Add f(x)=2x^3 and g(x) = log(x+4) + 100

To find the dimensions of the rectangle with the greatest possible area inscribed in the parabola y = 2 - x^2, we need to maximize the area function by determining the x-coordinate where the derivative of the area function is zero.

Let's consider a rectangle with its base on the x-axis, which means its height will be given by the y-coordinate of the parabola. The width of the rectangle will be twice the x-coordinate. Therefore, the area of the rectangle is given by A = 2x(2 - x^2).
To maximize the area, we take the derivative of A with respect to x and set it equal to zero to find critical points. Differentiating A, we get dA/dx = 4 - 6x^2.
Setting 4 - 6x^2 = 0 and solving for x, we find x = ±√(2/3).
Since the rectangle is inscribed, we consider the positive value of x. Therefore, the x-coordinate of the upper corner of the rectangle is √(2/3). Plugging this value back into the equation of the parabola, we get y = 2 - (√(2/3))^2 = 2 - 2/3 = 4/3.
Hence, the dimensions of the rectangle with the greatest possible area are a base of length 2√(2/3) on the x-axis and a height of 4/3.

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a) The function f is not injective but is surjective.

b) The function f is injective and surjective.

c) The function f is not injective but is surjective.

d) The function f is not injective and not surjective.

a) The function f maps four elements from the domain {a, b, c, d} to five elements in the codomain {1, 2, 3, 4, 5}. Since there are more elements in the codomain than the domain, f cannot be injective. However, since every element in the codomain is mapped to by at least one element in the domain, f is surjective.

b) The function f(x) = x + 1 is a linear function that maps every real number to a unique real number. Hence, f is injective. Additionally, for every real number y, there exists x = y - 1 such that f(x) = y, meaning f is surjective.

c) The function f(m, n) = m + n maps pairs of integers from the domain Z × Z to integers in the codomain Z. Since there are infinitely many pairs that can result in the same sum, f cannot be injective. However, for every integer in the codomain, there exists at least one pair of integers in the domain whose sum is equal to it, making f surjective.

d) The function f(m, n) = m^2 + n^2 maps pairs of integers from the domain Z × Z to integers in the codomain Z. Since different pairs of integers can have the same sum of squares, f is not injective. Furthermore, there are integers in the codomain that cannot be obtained as a sum of squares, making f not surjective.

In summary, the injectivity and surjectivity of the given functions are as follows: a) not injective, surjective; b) injective, surjective; c) not injective, surjective; d) not injective, not surjective.

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Answer:

a

Step-by-step explanation:

Answer:

84500 is the correct answer

Answer:

40182 delta math

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D

Answer:

oblique

Step-by-step explanation:

Step-by-step explanation:

The axis of symmetry: is the line that makes the parabola split in exactly half and lines up with the vertex. For that parabola x=1 is the line of symetry.

The vertex is where the minimum of the graph is, on this graph you can eyeball it to be (1,-9)

The x-intercept is where y is 0 so that's where the lines intersex with the x-axis. (-2,0) and (4,0)

The y-intercept of the function is where x is 0 and where the parabola intersects with the y-axis. On this graph it would be (0,-8)

Hope that helps :)

The value of dy/dt for the given equation and values is -6.

To evaluate dy/dt, we can differentiate the given equation with respect to t using the chain rule. Starting with the equation 4xy - 3x + 4y^3 = -76, we differentiate both sides with respect to t.

Differentiating each term separately, we get:

(d/dt)(4xy) - (d/dt)(3x) + (d/dt)(4y^3) = 0

Using the chain rule, we can rewrite this as:

4(dy/dt)(x) + 4x(dy/dt) - 3(dx/dt) + 12y^2(dy/dt) = 0

Substituting the given values dx/dt = -8, x = 4, and y = -2, we have:

4(dy/dt)(4) + 4(4)(dy/dt) - 3(-8) + 12(-2)^2(dy/dt) = 0

Simplifying the equation, we get:

16(dy/dt) + 16(dy/dt) + 24 + 48(dy/dt) = 0

80(dy/dt) = -24

(dy/dt) = -24/80

(dy/dt) = -3/10

(dy/dt) = -0.3

Therefore, dy/dt evaluates to -0.3.

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Answer : a) a random variable X can only take the six values (1,2,3,4,5, and 6 ). If each value has equal probability, then p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6

b) The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9

Explanation :

A probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.[1] Sometimes it is also known as the discrete density function.

The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.

a) If each value has equal probability, the pmf of the random variable X which can only take the six values (1,2,3,4,5, and 6) is : p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6

b)If the probabilities of X(0,1,2, and 3) are 1/9,2/9,2/9, and 4/9. The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9

The sum of these probabilities is:p(0) + p(1) + p(2) + p(3) = 1/9 + 2/9 + 2/9 + 4/9 = 9/9 = 1

So, the pmf is defined for all X.

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Answer:

(f*g)(x) = 3x^2 + 25x - 18

Step-by-step explanation:

(f*g)(x) represents the product of the two functions f and g:

(f*g)(x) = 27x - 18 + 3x^2 - 2x, or, after simplification,

(f*g)(x) = 25x - 18 + 3x^2, or

(f*g)(x) = 3x^2 + 25x - 18

The exponent on the (x - 1) term include the following: A. 3.

In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.

Mathematically, an exponent can be represented or modeled by this mathematical expression;

bⁿ

Where:

By critically observing the graph of this polynomial function, we can logically deduce that it has a zero of multiplicity 3 at x = 1, a zero of multiplicity 1 at x = 3, and zero of multiplicity 2 at x = 4;

x = 1 ⇒ x - 1 = 0.

(x - 1)³

x = 3 ⇒ x - 3 = 0.

(x - 3)

x = 4 ⇒ x - 4 = 0.

(x - 4)²

Therefore, the required polynomial function is given by;

P(x) = (x - 1)³(x - 3)(x - 4)²

Exponent of (x - 1)³ = 3.

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The value of limits after using limit laws is [tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]

What are Limit Laws?

Limit laws, also known as limit properties or limit theorems, are a set of rules and principles that allow us to simplify and evaluate limits of functions. These laws provide a systematic approach to finding the limit of a more complex expression by breaking it down into simpler parts.

Given:

[tex]\lim_{x \to 2} f(x) &= -3 \\\lim_{x \to 2} g(x) &= 4 \\\lim_{x \to 2} h(x) &= 7\end{align*}\textbf{(a) Calculate} $\lim_{x \to 2} (f(x) - 2g(x))$:[/tex]

Using the limit laws, we can split the expression and apply the limit laws individually:

[tex]\lim_{x \to 2} (f(x) - 2g(x)) &= \lim_{x \to 2} f(x) - \lim_{x \to 2} (2g(x)) \\&= \lim_{x \to 2} f(x) - 2 \lim_{x \to 2} g(x) \\&= (-3) - 2(4) \\&= -3 - 8 \\&= -11[/tex]

Therefore,[tex]$\lim_{x \to 2} (f(x) - 2g(x)) = -11$.[/tex]

[tex]\textbf{(b) Calculate} $\lim_{x \to 2} (h(x))^2$:[/tex]

Again, using the limit laws, we can apply the limit to the expression:

[tex]\lim_{x \to 2} (h(x))^2 &= \left(\lim_{x \to 2} h(x)\right)^2 \\&= (7)^2 \\&= 49[/tex]

Therefore,

[tex]\lim_{x \to 2} (h(x))^2 = 49$.\textbf{\\\\(c) Calculate} $\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)}$:[/tex]

Applying the limit laws, we can evaluate the limit as follows:

[tex]\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} &= \frac{\lim_{x \to 2} h(x) \cdot \lim_{x \to 2} g(x)}{\lim_{x \to 2} f(x)} \\\\&= \frac{7 \cdot 4}{-3}\\ \\&= \frac{28}{-3}[/tex]

Therefore,[tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]

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Answer:

Select all possible values for x in the equation.

x cubed=375.

5*the cubed root of 3

the cubed root of 375

75*the cubed root of 5

125*the cubed root of 3

I am trying to do a practice test to prepare for my real test tomorrow and I don't understand the question. Can anyone help explain it plz any help would be great.

Step-by-step explanation:

(a) The probability that a randomly chosen wedge of cheddar cheese is greater than 10.14 is found using the standard normal distribution as follows:

P(Z > z) = P(Z > (10.14 - µ)/σ)

= P(Z > (10.14 - 10.2)/0.2)

≈ 0.3085.

Therefore, the probability is approximately 0.3085.

(b) If a sample of 16 is randomly chosen, then the distribution of the sample mean weight is approximately normal with a mean of 10.2 ounces and a standard deviation of σ/√n,

Where n = 16.

The sample standard deviation is given by σ = 0.2, so the standard deviation of the sample mean weight is:

σ/√n = 0.2/√16

= 0.05.

Therefore, the distribution of the sample mean weight is approximately normal with a mean of 10.2 ounces and a standard deviation of 0.05 ounces.

(c) The probability that the sample mean weight of this sample of 16 is less than 10.14 is found using the standard normal distribution as follows:

P(Z < z) = P(Z < (10.14 - µ)/(σ/√n))

= P(Z < (10.14 - 10.2)/(0.2/√16))

≈ P(Z < -1.6)

≈ 0.0548.

Therefore, the probability is approximately 0.0548.

(d) The probability that the sample mean weight of this sample of 16 is greater than 10.14 is found using the standard normal distribution as follows:

P(Z > z) = P(Z > (10.14 - µ)/(σ/√n))

= P(Z > (10.14 - 10.2)/(0.2/√16))

≈ P(Z > -1.6)

≈ 0.9452.

Therefore, the probability is approximately 0.9452.

(e) The probability that the sample mean weight of this sample of 16 is between 10.14 and 10.3 is found

Using the standard normal distribution as follows:

P(a < Z < b) = P((a - µ)/(σ/√n) < Z < (b - µ)/(σ/√n))

= P((10.14 - 10.2)/(0.2/√16) < Z < (10.3 - 10.2)/(0.2/√16))

≈ P(-1.6 < Z < 2)

≈ 0.9452 - 0.0548

= 0.8904.

Therefore, the probability is approximately 0.8904.

(f) Let x be the average weight of a sample of these 16 cheese wedges that is below some value z.

Then, the probability that x is less than z is 0.07.

Using the standard normal distribution, we can find the z-score such that

P(Z < z) = 0.07 as follows:

z = inv Norm(0.07)

≈ -1.4758.

Therefore, the average weight of a sample of these 16 cheese wedges that is below the value z is:

x = µ + z(σ/√n)

= 10.2 + (-1.4758)(0.2/√16)

≈ 10.0625.

Therefore, there is only a 7% chance that the average weight of a sample of these 16 cheese wedges will be below 10.0625.

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Answer:

$27.50

Step-by-step explanation:

Hope this helps and have a great day!!!!

Step-by-step explanation:

Since his pay is increased by 10 percent, then you multiply 10% by 25 and then add that to 25.

25+10/100(25)=55/2

27.5

Hope that helps :)

Answer: 11

Step-by-step explanation:

Sooooo all I did was take the formula for the area of a triangle ( A= 1/2(b)(h) 0 and plug In the values. So 'b' would be 4 and 'h' would be 5.5. I assumed this rectangle had equal widths and equal heights.

Answer:

i. <DCB = [tex]53.13^{o}[/tex]

ii. Sin of <DCB = 0.8

Step-by-step explanation:

Let <DCB be represented by θ, so that;

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Thus from the given diagram, we have;

Sin θ = [tex]\frac{4}{5}[/tex]

        = 0.8

This implies that,

θ = [tex]Sin^{-1}[/tex] 0.8

   = 53.1301

θ = [tex]53.13^{o}[/tex]

Therefore, <DCB = [tex]53.13^{o}[/tex].

So that,

Sin of <DCB = Sin [tex]53.13^{o}[/tex]

                    = 0.8

Sin of <DCB = 0.8

The probability of three people sharing the same birthdays is approximately [tex]0.0000075[/tex] or [tex]0.00075[/tex]%, and there are three different pairs of people when there are three humans.

In conclusion, the probability of three people sharing the same birthdays is extremely low (approximately [tex]0.0000075 \ or \ 0.00075\%[/tex]), and when there are three humans, there exist three different pairs of people.

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a) the reading on the thermometer after 3 more minutes will be -3 degrees Celsius.

b) the thermometer will read 6 degrees Celsius after 1.5 minutes.

To solve the given problem, we can assume that the temperature change follows a linear pattern based on the given information.

(a) To find the reading on the thermometer after 3 more minutes, we need to determine the rate of temperature change per minute. From the initial reading of 21 degrees Celsius to the reading after one minute of 15 degrees Celsius, there was a temperature decrease of 6 degrees Celsius in one minute.

Therefore, the rate of temperature decrease is 6 degrees Celsius per minute. If this rate remains constant, after 3 more minutes, the thermometer will show a further temperature decrease of:

3 minutes * 6 degrees Celsius per minute = 18 degrees Celsius

Thus, the reading on the thermometer after 3 more minutes will be 15 degrees Celsius - 18 degrees Celsius = -3 degrees Celsius.

(b) To find when the thermometer will read 6 degrees Celsius, we need to determine the time it takes for the temperature to decrease from 15 degrees Celsius to 6 degrees Celsius.

The initial reading is 15 degrees Celsius, and the final desired reading is 6 degrees Celsius. Therefore, we need to calculate the time it takes for a temperature decrease of:

15 degrees Celsius - 6 degrees Celsius = 9 degrees Celsius

Since the rate of temperature decrease is 6 degrees Celsius per minute, we can set up the equation:

9 degrees Celsius = 6 degrees Celsius per minute * t minutes

Solving for t (the time it takes to reach 6 degrees Celsius):

t = 9 degrees Celsius / 6 degrees Celsius per minute = 1.5 minutes

Therefore, the thermometer will read 6 degrees Celsius after 1.5 minutes.

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Answer:

122

Step-by-step explanation:

180 - (43 + 15)

Answer:

The answer is 2.86

Step-by-step explanation:

you just have to divide 43 by 15

The range of the repair costs for the four car crashes is $5452.54 - $232 = $5220.54. The sample variance of the repair costs is $4,898,414.69, and the sample standard deviation is $2,214.17.

The range of the repair costs for the four car crashes is the difference between the highest and lowest cost, resulting in a range of $5220.54. This indicates the variability in the repair costs. The sample variance is a measure of the average squared deviation from the mean, calculated to be $4,898,414.69. It shows the dispersion of the repair costs from the average. The sample standard deviation is the square root of the variance, amounting to $2,214.17. It provides a measure of how spread out the repair costs are, with a higher value indicating greater variability.

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Answer:

10a-3b is your answer

Step-by-step explanation:

7a - 3(b - a)

7a-3b+3a

10a-3b

Answer:

[tex]f(t) = 1450(1.025)^{t}[/tex]

Step-by-step explanation:

Given

[tex]P =1450[/tex] -- principal

[tex]r = 2.5\%[/tex] --- rate

[tex]n = 1[/tex] --- compounded once a year

Required

Determine the function for compound interest

Compound interest f(t) is calculated as:

[tex]f(t) =P(1 + r/n)^{nt[/tex]

So, we have:

[tex]f(t) = 1450(1 + 2.5\%/1)^{1 * t}[/tex]

[tex]f(t) = 1450(1 + 2.5\%)^{t}[/tex]

[tex]f(t) = 1450(1 + 0.025)^{t}[/tex]

[tex]f(t) = 1450(1.025)^{t}[/tex]

Given that a random-sample of 250 people is surveyed to determine if they own a tablet, where 98 people own a tablet.

We have to find a confidence interval estimate for the true proportion of people who own tablets using a 95% confidence-level.

The formula to compute confidence interval estimate is given by;

[tex]CI = p \pm Z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}}[/tex]

Where;[tex]p[/tex] = Sample proportion[tex]Z_{\frac{\alpha}{2}}[/tex] = Critical value of Z at [tex]\frac{\alpha}{2}[/tex][tex]n[/tex] = Sample size

From the given data,Sample proportion, [tex]p = \frac{98}{250} = 0.392[/tex]

Level of Confidence, [tex]C= 95%[/tex]

As level of significance [tex]\alpha = (1-C) = 0.05[/tex]So, [tex]\frac{\alpha}{2} = \frac{0.05}{2} = 0.025[/tex]

Sample size, [tex]n = 250[/tex]

Now, we need to find the critical value of [tex]Z_{0.025}[/tex] such that the area to its right in the z-distribution is 0.025.Z-table shows the values of Z for given probabilities.

The closest value to 0.025 is 1.96. So, we can take [tex]Z_{0.025} = 1.96[/tex].

Therefore, the confidence interval estimate for the true proportion of people who own tablets using a 95% confidence level is given as;[tex]CI = 0.392 \pm 1.96\sqrt{\frac{0.392(1-0.392)}{250}}[/tex][tex]\Rightarrow CI = 0.392 \pm 0.067[/tex]

So, the lower limit of the interval is obtained as;

[tex]0.392 - 0.067 = 0.325[/tex]

And the upper limit of the interval is obtained as;

[tex]0.392 + 0.067 = 0.459[/tex]

Therefore, with 95% confidence, we say that the proportion of people who own tablets is between 32.5% and 45.9%.

The correct option is (A).

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Main Answer: The base of C' is {0110, 1001, 1100, 0011}.

Supporting Explanation: In a communication system, codification and decodification are used to encode and decode messages. C is the code for the message, where C={0000, 1100, 1010, 0110, 0101, 0011, 1001, 1111}. The code is a binary code since F=Z2. C' is the dual code of C. The codewords in C' are orthogonal to those in C. A basis for C' can be determined by finding a generator matrix for C'. Thus, the generator matrix for C is the parity check matrix for C'. A generator matrix for C is given as, G = [I | P] where P is the parity check matrix. The parity check matrix for C can be determined as, P = [-AT | Im-k]. Therefore, P = [0101; 1010; 1111].The rows of C' correspond to the columns of P. Thus, a basis for C' is {0110, 1001, 1100, 0011}.

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Answer:

24 units by 15 units

Step-by-step explanation: To find how many units the length and width are, divide each by 5:

120/5 = 24

75/5= 15

For every 5 feet, there is 1 unit .