9. Determine how long it takes for 80% of the material to decay.
lodine 131, used in nuclear medicine, initial amount 85 milligrams, half-life 8 days.

The translated vertices are:

The vertices of the original figure are:

Now we want to apply a translation of four units to the right and 2 units down, then each point (x, y) becomes (x + 4, y - 2).

This means that the translated vertices are:

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Caitlyn used 4 of the 47-cent stamps and 6 of the 8-cent stamps.

To find out how many of each stamp Caitlyn used, we can set up a system of equations. Let's say Caitlyn used x 47-cent stamps and y 8-cent stamps.
According to the given information, Caitlyn used a total of 47x + 8y cents in postage, which is equal to $2.52 or 252 cents.
So, our first equation is 47x + 8y = 252.
Now, we need to find the values of x and y that satisfy this equation.
We can use a method called substitution to solve the system of equations. First, we can solve the first equation for x in terms of y:
47x = 252 - 8y
x = (252 - 8y) / 47
Now, we can substitute this expression for x into the second equation:
(252 - 8y) / 47 + y = 0
Simplifying this equation, we get:
252 - 8y + 47y = 0
39y = 252
y = 6
Now, we can substitute the value of y back into the equation to find the value of x:
x = (252 - 8(6)) / 47
x = (252 - 48) / 47
x = 204 / 47
x ≈ 4.34
Since we can't have a fraction of a stamp, Caitlyn must have used 4 of the 47-cent stamps and 6 of the 8-cent stamps.

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The best statistical test for them to utilize is two sample chi square test

Given that,

Diphtheria, tetanus, and pertussis (DTaP) vaccination administration in the thigh vs. arm was the topic of a study. By gender, data was gathered.

To find: Which statistical test would be the most appropriate for them to use

As here there are two independent samples in which each sample represent severe reactions to vaccine based on if shot is on thigh or the arm.

What is two sample chi square test?

Based on binned data, the chi-square two sample test is used. The binning for both data sets should be the same, it should be noted. The chi-square two sample test's fundamental premise is that if the two data samples are drawn from similar distributions, then there should be a similar number of observed points in each bin (adjusted for different sample sizes).

Therefore, two sample chi square test of independence would be best.

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(2x - 10) - (3x² + 10x) + (2x³ + 3x²)

= 2x - 10 - 3x² - 10x + 2x³ +3x²

= 2x³ - 8x - 10

Answer: A

Step-by-step explanation:

You have:

\(20cos(\frac{2\pi }{5} x)=10\sqrt{2}\)

Begin by dividing both sides by 20 to get:

\(cos(\frac{2\pi }{5} x)=\frac{\sqrt{2} }{2}\)

Take the arccosine of both sides to get:

\(arccos(cos(\frac{2\pi }{5} x))=arccos(\frac{\sqrt{2} }{2})\)

\(\frac{2\pi }{5} x=arccos(\frac{\sqrt{2} }{2} )\)

First of all, lets find the right side. Cosine of what gives sqrt 2 over 2? That would be pi/4, plus 2npi. Another solution would be 7pi/4, plus 2npi. We have:

\(\frac{2\pi }{5} x=\pi /4+2n\pi\)

\(\frac{2\pi }{5} x=7\pi /4+2n\pi\)

Isolate 'x' to get:

\(x=\frac{5}{2\pi } (\pi /4+2n\pi)=\frac{5}{8} +5n\)

\(x=\frac{5}{2\pi } (7\pi /4+2n\pi)=\frac{35}{8} +5n\)

The value of x is 1/3

Equations are expressions separated by an equal sign

Given the following equation

21x = 7

We are to find the value of x. Divide both sides by 21

21x/21 = 7/21

x = 7/21

x = 1/3

Hence the value of x is 1/3

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Answer:

if this is 4.88/16 then the answer is 0.305.

Answer:

hector's toy

Step-by-step explanation:

it traveled .02 m farther

Answer:

Step-by-step explanation:

Think money

which is more 70 cents or 72 cents?

The answer should be 72 cents.

So .72 - .70 = 0.02

.72 is larger.

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are equal then the two lines are parallel.

The four sets of opposing angles that each have their own vertex point, are on different sides of the transversal and are both either internal or exterior are called alternate angles.

In geometry, a transversal line is one that cuts across the plane in two places. It does so at two spots where two lines meet. Many right angles are produced when two transverse lines meet. There are four types of similar angles: matching, alternative interior, alternate exterior, and co-interior.

In geometry, two lines are considered parallel if and only if all pairs of alternative interior angles in any transversal are equal.

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7.7 in

Explanation

Step 1

Let

AB=5.1( black)

BC=2.6(red)

AC=?

AC is the line that goes from A to C, (blue)

Also

Step 2

replace

so, the answer is 7.7

Answer:

(4.5, 8) and (8, 4.5)

Step-by-step explanation:

Given the equations

(x+y)=12.5 ... 1

X ×Y=36 .... 2

From 2, Y = 36/X

Substitute into 1

x+ 36/x = 12.5

x^2 + 36 = 12.5x

x^2 - 12.5x + 36 = 0

10x^2 - 125x + 360 = 0

2x^2 - 25x + 72 = 0

Factorize

2x^2 - 16x - 9x + 72 = 0

2x(x-8)-9(x-8) = 0

2x-9 = 0 and x-8 = 0

x = 9/2 and x = 8

when x = 9/2

Y = 36/(9/2)

Y = 36 * 2/9

Y = 8

When x = 8

Y = 36/X

Y = 36/8

Y =  4.5

Hence the solutions are (4.5, 8) and (8, 4.5)

Answer:

Point A

Step-by-step explanation:

The question is asking for a drop in 3 degrees. That means whatever point we start on, we subtract 3 from it. We start on 0, so 0-3=-3. That is point A.

Answer:

A

Step-by-step explanation:

Answer:

10 units

Step-by-step explanation:

\(\sqrt{(0-6)^{2} +(10-2)^{2} }\\\\\sqrt{(-6)^{2}+(8)^{2} } \\\\\sqrt{36+64}\\\\\sqrt{100}\\\\10\)

Answer:

Step-by-step explanation:

reflect the graph over the x-axis

translate the graph up

vertically stretch the graph

The  p = 68/81 - 8/9^4On calculation, we get, p= 68/81 - 8/6561p= (68*6561 - 8*81)/(81*6561)p= 4220/534441Therefore, p= 4220/534441 Hence, the values of p and q are p= 4220/534441 and q= 4.

Given expression is 508₉ = (p×9²) + (8×9^q)In this expression, we have to convert the number 508₉ into decimal format to find the values of p and q.Step-by-step explanation:The conversion of the base 9 to decimal is: 5*9^2 + 0*9^1 + 8*9^0= 405 + 0 + 8 = 413Now the expression becomes, 413 = (p*81) + (8*9^q)We will find out the highest power of 9 which is less than 413. That is 9^2 = 81Let us divide 413 by 81. On division, we get 5 as quotient and 68 as remainder. Therefore,413 = 5*81 + 68Now the expression becomes, 68 = (p*81) + (8*9^q)

Therefore, 8*9^q = 68 - p*81We have to factorize 68 and 81.68 can be factored as: 2*2*17, and 81 can be factored as: 3*3*3*3Therefore, 8*3^2*3^q = 2*2*17 - p*3^4p= 2*2*17/(3^4) - 8*3^q/3^2p= 68/81 - 8/9^qNow the expression becomes, 68 - 8*9^q = (68/81 - 8/9^q)*81(68*81 - 8*9^q*81)/81 = 68 - 8*9^q5520 - 8*9^q = 68 - 8*9^qWe will add 8*9^q on both sides. Then, 8*9^q gets canceled out.5520 = 68 + 8*9^qWe will subtract 68 on both sides. Then, we get, 5452 = 8*9^qDividing 5452 by 8, we get, 681.5 = 9^qWe will find out the power of 9, which is equal to 681.5.

That is, 9^3 = 729, and 9^4 = 6561Therefore, 9^3 < 681.5 < 9^4We will take log base 9 on both sides of the equation, 9^3 < 681.5 < 9^4. Then, we get, 3 < log base 9 of 681.5 < 4On simplification, we get, 3.207 < q < 4We will take the value of q as 4, since it lies in the range of 3.207 < q < 4.We will substitute the value of q as 4 in the equation, p= 68/81 - 8/9^q

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Answer:

\(\boxed{\checkmark}\quad x+2=\pm\sqrt{\dfrac{27}{5}}\)

\(\boxed{\checkmark}\quad 5(x^2+4x)=7\)

\(\boxed{\checkmark}\quad 5(x^2+4x+4)=7+20\)

Step-by-step explanation:

Sergey is solving the quadratic equation 5x² + 20x - 7 = 0.

To solve the quadratic equation by completing the square, begin by moving the constant to the right side of the equation by adding 7 to both sides:

\(\implies 5x^2+20x-7+7=0+7\)

\(\implies 5x^2 + 20x =7\)

The next step is to factor out the leading coefficient from the terms on the left side:

\(\implies 5(x^2+4x)=7\)

Now we need to make the terms inside the parentheses a perfect square trinomial. To do this, add the square of half the coefficient of the term in x inside the parentheses, and add the distributed value to the right side of the equation:

\(\implies 5\left(x^2+4x+\left(\dfrac{4}{2}\right)^2\right)=7+5\left(\dfrac{4}{2}\right)^2\)

\(\implies 5(x^2+4x+4)=7+20\)

Factor the perfect square trinomial on the left side and simplify the right side of the equation:

\(\implies 5(x+2)^2=27\)

Divide both sides of the equation by 5:

\(\implies \dfrac{5(x+2)^2}{5}=\dfrac{27}{5}\)

\(\implies (x+2)^2=\dfrac{27}{5}\)

Square root both sides of the equation:

\(\implies \sqrt{(x+2)^2}=\sqrt{\dfrac{27}{5}}\)

\(\implies x+2=\pm\sqrt{\dfrac{27}{5}}\)

Finally, subtract 2 from both sides:

\(\implies x+2-2=-2\pm\sqrt{\dfrac{27}{5}}\)

\(\implies x=-2\pm\sqrt{\dfrac{27}{5}}\)

(a) ∃x ∈ T, F(x)

There exists a dog x that is a terrier and fierce.

(b) ∀x ∈ T, F(x)

For all dogs x that are terriers, x is fierce.

(c) ∃x ∈ D, (F(x) ∧ ∀y ∈ T, S(x,y))

There exists a dog x that is fierce and smaller than all terriers.

(d) ∃x ∈ T, ∀y ∈ (F∩D), y ≠ x → S(y,x)

There exists a terrier x such that for all dogs y that are both fierce and in the set D, if y is not equal to x, then y is bigger than x.

Quantifiers are used in symbolic logic to convey the meaning of phrases like "all" and "some". In this problem, we have a set D of dogs and a subset T of terriers, represented by the predicate T(x) which means "dog x is a terrier". We also have the predicates F(x) which means "dog x is fierce" and S(x,y) which means "dog x is smaller than dog y".

To write quantified statements for the given criteria, we need to express them using quantifiers. The first statement (a) requires the existence of a fierce terrier, which can be expressed as ∃x ∈ T, F(x). The second statement (b) requires that all terriers are fierce, which can be expressed as ∀x ∈ T, F(x).

The third statement (c) requires the existence of a dog who is fierce and smaller than all terriers. This can be expressed as ∃x ∈ D, (F(x) ∧ ∀y ∈ T, S(x,y)). Finally, the fourth statement (d) requires the existence of a terrier who is smaller than all fierce dogs, except itself. This can be expressed as ∃x ∈ T, ∀y ∈ (F∩D), y ≠ x → S(y,x).

In summary, quantified statements are an essential tool in symbolic logic that help to represent complex statements in a concise and precise way. They allow us to reason about the properties of sets and their elements, and to make logical deductions from given assumptions.

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The nurse manager approves two staff nurses to attend a national conference.

The nurse manager has given their authorization or consent for two staff nurses to participate in and attend a national conference. This decision indicates that the nurse manager recognizes the value and relevance of the conference for professional development and sees the benefit of the staff nurses' participation. By approving their attendance, the nurse manager demonstrates support for their growth, learning, and exposure to new knowledge, experiences, and networking opportunities available at the conference.

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The solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:

Given the set of inequalities expressed as;

x + 1 ≤ -3 or -4x < -8

For the inequality expression x + 1  ≤ -3

x  ≤ -3 - 1

x ≤ -4

For the inequality expression:

-4x < -8

Divide both sides by -4

-4x/-4 > -8/-4

x > 2

Hence the solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:

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Scenario 2 Magnifi Co. produces a high-end amplifier for musical aficionados. Historically, only 85% of the 200 amplifiers produced per month on average have met the company's demanding standards for quality control. Suppose a random sample of 50 amplifiers is taken from a month's production..

What is the probability that less than 40 of the amplifiers will meet the company's quality standards? b) What is the probability that between 40 and 45 inclusive of the amplifiers will meet the company's quality standards? c) What is the probability that more than 45 of the amplifiers will meet the company's quality standards? a) In order to solve for the probability that less than 40 amplifiers will meet the company's quality standards, we can use the binomial distribution formula: P(X < 40) = Σi=0^39 C(50, i) (0.85)i(1-0.85)50-i

This can be solved using a computer, calculator, or by using a binomial probability table. Using a binomial table, we can find that P(X < 40) = 0.024. Therefore, there is a 0.024 probability that less than 40 amplifiers will meet the company's quality standards. b) To solve for the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards, we can use the binomial distribution formula again. We need to solve for P(40 ≤ X ≤ 45): P(40 ≤ X ≤ 45) = Σi=40^45 C(50, i) (0.85)i(1-0.85)50-i This can also be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(40 ≤ X ≤ 45) = 0.435. Therefore, there is a 0.435 probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards. c) To solve for the probability that more than 45 amplifiers will meet the company's quality standards, we can use the binomial distribution formula one more time. We need to solve for P(X > 45): P(X > 45) = Σi=46^50 C(50, i) (0.85)i(1-0.85)50-i Once again, this can be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(X > 45) = 0.056. Therefore, there is a 0.056 probability that more than 45 amplifiers will meet the company's quality standards.Overall, it can be concluded that the probability that less than 40 amplifiers will meet the company's quality standards is low, the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards is relatively high, and the probability that more than 45 amplifiers will meet the company's quality standards is relatively low.

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Triangles

Looking at the image, It is safe to say there are two similar triangles having similar base and sides there.

Triangle BAC has the same base as Triangle DAC

Therefore, the vertices of the angle B is equivalent to the vertice of angle D

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There will be 640 possible combinations in total if there's no repetitions.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The different cards depends on if repetition are permitted in a 3 digit numerical combination, you were given 4 numbers.

If repetition are not permitted:

This mean that you have;

4 turns for the first digit,

5 turns for the second digit,

4 turns for the third digit,

8 turns for the fourth digit.

which means you have 4 x 4 x 5 x 8 possible solutions.

4 x 4 x 5 x 8 = 640

Hence, There will be 640 possible combinations in total if there's no repetitions.

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If X has the hypergeometric distribution, the minimum value that X can take is option (e) 0

The hypergeometric distribution models the probability of getting a certain number of successes in a fixed-size sample drawn without replacement from a finite population containing a known number of successes and failures.

The minimum value that X can take depends on the specific parameters of the distribution.

If the population size is N, the number of successes in the population is K, and the sample size is n, then the minimum value that X can take is max(0, n - (N - K)).

This is because the sample can contain at most n items, and if all of them are failures (i.e., none of them are successes), then X would be 0. On the other hand, if there are fewer than n failures in the population, then the sample can contain at most n - (N - K) successes. If n - (N - K) is negative, then there are more successes than failures in the population, and X can take any value between 0 and n, inclusive.

Therefore, the correct option is (e) 0

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Given:

The expression is

\(\sqrt{180m^2}\)

To find:

The value of the given expression by using the perfect squares.

Solution:

We have,

\(\sqrt{180m^2}\)

It can be written as

\(=\sqrt{2\times 2\times 3\times 3\times 5\times m^2}\)

\(=\sqrt{(2)^2(3)^25m^2}\)

\(=\sqrt{(2\times 3\times m)^25}\)

\(=\sqrt{(6m)^25}\)

\(=6m\sqrt{5}\)

Therefore, the value of given expression is \(6m\sqrt{5}\).

Answer:

1.35 miles

Step-by-step explanation:

5.4/4 = 1.35 miles per minute

The limit of |an+1 / an| as n approaches infinity is infinity, the ratio test tells us that the series diverges.

The series is defined by `∑(n=1 to ∞) n!/(120^n)`.

To determine whether this series is convergent or divergent, we can use the ratio test.

A series ∑is said to converge if the limit of the sequence of partial sums converges to a finite number and diverges otherwise.

The ratio test is a convergence test that is used to check whether an infinite series converges or diverges to infinity.

The Ratio Test: Let ∑a be a series such that limn→∞|an+1/an| = L.

Then the series converges absolutely if L < 1 and diverges if L > 1. If L = 1, then the test is inconclusive.

In this case, the nth term of the series is given by:

an = n! / (120^n)The (n+1)th term is given by:an+1 = (n+1)! / (120^(n+1))

We will now apply the ratio test to determine whether the series converges or diverges.

Let's simplify the ratio of the (n+1)th term to the nth term:

\(`|an+1 / an| = [(n+1)!/(120^(n+1))] / [n!/(120^n)]``|an+1 / an| = (n+1)120^n/120^(n+1)``|an+1 / an| = (n+1)/120``limn→∞ |an+1 / an| = limn→∞ (n+1)/120 = ∞`\)

Since the limit of |an+1 / an| as n approaches infinity is infinity, the ratio test tells us that the series diverges.

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Answer:

the slope is -1/2

the slope form is y = -1/2x -2

Step-by-step explanation:

Answer: The slope is -0.5

Step-by-step explanation:

The slope form is y = -0.5x -2

Answer:

1/6, 2/5, 3/7, 3/5

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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