Let F be the set of fractions in simplest form between 0 and 1 that can be written with a single-digit denominator. Find F and |F|​

Answers

Answer 1

Answer:

|F| is 27, the whole F is "listed" below.

Step-by-step explanation:

The set of possible denominators is the numbers from 2 to 9. Each of them produces a single fraction for each numerator that's coprime to it.

Let's list those for each:

2: 1

3: 1 2

4: 1 3 (2 is not coprime)

5: 1 2 3 4

6: 1 5 (2 3 and 4 are not coprime)

7: 1 2 3 4 5 6

8: 1 3 5 7

9: 1 2 4 5 7 8 (3 and 6 are not coprime)

To make any number from F, just take the denominator from the rows and the numerator from the list. The size of F is 1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 = 27

Answer 2

The set/number of fractions F for each denominator are ; ( 1, 2, 2, 4, 2, 6, 4, 6 ) .while the value | F | = 27

Given that the set of fractions are between 0 and 10. the possible single digit denominators will be ( 2 through 9 ). also the single digit denominators will have to produce a single fraction where its numerator is coprime to the denominator.

note : coprime numbers are a set of numbers whose HCF (highest common factor ) equals 1

denominators                co-prime numerators

    2                                             1

     3                                           1,  2

     4                                           1,  3  

     5                                           1, 2, 3, 4

     6                                           1, 5  

     7                                           1, 2, 3, 4, 5, 6

     8                                           1, 3, 5, 7

     9                                           1, 2, 4, 5, 7, 8

next : Determine the size of F i.e. | F |

The size of F = ∑ number of coprime numerators for each denominator

                     =  1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 = 27

set of fractions F for each single digit denominator  = ( 1, 2, 2, 4, 2, 6, 4, 6 )

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Which line has the same slope as the line passing through (-4, -1) and (-1, -7) ?

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Answer:

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Step-by-step explanation:

Answer:

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The answer is -11

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What is the error in this equation for a trigonometric ratio? Explain the error in full sentences and give a corrected ratio. (5 points)

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Answer:

[tex]\cos\ A = \frac{2}{4.5}[/tex]

Step-by-step explanation:

Given

[tex]sin\ A = \frac{2}{4.5}[/tex]

See attachment

Required

Explain and correct the error

The error in the equation is that: the formula of cosine of angle A is used to calculate the sine of angle A.

The ratio can be corrected as by using:

[tex]\cos\ A = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos\ A = \frac{AC}{AB}[/tex]

[tex]\cos\ A = \frac{2}{4.5}[/tex]

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Answer

Hola la respuesta que buscas es bastante simple pero no lo sé

Step-by-step explanation:

The following expression represents the profit made by John as he mows
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Which description correctly interprets each part of the expression?

Answers

Answer:

P is price per lawn, 20 is the money made per lawn, L is the number of lawns mowed, 100 is his initial cost.

Step-by-step explanation:

Zander found these coins in his Couch

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Answer:

91 cents

Step-by-step explanation:

3 quarters+3 nickel+1 penny=91 cents

Answer:

91 cents

Step-by-step explanation:

3 quarters=75c

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1 penny=1c

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Answer:

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Step-by-step explanation:

The local park has a circular pond with a radius of 9 feet. What is the pond's circumference?

Answers

Answer:

Using 3.14 as pi, the answer would be 56.52, and using just pi (as in the input on a calculator) would be 56.54867.

Step-by-step explanation:

The equation for circumference of a circle is C = πd, C representing the circumference and d representing the diameter. Since the equation shows the radius, the equation can also be C = 2πr, since the radius is half of the diameter. Multiply nine by two to get eighteen. 18 times 3.14 = 56.52.

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Answer:

Step-by-step B. is your answer

explanation:

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Answer:

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Step-by-step explanation:

If the critic rates a total of 100 movies, what is the best prediction for the number of movies she gives exactly 3 stars?
А
27
B
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D
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Answers

Answer:

I think its gonna be 35 I'm not sure

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Select all of the applicable transformations from the parent function y=x^2 to y=-(x+2)^2-3

reflection

vertical translation up 2

vertical translation down 3

vertical translation up 3

horizontal translation left 3

horizontal translation right 2

horizontal translation left 2

compression by a factor of 3

stretch by a factor of 2

Answers

Answer:

reflection

vertical translation down 3

horizontal translation right 2

Step-by-step explanation:

Given

[tex]y = x^2[/tex] ---> Parent function

[tex]y = -(x+2)^2-3[/tex]

Required

All possible transformations

First, the parent function is reflected across the x-axis:

This gives:

[tex]y = x^2[/tex] [tex]==>[/tex] [tex]y =-x^2[/tex]

Next, it is translated horizontally right by 2

The rule is:

[tex](x,y)==>(x+2,y)[/tex]

So:

[tex]y =-x^2[/tex] [tex]==>[/tex] [tex]y = -(x +2)^2[/tex]

Lastly: it is translated vertically down by 3

The rule is:

[tex](x,y)==>(x,y-3)[/tex]

So:

[tex]y = -(x +2)^2[/tex] [tex]==>[/tex] [tex]y = -(x +2)^2 - 3[/tex]

pleas help me the question is the image below

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FOR ALL MY POINTS write an argumentative essay on why dog parks are "helpful or harmful"

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Step-by-step explanation:

(Urgent) Worth 10 points 7.3

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Step-by-step explanation:

A straight line adds up to 180°

m+3m=180°

4m=180°

m=45°

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=135°

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What is the solution to the system of equations
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Answers

Answer:

[tex]y = 4 \\ x = - 2[/tex]

Find the volume of the given solid. Bounded by the cylinder y2 + z2 = 16 and the planes x = 2y, x = 0, z = 0 in the first octant

Answers

Answer:

[tex]\mathbf{ \dfrac{128}{3}}[/tex]

Step-by-step explanation:

Given that:

[tex]y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0[/tex]

[tex]Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16[/tex]

[tex]Then;[/tex]

[tex]y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4[/tex]

[tex]\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y[/tex]

[tex]\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy[/tex]

[tex]Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0[/tex]

[tex]V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\[/tex]

[tex]= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )[/tex]

[tex]= - \dfrac{2}{3} \Big(64\Big )[/tex]

[tex]\mathbf{V = \dfrac{128}{3}}[/tex]

Find the value of x

Please help

Answers

Answer:

128 degrees

Step-by-step explanation:

360-90-90-52=128

Solve triangle ABC. (Round your answers to one decimal place.)
∠A =
13.5
°
∠B =
63.9
°
∠C =

Answers

< A + < B + < C = 180
13.5 + 63.9 + < C = 180
< C = 102.6

What is the slope of the line ?(khan academy)

Answers

Answer:

The slope of the line is 2.

Step-by-step explanation:

Slope of a line:

Suppose that we have two points. The slope of the line is given by the change in y divided by the change in x.

In this question:

Points (0,0) and (1,2)

Change in y: 2 - 0 = 2

Change in x: 1 - 0 = 1

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The slope of the line is 2.

What is the median of the data set?



9
8.5
8
10

Answers

Answer:

8.5

Step-by-step explanation:

When you write out the data set, it looks like this:

5, 8, 8, 8, 8, 9, 9, 9, 10, 10

The median means the exact middle of the data set. In this case, it falls between the 8 and the 9, so the middle would be 8.5, so that's the median of the set. I hope this helps :)

Answer:

The median is 8.5

Step-by-step explanation:

The median is the middle number in a data set. For example, if you had a data set:

2, 2, 3, 4, 4

You would go forwards and backwards in the set until you found the middle number, which is 3. 3 would be the median.

However, if there is no middle number (there are an even number of points in the set), you add the two remaining numbers and divide it by two.

For example, if the final two numbers were:

2, 6

You would add 2 and 6 to get 8, and divide by 2, and you get the median 4.

In this set, we have

5, 8, 8, 8, 8, 9, 9, 9, 10, 10.

The final two numbers are 8 and 9, so you add 8+9=17, divided by 2 = 8.5.

Information collected from runner 3# is in the table below

The constant proportionality for runner 3 is..?

Answers

Answer:

the constant of proportionality would be 9

The top of a ladder slides down a vertical wall at a rate of 2 feet per second. At the moment when the bottom of the ladder is 4 feet from the wall, it slides away from the wall at a rate of 3 feet per second. How long is the ladder

Answers

Answer:

The length of the ladder is 7.21 feet

Step-by-step explanation:

Let

y = Height of the wall

x = Distance between the wall and the ladder (bottom)

L = Length of the ladder

So, the given parameters are:

[tex]\frac{dy}{dt} = -2ft/s[/tex]

When [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]

The ladder, the wall and the ground forms a right-angled triangle where the hypotenuse is the length of the ladder; So:

[tex]L^2 = x^2 + y^2[/tex]

Differentiate with respect to time

[tex]2L\frac{dL}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

The length of the ladder does not change with time. So:

[tex]2L*0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

[tex]0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

Rewrite as:

[tex]2x\frac{dx}{dt} =- 2y\frac{dy}{dt}[/tex]

Divide both sides by 2

[tex]x\frac{dx}{dt} =- y\frac{dy}{dt}[/tex]

Recall that:

[tex]\frac{dy}{dt} = -2ft/s[/tex] and  [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]

So:

[tex]4 * 3 = -y * -2[/tex]

[tex]12 = 2y[/tex]

[tex]6 = y[/tex]

[tex]y = 6[/tex]

Substitute [tex]y = 6[/tex] and [tex]x =4[/tex] in: [tex]L^2 = x^2 + y^2[/tex]

[tex]L^2 =4^2 + 6^2[/tex]

[tex]L^2 =52[/tex]

[tex]L = \sqrt{52[/tex]

[tex]L = 7.21ft[/tex]

7. Below are the steps taken to simplify the expression. Which justification matches Step c of the simplified expression? *

7x+8y+5x+3(y+1)

a. 7x + 8y + 5x + 3y + 3
b. 7x + 5x + 8y + 3y + 3
c. (7x + 5x) + (8y + 3y) + 3
d. 12x + 11y+ 3

A. Associative Property of Addition

B. Commutative Property of Addition

C. Combine Like Terms

D. Distributive Property​

Answers

Answer:

A. Associative property of addition

Step-by-step explanation:

The associative property is about the grouping of terms/numbers in parentheses in an equation.

What TWO steps do you take to solve the following equation: 5x - 3 = 12

Answers

Answer:

First add 3 to each side

Then divide each side by 5

Step-by-step explanation:

5x - 3 = 12

First add 3 to each side

5x-3+3 = 12+3

5x = 15

Then divide each side by 5

5x/5 = 15/5

x = 3

Answer:

3

Step-by-step explanation:

5x = 12 + 3

x = 15/5

x = 3

The Spanish club collected $13.45 from each of its nine members. How
much did the Spanish club collect?

Answers

Answer:

$121.05

Step-by-step explanation:

Answer:

$121.05

Step-by-step explanation:

Since we are told that there is 9 members and each once is 13.45 we can simply do 13.45 times 9 to get the number 121.05.

Question 7 (3 points) Write this decimal division as equivalent whole number division. 19.05 ÷ 1.5 = ÷ Find the quotient.

Answers

Answer:

~12.7~

Step-by-step explanation:

hope this helps brainlest!

PLS HELP ME!!! i’ll give you a brainliest answer :)

Answers

Answer:

B is the correct answer

If one-fourth of 2^30 is equal to 2^x, what is x?

Answers

Answer:

28

Step-by-step explanation:

1/4 can be rewritten as  1 / (2^2)

or 2^-2.

using the 2nd form,

we have 2^-2 * 2^30 = 2^x

By exponent rule

2^28 = 2^x

So we can observe now that x = 28

Answer:

23

Step-by-step explanation:

Becky wants to eat 1/4 of a small pumpkin pie. which if the following statements are correct? select all that apply

a) If she cuts the pie into 8 pieces of the same size, she should eat 2 pieces

b) If she cuts the pie into 10 pieces of the same size, she would eat 4 pieces

c) If she cuts the pie into 12 pieces of the same size, she should eat 3 pieces

Answers

I think the correct answer is C
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