3. A circus performer trots her pony into the ring. The pony circles

the ring 22 times as the performer flips and turns on the pony's

back. At the end of the act, the pony exits on the side of the ring

opposite its point of entry. Through how many degrees

does the pony trot during the entire act?

Here, we are required to determine how long after the first car accelerates will the cars be side by side.

The cars will be side by side at Time, t = 9.11seconds after the first car accelerates.

The position of each car is given by the function of its distance, i.e C1 and C2.

At the point when the cars are side by side;

C^1(t) must be equal to C^2(t).

Mathematically;

Therefore, we have;

By solving quadratically;

We have ; Time, t = 9.11 seconds. (to the nearest hundredth).

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Answer:

Step-by-step explanation:

y +2(y-5)=2y+2

y + 2y - 10 = 2y +2

3y - 10 = 2y +2

3y - 2y = 2 + 10

y = 12

---------------------------------

check

12 + 2 * (12 - 5) = 2 * 12 + 2             (remember PEMDAS)

12 + 24 - 10 = 24 + 2

26 = 26

the answer is good

Answer:

Slope: 1/4

Y intercept: (0,-3)

Slope intercept equation: y= 1/4x - 3

Step-by-step explanation:

The Bernoulli, Poissonian, regular, and exponential random variables are distinct types of discrete or continuous random variables; for example, a Bernoulli random variable models a binary outcome, a Poisson random variable represents the number of events in a fixed interval, a regular random variable is a generic random variable, and an exponential random variable models the time between events in a Poisson process.

Bernoulli Random Variable: A Bernoulli random variable represents a binary outcome, where there are only two possible outcomes, often labeled as "success" and "failure." The variable takes a value of 1 for success with probability p and a value of 0 for failure with probability (1 - p), where 0 ≤ p ≤ 1. Example: Consider flipping a fair coin. Let's define "heads" as success (1) and "tails" as failure (0). The outcome of a single coin flip can be modeled using a Bernoulli random variable.

Poisson Random Variable: A Poisson random variable represents the number of events occurring in a fixed interval of time or space. It is used when the events occur randomly and independently, with a constant average rate λ over the interval. The Poisson random variable is defined for non-negative integers (0, 1, 2, ...) and has a single parameter λ, which represents the average rate of occurrence. Example: The number of emails received per hour follows a Poisson distribution with an average rate of 5 emails per hour. We can model this using a Poisson random variable.

Regular Random Variable: The term "regular random variable" is not a standard term in probability theory. It might refer to a generic random variable that does not belong to any specific named distribution. Regular random variables can have various distributions, discrete or continuous, depending on the context or problem at hand. Example: Let's consider a random variable representing the number of defects in a manufactured item. Suppose the number of defects can take values from 0 to 10 with equal probabilities. This would be an example of a regular random variable.

Exponential Random Variable: An exponential random variable models the time between events in a Poisson process, where events occur continuously and independently at an average rate λ. The exponential random variable is continuous and positive, with the probability density function f(x) = λe^(-λx), where x ≥ 0 and λ > 0. Example: The time between successive earthquakes in a particular region follows an exponential distribution with an average rate of 0.5 earthquakes per year. We can use an exponential random variable to model this time between events.

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The simplified trigonometric expression is sin²t.

Option D is the correct answer.

We have,

Given,

Trigonometric expression:

cost (sect - cost)

[ sec t = 1/ cos t ]

= cost (1/cos t - cos t)

Applying the distributive properties.

= cos t/cos t - cos²t

= 1 - cos²t

= sin²t

(using the trigonometric identity sin²t + cos²t = 1)

Therefore,

The simplified trigonometric expression is sin²t.

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Step-by-step explanation:

(-1)÷(-1)=1 Answer

hope you understood.....

Comment if not understood

Answer:

y=61, x=112

Step-by-step explanation:

119+y=180

180-119=y

61=y

131+56+61+x=360

248+x=360

360-248=x

112=x

Answer:

f(1) = 15

f(-9) = -65

f(0) = 7

Step-by-step explanation:

f(1) = 8(1) + 7

f(1) = 8 + 7

f(1) = 15

f(-9) = 8(-9) + 7

f(-9)  = -72 + 7

f(-9) = -65

f(0) = 8(0) + 7

f(0) = 7

Given the average cost of a gallon of milk is the dependent variable, and the year is the independent variable, assuming that a linear relationship exists, you can determine the slope and y-intercept values.

Since the relationship is linear, you can use a simple linear regression equation of the form:

y = mx + b where y represents the average cost of a gallon of milk and x represents the year.

For example, if the average cost of a gallon of milk in 1980 is $2.50, and the average cost in 1985 is $3.25, then the slope would be

(3.25 - 2.50) / (1985 - 1980) = 0.15.

This indicates that for every one year increase, the cost of milk increases by $0.15.

The y-intercept can be found by using either of the years and the slope value.

Substituting the slope and y-intercept values into the equation y = mx + b gives the equation

y = 0.15x + b,

where x is the year and y is the average cost of a gallon of milk.

To predict the average cost of a gallon of milk in 1986,

you would substitute x = 1986 into the equation and solve for y.

Therefore, the predicted average cost of a gallon of milk in 1986 would be:

y = 0.15(1986) + b

y = 298.9 + b

where b is the y-intercept.

Since we do not know the value of b, we cannot determine the exact predicted cost of milk in 1986.

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The sandbox will not be covered. 450ft² is the area of the shredded tire portion of the playground.

Modern mathematics heavily relies on the concept of area. A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane. Simply put, the area is the amount of fabric or material with the specified thickness needed to build an accurate representation of the shape and the quantity of paint required to cover the shape's surface in a single layer, or one coat.

area = 15×30

       =450ft²

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Answer:

a. The probability that a particular student arrives by car is \(\frac{1}{20}\) = 0.05, which equals 5%.

b. The probability that a particular student walks to school is \(\frac{3}{10}\) = 0.3, which equals 30%.

c. The probability that a particular student does not walk to school is \(\frac{7}{10}\) = 0.7, which equals 70%.

d. The probability that a particular student does not walk or come by car is \(\frac{13}{20}\) = 0.65, which equals 65%.

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

\(P(A)=\frac{number of favorable cases}{number of possible cases}\)

In this case, the number of possible cases is always the same, which is equal to the total number of students. So the number of possible cases is 320 students. The number of favorable cases varies as follows:

a. Number of favorable cases= number of students that arrive by car= 16

So: \(P(A)=\frac{16}{320}\)

P(A)=\(\frac{1}{20}\) = 0.05, which equals 5%

The probability that a particular student arrives by car is \(\frac{1}{20}\) = 0.05, which equals 5%.

b. Number of favorable cases= number of students that walk to school= 96

So: \(P(A)=\frac{96}{320}\)

P(A)=\(\frac{3}{10}\) = 0.3, which equals 30%

The probability that a particular student walks to school is \(\frac{3}{10}\) = 0.3, which equals 30%.

c. Number of favorable cases= number of students that do not walk to school = 320 students - number of students that walk to school= 320 students - 96 students= 224 students

So: \(P(A)=\frac{224}{320}\)

P(A)=\(\frac{7}{10}\) = 0.7, which equals 70%

The probability that a particular student does not walk to school is \(\frac{7}{10}\) = 0.7, which equals 70%.

d. Number of favorable cases= number of students that do not walk or come by car= 320 students - number of students that walk to school - number of students that arrive by car= 320 students - 96 students - 16 students= 208 students

So: \(P(A)=\frac{208}{320}\)

P(A)=\(\frac{13}{20}\) = 0.65, which equals 65%

The probability that a particular student does not walk or come by car is \(\frac{13}{20}\) = 0.65, which equals 65%.

Linear functions are used to represented straight lines.

The linear function is \(y = -\frac 12x + 1\)

The points on the graph are: (2,0) and (0,1)

Start by calculating the slope (m) using:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

Substitute values for x and y

\(m = \frac{1 - 0}{ 0 -2}\)

\(m = \frac{1 }{ -2}\)

Rewrite as:

\(m = -\frac{1 }{2}\)

The equation is then calculated as:

\(y = m(x - x_1) + y_1\)

This gives

\(y = -\frac 12(x -0) + 1\)

\(y = -\frac 12(x) + 1\)

Open bracket

\(y = -\frac 12x + 1\)

Hence, the linear function is \(y = -\frac 12x + 1\)

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0.50 sample proportion will require the largest number of work sampling observations for a given confidence level and allowable error as the variability is largest at 0.50.

A part, share, or quantity is a percentage when it is compared to the total. It can be any number between 0 and 1, 0, or 1. A number or percentage can be used to represent it. The percentage of Canadians who reside in a certain province is one illustration from official statistics. A special class of ratio called a proportion has the numerator and denominator combined. An illustration is the ratio of deaths to men, which is calculated by dividing deaths to men by deaths to men and women.

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Answer:

The correct solution is,

x > 9

(if the inequality is 3x ≥ 72-5х then the solution is x ≥ 9, so the 3rd option I suppose)

Step-by-step explanation:

3x > 72-5х

adding 5x on both sides,

3x + 5x > 72

8x > 72,

dividing by 8 on both sides,

8x/8 > 72/8

x > 9

The Diagrams 2 and 4 are correct while diagrams 1 and 3 are incorrect.

How to determine similar triangles and trapeziums?

From the given parameters

Triangle 1 has the following features

Let us label the triangle ABCD;

ΔABD is isosceles.

The base angles are equal =52⁰

Also, ΔBCD is also isosceles

The base angles are equal =74⁰

∠DBC  is not equal to ∠BAD

Therefore; the image is not correct.

From figure 2

Let it be MNOP;

ΔMNO is isosceles base angles are equal=76⁰

∠MNO  is not equal to ∠MOP=28⁰

From figure 3

A Plane geometry deals with flat shapes that you can draw on a piece of paper, such as squares, circles, and triangles.

The image does not resemble these shapes.

therefore it is incorrect.

From figure 4

A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other.

∠ACB=∠ABC=27⁰

The triangles on opposite sides are equal to each other.

Therefore the image is correct.

In conclusion, images 2 and 4 are correct while images 1 and 3 are incorrect.

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A random sampling method could be used to find the percentage of students in your grade who eat five servings of fruit and vegetables each day.

This method involves selecting a random sample of students from the entire population of your grade and surveying them about their eating habits.

In other word, its involves randomly selecting a subset of students from the entire grade population and collecting data on their eating habits. By selecting students at random, the sample is more likely to be representative of the entire grade. This cam provide accurate insights into the percentage of students meeting the desired dietary recommendation.

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Answer:

Domain: all real numbers

Step-by-step explanation:

This graph is a parabola. It's equation looks like it should be:

y = x^2 - 1

If you have a graph and are looking for the domain, you are determining where the graph exists. For what x's the graph exists. If you have the equation then the domain is what x's may be put into the equation. There are no limitations on what numbers can go into this equation so the domain is all real numbers.

There are several ways to write the domain is all real numbers, set builder notation and interval notation. But the main idea is that it is all real numbers.

Answer:

D

Step-by-step explanation:

The difference between 63y and 35y is 28y. 28/2=14, 28/4=7, 28/7=4, 28/9=not whole number so I'm not doing the math, and to make sure we are right, 28/14=2

Answer:

Step-by-step explanation:

\(63y-35y\\=28y\)

\(\frac{28y}{2} = 14y\\\\\frac{28y}{4} = 7y\\\\\frac{28y}{7} =4y\\\\\frac{28y}{14} = 2y\\\\\frac{28y}{9} =3.1111y\)

Answer:

No

Step-by-step explanation:

Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.

A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.

-x + 3y² = 18

We know here that this is not a linear function. But we can try to write it in slope-intercept form:

3y² = x + 18

y² = x/3 + 6

y = √(x/3 + 6)

We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).

Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:

3.88 milligrams is equal to 0.0388 centigrams, as milligrams are converted to centigrams by moving the decimal point two places to the left.

To convert from milligrams to centigrams, we need to understand their relationship in the metric system. There are 10 milligrams in 1 centigram and 100 centigrams in 1 gram.

Given the value of 3.88 milligrams, we need to convert it to centigrams. To do this, we move the decimal point two places to the left, resulting in 0.0388 centigrams. This is because there are 10 milligrams in 1 centigram, so dividing 3.88 milligrams by 10 gives us the equivalent value in centigrams.

Therefore, 3.88 milligrams is equal to 0.0388 centigrams. It's important to keep track of decimal placement when converting between different units of measurement in the metric system.

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Answer:

Points N and K are on plane A and plane S.

Point P is the intersection of line n and line g.

Points M, P, and Q are noncollinear.  

e2020

Step-by-step explanation:

According to the given diagram of Intersecting planes, Option (1), Option (3), Option (4) are True.

A plane is a two-dimensional, flat surface that stretches indefinitely.

A point is said to lie on a plane when it satisfies the equation of plane which is ax^3 + bx^2 + cx+ d = 0 and sometimes it is just visible in the figure whether a point is lying on a plane or not.

In Option(1) : Points N and K are lying on the line of intersection of plane A and S and will satisfy the equation of both planes.

In Option(2) : Point P is lying on both planes B and S, but the point M is lying only on plane B, hence this option is wrong.

In Option(3) : It is clearly visible the Point P is the point of intersection of lines n and g.

In Option(4) : It is clearly visible that Points M,P,Q are not lying on the same line, hence they are non-collinear.

In Option(5) : Line d intersects the plane A at point L and not point N, hence this is also wrong.

Hence the correct options are 1,3,4.

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Answer:

A) ∠5 = 160°

B) ∠4 = 37°

C) ∠3 = 98°

Step-by-step explanation:

A)

If ∠1 = 160°

⇒ ∠5 = ∠1 = 160° (∵ Corresponding angles are always equal)

B)

If ∠6 = 37°

⇒ ∠4 = ∠6 = 37° (∵ Vertical angles are always equal)

C)

If ∠8 = 82°

⇒ ∠8 = ∠6 = 82° (∵ Alternate interior angles are always equal)

Now ,

∠6 + ∠3 = 180° (∵ Linear pair)

⇒ ∠3 + 82° = 180°

⇒ ∠3 = 180° - 82° = 98°

Susan has more candy in weight compared to Isabel.

To compare the candy weights between Susan and Isabel, we need to ensure that both weights are in the same unit of measurement. Let's convert Isabel's candy weight to ounces for a fair comparison.

Given:

Susan: 4 bags x 6 ounces/bag = 24 ounces

Isabel: 1 bag x 16 ounces/pound = 16 ounces

Now that both weights are in ounces, we can see that Susan has 24 ounces of candy, while Isabel has 16 ounces of candy. As a result, Susan is heavier on the candy scale than Isabel.

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Answer:

Option D

Step-by-step explanation:

SAS criterion- two sides and an included angle.

This means that we have

(i) AC = DE

(ii) ∠C = ∠D

(iii) the third should be another side so that there are 2 sides with an included angle.

Hence, it will be

BC = FE                     (Option D)

Hope this helps you!

Answer:

1 and 1/4

Step-by-step explanation:

add 3/4 and 1/2, divide 1/2 into 2/4 and when you add 2/4 to 3/4 you have an extra quarter. therefor you have 4/4 and 1/4 which is 1 and 1/4.

hope this helps <3

Answer:

\(1\frac{1}{4}\)

Step-by-step explanation:

Step 1: Add the given values (Since we don't know the original amount and we are given the amount of which is changed with, we need to add those amounts together to know by how much the liquid beaker changed.)

\(\frac{3}{4} = 0.75\\\\\frac{1}{2} = 0.5\\\\0.5 + 0.75 = 1.25\\\\\frac{3}{4} + \frac{1}{2} = 1\frac{1}{4}\)

Therefore, the overall change in the amount of liquid in the beaker is \(1\frac{1}{4}\) liters.

Answer:

B?

Step-by-step explanation:

What is the multiple choice here? I can only assume that it meant 51 miles/ 3 gallons but I can't be certain.

The yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

To calculate the yearly deposits needed, we can use the concept of future value of an annuity. The future value formula for an annuity is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity

P = Yearly deposit amount

r = Interest rate per period

n = Number of periods

In this case, the future value needed is $2 million, the interest rate is 8% (0.08), and the number of periods is 30 years. We need to solve for the yearly deposit amount (P).

Using the given formula:

2,000,000 = P * [(1 + 0.08)^30 - 1] / 0.08

Simplifying the equation:

2,000,000 = P * [1\(.08^3^0 -\) 1] / 0.08

2,000,000 = P * [10.063899 - 1] / 0.08

2,000,000 = P * 9.063899 / 0.08

Dividing both sides by 9.063899 / 0.08:

P = 2,000,000 / (9.063899 / 0.08)

P ≈ 2,000,000 / 113.298737

P ≈ 17,650.23

Therefore, the yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

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The 95% confidence interval for the population proportion of student loan borrowers with loans totaling more than $20,000 is approximately (0.3235, 0.3765).

To construct a 95% confidence interval for the population proportion of student loan borrowers with loans totaling more than $20,000, we need to calculate the sample proportion, standard error, and critical value.

1. Sample proportion (p) = Number of students with loans over $20,000 / Total sample size
p = 448 / 1280 ≈ 0.35

2. Standard error (SE) = √(p * (1 - p) / n)
SE ≈ √(0.35 * (1 - 0.35) / 1280) ≈ 0.0135

3. For a 95% confidence interval, we use a critical value (z) of 1.96.
Margin of error (ME) = z * SE
ME ≈ 1.96 * 0.0135 ≈ 0.0265

4. Calculate the confidence interval:
Lower limit = p - ME ≈ 0.35 - 0.0265 ≈ 0.3235
Upper limit = p + ME ≈ 0.35 + 0.0265 ≈ 0.3765

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