what are the common factors of 24 and 36
A. 1,3,4,9,18
B. 1,2,4,6,12
C. 1,2,3,4,1,2
D. 1,2,3,4,6,8,12

Social scientists gather data from samples instead of populations because c. populations are often too large to test.

Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.

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Answer:

Step-by-step explanation:

In the given cirlce, the value of x is 15

From the question, we are to determine the value of x in the given diagram

From the given information,

We have a circle and we are given the angles subtended by the arcs at the center of the circle.

We know that the sum of angles in a circle is 360°.

Then,

We can write that

(8x - 10)° + (6x)° + (10x + 10)°  = 360°

Solving for x

8x - 10 + 6x + 10x + 10  = 360

Collect like terms

8x + 6x + 10x - 10 + 10 = 360

24x = 360

Divide both sides by 24

24x / 24 = 360 / 24

x = 15

Hence, the value of x is 15

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To create a valid matched pair test, the researcher should consider random assignment, similarity, blinding, sample size, and duration.

To create a valid matched pair test, the researcher should consider the following:

Random assignment: The pairs should be randomly assigned to the treatment and control groups to avoid bias.

Similarity: The pairs should be matched based on similar characteristics that could affect the outcome, such as age, gender, prior algebra performance, and socioeconomic status.

Blinding: The researcher should ensure that the students do not know which group they are assigned to, and the person administering the test should also be blinded to the group assignments.

Sample size: The sample size should be large enough to provide sufficient statistical power to detect a meaningful difference between the two groups.

Duration: The length of the study should be sufficient to allow for meaningful differences to occur between the groups, but not so long that other factors could interfere with the outcome.

By considering these factors, the researcher can create two groups that are well-matched and comparable, allowing for a valid matched pair test to be conducted.

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z1 = (lb - lb) / lb = z1, z2 = (lb - lb) / lb = z2. If the percentage is high, it means many women are within the limits and few are excluded. If the percentage is low, it means many women are excluded.

To find the percentage of women whose weights are within the specified limits, we need to calculate the z-scores for the lower and upper limits and then find the area under the normal distribution curve between those z-scores.

First, we calculate the z-score for the lower limit: z1 = (lower limit - mean) / standard deviation.
z1 = (lb - lb) / lb = z1

Next, we calculate the z-score for the upper limit: z2 = (upper limit - mean) / standard deviation.
z2 = (lb - lb) / lb = z2

Using the z-table or a calculator, we can find the area between z1 and z2. This area represents the percentage of women whose weights are within the specified limits.

Now, to determine if many women are excluded from those specifications, we need to look at the percentage calculated in the previous step. If the percentage is high, it means many women are within the limits and few are excluded. If the percentage is low, it means many women are excluded.

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To start, you would need the relevant data, such as the number of successful attempts and the total number of trials for each group or time interval. Then, you can perform a statistical test, like the chi-square test or a two-proportion z-test, to evaluate if the difference in probability is statistically significant at the 0.05 level. If the resulting p-value is less than 0.05, it would indicate a significant difference in the probability of solving the puzzle within one minute.

To answer your question, we would need to conduct a statistical analysis to compare the probability of solving the puzzle within one minute in two different groups or conditions. We would also need to establish a null hypothesis and an alternative hypothesis and use a statistical test such as a t-test or a chi-square test to determine whether the observed difference in probability between the two groups is statistically significant at the 0.05 level, which means that there is less than a 5% chance that the observed difference is due to chance alone. Without more information about the specific groups or conditions being compared, it is difficult to provide a definitive answer.

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Answer:

Domain :

R (all real numbers)

Range :

{y element R : y>=-9}

For the given triangle FGH, ∠x is 36.4°.

What is the definition of a triangle?

Triangles are polygons with three sides and three vertices in geometry. This figure is two-dimensional and has three straight sides. A triangle is a polygon with three sides. The sum of a triangle's three angles equals 180°. The triangle is contained inside a single plane. Triangles are categorized into three types based on their sides.

Based on its sides, a triangle is classified into three types:

Scalene Triangle - Each side is different in length.

Isosceles Triangle - A triangle with two sides that are equal in length and one side that is not.

Equilateral Triangle - A triangle with three equal-length sides.

Now,

For triangle FGH,

perpendicular=5

Hypotenuse=8.8

then, sin x=P/H=5/8.8

x=sin⁻¹(0.5681)

x=36.4°

Hence,

           ∠x is 36.4°.

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The simplified boolean expression for f(a, b, c, d) is a'c' + d + b'cd.

Provided expression: f(a, b, c, d) = (a' + c)'d + c'(a + bd')

1. Apply De Morgan's Laws

Recall the De Morgan's Laws:

- (A + B)' = A' · B'

- (A · B)' = A' + B'

Using De Morgan's Laws, we can rewrite the expression as follows:

f(a, b, c, d) = (a'c')'d + c'(a + bd')

2. Distributive Law

We can apply the distributive law to the second term c'(a + bd'):

f(a, b, c, d) = (a'c')'d + c'a + c'bd'

3. Apply De Morgan's Laws again

We can apply De Morgan's Laws to the first term (a'c')':

f(a, b, c, d) = (a' + c)d + c'a + c'bd'

4. Distributive Law (again)

We can apply the distributive law to the first term (a' + c)d:

f(a, b, c, d) = a'd + cd + c'a + c'bd'

5. Simplify

By observing the terms, we can identify some common factors:

In the first term a'd + c'a, we can factor out a': a'd + c'a = a'd + a'c' = a'(d + c')

In the last term c'bd', we can factor out b': c'bd' = b'cd'

Now we can simplify the expression further:

f(a, b, c, d) = a'(d + c') + cd + b'cd'

6. Factor out common terms

We can factor out c' from the first two terms and factor out d from the last two terms:

f(a, b, c, d) = a'c' + c'd + cd + b'cd'

7. Combine like terms

We can combine the terms with c'd and cd:

f(a, b, c, d) = a'c' + (c'd + cd) + b'cd'

Simplifying further, we can observe that c'd + cd = c'd + cd + 0 = (c' + c)d = 1 · d = d:

f(a, b, c, d) = a'c' + d + b'cd

Final simplified form:

f(a, b, c, d) = a'c' + d + b'cd

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Answer:

50 in²

Step-by-step explanation:

What is the area in square inches of the trapezoid below.

Area of a trapezoid = 1/2(b1 + b2) h

Where

b1 = First base = 8in

b2 = Second base = 12in

h = Height = 5in

Area of trapezoid = 1/2(8 + 12) × 5

= 1/2 × 20 × 5

= 50 in²

The area of the trapezoid is 50 square inches

Answer:

The answer is "64".

Step-by-step explanation:

Given:

8-sided fair die

output of Die = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

if the Dice is thrown two times. so, the possible outputs are as follows:

\(\to 8 \times 8=64\)

\(\texttt{ = (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),}\\ \ \ \texttt{(1,7),( 1, 8),(2,1),(2,2),(2,3),(2,4),}\)

\(\texttt{(2,5),(2,6),(2,7),(2,8),(3,1), (3,2),}\\ \texttt{(3,3),(3,4),(3,5),(3,6),(3,7),(3,8) ,}\\\texttt{(4,1),(4,2),(4,3), (4,4),(4,5),(4,6),} \\\)

\(\texttt{(4,6),(4,7),(4,8),(5,1),(5,2),(5,3),}\\\texttt{(5,4),(5,5),(5,6),(5,7),(5,8),(6,1),}\\\texttt{(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),}\)

\(\texttt{(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),} \\\texttt{(7,6),(7,7),(7,8),(8,1),(8,2),(8,3),}\\ \texttt{(8,4),(8,5),(8,6),(8,7),(8,8)}\)

That's why the product is 64.

Answer:

He can fill 38 pint containers

Answer:

450

Step-by-step explanation:

750 x .80 (20% decrease) =  600

600 x .75 (25% decrease) = 450

Answer:

Step-by-step explanation:

Answer:

The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.

Step-by-step explanation:

Answer:i believe it is length times width

Step-by-step explanation:

The ODE has a solution for any point (xo, yo) where yo is a real number and y(x) is continuous in the neighborhood of (xo, yo), and it has a unique solution for any point (xo, yo) where yo is a real number and the interval of consideration includes xo. The solution to the ODE via separation of variables is y = -1/((1/10)x^2 + C), and the particular solution can be found by substituting the initial condition y(xo) = yo into the general solution.

(a) For what points (xo, yo) does this ODE have any solution? Explain.

To determine the points (xo, yo) for which the given ODE has a solution, we need to consider the conditions under which the equation is well-defined and solvable. In this case, the equation is \(y' = xy^2/5.\)

Since y' is a derivative with respect to x, for the equation to have a solution at a particular point (xo, yo), the function y(x) must be differentiable at that point. This means that yo must be a real number and the function y(x) must be continuous in the neighborhood of (xo, yo).

Therefore, the ODE has a solution for any point (xo, yo) where yo is a real number and y(x) is continuous in the neighborhood of (xo, yo).

(b) For what points (xo, yo) does this ODE have a unique solution? Explain.

To have a unique solution for the ODE, we need to satisfy the conditions for existence and uniqueness of solutions. In this case, the equation is \(y' = xy^2/5.\)

The existence and uniqueness theorem states that if a function and its derivative are continuous on a closed interval [a, b], then there exists a unique solution to the initial value problem y(xo) = yo for any point (xo, yo) within that interval.

Therefore, the ODE has a unique solution for any point (xo, yo) where yo is a real number and the interval of consideration includes xo.

(c) Find this solution via separation of variables.

To find the solution of the given ODE via separation of variables, we can rewrite the equation as follows:

\(dy/y^2 = (x/5) dx\)

Integrating both sides:

∫(dy/y²) = ∫(x/5) dx

Using the power rule for integration, we have:

\(-1/y = (1/10)x^2 + C\)

Where C is the constant of integration. Solving for y:

\(y = -1/((1/10)x^2 + C)\)

This represents the general solution of the given ODE. To find the particular solution, we need to use the initial condition y(xo) = yo. Plugging in the values xo and yo into the general solution, we can solve for the constant C and obtain the unique solution for the initial value problem.

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Answer:

5b; when b=3.4 the distance Sandra rode is 17 miles.

Step-by-step explanation:

Given that:

Sandra rode her bike 5 times as many as miles as Barbara.

It means that 5 will be multiplied by the distance rode by Barbara.

Distance by Sandra = 5b

When b=3.4 miles

Distance by Sandra = 5(3.4)

Distance by Sandra = 17 miles

Hence,

5b; when b=3.4 the distance Sandra rode is 17 miles.

The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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Answer:

Step-by-step explanation:

To determine which statement must be true about the mean, median, and mode of the data, we need to analyze the bar graph provided.

We see that the data is not normally distributed, but rather skewed to the right. Therefore, the mean will be greater than the median, as the mean is affected by outliers and extreme values, which in this case will pull it towards the higher end.

Furthermore, since there is no single value that appears more frequently than any other, there is no mode for this data set.

Therefore, the statement that must be true is:

The mean number of food items donated is greater than the median number of food items donated. (Option K)

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Answer:

Distance=y•x

Step-by-step explanation:

You need to multiply the time by the distance to get the total distance e oer hour

Answer:

65 inches

Step-by-step explanation:

The concept that relates how much one variable changes as another variable changes is Slope.

Slope is a numerical representation of how inclined a line is with respect to the horizontal. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts changes in y or the vertical axis with changes in x or the horizontal axis.

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Answer: It's a 50/50 chance of winning or losing.

Step-by-step explanation:

Answer:

The leading coefficient in the polynomial 10x2 + 3x - 5 is 10.

Step-by-step explanation:

To find the leading coefficient of the polynomial function, we must first locate the leading term. In a polynomial function, the leading term is the term containing the highest power of x. In this polynomial function, the leading term is 10x2. The leading coefficient of a polynomial function is the coefficient of the leading term, and so the leading coefficient of this polynomial function is 10.

Answer:

The third one

Step-by-step explanation:

Answer:

Slope intercept form is y=-5/2x+9

Step-by-step explanation:

the y-intercept is −9 and the point is (0,−9)

the x-intercept is −3.6 and the point is (−3.6,0)

Explanation:

First, we find the slope and y-intercept

Now, the equation of a line is of the form

y=mx+c

Where,

m is the slope of the line and c is the y-intercept.

Let us write the given line in the standard form:

y=−5x2−82⇒y=−5x2−9

Comparing y=mx+c

to the given equation, y=−5x2−9

m=−52 and c=−9⇒Slope =−52and

y-intercept =−9

Next, we work out the

x-intercept.

the x-intercept is the point where the line cuts the x-axis. i.e. to find the point when y=0.

The equation in slope-intercept form for the line is y = -5x/2+9

The slope intercept formula y = mx + c is used when you know the slope of the line to be examined and the point given is also the y intercept (0, c).

Given that, a line has equation 5x + 2y = 18

The general form of the slope-intercept form for the line is y = mx+c, where m is the slope and c is the y-intercept.

Therefore, the required equation will be =

5x+2y = 18

2y = 18-5x

y = -5x/2+9

Hence, the equation in slope-intercept form for the line is y = -5x/2+9

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Answer:

The number of people living in both countries is 1.704 x 10⁹

Step-by-step explanation:

Given;

Population of people in China, = 1.381 x 10⁹

Population of people in united states, = 3.23 x 10⁸

The total number of people living in both countries is given as;

Total population = 1.381 x 10⁹ + 3.23 x 10⁸

Total population = 1.381 x 10⁹ +  0.323 x 10⁹

Total population = (1.381 + 0.323) x 10⁹

Total population = 1.704 x 10⁹

Therefore, the number of people living in both countries is 1.704 x 10⁹

The vector orthogonal to both ⟨3,−2,0⟩ and to ⟨0,−2,−1⟩ of the form is ⟨2, 3, -6⟩. It is vector to both the coordinates mentioned in the question, by using cross product.

To find a vector orthogonal to both ⟨3,−2,0⟩ and to ⟨0,−2,−1⟩ of the form, we can use the cross product of the two vectors. The cross product of two vectors is a vector that is orthogonal to both of the original vectors.

The cross product of ⟨3,−2,0⟩ and ⟨0,−2,−1⟩ is calculated as follows:
= ⟨2, 3, -6⟩. Therefore, the vector orthogonal to both ⟨3,−2,0⟩ and to ⟨0,−2,−1⟩ of the form is ⟨2, 3, -6⟩.

Note that any scalar multiple of this vector will also be orthogonal to both of the original vectors. For example, ⟨4, 6, -12⟩ and ⟨-2, -3, 6⟩ are also orthogonal to both ⟨3,−2,0⟩ and to ⟨0,−2,−1⟩.

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