A group of 3 students plants 141 seeds. Each student plants the same number of seeds.
How many seeds does each student plant?
Write an expression you can use to solve
the problem.

If f is F-measurable and non-negative on E ∈ F and µ(E) = 0

thenREf dµ = 0.ProofLet 0 ≤ s ≤ f be a simple, F-measurable function. So s =PNn=1 anχAnfor some an ≥ 0,

An ∈ F. Then IE(s) = PNn=1 anµ(An ∩ E). But µ ismonotone which means that µ(An ∩ E) ≤ µ(E) = 0 for all n and so IE(s) =0 for all such simple functions.

Hence I(f, E) = {0} and so REf dµ =sup I(f, E) = 0. ¥Lemma 4.7 If g ≥ 0 and REgdµ = 0 thenµ{x ∈ E : g(x) > 0} = 0.Proof Let A = {x ∈ E : g(x) > 0} and An = {x ∈ E : g(x) >1n}.

Thenthe sets An = E ∩ {x : g(x) >1n} ∈ F satisfy A1 ⊆ A2 ⊆ A3 ⊆ ... withA =S∞n=1 An. By lemma 4.1 µ(A) = limn→∞ µ(An). Usingsn(x) = ½ 1nif x ∈ An0 otherwise,so sn ≤ g on An we have1nµ(An) = IAn(sn)≤RAngdµ by the definition of RAn≤REgdµ

Thereom 4.4(iii)= 0 by assumption.So µ(An) = 0 for all n and hence µ(A) = 0. ¥Definition If a property P holds on all points in E \ A for some set A withµ(A) = 0 we say that P holds almost everywhere (µ) on E, written as a.e.(µ)on E.

(*It might be that P holds on some of the points of A or that the set ofpoints on which P does not hold is non-measurable.

This is immaterial. Butif µ is a complete measure, such as the Lebesgue-Steiltje’s measure µF, thenthe situation is simpler.

Assume that a property P holds a.e.(µ) on E.

Thedefinition says that the set of points, D say, on which P does not hold can becovered by a set of measure zero, i.e. there exists A : D ⊆ A and µ(A) = 0.

Yet if µ is complete then D will be measurable of measure zero.In this section we are not assuming that µ is complete.)

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

Answer:

1560 cm²

Step-by-step explanation:

4*5*22 = 440 cm²

25*8*10 = 2000 cm²

find the difference between the two numbers to find the volume of the solid part of the box

Brₐinliest plz close to leveling up

Answer:

Step-by-step explanation:

Cost for ordering n tickets online. = 16n+2.50

N=Number of tickets ordered.

N= 66.50 dollars

Answer:

93.75 miles if im not mistaken

Step-by-step explanation:

because the most miles is 375 so you would divide that number by four to see how many miles u can go before filling up again.

Answer:

parallel

Step-by-step explanation:

The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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Answer:

\( - 2 = k + \frac{7}{3} \\ - 2 \times 3 = k + \frac{7}{3} \times 3 \\ - 6 = k + 7 \\ - 6 - 7 = k + 7 - 7 \\ - 13 = k \\ or \\ k = - 13\)

Answer:

-13/3

Step-by-step explanation:

-2=k+7/3

k=-2-7/3

k=-6/3-7/3

k=-13/3

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Answer:

A. 13 units is the answer

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Answer:

13 Units

Step-by-step explanation:

Answer:

1/0.05

Step-by-step explanation:

The formula for the money multiplier is :

1/ Reserve rate

If is wrong i'm sorry

Answer:

1/0.05

Step-by-step explanation:

Just did test

a = amount invested at 4%

how much is 4% of "a"? (4/100) * "a", namely 0.04a.

b = amount invested at 10%

how much is 10% of "b"? (10/100) * "b", namely 0.10b.

c = amount invested at 14%

how much is 14% of "c"? (14/100) * "c", namely 0.14c.

we know the total amount invested is 6000, so whatever "a" and "b" and "c" might be, we know that a + b +c = 6000.

we also know that the yielded amount in interest is $652, so if we simply add their interest, that'd be 0.04a + 0.10b + 0.14c.

the combined amount of "a" and "b" is simply a + b, and we also know that "c" is that much plus 200, namely "c = a + b + 200".

\(a+b+c=6000\hspace{5em}\underline{c=a+b+200} \\\\\\ a+b+\stackrel{c}{(a+b+200)}=6000\implies 2a+2b+200=6000\implies 2a+2b=5800 \\\\\\ 2b=5800-2a\implies b=\cfrac{5800-2a}{2}\implies \boxed{b=2900-a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{c=a+b+200}\implies \stackrel{substituting}{c=a+(\underset{b}{2900-a})+200}\implies c=a+2900-a+200 \\\\\\ c=2900+200\implies {\Large \begin{array}{llll} c=3100 \end{array}} \\\\[-0.35em] ~\dotfill\)

\(0.04a+0.10b+0.14c=652\implies \stackrel{\textit{substituting}}{0.04a+0.10(\underset{b}{2900-a})+0.14(\underset{c}{3100})}=652 \\\\\\ 0.04a+290-0.10a+434=652\implies 0.04a-0.10a+724=652 \\\\\\ 0.04a-0.10a=-72\implies -0.06a=-72 \\\\\\ a=\cfrac{-72}{-0.06}\implies {\Large \begin{array}{llll} a=1200 \end{array}} \hspace{5em} \stackrel{6000-3100-1200}{{\Large \begin{array}{llll} b=1700 \end{array}}}\)

Answer:

A

Step-by-step explanation:

Answer:

1 is multiplication

2 is addition

3 is simplification

4 is division

5 is simplification

Step-by-step explanation:

Answer:

9 hours

Step-by-step explanation:

$273/13 hours=$21 per hour

$189/$21 =9 hours

His total earnings for a total sale of 7,000​ could be 1450sh

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

Salary = 400

Commission = 15%

using the above as a guide, we have the following:

Total earnings = 400 + 15% * Total sales

So, we have

Total earnings = 400 + 15% * 7000

Evaluate

Total earnings = 1450

Hence, the total earnings is 1450

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Question

Simon earned 400sh weekly for goods sold and a commission of 15%

What could be his earnings for a total sale of 7,000​.

To sketch the graph of the function f(x) = 2cos^2(x) - 3x + 4 for the values of x between 0 and 2, we can follow these steps:

1. Determine key points: Find the critical points and important features of the function within the given range. This includes the x-intercepts, local maxima, and minima.

2. Plot the x-intercepts: To find the x-intercepts, set f(x) = 0 and solve for x. In this case, cos^2(x) = (0 + 3x - 4)/2. Find the values of x where this equation holds true.

3. Identify local maxima and minima: Use calculus or other methods to find the local maximum and minimum points of the function within the given range.

4. Sketch the graph: Once you have the key points, plot them on a graph and connect them smoothly. Pay attention to the shape and behavior of the function.

Since the process of sketching a graph is best done visually, I'm unable to provide an image here. However, by following the steps outlined above, you can plot the graph of f(x) within the range of x between 0 and 2. Remember to label the axes and indicate any important points you have found.

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b) The critical value is 11.34.

c) By Using a chi-squared distribution table with 100 degrees of freedom and a significance level of 0.005, the critical value is 137.18.

Now, WE can simplify as;

a) For conduct a chi-squared test for the fairness of a 6-sided die with a significance level of 0.05,

we have 5 degrees of freedom

Hence, By Using a chi-squared distribution table with 5 degrees of freedom and a significance level of 0.05, the critical value is 11.07.

And, When calculated chi-squared value exceeds 11.07, then the results are statistically significant at the given level.

b) Now, When examining the results of an experiment with 4 treatments and a significance level of 0.01, we have 3 degrees of freedom

Hence, By Using a chi-squared distribution table with 3 degrees of freedom and a significance level of 0.01, the critical value is 11.34.

And, When calculated chi-squared value exceeds 11.34, then the results are statistically significant at the given level.

c) Hence, For comparing outcomes in 101 different categories with a significance level of 0.005, we have 100 degrees of freedom.

So, By Using a chi-squared distribution table with 100 degrees of freedom and a significance level of 0.005, the critical value is 137.18.

And, When calculated chi-squared value exceeds 137.18, then the results are statistically significant at the given level.

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Step-by-step explanation:

(-2)(4)+12/2= -8 +6 = -2

Hope it helps

The slope of equation is 3x + y = 3 is -3

The standard from of Slope - intercept form of equation is y = mx +b

where , m is slope of line

b is y-intercept

and x and y are the variables

Slope of line represents steepness of a line and also termed as gradient .

Y- intercept represents the y- coordinate of the point where the line intersect the y-axis.

In the given question ,

The equation of the line is given as : 3x + 1y = 3

bring 3x to right side,

y = -3x + 3

comparing the equation to standard from

slope of line : m = -3

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The complete table for the time it takes to empty the barrel for the given rates is attached below. The value of constant k is 60.

To solve the problem, we can use the formula for inverse variation

time = k/leaking rate

where k is a constant of proportionality. We can find k by using the information given in the problem

30 = k/2

Solving for k, we get:

k = 60

Now we can use this value of k to fill in the table

Leaking rate (gallons per minute)                Time to empty (minutes)

      2                                                                           30

      1                                                                            60

      0.5                                                                        120

      0.25                                                                     240

      0.1                                                                        600

As the leaking rate decreases, the time to empty the barrel increases, because the liquid is leaking out more slowly.

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Answer:

The first step is to calculate the average daily balance for the billing cycle. This is done by adding up the daily balances for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the billing cycle is from July 7 to August 6, so there are 31 days in the billing cycle.

The daily balances are as follows:

* July 7: $216.71

* July 14: $268.75

* July 17: $284.37

* July 21: $116.71

* July 24: $260.74

The average daily balance is therefore $226.81.

The next step is to calculate the finance charge. This is done by multiplying the average daily balance by the interest rate and then by the number of days in the billing cycle. In this case, the interest rate is 1.25% and the number of days in the billing cycle is 31 days.

The finance charge is therefore $7.43.

The final step is to calculate the new balance. This is done by adding the finance charge to the previous balance. In this case, the previous balance is $216.71 and the finance charge is $7.43. The new balance is therefore $224.14.

Here is the solution in mathematical form:

* Average daily balance = (216.71 + 268.75 + 284.37 + 116.71 + 260.74) / 31 = 226.81

* Finance charge = 226.81 * 0.0125 * 31 = 7.43

* New balance = 216.71 + 7.43 = 224.14

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive exponents is (7)²⁰  .

In the question ,

it is given that ,

the expression is 7⁻⁴/(7⁻⁴)⁶ .

we need to find the simplified value of the expression .

So ,

= 7⁻⁴/(7⁻⁴)⁶

we know that (xᵃ)ᵇ = (x)ᵃˣᵇ

By using the above property , we get

= 7⁻⁴/(7)⁻⁴ˣ⁶

= 7⁻⁴/(7)⁻²⁴

we know that xᵃ/xᵇ = xᵃ⁻ᵇ

By using the above property , we get

= (7)⁻⁴×(7)²⁴

= (7)²⁴⁻⁴    ... by using the property xᵃ.xᵇ = xᵃ⁺ᵇ

= (7)²⁰

Therefore , The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive

exponents is (7)²⁰  .

The given question is incomplete , the complete question is

Simplify the following expression. Write your answer using positive exponents.

7⁻⁴/(7⁻⁴)⁶

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