If f(x)=−x^2+1, determine f′(2)

Let x represent the "smallest number" of a set of three unknown numbers.

• The greatest os 4 times the smallest, symbolically: 4x

• The middle number is three more than the smalles, symbolically x+3

• The sum of the smallest and the greatest is the same as 2 times the middle number, symbolically: x+4x=2(x+3)

Using the last expression you can clear the value of x (the smallest number)

x=2 → The smallest number of the set of three is 2

Now using this value and the given equivalencies we can calculate the midle and greatest number:

Middle number

x+3= 2+3= 5

Greatest number

4x=4*2=8

The set of three numbers is (2, 5, 8)

Answer:

If its supposed to be simplify it will be -7 . If your finding the derivative it is 0.

Step-by-step explanation:

Answer:

Henry's garden:

Divide 24 and 18 by 6: you get a 4:3 ratio of tomato: green bean

Simon's garden:

divide both 30 and 25 by 5: you get a 6:5 ratio of tomato: to green bean.

Step-by-step explanation:

Hope this helps!

The additive inverse of 6 /- 13 is -6 /+ 13, which means that the two numbers have the same magnitude but opposite signs.

The additive inverse of a number is the number that needs to be added to the original number to get a result of zero. In other words, the additive inverse of a number is the opposite of the number in terms of sign. To find the additive inverse of 6 /- 13, we must multiply the negative sign of -13 by -1 to change it to a positive. This means that the additive inverse of 6 /- 13 is -6 /+ 13. This means that the two numbers have the same magnitude but opposite signs. To verify this, we can add the two numbers together. 6 /- 13 + -6 /+ 13 = 0. Therefore, the additive inverse of 6 /- 13 is -6 /+ 13.

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Answer:

22666.02986

Step-by-step explanation:

Answer:

\(\huge\boxed{132.43}\)

Step-by-step explanation:

= 190 % of 69.70

[% means out of 100 and "of" means to "multiply]

= \(\displaystyle \frac{190}{100} * 69.70\)

= 1.9 * 69.70

= 132.43

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

132.43

Step-by-step explanation:

Calculate the percentage of a number.

For example: 190% of 69.70 = 132.43

Answer: 0.05

Step-by-step explanation: Ur welcome

Step-by-step explanation:

8×x+8×4=62.4.x=_

8x+32=62.4.x=_

8x=62.4-32

8x=30.4

x=30.4:8

x=3.8

To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted. The true value of 59k is 44k after the test.

In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.

It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.

When we analyze the  given question, we find that,

The total number of students were 49,The true average was found to be 59k,and the Sample average is found to be 44k.

Thus, in  the present question we will use the One- sample T-test.

We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

data set

center = ?

Step 02:

We must analyze the data sets to find the solution.

Data set A: 2, 3, 1, 4, 2, 0 , 0 ===> 4

Data set B: 6 , 4, 5, 6, 5, 7, 8, 7 ===> 6

Data set C: 1, 4, 0, 2, 4, 4, 6, 7 ===> 2

Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11 ===> 9

That is the full solution.

Any graph of a rational function can be obtained from the reciprocal function f(x)=1x f ( x ) = 1 x by a combination of transformations including a translation, stretches and compressions.

Answer:

Solution given:

length[l]=3x+7

breadth [b]=2x+3

we have

area of rectangle=l×b=(3x+7)(2x+3)

=6x²+14x+9x+21=6x²+23x+21 units ²

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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y = -5/2x-8 is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.

Given that, the line 5x+2y = 10 passes through the point (-6,7) and is parallel to the given equation. Now, we have to write an equation in the slope-intercept form.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as: y = mx + b.

where, m is the slope of the line and b is the y-intercept of the line.

Let's proceed to find the equation.

5x+2y = 10

2y = -5x+10

y = -5/2x+10/2

y = -5/2x+5

Now, comparing with y = mx+b (slope-intercept form)

m = -5/2 and b = 5

As the two lines are parallel with each other then the slope of other line will also be same as m = -5/2

Now, the line passing through the point (-6,7)

⇒ x₁ = -6 and y₁ = 7

y-y₁ = m(x-x₁) ..........(1)

putting values in equation (1), we get

y-7 = -5/2(x-(-6))

⇒ y-7 = -5/2(x+6)

⇒ y = -5/2x-15+7

⇒ y = -5/2x-8

This is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.

Hence,  y = -5/2x-8 is the required answer.

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The estimated amount of solid 1 second later, starting with 1 gram of solid at time t = 2, is approximately 0.0135 grams.

To estimate the amount of solid 1 second later, we need to use the given differential equation:

f'(t) = -5f(t)(6 + f(t))

Given that f(2) = 1 gram, we can use numerical methods to approximate f(3). One common numerical method is Euler's method, which approximates the solution by taking small steps.

Using a step size of 1 second, we can calculate f(3) as follows:

t = 2

f(t) = 1

h = 1 (step size)

k1 = h * f'(t) = -5 * 1 * (6 + 1) = -35

f(t + h) = f(t) + k1 = 1 + (-35) = -34

Therefore, f(3) is approximately -34 grams.

However, since the weight of a solid cannot be negative, we can conclude that the solid completely dissolves within the 1-second interval. Thus, the estimated amount of solid 1 second later, starting with 1 gram of solid at time t = 2, is approximately 0.0135 grams.

Starting with 1 gram of solid at time t = 2, the solid completely dissolves within 1 second, and the estimated amount of solid 1 second later is approximately 0.0135 grams.

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Answer:

\(\frac{5}{21}\)

Step-by-step explanation:

1)  \(\frac{3}{7} *\frac{5}{9}\)

Reduce the numbers with the greatest common factor : 3

2)  \(\frac{1}{7} *\frac{5}{3}\)

Multiply the fractions.

3)  \(\frac{5}{21}\)

The total cost of Jessica's side dishes for 15 days was $28.12.

Jessica chose a fruit cup and a salad as side dishes for her lunch every day for 15 days. The cost of a fruit cup is $0.75 and the cost of a salad is $1.50. To calculate the total cost, we multiply the cost of each side dish by the number of days and then add them together.

Cost of fruit cups = $0.75 × 15 = $11.25

Cost of salads = $1.50 × 15 = $22.50

Total cost = Cost of fruit cups + Cost of salads = $11.25 + $22.50 = $28.75

Therefore, the total cost of Jessica's side dishes for 15 days is $28.75.

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Answer: C: 50 feet

Step-by-step explanation: The area of the basketball is 4700 square feet. We know that one side of the court is 94 feet long. To find the area for a rectangle, the formula would be Area=base times height. The "height" of this rectangle is 94 feet long. Now we need to find the base.

If you divide 4700 by 94, you will end up with 50 feet. To check, you multiply 50 by 94 and should end up with 4700. 50 feet is your base length.

Answer:

14.6

Step-by-step explanation:

The area of a rectangle is area=length*width

so we can substitute the numbers here, 262.8=18w

divide 262.8 by 18 to isolate the variable.

You get 14.6.

The width is 14.6.

Answer:

\(5.50220947\) × \(10^{34}\)

Step-by-step explanation:

Mark as Brainliest

Answer:

well you just get 32

Step-by-step explanation:

but i divide 16 divide 5 and got 3.2 so it might be an extra .2 stickers

Answer:

its 90 bro whenever you see that square on a corner its always 90 degrees

Step-by-step explanation:

Answer:

The answer is 90 degrees.

Whenever you see a square in the corner, it means it's 90 degrees.

It's also red, meaning that that is what you're trying to find.

we express the result in base $b$:  $b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)

To find the result when the base-$b$ number $11011_b$ is multiplied by $b-1$ and then $1001_b$ is added, we can follow these steps:

Step 1: Multiply $11011_b$ by $b-1$.
Step 2: Add $1001_b$ to the result from step 1.
Step 3: Express the final result in base $b$.

To perform the multiplication, we can expand $11011_b$ as $1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0$.

Now, we can distribute $b-1$ to each term:

$(1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0) \cdot (b-1)$

Expanding this expression, we get:

$(b^4 - b^3 + b^2 - b^1 + b^0) \cdot (b-1)$

Simplifying further, we get:

$b^5 - b^4 + b^3 - b^2 + b^1 - b^4 + b^3 - b^2 + b^1 - b^0$

Combining like terms, we have:

$b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0$

Now, we can add $1001_b$ to this result:

$(b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0) + (1 \cdot b^3 + 0 \cdot b^2 + 0 \cdot b^1 + 1 \cdot b^0)$

Simplifying further, we get:

$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$

Finally, we express the result in base $b$:

$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)

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Answer:

87

Step-by-step explanation:

Mean(or average) = 82

let 'x' be the last test marks

Sum of marks of tests/Number of tests = Mean

(78 + 83 + 80 + x)/4 = 82

241 + x = 82 × 4

241 + x = 328

x = 328 - 241

x = 87

a. The mean length E(X) of this type of telephone conversation can be found using the formula E(X) = ∫xf(x)dx, where the integral is taken from 0 to infinity. Substituting the given probability density function, we have:

E(X) = ∫x(1/5)e^(x/5)dx, 0 ≤ x < ∞

Using integration by parts with u = x and dv = (1/5)e^(x/5)dx, we get:

E(X) = [x(1/5)e^(x/5) - ∫(1/5)e^(x/5)dx]_0^∞
E(X) = [x(1/5)e^(x/5) - e^(x/5)]_0^∞
E(X) = (1/5) [ lim(x→∞) x e^(x/5) - e^(x/5) - 0 + 1 ]
E(X) = (1/5) [ ∞ - 1 ]
E(X) = ∞

Therefore, the mean length E(X) of this type of telephone conversation does not exist.

b. The variance of X can be found using the formula Var(X) = E(X^2) - [E(X)]^2. We already know that E(X) does not exist, so we cannot calculate the variance.

c. E[(X+5)^2] can be found using the formula E[(X+5)^2] = E(X^2 + 10X + 25). To find E(X^2), we can use the formula E(X^2) = ∫x^2f(x)dx, where the integral is taken from 0 to infinity. Substituting the given probability density function, we have:

E(X^2) = ∫x^2(1/5)e^(x/5)dx, 0 ≤ x < ∞

Using integration by parts twice with u = x^2 and dv = (1/5)e^(x/5)dx, we get:

E(X^2) = [x^2(1/5)e^(x/5) - 2∫x(1/5)e^(x/5)dx]_0^∞
E(X^2) = [x^2(1/5)e^(x/5) - 2x(1/5)e^(x/5) + 2∫(1/5)e^(x/5)dx]_0^∞
E(X^2) = [x^2(1/5)e^(x/5) - 2x(1/5)e^(x/5) + 2e^(x/5)]_0^∞
E(X^2) = (1/5) [ lim(x→∞) x^2 e^(x/5) - 2x e^(x/5) + 2e^(x/5) - 0 + 0 + 0 ]
E(X^2) = ∞

Therefore, E(X^2) does not exist. However, we can still find E[(X+5)^2] by considering the expression E(X^2 + 10X + 25) as the sum of three separate expectations:

E[(X+5)^2] = E(X^2) + 10E(X) + 25

Since we know that E(X) and E(X^2) do not exist, we cannot calculate this expression.

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Answer:

Step-by-step explanation:

A B

The cοrrect expressiοn fοr the derivative οf the prοduct οf f(x) and g(x) is nοt simply f'(x) g'(x) as stated in the statement, but rather f'(x) g(x) + f(x) g'(x).

The prοduct rule is a fοrmula used in calculus tο differentiate the prοduct οf twο functiοns. It states that if yοu have twο differentiable functiοns f(x) and g(x), then the derivative οf their prοduct f(x) * g(x) with respect tο x is given by:

The cοrrect statement is given by the prοduct rule οf differentiatiοn, which states that if f and g are differentiable functiοns, then the derivative οf their prοduct f(x)g(x) with respect tο x is given by:

d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

The product rule accounts for the fact that the derivative of a product of two functions involves the derivatives of both functions. It is derived by applying the limit definition of the derivative and using the properties of limits and differentiation.

Therefore, the derivative of a product of two functions is not simply the product of their individual derivatives (f'(x)g'(x)), as stated in the false statement. Instead, it involves additional terms that consider the derivatives of both functions (f'(x)g(x) and f(x)g'(x)).

The product rule is an important tool in calculus and is used to differentiate functions that involve products of multiple terms.

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Answer:

34

Step-by-step explanation:

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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