All of the following expressions are equivalent except _____.
a) -5(x - 1)
b) (5 - 5)x
c) -5x
d) 5x
e) 5 - 5x

-6 + x = -7

+6        +6        add 6 to both sides, 6's cancel out on the left.

________

x = -1, is the answer.

Hope this helps! Let me know if you have any other questions related to this problem. :)

Answer:

x= -1

Step-by-step explanation:

-6+x = -7

x = -7+6

x= -1

The probability of getting a green marble first and a red marble second exists 5/26.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given: Red marbles = 3

Green marbles = 10

So, the total marbles = 3 + 10 = 13

Probability = Favorable outcomes  / Total outcomes

Since, here replacement is not allowed,

Therefore, the probability of getting a green marble and a red marble

= first red and second green + first green second red

= 3/13 × 10/12+ 10/13 × 3/12

= 2 × 3/13 × 10/12

= 30/78

= 5/13

The probability of getting a green marble first and a red marble second

= 10/13 × 3/12

= 30/156

= 5/26

Therefore, the probability of getting a green marble first and a red marble second exists 5/26.

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Comparing distributions and understanding the expected outcomes of a simulation can help ensure accuracy and reliability in statistical analysis.

To compare two distributions of the proportions of heads observed in your simulations, you can create histograms and compare their shapes, centers, and spreads. Ideally, the histograms should be roughly symmetric, with similar centers and spreads. Additionally, you can calculate summary statistics such as mean and standard deviation to further compare the two distributions.
What should have happened is that the two distributions should have been similar, as each coin has an equal probability of landing heads or tails. If the distributions are very different, it may suggest that the simulation was not run properly or that the coins were biased in some way.
To ensure accuracy in the simulation, it is recommended to run multiple trials with a large sample size to account for any chance variation. This will help ensure that the results accurately reflect the true probabilities of the coins landing heads or tails. Additionally, it may be helpful to physically examine the coins to ensure that they are not biased in any way that could affect the results.

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Answer:

region D

Step-by-step explanation:

all other regions are higher than $300

Answer:

C

Step-by-step explanation:

because its either A or C and when I did it I picked C and it was wrong.

¯\_(ツ)_/¯

In this situation, the value of the slope is equal to 4.90.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this taxi company, the total taxi service charge is given by;

y = 4.90x + 16.40

By comparison, we have the following:

Slope, m = 4.90.

y-intercept, c = 16.40.

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The value of g in g/3 + 18 = 20 is 6.

Two expressions with variables or integers are said to be equal when they are declared to be in an equation. Equations are questions at their core, and attempt to methodically find the answers to these questions have been the inspiration for the development of mathematics.

Given:

The equation, g / 3 + 18 = 20,

g / 3 = 20 - 18

g = 2 × 3

g = 6

Therefore, the value of g in g/3 + 18 = 20 is 6.

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Answer:

y=9/2x+2

Step-by-step explanation:

Answer:

x=2/9y + -4/9

Step-by-step explanation:

Solve for x:

2y−9x=4

Add -2y to both sides:

−9x+2y+−2y=4+−2y

−9x=−2y+4

Divide both sides by -9:

−9x /−9 =−2y+4 /-9

Then your answer is:

x= 2 /9 y+ −4/ 9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope I helped!

Good luck! :)

Answer:

1

Step-by-step explanation:

As can be seen, for h(t) where t is a multiple of 6, we get -6. Since 150 is a multiple of 6, 153 is 3 more and since the graph visually repeats every 6 units, we can see that h(t) when t is a (multiple of 6) + 3 = 1

Thus h(153)=1

Answer:

m=12.5    b=235 right? so multiply it and you get 2,937.5

Step-by-step explanation:

calculate it yourself if you no beleive

The integral using integration by parts with the indicated choices of u and dv is equal to,   \(\int\limits 5x^{2} lnx dx\) = \(\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )\) + c

Basic Power Rule:

f(x) = cxⁿ

f’(x) = c· n xⁿ⁻¹

Integration

Integrals

[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]:              

\(\int\limits cf(x)dx\) = c \(\int\limitsf(x) dx\)

Integration Rule [Reverse Power Rule]:

\(\int\limits x^{n} dx\) = \(\frac{x^{n+1} }{n+1}\) + c

Integration by Parts:  

\(\int\limits u dv\) = uv - \(\int\limits v du\)

Given that,

= \(\int\limits 5x^{2} lnx dx\)

Rewrite [Integration Property - Multiplied Constant]:

\(\int\limits 5x^{2} lnx dx\) = 5 \(\int\limits x^{2} lnx dx\)

Set u:  

u = \(lnx\)

[u] Logarithmic Differentiation:          

du = \(\frac{1}{x}\) dx

Set dv:  

dv = \(x^{2}\)                                                                                                        

[dv] Integration Rule [Reverse Power Rule]:  

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

Integration by Parts:  

\(\int\limits 5x^{2} lnx dx\) = 5 \(( \frac{x^{3}ln(x) }{3} - \int\limits \frac{x^{2} }{3} dx )\)

Rewrite [Integration Property - Multiplied Constant]:  

\(\int\limits 5x^{2} lnx dx\) = 5 \((\frac{x^{3}ln(x) }{3} -\frac{1}{3} \int\limits x^{2} dx )\)

Factor:  

\(\int\limits 5x^{2} lnx dx\) = \(\frac{5}{3} (x^{3} ln(x) - \int\limits x^{2} dx )\)

Integration Rule [Reverse Power Rule]:  

\(\int\limits 5x^{2} lnx dx\) = \(\frac{5}{3} (x^{3} ln(x) - \frac{x^{3} }{3} )\) + c

Factor:

\(\int\limits 5x^{2} lnx dx\) = \(\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )\) + c

Therefore,

The integral using integration by parts with the indicated choices of u and dv is equal to,   \(\int\limits 5x^{2} lnx dx\) = \(\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )\) + c

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The probability that the equipment will operate for at least 200 hours without failure is \((1-e^{-2} )^2[2e^-2+1]\).

Given:

mean = 1/100

Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.

probability p = 3/2\(p^{2} (1-p)\) + 3/3 \(p^{3}\).

= 3(\(1-e^-2)^2\)\(e^-2\) + (\(1-e^-2)^3\)

= \((1-e^-^2)^2[3e^-^2 - e^-^2+1]\)

= \((1-e^{-2} )^2[2e^-2+1]\)

Therefore the probability that the equipment will operate for at least 200 hours without failure is \((1-e^{-2} )^2[2e^-2+1]\).

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By answering the presented question, we may conclude that So Christian  equation spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

What is equation?

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry. Let's start by defining some variables to represent the number of words each student spelled correctly:

Let x be the number of words Christian spelled.

x + (3x - 2) + (2x + 1) = 95

6x - 1 = 95

6x = 96

x = 16

So Christian spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

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The all zeros of given function f(x)= x²+3x-18 are: x = -6  and x = 3.

The values of a variable in a function that cause the function to equal zero are known as the zeros of the function.

The given function:

f(x)= x²+3x-18

Or,

x²+3x-18 = 0

On factorizing:

x²+6x- 3x -18 = 0

Taking 'x' common.

x(x + 6) - 3(x + 6) = 0

Taking (x + 6) common.

(x + 6)(x - 3) = 0

x = -6  and x = 3.

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Answer:

The sum of interior angles in a triangle is 180°.

So we just have to add Al the angles and equate them to 189°

Step-by-step explanation:

\(70 + 65 + x + 35 = 180 \\ 135 + 35 + x = 180 \\ 170 + x = 180 \\ x = 180 - 170 \\ x = 10\)

Step-by-step explanation:

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If a raindrop falls to the ground from a raincloud at an altitude of 3000 meters, then it will take 24.74 seconds to fall

A raindrop falls to the ground from a raincloud at an altitude of 3000 meters.

We know the equation of motion

S = ut + 1/2at^2

Where S is the Displacement

u is the initial velocity

a is the acceleration

t is the time of motion

The value of S = -3000

u = 0 m/s

a = g = -9.8 meter per second square

Substitute the values in the equation

-3000 = 0×t + 1/2 ×-9.8 × t^2

-3000 = -4.9t^2

t^2 = -3000 / -4.9

t = 24.74 seconds

Therefore, it will take 24.74 seconds to fall

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Answer:

2(w+6)

Step-by-step explanation:

The radioactive element decays by 2% of its original mass every 3 days. The equation for the mass of the element as a function of time is given by: Mass(t) = Mass(0) * (0.98)^(t/3).

The decay of the radioactive element follows an exponential decay model. The equation for the mass of the element as a function of time can be derived from the given information. Since the element decays by 2% of its original mass every 3 days, we can express this as a decay factor of 0.98 (100% - 2% = 98%). Let Mass(t) be the mass of the element at time t, and Mass(0) be the initial mass of the element. The equation for the mass of the element as a function of time is given by Mass(t) = Mass(0) * (0.98)^(t/3), where t represents the time elapsed in days.

To predict the mass of the element after 10 days, we can substitute t = 10 into the mass equation. Using Mass(0) = 20 grams, we get Mass(10) = 20 * (0.98)^(10/3) ≈ 18.275 grams.

To find the instantaneous decay rate at 10 days, we need to take the derivative of the mass equation with respect to time and evaluate it at t = 10. Taking the derivative of Mass(t) = Mass(0) * (0.98)^(t/3) gives dMass(t)/dt = (Mass(0) * ln(0.98) * (1/3)) * (0.98)^(t/3). Evaluating this at t = 10, we get dMass(10)/dt ≈ -0.012695 grams/day. This represents the rate at which the mass is decreasing at t = 10 days.

To determine when the mass will be only half of its original amount, we need to find the value of t that satisfies Mass(t) = Mass(0)/2. Setting Mass(t) = 10 grams (half of the initial mass of 20 grams), we can solve the equation 10 = 20 * (0.98)^(t/3) for t. By taking the logarithm of both sides and solving for t, we find t ≈ 34.656 days. Therefore, the mass will be halved approximately 34.656 days after the start of the decay process.

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Answer:

B 7/8

Hope this helped.

The number of reindeer in St. Elsewhere in 1920 will be approximately 475.

The growth rate of .12 indicates an annual increase of 12%, meaning that each year the number of reindeer will be multiplied by 1.12. To find the number of reindeer in 1920, we need to use this growth rate over the 20-year period from 1900 to 1920.
Starting with the initial 52 reindeer, we can multiply by 1.12 for each year. This gives us:
Year 1: 52 * 1.12 = 58.24
Year 2: 58.24 * 1.12 = 65.10
Year 3: 65.10 * 1.12 = 72.90
Year 4: 72.90 * 1.12 = 81.60
Year 5: 81.60 * 1.12 = 91.15
Year 6: 91.15 * 1.12 = 101.66
Year 7: 101.66 * 1.12 = 113.27
Year 8: 113.27 * 1.12 = 126.13
Year 9: 126.13 * 1.12 = 140.43
Year 10: 140.43 * 1.12 = 156.36
Year 11: 156.36 * 1.12 = 174.16
Year 12: 174.16 * 1.12 = 194.10
Year 13: 194.10 * 1.12 = 216.45
Year 14: 216.45 * 1.12 = 241.58
Year 15: 241.58 * 1.12 = 269.87
Year 16: 269.87 * 1.12 = 301.72
Year 17: 301.72 * 1.12 = 337.62
Year 18: 337.62 * 1.12 = 378.10
Year 19: 378.10 * 1.12 = 423.77
Year 20: 423.77 * 1.12 = 475.30
Therefore, the number of reindeer in St. Elsewhere in 1920 will be approximately 475.

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Is the cost of a small art paintbrush $0.095 or $0.95?

Answer: 5

Step-by-step explanation: The answer is 5 because if you do 4.75 divided by 0.95 you will get 5.

(a) The independent variable in this study is writing positive statements may not. (b) The dependent variable in this study is happiness.

(c) the point estimate for the mean increase in happiness for the treatment group is 2 with a margin of error of 0.395.

(a) The independent variable in this study is writing positive statements or not, as this is the variable being manipulated to see its effect on the participants' happiness.

(b) The dependent variable in this study is the participants' happiness, as it is being measured to see if it is affected by the manipulation of the independent variable.

(c) Since the point estimate for the mean increase in happiness for the treatment group is:

9 - 7 = 2

The margin of error of the point estimate can be found;

Margin of error = z*(s√(n))

Where z is the z-score for the 90% confidence level, s is the standard deviation, and n is the sample size.

From the z-table, the z-score for the 90% confidence level will be 1.645.

Substituting the values;

Margin of error = 1.645*(1.2√(25))

Margin of error = 0.395

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Step-by-step explanation:

p(A|B) = p(A and B) / p(B) =(1/5) / (2/9) = 0.9

The probability that event A occurs is 5/8 , the probability that event B occurs is 2/9 , and the probability that events A and B both occur is 1/5 . The probability that A occurs given that B occurs is 0.9.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

The probability that event A occurs is 5/8

The probability that event B occurs is 2/9

The probability that events A and B both occur is 1/5.

So, The probability that A occurs given that B occurs

P(A|B) = P(A and B) / P(B)

          = (1/5) / (2/9)

          = 0.9

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After finding the value of theta, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

The equation tan(theta) = s^2/49 represents the speed, s, in feet per second, of a toy car driving around a circular track with an angle of incline, theta, where sin(theta) = 1/2.

To solve this problem, we need to use the given information about sin(theta) to find the value of theta. Since sin(theta) = 1/2, we can determine that theta is equal to 30 degrees.

Now that we know the value of theta, we can substitute it into the equation tan(theta) = s^2/49. Plugging in 30 degrees for theta, the equation becomes tan(30) = s^2/49.

The tangent of 30 degrees is equal to √3/3. So, we have √3/3 = s^2/49.

To solve for s, we can cross multiply and solve for s^2. Multiplying both sides of the equation by 49 gives us 49 * (√3/3) = s^2.

Simplifying, we get √3 * 7 = s^2, which becomes 7√3 = s^2.

To find the value of s, we take the square root of both sides. So, s = √(7√3).

Therefore, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

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The probability of a random patient being alcoholic with elevated cholesterol levels is 55/80, or 0.6875. The probability of a random patient being nonalcoholic is 320/400, or 0.8. Lastly, the probability of a random patient being nonalcoholic with Non elevated cholesterol levels is 248/400, or 0.62.

To calculate the probability of a random patient being alcoholic with elevated cholesterol levels, we must first determine the total number of patients with elevated cholesterol levels. This can be done by adding the number of alcoholic patients (55) with elevated cholesterol levels to the number of nonalcoholic patients (72) with elevated cholesterol levels.

The result is a total of 127 patients with elevated cholesterol levels. This means that out of 400 patients, 55 of them were alcoholic and had elevated cholesterol levels. Therefore, the probability of a random patient being alcoholic with elevated cholesterol levels is 55/400, or 0.6875.

The probability of a random patient being nonalcoholic is equal to the total number of nonalcoholic patients (320) divided by the total number of patients (400). This yields a probability of 0.8.

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Answer:

I think when X is two Y is gonna be 4

Answer: y=4

Step-by-step explanation:

y=1/2 x 2+3

y=1/2x2 + 3 (cancel the 2's) if you want to check if is correct take your calculator and do: 1/2 X 2

y=1+3

y=4

To find the volume of the solid generated by rotating the region bounded by the curves y = cos(x) and the x-axis on the interval [0, π/2] about the x-axis, we can use the method of cylindrical shells.

The volume V is given by the integral:

V = ∫[a,b] 2πx f(x) dx

In this case, the interval [a,b] is [0, π/2], and the function f(x) is cos(x).

V = ∫[0,π/2] 2πx cos(x) dx

To evaluate this integral, we can use integration by parts. Let's consider u = x and dv = 2π cos(x) dx. Then du = dx and v = 2π sin(x).

Using the formula for integration by parts, the integral becomes:

V = [2πx sin(x)]|[0,π/2] - ∫[0,π/2] 2π sin(x) dx

Evaluating the definite integral and plugging in the limits, we have:

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

V = π^2

Therefore, the volume of the solid is π^2 cubic units.

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Yes, a binomial can have three terms; however, this is referred to as a trinomial.

Binomials: What Are They?

The word "Binomial" refers to algebraic statements containing two dissimilar terms. For instance, 3x + 4x^2 is a binomial expression because it combines the two dissimilar terms 3x and 4x^2. The binomial 10pq + 13p^2q is the same.

What is a trinomial ?

The word "trinomial" refers to algebraic statements containing three dissimilar terms. An example of a trinomial is 3x + 5x^2 - 6x^3. This is because there are three phrases that are dissimilar to one another: 3x, 5x^2, and 6x^3. The trinomial 12pq + 4x^2 - 10 is the same.

These polynomial types contain a monomial as well.

The word "monomial" refers to algebraic expressions having just one term. In other words, it is a statement that includes any number of concepts that are similar. For instance, 2x + 5x + 10x is a monomial because it equals 17x when the like components are added. Furthermore, because each of these expressions comprises just one term, monomials, 4t, 21x2y, 9pq, etc.

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Answer:

48

Step-by-step explanation:

48 is divisble by all of them

LCM of the given number is 24, and we know that age of your sister lies between 40 and 50, so the number divisible by 24 and lying in the given range is your sister's age,

that is 48

( because 48 is only number between 40 and 50 which is divisible by 24 )

Answer:

b) 1.82n

Step-by-step explanation:

n + n - 0.18n

2n - 0.18n (combine like terms)

1.82n

Hope this helps!