write each ratio statement as a fraction and reduce to lowest terms if possible.(i)18 to 24 (ii)5 to 15 (iii)14:42 (iv) 15 cents to 18 cents.

Answer:

R (t) = 60 - 60 cos (6t)

Step-by-step explanation:

Given that:

R(t) = acos (bt) + d

at t= 0

R(0) = 0

0 = acos (0) + d

a + d = 0 ----- (1)

After [tex]\dfrac{\pi}{12}[/tex] seconds it reaches a height of 60 cm from the ground.

i.e

[tex]R ( \dfrac{\pi}{12}) = 60[/tex]

[tex]60 = acos (\dfrac{b \pi}{12}) +d --- (2)[/tex]

Recall from the question that:

At t = 0, R(0) = 0 which is the minimum

as such it is only  when a is  negative can acos (bt ) + d can get to minimum at t= 0

Similarly; 60 × 2 = maximum

R'(t) = -ab sin (bt) =0

bt = k π

here;

k  is the integer

making t the subject of the formula, we have:

[tex]t = \dfrac{k \pi}{b}[/tex]

replacing the derived equation of k into R(t) = acos (bt) + d

[tex]R (\dfrac{k \pi}{b}) = d+a cos (k \pi)[/tex] [tex]= \left \{ {{a+d \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.[/tex]

Since we known a < 0 (negative)

then d-a will be maximum

d-a = 60  × 2

d-a = 120 ----- (3)

Relating to equation (1) and (3)

a = -60 and d = 60

∴ R(t) = 60 - 60 cos (bt)

Similarly;

For [tex]R ( \dfrac{\pi}{12})[/tex]

[tex]R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60[/tex]

where ;

[tex]cos (\dfrac{\pi b}{12}) =0[/tex]

Then b = 6

∴

R (t) = 60 - 60 cos (6t)

Answer:

50%

Step-by-step explanation:

If there's only either a gray piece or a white piece on the spinner and you spun it once, the probability of it landing on gray or white is 50%. But if there are more pieces the answer will be incorrect.

Answer:

Step-by-step explanation:

5.

[tex]12,\:30\\\\\mathrm{Prime\:factorization\:of\:}12:\quad 2\times\:2\times\:3\\\mathrm{Prime\:factorization\:of\:}30:\quad 2\times\:3\times\:5\\\\=2\times\:2\times\:3\times\:5\\\\=60[/tex]

6.

[tex]6,\:10\\\\\mathrm{Prime\:factorization\:of\:}6:\quad 2\times\:3\\\mathrm{Prime\:factorization\:of\:}10:\quad 2\times \:5\\\\=2\times \:3\times \:5\\\\=30[/tex]

7.

[tex]16,\:24\\\\\mathrm{Prime\:factorization\:of\:}16:\quad 2\times \:2\times\:2\times\:2\\\mathrm{Prime\:factorization\:of\:}24:\quad 2\times\:2\times\:2\times\:3\\\\=2\times\:2\times\:2\times\:2\times\:3\\\\=48[/tex]

8.

[tex]14,21\\\\\mathrm{Prime\:factorization\:of\:}14:\quad 2\times\:7\\\mathrm{Prime\:factorization\:of\:}21:\quad 3\times\:7\\\\=2\times\:7\times\:3\\\\=42[/tex]

9.

[tex]9,15\\\\\mathrm{Prime\:factorization\:of\:}9:\quad 3\times\:3\\\mathrm{Prime\:factorization\:of\:}15:\quad 3\times\:5\\\\=3\times\:3\times\:5\\\\=45[/tex]

10.

[tex]5,\:11\\\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Prime\:factorization\:of\:}11:\quad 11\\\\=5\times \:11\\\\=55[/tex]

Answer:

let angle AOB and angle COD be x

the it would be

x+x+110=180

2x+110=180

2x=180-110

2x=70

x=70/2

x=35 degree.

hope it will help you.

Answer:

x = ± sqrt(k)

x = ± 8 by the square root property

Step-by-step explanation:

x^2 = k

K is a real number

Take the square root of each side

sqrt(x^2) = ± sqrt(k)

x = ± sqrt(k)

Letting k = 64

x = ± sqrt(64)

x = ± 8 by the square root property

Answer:

x = ± √k

x = ± √8 by the square root property

Step-by-step explanation:

x² = k

where k is a real number

square root of each side

√x² = ± √k

x = ± √k

let k = 64

x = ± √64

therefore

x = ± 8 by the square root property

Answer:

[tex]8n[/tex]

Step-by-step explanation:

The answer would be [tex]8n[/tex] because [tex]8*n[/tex] = [tex]8n[/tex]

Answer:

1144.18 e-12 chips

Step-by-step explanation:

Conversation rate of nanometers

1 nanometers =1* 10^-12 km

35 nanometers= 35 *10^-12

Radius of earth= 6371 km

Circumference of earth = 2πr

Circumference= 2*22/7*6371

Circumference=40046.29 km

The number of chips to be used to circle the earth

= 40046.29/35 *10^-12

=1144.18 *10^-12

= 1144.18 e-12 chips

Answer:

x + 13

Step-by-step explanation:

5x + 2(3 - 2x) +7

Distribute the 2 into (3 - 2x)

5x + 6 - 4x + 7

Combine like terms

x + 13

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.

The given expression 5x+2(3−2x)+7 can be simplified as shown below.

5x + 2(3−2x) + 7

Open the parenthesis,

= 5x + 6 − 4x + 7

Bring the like terms together,

= 5x − 4x + 7 + 6

Add the like terms,

= x + 13

Hence, The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.

Learn more about PEMDAS here:

https://brainly.com/question/36185

#SPJ2

Answer:

142

Step-by-step explanation:

Step-by-step explanation:

70 - -72

= 70+ 72

= 142

I think this should be the answer

Answer:

-5

Step-by-step explanation:

-3 - 2 = -5

Answer:

14 is 4

15 is check your self

in Google

Answer: see explanation

Step-by-step explanation:

you would add AB (14) and BC (3x-4) to get the length of AC (4x+4).

14 + 3x-4 = 4x + 4

then, just solve for the value of x. (isolate x)

and then plug the value of x back in to "4x+4" and that's your answer.

Answer:

6

Step-by-step explanation:

14+3x-4=4x+4

3x+10=4x+4

3x-4x=4-10

-1x=-6

x=6

Answer:

5

Step-by-step explanation:

[tex]-2x\left(-12\right)=24x[/tex]

Answer:

24x

Step-by-step explanation:

Parenthesis implies multiplication, and when a negative and a negative are multiplied, the answer becomes positive. Adding on the x, the answer to this equation if 24x.

Answer:

Step-by-step explanation:

To find the value of y when x= 18 we must first find the relationship between them

The statement

y varies directly as x is written as

[tex]y \: \: \alpha \: \: kx[/tex]

where k is the constant of proportionality

when y = 37

x = 5

Substitute the values into the above formula and solve for k

That's

37 = 5k

Divide both sides by 5

So the formula for the variation is

When x = 18

y = 7.4(18)

We have the answer as

Hope this helps you

Answer:

Snacks are distributed in a school.

There are only 36 apples and 44 bananas for the students, but there are 72 orange juices and 28 tangerine juices. The distribution would be 4/5, it would take 20 fruits so that the snack per student be the same.

Step-by-step explanation:

A fraction is a whole number that expresses a certain number of portions that are taken from a whole divided into parts.

It is represented by a bar that separates the first part (numerator) from the second (denominator).

The numerator represents the number of parts taken and the denominator represents the entire element.

For example, 3 eaten parts of a 4-piece cake.

3/4 of the cake was eaten.

Answer:

Depends on how many spoonfuls they use per sundae. If they use one spoonful they made 32 sundaes, if they use 2 spoonfuls they made 16 sundaes.

Answer:The E indicates scientific notation. The first number is the coefficient of the number in scientific notation. This number is multiplied by a power of 10. The number following the E, which is -8, is the exponent, and the base is 10.

REAL ANSWER

Step-by-step explanation:I did the assignment

Answer:

SIMPLE RESPONES: The E indicates scientific notation. The first number is the coefficient of the number in scientific notation. This number is multiplied by a power of 10. The number following the E, which is –8, is the exponent, and the base is 10.

Step-by-step explanation:

Step-by-step explanation:

Hey there!!

During evaluating the expression, you must follow,

Here,

[tex]i). \: b + {c}^{2} [/tex]

[tex] = 30 + {6}^{2} [/tex]

= 30+36

= 66.

ii). b-4c

= 30 - 4×6

= 30 - 24

= 6

Hope it helps...

Answer:

Hey there!

-6-(-12)

-6+12

6

Hope this helps :)

Answer:

[tex]6[/tex]

Step-by-step explanation:

[tex]-6-(-12)[/tex]

[tex]-6+12[/tex]

Since 12 - 6 is equal to 6, -6 + 12 would be 6.

[tex]=6[/tex]

Now you have your answer!

Hope this helps!

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected number of outcome/Total outcome

Since a pair of die with six faces is rolled, the total number of outcome will be 6^2 = 36

Expected outcome is the sum of dice greater than 10. The only time we can get a sum of the dice grater than 10 is when the following are rolled; (5,6), (6, 5) and (6, 6). The sum of the numbers will give us 11 ans 12 respectively which are values greater than 10.

The expected outcomes = 3 outcomes

The probability that the sum of my dice is greater than 10 = 3/36

Hence the probability that the sum of my dice is greater than 10 is 1/12

Answer:

I think it's     (16/81)

Step-by-step explanation:

Answer:

14 [tex]\frac{5}{48}[/tex]

Step-by-step explanation:

rectangular volume = length * height * width

1354 = (20+4) * 4 * width

1354 = 24 * 4 *w

1354 = 96w

14.1 = w

Answer:

Domain: [-4, 4]

Range: [-3, 5]

Function? No

Step-by-step explanation:

Domain is all x-values that can be inputted in the graph that returns an output.

Range is all y-values that are outputted when x is inputted.

A function has to pass the Vertical Line Test.

(- 1 - 2√3)²

applicating (a - b)² = a² + b² - 2ab

a = - 1

b = 2√3

so:

(- 1 - 2√3)² =

(- 1)² + (2√3)² - 2(- 1)(2√3) =

1 + (2² * √3²) + 2(2√3) =

1 + (4 * 3) + 4√3

1 + 12 + 4√3 = 13 + 4√3

Answer: 1.12099824328 or estimated is 1

Answer:

[tex]42\pi -78[/tex]

Step-by-step explanation:

Attached below is the detailed solution of the volume of the solid in the first octant bounded by the cylinders r = 2 r = 5  z = 8-x-y

The volume of the solid in the first octant bounded by the cylinders r = 2 r = 5,  z = 8-x-y  : [tex]42\pi -78[/tex]