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3 years ago

Answer each question and explain your reasoning.How long is 75% of 60 minutes?

Mathematics

2 answers:

uysha [10]3 years ago

5 0

Answer:

45 minutes

Step-by-step explanation:

75% is the same as $\frac{3}{4}$ . This means that we can multiply 60 by $\frac{3}{4}$ to find 75% of 60.

$60*\frac{3}{4} \\\\\frac{180}{4} \\\\\frac{90}{2}\\\\45$

Irina18 [472]3 years ago

4 0

Answer:

45 minutes

Step-by-step explanation:

Of means multiply

75% * 60

Change to a decimal

.75 * 60

45 minutes

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If 13cos theta -5=0 find sin theta +cos theta / sin theta -cos theta

Ivahew [28]

Step-by-step explanation:

We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.

$\red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}$

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

Where,

PQ = Opposite side
QR = Adjacent side
RP = Hypotenuse
∠Q = 90°
∠C = θ

As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

$\rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}}$

Since, we know that,

cosθ = 5/13
QR (Adjacent side) = 5
RP (Hypotenuse) = 13

So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.

Therefore,

$\red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}}$

$\rule{200}{3}$

$\sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}}$

∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.

$\rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}}$

Where,

Opposite side = 12
Hypotenuse = 13

Therefore,

$\sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}}$

Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.

$\rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}}$

By substituting the values, we get,

$\rule{200}{3}$

$\sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}}$

∴ Hence, the required answer is 17/7.

6 0

2 years ago

A coin is thrown 3 times. What is the probability that at least one head is thrown?.

zvonat [6]

Answer:7/8

A coin is tossed 3 times. The probability of getting at least one head is 7/8.

3 0

2 years ago

Read 2 more answers

Carmen currently has $5; she makes $2 a week in allowance. Question: a) Write a function C(x) that represents how much money she

aivan3 [116]

For question a) you can do 2 x 7 sine their are 7 days in a week 2 x 7 = 19 so by the end of each week Carmen has $19. in 10 weeks she will have $20 dollars. if in 10 weeks she has $20 wait if it is time two there can't be 35 try 17 cause that's closes so in 17 she will have $36. Same thing Lilly starts with $10 each week she gets $1 a week so 1 x 7 = 7 and since she started with $ 10 she has $17 Lilly must earn 19 dollars to be equal with Carmen. Hope this helps

6 0

3 years ago

Read 2 more answers

An indoor sport exhibition is coming to the arena. Your supervisor has asked you to help set up a handball pitch and seating are

Sphinxa [80]

Answer:

Perimeter: 174.8 m

Area: 1,394 sq m

Step-by-step explanation:

First, the perimeter.

Before we start, let's calculate the circumference of the half-circles at the ends of the field.

The measurement says 2,000 cm, so let's convert it to 20 m for ease.

Circumference of a circle: πd, where d = diameter.. in our case d = 20 m

Circumference of a 20m diameter circle: 20π = 62.8 m

We have 2 half circles... so the perimeter of each half-circle will be: 31.4 m

We also have 800 cm measurement for the "height" of the seating areas... let's convert that in 8 m

We also need to find out the space between the seating area... We know the whole rectangular pitch is 40 m, then we have to subtract the width of both seating areas (20 and 15 m)... so the space between them is 5m

So, starting with the upper left corner of the rectangular pitch, and working our way clockwise, we encounter the following lengths:

P = 40 + 31.4 + 8 + 10 + 8 + 5 + 8 + 25 + 8 + 31.4 = 174.8 m

The total perimeter is then of 174.8 m

For the area, we need to calculate the area of all forms:

Large rectangular pitch:

LR = 40 x 20 = 800 sq m

The two half circles, form a circle, so A = πr², where r is the radius, which is half the diameter.

AC = π (10)² = 100 π = 314 sq m

Then the seating areas:

SA1 = 25 x 8 = 200 sq m

SA2 = 10 x 8 - 80 sq m

Then, we add up everything:

TA = LR + AC + SA1 + SA2

TA = 800 + 314 + 200 + 80 = 1,394 sq m

3 0

3 years ago

Help for just 50 points!

liraira [26]

Answer:

It may be 9

Step-by-step explanation:

Solution:

Here,

Median = n+1/2th term

=5+1/2 th term

=6/2 th term

=3rd term

Now,

Arranging the data in ascending order...

6,8,9,10,12

Since, 9 is the third term. So, 9 is the median.....

8 0

2 years ago

Answer each question and explain your reasoning.How long is 75% of 60 minutes?​

Answer each question and explain your reasoning.How long is 75% of 60 minutes?