sixty five percent of all divorce cases cite incompatibility as the underlying reason. if four couples file for a divorce, what is the probability that exactly two will state incompatibility as the reason?

The formula for the number of bacteria at time t is given by N = 10,000e^(0.0173t).

The formula for the number of bacteria at time t can be found using the exponential growth formula. The formula for exponential growth is given by;N = N0ertWhere;N is the number of bacteria after t minutes.N0 is the initial number of bacteria.r is the growth rate.t is the time interval.

To find the formula for the number of bacteria at time t, substitute the given values into the exponential growth formula.N0 = 10,000r = ln2/40 = 0.0173 (since the number of bacteria doubles every 40 minutes, the growth rate is equal to the natural log of 2 divided by 40.)t = t minutesN = 10,000e^(0.0173t)

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The answer of the given question is , the predicted average retail price of a car in 2003 is $9860.40.and  the car will be worth $814 in the year 2010.

A regression equation is a mathematical formula that is used to describe the relationship between two or more variables. It is typically used in statistical analysis to model the relationship between a dependent variable and one or more independent variables.In simple linear regression, there is only one independent variable, and the regression equation takes the form of a straight line. In multiple regression, there are two or more independent variables, and the regression equation takes the form of a more complex mathematical function.

Using a calculator, we can input the data points into a regression equation to find the line of best fit. Using the given data, we get the regression equation:

y = -1357.4x + 18003.8

where y represents the retail price of a car and x corresponds to the year, with x = 1 representing 1998.

To predict the average retail price of a car in 2003, we need to substitute x = 6 (since 2003 corresponds to x = 6) into the regression equation:

y = -1357.4(6) + 18003.8

y = -8144.4 + 18003.8

y = 9860.4

So, the predicted average retail price of a car in 2003 is $9860.40.

To determine the year when the car will be worth $814, we need to substitute y = 814 into the regression equation and solve for x:

814 = -1357.4x + 18003.8

Simplifying, we get:

-1357.4x = -17189.8

x = 12.65

Rounding up to the nearest whole number, we get x = 13, which corresponds to the year 2010. Therefore, the car will be worth $814 in the year 2010.

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The value of k that makes the three points lie on the same line is -8.

To determine the value of k such that the given points lie on the same line, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

First, we can find the slope of the line passing through the two points (0, -2) and (10, -7):

m = (y2 - y1) / (x2 - x1)

m = (-7 - (-2)) / (10 - 0)

m = -5 / 10

m = -1/2

Now, we can use the slope-intercept form with the point (0, -2) to find the value of b:

-2 = (-1/2)(0) + b

b = -2

So the equation of the line passing through the two points (0, -2) and (10, -7) is:

y = (-1/2)x - 2

To check if the point (k, 2) lies on this line, we can substitute k for x and 2 for y in the equation:

2 = (-1/2)k - 2

4 = (-1/2)k

k = -8

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Answer:

The divisors of 20 are 1, 2, 4, 5, 10, and 20. A 6-sided dice has the numbers 1 to 6 on its faces. The probability of rolling a number that is a divisor of 20 is the number of favorable outcomes divided by the number of possible outcomes. There are four favorable outcomes (1, 2, 4, and 5) and six possible outcomes (1 to 6). Therefore, the probability is 4/6 or 2/3 or about 0.67.

Therefore, the derivative of y = 7x⁴ with respect to x is dy/dx = 28x³.

Differentiation is a mathematical concept that refers to the process of finding the derivative of a function. The derivative of a function is the rate at which the function changes with respect to its independent variable. In other words, it measures how quickly the output of the function is changing as the input value is changing.

The derivative of a function can be used to determine many properties of the function, such as its slope, maximum and minimum values, and whether it is increasing or decreasing. It is an important tool in calculus and is used in many fields, including physics, engineering, economics, and finance.

The process of differentiation involves applying specific rules to a given function to determine its derivative. The most common method of differentiation is using the power rule, which states that the derivative of a function raised to a power is equal to the product of the power and the function raised to the power minus one. Other rules include the product rule, the quotient rule, and the chain rule, which are used to differentiate more complex functions.

by the question.

To differentiate y = 7x⁴, we need to use the power rule of differentiation, which states that if [tex]y = kx^{n}[/tex], where k is a constant and n is a non-negative integer, then the derivative of y with respect to x is dy/dx = [tex]\frac{dy}{dx} = nkx^{(n-1)}[/tex].

Using this rule, we can differentiate y = 7x⁴ as follows:

dy/dx = 47[tex]x^{4-1}[/tex] [applying the power rule]

dy/dx = 28x³

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The solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.

What are equations?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To solve the equation [tex]\frac{4}{q}(q-10) = 8[/tex] we can begin by simplifying the left side of the equation:

[tex]\frac{4}{q}(q-10) = 8[/tex]

[tex]\Rightarrow \qquad 4(q-10) = 8q \text {multiply both sides by }q[/tex]

[tex]\Rightarrow \qquad 4q - 40 &= 8q && \text{distribute }4 \\\\\Rightarrow \qquad -40 &= 4q && \text{subtract }4q\text{ from both sides} \\\\\Rightarrow \qquad -10 &= q && \text{divide both sides by }-4.\\\end{align*}[/tex]

Therefore, the solution to the equation is q= -10. We can check our answer by plugging q= -10 back into the original equation:

[tex]\frac{4}{q}(q-10) &= 8 \\\\\\\Rightarrow \qquad \frac{4}{-10}(-10-10) &= 8 && \text{substitute }q=-10\\\\\\\Rightarrow \qquad -\frac{4}{5} \cdot (-20) &= 8 \\\\\\\Rightarrow \qquad 16 &= 8\end{align*}[/tex]

Since the last equation is false, the solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.

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Perimeter of the figure is 56 units.

Area of figure is 100sq. units²

Cost to sold the yard is $299

For edging, total cost is $82.8

Perimeter and area are two important measurements used in geometry to describe the size and shape of two-dimensional figures.

Perimeter is the measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

Area is the measurement of the space inside a two-dimensional shape. It is the amount of surface that the shape covers. For example, the area of a rectangle can be calculated by multiplying the length of the rectangle by its width.

Perimeter of the figure=sum of all sides of the figure

=10+4+2+12+6+6+2+4+6+4=56 units.

Area of figure=10×4+6×6+4×6

=40+36+24

=100sq. units²

Cost to sold the yard=area× cost per square foot

=100×2.99

=$299

Given: edging  costs $8.87 per 6 foot piece

For edging, total cost =total perimeter/no.of foot piece×$8.87

=(56/6)×8.87

=496.72/6

=$82.78≈$82.8

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We can be reasonably confident that our estimate of 67% is within 2.5% of the true proportion.

What is percentage?

A percentage is a way to describe a part of a whole. such as the fraction  1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

To determine if a sample size of 1,400 is adequate for estimating a proportion of 67%, we need to calculate the margin of error and compare it to the given tolerance level of 0.025.

We can use the following formula to calculate the margin of error:

E = z x √(p x (1-p)/n)

where:

Plugging in the values, we get:

E = 1.96 x √(0.67 x (1-0.67)/1400) ≈ 0.025

So, the margin of error is approximately 0.025. This means that we can expect the true proportion to be within 0.025 of the estimated proportion with 95% confidence.

Since the calculated margin of error is equal to the desired tolerance level, we can conclude that a sample size of 1,400 is adequate for estimating a proportion of 67% with the given level of confidence and tolerance. Therefore, we can be reasonably confident that our estimate of 67% is within 2.5% of the true proportion.

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Answer:

11/20

Step-by-step explanation:

1,10,11,12,13,14,15,16,17,18,19 All have the number "1"

there are 11 of them so 11/20 have the digit 1.

:)

Answer:

To find the fraction of the numbers from 1 to 20 that contain the digit 1, we can count the number of such numbers and divide by the total number of numbers from 1 to 20.

The numbers from 1 to 20 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

The numbers that contain the digit 1 are: 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

Therefore, there are 11 numbers from 1 to 20 that contain the digit 1.

The fraction of the numbers from 1 to 20 that contain the digit 1 is:

fraction = number of numbers containing 1 / total number of numbers

fraction = 11 / 20

So, the fraction of the numbers from 1 to 20 that contain the digit 1 is 11/20 or 0.55.

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If you are 25 years of age, your typing speed is equal to 82.8 units.

In Mathematics, a line of best fit is sometimes referred to as a trend line and it can be defined as a statistical or analytical tool that is typically used by researchers and mathematicians in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.

Based on the scatter plot, we can logically deduce that an equation which represents the line of best fit include the following:

y = -1.4x + 117.8

When you are 25 years of age, your typing speed can be calculated as follows;

y = -1.4x + 117.8

y = -1.4(25) + 117.8

y = -35 + 117.8

y = 82.8 units.

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The total area of the shaded region is 67.92 sq. in.

A sector is a section of a circle that may be described using the following four criteria:

Two radii and an arc surround a section of a circle. The two sectors that make up a circle are referred to as the minor and major sectors. The main sector of the circle is the larger area, while the minor sector is the smaller area. The circle is split into two equally sized sections in the case of semicircles.

Let us suppose the central angle of the shaded portion = x.

From the given figure we observe that angle DEC = 143 degrees, and angle AEB are equal as they are vertically opposite angles.

The angle formed by the shaded regions are same as they are vertically opposite angles.

Thus,

143 + 143 + x + x = 360

286 + 2x = 360

2x = 74

x = 37

Now, the area of the sector is given as:

A = α/360 πr²

Here, r = 10.4 in.

Substituting the values:

A = (37/360)π(10.4)²

A = (0.10)(3.14)(10.4)²

A = 33.96 sq in.

There are two shaded portions thus:

Total area = 2(33.96)

Total area = 67.92 sq. in.

Hence, the total area of the shaded region is 67.92 sq. in.

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The probability that daily production is less than 44.4 liters is  96.71%

According to the given data, the mean daily production of a herd of cows is assumed to be normally distributed with a mean of 37 liters and a standard deviation of 4 liters.

We need to calculate the probability that daily production is less than 44.4 liters using technology, not tables.Using technology, we can use the standard normal distribution formula to get the required probability.

We can use the standard normal distribution to calculate the probability that the daily production is less than 44.4 liters. To do this, we first need to standardize the variable:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have:

z = (44.4 - 37) / 4 = 1.85

Using a standard normal distribution table or a calculator with a normal distribution function, we can find that the probability of a standard normal random variable being less than 1.85 is approximately 0.9671.

Different calculators may have slightly different ways to calculate normal probabilities. Here is an example using a TI-84 calculator:

Therefore, the probability that the daily production is less than 44.4 liters is approximately 0.9671, or 96.71% (rounded to two decimal places).

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Answer: D or the Fourth Choice-The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12

PEDMAS means Parentheses, Exponents, Divide, Multiply,Add,Subtract. The first thing we must solve is what is in the parentheses, that is 14.8 divided by 2. We don't have any exponents, so we move to divide. We have already solved the division sentence that was in the parentheses, so we have to multiply 6x3 next. 6x3 will then be added to the answer that was divided by 14.2 and 2, and lastly we will subtract 12. The only answer choice that follows that pattern is D or The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12.

I hope this helped & Good Luck <3!!!!

According to the solving this word problem It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real life." In order for kids to understand the word problem, they must be acquainted with the vocabulary that goes along with the mathematical symbols that they are used to.

According to the given information,

The first pump can fill the pool in 4 hours, so its rate is 1/4 of the pool per hour.

The second pump can fill the pool in 6 hours, so its rate is 1/6 of the pool per hour.

The total work done in fraction by both pumps in an hour is:

[tex]\frac{1}{4} + \frac{1}{6} = \frac{5}{12}[/tex]

The remaining work to be completed by the slowest pump is:

[tex]1 - \frac{5}{12} = \frac{7}{12}[/tex]

The ratio of the amount of work left to be done by the weakest pump's work rate determines how long it will take to fill the pool:

[tex]\frac{7}{12} \frac{1}{6} = \frac{7}{12} * 6 = \frac{7}{2}[/tex]

According to the solving It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.

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Answer:

C = 11,21 cm

using the formulas :

A (area) = 10 [tex]cm^{2}[/tex]

A = π [tex]r^{2}[/tex]

C = 2 π r

colving for C :

C = 2 *√(π*Α) = 2 *√(π * 10) = 11,20998 cm

The expression 2⁻³ = 1/8 into logarithmic form is log₂(1/8) = -3

In logarithmic form, the equation 2⁻³ = 1/8 can be written as log base 2 of 1/8 = -3.

Mathematically, we have

log₂(1/8) = -3

This means that the exponent that gives 2⁻³ is -3, and the logarithm base 2 of 1/8 is -3.

Logarithmic form is often used to solve exponential equations where the variable is in the exponent.

In logarithmic form, the variable is moved from the exponent to the logarithm, making it easier to solve for the unknown variable.

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To serve 50 people, the minimum square footage needed would be 750 square feet.

Let us analyze the given question and solve the problem given. The problem is asking about the minimum square footage of the multi-story building that is required to open a small restaurant on the lowest floor. The building is already zoned for mixed use.

John wants to open a small, by-reservation-only restaurant on the lowest floor. He needs to calculate the minimum square footage he needs to serve 50 people. Let's calculate the minimum square footage that John needs to open the restaurant. If local code requires 15 square feet per person, then 15 x 50 = 750 square feet are needed for 50 people. In other words, John needs at least 750 square feet of space to serve 50 people at his restaurant.

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The depth of water changes at a rate of -13/72π feet per minute when the water is 2 feet high.

To begin, we must use the formula for the volume of a cone, which is given as:

V = 1/3πr2hwhere V represents the volume, π represents the constant pi, r represents the radius, and h represents the height.

Substituting the given values into the formula, we get:

V = 1/3π (6 ft)2(14 ft)V = 1/3π (36 ft2) (14 ft)V = 1/3π (504 ft3)V = 168π ft^3

Now, we must determine the rate at which water is leaking. It is given that the cone leaks water at a rate of 13 cubic feet per minute. This implies that the volume of the water reduces by 13 cubic feet every minute. Therefore, the rate of change of the volume of water is -13 cubic feet per minute. Here, the negative sign indicates a decrease in the volume of water.

Now, we must find how fast the depth of water changes when the water is 2 feet high. Let d represent the depth of water. Then, the volume of water is given as:

V = 1/3πr^2d

We know that when d = 2 ft, V = 1/3π(6 ft)2(2 ft)

V = 8π ft^3

Now, we must determine how fast the volume of water is changing with respect to time when d = 2 ft. We differentiate the expression for V with respect to time to get:

dV/dt = (d/dt)[1/3πr2d]

dV/dt = 1/3πr^2(d/dt)[d]

dV/dt = 1/3πr^2(d/dt)[2]

dV/dt = 2/3πr^2

The rate of change of the volume of water with respect to time is given as -13 cubic feet per minute. Therefore, substituting this into the expression above, we get:

-13 = 2/3π(6 ft)2(d/dt)

When we simplify the above equation, we get:

d/dt = -13/72π

Therefore, when the water is 2 feet high, the depth of the water changes at a rate of -13/72π feet per minute.

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Let's start by finding the current monthly revenue of the airline for the given number of passengers and ticket price:

Monthly revenue = number of passengers x ticket price

Monthly revenue = 9000 x $30

Monthly revenue = $270,000

Now, let's find the number of passengers for each $1 increase in the ticket price:

Number of passengers lost = 50

So, for a ticket price increase of $x, the number of passengers will be:

Number of passengers = 9000 - 50x

The ticket price will then be $30 + $x, and the revenue will be:

Revenue = (9000 - 50x) x ($30 + $x)

Revenue = 270,000 - 1500x + 30x + x^2

Revenue = x^2 - 1470x + 270,000

To find the ticket price that will maximize the revenue, we need to find the vertex of the parabola given by the revenue equation. The x-coordinate of the vertex is:

x = -b/2a

Where a = 1, b = -1470, and c = 270,000.

x = -(-1470)/2(1)

x = 1470/2

x = 735

So, the ticket price that will maximize the revenue is $30 + $735 = $765. The maximum monthly revenue is then:

Revenue = (9000 - 50(735)) x ($30 + $735)

Revenue = 105 x $765

Revenue = $80,325

Therefore, the ticket price that will maximize the airline's monthly revenue for the route is $765, and the maximum monthly revenue is $80,325.

The solution of the given differential equation by using variable separable is [tex]y=\frac{x^2c}{2}-2[/tex]

An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics. The study of solutions that satisfy the equations and the characteristics of the solutions is the main goal of the differential equation.

The rules to solve differential equations using variables separable,

1) [tex]\frac{dy}{dx}=f(x)/f(y)[/tex]

2) separate terms with the same variable

f(y)dy=f(x)dx

3) Take integration on both sides

4) solve integration by using a suitable method

5) Then get the Solution of the differential equation.

The given differential equation is-

[tex]\frac{dy}{dx}=\frac{2y+4}{x}\\\\\frac{dy}{2y+4}=\frac{dx}{x}\\\\\int\frac{dy}{2y+4}=\int\frac{dx}{x}\\\\\frac{log(2y+4)}{2}=logx+logc\\log(2y+4)=2logxc\\2y+4=x^2c\\2y=x^2c-4\\y=\frac{x^2c}{2}-2[/tex]

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According to the student question, the sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the number of people who respond "yes" has binomial distribution. The correct answer is A.

The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the sample size is sufficiently small and each person's response is independent of the others.

Binomial distribution is used to model the number of successes in a fixed number of independent trials, where the probability of success is constant for each trial. In this case, the proportion of people who respond "yes" is the number of successes out of the total number of trials (i.e., 4 people).

Moreover, the responses of each individual are independent of each other, meaning that the probability of one person answering "yes" does not affect the probability of another person answering "yes."  The correct answer is A.

Your question is incomplete but most probably your full question was

Samples of four people were asked whether gun laws should be more stringent. Respondents had a choice to answer "yes" or "no." The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is

a.  Binomial because the number of people who respond "yes" has binomial distribution

b. Not possible to say because the sample size it too small

c. Not possible to say because population distribution is not known

d. Normal

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It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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The expression for the total length of ribbons left is: r - 16 . But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The expression that represents the total length of ribbons left is:

4 x (r - 4)

This is because Ava uses 4 inches from each roll of ribbon, and there are 4 rolls of ribbon in total. So the total length of ribbon used is 4 x 4 = 16 inches.

To find the total length of ribbon left, we need to subtract the length of ribbon used from the original length of ribbon, which is r inches.

Therefore, the expression for the total length of ribbons left is: r - 16

But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.

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Answer:

Step-by-step explanation:

We are given with a circle whose diameter is 28.2 m

Then, Radius will be diameter/2

=> 28.2 /2

=> 14.1 m

Area of circle = πr²

=> 31.4 × (14.1)²

=> 31.4 × 198.81

=> 624.26 m²

Therefore, the area of the given circle is 624.26 m²

Answer:

The monthly installment for the hire purchase of the motorbike is GHC 27.00

Step-by-step explanation:

To calculate the monthly installment for the hire purchase, we can divide the total cost by the number of months:

Monthly installment = Total cost / Number of months

In this case, the total cost is GHC 540.00 and the number of months is 20:

Monthly installment = GHC 540.00 / 20

Monthly installment = GHC 27.00

Therefore, the monthly installment for the hire purchase of the motorbike is GHC 27.00

Answer:

x = 7 ft

Step-by-step explanation:

[tex]tan 55=\frac{10}{x}\\x=\frac{10}{tan 55}\\x=7.0020\\x=7[/tex]