Sharon watched 1/2 of a movie in the morning, and she watched some more at night. By the end of the day, she still had 1/3 of the movie left to watch. How much of the movie did Sharon watch at night?

In essence, a function is a rule that assigns to each value of the input set (also known as the domain), a unique value of the output set (also known as the range).

A function is a fundamental mathematical concept that is used to describe the relationship between two sets of values.

To understand the idea of a function, imagine a machine that takes in an input and produces an output. The input values are the domain of the function, and the output values are the range. A function can be represented as an equation, a graph, or a table. For example, the equation f(x) = x + 3 represents a function that takes in an input value x and produces an output value that is 3 greater than the input value.

One of the key features of a function is that each input value must have a unique output value. This means that if you input the same value into the function twice, you should get the same output value both times. In mathematical terms, we say that a function is well-defined if it has a unique output value for each input value.

Functions are used in a wide range of mathematical applications, from algebra and calculus to statistics and data analysis. They provide a powerful tool for describing and analyzing relationships between different sets of values.

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Answer: 57.27

Step-by-step explanation:

using the proportion we have x= (5*126)/11= 57.27

a. (H0): p = 0.50 (the politician is supported by exactly 50% of voters). (H1): p > 0.50 (the politician is supported by more than 50% of voters).

b. Sample proportion = 42/70 = 0.60 (or 60%).

c. Test statistic = (0.60 - 0.50) / sqrt(0.50 * (1 - 0.50) / 70) ≈ 1.61

d. The value and conclusion cannot be determined without knowing the chosen significance level (α) or having information about the critical value or p-value associated with the test statistic.

a. The null hypothesis (H0) in this case would be P = 0.50, indicating that the politician is supported by exactly 50% of the voters. The alternative hypothesis (Ha) would be p ≠ 0.50, suggesting that the proportion differs from 50%.

b. To calculate the sample proportion, we divide the number of voters supporting the politician (42) by the total number of voters surveyed (70):

Sample proportion (p) = 42/70 = 0.60 (rounded to 2 decimal places).

c. The test statistic (z) can be computed using the formula:

z = (p - P) / √(P(1 - P) / n),

where p is the sample proportion, P is the null hypothesis proportion, and n is the sample size. In this case, P = 0.50 and n = 70. Substituting these values, we have:

z = (0.60 - 0.50) / √(0.50(1 - 0.50) / 70) = 2.26 (rounded to 2 decimal places).

d. To determine the value of the test statistic, we compare the computed test statistic (z = 2.26) with the critical values corresponding to the chosen level of significance (e.g., 0.05). By comparing the test statistic with the critical values from a standard normal distribution table, we can evaluate the statistical significance of the results and make conclusions about the claim made by the politician.

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Answer: $25

Step-by-step explanation:

2500/100 = 25

The exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

The exterior angle adjacent to the largest interior angle in a triangle is equal to the sum of the other two interior angles.

Let's call the measures of the angles in the triangle x, x, and 2x. Then,

x + x + 2x = 180 degrees,

so 4x = 180 degrees, and

x = 45 degrees.

The largest interior angle is 2x, or 90 degrees. The exterior angle that is adjacent to this angle is equal to 180 degrees minus the interior angle, which is 180 - 90 = 90 degrees.

So the exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

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Answer:

A

Hope I helped

Answer:90 the height of the tallest man is 90

To solve this problem, we first need to find the total number of marbles in the goblet. Adding up the number of red, green, and blue marbles, we get a total of 2 22 + 6 66 + 4 44 = 13 32 marbles, Next, we need to find the probability of choosing a green marble on the first draw.

There are 6 66 green marbles out of 13 32 total marbles, so the probability is 6 66 / 13 32, Since we didn't put the first marble back in the goblet, there are now 13 31 marbles left in the goblet and one less green marble. So, the probability of choosing a green marble on the second draw, given that we already chose a green marble on the first draw, is 5 65 / 13 31.

To find the probability of both events happening together (choosing a green marble on the first draw and another green marble on the second draw), we multiply the probabilities of each event: (6 66 / 13 32) * (5 65 / 13 31) = 0.073 or approximately 7.3%.


To find the probability of picking two green marbles one after another without replacement, we can use the following steps:

1. Calculate the total number of marbles in the goblet:
Total marbles = 22 red marbles + 6 green marbles + 4 blue marbles = 32 marbles

2. Find the probability of picking a green marble on the first draw:
P(Green1) = (number of green marbles) / (total number of marbles)
P(Green1) = 6/32

3. Update the number of marbles after the first green marble is drawn:
Total marbles remaining = 32 - 1 = 31 marbles
Green marbles remaining = 6 - 1 = 5 marbles

4. Find the probability of picking a green marble on the second draw:
P(Green2) = (number of green marbles remaining) / (total number of marbles remaining)
P(Green2) = 5/31

5. Calculate the probability of both events occurring:
P(Green1 and Green2) = P(Green1) * P(Green2)
P(Green1 and Green2) = (6/32) * (5/31)

6. Simplify the probability:
P(Green1 and Green2) = 30/992

So, the probability of picking two green marbles consecutively without replacement is 30/992.

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annual salary of the 6 employees of a toy company is given below:

Correct option is: Statements (1) and (2) TOGETHER are not sufficient.

The average, sometimes referred to as the arithmetic mean, is calculated by dividing the total number of variables by their sum. Mean, however, represents the data's average. The mean is the sum of the data divided by the total of observations in statistics.

If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.

x, x + 6300, x + (2 × 6300), x + (3 ×6300), x + (4 × 6300), x + (5 × 6300)

Avg = ( x + ( x + 5 × 6300 )) / 2

Avg = ( 2x + 5 × 6300 ) / 2

The range of the 6 annual salaries is $31,500

Thus, no new information, Statement 2) can be derived from Statement 1) itself.

So, Statements (1) and (2) TOGETHER are not sufficient, this is correct option.

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The complete question is as follows:

What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.

(2) The range of the 6 annual salaries is $31,500.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Answer:

1.2 mph

Step-by-step explanation:

3/5 = 0.6

Multiply 0.6 by 2 to find the distance gone in a whole hour

0.6*2 = 1.2

(3.6x - 1.9)4 = 28.4

3.6x -  1.9 = 7.1

3.6x = 7.1 + 1.9

3.6x = 9

x = 9 / 3.6

x = 2.5 (value of x)

3.6(2.5) - 1.9 = 7.1 (side length)

you want to multiply it by 4 because right now its only showing one side. perimeter is all 4 sides combined

The correct answer is (B) I and IV.

If Fcalculated > Ftable, then the p-value is less than the significance level (usually 0.05), which means we reject the null hypothesis that the two sets of calcium data have the same variance. Therefore, the conclusion is that the difference in standard deviations for the two instrumental methods is significant. This corresponds to statement I.

Furthermore, if the null hypothesis is rejected, it means the alternative hypothesis is accepted, which is that the data does not come from populations with the same standard deviation. This corresponds to statement IV.

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Answer:

80,800

Step-by-step explanation:

Antoya's overall profit is $23.00.

To solve this problem, let's break it down step by step.

First, let's consider the purchase of two bracelets. Antoya paid $5.00 each for them, so the total cost for the two bracelets is 2 * $5.00 = $10.00. She later sold each bracelet for $15.00, which means the total revenue from selling the two bracelets is 2 * $15.00 = $30.00.

Next, let's look at the purchase of three bracelets. Antoya paid $8.00 each for them, so the total cost for the three bracelets is 3 * $8.00 = $24.00. She then sold each bracelet for $9.00, which means the total revenue from selling the three bracelets is 3 * $9.00 = $27.00.

To find the profit or loss, we need to calculate the net gain or loss by subtracting the total cost from the total revenue. For the two bracelets, the net gain is $30.00 - $10.00 = $20.00. For the three bracelets, the net gain is $27.00 - $24.00 = $3.00.

To find the overall profit or loss, we add up the net gains from the two transactions. $20.00 + $3.00 = $23.00.

Therefore, Antoya's overall profit is $23.00.

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Answer:

I believe the answer is $70

Step-by-step explanation:

hope I could help

Answer:

The ratio of their surface areas would 1:9 and the ratio of their volumes would be 1:27

Step-by-step explanation:

Given Info: The sides of two cubes are in ratio of 1:3. We can assign one square x and the other square 3x.

We know that the area of a square is its side squared, and that a cube has 6 sides. So thus if we assign one side of the cube x we can assume that surface area is 6x^2:

Surface Area of Cube #1= 6x^2

Surface Area of Cube #2= 6((3x)^2) = 6(9x^2) = 54x^2

Ratio of Surface Area: 6x^2 : 54x^2 = 6:54 = 1:9

Now for the volume we know that it is equivalent to one side cubed. So after assigning x to one cube, we can assume that volume would be x^3.

Volume of Cube #1= x^3

Volume of Cube #2= (3x)^3 = 27x^3

Ratio of Volume: x^3: 27x^3 = 1:27

Hope this helps!

Answer:

Below in bold.

Step-by-step explanation:

y = 2x²-4

First find x in terms of y:

2x² = y - 4

x² = (y - 4)/2

x = √ [(y - 4)/2]

Now replace x by the inverse f-1(x) and y by x:

f-1(x) = √ [(x - 4)/2]  (Note: it's the positive square root only)

Answer:

A: It would be 24 points per game.

B: It would be 15 points per game

C: 33.33%

Step-by-step explanation:

A explanation:

100% of 12 is 24

12 + 12 = 24

B explanation:

25% of 12 = 3

12 + 3 = 15

C explanation:

12/18 = 66.66%

100 - 66.66 = 33.33%

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To investigate whether there is convincing evidence, at a 5 percent level of significance, that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle, the researcher should use a linear regression t-test.

1. The researcher collects data on hand length and 100-meter freestyle completion time for twenty randomly selected swimmers.
2. Calculate the correlation coefficient (r) to measure the strength and direction of the relationship between hand length and freestyle completion time.
3. Perform a linear regression analysis to obtain the slope (b) and the y-intercept (a) of the best-fit line.
4. Conduct a linear regression t-test to determine if the slope (b) is significantly different from zero at a 5 percent level of significance.
5. If the t-test results in a p-value less than 0.05 (5 percent level of significance), there is convincing evidence that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle.

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The measure of the mid - segment is 53 .

Given :

the measures of the bases of a trapezoid are 35 and 71.

What is trapezoid ?

A trapezoid is a four-sided shape which has one pair of sides as parallel. It is basically a two-dimensional shape or figure similar to a square etc .

Mid segment :

A mid segment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

A trapezoid mid segment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.

Measure of mid segment = sum of two bases / 2

= 35 + 71 / 2

= 106 / 2

= 53

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To plant 10 acres of land, the farmer should plant 6.25 acres of corn and 3.75 acres of soybeans. This allocation maximizes the farmer's profit given the assumptions of the problem.

To determine how much of each crop to plant on 10 acres of land, we need to consider the profit per acre for each crop and the total profit that can be obtained by planting a combination of the two crops.

From the problem statement, we know that the profit per acre for corn is $300 and the profit per acre for soybeans is $200. We also know that the total amount of money available to the farmer is $2500.

Let x be the number of acres of corn to plant, and y be the number of acres of soybeans to plant. Then we have the following constraints:

x + y = 10 (the total area planted is 10 acres)

300x + 200y ≤ 2500 (the total profit cannot exceed $2500)

To solve this problem, we can use linear programming techniques. We want to maximize the objective function:

P = 300x + 200y

subject to the constraints above. We can graph the feasible region determined by the constraints, and then find the corner points of this region. The maximum value of P occurs at one of these corner points.

The feasible region is a triangle with vertices at (0, 0), (8.33, 1.67), and (10, 0). Evaluating the objective function at each of these vertices gives:

P(0, 0) = 0

P(8.33, 1.67) = $2416.67

P(10, 0) = $3000

Therefore, the maximum profit of $3000 occurs when the farmer plants 10 acres of corn and 0 acres of soybeans.

However, this requires planting more than the available land. The next best option is to plant 6.25 acres of corn and 3.75 acres of soybeans, which yields a profit of:

P(6.25, 3.75) = $2125

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Answer:

12 inches

Step-by-step explanation:

The distance between \(M\)and \(N\), which are the midpoints of segments \(AB\) and \(CD\) is \(12cm\).

Segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

Line is defined as a straight \(1D\) figure having no thickness and extending infinitely in both directions.

We have,

\(AB=BC=CD=6cm\),

And, \(M\)and \(N\)  are the midpoints of segments \(AB\) and \(CD\).

According to question,

\(AB=BC=CD=6cm\),

So,

Total length of line is \(18cm\).

As \(M\) and \(N\) are midpoints of   and \(AB\) and \(CD\),

So,

\(MN=18-(AM+BN)\)

\(MN=18-6\)

\(MN=12cm\)

Hence, we can say that the distance between \(M\)and \(N\), which are the midpoints of segments \(AB\) and \(CD\) is \(12cm\).

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Answer:

277.46

Step-by-step explanation:

√131 lies between 11 and 12.

The numbers that include natural numbers and zero are called whole numbers.

Given is the square root of 131.

We can write the square root of 131 as -

√131 = 11.45

We can write the whole numbers as -

11 < 11.45 < 12

Therefore, √131 lies between 11 and 12.

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Step-by-step explanation:

an = 7 + 2(n-1)

   or     an =  5 + 2n

When using Romberg integration, the Romberg method is an iterative process that improves the accuracy of the approximation by extrapolating values from a table of previous approximations. The notation R3,3 refers to the third row and third column of this table.

The Romberg integration method is known to provide an approximation of order O(h^k), where h is the step size and k is the number of iterations. In this case, R3,3 indicates that the Romberg method has been performed for three iterations.

Since the order of the Romberg approximation is equal to the number of iterations, the approximation of order for R3,3 would be 3. Therefore, the approximation of order for R3,3 is 3.

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Answer:

 Perimeter of the polygon p = 24

Step-by-step explanation:

Step(i):-

Given the vertices of a polygon are

P(0,4) ,Q( 5,4) ,R( 5,-3) and S(0,-3)

The distance of PQ

 \(a = PQ = \sqrt{(4-4)^{2} +(5-0)^{2} } = \sqrt{25} =5\)

The distance of QR

\(b = Q R= \sqrt{(-3-4)^{2} +(5-5)^{2} } = \sqrt{49} =7\)

The distance of RS

\(c = RS = \sqrt{(0-5)^{2} +(-3+3)^{2} } = \sqrt{25} =5\)

The distance of PS

\(d = PS = \sqrt{(0-0)^{2} +(-3-4)^{2} } = \sqrt{49} =7\)

Step(ii):-

Perimeter of the polygon

       = sum of all sides of polygon

p = a+ b+ c+ d

p = 5+7+5+7

p = 24

Final answer:-

 Perimeter of the polygon p = 24

Answer:

137

Step-by-step explanation:

38 + 48 = 86

86/2 = 43

180 - 43 = 137