Given a doubling time of 934 minutes, how long will it take a culture in the exponential growth phase to grow from 15 cells per mL, to 86,059 cells per mL? Explain.

So Abbie was asked to randomly select at least 368 of her high school unitary method students to estimate the percentage of students planning to go to college. With a 90% confidence level and a 5% error rate. 

The unit method is an approach to problem solving that first determines the value of a single unit and then multiplies that value to determine the required value. Simply put, the unit method is used to extract a single unit value from a given multiple. For example, 40 pens cost 400 rupees or pen price. This process can be standardized. single country. Something that has an identity element. (Mathematics, Algebra) (Linear Algebra, Mathematical Analysis, Matrix or Operator Mathematics) Adjoints and reciprocals are equivalent. 

To determine the required sample size, the following formula should be used:

[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]

where:

N:sample size required

Z:The Z-score corresponds to the desired confidence level and is 1.645 at the 90% confidence level.

Pa:Estimated Percentage of Students Planning to Go to College

1-p:Percentage of students not planning to go to college

E:Desired error margin of 0.05

Since we don't know the actual percentage of students who want to go on to college, we must use estimates based on past studies and surveys. Let's assume the estimated proportion is 0.6 (her 60% of students).

After plugging in the values ​​it looks like this:

[tex]n = (1.645^2 * 0.6 * 0.4) / 0.05^2\\n = 368.03[/tex]

So Abbie was asked to randomly select at least 368 of her high school students to estimate the percentage of students planning to go to college. With a 90% confidence level and a 5% error rate. 

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The pairs of events of random integers are pairs of events are,

even and odd , negative and positive integers, zero and non-zero integers.

Two events are mutually exclusive if they cannot occur at the same time.

Selecting a random integer from -200 to 200,

Any two events that involve selecting a specific integer are mutually exclusive.

For example,

The events selecting the integer -100

And selecting the integer 50 are mutually exclusive

As they cannot both occur at the same time.

Any pair of events that involve selecting a specific integer are mutually exclusive.

Here are a few examples,

Selecting an even integer and selecting an odd integer.

Selecting a negative integer and selecting a positive integer

Selecting the integer 0 and selecting an integer that is not 0.

But,

Events such as selecting an even integer and selecting an integer between -100 and 100 are not mutually exclusive.

As there are even integers between -100 and 100.

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Answer:

Step-by-step explanation:

The probability of a baby being a boy or a girl is 1/2 or 50% each. Since the couple has already had three boys, the probability of the fourth child being a boy or a girl is still 1/2 or 50%, as the gender of each child is independent of the others. Therefore, the probability of the couple's last child being a baby boy is 50%.

The required probability of a couple having a baby boy when their third child is​ born is 1/2 / 50%.

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

Assuming boys and girls are equally​ likely.

The first two children were both boys

According to given question we have

The probability of having a baby girl is an independent probability.

The first two children were both boys

So, it is not related to the previous child.

So required probability = 1/2 / 50%

Therefore, the required probability of a couple having a baby boy when their third child is​ born is 1/2 / 50%.

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Answer:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

invNorm(0.484)= 1.96

Therefore, the Z-score that has 48.4% of the distribution's area to its left is approximately 1.96.

Step-by-step explanation:

Speed =  distance / time    

  you are given distance = 23 miles  and time = .5 hr

      distance / time =  23 miles / .5 hr =   46 mph

The final closed formula answers for each part,

(a) an = n^2 + 1

(b) an = n(n + 1)(n + 2)/6

(c) an = 2n + 6

(d) an = n! + (n-1)! + ... + 2! + 1!

(a) The given sequence can be seen as the sequence of partial sums of the sequence of odd numbers: 1, 3, 5, 7, 9, . . . . That is, the nth term of the given sequence is the sum of the first n odd numbers, which is n^2. Therefore, the closed formula for the given sequence is an = n^2 + 1.

(b) The given sequence can be seen as the sequence of partial sums of the sequence of triangular numbers: 1, 3, 6, 10, 15, . . . . That is, the nth term of the given sequence is the sum of the first n triangular numbers, which is n(n + 1)(n + 2)/6. Therefore, the closed formula for the given sequence is an = n(n + 1)(n + 2)/6.

(c) The given sequence can be seen as the sequence of differences between consecutive squares: 1, 5, 9, 16, 21, . . . . That is, the nth term of the given sequence is the difference between the (n+1)th square and the nth square, which is (n + 1)^2 - n^2 = 2n + 1. Therefore, the closed formula for the given sequence is an = 2n + 6.

(d) The given sequence can be seen as the sequence of partial sums of the sequence defined recursively by a1 = 1 and an+1 = an(n + 1) for n ≥ 1. That is, the nth term of the given sequence is the sum of the first n terms of the recursive sequence. It can be shown that the nth term of the recursive sequence is n! (n factorial), and therefore the nth term of the given sequence is the sum of the first n factorials. That is, an = 1 + 1! + 2! + ... + (n-1)! + n!. Therefore, the closed formula for the given sequence is an = n! + (n-1)! + ... + 2! + 1!.

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The value of the triple integral[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex] by using spherical coordinates [tex]2\pi(e^{-1}-e^{-9})[/tex].

Given that the triple integral is-

[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]

E is the region bounded by the spheres which are,

[tex]x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9[/tex]

In spherical coordinates we have,

x = r cosθ sin ∅

y = r sinθ sin∅

z = r cos∅

dV = r²sin∅ dr dθ d∅

E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,

1 ≤ r ≤ 3

0 ≤ θ ≤ 2π

0 ≤ ∅ ≤ π

Then

[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]

[tex]\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})[/tex]

The complete question is-

Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.

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The peak of the histogram appears at age 19, and its shape is approximately symmetric. This indicates that the students' ages are evenly distributed, with a mean age of around 19.

Probability is a gauge of how likely an occurrence is to take place. It is expressed as a number between 0 and 1, with 0 designating an impossibility and 1 designating a certainty for the occurrence.

For instance, if you flip an impartial coin, you could get either heads or tails. Because there is an equal possibility that the coin will land on its head or tails, the probability of getting heads on a single toss is [tex]0.5[/tex] , or 50%.

Given

c) To determine the likelihood that a pupil chosen at random is under 20 years old, we must add the probabilities of the top two bars in the histogram. Following are the results: P(age 20) = P(age = 17) + P(age = 18)  [tex]= 0.05 + 0.15 = 0.2[/tex]

The likelihood that a pupil chosen at random is under  [tex]20[/tex] years old is therefore  [tex]0.2, or 20%[/tex] .

d) We must add the probabilities of the bars between the ages of 19 and 21, inclusive, in order to determine the likelihood that an arbitrarily chosen student is older than 18 but not older than 21. P(18 age 21) equals P(age = 19) + P(age = 20) + P(age = 21)  [tex]= 0.35 + 0.25 + 0.1 = 0.7[/tex] .

Therefore,  [tex]0.7, or 70%[/tex] , of an arbitrarily chosen student having an age that is greater than 18 but not greater than [tex]21[/tex]  .

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By conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.

The four arithmetic operations are addition, multiplication, division, and subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

The number that the other number is deducted from is known as a minuend.

Subtrahend: The amount that needs to be deducted from the minuend is known as a subtrahend.

Difference: A difference is an outcome obtained by deducting a subtractor from a minimum.

So, more miles Michael ran on day 3 than on day 2:

= 7 - 2

= 5 miles

Therefore, by conducting subtraction we know that Michael ran 5 miles more on day 3 than on day 2.

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Using probability, we can find that:

E(Y)= 2.4, Var (Y) = 0.64

E(Y) = 480, Var(Y) = 25,600

The probability of an event is the proportion of favourable outcomes to all other potential outcomes. To determine how likely an event is, use the following formula:

Probability (Event) = Positive Results/Total Results = x/n

Given,

The weekly CPU time is as follows:

f(y) where, 0≤y≤4

Here, probability density function is 4-y is correct, or else we get negative expected values.

We have to find E(Y) and var(Y)

E(Y) = 2.4

var (Y) = E(Y²)-(E(Y)) ²

= 6.4 - (2.4) ²

= 0.64

The CPU time is costing the firm $200 per hour.

Now, we find E(Y) and var(Y) of the weekly cost for the CPU time.

Y = 200E

E(Y) = 200 × 2.4

= 480

var(Y) = 200V(Y)

= 200 × 0.64

= 25600

We can observe that the weekly cost is not exceeding $600 as weekly cost for CPU time = 480.

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Your total grade point average (GPA) for the semester is 2.67.

GPA stands for Grade Point Average. It is a numerical calculation used to measure the academic success of a student. It is calculated by taking the average of all grades received by a student across all courses taken in a given semester or academic year. Each course is assigned a specific number of credit hours, and each grade is assigned a numerical value based on the school’s grading scale. The numerical value of each grade is then multiplied by the number of credit hours for the course, and the total of all courses is added together to determine a student’s GPA.

A higher GPA is generally indicative of higher academic performance while a lower GPA is generally indicative of lower academic performance. A student’s GPA is used by schools, employers, and other organizations to evaluate a student’s academic record.

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This would give you a total of 29.0. Divide this by 10 credit hours and you get a GPA of 2.85 for the semester.

GPA stands for Grade Point Average. It is an academic measure of a student's performance in a course or program of study. It is calculated by dividing the total number of grade points earned by the total number of credit hours taken. A grade point average is typically expressed as a number on a 4.0 scale. A 4.0 GPA is considered to be the highest possible grade point average, while anything below a 2.0 GPA is usually considered to be failing.

This is calculated by adding up the total number of credit hours (10 credit hours) and then multiplying each grade by the respective number of credit hours. A=4.0, B=3.0, C=2.0.
So, you would multiply 4.0 by 3 for FYE 105, 3.0 by 3 for ENG 101, 2.0 by 3 for MAT 150, 2.0 by 3 for BIO 112, and 4.0 by 1 for BIO 113.
This would give you a total of 29.0.
Divide this by 10 credit hours and you get a GPA of 2.85 for the semester.

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Answer:

8.7 m
Option B

Step-by-step explanation:

The tree, the shadow and the line of sight from the tip of the shadow to the top of the tree form a right triangle

The angle formed is 30°

Using the relationship
[tex]\tan 30 = \dfrac{h}{15}[/tex]

we get
[tex]h = 15 \times \tan 30[/tex]

[tex]h = 15 \times \dfrac{1}{\sqrt{3}}[/tex]

[tex]h = 8.66 m[/tex]

Rounded up this would be 8.7 m which is option B

Answer: D. Square

Step-by-step explanation:

The shape created by the cross section of the cut through a square pyramid is a square.

To see why, imagine the pyramid sitting on a table with its square base flat against the surface. The cut goes through the vertex, which is the point at the top of the pyramid. Since the cut is perpendicular to the base, it divides the pyramid into two smaller pyramids with congruent, but not identical, bases. Each of these smaller pyramids has a triangular base that is an isosceles right triangle. The two triangles share a common hypotenuse, which is the line of the cut.

The cross section of the cut is the shape formed where the two triangles meet along the hypotenuse. Since both triangles are congruent and the hypotenuse is the same for both, the cross section is a square. The sides of the square are equal to the base of the original pyramid, which is one of the legs of the isosceles right triangles formed by the cut. Therefore, the answer is D, a square.

The correct option is D. $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.

In math, addition is the process of adding two or more integers together. The numbers having added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is among the most fundamental mathematical operations we employ on a daily basis.

Quarterly profit for Mr. Brown's Goodwill Store in 2012 (in dollars)

1 $9,841.28

2 $8,957.67

3 $7,429.84

4 $11,095.67

Total profit = profit of 3rd quarter + profit of 4th quarter

Total profit = $7,429.84 + $11,095.67

Total profit =  $18,525.51.

Thus, $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.

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cardinality of the given set n(A'∩B') is 19

In a Venn diagram, circles are used to represent connections between objects or small groups of objects. Circles that overlap have some properties, but circles that do not overlap do not have properties. Venn diagrams are very useful for showing how two concepts are related and different graphically.

This Venn diagram illustrates the relationship between the subsequent set of integers.

Whereas the other set comprises the numbers in the 5x table from 1 to 25, the first set only contains even numbers from 1 to 25.

The intersection component demonstrates that 10 and 20 are both multiples of 5 from 1 to 25 and even integers.

Complement of A =14+5+12+7=38

Complement  of B=7+4+3+9+12+7=42

n(A'∩B')=19

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Answer:

the value of r that makes the slope of the line passing through (3, 5) and (-3, r) equal to 3/4 is r = 1/2

Step-by-step explanation:

We can use the formula for the slope of a line passing through two points, which is:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, we have two points (3, 5) and (-3, r), and we know that the slope m is 3/4. So we can write:

3/4 = (r - 5)/(-3 - 3)

Simplifying this equation, we get:

3/4 = (r - 5)/(-6)

Multiplying both sides by -6, we get:

-9/2 = r - 5

Adding 5 to both sides, we get:

r = -9/2 + 5

Simplifying, we get:

r = 1/2

Answer:

your answer to the lowest terms

The probability of rolling a sum of 6 with these dice is 1/12.

Answer:

Let's assume that Mr. Nkalle invested an amount of x in Scheme A and (20900 - x) in Scheme B.

The simple interest earned on Scheme A in 2 years would be:

SI(A) = (x * 9 * 2)/100 = 0.18x

The simple interest earned on Scheme B in 2 years would be:

SI(B) = [(20900 - x) * 8 * 2]/100 = (3344 - 0.16x)

The total simple interest earned in 2 years is given as N$3508:

SI(A) + SI(B) = 0.18x + (3344 - 0.16x) = 3508

0.02x = 164

x = 8200

Therefore, Mr. Nkalle invested N$8200 in Scheme A and N$12700 (20900 - 8200) in Scheme B. So the amount invested in Scheme B was N$12700.

Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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The first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get 118096.

What is Geometric Progression?

A progression of numbers with a constant ratio between each number and the one before

Let the first term of the geometric progression be denoted by "a" and the common ratio be denoted by "r".

We know that the 4th term is 108, so we can use the formula for the nth term of a GP to write:

a*r³ = 108 .....(1)

We also know that the 8th term is 8748, so we can write:

a*r⁷ = 8748 .....(2)

To find the sum of the first 10 terms, we can use the formula for the sum of a finite geometric series:

S = a(1 - rⁿ)/(1 - r)

where S is the sum of the first n terms of the GP. We want to find the sum of the first 10 terms, so we plug in n = 10:

S = a(1 - r¹⁰)/(1 - r)

We now have two equations (1) and (2) with two unknowns (a and r). We can solve for a and r by dividing equation (2) by equation (1) to eliminate a:

(ar⁷)/(ar³) = 8748/108

r⁴ = 81

r = 3

Substituting r = 3 into equation (1) to solve for a, we have:

a*3³ = 108

a = 4

Therefore, the first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get:

S = 4(1 - 3¹⁰)/(1 - 3)

S = 4(1 - 59049)/(-2)

S = 4(59048)/2

S = 118096

Therefore, the sum of the first 10 terms of the GP is 118096.

118096.

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The volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

To find the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis, we use the formula:

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to find the equation of the curve that is generated when we rotate y = 4 - 2x² around the y-axis. To do this, we use the formula for the equation of a curve generated by revolving y = f(x) around the y-axis, which is:

x² + y² = r²

where r is the distance from the y-axis to the curve at any point (x, y).

Substituting y = 4 - 2x² into this formula, we get:

x² + (4 - 2x²) = r²

Simplifying, we get:

r² = 4 - x²

Therefore, the radius of the circular cross-sections perpendicular to the y-axis is given by:

r = √(4 - x²)

Now, we can integrate πr²dy from y = 0 to y = 2:

V = ∫[0,2] π(√(4 - x²))²dy

V = ∫[0,2] π(4 - x²)dy

V = π∫[0,2] (4y - y²)dy

V = π(2y² - (1/3)y³)∣[0,2]

V = π(8 - (8/3))

V = (16/3)π

Therefore, the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

b. To find the volume of the solid generated by revolving the region enclosed by the curves x = √y+9, x = 0, and y = 1 through 360° about the y-axis, we use the same formula as in part (a):

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to solve the equation x = √y+9 for y in terms of x:

x = √y+9

x² = y + 9

y = x² - 9

Next, we need to find the equation of the curve that is generated when we rotate y = x² - 9 around the y-axis. Using the same formula as in part (a), we get:

r = x

Now, we can integrate πr²dy from y = 1 to y = 10 (since x = 0 when y = 1 and x = 3 when y = 10):

V = ∫[1,10] π(x²)²dy

V = π∫[1,10] x⁴dy

V = π(1/5)x⁵∣[0,3]

V = π(243/5)

Therefore, the volume of the solid generated by revolving the region.

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Answer:

8(3/4y - 2) + 6(-1/2x + 4) + 1 can be simplified as:

6(-1/2x) = -3x

8(3/4y) = 6y

8(-2) = -16

6(4) = 24

1 remains as 1.

So the expression becomes:

6y - 3x - 16 + 24 + 1

which simplifies to:

6y - 3x + 9

Therefore, the expressions that are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1 are:

6y - 3x + 9

Answer:

The claim that healthcare laptop replacement costs are higher than in other industries.

Answer:

(a) Find (f + g)(x)

To find (f + g)(x), we add the two functions f(x) and g(x):

(f + g)(x) = f(x) + g(x) = (4x + 9) + (9x - 5) = 13x + 4

The domain of (f + g)(x) is all real numbers, since there are no restrictions on x that would make (f + g)(x) undefined.

(b) Find (f - g)(x)

To find (f - g)(x), we subtract the function g(x) from f(x):

(f - g)(x) = f(x) - g(x) = (4x + 9) - (9x - 5) = -5x + 14

The domain of (f - g)(x) is all real numbers, since there are no restrictions on x that would make (f - g)(x) undefined.

(c) Find (f * g)(x)

To find (f * g)(x), we multiply the two functions f(x) and g(x):

(f * g)(x) = f(x) * g(x) = (4x + 9)(9x - 5) = 36x^2 + 11x - 45

The domain of (f * g)(x) is all real numbers, since there are no restrictions on x that would make (f * g)(x) undefined.

(d) Find (f / g)(x)

To find (f / g)(x), we divide the function f(x) by g(x):

(f / g)(x) = f(x) / g(x) = (4x + 9) / (9x - 5)

The domain of (f / g)(x) is all real numbers except x = 5/9, since this value would make the denominator of (f / g)(x) equal to zero, resulting in division by zero, which is undefined.

(e) Find f(g(x))

To find f(g(x)), we substitute g(x) into the expression for f(x):

f(g(x)) = 4g(x) + 9

Substituting the expression for g(x), we get:

f(g(x)) = 4(9x - 5) + 9 = 36x - 11

The domain of f(g(x)) is all real numbers, since there are no restrictions on x that would make f(g(x)) undefined.

(f) Find g(f(x))

To find g(f(x)), we substitute f(x) into the expression for g(x):

g(f(x)) = 9f(x) - 5

Substituting the expression for f(x), we get:

g(f(x)) = 9(4x + 9) - 5 = 36x + 76

The domain of g(f(x)) is all real numbers, since there are no restrictions on x that would make g(f(x)) undefined.

(g) Find f(f(x))

To find f(f(x)), we substitute f(x) into the expression for f(x):

f(f(x)) = 4f(x) + 9

Substituting the expression for f(x), we get:

f(f(x)) = 4(4x + 9) + 9 = 16x + 45

The domain of f(f(x)) is all real numbers, since there are no restrictions on x that would make f(f(x)) undefined.

(h) Find g(g(x))

To find g(g(x)), we substitute g(x) into the expression for g(x):

g(g(x)) = 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) Find f(g(x)).

To find f(g(x)), we first need to find g(x) and then substitute it into f(x).

g(x) = 9x - 5

f(g(x)) = f(9x - 5) = 4(9x - 5) + 9 = 36x - 11

Therefore, f(g(x)) = 36x - 11.

(b) Find g(f(x)).

To find g(f(x)), we first need to find f(x) and then substitute it into g(x).

f(x) = 4x + 9

g(f(x)) = g(4x + 9) = 9(4x + 9) - 5 = 36x + 76

Therefore, g(f(x)) = 36x + 76.

(c) Find f(f(x)).

To find f(f(x)), we need to substitute f(x) into f(x).

f(f(x)) = 4(4x + 9) + 9 = 16x + 45

Therefore, f(f(x)) = 16x + 45.

(d) Find g(g(x)).

To find g(g(x)), we need to substitute g(x) into g(x).

g(g(x)) = 9(9x - 5) - 5 = 81x - 50

Therefore, g(g(x)) = 81x - 50.

Domain of f(x) and g(x): Since both f(x) and g(x) are linear functions, their domains are all real numbers.

(e) Find the inverse of f(x).

To find the inverse of f(x), we need to switch the roles of x and f(x) and solve for f(x).

y = 4x + 9

x = 4y + 9

x - 9 = 4y

y = (x - 9) / 4

Therefore, the inverse of f(x) is f^(-1)(x) = (x - 9) / 4.

(f) Find the inverse of g(x).

To find the inverse of g(x), we need to switch the roles of x and g(x) and solve for g(x).

y = 9x - 5

x = 9y - 5

x + 5 = 9y

y = (x + 5) / 9

Therefore, the inverse of g(x) is g^(-1)(x) = (x + 5) / 9.

(g) Find the domain of f^(-1)(x).

The domain of f^(-1)(x) is the range of f(x). Since f(x) is a linear function, its range is all real numbers. Therefore, the domain of f^(-1)(x) is also all real numbers.

(h) Find the domain of g^(-1)(x).

The domain of g^(-1)(x) is the range of g(x). Since g(x) is a linear function, its range is all real numbers. Therefore, the domain of g^(-1)(x) is also all real numbers.

Answer:

To find the perpendicular line to the line y = 1/2x + 4 that passes through the point (-8, 3), we can follow these steps:

Determine the slope of the given line. The line y = 1/2x + 4 is in slope-intercept form (y = mx + b), where the slope is m = 1/2.

Find the negative reciprocal of the slope from step 1 to obtain the slope of the perpendicular line. The negative reciprocal of 1/2 is -2, so the slope of the perpendicular line is -2.

Use the point-slope form of a line (y - y1 = m(x - x1)) and plug in the slope from step 2 and the point (-8, 3) to find the equation of the perpendicular line.

y - 3 = -2(x + 8)

Simplifying this equation gives:

y = -2x - 13

Therefore, the equation of the perpendicular line passing through (-8, 3) is y = -2x - 13.

The cost of the fat-free cottage cheese required in the recipe is R17.98.

How to determine the cost ?

To determine the cost, we first need to calculate the amount of fat-free cottage cheese required in the recipe. The recipe calls for 250g of fat-free cottage cheese, which can be obtained by using 2 units of 125g each. Knowing the cost of ingredients is important for Mrs Gilfillan to price the cake appropriately to cover her costs and make a profit.

What is the cost of the fat-free cottage cheese required to make the Mixed Berry and Almond Polenta Cake recipe that serves 15 espresso cups at Mrs Gilfillan's coffee shop?

The cost of 1 unit of 125g fat-free cottage cheese is R8.99.

Therefore, the cost of 2 units of 125g is calculated as:

R (2 x 8.99) =R 17.98

Hence, the cost of the fat-free cottage cheese required in the recipe is R 17.98.

This cost is in addition to the cost of the other ingredients, such as butter, sugar, ground almonds, mixed frozen berries, and polenta, as well as the cost of labor, overhead, and other expenses involved in making and selling the cake.

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The probability of the union of events A, B, and C is 0.7 where P(A)=0.2, P(B)=0.2 and P(C)=0.3.

In set theory, the union of two or more sets is a set that contains all the distinct elements of the sets being considered. Formally, the union of sets A and B, denoted as A ∪ B, is the set of all elements that are in either set A or set B, or in both.

When A, B, and C are mutually exclusive events, it means that they cannot happen at the same time. Therefore, the probability of the union of these events is equal to the sum of their individual probabilities.

In this case, we are given that:

P(A) = 0.2

P(B) = 0.2

P(C) = 0.3

To find the probability of the union of these events, we need to add their probabilities:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C)

Substituting the given probabilities, we get:

P(A ∪ B ∪ C) = 0.2 + 0.2 + 0.3

P(A ∪ B ∪ C) = 0.7

Therefore, the probability of the union of events A, B, and C is 0.7.

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The question is A, B, and C are mutually exclusive. P(A) = 0.2, P(B) = 0.2, P(C) = 0.3. Find P(A ∪ B ∪ C).

P(A ∪ B ∪ C) = ?

Answer:

60 degrees

Step-by-step explanation:

cos(x)=1/2

cos(x)=0.5

(x)=[tex]cos^-1[/tex] (0.5)

(x)=60

Answer:

y = 4 sin(π x) + 5

Step-by-step explanation:

A sine function with a midline of y=5, an amplitude of 4, and a period of 2 can be written in the following form:

y = A sin(2π/ x) +

where A is the amplitude, is the period, is the vertical shift (midline), and x is the independent variable (usually time).

Substituting the given values, we get:

y = 4 sin(2π/2 x) + 5

Simplifying this expression, we get:

y = 4 sin(π x) + 5

Therefore, the sine function with the desired characteristics is:

y = 4 sin(π x) + 5