A. 35.5
B. 10
C. 45
D. 39.3

The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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Answer:

0.68

Step-by-step explanation:

According To the Question,

Let, H ⇒ "heavy traffic" & T ⇒  "get there on time".

Then, "half of the time there is heavy traffic" ⇔ P(H)=0.5.

Now, you are given that there is heavy traffic, so We need to find P(T I H).

 P(T l H) = P(H and T) / P(T)

P(T l H) = 0.34/0.5 ⇒ 0.68

Using the formula shown replace r with 11 and pi with 3:

Volume = 4/3 x 3 x 11^3

Volume = 5,324 in^3

The answer is a. True. the p-value turns out to be 0.103, which is greater than 0.1. Therefore, we don't have enough evidence to reject the null hypothesis.

According to the genetic theory, the proportion of red flowering plants produced from a cross between two pink flowering plants is 0.25. In the experiment, out of 100 crosses made, 31 produced a red flowering plant. To determine whether the observed results are statistically significant, we need to conduct a hypothesis test. The null hypothesis (H0) in this case is that the proportion of red flowering plants produced from a cross between two pink flowering plants is 0.25. The alternative hypothesis (Ha) is that the proportion is not 0.25. To test the hypothesis, we can use a binomial test. At a significance level of 0.1, we compare the observed proportion (31/100 = 0.31) to the expected proportion (0.25) and calculate the p-value. If the p-value is less than 0.1, we reject the null hypothesis. However, if the p-value is greater than 0.1, we fail to reject the null hypothesis, which means that we don't have enough statistical evidence to conclude that the true proportion is different from 0.25. In this case, the p-value turns out to be 0.103, which is greater than 0.1. Therefore, we don't have enough evidence to reject the null hypothesis. Hence, the answer is true.

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Answer:

it would take 10 minutes if they worked together

Step-by-step explanation:

The probability that the selected student was the youngest student from Section B is 2/6.

The total number of  students is 18 which include

Section A: 5 students

Section B: 6 students

Section C: 7 students

Given that the selected student was from Section B

Calculate the probability of selecting a student from Section B

P(Section B) = 6/18 = 1/3

Calculate the probability of selecting the youngest student from Section B

Since there are 6 students in Section B, the probability of selecting the youngest student is 1/6.

Calculate the probability of selecting the youngest student from Section B given that the selected student was from Section B

P(Youngest student from Section B|Section B) = P(Youngest student from Section B ∩ Section B) / P(Section B)

= (1/6) / (1/3)

= 2/6

Therefore, the probability that the selected student was the youngest student from Section B is 2/6.

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The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

What is the probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

An order does not matter so it is a Combination.

There are 16 men and we are going to choose 12 --> ₁₆C₁₂

There are 30 people and we are going to choose 12  --> ₃₀C₁₂

₁₆C₁₂ / ₃₀C₁₂

\(= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}\)  

= 0.00002104211

= 2.1 × 10⁻⁵

Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

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After solving the equation the length of side is 47.97 unit.

What is triangle?

A triangle is a three-sided geometric shape. It is a closed figure, meaning the sides are connected, and it has three angles, each of which is less than 180 degrees. Triangles can be classified by their angles and sides. The three most common types of triangles are equilateral, isosceles, and scalene. An equilateral triangle has three equal sides and three equal angles. An isosceles triangle has two equal sides and two equal angles. A scalene triangle has three unequal sides and three unequal angles. All triangles have an area, perimeter, and at least one line of symmetry. Triangles are used in a variety of fields, such as engineering, architecture, and art.

Main body:

according to question :

As the vertices are A,B,C

∠C= 51°

BC = 39

as we need to find relation between perpendicular and base , we will use tangent trigonometric ratio.

AB/BC = tan 51°

x/39 = tan 51°

x = 1.23*39

x = 47.97

Hence ,the length of side is 47.97 unit.

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Answer:

x=13

Step-by-step explanation:

3x=2x+21−8

3x=2x+13

3x−2x=13

x=13

Answer:

x = 13

Step-by-step explanation:

3x + 8 = 2x + 21

x + 8 = 21

x = 13

Answer:  9 - 6n6n - 9(6 + n) - 99 - (6 + n)

The dimension of the larger shipping box is given as

The volume of a box is calculated by the formula

Substituting the given dimension

The given statement "Measuring the entire population is usually preferred over measuring a sample from the population" is False because measuring the entire population is often impractical or impossible.

When dealing with large populations, it is typically more feasible to gather data from a representative sample rather than measuring the entire population. This approach saves time, resources, and effort. Sampling allows statisticians to make reliable inferences about the population based on the characteristics observed in the sample.

Carefully chosen samples can accurately reflect the population's attributes and provide valuable insights.

However, it is crucial to ensure that the sample is representative and unbiased to avoid potential sampling errors and ensure the validity of the conclusions drawn from the data.

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(a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.

(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.

(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .

In the question ,

a fraction 9/15 is given ,

Part(a)

to scale up the fraction by a factor of 2 , we multiply the numerator and denominator by 2 .

On multiplying , we get

9/15 = (9*2)/(15*2) = 18/30 .

Part(c)

to scale up the fraction by a factor of 3 , we multiply the numerator and denominator by 3 .

On multiplying , we get

9/15 = (9*3)/(15*3) = 27/45 .

Part(c)

to scale down the fraction by a factor of 3 , we divide the denominator and numerator by 3 .

On dividing , we get

9/15 = (9/3)/(15/3) = 3/5 .

Therefore , (a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.

(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.

(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .

The given question is incomplete , the complete question is

Write three fractions equivalent to 9/15 .

Scale the numerator and denominator up for the first two and down for the third.

(a) Scale up by: __ Equivalent fraction: __

(b) Scale up by: __ Equivalent fraction: __

(c) Scale down by: __ Equivalent fraction: __

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The equation of the parabola that has its vertex at the origin and satisfies the given condition directrix x = −2 is \(y^2 = 8x.\)

To find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Directrix x = −2 and \(y^2 = −8x\) , we can use the following steps:

Step 1: As the vertex of the parabola is at the origin, the equation of the parabola is of the form \(y^2 = 4ax\), where a is the distance between the vertex and the focus. Therefore, we need to find the focus of the parabola. Let's do that.

Step 2: The equation of the directrix is x = −2. The distance between the vertex (0, 0) and the directrix x = −2 is |−2 − 0| = 2 units. Therefore, the distance between the vertex (0, 0) and the focus (a, 0) is also 2 units. So, we have:a = 2Step 3: Substitute the value of a into the equation of the parabola to get the equation:

\(y^2 = 8x\)

Hence, the equation of the parabola that has its vertex at the origin and satisfies the given condition directrix x = −2 is \(y^2 = 8x\). Here's a graph of the parabola: Graph of the parabola that has its vertex at the origin and satisfies the given condition.

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In order to factor our polynomial must be written in a way that we will factor out the greatest common factor

A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division.

A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.

To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.

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Answer:

\(Slope\ of\ A'B'= 3\)

Step-by-step explanation:

Given

\(Slope\ of\ AB= 3\)

Required

Determine the slope of A'B'

Represent the coordinates of AB with (x,y), such that

\(AB = (x,y)\)

Since A'B' is 3 * AB, we have

\(A'B' = 3 * AB\)

Substitute (x,y) for AB

\(A'B' = 3 * (x,y)\)

\(A'B' = (3x,3y)\)

Since the slope of AB = 3, then the slope of A'B' is also equal to 3 because dilation through (0,0) does not have effect on the slope

Answer:

3, Does not Pass

Step-by-step explanation:

Good luck with edmentum everyone :D

Answer:

0.84375

Step-by-step explanation:

The Answer:the answer is D

Step-by-step explanation:

The break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

What is average ?

The average is a measure of central tendency that is calculated by adding a set of values together and dividing the sum by the number of values. It is also known as the arithmetic mean. It is a way to represent a typical value of a dataset.

The break-even point is the point at which the cost of the products equals the revenue from the sales of the products. To find the break-even point, we need to set the cost function (C(x) = 550 + 3.00x) equal to the revenue function (R(x) = 5.50x) and solve for x.

C(x) = 550 + 3.00x = R(x) = 5.50x

3.00x = 5.50x - 550

0.50x = 550

x = 1100

So the break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

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As no graph is shown some basic information of parabola can be helpful

And a coordinate is given check it whether it is equal to second part of options

We get

Last two are radar now

As a must be negative option D has such similarities.

Answer:

\(\sf y = -0.006x^2 + 0.35x + 6\quad and\quad y = 0.2x\)

Step-by-step explanation:

As the archer shoots the arrow up, the trajectory of the arrow can be modeled as a parabola that opens downwards.  Therefore, this is a quadratic equation with a negative leading coefficient.

From inspection of the answer options, the path of the arrow is :

\(y=-0.006x^2+0.35x+6\)

This means the options for the line equation are \(y=-x\) and \(y=0.2x\)

We are told that the point of intersection of the line and the parabola is at (46.5, 9.3).  As both the x-value and y-value are positive, the equation of the line must be \(y=0.2x\)

To confirm, substitute \(x=46.5\) into the equation:

\(\implies y=0.2(46.5)=9.3\)

The equation log₁₀ 0.001 = x can be solved by rewriting it in exponential form: 10^x = 0.001. Taking the logarithm of both sides with base 10, we find that x = -3.

To solve the equation log₁₀ 0.001 = x, we need to convert it to exponential form. The logarithm with base 10 is equivalent to an exponentiation with base 10. In this case, the logarithm of 0.001 with base 10 is equal to x.

To rewrite the equation in exponential form, we raise 10 to the power of both sides: 10^x = 0.001. This equation states that 10 raised to the power of x is equal to 0.001.

To find the value of x, we need to determine the exponent that yields 0.001 when 10 is raised to that power. By calculating the value of 10^x, we find that x = -3.

Therefore, the solution to the equation log₁₀ 0.001 = x is x = -3. This means that the logarithm of 0.001 with base 10 is equal to -3.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{7}}}}}\)

Step-by-step explanation:

\( \sf{ \frac{1}{3} \times (15 + 6)}\)

Add the numbers : 15 and 6

\( \dashrightarrow{ \sf{ \frac{1}{3} \times 21}}\)

Multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term

\( \dashrightarrow {\sf{ \frac{1 \times 21}{3 \times 1}}} \)

\( \dashrightarrow{ \sf{ \frac{21}{3} }}\)

\( \dashrightarrow{ \sf{7}}\)

Hope I helped!

Best regards! :D

The value of Expression 1/3 x (15+6) on simplification gives 7.

To simplify the expression 1/3 x (15+6),

we start by simplifying the addition inside the parentheses.

=15 + 6

= 21

Now, we can multiply the result by 1/3:

= 1/3 x 21

= 21/3

= 7

Therefore, 1/3 x (15+6) simplifies to 7.

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The p-value for the test of the hypothesis that the company's average days sales in receivables is 48 days or less ≈ 0.295.

To calculate the p-value using the normal approximation, we will perform the following steps:

1.  Define the null and alternative hypotheses.

Null Hypothesis (H₀): The company's average days sales in receivables is 48 days or less.

Alternative Hypothesis (H₁): The company's average days sales in receivables is greater than 48 days.

2. Determine the test statistic.

The test statistic for this hypothesis test is the z-score, which measures the number of standard deviations the sample mean is away from the hypothesized population mean.

The formula for calculating the z-score is:

z = (x - μ) / (σ / √n)

Where:

x = sample mean

μ = hypothesized population mean

σ = population standard deviation

n = sample size

In this case:

x = 49 (sample mean)

μ = 48 (hypothesized population mean)

σ = 20 (population standard deviation)

n = 82 (sample size)

Plugging in these values, we get:

z = (49 - 48) / (20 / √82) ≈ 0.541

3. Calculate the p-value.

The p-value is the probability of observing a test statistic as extreme as the one obtained or more extreme, assuming the null hypothesis is true.

Since we are testing whether the company's average days sales in receivables is 48 days or less (one-tailed test), we need to calculate the area under the standard normal curve to the right of the calculated z-score.

Using the NORMSDIST() function in a spreadsheet, we can obtain the area to the left of the z-score:

NORMSDIST(0.541) ≈ 0.705

To obtain the p-value, subtract the area to the left from 1:

∴ p-value = 1 - 0.705 ≈ 0.295

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let other one be (x,y)

We know midpoint formula

\(\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}\)

\(\\ \sf\longmapsto (6,-4)=\left(\dfrac{13+x}{2},\dfrac{-2+y}{2}\right)\)

\(\\ \sf\longmapsto \dfrac{13+x}{2}=6\)

\(\\ \sf\longmapsto 13+x=12\)

\(\\ \sf\longmapsto x=12-13\)

\(\\ \sf\longmapsto x=-1\)

And

\(\\ \sf\longmapsto \dfrac{-2+y}{2}=-4\)

\(\\ \sf\longmapsto -2+y=-8\)

\(\\ \sf\longmapsto y=-8+2\)

\(\\ \sf\longmapsto y=-6\)

Answer:

(- 1, - 6 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) ) ← midpoint formula

Use this formula on the endpoints and equate to the coordinates of the midpoint.

let the other endpoint = (x, y) , then

\(\frac{13+x}{2}\) = 6 ( multiply both sides by 2 )

13 + x = 12 ( subtract 13 from both sides )

x = - 1

\(\frac{-2+y}{2}\) = - 4 ( multiply both sides by 2 )

- 2 + y = - 8 ( add 2 to both sides )

y = - 6

The coordinates of the other endpoint are (- 1, - 6 )

7. The monthly payment that the Domingue family will make for the home listed at $253,000 with a down payment of 13% and 4.75% APR for 25 years is $1,254.89.

8. The total of all the monthly payments the Domingue family will make over the 25 years is $376,467.

9. The Domingue family will incur a total interest for the 25 years amounting to $156,357.

The monthly payment represents the amount of periodic payment made to settle the mortgage loan including the interest.

To determine the monthly payment, total monthly payments, and total interest, we can use an online finance calculator as follows:

Home Price = $253,000

Down Payment = 13%

Loan Term = 25 years or 300 months

Interest Rate = 4.75%

Results:

Monthly Payment = $1,254.89

House Price = $253,000

Loan Amount = $220,110 ($253,000 - $32,890)

Down Payment = $32,890 ($253,000 x 13%)

Total of 300 Mortgage Payments = $376,467

Total Interest = $156,357

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Answer:

me me me omg

Step-by-step explanation:

To find the probability that the mean weight of 19 fish is between 16.1 and 20.6 lb, you would need to know the distribution of the weights of the individual fish. If the weights of the fish are normally distributed with a mean of 18.4 lb and a standard deviation of 2.5 lb, then you can use a normal distribution to find the probability that the mean weight of the 19 fish falls in the specified range.

How does probability work exactly?

Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible. Probability differs from odds in this regard. Calculating odds involves dividing the likelihood of a particular event by the likelihood that it won't occur.

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The work you must do to change the length of the spring from 8 cm to 11 cm is 0.0225 Joules.

Calculation of work done:

To calculate the work done to change the length of the spring from 8 cm to 11 cm, given its relaxed length is 5 cm and its stiffness is 50 N/m:

1: Convert the given lengths from centimeters to meters.
Relaxed length = 5 cm = 0.05 m
Initial length = 8 cm = 0.08 m
Final length = 11 cm = 0.11 m

2: Calculate the change in length.
Δx = Final length - Initial length = 0.11 m - 0.08 m = 0.03 m

3: Apply Hooke's Law to find the force needed to stretch the spring.
F = k × Δx
Where F is the force, k is the stiffness (50 N/m), and Δx is the change in length (0.03 m).
F = 50 N/m × 0.03 m = 1.5 N

4: Calculate the work done.
Work = 0.5 × F × Δx
Work = 0.5 × 1.5 N × 0.03 m = 0.0225 J

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To determine the possible number of positive real zeros and negative real zeros for the polynomial function P(x) = 5x³ + 7x² - 2x - 1 using Descartes' Rule of Signs, we need to analyze the sign changes in the coefficients of the polynomial. First, we count the sign changes in the coefficients when we write the polynomial in its standard form.

In this case, we have one sign change from positive to negative as we move from 5x³ to 7x², and another sign change from negative to positive as we move from -2x to -1. Therefore, according to Descartes' Rule of Signs, the polynomial P(x) can have either one positive real zero or. Next, we consider the polynomial P(-x) = 5(-x)³ + 7(-x)² - 2(-x) - 1, which corresponds to reversing the sign of the variable x. Counting the sign changes in this polynomial, we find that there ar three positive real zerose no sign changes or an even number of sign changes. Therefore, according to Descartes' Rule of Signs, the polynomial P(x) = 5x³ + 7x² - 2x - 1 has no negative real zeros or an even number of negative real zeros.

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