What is the value of Y?

What Is The Value Of Y?

Answers

Answer 1

I would say y=1.5x +8

When Aaron started, he was on page 8 (Which is the +8 part.) he reads 1.5 pages every minute (Which is the 1.5x part.)


Related Questions

10√ pleses help meeeeeeeeeeeee

Answers

putting this in a calculator as 10√ gave me an error message, but when I put in √10 I got an infinite decimal. perhaps you read or typed the question wrong?

out of 232 tourists shopping in venice florida 25% purchased seashells as souvenirs. Using the percent as a rate per 100 how many tourists purchased seashells

Answers

Answer:

58 tourists

Step-by-step explanation:

25% = .25

.25 x 232

=58

A train is moving at a speed of 40 km/h.
Which additional information would be required to determine the velocity of the train?

A train is moving at a speed of 40 km/h.Which additional information would be required to determine the

Answers

Answer:

A train which moving at a speed of 40 km/h, requires the direction of the train to determine the velocity of the train.

Step-by-step explanation:

The rate at which an object changes its position with respect to time is indicated by the vector quantity known as velocity. It is described as the variation in displacement with respect to time in both magnitude and direction. Meters per second (m/s) is the SI unit of velocity.

An object's speed and direction are both included in its velocity, which is a vector quantity. The direction of motion must also be known in order to calculate the velocity of a train traveling at 40 km/h.

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Elevator 1 moved up 10 feet from the ground level. its position is labeled as +10. Elevator 2 moved down 5 feet from the ground level. It’s position is labeled as _____

Answers

Answer:

I believe your answer would be -5 because in the first part of the question, it tells you that ground level is 0. (by saying that when you go up 10 from ground level, you are at postitive (+)10)

so... if you go 5 down from ground level (0), it the same as 0-5 which is -5. hope this helps! :)

Step-by-step explanation:

Which equation would calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown?

a cylinder with the diameter labeled 2.6 centimeters and the height labeled 3.8 centimeters

SA = 2π(1.3)2 + 1.3π(3.8)
SA = 2π(2.6)2 + 2.6π(3.8)
SA = 2π(2.6)2 + 1.3π(3.8)
SA = 2π(1.3)2 + 2.6π(3.8)

Answers

Option A. The amount of wrapping paper needed to completely cover the cylinder is approximately 41.7 square centimeters (rounded to one decimal place).

The correct equation to calculate the amount of wrapping paper needed to completely cover the cylinder is:

SA = 2πr(r + h)

where r is the radius of the cylinder (half the diameter), and h is the height of the cylinder.

Using the given measurements of the cylinder:

The radius, r = 2.6/2 = 1.3 cm

The height, h = 3.8 cm

Substituting these values into the formula, we get:

SA = 2π(1.3)(1.3 + 3.8)

SA = 2π(1.3)(5.1)

SA = 13.26π

Therefore, 41.7 square centimeters of wrapping paper are required to fully cover the cylinder (rounded to one decimal place).

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What is 133413.12cm in metres

Answers

Answer:

1334.1312

Step-by-step explanation:

Answer:

1334.1312

Step-by-step explanation:

order these from least to greatest
9, 3, π

Answers

Answer:

3 pi 9

Step-by-step explanation:

Which of the following is a solution for the inequality 2x < 9?x = 5.5x = 4.5x = 6x = 4

Answers

Given:

The inequality is 2x < 9

Required:

Find solution for inequality.

Explanation:

We will solve as

\(\begin{gathered} 2x>9 \\ \text{ DIvide both sides by 2} \\ \frac{2x}{2}<\frac{9}{2} \\ x<\frac{9}{2} \end{gathered}\)

Answer:

Hence, answer is x < 4.5

Which of the following is a solution for the inequality 2x &lt; 9?x = 5.5x = 4.5x = 6x = 4

How to find a quadratic equation with y-intercept and vertex? Explain with examples.

Answers

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

Step 1: Identify the coordinates of the y-intercept. The y-intercept has the form (0, c), where c is the y-coordinate.Step 2: Identify the coordinates of the vertex. The vertex has the form (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the quadratic equation.Step 3: Substitute the coordinates of the y-intercept and vertex into the general form of the quadratic equation, y = ax^2 + bx + c.Step 4: Solve the resulting system of equations to find the values of a, b, and c.Step 5: Substitute the values of a, b, and c back into the general form of the quadratic equation to obtain the final equation.

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Start with the standard form of a quadratic equation: y = ax^2 + bx + c, where a, b, and c are constants.Use the vertex form of a quadratic equation: y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.Substitute the vertex coordinates (h, k) into the equation to obtain the equation in vertex form.Use the y-intercept to find another point on the curve. The y-intercept has the form (0, c), where c is the value of y when x is zero.Substitute the coordinates of the additional point into the equation to obtain a system of two equations. Solve the system to find the values of a, b, and c.Substitute the determined values of a, b, and c into the standard form of the quadratic equation to obtain the final equation.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

Using the vertex form, we have y = a(x - 2)^2 - 1.Substituting the y-intercept coordinates, we get 4 = a(0 - 2)^2 - 1, which simplifies to 4 = 4a - 1.Solving the equation above, we find a = 1.Substituting the values of a and the vertex coordinates into the vertex form equation, we have y = 1(x - 2)^2 - 1.Expanding the equation and simplifying, we get y = x^2 - 4x + 3.The final quadratic equation with the given y-intercept and vertex is y = x^2 - 4x + 3.

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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What are 4 signs someone is having an allergic reaction?.

Answers

The 4 sign that someone is having as allergic reaction are cell mediated, cytotoxic, immunocomplex and anaphylactic ?

What are the symptoms that someone having allergic reactions ?

The symptoms and signs that someone having allergic reaction is that

Skin reactionsPale skin Itching Itchy red spots on the body. Watery eyes

People experienced food allergies also like hives, swelling of the tongue, swelling of tongue, swelling of face. Some of the respiratory symptoms are chest tightness, coughing, shortness of breath, wheezing, throat tightness. There are also some GI symptoms which are diarrhea, vomiting, cramps and abdominal pain.

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The area of the square in the figure below is 16 square inches. Solve for "s", the length of one side. Explain
the solution.

▪️▪️▪️▪️
▪️▪️▪️▪️
▪️▪️▪️▪️
▪️▪️▪️▪️

Area = 16 in²
A=S²
A=16
s²=16

Answers

Answer:

4

Step-by-step explanation:

\(\sqrt{16}\) = 4

The side lengths of the square is 4.

Area = Length times width

Area = 4 x 4

Are = 16

as many. How many successful free throws did Priya make today?
free throws
vitamin C (mg)
25%
0
50%
0
75%
2.
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C,
which is 250% of the daily recommended allowance of vitamin C for adults. What is
100% of the daily recommended allowance of vitamin C for adults?
10000
100%
1500
125%
150%
20006
25006

Answers

Answer:

A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?

list and describe two specialized alternatives not often used as a continuity strategy. quizlet

Answers



1. P-adic Numbers:

P-adic numbers are a specialized alternative not commonly used as a continuity strategy in mathematics. They are an extension of the real numbers that provide a different way of measuring and analyzing numbers. P-adic numbers are based on a different concept of distance, known as the p-adic metric. This metric assigns a measure of closeness or distance between numbers based on their divisibility by a prime number, p. P-adic numbers have unique properties and can be useful in number theory, algebraic geometry, and other branches of mathematics. However, they are not typically employed as a continuity strategy in practical applications.

2. Nonstandard Analysis:

Nonstandard analysis is a mathematical framework that provides an alternative approach to calculus and analysis. It introduces new types of numbers called "infinitesimals" and "infinite numbers" that lie between the standard real numbers but are infinitely smaller or larger than any real number. Nonstandard analysis allows for more rigorous treatment of infinitesimal quantities and provides a different perspective on limits, continuity, and differentiation. While nonstandard analysis has theoretical implications and can provide valuable insights in mathematical research, it is not commonly used as a continuity strategy in practical applications where standard analysis and calculus are more prevalent.

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you are ordering shirts for a club at your school. the function f(x)=8x+12 represents the cost of ordered x shirts how much would it cost to buy 32 shirts

Answers

The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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Draw a rectangular array on graph paper for 24 x 18. Solve the problem 24 x 18 using the partial-products algorithm. Use your array to explain why the partial-products algorithm calculates the correct answer to 24 x 18.

Answers

To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.

The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.

For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.

The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.

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Which value of x makes this equation true? –5(– 20 ) = 35
A. -11
B. -3
C. 13
D. 27​

Answers

Answer:

c

Step-by-step explanation:

its right

Answer:

C. 13

Step-by-step explanation:

-5( 13 - 20 ) = 35

-5( -7) = 35

35 = 35

Hope this helps!

i need help whats the answer to this
49-25x^2

Answers

Answer:

x = 7/5 or x = (-7)/5

Step-by-step explanation:

Solve for x over the real numbers:

49 - 25 x^2 = 0

Multiply both sides by -1:

25 x^2 - 49 = 0

x = (0 ± sqrt(0^2 - 4×25 (-49)))/(2×25) = ( ± sqrt(4900))/50:

x = sqrt(4900)/50 or x = (-sqrt(4900))/50

sqrt(4900) = sqrt(4×25×49) = sqrt(2^2×5^2×7^2) = 2×5×7 = 70:

x = 70/50 or x = (-70)/50

70/50 = 7/5:

x = 7/5 or x = (-70)/50

(-70)/50 = -7/5:

Answer:x = 7/5 or x = (-7)/5

Answer:

(7-5x) (7+5x)

Step-by-step explanation:

49-25x^2

This is the difference of squares

7^2 - (5x)^2

The difference of squares is (a^2 - b^2 = (a-b)(a+b)

(7-5x) (7+5x)

How many terms are in the expression 1 over 6x - 18y + 9z - 2 =

Answers

Answer:

I believe there are four terms in this expression.

a poll shows that of all voters approve of the mayor's work. on three separate occasions a pollster selects a voter at random. what is the probability that on exactly one of these three occasions the voter approves of the mayor's work?

a poll shows that of all voters approve of the mayor's work. on three separate occasions a pollster selects

Answers

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

What is the binomial distribution formula?

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

Missing Information

The proportion of voters that approve the mayor's work is of 70%.

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a cyclist bikes a certain distance in 45 minutes , write an equation that shows the relationship between speed,s, and time,t, whne the distance is 100 miles

Answers

Step-by-step explanation:

d = 100miles

t = 45 × 60 = 2700sec

dis = speed × time

relationship btw speed and time when d distance is 100miles is

100 = speed × 2700sec

speed = 100 = 0.037m/s

2700

Given the measures shown in the diagram, which two triangles are congruent? 10 65° 45° 45° 70° S 10 60° 10 45° 45° R 10 65° T O A Q and S BR and T CR and S D Q and T​

Given the measures shown in the diagram, which two triangles are congruent? 10 65 45 45 70 S 10 60 10

Answers

Triangle Q ant T are congruent by ASA Criteria.

Using Angle Sum property

In triangle Q

Third angle = 180 - (65+ 45) = 180 - 110 = 70

In triangle R

Third angle = 180 - (60+ 45) = 180 - 105 = 75

In triangle S

Third angle = 180 - (70+ 45) = 180 - 115 = 65

In triangle T

Third angle = 180 - (65+ 45) = 180 - 110 = 70

As from all triangle the one length all have of 10 unit.

So, Triangle Q ant T are congruent by ASA Criteria.

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Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?

Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!! HELP, and can someone

Answers

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

How do you do trigonometric ratios step by step?Determining Side Lengths Using Trigonometric Ratios.The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.Identify the reference angle, the adjacent leg, the opposite leg, and the hypotenuse.Identify the information you are given and the information you are looking for.Identify the trigonometric ratio that relates the two side lengths from Use cos because it deals with the adjacent angle and the hypotenuse, which is all that we have here.The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).The three basic functions in trigonometry are sine, cosine and tangent. Based on these three functions the other three functions that are cotangent, secant and cosecant are derived.Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding.

cos (61 degrees) = c/19

plug in cos(61) degrees into your calculator to get .484

484 = c/19

Multiply both sides by 19 to isolate c by itself.

9.20 = c

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we assume that with a linear relationship between two variables, for any fixed value of x, the observed ________ follows a normal distribution.

Answers

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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to construct a confidence interval using matched pairs, we must compute the standard deviation of the

Answers

We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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OK so I need help on this trigonometry problem, I need it by June 3rd HELP ME PLZ!
I asked my teacher and he said it's not a right triangle at all,
You must create a triangular Animal pen that covers 40 square yards however it has to contain a 30-degree angle. Give the lengths of two sides of a triangle that include the angle but has an area of 40 sq yards.

Answers

Answer:

a=16 b =10 or any other combination that gives 160

a = 20 b=8

a = 32 b = 5

Step-by-step explanation:

The area of a triangle using the lengths of two sides and the sine of the included angle is ½ ab sin C  where a and b are sides and C is the angle.

A =40 = 1/2 ab sin 30°

sin 30° = 1/2 so

40 = 1/2*ab*1/2

40 =1/4 ab multiply each side by 4

160 = ab

any combination of sides that gives you 160 will work

Let's check if a=16 b =10

A = 1/2*16*10 sin 30°

A = 1/2*160*1/2

A = 40

OK so I need help on this trigonometry problem, I need it by June 3rd HELP ME PLZ!I asked my teacher

Crownfashions.com wants to estimate the average time that visitors to its website spend browsing the site. In a random sample of 49 visits this week, average browsing time is 13.6 minutes. Assume you know the population standard deviation is 5.2 minutes. Construct an 80% confidence interval estimate of average browsing time for the population of crownfashion.com visitors this week. Report the margin of error indicated by the interval.

Answers

The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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Daniel buys a refrigerator for Rs 21 850 . The price includes a Value Added Tax (VAT) of 15 %. How much is the VAT?

Answers

\(\large \mathfrak{Solution : }\)

let's find the value of added tax :

\( \dfrac{15}{100} \times 21850\)

\( \dfrac{3}{2} \times 2185\)

\( \dfrac{6555}{2} \)

\(3277.5\)

The value of added tax (VAT) = ₹ 3277.5

Given the expression

Choose all the equivalent expressions as your answer.

Given the expression Choose all the equivalent expressions as your answer.

Answers

The equivalent expressions of \(x^3\) are\(\frac{(x ^ 6)}{(x ^ 3)}\)and \(\frac{(x^{-3}) }{(x^{-6}) }\), the expressions \(\frac{(x^{30}) }{(x^{10})}\) and \(\frac{(x ^ 4) ^ 2)}{x ^ 2}\) are not equivalent to \(x^3\).

What are equivalent expressions?

Equivalent expressions are different algebraic expressions that have the same value when evaluated for a particular set of variables.

The equivalent expressions  \(x^3\) are:

\(\frac{(x ^ 4) ^ 2)}{x ^ 2}\) : This expression can be simplified as follows:

=\(\frac{(x ^ 4) ^ 2)}{x ^ 2}\)

= \(\frac{(x ^ 8)}{(x ^ 2) }\)

=\(x^{8-2}\)

= \(x^6\)

\(\frac{(x ^ 6)}{(x ^ 3)}\) : This expression can be simplified as follows:

=\(\frac{(x ^ 6)}{(x ^ 3)}\)

= \(x^{6-3}\)

=\(x^3\)

\(\frac{(x^{30}) }{(x^{10})}\) : This expression can be simplified as follows:

=\(\frac{(x^{30}) }{(x^{10})}\)

=\(x^{30-10}\)

=\(x^{20}\)

\(\frac{(x^{-3}) }{(x^{-6}) }\) : This expression can be simplified as follows:

=\(\frac{(x^{-3}) }{(x^{-6}) }\)

=\(x^{-3-(-6)}\)

=\(x^{-3+6}\)

=\(x^{3}\)

Therefore, the equivalent expressions of \(x^3\) are\(\frac{(x ^ 6)}{(x ^ 3)}\)and \(\frac{(x^{-3}) }{(x^{-6}) }\) , the expressions \(\frac{(x^{30}) }{(x^{10})}\) and \(\frac{(x ^ 4) ^ 2)}{x ^ 2}\) are not equivalent to \(x^3\).

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Identify the solution(s) of t2+15t=−36.

Answers

Answer:

i solved for t and got

t= -3, -12

Step-by-step explanation:

Answer:

t = - 12, t = - 3

Step-by-step explanation:

Given

t² + 15t = - 36 ( add 36 to both sides )

t² + 15t + 36 = 0 ← in standard form

(t + 12)(t + 3) = 0 ← in factored form

Equate each factor to zero and solve for t

t + 12 = 0 ⇒ t = - 12

t + 3 = 0 ⇒ t = - 3

a fair coin is tossed 29 times. what is the probability that at most 27 heads occur? a) 0.00000006 b) 0.00000081 c) 0.00000076 d) 0.99999994 e) 0.99999919 f) none of the above.

Answers

Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

Given that,

A fair coin is tossed 29 times.

We have to find what is the probability that at most 27 heads occur.

We know that,

A fair coin is tossed 29 times.

n=29

Probability of heads p=1/2

q= 1-p

q=1-1/2=1/2

We get

P (X=x) = ⁿCₓ qⁿ⁻ˣ pˣ

Now, the probability that at most 27 heads occurs is

P(X<27)

=1-[P(X=28)+ P(X=29)]

=1-[²⁹C₂₈(1/2)²⁹⁻²⁸(1/2)²⁸- ²⁹C₂₉(1/2)²⁹⁻²⁹(1/2)²⁹]

=1-[²⁹C₂₈(1/2)²⁹- ²⁹C₂₉(1/2)²⁹]

=1-[28+1](1/2)²⁹

=1-29×0.00000000186

=0.999999945

Therefore, Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

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