muriel is conducting research for a study about the work habits of employees in an office. she collects data by interviewing 10 employees out of a total a total of 40 employees that work in the office. what sampling method would provide her the most representative sample?

The probability that the number will be more than 7 or odd is 7/10.

The number more than 7 or odd is 1, 3, 5, 7, 8, 9, 10

So probability of 7 number is,

P(A) = number of favorable outcomes of an event /  total number of events occurring in a sample

P(A) = 7/10

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject because it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

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The ratio of the price of pints of beer to the price of cups of coffee if Jim chooses to buy 4 pints of beer and 9 cups of coffee is: b/c = 4b/9c , b/c = 1.125

Jim bought 3 pints of beer and 7 cups of coffee for $14, and the ratio of the price of pints of beer to the price of cups of coffee is 2:3,

To determine the cost of one pint of beer and one cup of coffee, let's solve the system of equations.

                     2b + 3c = 7 (dividing both sides of the equation by 7)

                                    2b/7 + 3c/7 = 1b/3.5 + c/2.333

                  = 1b + 1.5c

                  = 4.666... (dividing both sides of the equation by 3.5)

                              b/3.5 × 4 + c/2.333 × 9

                            = 14b/0.875 + c/0.259

                                       = 14.666...

Therefore, the ratio of the price of pints of beer to the price of cups of coffee if Jim chooses to buy 4 pints of beer and 9 cups of coffee is:

                       b/c = 4b/9c (multiplying both sides by 9c)

                                       b/c = 1.125

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A stratified random sample size is being used by Donald. He is segmenting the population into groups and choosing a representative sample of pupils from each category at random.

To examine the eating patterns of all pupils attending his school, Donald is utilising stratified random sampling. In this kind of sampling, the population is divided into strata, or groups, and a proportionate number of people from each category are randomly chosen to make up the sample. To make sure the sample is representative of the total community, Donald in this instance is grouping the pupils by grade level. Then he gathers information from the sample in order to make generalisations about the eating patterns of all the pupils enrolled in his school. A representative sample can be obtained and reliable population inferences can be made using stratified random sampling

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The expression as a sum or difference of logarithm is log(x^3) + log(√x + 1) - 2log(x - 2)

The expression is given as:

log [x^3 square root x 1/(x-2)^2

Rewrite properly as:

log [x^3 √x + 1/(x-2)^2]

Express the above expression as products and quotients

log [x^3 * √x + 1/(x-2)^2]

Apply the product and quotient of logarithm

log(x^3) + log(√x + 1) - log(x - 2)^2

Rewrite  as:

log(x^3) + log(√x + 1) - 2log(x - 2)

Hence, the expression as a sum or difference of logarithm is log(x^3) + log(√x + 1) - 2log(x - 2)

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Answer:

The product 12 × 15 in friendlier numbers is (10 + 2) × (10 + 5) = 180

Step-by-step explanation:

The parameter given are;

To 12 × 15 by changing the numbers into friendlier numbers

The product in 12 × 15 written with friendlier numbers (or in a simplified format can be given as follows;

12 × 15 = (10 + 2) × (10 + 5)

Which gives;

(10 + 2) × (10 + 5) = 10² + 10 × 5 + 2 × 10 + 2 × 5

From which we have;

10² + 10 × 5 + 2 × 10 + 2 × 5 = 100 + 50 + 20 + 10 = 180

Therefore;

12 × 15 = 180.

Answer:

a. Simplify each term. 49/2+0

Add 49/2 and 0.

49/2

The result can be shown in multiple forms.

Exact Form:

49/2

b. Replace the variable a with −13 in the expression.

−(−1/3)²b²−3(−1/3)³b²

Replace the variable b with −1 in the expression.

−(−1/3)²(−1)²−3(−1/3)³(−1)²

Simplify each term. −1/9+1/9 = 0

Combine fractions. 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.29 as a fraction is 29/100. Anytime you have a decimal, just turn it into a whole number and simplify it. However, 29/100 is already in its simplest form.

Answer:

i think it's 4^ 19

4^11/4^-8

4^ 11 +8

4^19

Answer:

- 7.2

Step-by-step explanation:

it is division and we need to take the reciprocal and multiply it will be -9/5. we need to simplify leaving us -7.2

Buss and Plomin's model of temperament proposes that there are three general temperaments: emotionality, activity, and sociability.

These temperaments are believed to be genetically based and to influence an individual's personality traits and behaviors throughout their life. Emotionality refers to an individual's tendency to experience strong emotional reactions, while activity refers to an individual's level of energy and impulsiveness.

Emotionality refers to an individual's tendency to experience and express emotions, such as fear, anger, and sadness.

Activity refers to an individual's level of physical and mental energy, and their tendency to seek out stimulation and engage in activities.

Sociability refers to an individual's preference for social interaction, including their level of interest in and enjoyment of socializing with others.

According to Buss and Plomin's model, these three temperaments are considered to be broad, genetically influenced traits that are present in varying degrees in every individual, and which can have a significant impact on a person's personality and behavior throughout their life.

Sociability, on the other hand, refers to an individual's degree of interest in social interaction and the degree to which they seek out social stimulation.

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The null and alternative hypotheses are:

H0: β1 = 0 (The slope is not significant.)

H1: β1 ≠ 0 (The slope is significant.)

Here,β1=0.0943seβ1=0.107α=0.05

Test the slope significance and find the t-test statistic.

We need to find the t-test statistic so that we can compare it with the t-distribution, whose distributional properties we know, to determine if we can reject or fail to reject the null hypothesis.t-test statistic is calculated by dividing the value of β1 by its standard error (seβ1) and taking the absolute value of this quotient.

t-test statistic = | β1/seβ1 | = |0.0943/0.107| = 0.881

The degrees of freedom (df) associated with this t-test are df = n - 2, where n is the sample size for the explanatory variable x.

In this problem, the decision rule and conclusion are as follows:

Decision Rule: Reject the null hypothesis if |t-test statistic| > tc where tc is the critical value obtained from the t-distribution with df degrees of freedom and a significance level of α/2 in each tail.

Conclusion: The slope is not significant if we fail to reject the null hypothesis, but the slope is significant if we reject the null hypothesis. Since the t-test statistic (0.881) is less than the critical value (1.987), we fail to reject the null hypothesis. Therefore, we conclude that the slope is not significant.

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The width of the rectangular backyard is 9 yards.

The width of the yard is three less than four times the length.

Therefore,

w = 4l - 3

Perimeter of a rectangle = 2l + 2w

where

l = length

w = width

Hence,

24 = 2l + 2(4l - 3)

24 = 2l + 8l - 6

24 = 10l - 6

24 + 6 = 10l

30 = 10l

l = 30 / 10

l = 3 yards

Hence,

w = 4(3) - 3

w = 12 - 3

w = 9 yards

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Answer: third number line

Step-by-step explanation:

Answer:

Here's one way to do it

Step-by-step explanation:

1. Solve the inequality for y

5x - y > -3

      -y > -5x  -  3

       y < 5x + 3

2. Plot a few points for the "y =" line

I chose

\(\begin{array}{rr}\mathbf{x} & \mathbf{y} \\-2 & -7 \\-1 & -2 \\0 & 3 \\1 & 8 \\2 & 13 \\\end{array}\)

You should get a graph like Fig 1.

3. Draw a straight line through the points

Make it a dashed line because the inequality is "<",  to show that points on the line do not satisfy the inequality.

See Fig. 2.

4. Test a point to see if it satisfies the inequality

I like to use the origin,(0,0), for easy calculating.

y < 5x + 3

0 < 0 + 3

0 < 3. TRUE.

The condition is TRUE.

Shade the side of the line that contains the point (the bottom side).

And you're done (See Fig. 3).

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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Step-by-step explanation:

In my opinion Option A is the correct answer because

Product of 3 and x = 3x

7.5 more than that = 3x + 7.5

Answer:

the answer is option A

Step-by-step explanation:

product of 3 and x = 3x

7.5 more than the product of 3 and x = 3x+7.5

Answer:

Maria

Step-by-step explanation:

Find the ratio of powdered mix to water for each drink.

For Maria:

(2/3 cup) / (2 gallon)

= 1/3 cup per gallon

For Franco:

(1 1/4 cup) / (5 gallon)

= (5/4 cup) / (5 gallon)

= 1/4 cup per gallon

Since 1/3 is bigger than 1/4, Maria's sports drink is stronger.

Answer:

45 degree..................................

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

Answer:

Step-by-step explanation:

x=0

Answer:

∠ 2 = 140°

Step-by-step explanation:

∠ 1 and ∠ 2 are alternate exterior angles and are congruent , so

∠ 2 = ∠ 1 = 140°

The probability of three numbers the same is  = 1/36.

Probability:

                   Probability is simply how likely something is to happen.

The maximum value of probability can be 1,that is,

                                   0 ≤ P ≤ 1

                                                  where P is the probability.

          A die has total six faces showing numbers 1,2,3,4,5 and 6.

A die is thrown three times,we have to find the probability that same number shows up in all thrown.

that is either,

                     1,1,1  or  2,2,2  or  3,3,3  or  4,4,4  or  5,5,5  or  6,6,6

Now,

      Throw the first die. It doesn't matter what number you get.

Again,

         Throw the second die. The probability of getting the same number is 1/6.

And again,

                 Throw the third die. The probability of getting the same number is again 1/6.

So,

      The probability of three numbers the same is = 1/6×1/6.

                                                                                    = 1/36

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The dot product of vectors a and b  || a |= 6,|| b ||= 4 and the angle between the vectors θ = π/3 is (c) 12.

The dot product of two vectors, we can use the formula:

a · b = ||a|| ||b|| cos(theta)

where ||a|| and ||b|| represent the magnitudes of vectors a and b, respectively, and theta is the angle between the vectors.

In this case, we are given that ||a|| = 6, ||b|| = 4, and the angle between the vectors is theta = π/3.

Substituting these values into the formula, we have:

a · b = 6 × 4 × cos(π/3)

To evaluate cos(π/3), we can use the fact that it is equal to 1/2. So we have:

a · b = 6 × 4 × 1/2

= 12

Therefore, the dot product of vectors a and b is 12.

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The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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True

In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.

When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.

The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.

If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.

If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.

In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.

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The algebraic expression that represents the given phrase is b + 15 = 180.

The algebraic expression that represents the phrase "the sum of the number of boys and 15 girls is 180" is:b + 15 = 180Explanation:Let's assume that the number of boys is "b".

According to the question, the total number of students in the class can be calculated by adding the number of boys (b) to the number of girls (15) which is equal to 180 students.Using algebra,

we can write this statement as an equation: b + 15 = 180Hence, the algebraic expression that represents the given phrase is b + 15 = 180

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The reference angle of 17π/3 is π/3.

The reference angle of -7π/12 is 5π/12.

The reference angle of -31π/6 is π/6.

The acute angle formed by the terminal arm or side and the x-axis is known as the reference angle. There is always a positive reference angle. The reference angle is, in other words, the angle formed by the terminal side and the x-axis. It must always be positive and less than 90 degrees.

Given that first angle is 17π/3

= 15π/3 + 2π/3

= 5π + 2π/3

The reference angle of 17π/3 is

π - 2π/3

= (3π - 2π)/3

= π/3

The second angle is -7π/12

The reference angle of -7π/12 is

= π - 7π/12

= (12π - 7π)/12

= 5π/12

The third angle is -31π/6

= -30π/6 - π/6

= -5π -π/3

The reference angle of -31π/6 is

= π/6

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