An element with a mass of 840 grams decays by 22.9% per minute. To the nearest minute, how long will it be until there are 70 grams of the element remaining?

The middle is a square with side length of 12cm

Area of the square = 12 x 12 = 144 cm^2

There are 4 triangles with base of 13cm and height of 8 cm

Area of triangle = 1/2 x base x height

Area = 1/2 x 12 x 8 = 48cm^2 each

48 x 4 = 192 cm^2

Total area = 144 + 192 = 336 cm^2

The correct answer is, [–5, 3]. In the other words, the interval in which the function [tex]f(x) = \sqrt{x^2 + 2x - 15}[/tex] is increasing is [–5, 3].

To determine the interval in which the radical function [tex]f(x) = \sqrt{x^2 + 2x - 15}[/tex] is increasing, we need to find the interval(s) where the derivative of the function is positive.

Let's first find the derivative of f(x):

[tex]f'(x) = (1/2) * (x^2 + 2x - 15)^(-1/2) * (2x + 2)[/tex]

To find where f'(x) > 0, we set f'(x) = 0 and solve for x:

[tex](1/2) * (x^2 + 2x - 15)^(-1/2) * (2x + 2) = 0[/tex]

Since the derivative is never equal to zero (since the denominator (x^2 + 2x - 15)^(-1/2) is never equal to zero), there are no critical points.

To determine the intervals of increase, we can evaluate f'(x) at test points in each interval. We'll consider the intervals defined by the given answer choices:

[3, ∞):

Choose a test point x > 3, let's say x = 4.

Evaluate [tex]f'(4) = (1/2) * (4^2 + 24 - 15)^{(-1/2)} * (24 + 2)[/tex]

[tex]= (1/2) * (16 + 8 - 15)^{(-1/2)} * 10[/tex]

[tex]= (1/2) * (9)^{(-1/2)} * 10[/tex]

= (1/2) * (1/3) * 10

= 5/3

Since f'(4) > 0, the function is increasing in the interval [3, ∞).

(4, ∞):

Choose a test point x > 4, let's say x = 5.

Evaluate f'(5) = (1/2) * (5^2 + 25 - 15)^(-1/2) * (25 + 2)

= (1/2) * (25 + 10 - 15)^(-1/2) * 12

= (1/2) * (20)^(-1/2) * 12

Since f'(5) = 0, the function is not increasing in the interval (4, ∞).

[–5, 3]:

Choose a test point x in the interval, let's say x = 0.

Evaluate [tex]f'(0) = (1/2) * (0^2 + 20 - 15)^{(-1/2)} * (20 + 2)[/tex]

[tex]= (1/2) * (-15)^{-1/2} * 2[/tex]

[tex]= (1/2) * (1/\sqrt{15}) * 2[/tex]

[tex]= 1/\sqrt{15}[/tex]

Since f'(0) > 0, the function is increasing in the interval [–5, 3].

(–∞, –5] ∪ [3, ∞):

Since we have already determined the function is increasing in [–5, 3] and [3, ∞), this interval is valid.

Therefore, the correct answer is, [–5, 3]. In the other words, the interval in which the function [tex]f(x) = \sqrt{x^2 + 2x - 15}[/tex] is increasing is [–5, 3].

Learn more about intervals of increase here:

https://brainly.com/question/29096174

#SPJ12

Answer:

[tex]y=-\frac{1}{3}[/tex]

Step-by-step explanation:

- 3 + 9y = - 6

- 3 + 3 + 9y = - 6 + 3

9y = - 3

9y ÷ 9 = - 3 ÷ 9

[tex]y=- \frac{1}{3}[/tex]

Answer:

The First choice

Step-by-step explanation:

Answer:

A= 4.5×10^11

B= 3.5×10^3

Step-by-step explanation:

A

(5×10^3)= 5000

(9×10^7)=90000000

multiply both of them

=450000000000 or 4.5×10^11

B

(7×10^5)=700000

(2×10^2)=200

700000÷200

3500 or 3.5×10^3

The general solution of the given differential equation 7dy/dx + 56y = 8 is y(x) = -x/8 + C e^(-8x/7), where C is a constant.

To solve the differential equation, we first rearrange it to isolate dy/dx: dy/dx = (8 - 56y)/7. This is a first-order linear differential equation. The integrating factor is e^(∫(-56/7)dx) = e^(-8x/7). Multiplying both sides of the equation by this integrating factor, we obtain e^(-8x/7) dy/dx + 8e^(-8x/7)y = 8e^(-8x/7). The left-hand side can be written as the derivative of y multiplied by e^(-8x/7). Integrating both sides gives ∫d(y e^(-8x/7)) = ∫8e^(-8x/7) dx. Solving these integrals and rearranging, we find the general solution y(x) = -x/8 + C e^(-8x/7), where C is the constant of integration.

The largest interval I over which the general solution is defined is (-∞, ∞) since there are no singular points or restrictions mentioned in the differential equation. This means that the solution is valid for all real values of x.

To know more about general solution, click here: brainly.com/question/32062078

#SPJ11

Answer: -633

Explanation:

formula is a0= a1 + (n-1)d

a0 is what ur tryig to find

a1 = -14

n= 60

d = -11

Answer:

Step-by-step explanation:

As,

There is always a gap of -11 in all the proceedings

Hence,

- 14 -11 = -25

-14 -(11 ×2) = -36

So,

60th term

-14 -(11 × 60) = -674 (Ans)

Answer:

18 Skittles

6 M&Ms

Step-by-step explanation:

Set up an equation:

Variable x = number of skittles

Variable y = number of M&Ms

1.50x + 2y = 39

x + y = 24

In the second equation, isolate a variable:

x = 24 - y

Substitute the value of x for 24 - y in the first equation:

1.50(24 - y) + 2y = 39

Use distributive property

36 - 1.5y + 2y = 39

Combine like terms

36 + 0.5y = 39

Isolate variable y:

0.5y = 3

y = 6

Substitute the value of y for 6 in the second equation:

x + 6 = 24

Isolate variable x:

x = 18

Plug these values into any equation of your choice to see if these values are correct (I'll do both equations just to prove it):

1.50(18) + 2(6) = 39

27 + 12 = 39

39 = 39

Correct

x + y = 24

18 + 6 = 24

24 = 24

Correct

Answer:

1271.7 inches

Step-by-step explanation:

Given

[tex]d = 27in[/tex]

[tex]Rotations = 15[/tex]

Required

The total distance moved

First, we calculate the circumference of the wheel

[tex]c = \pi *d[/tex]

[tex]c = 3.14 * 27[/tex]

[tex]c = 84.78[/tex]

This represents the distance traveled in one complete rotation.

So, in 15 rotations.

[tex]Total = 15 * 84.78[/tex]

[tex]Total = 1271.7[/tex]

Answer: taake this link,  it has all the answers

Step-by-step explanation:                 https://quizlet.com/183183758/statistical-studies-scatterplots-practiceamdm-flash-cards/

The best option for the points on the graph is points are at (0.4, 7.8), (3.1, 6.0), and (9.8, 0.5).

In two-dimensional Cartesian geometry, two intersecting straight lines are used as reference lines. In three-dimensional Cartesian geometry, three straight lines with a common point are the intersections of the three coordinate reference planes.

From the attached file of scatter plot for the data, it is clear that the for every value of x there is a suitable value of y which was given in the question.

Considering x values and plot the y vale on the graph.

For x = 0.4; y = 7.8

For x = 3.1; y = 6.0

and for x = 9.8; y = 0.5

To know more about the Cartesian system, here

https://brainly.com/question/4726772

#SPJ2

Answer:

The sample is the amount of people because not everyone is getting chosen

Step-by-step explanation:

I also agree, the coach choose certain people to march cuz not everyone is gonna be able to get used.

Answer:

A 3-inch slice of the food item contains 255 calories.

Step-by-step explanation:

Set calories per inch slice as variable x.

2x = 170

x = 85 cal

Since each inch slice of the food item contains 85 calories, a 3-inch slice would contain:

3x = 3(85) = 255 cal

Answer:

(240,20)

Step-by-step explanation:

Answer:

10 km/h

Step-by-step explanation:

I'm not really sure about this but no ones answering your question and I wanna help.

So basically to calculate the average speed you need to divide the distance travelled by time taken

But you do not have the distance traveled. But it is mentioned that it takes u 30 minutes to walk from home to school when walking at 5 km/h so to find the distance all you have to do is... 30 x 5 = 150 km

Now that we have the time and distance all we have to do is find the average speed.

Average Speed = distance ÷ time

So 150 ÷ 15 = 10 km/h

Using the MGF and its derivatives, we have shown that the mean and variance of the standard normal distribution are both 0.

The MGF for the standard normal distribution is given as:

M(t) = e^(t²/2)

To find the mean of the standard normal distribution, we take the first derivative of the MGF with respect to t and evaluate it at t = 0:

M'(t) = (1/2)e^(t²/2) × 2t

Evaluating at t = 0:

M'(0) = (1/2)e⁰ × 2(0) = 0

Since the first derivative of the MGF evaluated at t = 0 is 0, this implies that the mean of the standard normal distribution is 0.

To find the variance of the standard normal distribution, we take the second derivative of the MGF with respect to t and evaluate it at t = 0:

M''(t) = (1/2)e^(t²/2) × 2t² + (1/2)e^(t²/2)×2

Evaluating at t = 0:

M''(0) = (1/2)e⁰ × 2(0)² + (1/2)e⁰ × 2

= 0 + 1

= 1

Since the second derivative of the MGF evaluated at t = 0 is 1, this implies that the variance of the standard normal distribution is 1.

To learn more on Normal Distribution click:

https://brainly.com/question/15103234

#SPJ1

Answer: g-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 is the correct answer

The inverse Laplace transform of X(s) = [tex]1/s^7[/tex] is f(t) =[tex]t^6.[/tex]

To locate the inverse Laplace rework of X(s) =[tex]1/(s^7[/tex]), we are able to use algebraic manipulation and the inverse Laplace transform assets said in Theorem 7.2.1, which permits us to discover the original characteristic while given its Laplace rework.

Using the assets of the Laplace transform, we will rewrite the given expression as:

X(s) = [tex]x^-1(1/s^7) = (1/s^7)[/tex]

We need to locate the feature f(t) such that its Laplace transform is X(s) = [tex]1/s^7[/tex]. By making use of Theorem 7.2.1, we understand that the inverse Laplace remodels of X(s) will give us f(t).

Now, we need to find a characteristic f(t) that has a Laplace transform [tex]1/s^7[/tex]. By examining the Laplace transform a desk or the usage of regarded formulas, we will decide that the Laplace remodel of [tex]t^n[/tex](wherein n is a high-quality integer) is given by means of[tex]n!/s^(n+1).[/tex]

In our case, we're looking for a function whose Laplace remodel is[tex]1/s^7.[/tex]Comparing this with the Laplace transform formulation cited earlier, we see that the exponent within the denominator of sought to be [tex]8 ^(7+1).[/tex]

Hence, f(t) must be t^6 (given that 6+1 = 7), and its Laplace remodel maybe [tex]6!/s^7 = 720/s^7.[/tex]

Therefore, the inverse Laplace transform of X(s) = [tex]1/s^7 is f(t) = t^6.[/tex]

In precis, by applying algebraic manipulation and making use of the inverse Laplace rework assets, we determined that the inverse Laplace transform of [tex]1/s^7 is f(t) = t^6[/tex]. This approach that a unique feature corresponding to the given Laplace rework is [tex]t^6.[/tex].

To know more about Inverse Laplace transformation,

https://brainly.com/question/27753787

#SPJ4

Answer:

.5428571 repeating

or 19/35

Answer:

2•15k

Step-by-step explanation:

Answer:

2(15k)

Step-by-step explanation:

PLZZ GIVE BRAINLIEST

The duration in minutes for 40 consecutive dormant periods are given in the following table:91 82 84 85 80 73 72 84 86 76 51 70 71 83 79 79 67 76 60 81 55 53 51 53 45 49 67 76 86 88 82 68 82 51 51 75 86 575 66.

Assuming that the waiting time follows an exponential distribution with mean parameter A, a uniformly most powerful test of size α = 0.01 for H o λ^2=80 vs H1 A<80 can be developed as follows: The null and alternative hypotheses are as follows:H0:λ^2=80, that is, the mean of the exponential distribution is 80 squared.H1:A<80, which implies that the mean waiting time between eruptions is less than 80 squared.α=0.01 is the level of significance.

The following test statistic T is used: T = [n(λ^2-80)] / 80^2where n is the sample size, and the critical region is the left-tail rejection area. The probability of observing the values in the given sample or a more extreme set of values is calculated as follows: Since we are performing a one-tailed test, we divide α by 2.α/2 = 0.005

The area in the left tail is 0.005, and the corresponding z-score is -2.33.The null hypothesis is rejected if the computed value of the test statistic falls in the critical region, which is in the left-tail rejection region. T < -2.33

Since the test statistic T = -1.91 falls in the non-critical region, we fail to reject the null hypothesis at the α=0.01 level of significance. Therefore, based on this test, we can conclude that there is insufficient evidence to suggest that the mean waiting time between eruptions is less than 80 squared.

Know more about exponential distribution:

https://brainly.com/question/30669822

#SPJ11

Answer:

The number will decrease in value

Step-by-step explanation: For example if we had 638.23 if I move the decimal to the left 3 times it would be .63823, and if we add zeros it would look like this, 0.63823 so the number would decrease in value

By classifying sets of three numbers from the interval [0...n] by their maximum element, we have provided a combinatorial proof of the identity 1, 2 + 2.3 + 3.4 + ... + (x - 1)^n = 2^(n+1).

The combinatorial proof of the identity 1, 2 + 2.3 + 3.4 + ... + (x - 1)^n = 2^(n+1) revolves around classifying sets of three numbers from the integer interval [0...n] by their maximum element.

Let's consider the right-hand side of the equation, which is 2^(n+1). This represents the number of subsets of an n-element set. We can think of each element in the set as having two choices: either it is included in a subset or not. Therefore, there are 2 choices for each element, resulting in a total of 2^(n+1) subsets.

Now, let's look at the left-hand side of the equation, which is the sum 1 + 2 + 2.3 + 3.4 + ... + (x - 1)^n. We can interpret each term as follows:

1: Represents the number of subsets with a maximum element of 0, which is only the empty set.

2: Represents the number of subsets with a maximum element of 1, which includes the subsets {0} and {1}.

2.3: Represents the number of subsets with a maximum element of 2, which includes the subsets {0, 1}, {0, 2}, and {1, 2}.

Similarly, for each subsequent term (x - 1)^n, it represents the number of subsets with a maximum element of x-1.

Now, if we add up all these terms, we are essentially counting the total number of subsets from the original set. This matches the right-hand side of the equation, which is 2^(n+1).

To know more about the combinatorial proof, click here;

https://brainly.com/question/32415345

#SPJ11

Answer:

i dont what an ellipse is but here's the answer:

8x + 32y = 121

Answer:

123‐10×40y=0

10×+40y=123

Answer:

91in^2

Step-by-step explanation:

First, add 11 and 15:   11 + 15 = 26

Second, divide it by 2: 26/2 = 13

Third, multiply it by the height: 13 * 7 = 91in^2

Answer:

surface area of cuboid=2(lb+bh+hl)

surface area of cuboid=2(12×5+5×2+2×12 )

surface area of cuboid=188in²

Answer: They need to complete 21 more jumps all together .

Step-by-step explanation: So 14+13=J

14+13=27

27=j

World record: 48; 48-27=21

They will have to jump 21 more times in a row .

We cannot construct a square that equals the sum of the areas of two given squares. This statement contradicts the mathematical principles and properties of squares and the Pythagorean theorem.

The statement that given any two squares, we can construct a square that equals the sum of the two given squares is actually false. This statement goes against the well-known mathematical concept known as the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem holds true for right-angled triangles, but it does not hold true for squares.

In fact, if we take two squares and try to add their areas together, the result will not be a square with an area equal to the sum of the two given squares. The resulting shape will be a non-square rectangle or some other irregular shape.

Therefore, we cannot construct a square that equals the sum of the areas of two given squares. This statement contradicts the mathematical principles and properties of squares and the Pythagorean theorem.

to learn more about Pythagorean theorem click here:

brainly.com/question/15624595

#SPJ11

The orthonormal basis for (2, 1), (2, 5) is therefore u1, u2 = (2/5, 1/5), (2/5, -1/5) because u2 = v2_orth/||v2_orth|| = (2/5, -1/5).

In R2, the internal result of the two vectors u and v is as follows: The Gram-Schmidt procedure can be used to request the transformation of (2, 1), (2, 5) into an orthonormal premise. u, v = 2u1v1 + u2v2. An orthonormal premise is made by changing over a bunch of directly free vectors utilizing the Gram-Schmidt process. Our set's principal vector, v1 = (2, 1), should serve as our starting point.

We standardize v1 to obtain our first orthonormal premise vector: We must locate the second vector in our set, v2 = (-2, -5), and we can orthogonalize v2 by deducting its projection from u1: u1 = v1/||v1|| = (2/5, 1/5) proj_u1(v2) = (v2 u1)u1 = (- 8/5, - 4/5)v2_orth = v2 - proj_u1(v2) = (6, - 21/5)Our second orthonormal premise vector is acquired by normalizing v2_orth: The orthonormal reason for (2, 1), (2, 5) is subsequently u1, u2 = (2/5, 1/5), (2/5, - 1/5) in light of the fact that u2 = v2_orth/||v2_orth|| = (2/5, - 1/5).

To know more about  orthonormal refer to

https://brainly.com/question/31992754

#SPJ11