Select all the correct answers. what is 221,000,000,000,000,000,000 expressed in scientific notation? 2.21 × 1021 2.21e20 2.21e21 2.21e-20 2.21 × 10-21 2.21 × 10-20 2.21 × 1020 2.21e-21

Answer:

because of traingle

we have to firstly scale. the factor and add the numbers

Answer:

x=4 and y=−2

Step-by-step explanation:

Let's solve your system by substitution.

3x+8y=−4;2x−4y=16

Step: Solve 3x+8y=−4 for x:

3x+8y=−4

3x+8y+−8y=−4+−8y(Add -8y to both sides)

3x=−8y−4

3x/3=−8y−4/3 (Divide both sides by 3)

x=−8/3y+−4/3

Step: Substitute −8/3y+−4/3 for x in 2x−4y=16:

2x−4y=16

2(−8/3y+−4/3)−4y=16

−28/3y+−8/3=16 (Simplify both sides of the equation)

−28/3y+−8/3+8/3=16+8/3 (Add 8/3 to both sides)

−28/3y=56/3

−28/3y/−28/3=56/3/−28/3 (Divide both sides by (-28)/3)

y=−2

Step: Substitute−2 for y in x=−8/3y+−4/3:

x=−8/3y+−4/3

x=−8/3(−2)+−4/3

x=4 (Simplify both sides of the equation)

So the Answers are: x=4 and y=−2 or u can switch it around y=−2 and x=4

The expected rate of return on the common stock of CrisisGreat is 4.43%.

To calculate the expected rate of return on the stock of CrisisGreat, we need to use the formula:

Expected rate of return = (Probability of recession * Rate of return in recession) + (Probability of normal economy * Rate of return in normal economy) + (Probability of boom * Rate of return in boom)

Let's plug in the given values:

Therefore, the expected rate of return on the common stock of CrisisGreat is 4.43%.

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Therefore, we need to add approximately 0.0526 gallons of water (which is equivalent to about 6.63 fluid ounces) to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of one or more variables, coefficients, and constants, and it can include mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign, indicating that they have the same value. The goal of solving an equation is to determine the value of the variables that make the equation true. Equations are used in many areas of mathematics and science to model real-world phenomena and solve problems.

Here,

Let's assume that we need to add x gallons of water to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze. We know that the final solution will contain 1 gallon of antifreeze, and that this will be 95% of the total solution (the remaining 5% will be water). So, we can write:

1 gallon of antifreeze = 95% of (1 gallon of antifreeze + x gallons of water)

We can simplify this equation by converting 95% to a decimal:

0.95 × (1 gallon of antifreeze + x gallons of water) = 1 gallon of antifreeze

Now we can solve for x by isolating it on one side of the equation. First, let's distribute the 0.95:

0.95 gallons of antifreeze + 0.95x gallons of water = 1 gallon of antifreeze

Next, let's isolate x by subtracting 0.95 gallons of antifreeze from both sides:

0.95x gallons of water = 0.05 gallons of antifreeze

Finally, we can solve for x by dividing both sides by 0.95:

x = 0.05 gallons of antifreeze ÷ 0.95

x ≈ 0.0526 gallons of water

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the general form of the equation is

where m is the slope and b the y-intercept

from the graph we can notice the y-intercept is 0 because touch the y-axis on 0, so b=0

now we can repalce a point and b on the general equation to find the slope, m

i will use the point ( 90 , 30 )

so

the slope is 1/3

so the equation is

Answer:

C. y=1.6x-5

Explanation:

-5-(-8.2)= 1.6

1.6=m

-8.2=1.6(-2)=b

1.6(-2)=-3.2

-8.2-(-3.2)=-5

-5=b

hope this helps =3

The P-value for the hypothesis test is approx. 0.7064.

To find the P-value for the hypothesis test, we need to perform a two-sample proportion test. The formula to calculate the test statistic for this test is given by:

\(\[ z = \frac{{(\hat{p}_1 - \hat{p}_2) - 0}}{{\sqrt{\hat{p}(1 - \hat{p})\left(\frac{1}{{n_1}} + \frac{1}{{n_2}}\right)}}} \]\)

where \(\hat{p}_1\) and \(\hat{p}_2\) are the sample proportions, \(\hat{p}\) is the combined sample proportion, \(n_1\) and \(n_2\) are the sample sizes, and 0 is the hypothesized difference in proportions.

In this case, we have \(n_1 = 50\), \(x_1 = 8\) (number of successes in sample 1), \(n_2 = 50\), and \(x_2 = 7\) (number of successes in sample 2).

First, we calculate the sample proportions:

\(\[ \hat{p}_1 = \frac{x_1}{n_1} = \frac{8}{50} = 0.16 \]\)

\(\[ \hat{p}_2 = \frac{x_2}{n_2} = \frac{7}{50} = 0.14 \]\)

Next, we calculate the combined sample proportion:

\(\[ \hat{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{8 + 7}{50 + 50} = 0.15 \]\)

Then, we calculate the standard error:

\(\[ SE = \sqrt{\hat{p}(1 - \hat{p})\left(\frac{1}{{n_1}} + \frac{1}{{n_2}}\right)} = \sqrt{0.15(1 - 0.15)\left(\frac{1}{50} + \frac{1}{50}\right)} \approx 0.0529 \]\)

Finally, we calculate the test statistic:

\(\[ z = \frac{(\hat{p}_1 - \hat{p}_2) - 0}{SE} = \frac{(0.16 - 0.14) - 0}{0.0529} \approx 0.3772 \]\)

To find the P-value, we look up the test statistic in the standard normal distribution table. In this case, the P-value is the probability of observing a test statistic greater than 0.3772 or less than -0.3772.

Consulting the table, we find that the P-value is approximately 0.7064. Therefore, the P-value for the hypothesis test is approximately 0.7064.

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The radius of the circle is r = 3.78 cm for the given circle.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the angle of the sector of the circle is 1.2 radians the area of the sector is 54 cm².

The radius of the circle will be calculated as:-

Area = Angle x πr²

54 = 1.2 x πr²

r² = ( 54 ) / ( 1.2 x π )

r² = 14.32

r = √14.32

r = 3.78 cm

Therefore, the radius of the circle is 3.78 cm.

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Answer:

18

Step-by-step explanation:

125 = 7x - 1 ...... because if the two lines are parallel alternate interior angles are congruent

125 + 1 = 7x

126 = 7x

\( \frac{126}{7} = \frac{7x}{7} \)

x = 18

hope it helps

for any question comment me ❤❤

Answer:

x = -2

Step-by-step explanation:

\(f(x)=x^{2}+18x+7\)

\(g(x)=-3x^{2}+2x-9\)

\(f(x)=g(x)\)

\(\implies x^2 +18x+7=-3x^2 +2x-9\)

\(\implies 4x^2 +16x+16=0\)

\(\implies x^2 +4x+4=0\)

\(\implies (x+2)^2=0\)

\(\implies x+2=0\)

\(\implies x=-2\)

Answer:

Step-by-step explanation:

Area of square:

a=25mi

r=12.5mi

A=a²

A=25²=625

Area of semi circle:

As=1/2*πr²

As=1/2*3.14*12.5²=245.3125≈245.31

Shade Area:

A-As=625-245.31=379.69

Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

To solve the given system of equations using Laplace transforms, let's denote the Laplace transforms of the variables y and x as Y(s) and X(s) respectively.

The Laplace transform of a derivative can be calculated using the formula: L{f'(t)} = sF(s) - f(0), where F(s) represents the Laplace transform of f(t).

Given equations:

1) y + x + y = 0

2) x' + y' = 0

Taking the Laplace transform of equation 1:

L{y + x + y} = L{0}

Using linearity and differentiation properties of Laplace transforms:

L{y} + L{x} + L{y} = 0

Y(s) + X(s) + Y(s) = 0

Taking the Laplace transform of equation 2:

L{x' + y'} = L{0}

Using linearity and differentiation properties of Laplace transforms:

sX(s) + sY(s) - x(0) - y(0) = 0

sX(s) + sY(s) - 1 = 0

We also have the initial conditions:

y(0) = 0, y'(0) = 0, x(0) = 1

Applying the initial conditions to the Laplace transformed equations:

Y(0) + X(0) + Y(0) = 0           (equation A)

sX(s) + sY(s) - 1 = 0             (equation B)

Substituting Y(0) = 0 from equation A into equation B:

sX(s) + sY(s) - 1 = 0

Since x(0) = 1, X(0) = 1/s. Substituting this into the equation:

s(1/s) + sY(s) - 1 = 0

1 + sY(s) - 1 = 0

sY(s) = 0

Y(s) = 0

Now, substituting Y(s) = 0 back into equation A:

0 + X(0) + 0 = 0

1/s = 0

This equation is not possible, which indicates that there is no unique solution to the system of equations using Laplace transforms.

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Answer:

456748

Step-by-step explanation:

you 463uy2iuswhk then 13456

Answer:

27

Step-by-step explanation:

9 students = 1/3, 9 students = 1/2, 9 students = 1/3 so 9 x 3 =27

Answer:

4, 8 ,16​

Step-by-step explanation:

4 * 2 = 8

8 * 2 = 16

Answer:

5.91780821918

Step-by-step explanation:

432/73 is the same as 432 ÷73=5.91780821918

Hope this helps ∞<3

Answer:

the answer would be a % because of the divisibility rule

Answer:

what question

the last one you send?

Step-by-step explanation:

Answer:

2 people will take 90 days to complete the same house

Step-by-step explanation:

Given:

T1 = 30 days

P1 = 6

T2 = x

P2 = 2

This is an inverse proportion because if there are more people, less time will be taken to complete the house and vice versa.

So, We'll write it in the order of :

=> T1:T2 = P2:P1

=> 30:x = 2:6

Writing in fraction form

=> \(\frac{30}{x} = \frac{2}{6}\)

Cross Multiplying

=> 2x = 180

Dividing both sides by 2

=> x = 90 days

So, 2 people will take 90 days to complete the same house

Answer:

90 days

Step-by-step explanation:

6 people- 30 days

1 person- 30*6= 180 days

2 people- 180/2= 90 days

Answer: 29

Step-by-step explanation:

3x2= 6

4x2=8

3x5=15

6+8+15= 29

hoped I helped you a bit! Good luck! :)

We return "Yes"; otherwise, we return "No".

What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

To solve this problem, we can work backward from (c,d) to (a,b) and check if each step is valid. Specifically, we can use the following observations:

If c < a or d < b, it is impossible to reach (c,d) from (a,b) using the given operations.

If c - a = d - b, we can reach (c,d) from (a,b) using only the second operation. Specifically, we can perform the operation (a, a+b) repeatedly until we reach (c,d).

If c - a != d - b, we can reach (c,d) from (a,b) using a combination of the two operations. Specifically, we can perform the first operation (a,b) -> (a+b,b) repeatedly until we get to a point where c - a = d - b, and then use the second operation to get to (c,d).

Here, we first check if it is impossible to reach (c,d) from (a,b) using the observations above. If not, we perform the second operation as many times as possible to reduce the difference between c and a, and d and b. Once this is done, we check if we have arrived at (a,b).

Therefore, we return "Yes"; otherwise, we return "No".

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Answer:

819

Step-by-step explanation:

We solve the above question using simple interest

The formula for the total amount in a bank amount when it earn simple interest annually is:

A = P(1 + rt)

When

P = Initial amount in the account = 780

r = Simple Interest rate = 2.5% = 0.025

t = 2 years

A = 780(1 + 0.025 × 2)

A = 780(1 + 0.050)

A = 780(1 .050)

A = 819.00

The amount of money that will be in her account if she does not make any deposits or withdrawals in 2 years is 819.

By mathematical induction, we have shown that a_k=n^2 for all k.

To prove that a_k=n^2 for all k, we will use mathematical induction.

Base Case:

When k=1, a_1=2(1)-1=1. This is also equal to 1^2, so the base case is true.

Inductive Step:

Assume that a_k=k^2 is true for some arbitrary positive integer k, i.e., a_k=k^2.

Now, we want to prove that a_(k+1)=(k+1)^2.

We know that a_(k+1)=2(k+1)-1=2k+2-1=2k+1.

We can use our inductive hypothesis that a_k=k^2 and simplify the expression for a_(k+1):

a_(k+1) = 2k+1 = k^2 + 2k + 1 = (k+1)^2

Therefore, by mathematical induction, we have shown that a_k=n^2 for all k.

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(a) The number of one-to-one (injective) functions from X to Y can be calculated using the concept of permutations.

For each element in X, we have p choices to map it to an element in Y (since the function is one-to-one). Therefore, the total number of one-to-one functions from X to Y is given by p * (p - 1) * (p - 2) * ... * (p - n + 1). This is equivalent to the number of permutations of size n taken from a set of size p, denoted as P(p, n), which can be computed as:

P(p, n) = p! / (p - n)!

(b) To count the number of reflexive relations on X, we need to consider the possible subsets of X that contain all the elements with self-loops (reflexive pairs). For each element in X, we have two choices: either include it in the subset with a self-loop or exclude it. Therefore, the total number of reflexive relations on X is given by 2^(n^2), where n is the cardinality of X.

The justification for these answers lies in the definitions of one-to-one functions and reflexive relations. A one-to-one function is a mapping where each element in X is assigned to a unique element in Y, without repetition. The number of such functions can be determined by considering the available choices for each element in X.

A reflexive relation on X is a relation that includes a self-loop for each element in X, ensuring that every element is related to itself. To count the number of reflexive relations, we consider all the possible subsets of X that include the self-loops, which corresponds to the power set of X. Therefore, the total number of reflexive relations is given by 2^(n^2).

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Answer:

X = 34

Step-by-step explanation:

3x+44+x=180

4x+44=180

4x=136

x=34

hope this helps! :)

Answer: a) $90 for the first 200 containers picked on the rate of $0.45 per container.

b) $45.5 for every container over 200 that he picks.

c) $135.5 for total number of containers as $90 (for the first 200 containers) plus $45.5 (for the remaining 70 containers) equals $135.5.

Step-by-step explanation: