The half-life of radium is 1620 year what fraction of the radium sample will remain after 3240 years

Answer:

The answer to your problem is, [tex]7\frac{1}{9}[/tex]

Step-by-step explanation:

Calculation process:

= [tex]\frac{16}{3}[/tex] ÷ [tex]\frac{3}{4}[/tex]

= [tex]\frac{16}{3}[/tex] × [tex]\frac{4}{3}[/tex]

= [tex]\frac{16*4}{3*3}[/tex]

= [tex]\frac{64}{9}[/tex] = [tex]7\frac{1}{9}[/tex]

Thus the answer to your problem is, [tex]7\frac{1}{9}[/tex]

The non-permissible values are any values of n that would make the original equation undefined. In this case, there are no such non-permissible values.

a.

The given equation is:

[tex]1 + x^4 = x[/tex]

Rearranging terms, we get:

[tex]x^4 - x + 1 = 0[/tex]

To solve this equation, we can use the quartic formula:

x = [ -b ± sqrt( b^2 - 4ac ) ] / 2a

Here, a = 1, b = -1, and c = 1, so we have:

x = [ -(-1) ± sqrt( (-1)^2 - 4(1)(1) ) ] / 2(1)

x = [ 1 ± sqrt( -3 ) ] / 2

Since the discriminant is negative, the solutions are complex:

x = [ 1 ± i*sqrt(3) ] / 2

Therefore, the non-permissible values are any values of x that would make the original equation undefined. In this case, there are no such non-permissible values.

b.

The given equation is:

3^(n-1) / (3^n + 6) + 2^n = 0

To solve for n, we can start by simplifying the first term:

3^(n-1) / (3^n + 6) = 3^(-1) / (1 + 2*3^(-n))

Substituting this into the original equation, we get:

3^(-1) / (1 + 2*3^(-n)) + 2^n = 0

Multiplying both sides by (1 + 23^(-n)), we get:

3^(-1) + 2^n(1 + 2*3^(-n)) = 0

Simplifying, we get:

2^n + 2*3^(n-1) = 0

Dividing both sides by 23^(n-1), we get:

(1/2)(1/3)^n + 1 = 0

Multiplying both sides by -2 and taking the logarithm of both sides, we get:

n = log(2/3) / log(3) - log(2)

Therefore, the solution is:

n = log(2/3) / log(3) - log(2)

The non-permissible values are any values of n that would make the original equation undefined. In this case, there are no such non-permissible values.

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The area of the square is 49 in². (third option)

The area of the circle is 75.39 in². (fourth option)

The area of the shaded portion is 26.39 in².(first option)

A square is a quadrilateral with four equal sides.

Area of a square = length²

7² = 49 in²

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

3.14 x 4.9² = 75.39 in²

Area of the shaded portion = area of circle - area of square

75.39 in² - 49 in² = 26.39 in²

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Applying the formula for the length of an arc, the measure of angle LMN is approximately: 164°.

The length of an arc (s) = ∅/360 × 2πr, where r is the radius of the circle.

Given the following from the image attached below, we have:

Reference angle (∅) = m<LMN

length of an arc (s) =  14.3 cm

Radius (r) = 5 cm

Plug in the values:

∅/360 × 2π × 5 = 14.3

∅/360 × 10π = 14.3

∅/360 = 14.3/10π

∅ = 14.3/10π × 360

∅  ≈ 164°

The measure of angle LMN ≈ 164°

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The solution of the quadratic equations are shown below.

There are various methods that we could use when we want to solve a quadratic equation and these include;

1) Formula method

2) Graphical method

3) Completing the square method

4) Factor method

We have solved the following quadratic equations by factoring.

1)  3x^2 + 13x +10 = 0

x = - 1 and -10/3

2)  12n²-11n +2=0

n = 2/3 and 1/4

3) 5x^2 + 8x +3=0

x = -3/5 and -1

4)  10a²+ a -2=0

a = 2/5 and -1/2

5) 8x^2 + 10x + 3 = 0

x = -1/2 and -3/4

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Answer:

3.2

Step-by-step explanation:

Answer:

pythagorean theorem !!!!!!

Step-by-step explanation:

0.8²+1.6²=3.2²

0.64+2.56=10.24

THAT means the distance is

[tex] \sqrt{10.24} [/tex]

=3.2miles

Answer:

The soccer athlete completed 70 minutes of activity during this practice.

Step-by-step explanation:

mark brainliest

The 99% upper bound for the binomial proportion P is 0.790. To find the necessary confidence bound for the binomial proportion P, we can use the formula: Upper bound = x/n + Zα/2√(x/n(1-x/n))

In this case, we are looking for a 99% upper bound, so Zα/2 = 2.576. Plugging in the given values, we get:
Upper bound = 24/55 + 2.576√(24/55(1-24/55))
          = 0.526 + 2.576(0.100)
          = 0.790
Therefore, the 99% upper bound for the binomial proportion P is 0.790.
Interpreting the interval, we can say that we are 99% confident that the true proportion of whatever we are measuring (which is represented by P) is no higher than 0.790. In other words, we can be fairly certain that the actual proportion falls within the interval from 0 to 0.790.

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The number of different arrangements that can be formed is 7920

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

Pictures = 11

Arranged pictures = 6

These can be represented as

n = 11 and r = 6

The number of different arrangements that can be formed is

Number = nPr

So, we have

Number = 11P4

Evaluate

Number = 7920

Hence, the arrangements are 7920

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Answer:

yes

Step-by-step explanation:

let x be -2 and y be 7.

Then,

y = -5x-3

7= -5*(-2)-3

7= 10-3

7=7.

The minimum area of a poster that will contain 50 square inches of printed material and have 4-inch margins on the top and bottom and 2-inch margins on the left and right is 98 square inches.

To determine the minimum area of the poster, we need to consider the dimensions of the printed material and the margins. The printed material covers an area of 50 square inches. The margins on the top and bottom are each 4 inches, which means we need to add 8 inches to the height of the printed material. The margins on the left and right are each 2 inches, which means we need to add 4 inches to the width of the printed material.
To determine the minimum area of the poster, follow these steps:

1. Add the top and bottom margins to the height of the printed material:
  Height = Printed Height + Top Margin + Bottom Margin
  Height = 50 square inches (assuming printed material height is 1 inch) + 4 inches + 4 inches
  Height = 9 inches

2. Add the left and right margins to the width of the printed material:
  Width = Printed Width + Left Margin + Right Margin
  Width = 50 square inches / 1 inch (since printed material height is 1 inch) + 2 inches + 2 inches
  Width = 54 inches

So, the total height of the poster is the height of the printed material plus the top and bottom margins, which is 50/width + 8 inches. The total width of the poster is the width of the printed material plus the left and right margins, which is 50/height + 4 inches.
Therefore, the minimum area of the poster is 7 x 14 = 98 square inches.

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Using the first thirteen rules of inference to derive the conclusions of the given symbolized arguments.

A. Conclusion: v-X

B. Conclusion: L

C. Conclusion: Z

In the first argument, the disjunctive syllogism and conditional proof rules were used to derive the conclusion. In the second argument, the material implication, double negation, commutation, modus ponens, and disjunctive syllogism rules were used to derive the conclusion. In the third argument, the material implication, De Morgan's Law, disjunctive syllogism, addition, and negation elimination rules were used to derive the conclusion.

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Using the rules of inference to derive the conclusions of the given symbolized arguments.

A. Conclusion: v-X

X-M (Premise)

M (Assumption for Conditional Proof)

|-(v-M) (Premise)

v (Disjunctive Syllogism: 3, M)

v-X (Conditional Proof: 2-4)

B. Conclusion: L

L» (B v 0) (Premise)

-(-0.-B) (Premise)

-0 v -(-B) (Material Implication: 2)

-0 v B (Double Negation: 3)

B v 0 (Commutation: 1)

-B»0 (Material Implication: 5)

-B (Disjunctive Syllogism: 4,6)

0 (Modus Ponens: 6,7)

L (Disjunctive Syllogism: 1,8)

C. Conclusion: Z

Ko (Y.Z) (Premise)

(K.C) v ( MK) (Premise)

-Z (Assumption for Conditional Proof)

-(Y.Z) (Material Implication: 1)

-Y v -Z (De Morgan's Law: 4)

Y (Disjunctive Syllogism: 2, MK)

-Z v -Z (Addition: 3)

Z (Negation Elimination: 7)

The disjunctive syllogism and conditional proof procedures were employed to reach the conclusion in the first argument.

The material implication, double negation, commutation, modus ponens, and disjunctive syllogism rules were employed to reach the conclusion in the second argument. The material implication, De Morgan's Law, disjunctive syllogism, addition, and negation elimination rules were utilized to obtain the conclusion in the third argument.

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The solution to the inequality 15 ≤ 5x + 20 < 35 is -1 ≤ x < 3.

Option C is the correct answer.

We have,

To solve the inequality 15 ≤ 5x + 20 < 35,

We need to isolate the variable x by performing the same operation on all three parts of the inequality.

15 ≤ 5x + 20 < 35

Subtract 20 from all three parts:

-5 ≤ 5x < 15

Divide all three parts by 5:

-1 ≤ x < 3

Therefore,

The solution to the inequality 15 ≤ 5x + 20 < 35 is -1 ≤ x < 3.

This means that any value of x between -1 (inclusive) and 3 (exclusive) will satisfy the inequality

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Answer:

a) a = 1 ; b = 2 ;c =-1

c) -1 + √2  ; -1 - √2

Step-by-step explanation:

        x² + 2x = 1

a)      x² + 2x - 1 = 0

Compare with ax² + bx + c = 0

a = 1 ; b = 2 and c = -1

b)  

      [tex]\boxed{x=\dfrac{-b \± \sqrt{b^2-4ac}}{2a}}[/tex]

           [tex]= \dfrac{-2 \± \sqrt{2^2-4*1*(-1)}}{2*1}\\\\\\\\C) \ =\dfrac{-2 \± \sqrt{4+4}}{2}\\\\=\dfrac{-2 \± \sqrt{8}}{2}\\\\=\dfrac{-2 \±2\sqrt{2}}{2}\\\\=\dfrac{2(-1 \± \sqrt{2})}{2}\\\\= -1 \± \sqrt{2}[/tex]

          x  = -1 + √2   or x = -1 -√2      

The equivalent expression for -4/7-8/9+4/7+9/8 is given by option C. -8/9 + 9/8 and option D. - (4/7+ 8/9 ) + 4/7 + 9/8.

The expression is equals to,

-4/7-8/9+4/7+9/8

Verify  all attached options using property of addition.

-4/7- (8/9+4/7 )+9/8

Open the parenthesis as plus minus is minus we get,

- 4/7 - 8/9 - 4 /7 + 9/8

It is not equivalent to -4/7-8/9+4/7+9/8.

Incorrect option.

- ( 4/7-8/9+4/7 ) + 9/8

Open the parenthesis as (+)( - )is minus  and ( - ) ( - ) is plus we get,

- 4/7  + 8/9 - 4 /7 + 9/8

It is not equivalent to -4/7-8/9+4/7+9/8.

Incorrect option.

-8/9 + 9/8

= 0 -8/9 + 9/8

= -4/7 + 4/7  -8/9 + 9/8

Rearrange terms we get,

-4/7-8/9+4/7+9/8

It is equivalent to -4/7-8/9+4/7+9/8

Correct option.

- (4/7+ 8/9 ) + 4/7 + 9/8

Open the parenthesis as plus minus is minus we get,

-4/7 -8/9 + 4/7 + 9/8

It is equivalent to -4/7-8/9+4/7+9/8

Correct option.

0

Incorrect option.

Therefore, for the given expression equivalent terms are option C. -8/9 + 9/8 and option D. - (4/7+ 8/9 ) + 4/7 + 9/8.

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The above question is incomplete, the complete question is:

-4/7-8/9+4/7+9/8

Which of the following expressions are equivalent to

Attached options.

No, It is not a function because the x's (input) do repeat.

We know that;

A relation between a set of inputs having one output each is called a function.

Now, We have to given that;

In the given relation,  

The x's (input) do repeat.

Hence, It is not a function.

Thus, Correct statement is,

No, It is not a function because the x's (input) do repeat.

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An example of a tiered observation when measuring temperature would be measurements rounded off to the nearest degree.

This means that when you observe and measure the temperature, you would round the values to the nearest whole degree, providing a concise and uniform set of data points for analysis or comparison.

One example of a tiered observation when measuring temperature could be only considering those temperatures in a certain range, such as only observing temperatures that fall within the range of 60-70 degrees Fahrenheit. This would be a tiered observation because it is limiting the range of data being observed.

However, it's important to note that measurements rounded off to the nearest degree could also be considered a tiered observation because it's grouping data into discrete categories based on the rounding method used.
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The remaining eigenvalue is λ = -0.007. Thus, the eigenvalues of A are:
X1 = 0
X2 = 0
X3 = -0.007
Arranging them in ascending order, we get:
X1 = -0.007
X2 = 0
X3 = 0

To find the characteristic polynomial of A, we first need to compute the determinant of (A - λI), where I is the identity matrix and λ is a scalar variable:

|0-λ  0.00 0.007|
|0.00 0-λ  0.00 |
|0.00 0.00 0-λ  |

Expanding along the first row, we get:

(0-λ) |0-λ  0.00| - 0.00 |0.00 0-λ | + 0.007 |0.0 0.00|
       |0.00 0-λ |            |0.0 0.00|                 |0.00 0-λ |

Simplifying, we obtain:

-λ³ + (-0.007)λ² = 0

Factoring out λ², we get:

λ²(-λ - 0.007) = 0

Therefore, the characteristic polynomial of A is:

p(A) = λ³ + 0.007λ²

To find the eigenvalues of A, we need to solve the equation p(A) = 0. We can see that one of the roots is λ = 0, which has multiplicity 2 (since it appears as a factor of λ² in the characteristic polynomial). To find the third eigenvalue, we need to solve:

λ³ + 0.007λ² = 0

Factoring out λ² again, we obtain:

λ²(λ + 0.007) = 0

Therefore, the remaining eigenvalue is λ = -0.007. Thus, the eigenvalues of A are:

X1 = 0
X2 = 0
X3 = -0.007

Arranging them in ascending order, we get:

X1 = -0.007
X2 = 0
X3 = 0

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Based on the information provided, the researcher should choose option a, which is to fail to reject/retain the null hypothesis. This is because the absolute value of the obtained statistic (tobt) (-1.98) is less than the absolute value of the critical value (tcrit) for a two-tailed t test with an alpha level of .05 and with df=29 (which is +/-2.045).

To clarify some of the terms used, the researcher in this scenario is conducting a hypothesis test to compare the population of senior citizens' average hours of sleep to that of the general population. She collected a sample of 30 senior citizens to represent the population. The null hypothesis is the statement that there is no difference between the two populations in terms of average hours of sleep. The alternative hypothesis is the statement that the senior citizens sleep fewer hours than the general population. The obtained statistic (tobt) is a measure of how far the sample mean deviates from the null hypothesis. The critical value (tcrit) is the cutoff value used to determine whether the obtained statistic is significant enough to reject the null hypothesis.
c. Fail to Reject/Retain the null. absolute value of tobt < absolute value of tcrit

Explanation:
The researcher performed a two-tailed single-sample t-test to compare the sleep hours of a sample of 30 senior citizens with the general population. The obtained statistic (tobt) is -1.98, and the critical value (Tcrit) for this test with an alpha level of .05 and df=29 is +/-2.045.

To make a decision, we compare the absolute values of tobt and tcrit:

Absolute value of tobt: |-1.98| = 1.98
Absolute value of tcrit: 2.045

Since the absolute value of tobt (1.98) is less than the absolute value of tcrit (2.045), we fail to reject the null hypothesis. This means the researcher cannot conclude that there is a significant difference in sleep hours between senior citizens and the general population based on her sample.

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We have evidence to suggest that the standard deviation of the number of fish in a 20-gallon tank is different from twoat the 5% level.

To determine if the standard deviation is different from two at the 5% level, we can perform a hypothesis test. The null hypothesis is that the standard deviation is two, and the alternative hypothesis is that the standard deviation is different from two.

We can use a chi-square test statistic to test this hypothesis. The test statistic is calculated as:

χ² = (n - 1) * s² / σ²

where n is the sample size, s is the sample standard deviation, and σ is the hypothesized population standard deviation.

We can then compare this test statistic to the critical value from the chi-square distribution with n - 1 degrees of freedom at the 5% significance level.

Using the given data, we have:

n = 15

s = 1.256

σ = 2

Plugging these values into the formula, we get:

χ² = (15 - 1) * 1.256² / 2² = 42.891

Using a chi-square distribution table or a calculator, we find that the critical value with 14 degrees of freedom at the 5% level is 23.685.

Since our test statistic (42.891) is greater than the critical value (23.685), we reject the null hypothesis and conclude that the standard deviation is different from two at the 5% level.

Therefore, based on the data provided, we have evidence to suggest that the standard deviation of the number of fish in a 20-gallon tank is different from two.

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The t-value is generally larger than the corresponding z-value because the t-distribution has heavier tails than the standard normal distribution. This means that the t-distribution has more probability in the tails than the standard normal distribution. As a result, the critical values for the t-distribution are larger than the corresponding critical values for the standard normal distribution.

Another reason for this difference is that the t-distribution takes into account the variability of the sample mean, which is estimated using the sample standard deviation. In contrast, the standard normal distribution assumes that the population standard deviation is known and fixed.

When the sample size is small, the t-distribution is more appropriate because it accounts for the additional uncertainty introduced by estimating the population standard deviation from the sample. As the sample size increases, the t-distribution approaches the standard normal distribution, and the difference between the t-value and the corresponding z-value decreases.

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[tex] \sqrt{ \frac{3 - 1}{5} } = \sqrt{ \frac{2}{5} } = \frac{ \sqrt{2} }{ \sqrt{5} } = \frac{ (\sqrt{2} )}{ (\sqrt{5}) } \frac{( \sqrt{5})}{ (\sqrt{5} )} = \frac{ \sqrt{10} }{5} [/tex]

The answer is V10/5

Answer:

The volume of a cone is given by the formula:

V = (1/3)πr^2h

where r is the radius of the base, h is the height, and π is the constant pi (approximately 3.14).

Plugging in r = 6 and h = 15, we get:

V = (1/3)π(6^2)(15) = 540π cubic feet

Rounding to the nearest hundredth, we get:

V ≈ 1696.63 cubic feet

Therefore, the volume of the cone is approximately 1696.63 cubic feet.

To check, we can use the formula for the volume of a cone to calculate the volume using different methods. For example, we can use the fact that the cone is one-third the volume of a cylinder with the same base and height. The cylinder has radius 6 feet and height 15 feet, so its volume is:

V_cylinder = π(6^2)(15) = 540π cubic feet

Dividing by 3, we get:

V_cone = (1/3)V_cylinder = (1/3)(540π) = 180π cubic feet

Rounding this to the nearest hundredth, we get:

V_cone ≈ 565.49 cubic feet

This is reasonably close to our previous answer of 1696.63 cubic feet, so we can be confident that our calculation is correct.

Step-by-step explanation:

We can be 90% confident that the true mean reduction in systolic blood pressure for the population is between 51.433 and 56.367.

To estimate the confidence interval for the true mean reduction in systolic blood pressure, we can use the formula:

CI = X ± Zα/2 * (σ/√n)

where X is the sample mean, Zα/2 is the critical value of the standard normal distribution for a given level of confidence (α), σ is the population standard deviation, and n is the sample size.

In this case, X = 53.9, σ = 5.6, n = 24, and we want a 90% confidence interval, so α = 0.1 and Zα/2 = 1.645 (using a standard normal distribution table or calculator).

Substituting the values, we get:

CI = 53.9 ± 1.645 * (5.6/√24)

CI = 53.9 ± 2.467

CI = (51.433, 56.367)

Therefore, we can be 90% confident that the true mean reduction in systolic blood pressure for the population is between 51.433 and 56.367.

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the total area under the curve is 2400.

To find the number of vehicles that pass the intersection between time t = 0 and time t = 8, we need to calculate the definite integral of the function R(t) from t = 0 to t = 8:

∫(0 to 8) R(t) dt

Looking at the graph of R(t), we can see that it consists of two parts: a rectangle with base 2 and height 600, and a triangle with base 6 and height 400. The area of the rectangle is 2 x 600 = 1200, and the area of the triangle is (1/2) x 6 x 400 = 1200. Therefore, the total area under the curve is 2400.

So, the number of vehicles that pass the intersection between time t = 0 and time t = 8 is:

∫(0 to 8) R(t) dt = 2400

Since R(t) is measured in vehicles per hour, this means that 2400 vehicles pass the intersection between time t = 0 and time t = 8. Therefore, the answer is 2400, which is not one of the given answer choices.

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The 90% confidence interval for the true mean weight of the textbooks is approximately (70.062 ounces, 73.938 ounces).

Given that you measured 21 textbooks and found a mean weight of 72 ounces with a population standard deviation of 5.4 ounces, we can follow these steps:

1. Identify the sample size (n), sample mean (X), population standard deviation (σ), and confidence level (90%).

  n = 21
  X = 72 ounces
  σ = 5.4 ounces
  Confidence level = 90%

2. Determine the critical value (z) for a 90% confidence interval. For a 90% confidence interval, the critical value (z) is 1.645.

3. Calculate the standard error (SE) using the formula [tex]SE = \frac {σ }{\sqrt{n} }[/tex].

 [tex]SE = \frac{5.4}{\sqrt{21} } = 1.177[/tex]

4. Calculate the margin of error (ME) using the formula ME = z * SE.

  ME = 1.645 * 1.177 = 1.938

5. Construct the confidence interval using the formula: X ± ME.

  Lower limit = 72 - 1.938 = 70.062
  Upper limit = 72 + 1.938 = 73.938

Based on your measurements, the 90% confidence interval for the true mean weight of the textbooks is approximately (70.062 ounces, 73.938 ounces).

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The probability that (-3) < Y < (-2) for a sample size of 36 is approximately 0.0385.

Given, Yi, i=1, 2, ,…,n, are i.i.d. random variables, each distributed N(-3,81),

i.e., Yi ~ N(-3,81)

We need to find Pr[(-3) < Y < (-2)] for a sample size of 36.

First, we need to standardize the variable Y as follows:

Z = (Y - μ) / σ

where μ is the mean of Y, and σ is the standard deviation of Y.

Here, μ = -3 and σ = 9 (since the standard deviation is the square root of the variance, which is given as 81).

So,

Z = (Y - (-3)) / 9 = (Y + 3) / 9

Now, we need to find Pr[(-3) < Y < (-2)] in terms of Z:

Pr[(-3) < Y < (-2)] = Pr[(-3 + 3)/9 < Z < (-2 + 3)/9]

= Pr[0 < Z < 1/9]

We can use the standard normal distribution table or calculator to find the probability of Z lying between 0 and 1/9.

Using a standard normal distribution table or calculator, we get:

Pr[0 < Z < 1/9] ≈ 0.0385

Therefore, the probability that (-3) < Y < (-2) for a sample size of 36 is approximately 0.0385.

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The correct answer about the savings account that Zoe opened, represented by the equation b(x)=675(1.045)ˣ is B. Daniella says the balance in the account increases at a rate of 4.5% each year.

An equation is a mathematical statement that two or more algebraic expressions (the combination of variables with constants and mathematical operands) are equal or equivalent.

This equation is known as the future value equation, formula, or function.

Initial investment = $675

Compound interest rate = 4.5% (0.045 x 100)

Future value factor = 1.045 (100% + 4.5%)

Based on the future value function above, we can conclude that the compound interest rate is 4.5%, which is equivalent to 0.045 as given in the equation.

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The situation that can use the binomial probability distribution is a sampling of 100 parts to determine whether or not they meet specifications.

The binomial probability distribution is used to model the probability of a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. In the given situation, each part in the sample either meets the specifications (success) or does not (failure), which makes it a binomial experiment.

To use the binomial probability distribution, we need to know the probability of success (p) and the number of trials (n). In the given situation, we can determine the probability of a part meet specifications based on the given specifications, and the number of trials is fixed at 100, as we are sampling 100 parts.

Using the binomial probability distribution, we can calculate the probability of a certain number of parts meeting specifications out of the 100 sampled parts. This can be useful in determining whether the sample meets the expected specifications or if there are any issues with the manufacturing process.

In summary, the binomial probability distribution can be used in the given situation of sampling 100 parts to determine whether or not they meet specifications, as it involves a fixed number of independent trials with only two possible outcomes.

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