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2 years ago

Find the greatest rational number r such that the ratios 8/15 ÷r and 18/35 ÷r are whole numbers.

Mathematics

1 answer:

Akimi4 [234]2 years ago

5 0

Answer:

2/105

Step-by-step explanation:

"r" is the greatest common divisor (GCD) of the two fractions. It can be found using Euclid's algorithm in the usual way.

(8/15) - (18/35) = 56/105 - 54/105 = 2/105 . . . . . this is (8/15) mod (18/35)

We can see that the next step, division of 54/105 by 2/105, will produce a remainder of 0, so the GCD is 2/105.

The greatest rational number r is 2/105.

_____

<em>Check</em>

The ratios are (8/15)/(2/105) = 28; (18/35)/(2/105) = 27. These whole numbers are relatively prime, so there is no larger r than the one we found.

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Rachel is bowling with her friends. her bowling ball has a radius of 4 inches. as she bowls she tracks the location of the finge

Goshia [24]

Question Continuation

The finger hole changes by 45 degrees.

Define a function, f, that gives the height of the finger hole above the ground (in inches) in terms of the angle of rotation (measured in radians) it has swept out from the 12 o'clock position.

Answer:

f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

Step-by-step explanation:

Given

Let represent radius

r = 4 inches

Considering that she starts tracking the location when the finger hole is at the 12 o'clock; this means that the angle measurement at this point is 0°.

Let θ represent the angle

At 12 o'clock mark

θ = 0

When the finger hole changes by 45 degrees

θ = 45°

Convert 45° to radians

θ = 45° * π/180

θ = π/4

So, angle θ is such that θ∈[0, π/4]

This can be represented as

0 ≤ θ ≤ π/4

Calculating the measure of f(θ) in polar coordinates

When θ = 0, f(θ) = r (i.e. the current position of the bowl)

When θ = π/2, f(θ) = rcosθ

This is so because f(θ), being the function of the height is a measure of the radius* cos(θ)

Taking measurement of f(θ) from 0 to π/2

f(θ) = r + rcosθ

f(θ) = r(1 + cos(θ))

So, f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

7 0

2 years ago

The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of vi

baherus [9]

Answer: 2185

Step-by-step explanation:

Let p be the proportion of visitors are campers.

Given : The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state.

The prior proportion of visitors are campers : p=0.35

Allowable error : E= 2%= 0.02

We know that the z-value for 95% confidence = $z_c=1.96$

Then by Central Limit Theorem , the required sample size would be :

$n=p(1-p)(\dfrac{z_{c}}{E})^2$

$\Rightarrow\ n=0.35(1-0.35)(\dfrac{1.96}{0.02})^2\\\\ n= 0.35(0.65)(9604)$

Simply , we get

$n=2184.91\approx2185$ [Rounded to the next whole number.]

Hence, the smallest sample size to estimate the population proportion of campers =2185

7 0

2 years ago

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts Co

Darya [45]

Answer:

Step-by-step explanation:

Given that in the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College.

Table is prepared as follows

Bus coll. Lib Arts coll Educ. coll Total

Observed 90 120 90 300

Expected p.c. 35 35 30 100

Expected number 105 105 90 300

Percent*300/100

Hence expected frequency for business college = 105

4 0

2 years ago

A rectangular window has a length of 81.47 cm and a width of 34.2 cm. What is the least precise measurement of the perimeter of

Pie

The least precise measurement of the perimeter of the window is 231.30

Step-by-step explanation:

The least price measurement mean a value with the least number of significant figures.calculate the perimeter in this case as;

Perimeter of a rectangle = 2(l+w) where l is the length and w is the width

Perimeter= 2(81.47 + 34.2)

Perimeter=2(115.67)

Perimeter=231.34

Perimeter=231.30(4 significant figures)

Learn More

Significant figures : brainly.com/question/11566364

Keywords : Perimeter, Least precise measurement

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2 years ago

Solve the linear equation <br> 31x + 29y = 33<br> 29x + 31y = 27

Temka [501]

Answer:

x = 2

y = -1

Step-by-step explanation:

Make the coefficient of x the same

Multiply the first equation by 29

31x + 29y = 33 becomes

899x + 841y = 957

Multiply the second equation by 31

29x + 31y = 27 becomes

899x + 961y = 837

Subtract the equations

(899x + 841y) - (899x + 961y) = 957 - 837

(899x - 899x) + (841y - 961y) = 120

841y - 961y = 120

-120y = 120

y = 120/-120 = -1

Substitute the value of y into both equations to find the value of x and check its right.

31x + 29y = 33

31x + 29(-1) = 33

31x - 29 = 33

31x = 33 + 29

31x = 62

x = 62/31 = 2

29x + 31y = 27

29x + 31(-1) = 27

29x - 31 = 27

29x = 27 + 31

29x = 58

x = 58/29 = 2

6 0

2 years ago