What is x? I really dont get it please help

To solve the inequality −3|n - 5| ≥ 24, we can break it down into two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: n - 5 ≥ 0

In this case, the absolute value becomes n - 5, so we have:

-3(n - 5) ≥ 24

Simplifying the inequality gives:

-3n + 15 ≥ 24

-3n ≥ 9

Dividing both sides by -3 (and flipping the inequality sign):

n ≤ -3

Case 2: n - 5 < 0

In this case, the absolute value becomes -(n - 5), so we have:

-3(-(n - 5)) ≥ 24

Simplifying the inequality gives:

3n - 15 ≥ 24

3n ≥ 39

Dividing both sides by 3:

n ≥ 13

Combining the solutions from both cases, we find that the solution to the inequality is n ≤ -3 or n ≥ 13. This means n can be any value less than or equal to -3 or any value greater than or equal to 13.

As for the graph representing the solution, it would be a number line with a closed circle at -3 (indicating that it includes -3) and an open circle at 13 (indicating that it does not include 13). The area between -3 and 13 is shaded to represent the values that satisfy the inequality.

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(e) The complex number 5+2i in exponential form is (\sqrt{29}e^{i\text{tan}^{-1}\left(\frac{2}{5}\right)}\).
(f) The new period is \(0.31\sqrt{\frac{m}{1.6k}}\) when the spring constant is increased by 60%.

(e) To convert a complex number to exponential form, we need to determine its magnitude and argument. For the complex number 5+2i, the magnitude is given by the formula \(A = \sqrt{{\text{Re}}^2 + {\text{Im}}^2}\) where Re and Im represent the real and imaginary parts, respectively. In this case, the magnitude is \(\sqrt{5^2 + 2^2} = \sqrt{29}\).

The argument, \(\theta\), can be found using the formula \(\theta = \text{tan}^{-1}\left(\frac{{\text{Im}}}{{\text{Re}}}\right)\). For 5+2i, the argument is \(\text{tan}^{-1}\left(\frac{2}{5}\right)\).

Thus, the complex number 5+2i in exponential form is \(Ae^{i\theta} = \sqrt{29}e^{i\text{tan}^{-1}\left(\frac{2}{5}\right)}\).



(f) The period of a spring-mass system is determined by the mass and the spring constant. If the spring constant is increased by 60%, we can calculate the new period using the formula \(T' = T\sqrt{\frac{m}{k'}}\).

Given the original period \(T = 0.31\) seconds and an increase in the spring constant by 60%, we have \(k' = 1.6k\) where \(k\) is the original spring constant.

Substituting the values into the formula, the new period is \(T' = 0.31\sqrt{\frac{m}{1.6k}}\).

Increasing the spring constant causes the spring to become stiffer, resulting in a shorter period. The new period, \(T'\), will be less than the original period \(T\) due to the increased stiffness of the spring.

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The value of R when A equal 5 is 3.6 and the value of A when R equal 9 is 2 as R is varies inversely to A.

Proportional relationships are relationships between two variables where their ratios are equivalent.

If R is inversely proportional to A.

R ∝ 1/A, then

R = k/A

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

R = k/A

Plug in R = 12 and A = 1.5 and solve for k

k = R × A

k = 12 × 1.5

k = 18

a) The value of R when A = 5 will be;

R = k/A

R = 18 / 5

R = 3.6

b) The value of A when R = 9

R = k/A
R × A = k

A = k/R

A = 18 / 9

A = 2

Therefore, the value of A when R equal 9 is 2.

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Answer:

a is -9

b is 4

Step-by-step explanation:

we know that a and b are whole numbers.

we know that they are factors of 36.

1 * 36

2 * 18

3 * 12

4 * 9

6 * 6

i just did this as guess and check.

what numbers have a difference of 5?

the factors 4 and 9.

so, if a is the negative one, a has to be -9 to get -5 because

-9 + 4 = -5

and

(-9)(4) = 36

If a shopper pays for 517 for a 470 camera after sales tax is added then sales tax percentage is 10%.

To find the sales tax percentage, we will follow these steps:

1. Determine the amount of sales tax paid.

2. Divide the sales tax amount by the original price of the camera.

3. Multiply the result by 100 to find the sales tax percentage.

Step 1: Determine the amount of sales tax paid.

Sales tax amount = Total amount paid - Original price of the camera

Sales tax amount = 517 - 470

Sales tax amount = 47

Step 2: Divide the sales tax amount by the original price of the camera.

Sales tax rate = Sales tax amount / Original price of the camera

Sales tax rate = 47 / 470

Step 3: Multiply the result by 100 to find the sales tax percentage.

Sales tax percentage = Sales tax rate * 100

Sales tax percentage = (47 / 470) * 100

Sales tax percentage ≈ 10%

So, the sales tax percentage is approximately 10%.

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The factor of the given polynomial n² + 26n + 88 is (n + 4) and (n + 22). Then the correct option is B.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The polynomial is given below.

n² + 26n + 88

Then the factor of the given polynomial will be

n² + 22n + 4n + 88

n(n + 22) 4(n + 22)

(n + 4)(n + 22)

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The source of bias in the survey embarked upon would stem from that 'many people refuse to respond to telephone surveys.'

The behaviour whereby people refuse to respond to telephone surveys is called non-response bias. It can occur for a variety of reasons, such as people being too busy, not interested in the survey, or not trusting the surveyor. Non-response bias can lead to the survey results being inaccurate, as the people who do respond may not be representative of the population as a whole.

Therefore , the presence of bias would likely stem from the fact that "many people refuse to respond to telephone surveys."

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Answer:

B) m = 2 , b = -3

Step-by-step explanation:

b = y-intercept

The y-intercept is -3

b = -3

m = slope

The slope is 2

m = 2

Answer:

Step-by-step explanation:

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ 60- 40y = 20(3 - 2y)

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

Sally can solve minimum of 35 calculus problem and maximum of 50 calculus problem.

Calculus is a branch of mathematics that focuses on rates of change, to put it simply. For instance, you might want to determine how quickly a car will slow down as it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is useful in many different fields, including engineering, medicine, biological research, economics, architecture, space science, electronics, statistics, and pharmacology.

minimum = 35

maximum=50

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The difference in the means is two times the MAD.

To find the difference between the means as a multiple of the MAD, follow these steps:

Difference of the means = |mean of A - mean of B|

Multiplying the result by 1/MAD will give us the difference of the means as a multiple of the MAD.
1. Determine the difference between the means of the two data sets: Mean of data set A is 42, and the mean of data set B is 47.
  Difference = 47 - 42 = 5.

2. Divide the difference of the means by the MAD: The MAD of both data sets is 2.5.
  Multiple = Difference / MAD = 5 / 2.5 = 2.

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Answer and Step-by-step explanation:

For the triangles, all you have to do is subtract the two angles by 180 to find the missing angle.

2.

180 - 54 - 85 = 41

3.

180 - 36 - 59 = 85

4.

The square on the bottom represents a right angle, and right angles are always 90 degrees.

180 - 90 - 54 = 36

I hope this helps! (Sorry if more questions needed to be done, they're cut off so i don't know what they are asking)

#teamtrees #WAP (Water And Plant)

Answer:

5. If Nicole is tardy to class again, she will get detention and her mother will take away her phone.

6. If it is not raining, I will not bring my umbrella or rain boots. (This one could be incorrect but I think it’s right)

7. If a natural number ends in 0 then it is divisible by 10 and 5

Step-by-step explanation:

Answer

1242

Explanation

Given: 3% of 4.14 × 10⁴

3% of 4.14 × 10⁴ becomes

3 percent of the given number is 1242.

Given that, 3% of 4.14×10⁴.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, 3% of 4.14×10⁴ can be written as

3/100 ×4.14×10000

= (3×4.14×10000)/100

= 3×4.14×100

= 1242

Therefore, 3 percent of the given number is 1242.

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Samuel pay 5.81 for the 3 bottles of juice.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Samuel buys 3 bottles of juice that each have an original price of 2.80.

And, He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%.

Here, The original cost of 3 bottles of juice = 3 × 2.80

                                                                   = 8.40

Now, He uses a coupon for 35% off.

Hence, The off price = 35% of 8.40

                                = 35/100 × 8.40

                                = 2.94

So, The amount of 3 bottles of juice = 8.40 - 2.94

                                                        = 5.46

And, He is changed sales tax at a rate of 6.5%.

Thus, The sales tax on bottles = 6.5% of 5.46

                                               = 6.5/100 × 5.46

                                               = 0.35

Thus, The actual amount of 3 bottles of juice = 5.46 + 0.35

                                                                     = 5.81

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The null hypothesis would not be rejected and the researcher would fail to find statistical significance at the chosen alpha level of .05.

If a researcher sets the alpha level at .05 and obtains a p-value of .06, it means that the p-value is greater than the chosen significance level. The alpha level, also known as the significance level, represents the threshold for determining whether the results are statistically significant or not.

In hypothesis testing, the null hypothesis assumes that there is no significant difference or relationship between variables.

If the p-value is less than or equal to the alpha level, it suggests that there is enough evidence to reject the null hypothesis and conclude that there is a significant difference or relationship.

However, if the p-value is greater than the alpha level, as in this case with a p-value of .06, it means that the observed data does not provide sufficient evidence to reject the null hypothesis.

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According as per the given information line w y is dilated to created line w prime y prime. the length of q w is 2 and the length of w w prime is 3.5 the scale factor is 1.75.

To find the scale factor, we can compare the lengths of corresponding line segments before and after dilation.

Given:

Length of QW = 2

Length of WW' = 3.5

The scale factor (k) can be calculated as:

k = Length of WW' / Length of QW

Substituting the values:

k = 3.5 / 2

k = 1.75

Therefore, the scale factor is 1.75.

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Answer:

If the perimeter = 300m

let the ratio be in x

a/q.

3x + 5x + 7x. = 300m

15x = 300

x = 300/15

x = 20

hence angles are

60 , 100 and 140

hope it helps

Answer:

A ≈ 1500\(\sqrt{3}\) m²

Step-by-step explanation:

sum the parts of the ratio, 3 + 5 + 7 = 15 parts

Divide perimeter by 15 to find the value of one part of the ratio.

300 ÷ 15 = 20 m ← value of 1 part of the ratio , then

3 parts = 3 × 20 = 60 m

5 parts = 5 × 20 = 100 m

7 parts = 7 × 20 = 140 m

The 3 sides of the triangle are 60 m, 100 m , 140 m

To calculate the area (A) having all 3 sides use Hero's formula

A = \(\sqrt{s(s-a)(s-b)(s-c)}\)

where s is the semiperimeter and a, b , c the sides of the triangle

s = 300 m ÷ 2 = 150 m

let a = 60, b = 100 and c = 140 , then

A = \(\sqrt{150(150-60)(150-100)(150-140)}\)

   = \(\sqrt{150(90)(50)(10)}\)

   = \(\sqrt{6750000}\)

   = \(\sqrt{10000}\) × \(\sqrt{675}\)

   = 100 × \(\sqrt{25(27)}\)

    = 100 × 5\(\sqrt{27}\)    

    = 500 × \(\sqrt{9(3)}\)

   = 500 × 3\(\sqrt{3}\)

   = 1500\(\sqrt{3}\) m²

A polygon with 6 angles is called hexagon

The regular hexagon is a convex polygon with six equal sides and six equal angles, always divided into symmetric or asymmetric triangles. It is closely related to equilateral triangles: By joining each vertex with its opposite, the regular hexagon is divided into six equilateral triangles.

The sum of the interior angles of a hexagon is 720°

Sum of Interior Angles = (n-2) x 180°

Sum of Interior Angles = (6-2) x 180°

Sum of Interior Angles = 4 x 180°

Sum of Interior Angles = 720°

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

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Infinitely many position vectors with length 2 in xyz-space are orthogonal to the nonzero position vector v. (D)

A position vector in xyz-space is a vector that starts at the origin and ends at a point in xyz-space. The length of a position vector is the distance from the origin to the point it ends at.

If we want to find position vectors with length 2 that are orthogonal (perpendicular) to a given nonzero position vector v, we can use the dot product.

Let w be a position vector with length 2 that is orthogonal to v. Then, the dot product of v and w must be zero, since they are orthogonal. That is, v · w = 0. Since the length of w is 2, we can write w as 2u for some unit vector u. Thus, v · w = v · (2u) = 2(v · u) = 0.

This means that v and u are orthogonal as well, since the dot product of two vectors is zero if and only if they are orthogonal.

There are infinitely many unit vectors u that are orthogonal to v, and therefore, there are infinitely many position vectors with length 2 that are orthogonal to v. Therefore, the answer is (d) infinitely many.

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Answer:

4/3.28

Step-by-step explanation:

Answer:

4/3.28

Step-by-step explanation:

The final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them.

Let's clarify the itinerary for the 15-day tour visiting 5 national parks.

You have a 15-day tour, and you plan to visit 5 national parks. Each park will have a stay of two days.

When you multiply the number of parks (5) by the number of days spent in each park (2), you get a total of 10 days allocated for staying in those 5 parks.

However, there seems to be a discrepancy in the calculation because allocating 10 days for park stays leaves only 5 days remaining, not 15.

To resolve this issue and ensure a 15-day tour, we need to reevaluate the itinerary. Let's assume you want to spend two days at each park, which gives you a total of 10 days for park stays.

To fill the remaining 5 days, you have a few options:

1. Travel Days: You can allocate a day for travel between each park, which would require an additional 4 days. This accounts for the transportation time and allows you to enjoy the journey between the parks.

2. Additional Park Visits: If there are other nearby national parks or attractions in the area, you can extend your tour to include visits to these places. This would allow you to explore more diverse locations and make the most of your 15-day tour.

3. Rest and Relaxation: Alternatively, you might choose to use the extra days for relaxation or leisure activities. You can spend some time enjoying the amenities and attractions available near the parks, such as hiking trails, wildlife observation, or local cultural experiences.

Ultimately, the final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them. Make sure to consider travel times, desired activities, and any additional locations you wish to explore when creating your 15-day tour.

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Answer:

34.0522° N, 118.2437° W

Step-by-step explanation:

Answer:

The bench costs $425

Step-by-step explanation:

First lets define our variables:

t = garden table

b = bench

Next, we have to use the information to create two formulas. One formula is for the cost of a garden table and a bench. The second is for the cost of the garden table.

t + b = 755

t = b - 95

For the next step, we can solve for be by using the second formula we created and replacing (t) in the first formula:

b - 95 + b = 755

2b - 95 = 755

2b = 850

bench = 425

To find out how much the cost of the cost of the table is, you can plug in the cost of the bench (b) back into the second equation:

t = b - 95

t = 425 - 95

table = 330

I hope this helps!

-TheBusinessMan

a) To find the elements of the set \(XY\), we need to concatenate each element of \(X\) with each element of \(Y\  b) To list the elements of \(X^*\) of length 4 or less, we need to consider all possible combinations of elements from \(X\) with repetition.

Since the maximum length is 4, we can have elements with lengths 1, 2, 3, or 4. The elements of \(X^*\) are:

where ε represents the empty string.

c) To provide a regular expression for \(X^*\), we can represent the elements of \(X^*\) using the alternation operator \(+\). The regular expression for \(X^*\) is:

This regular expression matches any combination of elements from \(X\) including the empty string.

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