Sebastian grew 2 1/3 inches each year for the past 3 years. How many inches total has Sebastian grown in the past 3 years?

The statement "Rational expressions contain exponents" is sometimes true.

Sometimes true - ExplanationRational expressions are those expressions which can be written in the form of fractions with polynomials in the numerator and denominator. Exponents can appear in the numerator, denominator, or both of rational expressions, depending on the form of the expression. Therefore, it is sometimes true that rational expressions contain exponents, and sometimes they do not.For example, the rational expression `(x^2 + 2)/(x + 1)` contains an exponent of 2 in the numerator. On the other hand, the rational expression `(x + 1)/(x^2 - 4)` does not contain any exponents. Hence, the given statement is sometimes true.

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Answer:

  C. Vertical angles

Step-by-step explanation:

Given angles 5 and 8 where line c crosses line a, you want to know what type they are.

Where two lines cross, four angles are formed. They all share the vertex point where the lines intersect. If they share a side (and no interior space), they are adjacent angles that form a linear pair. As such, they are supplementary.

In the given figure the supplementary angle pairs where line c crosses line a are ...

  (5, 6), (6, 8), (7, 8), (5, 7)

If the angles do not share a side, but are formed from opposite rays, they are "vertical angles" and are congruent.

The vertical angle pairs there are ...

  (5, 8), (6, 7)

Angles 5 and 8 are vertical angles, choice C.

__

Additional comment

Angle pairs (1, 8) and (2, 7) are "alternate exterior angles." Angle pairs (3, 6) and (4, 5) are "alternate interior angles."

Assuming lines b and c are parallel, considering also angles where line b crosses line a, there are additional supplementary pairs of angles:

  (1, 2), (2, 4), (3, 4), (1, 3), (1, 6), (1, 7), (2, 5), (2, 8), (3, 5), (3, 8), (4, 6), (4, 7)

When parallel lines are crossed by a transversal, all of the acute angles are congruent, all of the obtuse angles are congruent, and the acute angles are supplementary to the obtuse angles. The angles are referred to by different names (and different theorems), depending on where they are in relation to the transversal and the parallel lines.

The problem here is mostly concerned with vocabulary. The "how to do this" is "learn the vocabulary."

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Answer:

Using the "AC Method" I got (w - 2) (w + 9)

Step-by-step explanation:

Answer:

(w−2)(w+ 9)

Step-by-step explanation:

Grouping

Step 1:

Use the sum-product pattern

w²  + 7 − 18

w² + 9 − 2 −18

Step 2:

Common factor from the two pairs

w²+ 9 − 2 − 18w

( w+ 9) − 2( w+ 9)

Step 3:

Rewrite in factored form

(w + 9) − 2( w+ 9)

(w−2)(w+9)

8) The percent of people that said that Pinocchio was their favorite Disney Movie is of: 28%.

9) The percent of people that said that Pinocchio or Cars was their favorite Disney movie is of: 39%.

10) The two movies that about half the people say were their favorite is of: Pinocchio and Toy Story.

From the pizza graph, the sum of all the percentages must be of 100%, hence the Pinocchio percentage is obtained as follows:

10 + 11 + 14 + 15 + 22 + P = 100

72 + P = 100

P = 100 - 72

P = 28%.

Then the percentage for Pinocchio or Cars is of:

28 + 11 = 39%.

The percentage for Pinocchio or Toy Story is of:

28 + 22 = 50%.

(about half).

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The hare ran 5.8 mph to win the race.

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

Given that, a tortoise and a hare run in the NYC marathon for 26.2 miles, the hare crosses the finish line first in a time of 4.5 hours.

Speed = distance/time

Speed of hare = 26.2/4.5 = 5.8 mph

Hence, The hare ran 5.8 mph to win the race.

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Answer:

y=-2x+17

Step-by-step explanation:

Answer:

\( \frac{6}{x} = \frac{8}{24} \)

\(8x = 144\)

\(x = 18\)

\( \frac{8}{24} = \frac{y}{12} \)

\(24y = 96\)

\(y = 4\)

So x = 18 and y = 4.

Answer:

9 days

Step-by-step explanation:

Answer:

180=90+10x  X = 9 days

Step-by-step explanation:

The youth hockey team already played 3 matches in which they scored 6, 9 and 2 goals.

Let

the score of the fourth goal = x

The number of goals must be greater than 3 for the average score to be greater than 5

Answer:

All real Numbers

Step-by-step explanation:

So, because there are arrows on both ends, it goes forever. And because it isn't straight horizontal or straight vertical, both the domain and range are (-∞,∞)

The critical value using a significance level of 0.01 is equal to 2.797.

According to the question, the total number of observations is given by the formula

Total number of observations = n₁ + n₂, Also, n₁ = 13 and n₂ = 13 so

Total number of observations = 13+13 = 26

We know that the Degree of freedom is equal to two less than the total number of observations that is

26 - 2 = 24

=> Degree of Freedom = 24

If we use the t-distribution table, the critical value which is corresponding to 24 degrees of freedom and 0.01 significance level is equal to 2.797

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Complete Question:

An operations manager with General Motors corporate offices wishes to determine if the true mean productivity of employees at its Detroit, Michigan plant is different from its Opel/Vauxhall Plant in Bochum, Germany. For this analysis, productivity will be measured by the number of cars that employees assemble per day. Random samples of employees in Detroit and Bochum are selected, and the productivity scores at each assembly plant are recorded. The following results are obtained.

t-Test: Two-Sample Assuming Equal Variances

Detroit

Bochum

Mean

58.5

54.3

Variance

42

56

Observations

13

13

Pooled Variance

XX

Hypothesized Mean Difference

0

df

XX

t Stat

XXXXX

P(T<=t) one-tail

XXXXX

t Critical one-tail

XXXXX

P(T<=t) two-tail

XXXXX

t Critical two-tail

XXXXX

Using a significance level of 0.01, the critical value of the appropriate test statistic to conduct the test of hypothesis for the belief that there is a difference in the mean productivity is:

Answer:

3 dozen cookies

Step-by-step explanation:

Let x = dozen of cookies using .75 cups of sugar

Equation is \(\frac{1.25}{5} = \frac{.75}{x}\)

1.25x = 5(.75)

1.25x = 3.75

x = 3 dozen cookies

10.Let's solve for f.

gx=fx−4

Step 1: Flip the equation.

fx−4=gx

Step 2: Add 4 to both sides.

fx−4+4=gx+4

fx=gx+4

Step 3: Divide both sides by x.

fx/x=gx+4/x

The correct answer would be f= gx+4/x

11. Let's solve for f.

hx=12fx+2

Step 1: Flip the equation.

12fx+2=hx

Step 2: Add -2 to both sides.

12fx+2+−2=hx+−2

12fx=hx−2

Step 3: Divide both sides by 12x.

12fx/12x = hx-2/12x

The correct answer would be F= hx-2/12x

12.  Let's solve for f.

kx=(−2f)(−x)

Step 1: Flip the equation.

2fx=kx

Step 2: Divide both sides by 2x

2fx/2x= kx/2x

The correct answer would be F= k/2

Side note: "/" is supposed to represent division and fractions

Answer:

10. f(x) was translated 4 units down

11. f(x) is stretched vertically by a factor of 12 and translated 2 units up

12. f(x) is stretched vertically by a factor of 2, reflected vertically along the x-axis, and reflected horizontally along the y-axis

Step-by-step explanation:

you have to explain what happened to f(x)

start by following the process SRT (stretch, reflection translation) for SR y then x transformations and for T x translation then y translation

Answer:

1.47 miles/min (to 3sf)

Step-by-step explanation:

Total amount of time taken for both parts of the journey

= 12 minutes + 122 minutes

= 134 minutes

Average speed for the entire journey = 197 miles ÷ 134 minutes

                                                              = 1.47 miles/min (to 3sf)

The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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Answer: w = -6

Step-by-step explanation:

-30 = 3(w + 6) + 5w

-30 = 3w + 18 + 5w

-30 = 8w + 18

-48 = 8w

w = -6

Hope this helps

Answer:

5

Step-by-step explanation:

Slope is number by X

Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.

Time is the duratiοn between twο events. Speed is the measure οf hοw fast sοmething mοves οver a given distance. Distance is the amοunt οf space between twο pοints οr οbjects.

Tο find οut hοw much faster Michael swam the 50-meter freestyle than the 100-meter freestyle, we need tο calculate the difference between their speeds.

Let's first find οut Michael's speed in meters per secοnd fοr each race.

Fοr the 50-meter freestyle:

speed = distance / time = 50 meters / 23.04 secοnds ≈ 2.17 meters/secοnd

Fοr the 100-meter freestyle:

speed = distance / time = 100 meters / 47.77 secοnds ≈ 2.09 meters/secοnd

Nοw, tο find the difference in speed, we can subtract the speed οf the 100-meter freestyle frοm the speed οf the 50-meter freestyle:

2.17 meters/secοnd - 2.09 meters/secοnd ≈ 0.08 meters/secοnd

Therefοre, Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.

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The power rule for logarithms states that logb(M^p) = p * logb(M). The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.

The power rule states that logb(M^p) = p * logb(M), where M, b, and p are positive real numbers.

To understand this rule, let's consider an example. Suppose we have log2(8^2). According to the power rule, this is equivalent to 2 * log2(8).

In this case, M is 8, b is 2, and p is 2. The power rule tells us that we can bring the exponent (p) down and multiply it with the logarithm of the base (b) raised to the number (M).

So, log2(8^2) can be simplified as 2 * log2(8), which is 2 * 3 = 6.

In general, the power rule allows us to simplify logarithmic expressions by bringing the exponent down and multiplying it with the logarithm of the base.

This rule is particularly useful when dealing with complex logarithmic expressions and simplifying them to a more manageable form.

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Answer:

A. Line segment.

Step-by-step explanation:

A straight path with 2 endpoints is a line segment. Line segments Are lines that stretch out but stop at a certain point.

hope this helps.

Answer:

53

Step-by-step explanation:

Sol'n

Let the remaining angle of a triangle be x.

x+71+56=180 (Sum of angles of a triangle is 180°)

or, x+127=180

or, x=180-127

.:, x=53°

.:, The measure of third angle is 53°

Answer:

3in. is the answer

doooo itttt fassstttt

mark it as brInlist

The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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The term (sin6nπ)2 oscillates between 0 and 1, but it does not affect the overall behavior of the sequence as n approaches infinity. Hence, the upper limit of the sequence is positive infinity (∞), and the lower limit is 0.

To find the upper and lower limits, we need to understand how the sequence behaves as n approaches infinity. For this sequence, as n gets larger, the term (-1)nn alternates between -1 and 1.

However, (-1)nn becomes insignificant compared to the other terms as n approaches infinity. Therefore, the upper limit of the sequence is positive infinity (∞), and the lower limit is negative infinity (-∞).

Similarly, to find the upper and lower limits, we need to analyze the behavior of the sequence as n approaches infinity. In this sequence, the term n2n dominates as n becomes larger. T

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The Solution of the 9x⁴ – 2x² – 7 = 0 is x = ±1, ±i √(7/9)

What are the quadratic equations?

A quadratic equation is a type of polynomial equation with degree 2 (the highest power of the variable is 2). Quadratic equations have the general form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

9x⁴ – 2x² – 7 = 0

Let's say that u = x²:

9u² – 2u – 7 = 0

Factor:

(u – 1) (9u + 7) = 0

u = 1, -7/9

Since u = x²:

x² = 1, -7/9

x = ±1, ±i √(7/9)

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Answer:

48

Step-by-step explanation:

The nth term of an AP is expressed as;

Tn = a+(n-1)d

Id 12th term is 32, hence;

T12 = a+11d

32 = a+11d ...1

If the 5th term is 18, then;

T5 = a+4d

18 = a + 4d ....2

Subtract 1 from 2;

32 - 18 = 11d - 4d

14 = 7d

d = 14/7

d = 2

From 1; 32 = a+11d

32 = a+ 11(2)

32 = a + 22

a = 32-22

a = 10

Get the 20th term

T20 = a+19d

T20 = 10 + 19(2)

T20 = 10 + 38

T20 = 48

Hence the 20th term is 48

Answer:

Obtuse triangle.

Step-by-step explanation:

A obtuse triangle has one angle that is larger than 90 degrees. There is a angle with 95 degrees.

Answer:

-2≤x≤2   f(x)=[x+3]

first  the sign is ≤ it means the point is solid point and the interval is x+3

By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.

A root of a function is a value for x that makes the function equal to zero.

In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.

The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.

So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.

Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.

The roots of f(x) will be the values of x that we used as factors in each step of the division process.

This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.

Complete Question

If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.

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