If two events, event a with probability p(a) and event b with probability p(b) are complementary events then __________.

Based on the angles addition theorem, the measure of the original angle = 44°.

The angles addition theorem states that if an angle is bisected to form two smaller angles, then the sum of the measures of the two smaller angles equals the measure of the original angle that is bisected.

Given that the two smaller angles formed when bisected are: (3+30)° and (5+6)°. Based on the angles addition theorem:

The measure of the original angle = (3+30)° + (5+6)°

The measure of the original angle = 33° + 11°

The measure of the original angle = 44°

Learn more about the angles addition theorem on:

https://brainly.com/question/13545681

#SPJ1

The original amount borrowed was $517.

Simple Interest is the method to calculate the interest charged for a given number of years and given rate , in simple interest the principle remains same for each year.

Simple interest =[tex]\frac{P*R*T}{100}[/tex]

where P= principle, R=rate in % , T= time

We know that Amount= Principle+ Simple Interest........(1)

According to the question

Amount=$610.06

Rate=18%

time = 1yr

Substituting the value in equation (1) we get

[tex]610.06=P+\frac{P*18*1}{100}[/tex]

[tex]610.06=\frac{100P+18P}{100}[/tex]

[tex]610.06=\frac{118P}{100}[/tex]

[tex]61006=118P[/tex]

[tex]P=\frac{61006}{118}[/tex]

[tex]P=517[/tex]

Therefore  , The original amount borrowed was $517.

Learn more about Simple Interest here https://brainly.com/question/26400531

#SPJ4

Answer:

(6, 7) and (-2, -1)

Step-by-step explanation:

if y=x+1 intersects with y=x^2-3x-11

then we need to find x and y such that both of those equations are true.

If y = x + 1 is true and y=x^2-3x-11, then

y - y = x^2-3x-11 - x - 1 is also true

0 = x^2 - 4x - 12

use your preferred method to solve the quadratic equation

0 = (x - 6)(x + 2)

x = 6 or x = -2

now for each x we take y from either equation, but y = x + 1 is simpler.

for x = 6 the coordinates are (6, 7) and for x = -2 the coordinates are (-2, -1)

Step-by-step explanation:

[tex] \frac{3x - 5}{4} \leq1[/tex]

[tex]3x - 5 \leq1 .4[/tex]

[tex]3x - 5 \leq4[/tex]

[tex]3x \leq4 + 5[/tex]

[tex]3x \leq9[/tex]

[tex]x \leq \frac{9}{3} [/tex]

[tex]x \leq3[/tex]

x = {3,2,1,0,...}

Answer:

2x – 12 + 12 = x + 9

2x = x + 9

x = 9

We need to know how to solve the equations by substituting values for this problem. (a)The number of rabbits on the farm at the end of June is 164 and (b) after a long time the number of rabbits on the farm will become zero.

In the given question we know that the number of rabbits on a farm at the end of month n is [tex]P_{n}[/tex] and that the number of rabbits at the end of the next month is [tex]P_{n+1} =1.2P_{n} -50[/tex]. We know that the number of rabbits at the end of March is 200, so we can have [tex]P_{1}[/tex]=200, we need to find the number of rabbits at the end of June, which will be [tex]P_{4}[/tex], we can form an equation from here

[tex]P_{4} =1.2P_{3} -50[/tex]

Since we don't know what [tex]P_{3}[/tex] is we can replace it by [tex]P_{2}[/tex] and then replace that by [tex]P_{1}[/tex].

[tex]P_{4} =1.2P_{3} -50\\P_{4} =1.2(1.2P_{2} -50)-50\\P_{4} =1.2(1.2(1.2P_{1} -50)-50)-50 = 1.2(1.44P_{1} -60-50)-50=1.728P_{1} -72-60-50=1.728P_{1} -182[/tex]

We know that [tex]P_{1} =200[/tex]

So, [tex]P_{4}[/tex]=1.728x200-182=345.6-182≈164

Therefore the number of rabbits at the end of June is 164 and after a long time the number of rabbits on the farm might become zero since the number of rabbits is decreasing with every month.

Learn more about substituion here:

https://brainly.com/question/3388130

#SPJ1

Answer:

4,      -1,         5,          -2

Step-by-step explanation:

Answer:

Could I see the available choices?

Step-by-step explanation:

Answer:

didnt have the choices but any that would have it as the same problem different order

Step-by-step explanation:

17+14+13=13+14+17=14+13+17=14+17+13=17+13+14=13+17+14

Answer:

Using the horizontal line test, the one to one functions are those which do not intersect with the line more than one time

In the given graphs, the fourth graph represents the one - one fucntion.

Use the concept of graph of fucntion defined as:

Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.

The graph of a one-to-one function is a representation that shows each input value (x) uniquely paired with a corresponding output value (y), with no repetition or overlap in the mapping.
It passes both the vertical line test and horizontal line test, ensuring each input has a distinct output and vice versa.

In the fourth graph:

Apply the vertical line test and we get,

Each input has a distinct output.

Hence,

The fourth graph represents the one-one fucntion.

To learn more about graph of function visit:

https://brainly.com/question/12934295

#SPJ7

Answer:

Line 3

Step-by-step explanation:

Proportional relationship:

• They are straight lines that have a constant slope

• The line must pass through the origin at (0,0)

• The y intercept is zero

The only line passing through the origin at the point (0,0), is Line 3

Answer:

923.08

Step-by-step explanation:

48000/52 weeks

Answer:

923.08

Step-by-step explanation:

There are 52.1429 weeks in a year, so divide.

Answer:

6

Step-by-step explanation:

10⁰=1

9⁰=1

7⁰=1

5⁰=1

3⁰=1

1¹⁰⁰=1

so,

10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰=1+1+1+1+1+1=6

Answer:

6

Step-by-step explanation:

We are working with exponents

Any number to the power of 0 is 1

a^0 = 1

1 to a power is 1

10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰​

1 + 1 + 1 + 1 + 1 + 1

6

Answer:

The 5 is in the thousandths place.  

825/1000

Step-by-step explanation:

Simplified this would be 33/40

825/1000  Divide the top and bottom by 25

Answer:

tear 35 is ans

pla mark me brainliest ans

Answer:

Hello,

Answer 80

Step-by-step explanation:

[tex]\left\{\begin{array}{cccc}t+e+a&=&30&(1)\\n+t+e+a&=&50&(2)\\t+a+n&=&40&(3)\\t+e+n&=&35&(4)\\t+e+a+r&=&55&(5)\end{array} \right.\\\\\\\left\{\begin{array}{cccc}n&=&20&(2)-(1)=(6)\\t+a&=&20&(7)\\t+e&=&15&(8)\\r&=&25&(5)-(1)=(9)\\t+e+a&=&30&(1)\end{array} \right.\\\\\\\left\{\begin{array}{cccc}n&=&20&(6)\\t&=&5&(7)+(8)-(1)=(10)\\a&=&15&(7)\ and \ (10)\\e&=&10&(8)\ and \ (10)\\r&=&25&(9)\\\end{array} \right.\\[/tex]

[tex]\\\\\boxed{ENTREE=3*e+n+t+r=3*10+20+5+25=80}\\[/tex]

Answer:

63 crayons are broken

Step-by-step explanation:

84 ÷ 4 = 21

21 x 3 = 63

can be checked by 84 - 63 = 21

Answer:

the equation is y=1/2+0.5

The correct option is the first one, (1.176*10¹) is 14.7 times larger than (8*10⁻¹)

Here we want to see how many times larger is (1.176*10¹) larger than (8*10⁻¹), we can see that both numbers are in scientific notation.

To check that, we just need to take the quotient between the two numbers, we will get:

(1.176*10¹)/(8*10⁻¹) = (1.176/8)*(10¹/10⁻¹)

(1.176/8)*(10¹/10⁻¹) =  (1.176/8)*(10¹⁻⁽⁻¹⁾) =  (1.176/8)*10² = 0.147*10²

Now, returning to standard notation, we can rewrite:

0.147*10² = 14.7

The correct option is the first one, (1.176*10¹) is 14.7 times larger than (8*10⁻¹)

If you want to learn more about scientific notation:

https://brainly.com/question/5756316

#SPJ1

Answer:

the answer is

Step-by-step explanation:

Q/R= G/F

= QF=GR

divide both sides by Q

Q and Q are off so

therefore F= GR/Q

Using the normal distribution, it is found that 21% of the riders go on more than 10 rides.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 8.4, \sigma = 2[/tex]

The proportion of riders that go on more than 10 rides is one subtracted by the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (10 - 8.4)/2

Z = 0.8

Z = 0.8 has a p-value of 0.7881.

1 - 0.7881 = 0.2119 = 21.19% = 21%(rounded to the nearest percent)

21% of the riders go on more than 10 rides.

More can be learned about the normal distribution at https://brainly.com/question/4079902

#SPJ1

The 715 cm² area of the disc and the ±5 cm² error tolerance, gives;

a) x = √(715/π) cm

b) The range for the radius is; [√(710/π) cm, √(720/π) cm]

c)

f(x) = π•x²

L = 715 cm²

E = 5 cm

d = √(5/π) cm

Area of the circular metal disk = 715 cm²

a) Required; The disk radius

Let A represent the area of the disk and let x represent the radius, we have;

A = π•x²

Therefore;

x = √(A/π)

Which gives;

x = √(715/π) cm

b) Allowed area error tolerance = ± 5 cm²

The allowed range of values for the area is therefore;

Which gives;

√(710/π) ≤ x ≤ √(720/π)

c) From the [tex] \epsilon / \delta [/tex] definition of limits, we have;

[tex] \lim\limits_{x → √(715/π)} f(x) = 715 [/tex]

Which gives;

f(x) = A = π•x²

L = 715

|f(x) - L| < E = 5 cm

|x - √(715/π)| < d = √(5/π)

Learn more about the properties of limits here:

https://brainly.com/question/13233499

#SPJ1

The linear equation to calculate the height is H(t)=33t.

Given that the elevator descends at the speed of 33 feet/second.

If a person gets on the elevator at the observer deck and after 10 seconds he finds himself at 1490 feet above the ground then height descended  in 10 seconds= 33×10

                                         = 330 feet

The height of the observer deck from the ground = 1490+330

                                                                             = 1820 feet

The required equation to calculate the height of above the ground H(t)=33t.

We can calculate  the height of the elevator at any instant using the above expression.

To learn more about speed, distance visit the link:

https://brainly.com/question/28224010

#SPJ9

Answer:

1; 1

2:3

3:9

4:27

5:81

6:243

7:729

8:2,187

9:6,561

10:19,683

11:59,049

12:177,147

a. Interest of the first year = $26.93

b. Balance after the first year = $1256.93

c. Interest for the second year = $27.52

d. Balance after the second year = $1284.45

Although a part of your question is missing, you might refer to this full question: Gerry deposited $1230 in an account that pays 2.19% simple interest for one year.

a. How much interest will he earn in one year?

b. What will be his balance after one year?

c. Gerry withdraws all of the principal and interest after the first year and deposits into another one-year account at the same rate. What will be his interest for the second year?

d. What will his balance be after two years?

Principal = $1230

Rate = 2.19%

Formula to be used:

Simple interest = (P*R*T)/100

where P = principal

R = rate

T = time in years

Calculating interest for the first year:

S.I = (1230*2.19*1)/100

S.I = 26.93

So, he will earn $26.93 as interest in the first year

And balance after the first year will be $1256.93

Solving for the second year:

P = 1256.93

S.I = (1256.93*2.19*1)/100

= 27.52

So, interest for the second year will be $27.52

And balance after the second year will be $1284.45

Learn more about Simple interests:

https://brainly.com/question/25845758

#SPJ4

Answer:

m = e/c

Step-by-step explanation:

We would use r = p/b formula to find 50 is what percent of 20.

The correct answer is an option (b)

For given question,

we need to find the formula which we use to find 50 is what percent of 20

We make the assumption that 20 is 100% since it is our output value.

Let the value we seek be m.

So, 100 % = 20 ...............(1)

m % = 50           ..............(2)

By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

[tex]\frac{100\%}{m\%}=\frac{2}{5}[/tex]

So, m = 250%

This means, 50 is 250% of 20

The formula PERCENTAGE  p = rb – The result obtained when a number is multiplied by a percent.

The formula BASE ( b = p/r) – The whole in a problem. The amount you are taking a percent of.

The formula RATE (r = p/b) – The ratio of amount to the base. It is written as a percent.

Therefore, we would use r = p/b formula to find 50 is what percent of 20.

The correct answer is an option (b)

Learn more about the percent here:

https://brainly.com/question/22111589

#SPJ4

2/3 would use a model or place-value concepts.

What is probability?

The possible rolls are 1,2,3,4,5,6  total of 6

2 or less than 5 rolls are 1,2,3,4  total of 4

P (2 or less than 5) = total number of choices of 2 or less than 5 / total

                               =4/6

                                   =2/3

Learn more about probability

brainly.com/question/11234923

#SPJ4

Answer:

Step-by-step explanation:

Answer:

1.1n represents the cost of the pencils

1.7m is the cost of the pads of paper

The expression represents that she bought a package of pencils and a pad of paper

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:D

Step-by-step explanation: