Dawn has mismatched socks in a drawer. She has 3 white, 2 red, and 1 green sock. Dawn randomly selects two socks from the drawer. What is the probability that she selects a matching pair? Show your work

The one-sample Z test is used when we want to know whether our sample comes from a particular population. The name of the one-sample Z test tells us the general research design of studies in which this statistic is selected to test hypotheses.

For instance, we are doing research on data collected from successive cohorts of students taking the Elementary Statistics class. We may want to know if this particular sample of college students is similar to or different from college students in general. The one-sample Z test is used only for tests of the sample mean. Thus, our hypothesis tests whether the average of our sample (M) suggests that our students come from a population with a know mean (m) or whether it comes from a different population.

The statistical hypotheses for one-sample Z tests take one of the following forms, depending on whether your research hypothesis is directional or nondirectional. In the equations below m1 refers to the population from which the study sample was drawn; m is replaced by the actual value of the population mean.

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The number of expected double crossover progeny when multiply by the total number of progeny is 47.

When chromosomal pieces are swapped out twice, it is known as a double crossover. In the case of a double crossing, the two ends of the chromosome are still parental, but another sister chromatid sequence has "swapped" into the space between the crossovers;

When homologous chromosomes are combined, crossovers happen.

Chromatids from various chromosomes can be aligned. Exchange chromatids from, for example, segments a collision between two identical chromosomes occurs at an similar spot along their respective lengths. they are After swapping the segments, the chromatids have split between the point of contact and the chromatids' tips.

We have,

number of double crossovers is 0.305 x 0.155 x 1000

so 0.305 x 0.155 x 1000 = 47

So number of expected double crossover progeny is 47.

Test cross:

Progeny whithered wing smooth body and speck body

Genetic distance between sm and sp is 15.5

15.5 = 2x + 33 /1000 x 100

155 = 2x + 33

2x = 155-33

x = 122/2

x = 61.

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Answer:

The number of chirps per minute is 72

Step-by-step explanation:

Here, using the formula given, we want to find the number N representing the number of chirps per minute.

To get this, we shall simply substitute the value of 58 for T in the equation;

Thus;

58 = 50 + (N-40)/4

58 -50 = (N-40)/4

8 = (N-40)/4

4 * 8 = N -40

32 = N -40

N = 40 + 32

N = 72

Answer:

\(y = 5x + 3\)  

I hope this helps!

Bob paid $600 for the computer before tax. California has an 8% sales tax, which means that the tax amount is $600 x 8% = $48. Therefore, Bob had to pay a total of $600 + $48 = $648 for the computer including the sales tax.

Bob bought a computer in California for $600. California has a sales tax of 8%, which means that an additional $600 x 8% = $48 must be added to the price of the computer to account for the tax. So, Bob paid a total of $600 + $48 = $648 for the computer, including the sales tax. This is an example of how the sales tax is calculated and added to the purchase price of a product.

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Answer:

The difference of two squares can be written in the form of (a^2 - b^2), where a and b are algebraic expressions.

From the given options, the expression that can be written in the form of (a^2 - b^2) is:

a) 8x^2 - 16y^2

We can write 8x^2 as (2x)^2 and 16y^2 as (4y)^2.

Therefore,

8x^2 - 16y^2 = (2x)^2 - (4y)^2

This is the difference of two squares, where a = 2x and b = 4y.

Therefore, the answer is option a) 8x^2 - 16y^2.

Step-by-step explanation:

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Answer:

c. g is the variable

Step-by-step explanation:

Answer:

The only true answer is that g is the variable

C

The minimum number of jumps required for the frog to go from (0,0) to (4,4) and each distance is 5 units is 3.

Graph Theory, in discrete mathematics, is the study of the graph. A graph is determined as a mathematical structure that represents a particular function by connecting a set of points. It is used to create a  pairwise relationship between objects.

The graph is made up of vertices (nodes) that are connected by the edges (lines). The applications of the linear graph are used not only in Maths but also in other fields such as Computer Science, Physics and Chemistry, Linguistics, Biology, etc. In real-life also the best example of graph structure is GPS, where you can track the path or know the direction of the road.

We have, the initial position of frog =(0,0)

The endpoint of the jump of frog is (4,4)

The minimum number of jumps required for the frog to go from (0,0) to (4,4) and each distance is 5 units is 3

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The derivative of f(x) = 2/x using the limit definition is

f'(x) = -2 / (x²).

To differentiate the function f(x) = 2/x using the limit definition of the derivative, we start by applying the definition:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

Let's substitute the function f(x) = 2/x into the expression:

f'(x) = lim(h->0) [2/(x + h) - 2/x] / h

Next, let's simplify the expression inside the limit:

f'(x) = lim(h->0) [(2x - 2(x + h)) / (x(x + h))] / h

f'(x) = lim(h->0) [-2h / (x(x + h))] / h

Now, we can cancel out the h in the numerator and denominator:

f'(x) = lim(h->0) -2 / (x(x + h))

Finally, we can take the limit as h approaches 0:

f'(x) = -2 / (x²)

Therefore, the derivative of f(x) = 2/x using the limit definition is

f'(x) = -2 / (x²).

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ANSWER

6.6 ft

EXPLANATION

The section of the course will contain a 12 foot ladder leaning against a 10 foot wall.

Let us draw a diagram of the situation:

This situation forms the shape of a Right Angle Triangle.

x represents the distance of the bottom of the ladder from the wall.

We can find the value of x by using Pythagoras rule:

From the question:

hyp = 12 ft

opp = 10 ft

adj = x ft

So, we have that:

The wall should be 6.6 ft from the bottom of the ladder.

Answer:

4 15 inches of chains

Step-by-step explanation:

Let's start on Friday's temperature, the problem says that it was -7°F and it was half of the temperature on Thursday, which means on Thursday is was:

-7*2 °F = -14°F.

On Thursday, the temperature was 8°F higher than on Wednesday, then on Wednesday it was:

-14°F - 8°F = -22°F.

On Wednesday the temperature was twice as low as for Tuesday, then on Tuesday it was:

-22°F/2 = -11°F.

On Tuesday, the temperature was 6°F colder than on Monday, then on Monday it was:

-11°F + 6°F = -5°F.

Therefore, the recorded temperature for Monday was -5°F.

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

the desired line is y = 3x - 4

Step-by-step explanation:

The slope formula is not needed here.  If the given line is y = 3x - 2, we can see immediately that the slope is 3, in both cases.

Find the y-intercept as follows:

y = mx + b => 5 = 3(3) + b, or b = -4

Then the desired line is y = 3x - 4

Answer:

Given,

p (x)=2x-3

g (x)=6x+4

p (x)×g (x)=?

Step-by-step explanation:

p (x)×g (x)=(2x-3)(6x+4)

=2x (6x+4)-3 (6x+4)

=12x^2+8x-18x-12

=12x^2-10x-12

Answer: k=m-7/4

Step-by-step explanation:

m-7=4k

m-7/4=k

k=m-7/4

Answer:

? = 120°

Step-by-step explanation:

the central angle is the same as the arc that subtends it , that is

? = 120°

The improper integral ∫ 1/x dx from 0 to ∞ is divergent. The improper integral ∫ 1/x dx from 0 to ∞ represents the integral of the function 1/x with respect to x over the interval from 0 to positive infinity.

To determine whether this integral is convergent or divergent, we need to evaluate it.

Let's split the integral into two parts: from 0 to 1 and from 1 to ∞.

∫(0 to 1) 1/x dx

This part of the integral is a finite integral, and it can be evaluated as:

∫(0 to 1) 1/x dx = [ln|x|] (0 to 1) = ln(1) - ln(0)

However, ln(0) is undefined, so this part of the integral does not converge.

Now let's evaluate the second part of the integral:

∫(1 to ∞) 1/x dx

This integral represents the area under the curve of the function 1/x from 1 to ∞. This is a well-known integral and is known to diverge. As x approaches infinity, the value of 1/x approaches 0, but it never reaches 0. Therefore, the area under the curve keeps increasing indefinitely, and the integral diverges.

Since either part of the integral diverges, the overall integral ∫ 1/x dx from 0 to ∞ is divergent.

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The advantages of writing in standard form include :

Standard form, also known as scientific notation, is a way of writing very large or very small numbers in a compact way. It is used in many fields, including science, engineering, and mathematics.

Therefore, standard form offers a more compact way of writing out the full number, and it is also easier to compare this number to other numbers in standard form.

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The slope of the line that passes through the points, (3, 4) and (-4, -5) is: A. 9/7.

The slope of a line can be calculated by using the slope formula, which is given as:

Slope (m) = change in y / change in x or rise / run.

Given that the following points lie on a line:

The slope of the line would be solved using the slope formula as explained below:

Slope (m) = change in y / change in x = (-5 - 4) / (-4 - 3)

m = -9 / -7

Slope (m) = 9/7.

Therefore, the slope is identified as:

a. 9/7.

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The rate of a molecule's migration through an electric field during electrophoresis is determined by factors such as the molecule's size, shape, and charge, as well as the properties of the electric field and the medium through which the molecule is moving.

The rate of a molecule's migration through an electric field during electrophoresis is determined by several factors. The size and shape of the molecule play a significant role. Larger molecules will migrate more slowly than smaller molecules, and molecules with more complex shapes will also migrate more slowly due to increased resistance to movement through the gel or solution. Secondly, the charge of the molecule is also a determining factor. Molecules with a higher charge will migrate more quickly than those with a lower charge.

The strength of the electric field and the properties of the gel or solution used for electrophoresis can also affect the rate of migration. The rate of a molecule's migration through an electric field during electrophoresis is a complex process with multiple factors influencing the final outcome.

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Answer:

\(y = \frac{x}{3} \)

Step-by-step explanation:

divide both sides by 3 to get the answer

9514 1404 393

Answer:

  c) 5n +25q = 365

     2q -4 = n

Step-by-step explanation:

The number of nickels (n) is 4 less than twice the number of quarters (q), so one of the equations is ...

  2q -4 = n

The face value is 365 cents, so another equation is ...

  5n +25q = 365

These equations seem to match choice C.

The value of x is 8

A quadrilateral with one pair of parallel sides. It is a typical mathematical shape that is employed in numerous disciplines. The area of a trapezoid is computed by multiplying the height by half of the sum of the lengths of the two bases.

Given that trapezoid PQRS ~ TUVW are similar;

So, VW/RS = UT/QP

      x/12 = 6/9

      x = 8

Therefore, the value of x is 8

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Trapezoid A trapezoid is a four-sided shape with one pair of parallel sides According to the question The value of x is 8

A trapezoid is a four-sided shape with one pair of parallel sides. It has two non-parallel sides, or legs, and two parallel sides, or bases. The bases are usually of different lengths, and the sides are typically not equal. The angles of a trapezoid are not necessarily all the same size, but the two opposite angles are always equal. Trapezoids can be found in everyday objects like the shape of a deck, a rectangular door frame, or a sloped roof. Trapezoids can also be found in geometry, where they are used to calculate the area and perimeter of the shape.

Given that trapezoid PQRS ~ TUVW are similar;
So, VW/RS = UT/QP
     x/12 = 6/9
     x = 8
Therefore, the value of x is 8

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A fraction that is sometimes used to approximate pi is 22/7.

One example of a fraction that is sometimes used to approximate pi is 22/7. This fraction is an approximation of pi that has been used for centuries, even though it is not an exact value of pi.

It is a good approximation that is accurate to within about 0.04%, which makes it useful in many practical applications.

The fraction 22/7 comes from dividing the circumference of a circle by its diameter, which is the definition of pi. While the exact value of pi is an irrational number that cannot be expressed as a fraction, 22/7 is a commonly used approximation that is easy to remember and calculate with. However,

there are more accurate approximations of pi that can be used for more precise calculations, such as 355/113 or 3.14159265359.

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Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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Answer:

A.

Step-by-step explanation:

The answer would be A because it has the same rate of change at the line in the graph.

The statistical unit for John's study is A. the 35 countries. John is trying to estimate the average literacy rate across all countries, and he randomly selected 35 countries to research their literacy rates. The statistical unit in this case is the individual country, as each country's literacy rate is being used to calculate the average.

The statistical unit for John's study is A. the 35 countries. This is because John's study is based on a sample of 35 countries that he randomly selected. The sample is used to estimate the average literacy rate for all countries. The sample size of 35 countries is large enough to provide a representative sample of the population of countries. If John had selected only a few countries or individuals, his estimate of the average literacy rate would not have been reliable. However, by selecting a sample of 35 countries, John can make a more accurate estimation of the average literacy rate for all countries. In conclusion, the statistical unit for John's study is the sample of 35 countries that he researched to estimate the average literacy rate for all countries.

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