Order the integers from least to greatest.
-10,-17, -12,-9, -2, -5

After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

Given that,

The half-life of curium-243 is 28.5 days.

We have to find how many grams of curium-243 will be left in a sample with 5.6 grams after 12 days.

We know that,

The formula is

A(t) = A₀(1/2\()^{t/h}\)

Here,

t= 12 days, half life,

h =28.5 days .

And the initial value, A(0)=5.6 grams

So we will get

A(t) = 5.6(1/2\()^{12/28.5}\)

A(t) = 5.6×0.747 = 4.2 grams

Therefore, After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

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Answer:

Angles vertically opposite to each other are equal.

Step-by-step explanation:

There are two lines AB and CD intersecting at point O making angles 1 ,2,3 and 4.

The angles 1 and3  , angles 2 and 4 are vertically opposite angles.

Now consider the line AB

<1 + <2= 180 degrees--------- eq A

Now consider the line CD

<2+ <3= 180 degrees-----------eq B

As both equations are equal

< 1+ <2= <2+ <3 = 180 degrees

or

< 1+ <2= <2+ <3     or

< 1=  <3                           subtracting <2 from both sides

Now consider the line BA

<3+ <4= 180 degrees--------- eq C

Now consider the line DC

<4+ <1= 180 degrees-----------eq D

As both equations are equal

< 3+ <4= <4+ <1 = 180 degrees

or

< 3+ <4= <4+ <1    

or

< 3=  <1                           subtracting <4 from both sides

This holds true for all vertically opposite angles that they are equal.

These can be measured with a protractor.

This can also be proved that if we add angles 1,2,3 and 4 we will get 360

and if we subtract  angles 1 & 2 from 360 we will get 180 degrees which angles 3&4 make together.

<1+<2+<3+<4= 360 degrees

But <1 +<2= 180  

360 - [ <1+<2] = 180 degrees

<3 +<4= 180  

<1 +<2= <3 +<4= 180  

Answer:

3/5

Step-by-step explanation:

1/2=2/4

2+1=3

1+4=5

3/5

Answer:

Answer on a graph

Answer:

no

Step-by-step explanation:

"in order for a relation to be a function, each x must correspond with only one y value. If an x value has more than one y-value associate with it"

The distributed computation (e, →) is said to be consistent if all computations lead to the same result, regardless of the order in which the steps are performed.

Let g and h be consistent cuts of a distributed computation (e, →).

We must demonstrate that g ∪ h and g ∩ h are also consistent cuts of (e, →).

Let R be the set of events that are in both g and h. If we remove R from either g or h, we get a consistent cut since the removed events cannot cause a change in the outcome.

By removing R from both g and h, we obtain two new consistent cuts: g − R and h − R.

Thus, we can write:g = (g − R) ∪ R and h = (h − R) ∪ R. Since (g − R) and (h − R) are consistent cuts, it follows that their union, g ∪ h, is also a consistent cut. I

f we let S be the set of events that are in both g and h, then we can write:g = (g ∩ h) ∪ (g − S) and h = (g ∩ h) ∪ (h − S).

Again, (g − S) and (h − S) are consistent cuts, so their intersection, g ∩ h, is also a consistent cut.

Therefore, if g and h are consistent cuts of a distributed computation (e, →), then so are g ∪ h and g ∩ h.

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Answer:

The first option is answer

Step-by-step explanation:

Increasing interval:

Interval of values of x for which y increases.

In this question:

It increases for all values of x which are lower than -2.

So the answer is:

The first option is the answerwer.

Answer:

6.5%

Step-by-step explanation:

1000 in a box and he orders 5 boxes.

1000x5= 5000

So he orders 5000 paper clips

1 box is £15.40 and he order 5, so £15.40x5= £77

£77 is between £55 and £79.99 so he will get 6.5% discount.

After the discount he will pay  £71.99

Answer: 15 months

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

First, you do the stuff in parentheses. 2+3/6 = 2.5

Then, exponent, 3 x 3 x 3 = 27

Then, do 6 x 2.5 = 15

15+27 = 42

The probability distribution of the number of hours per day people are able to relax is constructed, and probabilities of relaxing more than 4 hours, between 2 to 6 hours, and not relaxing at all are 0.283, 0.767 and 0.068 respectively. The mean and standard deviation are 3.326 hours and 1.950 hours (approx.) respectively.

The probability distribution of X is:

X Frequency Probability

0 114                    0.068

1 156                    0.093

2 336                    0.201

3 251                     0.150

4 316                      0.189

5 231                     0.138

6 149                    0.089

7 33                    0.020

8 60                    0.036

      1676                     1.000

The probability that a person relaxes more than 4 hours per day is:

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= 0.138 + 0.089 + 0.020 + 0.036

= 0.283

The probability that a person relaxes from 2 to 6 hours per day is:

P(2 ≤ X ≤ 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 0.201 + 0.150 + 0.189 + 0.138 + 0.089

= 0.767

The probability that a person does not relax at all is:

P(X = 0) = 0.068

The mean Mx is:

Mx = Σ(X * P(X))

= 00.068 + 10.093 + 20.201 + 30.150 + 40.189 + 50.138 + 60.089 + 70.020 + 8*0.036

= 3.326 hours

The standard deviation Ox is:

Ox = sqrt[Σ(X^2 * P(X)) - Mx^2]

= sqrt[(0^20.068)+(1^20.093)+(2^20.201)+(3^20.150)+(4^20.189)+(5^20.138)+(6^20.089)+(7^20.020)+(8^2*0.036) - 3.326^2]

= 1.950 hours (approx.)

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Answer:

13.91

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached.

From the diagram the length of the vector along x component is given as:

Vx = Vcos(theta)

theta is the angle between the vector and the x axis

V is the length of the vector

Given

theta = 22°

V = 15

Substitute the given values into the formula above

Vx = 15cos22°

Vx = 15×0.9272

Vx = 13.91

Hence the length of the x-component of the vector is approximately 13.91

To calculate the length of the curve defined by r(t) = 〈2 cos(t), 2 sin(t)〉 with the domain -π/2 ≤ t ≤ π/2, we need to find the arc length using the following formula:

Arc length = ∫(from a to b) ||r'(t)|| dt

First, let's find the derivative r'(t) of the given vector function r(t):

r(t) = 〈2 cos(t), 2 sin(t)〉
r'(t) = 〈-2 sin(t), 2 cos(t)〉

Next, find the magnitude ||r'(t)|| of the derivative vector:

||r'(t)|| = √((-2 sin(t))^2 + (2 cos(t))^2)
||r'(t)|| = √(4 sin^2(t) + 4 cos^2(t))

Factor out 4:

||r'(t)|| = √(4(sin^2(t) + cos^2(t)))

Since sin^2(t) + cos^2(t) = 1:

||r'(t)|| = √(4) = 2

Now, we can find the arc length by integrating ||r'(t)|| over the given domain:

Arc length = ∫(from -π/2 to π/2) 2 dt

To integrate, simply multiply the constant by the difference in t:

Arc length = 2(π/2 - (-π/2)) = 2(π) = 2π

So, the length of the curve is 2π.

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F distribution is used with the global test of the regression model to reject the null hypothesis.

The hypothesis test will be conducted using a novel distribution. After the English statistician Sir Ronald Fisher, it is known as the F distribution. A ratio, the F statistic is (a fraction). One set of degrees of freedom is for the denominator, and the other set is for the numerator.

According to the null hypothesis, all group population means are equal. Because it is assumed that the populations are normal and that they have similar variances, the equal means hypothesis indicates that the populations have the same normal distribution. All groups are samples from populations with the same normal distribution, according to the null hypothesis. According to the alternative theory, at least two of the sample groups are drawn from populations with various normal distributions.

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Answer:The value of 147 + (-43) + (-16) is 88.

Step-by-step explanation:

88

its basically 147 - 43 - 16=88

A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.

Using sample data, hypothesis testing is used to determine a hypothesis's credibility. It is represented as H0, and it is sometimes referred to as the "null."

Given; The average thickness and standard deviation of a sample of 50 eyeglass lens samples are 3.05 millimeters and.34 millimeters, respectively.

Such lenses should have a true average thickness of 3.20 mm. Utilizing a =.05

False hypothesis H0: Alternative hypothesis: mu1= mu2 HA: 'mu1' and 'ne'

Sample Size 50 Sample Mean 3.05 Sample Standard Deviation 0.34 Intermediate Calculations Standard Error of the Mean 0.0481 Degrees of Freedom 49 t Test Statistic -3.1196 Two-Tail Test Lower Critical Value -2.0096 Upper Critical Value 2.0096 p-Value 0.0030 Reject the null hypothesis

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Answer:

1/2

Step-by-step explanation:

1/4 (4x - 8) + 3x =0

distribute the 1/4

x-2+3x=0

combine like terms

-2+4x=0

move -2 to the other side [by ADDing +2 to each side

4x=2

divide [by 4 on both sides]

x=1/2

Answer:

The first step is to calculate the interest that accrues over the 3-month period:

Interest = Principal x Rate x Time

= $4,000 x 0.075 x (3/12)

= $75

The amount due on the loan is the sum of the principal and interest:

Amount due = Principal + Interest

= $4,000 + $75

= $4,075

Rounding to the nearest cent gives: $4,075.00

The volume of the pyramid is 30 inches cube.

The base of the pyramid is an equilateral triangle with an area of 6 inches².  The height of the pyramid is 15 inches.

Therefore, the volume of the pyramid can be calculated as follows:

volume of the pyramid = 1 / 3 BH

where

Therefore,

B = 6 inches²

H = 15 inches

Hence,

volume of the pyramid = 1 / 3 × 6 × 15

volume of the pyramid = 1 / 3 × 90

Therefore,

volume of the pyramid = 30 inches³

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Answer:

d is the correct answer to your question

Answer:

9.2 units

Step-by-step explanation:

cause the last guy is right...

Well, CEOs are on the top of the food chain. It takes a lot of work and ambition to become one, and once they are one, CEOs accept a huge amount of responsibility - that means having to take blame if things go wrong and having more tasks to complete such as having to attend numerous meetings, make decisions. They are also on the board of directors.

Assistants do not have to do as much, they likely won't have that much responsibility or experience, their tasks revolve around ensuring meetings are scheduled and performing other ad-hoc duties.

(Not Mine)

The sequence  {\(a_{n}\)} converges.

The limit of the sequence is \(\lim_{n \to \infty} a_n\) = 0

To determine whether the sequence {\(a_{n}\)} converges or diverges, we can analyze the behavior of the sequence as n approaches infinity.

Let's simplify the expression for \(a_{n}\):

\(a_{n}\) = \(\frac{ln(n+1)}{\sqrt[3]{n} }\)

As n becomes larger, the numerator ln(n+1) grows, grows, but at a slower rate compared to the denominator \(\sqrt[3]{n}\)  This is because the cube root function has a greater effect on the overall value as n increases. The cube root of n  becomes larger much faster than the natural logarithm of n+1.

Since the denominator dominates the behavior of the sequence, the terms \(a_{n}\) become increasingly small as n tends towards infinity. In other words, the sequence converges to zero.

the given sequence {\(a_{n}\)} converges to zero. The logarithmic term in the numerator grows slowly compared to the cube root term in the denominator as n approaches infinity. This dominance of the denominator leads to the convergence of the sequence to zero.

To provide a more rigorous explanation, we can use the limit properties. Let's consider the limit of the sequence as n approaches infinity:

\(\lim_{n \to \infty} \frac{ln(n+1)}{\sqrt[3]{n} }\)

We can apply L'Hôpital's rule to evaluate this limit. Taking the derivative of the numerator and the denominator with respect to n, we get:

\(\lim_{n \to \infty} \frac{1}{n+1}/ \frac{1}{3 \sqrt[3]{n^{2} } }\) =\(\lim_{n \to \infty}\frac{3\sqrt[3]{n^{2} } }{n+1}\)

Simplifying further, we have:

\(\lim_{n \to \infty}\frac{3\sqrt[3]{n^{2} } }{n+1}\) = \(\lim_{n \to \infty} \frac{3. n^{2/3} }{n+1}\) = 0

Therefore, the sequence {\(a_{n}\)} converges to zero as n approaches infinity

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Answer:

Step-by-step explanation:

Use compound interest formula

Given:

Substitute the values and calculate:

Correct choice is B

The height of triangle ABE is 24 cm

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

The triangle

From the triangle, we have the following ratios

h : 20 = (36 - h) : 10

Express as fraction

h/20 = (36 - h)/10

So, we have

h/2 = (36 - h)

This gives

h = 72 - 2h

So, we have

3h = 72

Divide

h = 24

Hence, the height is 24 cm

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The length and width are possible dimensions for the garden is l = 20 ft; w = 10 ft.

The characteristics of a square and a rectangle in a flat shape are very different. Although both are rectangular, the nature and characteristics of these two buildings are different.

The difference between a square and a rectangle can be seen from the properties they have. These properties are also characteristics of squares and rectangles. For this reason, if we want to mention the difference between the two wakes, then we must know their characteristics.

Your question is incomplete but most probably your full question was:

Which length and width are possible dimensions for the garden?

l = 20 ft; w = 5 ft

l = 20 ft; w = 10 ft

l = 60 ft; w = 20 ft

l = 55 ft; w = 30 ft

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Answer:  (c) a translation 5 units to the RIGHT

Step-by-step explanation:

Consider h(x) = A(x - h)² + k

f(x) = x²

g(x) = (x - +5)²

               ↓

              positive means to  the RIGHT

(c) a translation 5 units to the RIGHT

Here we have to considered that

h(x) = A(x - h)² + k

here

A represent the vertical stretch (by factor of A)

h represent the horizontal shift (positive = Right, negative = Left)

k represent the vertical shift (positive = Up, negative = Down)

f(x) = x²

g(x) = (x - +5)²

              ↓

             positive shows to  the RIGHT

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To find the local maximum and local minimum values of the function f(x) = 3 + 6\(x^2\) - 4\(x^3\), we can use the First and Second Derivative Tests.

The critical points of the function can be determined by finding where the first derivative is equal to zero or undefined. Then, by analyzing the sign of the second derivative at these critical points, we can classify them as local maximum or local minimum points.

To find the critical points, we first calculate the first derivative of f(x) as f'(x) = 12x - 12\(x^2\). Setting this derivative equal to zero, we solve the equation 12x - 12\(x^2\) = 0. Factoring out 12x, we get 12x(1 - x) = 0. So, the critical points occur at x = 0 and x = 1.

Next, we find the second derivative of f(x) as f''(x) = 12 - 24x. Evaluating the second derivative at the critical points, we have f''(0) = 12 and f''(1) = -12.

By the First Derivative Test, we can determine that at x = 0, the function changes from decreasing to increasing, indicating a local minimum point. Similarly, at x = 1, the function changes from increasing to decreasing, indicating a local maximum point.

Therefore, the local minimum occurs at x = 0, and the local maximum occurs at x = 1 for the function f(x) = 3 + 6\(x^2\) - 4\(x^3\).

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