Natalie earns $85 for 4 hours of work. If she makes a constant hourly wage, which table represents the relationship between the number of hours she works and her total earnings?

Answer:

photo not clear what to do ?

\(The given series can be represented as follows:$$\sum_{n=1}^{\infty}\frac{n^{3}}{(-1)^{n+2}}$$\)

The nth-term test should be used to verify whether this series is convergent or divergent.

That is to say, the series is convergent if the limit of the n-th term as n approaches infinity is zero, and it is divergent if the limit is not equal to zero.

So, let's use the nth-term test to find out whether the given series converges or diverges.

\(The limit of the nth term is$$\lim_{n \rightarrow \infty} \frac{n^{3}}{(-1)^{n+2}}$$Since $(-1)^{n+2}$ is either $-1$ or $1$\)depending on whether $n$ is even or odd, the numerator and denominator of the fraction are both positive when $n$ is odd, whereas they are both negative when $n$ is even.

\(The nth term of the series becomes $n^{3}$ when $n$ is odd, and $-n^{3}$ when $n$ is even.\)

As a result, the series alternates between positive and negative values.

The nth-term test should be used to verify whether this series is convergent or divergent.

That is to say, the series is convergent if the limit of the n-th term as n approaches infinity is zero, and it is divergent if the limit is not equal to zero.

\(We will now proceed with the limit calculation.$$ = \lim_{n \rightarrow \infty} \frac{n^{3}}{(-1)^{n+2}}$$$$ = \lim_{n \rightarrow \infty} \frac{n^{3}}{(-1) \times (-1)^{n}}$$$$ = \lim_{n \rightarrow \infty} \frac{n^{3}}{(-1)^{n}}$$This limit does not exist, since the sequence oscillates between $-n^{3}$ and $n^{3}$.\)

Because the nth term of the series does not approach zero, the series diverges by the nth term test, and the answer is therefore as follows: diverges by the nth term test.

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6n + 5 < 20

Subtract both sides 5

6n + 5 - 5 < 20 - 5

6n < 15

Divide both sides by 6

6n ÷ 6 < 15 ÷ 6

n < 15/6

n < 3×5/3×2

n < 5/2

n < 2.5

n《 2

Thus the largest value of n is :

The largest possible value of n is 2.

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

6n +5 <20

To find the largest value of n, simplify the inequality,

Subtract 5 from both the sides,

6n+5-5 < 20-5

6n < 15

n < 15/6

n < 2.5

Since, n is an integer, therefore, maximum value of n can be 2.

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The team utilizes 5-gallon coolers, small cups (5.75 fluid ounces), and large cups (7.25 fluid ounces) to manage and distribute water effectively during their soccer activities.

The soccer team uses 5-gallon coolers to hold water during games and practices. Each cooler has a capacity of 570 fluid ounces. This means that each cooler can hold 570 fluid ounces of water.

To serve the players, the team has small cups that hold 5.75 fluid ounces and large cups that hold 7.25 fluid ounces. The small cups are smaller in size and can hold 5.75 fluid ounces of water, while the large cups are larger and can hold 7.25 fluid ounces of water.

These cups are used to distribute the water from the coolers to the players during games and practices. Depending on the amount of water needed, the team can use either the small cups or the large cups to serve the players.

Using the cups, the team can measure and distribute specific amounts of water to each player based on their needs. This ensures that the players stay hydrated during the games and practices.

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Note the full question may be :

The soccer team wants to distribute water to the players using both small and large cups. If they want to fill as many small and large cups as possible from one 5-gallon cooler without any leftover water, how many small and large cups can be filled?

In order for a set of numbers to represent three sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem. Only option C represents three sides of a triangle.

Now let's check each option to see which one satisfies the triangle inequality theorem:

a. 5, 3, and 2

The sum of 5 and 3 is 8, which is greater than 2. The sum of 5 and 2 is 7, which is also greater than 3. The sum of 3 and 2 is 5, which is not greater than 5. Therefore, this set of numbers does not represents three sides of a triangle.

b. 9, 5, and 15

The sum of 9 and 5 is 14, which is less than 15. Therefore, this set of numbers does not represent three sides of a triangle.

c. 8, 10, and 6

The sum of 8 and 10 is 18, which is greater than 6. The sum of 8 and 6 is 14, which is also greater than 10. The sum of 10 and 6 is 16, which is greater than 8. Therefore, this set of numbers represents three sides of a triangle.

d. 4, 6, and 10

The sum of 4 and 6 is 10, which is less than 10. Therefore, this set of numbers does not represent three sides of a triangle. Therefore, only option C represents three sides of a triangle.

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Answer:

2 + (-4) equals -2

Answer:

-2

Step-by-step explanation:

A positive number plus a negative number equals another negative number

the given proportional relationship y=0.5x with proportional constant is 1/2.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

For every 1 scoop of ice cream, cup of milk is needed 1/2, and for every 5 scoops of ice cream, 2 cups of milk 2 1/2 are needed.

So the equation will be y = kx

or y = 0.5(x)

Here proportional constant is 1/2 or 0.5.

For 18 scoops of icecream, milk will be needed is 18/2 = 9 cups of milk.

Hence, we can say that the given proportional relationship y=0.5x with a proportional constant is 1/2.

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The solution to the differential equation xy' + (x - 2)y = 3x³e^(-x) with the initial condition y(1) = 0 is y(x) = x²e^(-x).

To solve the given linear differential equation, we can use an integrating factor. The integrating factor for the equation xy' + (x - 2)y = 3x³e^(-x) is e^(∫(x-2)/x dx) = e^(x - 2ln|x|).
Multiplying both sides of the equation by the integrating factor, we have:
e^(x - 2ln|x|) * (xy' + (x - 2)y) = e^(x - 2ln|x|) * 3x³e^(-x)
Simplifying, we get:
d/dx (x²e^(x - 2ln|x|)) = 3x³e^(-x) * e^(x - 2ln|x|)
Integrating both sides with respect to x, we have:
x²e^(x - 2ln|x|) = ∫(3x³e^(-x) * e^(x - 2ln|x|) dx)
Simplifying further, we get:
x²e^(x - 2ln|x|) = ∫(3x³ dx)
Integrating the right-hand side, we have:
x²e^(x - 2ln|x|) = 3/4 x^4 + C
Using the initial condition y(1) = 0, we can substitute x = 1 and y = 0 into the equation:
1²e^(1 - 2ln|1|) = 3/4 (1)^4 + C
e^1 = 3/4 + C
Solving for C, we get C = e - 3/4.
Therefore, the solution to the differential equation xy' + (x - 2)y = 3x³e^(-x) with the initial condition y(1) = 0 is y(x) = x²e^(x - 2ln|x|).

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Given:

From the above expression,

If David, Malachy and Paul share some sweets in the ratio 4:3:3 then Paul get 7.2 number of sweets

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that David, Malachy and Paul share some sweets in the ratio 4:3:3

All three shared 24 sweets together.

Let x be the number of sweets

4x+3x+3x=24

Add the like terms

10x=24

Divide both sides by 10

x=2.4

Now paul has 3x sweets so 3×2.4=7.2

Hence, Paul get 7.2 number of sweets

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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

i believe the table representing linear function would be the bottom left.

If you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x

The standard exponential function is expressed as:

y = ab^x

The value of x determines the nature of a graph whether vertical or horizontal stretch.

If x  > 1, it is a vertical stretch

Given the function f(x) = 2^x, if you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x

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Answer:

1. -5

2. -6

3. -10

Step-by-step explanation:

There are x = - 6, -7,  and - 8 three values for variable x that would make 5x < -20 true.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We have been given that the inequality is below as

⇒ 5x < -20   ...(i)

⇒ 5x / 5 < -20 / 5

⇒ x < - 4

Thus, all the negative values which are less than -4 for x would make it true.

For example, we take x = -8

Substitute the value of x = -8 in the inequality (i),

⇒ 5(-8) < -20

⇒ - 40 < -20

This is true.

Similarly x = - 6, and - 7 also for x would make it true.

Hence, there are x = - 6, -7,  and - 8 three values for variable x that would make 5x < -20 true.

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hello! here is your answer

Answer:

1) ∠2 ≅ ∠7

⇒ they are corresponding angles

2) ∠5 ≅ ∠9

⇒ they are alternate interior angles

3) ∠4 ≅ ∠7

⇒ they are vertically opposite angles

4) if ∠3 ≅ ∠8, then p║q

⇒ they are corresponding angles

5) ∠3 ≅ ∠9

⇒ they are vertically opposite angles

6) m∠2 + m∠3 = 180

⇒ they are co-interior angles

7) ∠4 is vertical to ∠7

8) ∠2 and∠3 are same side interior angles

9) ∠5 corresponds to ∠8

10) one alternate exterior pair is ∠1 and ∠8

hope it helps you!!

Answer:

a = 5

Step-by-step explanation:

3(a+3)+6 = 30

subtract 6 from both sides

3(a+3) = 24

divide both sides by 3

a+3 = 8

subtract 3 from both sides

a = 5

Answer:

the answer is 0.71

Step-by-step explanation:

it told me

The probability the next customer will pay with something other than a credit card is 0.71.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Number of customers paid cash = 83

Number of customers used a debit card = 16

Number of customers used a credit card = 41

Total number of customers = 140

The probability that the next customer will pay with something other than a credit card is

P(e) = (Number of customers paid cash + Number of customers used a  debit card) / Total number of customers.

⇒ \(P(e)=\frac{83+16}{140}\)

⇒ \(P(e)=\frac{99}{140}\)

⇒ \(P(e)=0.7071\) ≈ \(0.71\)

Hence we can conclude that the probability the next customer will pay with something other than a credit card is 0.71.

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Answer:

I believe the answer is

\(y = 4x - 7\)

Step-by-step explanation:

hope thai HELPS!

if you want an explanation ask me in the comments.

Answer:

Step-by-step explanation:

Comment

The answer is either 133 degrees or its supplement. The supplement is found by subtracting 133 from 180.

180 = 133 + x

180 - 133 = 133 -  133 + x

47 = x

So all the answers are either 133 or 47

Answers and reason

<2 = 47 it is the supplement of angle 1

<3 = 133. It is vertically opposite <1

<4 = 47. It is vertically opposite angle 2

You  can do the same thing with 4,6,7 and 8 if you can just find one of them. and you can.

<1 and <5 are corresponding angles. These angles are on the same side of the transversal (the slanted line) and they both are above the parallel line. They are equal.

<5 = <1 Corresponding angles

<6 = 47 degrees because it is the supplement of < 5

<7 = 133 degrees because it is vertically opposite <5

<8 = 47 degrees because it is opposite angle <6

Answer:

The price would be 7.20

Step-by-step explanation:

let's check each one of the options:

(A) is not equivalent

(B) is not equivalent

(C) is not equivalent

(D) it is equivalent to the given equation because

we divide in both sides of the equality by 3 and obtain:

then:

Answer: I think the answer is 3

Step-by-step explanation: I Divided 12 by 4 and got the answer 3

Answer:

Answer is 3

Step-by-step explanation:

According to the question,

j = 12

So

j / 4 = 12 / 4 = 3

Pls mark my answer as Brainliest

Answer:

7√2

Step-by-step explanation:

Answer:

I think that is simplyfied

Step-by-step explanation:

Answer:

No because 3x is variable and 3 is constant

Answer:

No

Step-by-step explanation:

Like terms is when a variable is raised in the same power. In this case 3xx and 3 are not like terms. An example of a like term would be 3x and 6x because they have both x.

Answer:

There are 11 pigs and 17 chickens.

Step-by-step explanation:

Lets let

p = number of pigs

c = number of chickens

Assuming each animal has only one head, then

p + c = 28

And assuming that pigs have four feet and chickens have two feet:

pig feet = 4p

that is, 4 feet for each pig, and



chicken feet = 2c

right? two feet per chicken.



All the feet are:

4p + 2c = 78

Now we have two equations and two unknowns, so we can solve this "system of equations". You can use substitution or elimination method (or even graphing or matrices) I will run through elimination method.

Multiply p+c=28 times -2.

-2p + -2c = -56

then add the whole equation to the other equation. Do this adding vertically, from top to bottom.

-2p + -2c = -56

4p + 2c = 78

_____________

2p = 22

Divide by 2 to solve

p = 11

There are 11 pigs.

Remember,

p + c = 28

11 + c = 28

subtract 11

c = 17

There are 17 chickens.

Answer:

10

Step-by-step explanation:

geometric mean theorem :

h = sqrt(pq)

p, q being the segments on the Hypotenuse of the right-angled triangle.

so, x = sqrt(9×10) = 3×sqrt(10)

Answer: 21 1/8 kilogram

Step-by-step explanation:

From the question, we are informed that Chef bought 3 3/4 kilograms of apples 7 1/4 kilograms of pears and 10 1/8 kilograms of oranges. The total kilogram of fruits bought would be:

= 3 3/4 + 7 1/4 + 10 1/8

Note that the Lowest Common Multiple is 8.

= 3 6/8 + 7 2/8 + 10 1/8

= 20 9/8

= 21 1/8 kilogram

Ans option 3? it can be converted to a fraction!

Answer:

it depends on the number of decimals

Step-by-step explanation:

Answer:

\(the \: two\: numbes \: are : \\ 7.777 \: and \: - 2.099\)

Step-by-step explanation:

\(let \: the \: two \: numbers \: be : x \: and \: y \\ x + y = 5.678.....eq(1) \\ x - y = 9.876 .....eq(2)\\ x = 9.876 + y....from \: eq(2) \\ y = 5.678 - x....frm \: eq(1) \\ eq \:...y \: in \: terms \: o f\: x : \\ x = 9.876 + 5.678 - x \\ 2x = 15.554 \\ x = 7.777 \\ y = 5.678 - x = y = 5.678 - 7.777 \\ y= - 2.099.\)

Answer:

1,000$

Step-by-step explanation:

1,000 x 6 = 6,000$ or 6,000 in math

Answer:

$1,000

Step-by-step explanation:

x = 6,000/6

x = 1,000