Determining the area of a sector of a circle...

Answer:

Step-by-step explanation:

Given a right angle triangle ABC.

If ∠BCA = 90°

the hypotenuse AB = 26

AC = 10 and BC = 24.

Using the SOH, CAH, TOA trigonometry identity, SInce we are to find tanA, we will use TOA. According to TOA;

Tan (A) = opp/adj

Taken BC as opposite side since it is facing angle A directly and AC as the adjacent;

tan(A) = BC/AC

tan(A) = 24/10

tan(A) = 12/5

Answer:

         \(\ tan \ A = \dfrac{24}{10}\)

Step-by-step explanation:

\(\sf Tan \ A = \dfrac{opposite \ side \ of \ angle \ A}{adjacent \ side \ of \ angle A}\\\\Tan \ A = \dfrac{BC}{AC}\\\\Tan \ A = \dfrac{24}{10}\)

The three solutions of the inequalities are x < 0 , x <  0.8 , x< -2

Inequalities are defined as mathematical expressions in which both sides are not made equal to each other.

Given the inequalities;

Let's solve for the value of x

x - 0.8 < 0

Make 'x' the subject

x < 0 + 0. 8

x < 0. 8

-5x < 10

Make 'x' the subject by dividing both sides by - 5

-5x/ 5 < 10/ -5

x < -2

Thus, the three solutions of the inequalities are x < 0 , x <  0.8 , x< -2

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12 students play defense. 1st step.  6/9 of 27 is 18.  2nd. the ratio of the students playing offense to the total number of students playing soccer is 1 to 3 which means the total amount of students is '3', in the ratio it's 3 because it's simplified (i like to think of it as 'groups'). since we know that there are a total of 18 students and there's 3 total 'groups' we divide 18 into 3 which is 6. so there's 6 students in each group. we subtract 6 (1 group) from 18 ( the total number of students) which is 12, so there are 12 students playing defense. if you wrote the ratio again without simplifying it would be  6:18

Answer:

-3x + 5

Step-by-step explanation:

like terms are the ones that have x and the ones that don't.

hope this makes sense

Answer:

-3x + 5

Step-by-step explanation:

2x - 3 - 5x + 8 can also be written as 2x - 5x - 3 + 8

→ Using the rewritten method collect the x terms

-3x - 3 + 8

→ Now collect the integers

-3x + 5

Answer:

can u  please attach the photo

Step-by-step explanation:

i cannot see it clearly

Answer:

x = 3 squared and it is the righr answer

Answer:

pretty hard to read. Sorry

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

X is the alternate corresponding angle to 50.   50+y=180

y=130

x and y = the  same thing so 130 is the value of x

Answer:

Tanisha = 14 years

Ana = 7 years

Elicia = 16 years

Step-by-step explanation:

Let T = age of Tanisha

Let A = age of Ana

Let E = age of Elicia

Tanisha is twice as old as Ana:  

T = 2A

⇒ A = (1/2)T

Elicia is 2 years older than Tanisha:

E = 2 + T

Sum of all their ages is 37:

A + E + T = 37

Substitute A = (1/2)T and E = 2 + T into A + E + T = 37 and solve for T:

⇒ (1/2)T + 2 + T + T = 37

⇒ (5/2)T = 35

⇒ T = 14

If T = 14, then

A = (1/2)T = (1/2) 14 = 7

If T = 14, then

E = 2 + T = 2 + 14 = 16

Answer:

30 mm, 2.5cm,20cm and 1m

Answer:

$ 14.08

Step-by-step explanation:

We have that the policy costs $ 94 and with life insurance with coverage of $ 120,000, to calculate the expected value, we must subtract the value of that life insurance multiplied with the probability of dying (complement of the probability of living) and the policy value multiplied by the probability of staying alive) like this:

120000 * (1 - 0.9991) - 94 * 0.9991 = 14.0846

Which means that the expected value of the policy is $ 14.08

Answer:

V = 144

Step-by-step explanation:

Formula for volume of a rectangular prism:

V = whl

Given:

w = 3

h = 8

l = 6

Work:

V = whl

V = 3(8)(6)

V = 144

Answer: Angle 1 and angle 2 will be the same number if t are vertical. So, 105 ... If the measure of angle 2 is 105 degrees, find the measure of angle 1.

The measures of angle 1 is the same as angle 2 angle 1 = 105 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that:

Angle 1 and angle 2 are vertical angles.

As we know from the definition of vertically opposite angles, the pair of vertically opposite angles will be equal in measure.

Angle 1 and angle 2 are vertical angles:

The measure of angle 1 = the measure of angle 2

Angle 2 = 105 degrees

Angle 1 = 105 degrees

Thus, the measure of angle 1 is the same as angle 2 angle 1 = 105 degrees.

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If ABCD is dilated by a scale factor of 3, the coordinate of B' would be (-6, 6).

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 3 centered at the origin as follows:

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3, 2 × 3) = Ordered pair B' (-6, 6).

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Answer: (C) -7

Step-by-step explanation:

Answer:

510,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

4/7÷3/5

20/21

Answer:

the amount of Basil Yamey's capital is £16,480.

Step-by-step explanation:

To calculate Basil Yamey's capital, we need to add up the value of his assets and subtract his liabilities.

The value of his assets is:

Van: £9,000

Market stall: £1,800

Computer: £280

Inventory of goods: £11,200

Cash in hand: £900

Money in the bank: £6,300

Total value of assets = £9,000 + £1,800 + £280 + £11,200 + £900 + £6,300 = £29,480

His liabilities are:

Amount still owed for inventory of goods: £5,000

Amount borrowed from Luca Pacioli: £8,000

Total liabilities = £5,000 + £8,000 = £13,000

Therefore, Basil Yamey's capital is:

Capital = Total value of assets - Total liabilities

Capital = £29,480 - £13,000 = £16,480

So the amount of Basil Yamey's capital is £16,480.

Answer:

Basil Yamey's capital is the total amount of money that he has invested in his business. This can be calculated as the sum of the cost of the assets that he has purchased, minus any outstanding debts, plus any cash or cash equivalents he has on hand.

The cost of the assets that Basil has purchased is:

£9,000 (van) + £1,800 (market stall) + £280 (computer) + £11,200 (inventory) = £21,280

He still owes £5,000 for the inventory, so the total cost of the assets minus the outstanding debt is:

£21,280 - £5,000 = £16,280

He borrowed £8,000, so the total amount of his capital is:

£16,280 + £8,000 = £24,280

He also has cash on hand and in the bank:

£900 (cash) + £6,300 (bank balance) = £7,200

So, Basil Yamey's total capital is £24,280 + £7,200 = £31,480.

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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Answer:

HaHaHaHaHaHa think u slick i know you touched that little boy

Step-by-step explanation:

HaHaHaHaHaHa

Answer:

........................

Solution

Case-control observational study

C is the correct option ...........

Answer:

-12-n

Step-by-step explanation:

(6+n)(−2)

=(6+n)(−2)

=(6)(−2)+(n)(−2)

=−12−2n

=−2n−12

The probability that Chris throws away the first chocolate but gets to eat the second one is 8/39.

To determine the probability that Chris throws away the first chocolate but gets to eat the second one, we need to calculate the probabilities of two events: the probability of Chris throwing away the first chocolate and the probability of Chris getting a caramel-filled chocolate on the second attempt.

Let's start with the first event: the probability that Chris throws away the first chocolate. Since Chris only likes the kind filled with caramel, there are 9 caramels out of a total of 9 + 6 + 8 + 4 = 27 chocolates in the box. Therefore, the probability of Chris throwing away the first chocolate is 1 - (9/27) = 18/27 = 2/3.

Now, for the second event: the probability of Chris getting a caramel-filled chocolate on the second attempt. After throwing away the first chocolate, there are now 8 caramels remaining in the box, out of a total of 26 chocolates. Thus, the probability of Chris getting a caramel-filled chocolate on the second attempt is 8/26 = 4/13.

To find the probability of both events occurring, we multiply the probabilities together: (2/3) * (4/13) = 8/39.

The probability that Chris throws away the first chocolate but gets to eat the second one is 8/39.

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Answer:

Step-by-step explanation:

x + y = 8

10x + y is the original number

so 10y + x + 18 = 10x + y           Subtract 10y and x from both sides

18 = 10x - x + y - 10y                  Combine the right

18 = 9x - 9y                                Divide by 9

2 = x - y

x - y = 2

x + y= 8            Add to find x

2x = 10             Divide by 2

x = 5

x + y = 8

5 + y = 8

y = 3

The original number is 53

Answer:

The bones were 12,485 years old at the time they were​ discovered.

Step-by-step explanation:

Amount of the element:

The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:

\(A(t) = A(0)e^{-kt}\)

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The radioactive element​ carbon-14 has a​ half-life of 5750 years.

This means that \(A(5750) = 0.5A(0)\), and we use this to find k. So

\(A(t) = A(0)e^{-kt}\)

\(0.5A(0) = A(0)e^{-5750k}\)

\(e^{-5750k} = 0.5\)

\(\ln{e^{-5750k}} = \ln{0.5}\)

\(-5750k = \ln{0.5}\)

\(k = -\frac{\ln{0.5}}{5750}\)

\(k = 0.00012054733\)

So

\(A(t) = A(0)e^{-0.00012054733t}\)

A scientist determined that the bones from a mastodon had lost 77.8 ​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Had 100 - 77.8 = 22.2% remaining, so this is t for which:

\(A(t) = 0.222A(0)\)

Then

\(0.222A(0) = A(0)e^{-0.00012054733t}\)

\(e^{-0.00012054733t} = 0.222\)

\(\ln{e^{-0.00012054733t}} = \ln{0.222}\)

\(-0.00012054733t = \ln{0.222}\)

\(t = -\frac{\ln{0.222}}{0.00012054733}\)

\(t = 12485\)

The bones were 12,485 years old at the time they were​ discovered.

Answer:

all you did multiply it

Step-by-step explanation:

Step-by-step explanation:

sin45 deg = 6/b

Root2/ 2 = 6/b

you will find b value

a = 8 + x

tan45 deg = 6/x

1 = 6/x

x = 6

a = 8+6

= 14

The value of a is 16 units and the value of b is 11.42 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sine rule for triangles a/sinA = b/sinB = c/sinC.

Let, (a - 8) = x and the angle opposite to the side b is 90°.

Therefore,

b/sin90° = 8/sin45° = x/sin45°.

b/sin90° = 8/sin45°

b = 8/0.7.

b = 11.42.

11.42/sin90° = x/sin45°.

11.42 = x/0.7.

x = 8.

So, The value of a is (8 + 8) = 16 units.

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Answer:

153

Step-by-step explanation:

If the table adds up to 20 and opened toe counts for 45% of the total. then 45% of 340 is 153 !