A couple has four children. what is the probability that they would have four boys?

The probability that sample is greater than 418 will be is 6.533.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

Here we have

\(\mu=397.64,n=40,\sigma=20\)

According to central limit theorem, the sampling distribution of mean will be normal with mean

\(\mu_{\bar{x}}=\mu=397.64\)

and standard deviation

\(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{40}}=3.1623\)

The z-score for\(\bar{x}=418\) is

\(z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{418-397.34}{3.1623}=6.533\)

Therefore, the probability that sample is greater than 418 will be

\(P(\bar{x} > 418)=P(z > 6.533)\)

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Incomplete Question

Carbon dioxide (CO2) is one of the primary gases contributing to the greenhouse effect and global warming. The mean amount of CO2 in the atmosphere for March 2013 was 397.34 parts per million (ppm). Suppose 40 atmospheric samples are selected at random in May 2013 and the standard deviation for CO2 in the atmosphere is σ = 20 ppm. (1 pt.)

c) Suppose the sample mean CO2 level is 400. Is there any evidence to suggest that the population mean CO2 level has increased?

Answer:

1.10

2.49z^4

Step-by-step explanation:

1.What I did was change 1/2 to a decimal and then go from there::0.5(8)-(-4)+2 ::0.5(8)=4-(-4)=8 because of KCC then 8+2=10

2.The power of a product is equal to the product of it's factors raised to the same power

The solutions of the given system of equations are: x = -20/7 and y = -128/7.

The given system of equations is:2x - y = 168y = 4(4x - 32)

To solve the system of equations, we can use the method of substitution.

The second equation gives us the value of y in terms of x. Let's substitute the value of y in the first equation using the second equation.2x - y = 168y = 4(4x - 32)Substitute y = 4(4x - 32) in the first equation2x - 4(4x - 32) = 168Simplify by distributing- 14x + 128 = 168Add 14x to both sides128 = 168 + 14xSimplify168 + 14x = 128Add -168 to both sides14x = -40Simplify by dividing both sides by 14x = -40/14x = -20/7

Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. We'll use the second equation. y = 4(4x - 32)y = 4(4(-20/7) - 32)y = -128/7

Therefore, the solutions of the given system of equations are: x = -20/7 and y = -128/7.

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The ordered pair given in the first row of the table can be written as (8, f(8)).

f(3) is equal to 7.

f(x) = -5 when x is -6 or -2.

The table represents a function where the input values (x) correspond to the output values (f(x)). Let's analyze the given information to complete the statements:

The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (8, f(8)). This means that when x is equal to 8, the corresponding function value is f(8).

To find f(3), we look for the row in the table where x is equal to 3. From the given table, we can see that when x is 3, the corresponding function value f(x) is 7. Therefore, f(3) is equal to 7.

Similarly, to find when f(x) is equal to -5, we look for the rows in the table where the function value is -5. From the table, we can see that when x is equal to -6 and -2, the function value f(x) is -5. Therefore, we can say that f(x) = -5 when x is -6 or -2.

In summary:

The ordered pair given in the first row of the table can be written as (8, f(8)).

f(3) is equal to 7.

f(x) = -5 when x is -6 or -2.

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Answer:

45

Step-by-step explanation:

6^2 + 3√9

=36 + (3 x 3)

=36 + 9

= 45

Answer:

45

Step-by-step explanation:

6^2 = (6x6)

36+3 √9

you can simplify √9 to 3

36+3(3)

36+9

45

Answer:

22.50

Step-by-step explanation:

The test value of z is 2.86, and the critical value of z is 2.17. Therefore, the correct answer is (a)To test the claim that the mean price of houses in an area is greater than $145,000, the researcher uses a hypothesis test with a significance level of 2%.

The null hypothesis (H₀) assumes that the mean price is not greater than $145,000, while the alternative hypothesis (H₁) assumes that the mean price is greater than $145,000.The test statistic used in this case is the z-score. In this case, the sample mean price is $149,759, and the alternative hypothesis assumes that the population mean is greater than $145,000. The formula for the z-score becomes (149,759 - 145,000) / (24,600 / √36). Simplifying this equation gives a z-score of 2.86. The critical value of z is determined based on the significance level and the type of test (one-tailed or two-tailed). Since the alternative hypothesis assumes the mean is greater, it is a one-tailed test. At a significance level of 2%, the critical value of z is 2.17. Comparing the test value of z (2.86) to the critical value of z (2.17), we find that the test value exceeds the critical value. This means that we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean price of houses in the area is greater than $145,000. Therefore, the correct answer is (a), with a test value of z equal to 2.86 and a critical value of z equal to 2.17.

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Answer:

Step-by-step explanation:

Diameter = 20 cm → radius = 10 cm

Each triangle has its side equal to radius = 10 cm

Each shaded region is the difference of area of the sector and triangle

Each sector is 60° as triangles are equilateral

Area of circle is:

Area of each triangle is:

So the shaded area is:

Since 100π is the area of circle, the shaded area is:

Correct choice is D

Learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called Adaptive learning

Adaptive learning platforms utilize algorithms to tailor the learning experience for individual students based on their needs, abilities, and learning progress.

By analyzing data and feedback, adaptive learning systems can dynamically adjust the content, pace, and difficulty level to optimize learning efficiency and personalize the educational journey for each student.

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Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The true solution to the equation \(\(x + 5 - \sqrt{x} = 3\)\) is \(\(x = \frac{4}{9}\)\), and there are no extraneous solutions.

To find the true solution(s) to the equation, we need to solve for x and check if the obtained solutions satisfy the original equation. The extraneous solution(s), if any, will be the solutions that do not satisfy the original equation.

To solve the equation, we can start by isolating one of the square root terms. Rearranging the equation, we have:

\(\sqrt{x + 5} = 3 + \sqrt{x}\).

The equation can be evaluated as:

\(\sqrt{x + 5} - \sqrt{x} &= 3 \\(\sqrt{x + 5})^2 &= (3 + \sqrt{x})^2 \\x + 5 &= 9 + 6\sqrt{x} + x \\6\sqrt{x} &= -4 \\\sqrt{x} &= \frac{-2}{3} \\x &= \frac{4}{9}\end{align*}\)

Therefore, the true solution to the equation \(\(x + 5 - \sqrt{x} = 3\)\) is \(\(x = \frac{4}{9}\)\), and there are no extraneous solutions.

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The complete question:

Solve the following equation and identify the true solution(s) as well as the extraneous solution(s):

\(\sqrt{x + 5} - \sqrt{x} = 3\).

Answer:

Step-by-step explanation:

Take 17 away from 1:00 = 12:43

Take 17 away from 1:43 = 1:26

Take 17 away from 2:26 = 2:09

Take 17 away from 3:09 = 2:52

There we are: at the time which the watch says now.

Now let's see what the correct time should be:

at 12:43 it is really 1:00

at 1:26 it is really 2:00

at 2:09 it is really 3:00

at 2:52 it is really 4:00

However, it says the watch stopped 6 hours ago meaning that the time should be 10:00 as 4 + 6 = 10.

Answer:

Perimiter :: 24

Area :: 28

Answer:

strong negative

Step-by-step explanation:

When comparing histograms, they should have the same horizontal axis this statement is false .

Histograms are graphical representations of data distribution, where the horizontal axis represents the range of values and the vertical axis represents the frequency or density of occurrence of those values.

When comparing histograms, it is not necessary for them to have the same horizontal axis. The alignment of the horizontal axis depends on the specific characteristics of the data being represented and the purpose of the comparison. Histograms can have different ranges, intervals, or units on the horizontal axis if the data being analyzed or compared differ in those aspects.

Comparing histograms with different horizontal axis can be useful when examining different data sets or comparing data distributions with varying scales or ranges. It allows for a visual assessment of the similarities and differences between the distributions and provides insights into the data patterns and characteristics being analyzed.

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True. When comparing histograms, they should have the same horizontal axis to ensure accurate comparisons between the data sets.

When comparing histograms, it is essential to have the same horizontal axis. Histograms are used to visualize the distribution of data, and the horizontal axis represents the different categories or intervals of the data. If the histograms being compared have different horizontal axes, it becomes challenging to make accurate comparisons between the data sets.

Having the same horizontal axis allows for a direct comparison of the frequencies or counts of data points falling within each category or interval. It ensures that the data is being compared consistently across the histograms.

For example, if one histogram represents the ages of students in a class with intervals of 10 years (0-10, 10-20, 20-30, etc.), and another histogram represents the ages of students in a different class with intervals of 5 years (0-5, 5-10, 10-15, etc.), comparing them directly would not provide an accurate representation of the data.

Therefore, to make meaningful comparisons between histograms, it is crucial to have the same horizontal axis, representing the same categories or intervals of the data.

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the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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With a greater mean value , we can conclude that the sixth period class test was better than the second period .

Second period class:

Mean = (55+70+6*75+6*80+2*85+3*90+95)/20

Mean = 1590/20 = 79.5

Sixth period class:

Mean = (65+3*75+5*80+6*85+3*90+2*95)/20

Mean = 1660/20 = 83

Therefore, From the mean values , we can infer that students performed better in test for the sixth period class than the second .

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Answer: B

Step-by-step explanation:

Because they are on opposite sides and they are outside the parallel lines

Answer:

ten x plus forty equals one- hundred

Step-by-step explanation:

i think verbal means word form right? lol

Answer:

Ten times X plus forty equals one hundred.

Step-by-step explanation:

Is this the answer u need or is this not what they mean by verbal description?

The mean, standard deviation, of the average number of moths in 30 traps is approximately 0.5 ± 0.018 and is approximately 0.5 respectively. The probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

The mean of the average number of moths in 30 traps can be calculated as the mean of a sample of 30 trap counts, where the mean of each sample follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30) (using the standard error of the mean formula). Therefore, the mean of the average number of moths in 30 traps is:

mean = 0.5 ± 0.1/sqrt(30) = 0.5 ± 0.018

So the mean of the average number of moths in 30 traps is approximately 0.5 ± 0.018.

The standard deviation of the average number of moths in 30 traps can also be calculated using the standard error of the mean formula:

standard deviation = standard error of the mean * sqrt(sample size)

standard deviation = 0.5/sqrt(30) * sqrt(30) = 0.5

So the standard deviation of the average number of moths in 30 traps is approximately 0.5.

Using the central limit theorem, we can assume that the sample mean of the 30 traps follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30). We want to find the probability that the average number of moths in 30 traps is greater than 0.4.

To do this, we can standardize the sample mean using the formula:

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

z = (0.4 - 0.5) / (0.5/sqrt(30)) = -1.8257

Using a standard normal distribution table or calculator, we can find the probability that Z is greater than -1.8257, which is approximately 0.965. Therefore, the probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

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Based on the vertices in the table above, the scale factor is equal to: B. 3.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

Scale factor = -6/-2

Scale factor = 3.

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The probability density function (PDF) f(x) of a continuous random variable x describes the probability of the random variable taking on any given value, while its distribution function F(x) describes the cumulative probability that the random variable is less than or equal to a given value.

a. The probability density function (PDF) of a continuous random variable x is a function that describes the probability of the random variable taking on any given value. It is written as f(x) and is defined as the probability that x is equal to a given value, divided by the width of the interval that contains this value.

b. The distribution function of a continuous random variable x is a function that describes the probability that the random variable is less than or equal to a given value. It is written as F(x) and is defined as the cumulative probability that the random variable is less than or equal to the given value.

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The electric monorail slows down by 124 ft between t = 1 and t = 5 seconds. To find the change in the rate of slowing down for the electric monorail transport between t = 1 and t = 5 seconds, we need to calculate the difference in its deceleration at these two points in time.

Given the deceleration formula: 2t + 25 ft/s², let's find the deceleration rates at t = 1 and t = 5:

Deceleration at t = 1:
2(1) + 25 = 2 + 25 = 27 ft/s²

Deceleration at t = 5:
2(5) + 25 = 10 + 25 = 35 ft/s²

Now, we will find the difference in deceleration between these two points in time:

Difference = Deceleration at t = 5 - Deceleration at t = 1
Difference = 35 ft/s² - 27 ft/s²
Difference = 8 ft/s²

The electric monorail slows down by 8 ft/s² between t = 1 and t = 5 seconds. However, this is not listed as one of your options. If you meant to ask how many feet it slows down in total between t = 1 and t = 5 seconds, we can calculate the integral of the deceleration formula:

∫(2t + 25)dt from t = 1 to t = 5

The integral of (2t + 25) is t² + 25t + C. Now, we can evaluate it:

(5² + 25*5) - (1² + 25*1) = (25 + 125) - (1 + 25) = 150 - 26 = 124 ft

So, the electric monorail slows down by 124 ft between t = 1 and t = 5 seconds. Your answer: 124 ft/sec.

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The value of x that will make the considered parallelogram ABCD a rhombus is 4 units.

Rhombus is a parallelogram whose all sides are of equal lengths.

For this problem, the missing figure is attached below.

We see that the angle between the diagonals is \((3x- 12)^\circ\)

It is given that ABCD is a parallelogram.

For ABCD parallelogram to be a rhombus, its diagonals need to be perpendicular to each other.

Perpendicular lines have 90° angle between them.

Thus, we need:

\((3x- 12)^\circ = 90^\circ\)

Evaluating value of x:

\((3x- 12)^\circ = 90^\circ\\3x - 12 = 90\\\text{Adding 12 on both the sides}\\3x = 102\\\text{Dividing both the sides by 3}\\\\x = 12/3 = 4\)

Thus, the value of x is 4

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Answer:

ANSWER:   x=34

Step-by-step explanation:

E2020

Ethan would need to score a 304 on exam B in order to do equivalently well as he did on exam A.

To compare Ethan's scores on the two exams, we need to standardize his scores by expressing them in terms of standard deviations above or below the mean.

We can do this using the following formula:

Standardized Score = (Raw Score - Mean) / Standard Deviation

For exam A, Ethan's standardized score would be:

Standardized Score = (800 - 700) / 50 = 10 / 50 = 0.2

This means that Ethan scored 0.2 standard deviations above the mean on exam A.

For exam B, we can use the same formula to find out what score Ethan would need to get in order to do equivalently well as he did on exam A:

Standardized Score = (Raw Score - 300) / 20

If we set this equation equal to the standardized score Ethan got on exam A (0.2), we can solve for the raw score Ethan needs to get on exam B:

0.2 = (Raw Score - 300) / 20

4 = Raw Score - 300

304 = Raw Score

Hence, Ethan would need to score a 304 on exam B in order to do equivalently well as he did on exam A.

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