If 3x = y, then y = 3x
What’s the property

Answer:

\(\{-9,-1,5,7\}\)

Step-by-step explanation:

The range would be the corresponding y-values for the given set:

\(h(-5)=2(-5)+1=-10+1=-9\\\\h(-1)=2(-1)+1=-2+1=-1\\\\h(2)=2(2)+1=4+1=5\\\\h(3)=2(3)+1=6+1=7\)

Thus, the range of \(h\) using set notation is \(\{-9,-1,5,7\}\). Also, see attached graph.

Answer:

43.95963871

Step-by-step explanation:

I used the tangent. Tangent is opposite over adjacent sides. To set it up, tan(7)=opp/16

move around to get opp=(16)tan(70)

opp=43.95963871

nearest whole height= 44 ft

Step-by-step explanation:

Step 1:  List out all of the formulas for the trigonometric functions

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

tan(x) = opposite/adjacent

Step 2:  Find the equation for h

tan(70) = h / 16

16 * tan(70) = h

Step 3:  Solve for h

h = 16 * tan(70)

h = 43.9596

h = 44 ft

Answer: 44 ft

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

\(\displaystyle \frac{d}{dx}\Big|_{x=3} & = \frac{9(3)-6}{\sqrt{(3(3)-2)^2-4}} = \frac{7\sqrt{5}}{5}\)

Step-by-step explanation:

We are given the two functions:

\(\displaystyle f(x) = \sqrt{x^2 -4} \text{ and } g(x) = 3x-2\)

And we want to find:

\(\displaystyle \frac{d}{dx}\left[f(g(x))\right] \text{ at } x = 3\)

Recall that from the chain rule:

\(\displaystyle \frac{d}{dx}\left[ f(g(x))\right] = f'(g(x)) \cdot g'(x)\)

Hence, find both f'(x) and g'(x).

The derivative of f(x) can be determined using the chain rule:

\(\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[ \sqrt{x^2-4}\right]\\ \\ & = \frac{1}{2\sqrt{(x^2-4)}}\cdot \frac{d}{dx}\left[x^2-4\right] \\ \\ & = \frac{x}{\sqrt{x^2-4}} \end{aligned}\)

Because g(x) is simply a linear function, its derivative will be the slope of the linear function at any point. That is:

\(\displaystyle g'(x) = 3\)

Hence:

\(\displaystyle \begin{aligned} \frac{d}{dx}\left[f(g(x))\right] & = \frac{(g(x))}{\sqrt{(g(x))^2-4}} \cdot (3) \\ \\ & = \frac{9x-6}{\sqrt{(3x-2)^2-4}} \end{aligned}\)

Then at the point x = 3, the derivative is:

\(\displaystyle \frac{d}{dx}\Big|_{x=3} & = \frac{9(3)-6}{\sqrt{(3(3)-2)^2-4}} = \frac{7\sqrt{5}}{5}\)

Answer:

\( \frac{1}{4} (3a + 2b)\)

The expression from the given condition is 1/4(3a+4b).

We have given that,

The product of a quarter of 3 more than a number a and 2 times a number b.

The quarter means divided into four equal or corresponding parts.

Therefore we get the expression from the given condition is

1/4(3a+4b).

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Answer:

red grapes

Step-by-step explanation:

Answer:

The two bags of green grapes are a lower unit rate.

Step-by-step explanation:

A bag of red grapes is $4 and two bags of green grapes is $7.50. If you buy two bags of red grapes the total amount of money you are spending is $8. If you buy two bags of green grapes the total is $7.50. If you divide $7.50 by two you get $3.50. This means that for one bag of green grapes it is $3.50. Therefore the two bags of green grapes are a lower unit rate.

Hope This Helps :)

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer:

D

Step-by-step explanation:

Since a fraction is a division problem, you can do every answer and compare them until you get them in order, which D is the most reliable.

Answer:

the act or process of comparing: such as. a : the representing of one thing or person as similar to or like another

Step-by-step explanation:

Answer:

first, dilate triangle ABC with respect to the origin by scale factor of 2.

then rotate it 90 degrees counterclockwise about the origin

Step-by-step explanation:

Expression which gives the same result as Σₙ₋₀⁴ ( 5 ( \(\frac{1}{3}\) )ⁿ) is 5 Σₙ₋₀⁴ ( \(\frac{1}{3}\) )ⁿ .

Hence 5 is the constant so it comes out, so the correct option is B.

A part which does not possess any change in the former equation by taking it out of the bracket as to make our calculation simple hence, helps in reducing time taken.

As Σ represents submission sign helps to represent sum of the all in individual cell.

Given Expression :-

   Σₙ₋₀⁴ ( 5 ( \(\frac{1}{3}\) )ⁿ) ,

After Evaluation we get that 5 as the constant part and can be taken out as it poses no any change in the original value of the result.

so we get it as,

   5 Σₙ₋₀⁴ ( \(\frac{1}{3}\) )ⁿ .

Hence option B is the correct choice.

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Answer:

Step-by-step explanation:

The matches are Offered by a company to employees= 401(K).

Opened and managed by an individual = IRA.

Offered by a nonprofit organization to employees is 403(b)

Three types of retirement and how to plan for each

Traditional Retirement.

Semi-Retirement.

Temporary Retirement

By the given data we have to match

Offered by a company to employees= 401(K)

A 401(k) plan is a company-sponsored retirement account to which employees can contribute income.

Opened and managed by an individual is IRA.

An individual retirement account (IRA) allows you to save money for retirement in a tax-advantaged way.

Offered by a nonprofit organization to employees is 403(b)

A 403(b) plan allows employees to contribute some of their salary to the plan.

Therefore the matches are 401(K), IRA and 403(b).

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Answer:

Step-by-step explanation:

11m

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer: See below

Step-by-step explanation:

To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:

Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.

Then, the addition problem becomes:

A B C

D E F

We know that the sum of each column must be the same, so:

C + F = 10 + B

B + E = 10 + A

We can rewrite these equations as:

C - B + F = 10

B - A + E = 10

Since we are given that the sum of the two numbers is the same, we know that:

C + F + D + E = 1112

We can substitute C and F in terms of A and B using the equations above:

C = 10 + B - F

F = 10 + C - B

Substituting these expressions into the equation for the sum, we get:

10 + B - F + C + D + E = 1112

Simplifying this equation, we get:

B - F + C + D + E = 1102

Now we can substitute in the expressions for C and F in terms of A and B:

B - (10 + B - F) + (10 + C - B) + D + E = 1102

Simplifying and canceling out terms, we get:

F - C - D - E = -92

We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.

Trying different values for A and D, we find that A = 2 and D = 3 works:

A B C

D E F

2 7 9

1 7 3

The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:

2 7 9

1 7 3

4 5 2

Answer:

Step-by-step explanation:

x - 12 ≤ 3 - 2x

3x ≤ 15

x ≤ 5

To graph this, just draw a VERTICAL line passing through x = 5, then shade the area to the LEFT

Systematic random sampling is used when selecting every nth item from a list of items. In this example, every 49th student starting with the 3rd student is selected.

In systematic random sampling, a list of items is created and every nth item is selected for the sample. This technique is useful when selecting a representative sample from a large population of items. In the example given, 496 students were listed and every 49th student starting from the 3rd student was selected. This is a systematic random sampling technique because the items were selected in a systematic and random fashion. The selection of every 49th student starting from the 3rd student ensures that the sample is representative of the population while also randomizing it so that all students have an equal chance of being selected.

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The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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Answer:

1) A giraffe's heart will beat 910 times in 14 minutes

Table for 1)

Beats      65     325    910

Minutes    1        5        14

2) $8.80 for 4 bags of chips

Explanation for 2)

8.8 divided by 4 equals 2.2

4.5 divided by 2 equals 2.25

The probabilities, using the binomial distribution, are given as follows:

a) Exactly five: 0.115 = 11.5%.

b) Exactly four: 0.224 = 22.4%.

The mass probability formula used to obtain the probability of x successes on n trials is presented as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in this problem are given as follows:

The probability that the number who have very little confidence in newspapers is exactly five is P(X = 5), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{8,5}.(0.39)^{5}.(0.61)^{3} = 0.115\)

The probability that the number who have very little confidence in newspapers is exactly four is P(X = 4), hence:

\(P(X = 4) = C_{8,4}.(0.39)^{4}.(0.61)^{4} = 0.224\)

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Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.

To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:

Time spent on videos = 10% of 40 hours = 4 hours

Time spent on homework = 15% of 40 hours = 6 hours

Time spent on games = 20% of 40 hours = 8 hours

Time spent on social media = 25% of 40 hours = 10 hours

Time spent on shopping online = 20% of 40 hours = 8 hours

Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.

The difference between these two amounts is:

6 hours - 8 hours = -2 hours

This means that Heracio spent 2 hours more on shopping online than on doing homework.

Step-by-step explanation:

The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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Answer:

Step-by-step explanation:

Yo figure it out there is a 90* and a 60*. first solve for m then multiply m by 36 so the equation is 36m = n

When c=0 It's 75 when x= 0 It's 75 when x= 100 It's 100 when x= 200 its 125 when x= 300 its 150

Step-by-step explanation:

For A, The printer would be 75 dollars and each newspaper printed is .25 cents

Answer:

c

Step-by-step explanation:

163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units

164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.

165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.

166. Missing side = 29 ft.

The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.

163. The distance between A(-5, 6) and B(5, -5):

AB = √[(5−(−5))² + (−5−6)²]

AB = √221

AB ≈ 14.9 units

164. Apply the Pythagorean theorem to find the diagonal:

Diagonal = √(15² + 15²) ≈ 21.2 ft.

165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:

c = √676 = 26 units.

166. Missing side = √(20² + 21²) = 29 ft.

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Answer:

Around 11.2

Step-by-step explanation:

The tangent of an angle in a right triangle is equivalent to the opposite side divided by the adjacent side. In this case:

\(\tan 24= \dfrac{5}{x} \\\\x=\dfrac{5}{\tan 24}\approx 11.2\)

Hope this helps!

Answer:

I think 20

Step-by-step explanation:

Answer:(0, 20)

Step-by-step explanation:

-6 stays the same so you keep it as 0.And you add 8 and -12 to get 20 so the distance is (0, 20)