles, hexagons, pentagons, and quadrilaterals are examples of polygons.

                               Polygons are flat two-dimensional shapes with straight sides that are completely closed. The sides should be straight, not curved. However, polygons can have any number of sides. The word polygon comes from the Greek word "polgonos". 

This figure is called a pentagon and has the shape of a trapezoid.

To find its area, we can calculate the area of the trapezoid, which is given by:

A = (b1 + b2)/2 * h

where b1 and b2 are the lengths of the parallel sides and h is the height.

In this case, the length of b1 is 43 meters and the length of b2 is 18 meters, and the height is 34 meters, so the area of the trapezoid is:

A = (43 + 16)/2 * 34 + (43 + 21) * 34

A = 1003 + 1088

A = 2091 square meters.

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Answer:

C. -7

Step-by-step explanation:

A rational expression will always be undefined when the denominator = 0 because we can't divide by 0.

-7 + 7 = 0 so -7 is the only number which makes the expression undefined

The weight of the pumpkins that Gina's class grew was measured.

a) There is a total of 23 pumpkins.

b) 7 pumpkins weigh 10 pounds.

c) The number of pumpkins that weigh 6 pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.

Based on the given information, we can complete the sentences as follows:

a) There is a total of 23 pumpkins.

To get this number, we need to add up the number of dots for each weight:

3 + 5 + 1 + 7 + 4 + 2 + 1 = 23

b) 7 pumpkins weigh 10 pounds.

To find the weight with the most dots, we look for the peak in the line plot, which corresponds to 10 pounds, and count the number of dots on this peak, which is 7.

c) The proportion of pumpkins that weigh 6 pounds to those that weigh 9 pounds is 3 times.

To find the number of pumpkins that weigh 6 pounds, we count the number of dots on the peak corresponding to 6 pounds, which is 3. To find the number of pumpkins that weigh 9 pounds, we count the number of dots on the peak corresponding to 9 pounds, which is 1. Multiplying the number of pumpkins at 9 pounds by 3, we get 3 x 1 = 3, which is the same as the number of pumpkins at 6 pounds. Therefore, the statement is true.

The complete question is:-

Gina's class measured the weights of the pumpkins that they grew.

A line plot named “Pumpkin Weights” shows data from six to fourteen pounds. Six has three dots. Eight has five dots. Nine has one dot. Ten has seven dots. Twelve has four dots. Thirteen has two dots. Fourteen has one dot. Fill in the boxes to complete the sentences below to make each statement true.

a)there is a total of ____ pumpkins.

b) 7 pumpkins weigh _____ pounds.

c) the number of pumpkins that weigh ____ pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.

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Answer:

Step-by-step explanation:

The total rainfall is given as 16

Average rainfall is given as 1.23

The average temperature is given as 22.8

we would add all of the weekly rain values

2.6 + 1.6 + 10.2 + 1.4 + 0.2 = 16

The total rainfall is 16

The average rainfall would be 16 divided by the total number of days that we have here:

16 / 13

= 1.23

The average rainfall is 1.23

total temperature

22.9 + 28.5 + 24.6 + 36.2 + 19 + 20.8 + 19.4 + 22.8 + 22.6 + 21.6 + 19.6 + 19.9 + 18.3

= 296.2

average = 296.2 / 13

= 22.8

average temperature is given as 22.8

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All real numbers make up the domain of a linear function, hence the domain of  [tex]f(x)=-5x+20x-7[/tex] is  [tex](-\infty , \infty )[/tex]  . The range of a linear function is also the set of all real numbers, hence   [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).

For the formula, [tex]y = 4x2 + 24x + 13[/tex]

All real numbers make up the domain of a polynomial function, hence the domain of y=4x2+24x+13 is [tex](-\infty , \infty )[/tex]

We can use calculus or the square root method to determine the function's range. At x=-3, where y=1, the function's minimal value is found. As a result, the function's range is  [tex][1, \infty )[/tex].

Using the formula [tex]f(x)=-5x+20x-7:[/tex]

Using related words together, we obtain [tex]f(x)=15x-7.[/tex]

Therefore, All real numbers make up the domain of a linear function, hence the domain of  [tex]f(x)=-5x+20x-7[/tex] is  [tex](-\infty , \infty )[/tex]  . The range of a linear function is also the set of all real numbers, hence   [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).

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Therefore, the rotated triangle has vertices at (-5, -10), (-3, -1), and (-4, -2), which forms a new triangle.

In mathematics, a vertex refers to a point where two or more lines, edges, or curves meet. In geometry, a vertex is a point where two or more edges of a polygon or polyhedron intersect. For example, in a triangle, each of the three points where the sides meet is a vertex.

A vertex is a fundamental unit of a graph, which is a collection of vertices connected by edges. Each vertex represents an entity or object, and the edges represent the relationships or connections between them. For example, in a social network graph, the vertices could represent individual users, and the edges could represent their friendships or connections with other users.

To perform a 270° counterclockwise rotation of a point about a center point, we can use the following formula:

[tex](x', y') = (x - a) * cos(theta) - (y - b) * sin(theta) + a, (x - a) * sin(theta) + (y - b) * cos(theta) + b[/tex]

where (x, y) is the original point, (x', y') is the rotated point, (a, b) is the center point, and theta is the angle of rotation in radians.

Let's first find the center point C(-5, -4) of the rotation. Then, we'll apply the formula to each vertex of the triangle to find its new location after the rotation.

[tex]Center point C = (-5, -4)[/tex]

Vertex P(-13, -3):

[tex]x' = (-13 - (-5)) * cos(270^{0} ) - (-3 - (-4)) * sin(270^{0} ) + (-5) = -5[/tex]

[tex]y' = (-13 - (-5)) * sin(270) + (-3 - (-4)) * cos(270) + (-4) = -10[/tex]

So, after the rotation, vertex P is at (-5, -10).

Vertex Q(-7, 3):

[tex]x' = (-7 - (-5)) * cos(270) - (3 - (-4)) * sin(270) + (-5) = -3[/tex]

[tex]y' = (-7 - (-5)) * sin(270) + (3 - (-4)) * cos(270) + (-4) = -1[/tex]

So, after the rotation, vertex Q is at (-3, -1).

Vertex R (-6, 2):

[tex]x' = (-6 - (-5)) * cos(270) - (2 - (-4)) * sin(270) + (-5) = -4\\y' = (-6 - (-5)) * sin(270) + (2 - (-4)) * cos(270) + (-4) = -2[/tex]

So, after the rotation, vertex R is at (-4, -2).

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Step-by-step explanation:

So what this question is asking is the volume of the cube. volume can be found with V=lwh or V=l^3 because it is a cube. So

V=(8)^3
V=512

The cube can fit 512 cubic inches.

Answer:

y = -2x + 5

Step-by-step explanation:

slope = rise/run = 2/-1 = -2

b = y-intercept = 5

y = -2x + 5

The series [tex]a_n=\frac{(-1)^{n+1}}{n}[/tex] is converges.

What is a series?

An n-arithmetic sequence is a sequence in which the difference d of successive terms is constant.

The general term of the arithmetic progression can be written using its first term [tex]a_1[/tex], tolerance [tex]d[/tex], and index [tex]n[/tex] as [tex]a_n=a_1+(n-1)d[/tex].

According to the alternating series test, if a sequence {b_n} satisfies the following three conditions:

[tex]b_n[/tex] is positive for all [tex]n[/tex].

[tex]b_n[/tex] is decreasing (i.e., [tex]b_n > = b_{n+1}[/tex] for all n).

[tex]\lim_{n \to \infty} b_n =0\\[/tex]

Then the alternating series [tex](-1)^n b_n[/tex] converges.

To apply the alternating series test to the sequence {a_n}, we first note that [tex]a_n = (-1)^{n+1}/n[/tex] satisfies condition 3, since [tex]\lim_{n \to \infty} \frac{1}{n} =0[/tex].

Next, we observe that [tex]a_n[/tex] is positive for n = 1, 3, 5, ... and negative for n = 2, 4, 6, ..., so [tex](-1)^n a_n = (-1)^{n+1}/n[/tex] is an alternating sequence.

Finally, we show that a_n is decreasing by considering the difference between successive terms,

[tex]a_{n+1} - a_n = (-1)^n/n - (-1)^{n+1}/(n+1)\\ = (-1)^{n} [(n+1)/(n(n+1))] \\= (-1)^{n}/n(n+1) < 0[/tex]

since n and n+1 are both positive. Therefore, a_n is decreasing.

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Scott Salman's net pay after subtracting all of his deductions is $1,620.26.

How To calculate Scott Salman's net pay?

To calculate Scott Salman's net pay, we need to first calculate his commission earnings and then subtract all of his deductions.

Commission Earnings:

3% of the first $20,000 in sales = $600

4% of the next $10,000 in sales = $400

6% of all sales over $30,000 = 6% × ($45,550 - $30,000) = $930

Total commission earnings = $600 + $400 + $930 = $1,930

Now we can calculate his gross pay by adding his commission earnings to his base salary:

Gross Pay:

Base salary = 0 (not given)

Commission earnings = $1,930

Total gross pay = $1,930

Next, we need to calculate his deductions. We'll assume the following rates for each deduction:

FICA: 7.65%

Medicare: 1.45%

Federal withholding: based on the IRS tax tables (not provided)

State disability insurance: 1%

State withholding: based on the state tax tables (not provided)

Retirement contribution: $45

Savings bond: $50

Charitable contributions: $20

Deductions:

FICA = 7.65% × $1,930 = $147.45

Medicare = 1.45% × $1,930 = $27.99

Federal withholding = based on the IRS tax tables (not provided)

State disability insurance = 1%×$1,930 = $19.30

State withholding = based on the state tax tables (not provided)

Retirement contribution = $45

Savings bond = $50

Charitable contributions = $20

Total deductions = $147.45 + $27.99 + $19.30 + $45 + $50 + $20 = $309.74

Finally, we can calculate Scott Salman's net pay by subtracting his total deductions from his gross pay:

Net Pay:

Gross pay = $1,930

Total deductions = $309.74

Net pay = $1,930 - $309.74 = $1,620.26

Therefore, Scott Salman's net pay after subtracting all of his deductions is $1,620.26.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

area of trapezoid

[tex]= \frac{sum~of~parallel~sides}{2} \times altitude\\69.6=\frac{sum~of~parallel~sides}{2} \times 8.7\\139.2=sum~of~parallel~sides \times 8.7\\sum~of~parallel~sides=\frac{139.2}{8.7} =16[/tex]

minimum parameter=16+2(8.7)=16+17.4=33.4 in

the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

We have two points p=(-7,-2) and E=(1,-9)

then the distance between PE is

d=√(1+7)²+(-9+2)²

d= √(64+49)

d=√113

the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

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