4. The usual 110-V household alternating current varies from -155 V
to 155 V with a frequency of 60 cycles/ sec (frequency is the
reciprocal of period). Assume the current starts at rest and then
rises.

Make a sketch of the curve.

Write an equation to describe the curve:_

Determine the value of y when t = 1/90 sec.:_

Approximate the value of t when y = 100 for the first time:_

The graph of the data from the table is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.

The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.

12) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

13) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

15) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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Answer:

1

Step-by-step explanation:

Use PEMDAS rules to answer this.

Parentheses first:

[tex](24-59)=-35[/tex]

Division next:

[tex]48:2=24[/tex]

Subtraction:

[tex]24-60=-36[/tex]

Currently we have:

[tex](-35)-(-36)[/tex]

This becomes:

[tex]-35+36 = 1[/tex]

The probability that point X is on segment DE is given as follows:

1/9.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The length of segment AE is given as follows:

28 - (-8) = 36 units.

The length of segment DE is given as follows:

28 - 24 = 4 units.

Hence the probability is given as follows:

p = 4/36

p = 1/9.

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Answer:162.1

Step-by-step explanation:We know that the sum of supplementary angles is 180°Let the unknown angle be xThus,100° + x = 180°X = 180° – 100°X = 80°Hence, the unknown angle is 80 …I did it my own way ok…

The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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If a cylinder has a volume of 2908.33 in³ and a radius of 11.5 in, the height of the cylinder include the following: C. 7 inches.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the parameters, we have the following:

2908.33 = 3.14 × 11.5² × h

Height, h = 7.00 inches.

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Central Limit Theorem forms the foundation for the inferential statistics branch of statistics

The Central Limit Theorem is a statistical concept that describes the behavior of the mean of a sufficiently large sample size drawn from any population with a finite mean and variance.

The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution. This theorem provides a basis for inferential statistics, which involves making inferences about a population based on a sample.

It allows us to use sample statistics to estimate population parameters with a certain level of confidence. This theorem has practical applications in many areas of research, such as in quality control, social sciences, and healthcare.

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Answer:

There are different methods to find the horizontal asymptote of a function, but one common approach is to take the limit of the function as x approaches positive or negative infinity. If the limit exists and is a finite number, then that is the horizontal asymptote.

To apply this method to the given function:

y = (-4x^6+6x +3)/(8x^2+9x+3)

As x becomes very large (either positive or negative), the highest power of x in the numerator and denominator dominates the other terms. This is because exponential functions grow or shrink much faster than polynomials as x goes to infinity or negative infinity.

Therefore, we can simplify the function by dividing both numerator and denominator by x^6:

y = (-4 + 6/x^5 + 3/x^6)/(8/x^4 + 9/x^5 + 3/x^6)

As x approaches infinity, all the terms with negative powers of x go to zero, leaving:

y ≈ (-4 + 0 + 0)/(0 + 0 + 0)

This is an indeterminate form of 0/0, which suggests that we need to do more algebraic simplification. One way to do this is to factor out the highest power of x in both numerator and denominator:

y ≈ (-4/x^6 + 6/x^11)/(8/x^4 + 9/x^5 + 3/x^6)

y ≈ (-4/x^6)(1 - 6x^5)/(8/x^4)(1 + 9x/x^4 + 3/x^2)

Now, as x approaches infinity, the fraction becomes dominated by the leading terms:

y ≈ (-4/x^6)(-6x^5)/(8/x^4)(9x/x^4)

y ≈ (24/72)(1/x)

As x goes to infinity, 1/x goes to zero, so:

y ≈ 1/3x

Therefore, the horizontal asymptote of the graph of y = (-4x^6+6x +3)/(8x^2+9x+3) is y = 1/3x.

Answer: its b

Step-by-step explanation: all coins have a heads and tails so that takes out c.

d is just for jokes

a.  a coin in a school problem is not gonna be wieghted.

The relative error in calculating the area of the rectangle is 0.0155.

The relative error means ratio of the absolute error of the measurement to the actual measurement.

The actual area of the rectangle is:

= 10 ft x 8 ft

= 80 sq ft

The measured area is:

= 10.46 ft x 7.53 ft

= 78.7638 sq ft

The relative error derive by the following formula:

= (Real - Measured)/Real

= (80 - 78.7638)/80

= 0.0154525

= 0.0155.

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Answer:

D, A, B, C

Step-by-step explanation:

-12/3, or -4, is lowest

-11/3, or -3.6, is 0.3 more, therefore closer to 0.

-2/3, or -0.6, is much closer to 0, precisely 3 units closer.

1/3, or 0.3, is the only positive number, so it is the most amount.

The table of ordered pairs is completed below

Here is the completed table and plotted points:

Point x y (x,y)

A 4 9 (4,9)

B 6 3 (6,3)

C 1 3 (1,3)

D 8 7 (8,7)

E 8 9 (8,9)

To plot these ordered pairs on a coordinate plane, we need to draw the x and y axes, and label the units on each axis.

Then we can plot each point by starting at the origin (0,0) and moving horizontally (to the right if x is positive, or to the left if x is negative) and vertically (up if y is positive, or down if y is negative) to the corresponding point.

The points plotted on the coordinate plane are attached

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Complete the table. Then, plot the ordered pairs on the coordinate plane. Make sure to label each point with its corresponding letter.

              x                y       (x, y)

A            4                9

B            6                3

C            1                3

D            8                7

E             8                9

Using combinations we know that 24 combinations of the flags can be used.

Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial.

Combos' components can be chosen in any hierarchy.

Combinations and permutations can coexist.

The expression "Selection of things" refers to a circumstance in which the chronology of occurrences is unimportant.

So, we know that we have 3 types of flags which are:

4 flags for the top position.

3 flags for the middle position.

2 flags for the bottom position.

Now, different combinations would be:

4 * 3 * 2 = 24

Therefore, using combinations we know that 24 combinations of the flags can be used.

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we cannot simply write equation 5c + 3d as 8c, 8d, or 8cd.

A variable in mathematics is a symbol or letter that is used to indicate a quantity in a mathematical statement or equation that can have many values. It is a symbol that may be used to represent an arbitrary or undefined integer in algebraic expressions and equations.

In the equation 5c + 3c = 8c, we can combine the two terms on the left side because they have the same variable (c) and the same exponent (1).

However, in the expression 5c + 3d, the two terms have different variables (c and d) and cannot be combined in the same way. Therefore, we cannot simply write 5c + 3d as 8c, 8d, or 8cd.

If we want to simplify the expression 5c + 3d, we can only write it in its simplest form or factor it further if possible.

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To find the 18th term of a pattern that repeats 5 times (which is a pentagon), we need to divide 18 by 5, which gives us a quotient of 3 and a remainder of 3.

This means that the pattern repeats 3 times, and we need to find the 3rd term of the pattern after the third pentagon.

The third term of the pattern after the third pentagon would be the fourth pentagon in the sequence, since each pentagon consists of 5 terms. Therefore, the 18th term would be the third term of the fourth pentagon in the sequence, which is the 13th term overall.

So the 18th term in the sequence would be the 13th term of the pattern, which is another pentagon.

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The ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Let h1 and h2 be the heights of the two similar prisms, and let A1 and A2 be the areas of their respective bases.

Also, let k be the scale factor that relates the smaller prism to the larger prism.

a. We know that the volumes of the two similar prisms are proportional to the cubes of their corresponding side lengths, so we have:

(kh1)³ / (kh2)³ = 135 / 5000

Simplifying this expression, we get:

h1³ / h2³ = 135 / 5000

Taking the cube root of both sides, we get:

[tex]h1 / h2 = (135 / 5000)^{(1/3)}[/tex]

Using a calculator, we find:

h1 / h2 ≈ 0.405

Therefore, the ratio of the heights of the two similar prisms is approximately 0.405 to 1.

b. The ratio of the areas of the bases of two similar prisms is equal to the square of the scale factor. That is:

A1 / A2 = k²

To find the scale factor k, we can use the fact that the volumes of the two prisms are proportional to k³. Therefore:

k³ = 5000 / 135

k ≈ 5.091

Using this value of k, we get:

A1 / A2 = k² = (5.091)² ≈ 26

Therefore, the ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.

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a). There are a total of 10 students in the class, according to the dot plot.

b). The students' ages, which vary from 1 to 5, indicate that this is not an adult swimming lesson.

c). Thus, just 20% (2/10) of the students are toddlers or preschoolers.

Numbers are mathematical units of measurement and labelling. It is an ethereal idea that can stand in for many different material quantities, including time, money, and distance. Real numbers, complex numbers, and even irrational numbers can all be considered numbers in mathematics.

Numbers are frequently employed in mathematical equations to express relationships and to represent data. They are also employed in the development of models, patterns, and data analysis.

a). There are a total of 10 students in the class, according to the dot plot.

b). The programme is a swimming lesson for adults.

No, it doesn't seem to be an adult swimming lesson based on the dot plot. The students' ages, which vary from 1 to 5, indicate that this is not an adult swimming lesson.

c). The majority of the students are between the ages of 2 and 3.

No, it doesn't seem like half of the students are between the ages of 2 and 3, according to the dot plot. There are two students who are two years old, one who is three, two who are four, and five who are five. Thus, just 20% (2/10) of the students are toddlers or preschoolers.

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Answer:

To complete the square for the equation -5x² + 10x = -315, we can follow these steps:

Move the constant term (-315) to the right side of the equation:

-5x² + 10x + 315 = 0

Divide both sides of the equation by the coefficient of the x^2 term (-5) to get a coefficient of -1 for the x^2 term:

x² - 2x - 63 = 0

Add the square of half the coefficient of the x term to both sides of the equation:

x² - 2x + 1 - 1 - 63 = 0 + 1

Simplify the left side of the equation by factoring the quadratic trinomial and combining like terms:

(x - 1)² - 64 = 1

Add 64 to both sides of the equation:

(x - 1)² = 65

So the intermediate step in completing the square for -5x² + 10x = -315 is:

(x - 1)² - 64 = 1

This is the result of adding the square of half the coefficient of the x term (-1) to both sides of the equation and simplifying.

For every 100 free throws Chris Paul attempted, he made approximately 93 of them.

We have,

Chris Paul's free throw percentage of 93.4 means that he made 93.4% of his free throw attempts during the 2020-21 season.

In other words, for every 100 free throws he attempted, he made approximately 93 of them.

This is a high free throw percentage and indicates that Chris Paul is a skilled free throw shooter.

Thus,

For every 100 free throws Chris Paul attempted, he made approximately 93 of them.

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A circle with center V and an inscribed equilateral triangle RST.

What is circle?

A circle is a closed two-dimensional shape consisting of all the points that are equidistant from a given point, called the center.

To construct a circle with center V and an inscribed equilateral triangle RST, follow these steps:

Draw point V as the center of the circle.

From point V, draw a radius that will serve as one side of the equilateral triangle RST. Label the endpoint of this radius as point S.

Using a compass, draw a circle with center V and radius VS. This circle will intersect the radius VS at two points, label these points as R and T.

Draw segments RT and RS to complete the equilateral triangle RST.

Your construction should show a circle with center V and an inscribed equilateral triangle RST.

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Let's assume that the original price of the camera is x.

Since Annie sold the camera at a loss of 12%, the selling price is 88% of the original price.

So we can set up the equation:

0.88x = $250

To solve for x, we can divide both sides by 0.88:

x = $250 ÷ 0.88

x = $284.09

Therefore, the original price of the camera was $284.09.

Answer:i thing the anwser is 56

Step-by-step explanation:

Applying the side-splitter theorem, the value of x in the image given is calculated as: x = 5.

The Side-Splitter Theorem states that if a line is drawn parallel to one side of a triangle and intersects the other two sides, the ratio of the length of the two segments of the divided sides is equal to the ratio of the lengths of the sides that form the two smaller triangles.

Using this theorem, we van apply it to solve for x in the image given:

24x/(24x - 50) = 84/49

Solve for x:

24x(49) = 84(24x - 50)

1,176x = 2,016x - 4,200

1176x - 2016x = -4200

-840x = -4,200

x = -4200/-840

x = 5

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The distance between the end of the water supply pipe and the sink should be 2 times the diameter of the supply pipe. Option B is the correct answer.

The distance between the end of the water supply pipe and the sink is determined by plumbing codes and standards to ensure safe and efficient water delivery.

The National Standard Plumbing Code requires a minimum distance of 2 times the diameter of the supply pipe between the end of the pipe and the nearest point of use, such as a faucet or sink.

This helps prevent any potential contamination from the supply pipe and ensures adequate flow and pressure for efficient operation.

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The time it will take to fill the pool at the given rate would be = 8 mins.

To calculate the volume of the cylindrical swimming pool the formula for the volume of the cylinder should be used which is = πr²h

where r = 5ft

h = 8ft

volume = π×5×5×8 = 200πft³

If 25πft³ = 1 minute

200πft³ = X

Make X the subject of formula;

X = 200/25 = 8mins

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1.75 in or 1 3/4 in (which ever form you need it in)

youre given the diameter and so to find radius, you simply divide the diameter by 2.