The sine of angle θ is 0.3.

What is cos(θ)?

Answer:

7/60

Step-by-step explanation:

Because the question is phrased such that it asks "the ratio of time with father to....", we know to put the time with father on top, or first. Similarly, since it is asked to put the ratio of time with the father to the time in daycare, we can put the daycare amount second/on the bottom. Therefore, we can write the ratio as

(42 minutes)/(6 hours)

To make both of these in terms of minutes to simplify it, we know that 60 minutes = 1 hour, so 1 hour / 60 minutes =1 . Since multiplying something by 1 keeps it the same, we can multiply our ratio by this amount. We want to multiply with the hour on top so the hours cancel out, as so:

[tex]\frac{42 minutes}{6 hours} * \frac{1 hour}{60 minutes} = \frac{42 minutes * hours}{360 minutes * hours} = \frac{42}{360}[/tex]

To simplify this even further, we can note that 6 is a factor of both 42 and 360*, so we can multiply this fraction by (1/6) / (1/6) to get

(42/360) * (1/6)/(1/6) = 7/60 as our final answer

If this doesn't come up immediately, you can always find the greatest common factor by listing the factors of each number and finding the highest one that fits both, e.g.

for 42: 42, 21, 14, 7 , 6...

for 360: 360,180, ... 6,5....

Answer:

10

Step-by-step explanation:

E = F + V - 2

E = edges

F = faces = 6

V = vertices = 6

E = 6 + 6 - 2

E = 12 -2

E = 10

To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, getting that it will take 7.6 years for for 21 of the trees to become infected.

Model:

The exponential model for the number of infected trees after t years is given by:

[tex]f(t) = e^{0.4t}[/tex]

How many years will it take for 21 of the trees to become infected?

This is t for which:

[tex]f(t) = 21[/tex]

Thus

[tex]e^{0.4t} = 21[/tex]

Applying the natural logarithm to both sides:

[tex]\ln{e^{0.4t}} = \ln{21}[/tex]

[tex]0.4t = \ln{21}[/tex]

[tex]t = \frac{\ln{21}}{0.4}[/tex]

[tex]t = 7.6[/tex]

It will take 7.6 years for for 21 of the trees to become infected.

For another example of a problem in which an exponential equation is solved, you can check brainly.com/question/24290183.

Answer:

7 : 5

Step-by-step explanation:

number of females = 3540 - 2065 = 1475

males : females

2065 : 1475

7 : 5

Answer:

A. p2=16

soln:

p=4×4=16

so,

p2=16

Answer:

5

Step-by-step explanation:

45=3×3×5

If we multiply by 5 it becomes a perfect square.

Answer:

Investment in company P = 12,000

Investment in company Q = 24,000

Step-by-step explanation:

Given that,

Total investment = 36,000

Dividend paid by company P = 11.25%

Dividend paid by company Q = 10.5%

Total return = 10.75%

Now, let investment made in company P be 'a' and company 'Q' be 'b.' So,

A.T.Q.

a + b = 36,000  ...(i)

11.25% of a + 10.5% of b = 10.75% of 36000  ...(ii)

On simplification,

a + b = 36,000

11.25% of a + 10.5% of b = 3870

Now,

11.25% of a + 10.5% of (36000 - a) = 3870

⇒ 0.1125 * a + 0.105 * (36000 - a) = 3870

⇒ 0.1125 a + 3780 - 0.105a = 3870

⇒ 0.1125a - 0.105 a - 3870 - 3780

⇒ 0.0075 a = 90

⇒ a = 90/0.0075

∵ a = 12000

Since, a = P = 12,000

Q = b = (36000 - a)

= 36000 - 12000

= 24,000

Thus,

Investment in company P = 12,000

Investment in company Q = 24,000

Answer:

Amount invested in P = 12,000

Amount invested in Q = 24,000

Step-by-step explanation:

Given:

Amount invested = 36,000 in two companies P and Q

P pays dividend = 11.25%

Q pays dividend = 10.5%

Total return = 10.75%

Find:

Amount invested in each company

Computation:

Total return = 36,000 x 10.75

Total return = 3870

Assume;

Amount invested in P = a

So,

Return in P = a x 11.25%

Return in P = 0.1125a

Return in Q = [36000 - a]10.5%

Return in Q = 3,780 - 0.105a

Total return = Return in P + Return in Q

3,870 = 0.1125a + 3,780 - 0.105a

90 = 0.0075a

a = 12,000

Amount invested in P = 12,000

Amount invested in Q = 36,000 - 12,000

Amount invested in Q = 24,000

Answer:

Step-by-step explanation:

y = 600 * (1.04)¹⁵

= 600 * 1.80094351

= $ 1080.57

Answer: ∠A = 20°; ∠B = 59°; ∠C = 101°

Step-by-step explanation:

According to the problem:

All interior angles within a triangle adds up to 180°:

∠A + ∠B + ∠C = 180°

[tex]A+(4A-21)+(5A+1)=180\\\\A+4A+5A-21+1=180\\\\10A=180+21-1\\\\10A=200\\\\A=20\°[/tex]

Substitute in the value of ∠A into the other equations:

∠B = 4 · ∠A - 21° = 4(20°) - 21° = 80° - 21° = 59°

∠C = 5 · ∠A + 1° = 5(20°) + 1° = 100° + 1° = 101°

Answer:

Mary wants to buy flowers and perfume. She has $13.50 to spend, but has already spent $12 on perfume. How much does she have left to spend on flowers?

Step-by-step explanation:

12 + c = 13.50

OpruonnA seems to be the best, hence, Breaking down in real world terms :

13.50 = total cost

Number of variables added to make up total cost = 2 ; this represents the cost of the 2 items purchased ; flowers and perfume

Cost of perfume = 12

Cost of flowers = c

Total cost of items = $13.50

Answer:

sqrt(2) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 45 = x/2

2 sin 45 =x

2 ( sqrt(2)/2) =x

sqrt(2) =x

Answer:

In 26 seconds to complete a transaction, 2 products are being purchased.

Step-by-step explanation:

1 item  = 9 seconds

Time taken in all to check out = 8 seconds

Time taken to shop = 26 seconds

Now as check out process takes 8 seconds, so the

Time left to ACTUALLY SHOP =  Total Time  - Time Used to check out

                                                  = 26 seconds = 8 seconds = 18 seconds

Shopping of 1 item = 8 seconds

Shopping of 2 items  = 2 x ( Time taken in 1 item) = 2 x  9 = 18 seconds

So, in 18 seconds, 2 clothing item can be selected.

Hence,in 26 seconds to complete a transaction, 2 products are being purchased.

Answer:

<a=32

<b=40

<c=40

Step-by-step explanation:

to find angle a you have to subtract the 50 minus 180 to find the angle close to the 50 because angles in a straight line add up to 180. the answer will be

180-50=130

after finding the angle in that triangle you must add it to the other angle present which is 18° then subtract by 180 because angles in a straight line add up to 180

130+18+a=180

a=180-148

a=32 and that's how you find a

to find b you must know that the angle at the center is twice the angle at the circumference meaning the large angle C is 90°,now if it's 90° inorder to find the big angle B you must add the 18+90 then subtract 180

18+90+B=180

B=180-108

=72

since the combination of angle a and b will give you 72 you can find angle c by subtracting a from 72

c=72-32

=40

then if you look at angle c and angle b you can tell that they are alternating meaning angle b is also 40

I hope this helps

Answer:

D

Step-by-step explanation:

Using the Cosine rule to find AC

AC² = BC² + AB² - (2 × BC × AB × cosB )

      = 18² + 12² - ( 2 × 18 × 12 × cos75° )

      = 324 + 144 - 432cos75°

      = 468 - 111.8

      = 356.2 ( take the square root of both sides )

AC = [tex]\sqrt{356.2}[/tex] ≈ 18.9

-----------------------------------------

Using the Sine rule to find ∠ A

[tex]\frac{18}{sinA}[/tex] = [tex]\frac{18.9}{sin75}[/tex] ( cross- multiply )

18.9 sinA = 18 sin75° ( divide both sides by 18.9 )

sinA = [tex]\frac{18sin75}{18.9}[/tex] , then

∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{18sin75}{18.9}[/tex] ) ≈ 66.9°

Answer:

The third exterior angle is [tex]103^o[/tex]

Step-by-step explanation:

Given

[tex]\theta = 158^o[/tex]

[tex]\alpha = 99^o[/tex]

Required

The third exterior angle [tex](\beta)[/tex]

The exterior angles of a triangle add up to 360 degrees.

So:

[tex]\theta + \alpha + \beta = 360^o[/tex]

Make [tex]\beta[/tex] the subject

[tex]\beta = 360^o - (\theta + \alpha)[/tex]

Substitute known values

[tex]\beta = 360^o - (158^o + 99^o)[/tex]

[tex]\beta = 103^o[/tex]

Answer:

2 1/4 cups.

Step-by-step explanation:

If we want to find the total amount of cheese Belle used, we have to add the number of cups of cheddar and parmesan together:

2 + 1/4 = 2 1/4

Therefore, our answer is 2 1/4, specifically, 2 1/4 cups.

Answer:

-31  

Step-by-step explanation:

2x - abs(4 - 7x)

2x = 2 * - 3 = - 6

4 - 7x = 4 - 7*-3 = 4 + 21 = 25

-6 - abs(25)

-6 - 25 = -31

You should note three things.

1. the absolute value of 25 is 25

2. There is a - sign outside the influence of the 25 so 25 becomes - 25

3. - 6 - 25 = - 31

Answer:

h = 4sqr(3)

Step-by-step explanation:

r = d/2

d =  8

r = 8/2

r = 4

a = 4

c = 8

b = h = ?

a^2 + h^2 = c^2

4^2 + h^2 = 8^2

16 + h^2 = 64

h^2 = 64 - 16

h^2 = 48

sqrt(h^2) = sqrt(16*3)

h = 4 sqrt3)

Answer:

48

Step-by-step explanation:

interest=4000

amount =6000

time =4yr

principal =6000-4000

=2000

interest=principal×time×rate/100

4000= 2000×4×r/100

4000=8000×r/100

r=8000-4000/100

r=2000/100

r=20

Answer:

12.5 %

Step-by-step explanation:

I = PRT

I is the interest, P is the Principle, R is the Rate and T is the time

The interest is 6000- 4000 = 2000

2000 = 4000* R *4

2000 = 16000R

Divide each side by 16000

2000/16000 = R

.125 = R

Changing to percent form

12.5 %

Answer:

d = 450 ft

Step-by-step explanation:

Hi there!

First, we can find the angle in the triangle at the point of the helicopter, the angle opposite [tex]d[/tex]. Subtract 48° from 90°:

90-48=42

Now, given that this is a right triangle and we have an angle and the side adjacent the angle, we can solve for [tex]d[/tex] by using the tangent ratio:

[tex]tan\theta=\displaystyle \frac{opposite}{adjacent}[/tex]

Replace θ with 42°, "opposite" with [tex]d[/tex], and "adjacent" with 500 ft:

[tex]tan(42)=\displaystyle \frac{d}{500}[/tex]

Multiply both sides by 500 to isolate [tex]d[/tex]:

[tex]500*tan(42)=d\\450=d[/tex]

Therefore, d = 450 ft when rounded to the nearest whole number.

I hope this helps!

Answer:

she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)

Answer:

Step-by-step explanation:

-4 and -3

Answer:

-4 and 3 because I tookt the test and the other guy was right too

Answer:

Step-by-step explanation:

We have;

P = 4500

A = 8550

T= 5 years

I= ?

R=?

We know,

A= P+I

or, 8550=4500+I

∴I=8550-4500= 4050

Now, I= PTR/100

Or, 4050= (4500*5*R)/100

Or, 4050=45*5*R

Or, R= 4050/225

∴R= 18%

Answer:

11.3

Step-by-step explanation:

a = AC × sin(A)/sin(B)

Now <A =180-25-48 = 107

a = 5×sin(107)/sin(25)

a ≈ 11.3

Answered by GAUTHMATH

Answer: [tex]60\ ft[/tex]

Step-by-step explanation:

Given

Side length of square shape [tex]a=15\ ft[/tex]

Length of the garden is equal to the perimeter of the square i.e. 4 times the side length

[tex]\Rightarrow \text{Lenght L= }4a\\\Rightarrow L=4\times 15\\\Rightarrow L=60\ ft[/tex]

Thus, the length of the require garden is [tex]60\ ft[/tex]

Answer:

1

Step-by-step explanation:

add 1/2 + 1/2 = 2/2 = 1

9/x and 20x⁹ are the monomials.

The correct option A and D.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

A monomial is a polynomial with just one term.

From the given choices:

9/x and 20x⁹ are the monomials.

11x - 9 and 20x⁹ -7x are the binomial.

Therefore, A and D are the monomials.

To learn more about the Polynomials;

brainly.com/question/11536910

#SPJ1

Answer:

(-8, 0) and (-2, 0)

Step-by-step explanation:

The root of a parabola are the places at which the parabola intersects the x-axis. As one can see, on the graph these points are the following: (-8, 0) and (-2, 0). Thus, the roots of the parabola are (-8, 0) and (-2, 0).

Answer:

-8 and -2

Step-by-step explanation:

Hello!

The roots of the parabola are the points where the graph intersects the x-axis. The x-axis is the equation y = 0.

There are two roots for this parabola, as the vertex is lower than y=0, and it opens up.

The two points of intersection are:

Therefore, the roots of the parabola are -8 and -2.

Answer:

it's the last option

Step-by-step explanation:

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