Let S be the universal set, where:
S= {1, 2, 3,..., 18, 19, 20}

Let sets A and B be subsets of S, where:

The percentage of students still writing the test is

23.75%

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign( %).

For example if there are 80 student in a class and 20 are boys, the percentage of boys in the class is ; 20/80 × 100 = 25%

The total number of students that finished the test before 1.75hours = 17+12+22 = 61

The number of students left in the class = 80-61

= 19

Therefore percentage of of the student still taking the test after 1.75 = 19/80 × 100

= 1900/80

= 23.75 %

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Answer: The answer is C

Answer:

  C.  (2x+3)/(x+2)

Step-by-step explanation:

You want the expression representing f(x)/g(x) where f(x) = 2x² -x -6 and g(x) = x² -4.

The ratio of the functions can be simplified by canceling common factors.

  [tex]\dfrac{f(x)}{g(x)}=\dfrac{2x^2-x-6}{x^2-4}=\dfrac{(x-2)(2x+3)}{(x-2)(x+2)}=\boxed{\dfrac{2x+3}{x+2}}\qquad\text{matches choice C}[/tex]

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The percentage of females that do not satisfy the requirement is given as follows:

55.17%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 998, \sigma = 202[/tex]

The proportion that does not satisfy the requirement is the p-value of Z when X = 1025(proportion less than 1025), hence:

Z = (1025 - 998)/202

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

Hence the percentage is given as follows:

0.5517 x 100% = 55.17%.

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Answer:

Step-by-step explanation:

A

Answer:

Step-by-step explanation:

Product means multiply.

-300

Answer:

Robert's semi-monthly salary is $2,500. This means he earns $5,000 per month. The Medicare tax rate is 1.45%, so his employer pays 1.45% of his salary for Medicare tax. This is equal to $72.50 per month. Since he is paid semi-monthly, his employer pays $36.25 for his Medicare tax each pay period. Therefore, the answer is C. $36.

The graphs of functions f(x) and g(x) compare as -

Option B: They have the same y-intercept, but the graph of g(x) rises more quickly over time.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function f(x) is given as [tex]f(x)=500(1.015)^x[/tex].

The function f(x) is given as [tex]g(x)=500(1.021)^x[/tex].

The y-intercept of both functions is 500, which represents the initial amount in the savings accounts.

To compare the rates at which the functions rise over time, we need to compare their growth factors, which are 1.015 and 1.021 for f(x) and g(x), respectively.

Since 1.021 is greater than 1.015, the function g(x) grows at a faster rate than f(x).

Therefore, the correct answer is -

Option B: They have the same y-intercept, but the graph of g(x) rises more quickly over time.

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Answer:

The given function f(x) is:

f(x) = { 1, -π < x < 0

{ -1, 0 < x < π

Since the function is odd and has period 2π, the Fourier series will only have sine terms. The Fourier series of f(x) can be written as:

f(x) = Σ[b_n sin(n x)], where n >= 1

where b_n is the n-th Fourier coefficient, given by:

b_n = (1/π) ∫[0,π] f(x) sin(n x) dx

We can evaluate the integral to find the Fourier coefficients:

b_n = (1/π) ∫[0,π] f(x) sin(n x) dx

= (1/π) [ ∫[0,π/2] sin(n x) dx - ∫[π/2,π] sin(n x) dx ]

= (1/π) [ -cos(n x)/n |[0,π/2] + cos(n x)/n |[π/2,π] ]

= (1/π) [ (-cos(n π/2)/n + 1/n) - (cos(n π) - cos(n π/2))/n ]

= (1/π) [ (1 - (-1)^n) / n ]

Therefore, the Fourier series of f(x) is:

f(x) = Σ[(1 - (-1)^n)/(n π) sin(n x)]

Where the sum is taken over all odd integers n.

The height of the pyramid is 6 units.

What is the formula of the volume of a pyramid?

The volume of a pyramid is [tex]V = ( \frac{1}{3} ) \times B \times h[/tex], where B is the area of the base and h is the height of the pyramid.

In this case, the base is a square with sides of length 5, so the area of the base is [tex]B = 5 \times 5 = 25 \: square \: units[/tex]

We are also given that the volume of the pyramid is 50 cubic units.

So we are putting these values into the formula and solve for h,

[tex]50 = ( \frac{1}{3} ) \times 25 \times h \\ 150 = 25 \times h \\ h = 6[/tex]

Therefore, the height of the pyramid is 6 units.

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Correct question is "The volume of a pyramid is 50 cubic units. The base is a square with sides of length 5. What is the height?

(A) 2 Units

(B)10 Units

(C) 6 Units

D) 4 Units"

Answer:

To solve the system of equations x + y + 3 = 0 and 2x + 3y - 4 = 0 graphically, we can plot the two lines and find their point of intersection.

First, let's rearrange the equations to the slope-intercept form y = mx + b:

x + y + 3 = 0 => y = -x - 3

2x + 3y - 4 = 0 => y = (-2/3)x + 4/3

Now we can plot these two lines on a graph:

  |          

3  |      o    

  |     /    

2  |    /      

  |   /      

1  |  /        

  | /        

0  |/          

  ------------

   0  1  2  3

The first line has a y-intercept of -3 and a slope of -1, so we plot a point at (0, -3) and then go down one unit and right one unit to plot another point. We can then draw a line through these two points.

The second line has a y-intercept of 4/3 and a slope of -2/3, so we plot a point at (0,4/3) and then go down two units and right three units to plot another point. We can then draw a line through these two points.

The point where the two lines intersect is the solution to the system. From the graph, we can see that the intersection point is approximately (-3,0).

Therefore, the solution to the system is x = -3 and y = 0.

Answer:

63 cm²

Concept used:

Area of a parallelogram = b · h

(b: base and h: height of the parallelogram)

Step-by-step explanation:

The given figure is a parallelogram.

Required Area = 9 * 7

= 63 cm²

The height of the object at any given time t is given by the function h(t) = -t^2 + 6t + 10. To find the maximum height, we need to find the vertex of the parabola described by this function.

The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the y-coordinate of the vertex.

In this case, a = -1, b = 6, and c = 10, so we have:

t = -b/2a = -6/(-2) = 3

To find the maximum height, we need to evaluate h(3):

h(3) = -(3)^2 + 6(3) + 10 = 9 + 18 + 10 = 37

Therefore, the maximum height of the object is 37 units, which occurs when t = 3 seconds.

We can infer that each runner will cover 352 yards in total using division.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

For instance, "12 divided by 4" translates to "12 shared into 4 equal groups," which would be 3 in our example.

This is represented by the division sign, or obelus, in mathematics.

So, calculate as follows: Using division

= 1760 / 5

= 352

Therefore, we can infer that each runner will cover 352 yards in total using division.

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Correct question:

The relay race is just over one mile long, approximately "1,760" "1" /"4" yards. If Jack and 4 other people each run a leg of the relay, how many yards will each runner run? Justify your answer using an estimation strategy.

Answer:

110 in 2 hours

Step-by-step explanation:

by using division and knowledge of unit rates, we can divide 220 by 2 and get 110, we also have to divide 4 by 2 which results in 2. hope this helps

the infusion rate is 88.89 ml/hr or 88.89 gtt/min.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Next, we can use the formula:

Flow rate (ml/hr) = (Volume infused ÷ Time in hours)

Flow rate (ml/hr) = (800 ml ÷ 9 hours)

Flow rate (ml/hr) = 88.89 ml/hr (rounded to two decimal places)

Finally, we can convert the flow rate from ml/hr to drops per minute (gtt/min) using the drop factor of 60 gtt/ml:

Flow rate (gtt/min) = Flow rate (ml/hr) x Drop factor (gtt/ml) ÷ 60 (min/hr)

Flow rate (gtt/min) = (88.89 ml/hr x 60 gtt/ml) ÷ 60 (min/hr)

Flow rate (gtt/min) = 88.89 gtt/min (rounded to two decimal places)

Therefore, the infusion rate is 88.89 ml/hr or 88.89 gtt/min.

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Answer:

The x-intercepts of a quadratic function are the points where the graph of the function intersects the x-axis. If a quadratic function has x-intercepts at (-3, 0) and (3, 0), then the graph of the function is symmetric with respect to the y-axis.

The line of symmetry of a symmetric function is a vertical line that passes through the vertex of the function. In this case, the vertex of the function is located at the midpoint of the x-intercepts, which is at the point (0,0). Therefore, the equation of the line of symmetry is simply the equation of the vertical line passing through (0,0), which is:

x = 0

So the equation of the line of symmetry is x = 0.

Step-by-step explanation:

1.

Plane with two axes as a frame of reference. - Coordinate plane

2.

The vertical number line in a coordinate plane - Y-axis

3.

The horizontal number line in a coordinate plane - X-axis

4.

A pair of numbers that are used to correspond to a point on a graph where the first number is the x-coordinate and the second number is the y-coordinate. - Ordered Pairs

5.

Where the x and y axis meet. The point (0, 0). - Origin

6.

One of the four regions into which the x and y axis separate the coordinate plane.- Quadrant

7.

An equation with two variables that makes up a straight line on a coordinate plane. - Linear Equation

8.

The vertical change in a line from one point (x1,y1) to a second point (x2, y2). - Rise

9.

The horizontal change in a line from one point (x1,y1) to a second point (x2,y2). - run

10.

The ratio of a line's rise over its run. - Slope

11.

The point where a graph crosses the x axis. - X Intercept

12.

The point where a graph crosses the y axis. - Y Intercept

13.

A linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. - Slope-intercept form

14.

Lines that have the same slope and never intersect. - Parallel Lines

15.

Two lines that intersect at a 90° angle. Slopes of these lines are opposite reciprocals. - Perpendicular Lines

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Answer:  the sides of the triangle are a ≈ 41.5, b = 15, and c = 57, and the measures of the angles are A ≈ 42.7°, B ≈ 29.3°, and C = 108°.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

18.09

Step-by-step explanation:2.4x2.4, then x3.14  

Answer:

answers below

Step-by-step explanation:

If you are trying to find the area the answers are:

Earth= 289.52918

Saturn=6,532.5021

The formula for area for a sphere is:

4 x pie x r2

If you are trying to find the volume the answers are:

Earth=57.90584

Saturn=46,647.01596

The formula for volume for a sphere is:

4/3 x pie x r3

Also the radius (r) is half of the diameter, so you divide the diameter by 2.

Answer:

x = 25

Step-by-step explanation:

the consecutive angles in a parallelogram sum to 180° , that is

∠ C + ∠ D = 180

4x + 28 + 52 = 180

4x + 80 = 180 ( subtract 80 from both sides )

4x = 100 ( divide both sides by 4 )

x = 25

The inverse function of [tex]y = (3/4)x - 1[/tex] is: [tex]y = (4/3)(x + 1)[/tex]).

An inverse function refers to the function that returns the original value for which a function has given the output.

To find the inverse function of y= 3/4x - 1, we must to interchange x and y and solve for y:

x = (3/4)y - 1

x + 1 = (3/4)y

y = (4/3)(x + 1).

b. Finding the inverse function of a given function without using algebra can be done by graphing the function and reflecting it across the line y = x which is known as the reflection property of inverse functions.

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Step-by-step explanation:

Triangle has 180 degrees in its interior angles .....90 degrees is the right angle leaving 90 degrees for 2x + 3x+ 5

2x +   3x+5 = 90

5x = 85

x = 17

smallest angle is then 2x = 34 degrees

Required value of the given expression (15w/9) + 4w - 6 is (-23)

What is substitution method?

The substitution method is an algebraic method for solving linear simultaneous equations. This method replaces the value of one variable in one equation with another equation. In this way, we can converted a pair of linear equations into a single linear equation with only one variable which can then be easily solved.

Here given expression is (15w/9) + 4w - 6 and value of w is (-3).

We are simply substituting -3 for w and simplify,

(15w/9) + 4w - 6 = (15(-3)/9) + 4(-3) - 6

= (-45/9) - 12 - 6

= -5 - 12 - 6

= -23

Therefore, when w = -3, the value of the expression (15w/9) + 4w - 6 is -23.

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At the end of 7 years, Tanner will have a total balance of approximately $3,101.29 in the two accounts.

For the first account with a principal of $1,100 and an annual interest rate of 3% compounded annually, we can use the compound interest formula:

Future Value (FV) = P * (1 + r)^n

where P is the principal, r is the annual interest rate (as a decimal), and n is the number of years.

FV1 = $1,100 * (1 + 0.03)^7

FV1 ≈ $1,100 * (1.03^7)

FV1 ≈ $1,100 * 1.22504

FV1 ≈ $1,347.54

For the second account with a principal of $1,150 and an annual interest rate of 7.5% simple interest, we can use the simple interest formula:

Future Value (FV) = P + P * r * n

where P is the principal, r is the annual interest rate (as a decimal), and n is the number of years.

FV2 = $1,150 + $1,150 * 0.075 * 7

FV2 = $1,150 + $1,150 * 0.525

FV2 = $1,150 + $603.75

FV2 ≈ $1,753.75

Now we add the future values of both accounts together:

Total Balance = FV1 + FV2

Total Balance ≈ $1,347.54 + $1,753.75

Total Balance ≈ $3,101.29

Answer:

below

Step-by-step explanation:

in the picture in the picture in the picture in the picture in the picture

The answers are given below:

Given the table, we solve for the probabilities:

P(CS Major and Not Hired) = (CS Majors Not Hired) / Total Applicants = 102 / 394

P(CS Major and Not Hired) = 25.9% (e. Joint - 25.9%)

P(Other Major) = (Total Other Majors) / Total Applicants = 234 / 394

P(Other Major) = 59.4% (a. Marginal - 59.4%)

P(Hired | CS Major) = (CS Majors Hired) / Total CS Majors = 58 / 160

P(Hired | CS Major) = 36.25% (d. Conditional - 36.25%)

P(Not Hired | Other Major) = (Other Majors Not Hired) / Total Other Majors = 138 / 234

P(Not Hired | Other Major) = 58.97% (f. Conditional - 58.97%)

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The correct answer is c) Other types of pseudo R-squares may be greater or less than 60% with the same logistic regression model.

Pseudo R-squares, such as the one used in logistic regression, are measures of how well the model fits the data, but they cannot be directly compared to R-squared values from other types of regression models. Therefore, we cannot conclude that the logistic regression model with a pseudo R-Square of 60% is better than another logistic regression with an R-square (CS) of 50% or a multiple linear regression model with an R-square of 55%. However, we can say that 60% of the variation in the data can be explained by the logistic regression model, based on its pseudo R-Square value.

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It is critical to ensure that the requirements for inference are satisfied before doing a two-sample t-test. These criteria include observation independence, normality of the sample distribution, and variance equality.

A test statistic is a number produced by a statistical test. It quantifies how much your observed data deviates from the null hypothesis, which states that there is no association between variables or that there is no difference between sample groups.

Shelby might use a two-sample t-test to assess the difference in the mean caffeine content of a huge coffee between the two types (light and dark) if the conditions for the study are met..

Shelby can take the following steps:

As follows, define the null and alternative hypotheses:

The null hypothesis (H0) states that the caffeine content of a large coffee is the same for both kinds (light and dark) (i.e., the difference in means is zero).

Alternative hypothesis (Ha): The mean caffeine amount of a large coffee for the two varieties (light and dark) is not equal (i.e., there is a nonzero difference in means).

Gather the data:

Shelby must acquire a sample of big coffees, both light and dark, and determine their caffeine level.

Determine the test statistic:

Shelby must compute the test statistic t = (x1 - x2) / (s * sqrt(1/n1 + 1/n2), where x1 and x2 are the sample means, s is the pooled standard n1 and n2 represent the sample sizes.

Determine the p-value:

Shelby may obtain the p-value associated with the estimated test statistic by using a t-distribution table or statistical software.

Make a choice:

Shelby can reject the null hypothesis and conclude that there is evidence that the mean caffeine content of a large coffee for the two kinds (light and dark) is different if the p-value is less than the significance threshold (alpha).

Shelby concludes that there is insufficient evidence to establish a difference in the mean caffeine content of a large coffee for the two varieties (light and dark) if the p-value is larger than the significance level (alpha).

It is critical to ensure that the requirements for inference are satisfied before doing a two-sample t-test. These criteria include observation independence, normality of the sample distribution, and variance equality. If these requirements are not satisfied, nonparametric tests, for example, might be employed instead.

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Standard error of the difference = sqrt[(s1²/n1) + (s2²/n2)]

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To estimate the difference in the mean caffeine content of a large coffee of the two types (light-dark), Shelby can follow these steps:

Collect a random sample of large coffees from each type, ensuring that the sample sizes are large enough to meet the conditions for inference. The conditions for inference include the independence of the samples, the normality of the population distributions, and the equality of the population variances.

Compute the sample mean and standard deviation for each sample.

Compute the difference in sample means, which will give an estimate of the difference in population means.

Construct a confidence interval or perform a hypothesis test to determine whether the difference in sample means is statistically significant.

For a confidence interval, Shelby can use the following formula:

(Difference in sample means) ± (t-value)*(Standard error of the difference)

where the standard error of the difference can be computed using the following formula:

Standard error of the difference = sqrt[(s1²/n1) + (s2²/n2)]

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

For a hypothesis test, Shelby can use the following steps:

State the null and alternative hypotheses.

Determine the level of significance and the appropriate test statistic (t-test).

Calculate the test statistic using the following formula:

t = (Difference in sample means) / (Standard error of the difference)

Determine the p-value associated with the test statistic using a t-distribution table or statistical software.

Compare the p-value to the level of significance to determine whether to reject or fail to reject the null hypothesis.

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In the problem given, the result of the polynomial long division shows that the quotient is 4x - 4 and the remainder is -5.

To perform polynomial long division of (4x²-24x+15) by (x-5), we follow these steps:

       4x - 4

    --------------

x - 5 | 4x² - 24x + 15

       4x² - 20x

       ------------

                -4x + 15

                -4x + 20

                ----------

                     -5

Therefore, the quotient is 4x - 4 and the remainder is -5.

We can check our answer by verifying that:

(4x - 4) * (x - 5) + (-5) = 4x² - 24x + 15

which is indeed the original polynomial.

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