End behavior of f(x)=−1/2x5 using the leading coefficient and degree, and state the domain and range

Answer:

66%

Step-by-step explanation:

\(-10x\:+\:\left(20\cdot \left(1-x\right)\right)=\:0\)

x = \(\frac{2}{3}\) = .666 = 66%

There are 28 ways to choose 6 teams for the playoffs if there are 8 college basketball teams in a certain sub-division.

To determine the number of ways to choose 6 teams for the playoffs out of the 8 college basketball teams in a certain Sub-Division, we can use the combination formula. The formula for combinations is given by

nCr = n! / (r! * (n-r)!),

where n represents the total number of teams and r represents the number of teams to be chosen.

In this case, n = 8 and r = 6.

Plugging in these values, we have

8C6 = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 28.

Therefore, there are total 28 ways to choose 6 teams.

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The likelihood of randomly selecting a chocolate chip cookie is (c) equally likely and unlikely

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

P(chocolate chip) = 50%

When a probability is at 50% ot 0.5, then it means that

The probability is equally likely and unlikely

Hence, the true statement is (c) equally likely and unlikely

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Answer:

The system has infinitely many solutions

Step-by-step explanation:

There are no variables left. And the final equation is correct.

It means the system is going to be correct for any value of variables. So there are infinitely many solutions

Answer:

Step-by-step explanation:

There are two equations in the question

\(2x+6y=12\ -->Equation\ 1\\\\x+3y=6\ -->Equation\ 2\\\\\)

If we take 2 common from the first Equation it becomes,

\(2(x+3y)=12\\\\x+3y=12/6\\\\x+3y=6\\\)

Now we can see that both the Equations are similar which means they would have the same graph.

Since both the equations have the same equation of line they have infinitely many solutions which means both the lines intersect at each and every point on the line, since both the lines are on top of each other.

We can also see that in Step 4 where 12 = 12 there are no variables in the equation which also means that the work is correct and Sean can say that the system of equations is consistent and dependent which means they have infinite number of solutions

Answer:

The answer is y=1

Step-by-step explanation:

hope this helps

Answer:

y = 1

Step-by-step explanation:

You need to find the a multiple divisible by all numbers, in this case that would be 90

you multiply everything so the denominator is 90

7/18 = 35/90

5/6 = 75/90

4/15 = 24/90

13/45 = 26/90

So 8 35/90 - (1 75/90 + y) = 3 24/90 + 2 26/90

6 50/90 - y = 5 50/90

subtract 6 50/90 from both sides

-y = -1

divide both sides by -1

y = 1

Answer:

It depends on what digits repeat

Step-by-step explanation:

A decimal with repeating digits after the decimal point can be converted to a fraction depending on the digits after the decimal point.

For example, let’s have 4/3

When we evaluate this using a calculator, we can see that we have recurring 3 after the decimal point

So 4/3 is actually 1.3333333333333

We can see that based on the number after the decimal point we can convert this to 4/3

Answer

It depends on what digits repeat

Step-by-step explanation:

I hope this helps!

Answer:

14/15÷3/5 =1 5/9

Step-by-step explanation:

14/15÷3/5=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

14/15×5/3=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

14×5 15×3=7045

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 70 and 45 using

GCF(70,45) = 5

70÷5 45÷5=14/9

The fraction

14/9

is the same as

14÷9

Convert to a mixed number using

long division for 14 ÷ 9 = 1R5, so

14/9=1 5/9

Therefore:

14/15÷3/5=1 5/9

Please mark brainliest

x²=y⇒x=√y

x=√112⇒10.583

x=√448⇒21.166

If the modified Harrod-Domar Growth model, c(g+δ)=(sπ- sW)(π/Y) +sW, if you're targeting a 4% growth rate with δ= 0.03, c= 3, π/Y = 0.5 and sπ= 25%= 0.25, then the rate at which the wage earners and rural households should save is 5.67%

To find the rate, follow these steps:

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Considering the definition of zeros of a function, the zeros of the function f(t)= (t-5)² - 9 are 2 and 8.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros of a function are those values ​​of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

Considering the function f(t)= (t-5)² - 9, if the zeros of a function are those values ​​of x for which the expression is equal to 0, you get:

(t-5)² - 9= 0

Solving:

(t-5)² = 9

t-5 = √9

t-5= ±3

Then:

t-5= 3

t= 3 +5

t= 8

and

t-5= -3

t= -3 +5

t= 2

Finally, the zeros of the function are 2 and 8.

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The sequence of the original DNA molecule, read 5' to 3', is 3' CTGTCCTAG 5'.

The Sanger sequencing method is a technique used to determine the nucleotide sequence of DNA. In this method, the DNA molecule is fragmented into different lengths and each fragment is then replicated using DNA polymerase and a mixture of regular nucleotides and dideoxynucleotides (ddNTPs). The ddNTPs lack a 3' hydroxyl group, preventing further DNA chain elongation after their incorporation.

In the given chromatogram, the sequence trace reads 5' GTCACGGATC 3'. The sequence is read in the 5' to 3' direction, which means that the first nucleotide in the sequence corresponds to the 5' end of the original DNA molecule.

To determine the original DNA sequence, we need to complement and reverse the given sequence. The complementary base pairing rules state that adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G). Complementing the sequence gives us 3' CAGTGCCGTA 5'. Reversing this sequence yields the final result of 3' CTGTCCTAG 5', which represents the original DNA sequence read from 5' to 3'.

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Answer:

distance covered in 2 hours = 80 km

distance covered in 1 hour = 80÷2 = 40 km

distance covered in 7/2 hours = 40 × 7/2

= 140 km

(3 1/2hours = 7/2 hours)

Answer:

the answer is -1 1/8

Step-by-step explanation:

-3/8 ÷-1/3

= -3/8×3/-1

= -3 × 3

  8 × -1

= 9/8

= -1 1/8

Answer:

4 is B

5 is C

Step-by-step explanation:

Answer:

You would have 3640 cookies, which is kinda crazy

Step-by-step explanation:

242424/333=728.

728 cookies per stick of butter.

Then do 728 x 5=3640

Let me know if it is correct!

Answer:

3x

Step-by-step explanation:

5x - 3x + 2x - x

2x + 2x - x

4x - x

3x

Hope this helps!

Answer:

5! (5 factorial) or 120 ways

Step-by-step explanation:

You can arrange P different ways. R can be arranged only 4 different ways because Pwill be in one of the spots. Next, you can arrange "I" 3 different ways because P and R are already arranged in 2 spots, meaning you cant put "I" there. Next, S can be arranged in 2 different ways for the same reason. And lastly, M can only be arranged in 1 different way because the other spots are taken.

You can put it in any order. For example, M could be arranged 5 ways and P could be arranged in 1 way. You will still get 120 ways

Hopefully this helped. The explanation might be a bit confusing but I tried my best. I'm not good with explaining my solutions but I always try

Answer:

120

Step-by-step explanation:

took the test and i got it right

Answer:

Step-by-step explanation:

\( \frac{20}{x} = 4\)

\( = > 20 = 4x\)

\( = > x = \frac{20}{4} \)

=> x = 5 (Ans)

It is true that the confidence intervals for the mean provide an estimate for where the true mean lies.

In statistics, a confidence interval denotes the likelihood that a population parameter will fall between a set of values for a given proportion of the time. A confidence interval depicts the likelihood that a parameter will fall between two values near the mean. Confidence intervals quantify the degree of uncertainty or certainty in a sampling procedure.

The mean is a basic mathematical average of two or more values. There are two sorts of means that may be calculated: the arithmetic mean and the geometric mean. A mean tells you the average of a bunch of values, which helps you contextualize each data point.

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The partial sum of the given sequence, 1 + 10 + 19 + ... + 199, can be found by identifying the pattern and using the formula for the sum of an arithmetic series.  Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

To find the partial sum of the given sequence, we can observe the pattern in the terms. Each term is obtained by adding 9 to the previous term. This indicates that the common difference between consecutive terms is 9.

The formula for the sum of an arithmetic series is Sₙ = (n/2)(a + l), where Sₙ is the sum of the first n terms, a is the first term, and l is the last term.

In this case, the first term a is 1, and we need to find the value of l. Since each term is obtained by adding 9 to the previous term, we can determine l by solving the equation 1 + (n-1) * 9 = 199.

By solving this equation, we find that n = 23, and the last term l = 199.

Substituting the values into the formula for the partial sum, we have:

S₂₃ = (23/2)(1 + 199),

= 23 * 200,

= 4600.

However, this sum includes the terms beyond 199. Since we are interested in the partial sum up to 199, we need to subtract the excess terms.

The excess terms can be calculated by finding the sum of the terms beyond 199, which is (23/2)(9) = 103.5.

Therefore, the partial sum of the given sequence is 4600 - 103.5 = 4496.5, or approximately 4497 when rounded.

Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

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If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

The equality statement is False (b) 7= -(-(7)).

The expression on the right side of the equation simplifies to -(-7), which is equal to 7, making the statement untrue. Therefore, 7=-(-7) should be used as the right equality declaration.

In other words, 7 is equal to the opposite of -(-7)

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical expression.

The associative, commutative, and distributive laws are the three fundamental principles of algebra. They facilitate the simplification or solution of problems and aid in illustrating the connection between different number operations.

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The final derivative is given by: (d/dx) y = sin(6x)^(1+2x) * [2 * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))]

To find the derivative of y = sin(6x)^(1+2x) using logarithmic differentiation, follow these steps:

Step 1: Take the natural logarithm (ln) of both sides of the equation:
ln(y) = ln(sin(6x)^(1+2x))

Step 2: Use the properties of logarithms to simplify the equation:
ln(y) = (1+2x) * ln(sin(6x))

Step 3: Differentiate both sides of the equation with respect to x:
(d/dx) ln(y) = (d/dx) [(1+2x) * ln(sin(6x))]

Step 4: Apply the chain rule to the right side of the equation:
(d/dx) ln(y) = (d/dx) (1+2x) * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))

Step 5: Simplify the derivatives on the right side:
(d/dx) ln(y) = 2 * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))

Step 6: Remember that (d/dx) ln(y) is equal to (d/dx) y / y.

Rewrite the equation as:
(d/dx) y / y = 2 * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))

Step 7: Multiply both sides of the equation by y:
(d/dx) y = y * [2 * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))]

Step 8: Substitute y = sin(6x)^(1+2x) back into the equation:
(d/dx) y = sin(6x)^(1+2x) * [2 * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))]

So, the derivative of y = sin(6x)^(1+2x) using  logarithmic differentiation is:
(d/dx) y = sin(6x)^(1+2x) * [2 * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))]



The final derivative is given by:

(d/dx) y = sin(6x)^(1+2x) * [2 * ln(sin(6x)) + (1+2x) * (d/dx) ln(sin(6x))]

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The derivative is: \(\[\frac{dy}{dx} = (1+2x) \cdot 6\cos(6x)\]\)

To find the derivative of the function \(\(y = \sin(6x)^{1+2x}\)\) using logarithmic differentiation, we can take the natural logarithm (ln) of both sides of the equation and then differentiate implicitly.

Taking the natural logarithm of both sides:

\(\[\ln(y) = \ln(\sin(6x)^{1+2x})\]\)

Using the properties of logarithms, we can simplify the right side:

\(\[\ln(y) = (1+2x) \ln(\sin(6x))\]\)

Now, we can differentiate both sides with respect to\(\(x\)\) using implicit differentiation:

\(\[\frac{1}{y} \cdot \frac{dy}{dx} = (1+2x) \cdot \frac{d}{dx}(\ln(\sin(6x)))\]\)

We can simplify the right side further by applying the chain rule:

\(\[\frac{1}{y} \cdot \frac{dy}{dx} = (1+2x) \cdot \frac{1}{\sin(6x)} \cdot \frac{d}{dx}(\sin(6x))\]\)

Using the chain rule on the right side:

\(\[\frac{1}{y} \cdot \frac{dy}{dx} = (1+2x) \cdot \frac{1}{\sin(6x)} \cdot 6\cos(6x)\]\)

Finally, solving for \(\(\frac{dy}{dx}\)\):

\(\[\frac{dy}{dx} = y \cdot (1+2x) \cdot \frac{6\cos(6x)}{\sin(6x)}\]\)

Substituting \(\(y = \sin(6x)^{1+2x}\)\) back in:

\(\[\frac{dy}{dx} = \sin(6x)^{1+2x} \cdot (1+2x) \cdot \frac{6\cos(6x)}{\sin(6x)}\]\)

Simplifying the expression, the derivative is:

\(\[\frac{dy}{dx} = (1+2x) \cdot 6\cos(6x)\]\)

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When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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The output when three workers are hired is 5 units..

To find the output when three workers are hired, we need to first determine the total cost and then use the marginal cost to calculate the output.

Find the total cost when three workers are hired.
Average total cost (ATC) = Total cost (TC) / Output (Q)
$50 = TC / Q
Since fixed cost (FC) is $130 and the marginal cost (MC) is $40 per worker, the total cost can be found by adding the fixed cost and the cost of the three workers.
TC = FC + 3(MC)
TC = $130 + 3($40)

Calculate the total cost.
TC = $130 + $120
TC = $250

Use the total cost and average total cost to find the output.
$50 = $250 / Q
Q = $250 / $50
Q = 5

Therefore, the output when three workers are hired is 5 units.

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