The change in water level of a lake is shown in the table. How much did the water level change between Weeks 2 and 3?

If the measure of the angle ∠RQT is 125°. Then the measure of the angles ∠RQS and ∠SQT will be 44° and 81°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

If the measure of the angle ∠RQT is 125°. Then the measure of the angles ∠RQS and ∠SQT will be

Then we have

      ∠RQS + ∠SQT = 125°

(3x - 10)° + (4x + 9)° = 125°

                      7x - 1 = 125°

                          7x = 126°

                            x = 18°

Then the measure of the angle ∠RQS will be

∠RQS = 3 × 18 - 10

∠RQS = 44°

Then the measure of the angle ∠SQT will be

∠SQT = 4 × 18 + 9

∠SQT = 81°

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From the graph, we have the amount of water (in liters) on the y-axis and the time (in minutes) on the x-axis

a)

To obtain the amount of water at zero minutes, we will trace the y-value that corresponds with the value of zero on the x-axis: we will see this to be 270 liters

Therefore, at time zero minutes, the amount of water is 270 liters

b)

We will answer this by picking two points that lie along the straight line and calculate the slope. We pick the points:

We will proceed to calculate the slope as shown below:

The slope is -90 liters per minute.

The negative sign (-) means that as time increases, the amount of water in the aquarium decreases

The water decreases at a rate of 90 liters per minute

Answer:

8p∧2 ± p - 1 ± 13/p ± 1

Step-by-step explanation:

Divide (9p2 + 8p3 + 12) ÷ (p + 1) and it equals 8p∧2 ± p - 1 ± 13/p ± 1

Answer:

8p^2+p-1 with a remainder of 13

Step-by-step explanation:

p+1 divided by 8p^3+9p^2+0p+12

It is false, that the margin of error of a confidence interval is the error from biased sampling methods.

The margin of error of a confidence interval is the amount of accuracy in a sample with respect to the population. It is calculated by taking the sample standard deviation and dividing it by the square root of the sample size. The margin of error helps to quantify the reliability of estimates and provides a range within which the population parameter is likely to fall. It does not refer to errors in sampling methods, which are typically a result of bias. Bias is a systematic error that arises from the sampling procedure, resulting in estimates that are not an accurate representation of the population.

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Step-by-step explanation:

Substitute y = 4 into the first equation:

\(4=2x^2+x-6\)

Subtract 4 from both sides:

\(2x^2+x-10=0\)

We can factor in order to find values of x.

Factor the equation:

\(2x^2+x-10=0\)

Factors of 10 we'll use:

5 and 2.

\((2x+5)(x-2)=0\)

Set the parentheses equal to 0 then find the values of x:

\((2x+5)=0\)

\(x=-2\frac{1}{2}\)

\((x-2)=0\)

\(x=2\)

\(x=2, \: or \: -2\frac{1}{2} .\)

Check:

\(4=2(2)^2+2-6\)

\(4=2(4)+2-6\)

\(4=4 \: \checkmark\)

\(4=2(-2\frac{1}{2} )^2-2\frac{1}{2} -6\)

\(4=2(6\frac{1}{4})-2\frac{1}{2} -6\)

\(4=12\frac{1}{2} -2\frac{1}{2} -6\)

\(4=10-6\)

\(4=4 \: \checkmark\)

Answer:

A. x = 75

Step-by-step explanation:

if two triangles are similar then we will be able to write the following equation:

YJ/LM = JK/KL

x/30 = 125/50 cross multiply expressions

50x = 3.750 divide both sides by 50

x = 75 is the value of x that proves the triangles are similar.

Answer:

13 × 10 = 130 ( it's a rectangle)

5² π /2 ≈ 12.5 × 3.14 = 39.25 ( semicircle)

130 + 39.25 = 169.25 ≈ 170

Answer:

B?

Step-by-step explanation:

Answer:

21.28

Step-by-step explanation:

Hey There!

So the law of sines says

\(\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}\)

To solve for c we just plug in the values that are given to us

\(\frac{25}{sin38} =\frac{c}{sin31.6}\)

step 1 multiply each side by sin31.6

now we have

\(c=\frac{25sin31.6}{sin38} \\c=21.2773548\)

assuming that you have to round

if you're supposed to round to the nearest whole number then the answer is 21

if you're supposed to round to the nearest tenth then the answer is 21.3

if you're supposed to round to the nearest hundredth then the answer is 21.28

Answer:

B. 17

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

We have a and b, so:

8² + 15² = c²

c = √(8² + 15²)

c = 17

And we have our final answer!

Answer:

To find the length of BC we use Pythagoras theorem.

BC² = AB² + AC²

AB = 8 AC = 15

BC² = 8² + 15²

BC = √64 + 225

BC = √ 289

BC = 17

BC is 17

Hope this helps.

The rate of change in the profit for the five months earned by the given small business is $2750.

The rate of change explains the relationship between two quantities.

Consider two quantities such profit and time in a small business.

Then, the rate of change in the profit is calculated by the ratio of change in the profit for the particular period to the time. I.e.,

rate of change in the profit = (change in the profit)/time

or

r = (p2 - p1)/(t2 - t1)

Where p1 is the profit gained at time t1 and p2 is the profit gained at time t2.

Given that, a small business earns a profit of $6500 in January (the first month of the year) and $17,500 in May (the fifth month of the year).

So, here p1 = $6500; p2 = $17,500; t1 = 1; and t2 = 5

Then, the rate of change in the profit for this period is

r = (17,500 - 6500)/(5 - 1)

 = 11000/4

 = 2750

Therefore, the rate of change in the profit for the five months is $2750.

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Answer:

To find the width of the garden, we need to use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we know the length is 1 yard and the area is 5 square yards. We can substitute these values into the formula and solve for the width:

5 = 1 x width

width = 5/1

width = 5

Therefore, the garden should be 5 yards wide.

After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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Answer:

33578

Step-by-step explanation:

3% of 32600

= 3/100 x 32600

= 97800/100

=978

original price + increase in price = 32600 + 978 = 33578

We can use a priority queue to keep track of the k most frequent strings. The priority queue should be sorted by the frequency of the strings, and in case of ties, we should sort by lexicographical order.

Here's the step-by-step algorithm to solve the problem:

1. Create a hash map to count the frequency of each string in the array.
2. Create a priority queue and define a custom comparator function that compares strings based on their frequency and lexicographical order.
3. Iterate over the keys of the hash map and add each string to the priority queue.
4. Pop the top k strings from the priority queue and add them to the result array.
5. Return the result array sorted in descending order of frequency.

Here's the Python code that implements this algorithm:

```
import heapq
from collections import defaultdict

def topKFrequent(words, k):
   freq = defaultdict(int)
   for word in words:
       freq[word] += 1
   
   pq = []
   for word, count in freq.items():
       heapq.heappush(pq, (-count, word))
   
   res = []
   for i in range(k):
       res.append(heapq.heappop(pq)[1])
   
   return sorted(res, key=lambda x: (-freq[x], x))
```

In this code, we use a defaultdict from the collections module to count the frequency of each string. We then use a heap (implemented as a list) to keep track of the k most frequent strings. The -count value is used as the first element of each tuple in the heap, so that we can sort the strings by frequency in descending order. The second element of each tuple is the string itself, which is used to break ties in case of equal frequency. Finally, we sort the result array based on the frequency and lexicographical order using the sorted function and a lambda function.

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Step-by-step explanation:

Use Distributive Property:

y + 1 = 4/5x - 2.4

Subtract 1 from both sides:

y = 4/5x - 3.4

Your Slope-intercept form equation is y = 4/5x - 3.4

Slope-intercept form: y = mx + b

m = slope

b = y-intercept

The vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

To determine if the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly independent, we need to find the scalars a, b, and c that satisfy the equation:

a * [-5 4 5] + b * [2 -1 5] + c * [-17 16 45] = [0 0 0]

If the only solution is a = b = c = 0, the vectors are linearly independent. If there are other solutions where a, b, and c are not all zero, the vectors are linearly dependent.

Let's form a matrix with these vectors as columns:

|-5  2 -17|
| 4 -1  16|
| 5  5  45|

Now, we can row reduce this matrix to its reduced row echelon form (RREF):

| 1 -2  5|
| 0  1 -3|
| 0  0  0|

From the RREF, we can write the system of linear equations:

x - 2y + 5z = 0
y - 3z = 0

Solving this system, we get:

y = 3z
x = 2y - 5z = 6z - 5z = z

Since z can be any scalar, we have infinitely many solutions where not all of a, b, and c are zero. For example, when z = 1, we get x = 1 and y = 3. So, the scalars (1, 3, 1) make the equation true.

Thus, the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

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A real estate agent has 17 properties that she shows,  the probability of selling no more than 3 properties in one week is 0.0464 or 4.64%.

There are only two possible outcomes for each attribute. Selling one home does not affect the likelihood of selling another. Therefore, to answer this query, we employ the binomial probability distribution.

Binomial probability distribution

The probability of precisely x successes on n repeated trials is known as a binomial probability, and X can only have two possible outcomes.

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

Given by the following formula.

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

And p is the probability of X happening.

n = 17

P = 0.4

P(X≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

In which,

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

\(P(X=x) = C_{n} , x.P^x.(1-P)^{n-x}\\P(X=0) = C_{17} ,0.(0.4)^0.(0.6)^{17} = 0.0002\\P(X=1) = C_{17} ,1.(0.4)^1.(0.6)^{16}=0.0019\\P(X=2) = C_{17} ,2.(0.4)^2.(0.6)^{15}=0.0102\\P(X=3) = C_{17} ,3.(0.4)^3.(0.6)^{14}=0.0341\)

P(X≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.0002 + 0.0019 + 0.0102 + 0.0341  = 0.0464

Therefore probability of selling no more than 3 properties in one week is 0.0464 or 4.64%.

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Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

The largest interval over which the general solution is defined is (-∞, +∞). There are no transient terms in the general solution, so the answer is NONE.

To find the general solution of given differential equation, we'll solve it using an integrating factor. The given differential equation is:

y' + 7x^6y = x^6

Identify the form of the equation as y' + P(x)y = Q(x), where P(x) = 7x^6 and Q(x) = x^6.

The integrating factor is given by IF = e^(∫P(x)dx). In this case, P(x) = 7x^6, so the integrating factor is:

IF = e^(∫7x^6dx) = e^(7/7 * x^7) = e^(x^7)

Multiply the original equation by integrating factor:

e^(x^7)(y' + 7x^6y) = e^(x^7)(x^6)

Simplify and integrate both sides:

e^(x^7)y + 7∫(x^6e^(x^7))dx = ∫(x^6e^(x^7))dx

The integral on the right side can be evaluated to find a particular solution. For the left side, we have:

e^(x^7)y = ∫(x^6e^(x^7))dx

Let u = x^7, du = 7x^6dx

∫(x^6e^(x^7))dx = (1/7)∫e^udu = (1/7)e^u + C1 = (1/7)e^(x^7) + C1

Substituting this back into the equation:

e^(x^7)y = (1/7)e^(x^7) + C1

Solve for y:

y = (1/7) + C1e^(-x^7)

Therefore, the general solution to the differential equation is:

y(x) = (1/7) + C1e^(-x^7)

The largest interval over which the general solution is defined is (-∞, +∞) since there are no singular points or restrictions specified.

So, the answer is NONE.

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Based on the results of the American Management Association/ePolicy Institute Survey on electronic monitoring and surveillance, companies reported that they had dismissed 30% of workers for misusing the Internet.

The survey conducted by the American Management Association/ePolicy Institute found that among the companies surveyed, 30% reported that they had dismissed employees for Internet misuse. This suggests that companies are taking Internet security seriously and are willing to take action against employees who violate company policies related to Internet use. It also highlights the importance of having clear policies in place to guide employees on appropriate Internet use to avoid potential security risks and the negative consequences that can result from misuse.

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The equation of the plane tangent to the given surface at the point (0,-2,-4) is given by:
2x + 8y + 16z = -192.

To derive this equation, let's first recall the general equation of a plane, which is given by ax + by + cz + d = 0.
Since the plane is tangent to the surface, the plane passes through the given point (0,-2,-4). Substituting these values in the general equation of a plane, we get:

0 + 8(-2) + 16(-4) + d = 0

Solving for d gives us d = 192. Substituting this value in the general equation of a plane, we get:

ax + by + cz + 192 = 0

Since the given surface is given by yze^(xz)-8 = 0, we can calculate the partial derivatives of the given surface w.r.t. x, y, and z. This gives us:

2x + 8y + 16z = 0

Adding 192 to both sides gives us the required equation of the plane, which is 2x + 8y + 16z = -192.

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We have to indicate the steps to follow in order to evaluate:

(12.9-3.1) x 6.2-2 + 43

So FIRST: we solve for the operation indicated inside the parenthesis

12.9 - 3.1 = 9.8 (we subtract 3.1 from 12.9)

This is the answer you need to select.

Answer:

27 :)

Step-by-step explanation:

$27 it D

Step-by-step explanation:

With this query, no effort is necessary. measure the tbsp. of all items.

A great source of both phosphorus and calcium, which are essential for the growth and upkeep of strong, strong teeth and bones, is milk. They lower the chance of developing osteoporosis and suffering broken bones later in life. Milk encourages strong bones.

1. Measure \(8\) tbsp. chocolate sauce and add \(2\frac{1}{2}\) cups of milk.

No work is required for this question. It is a simple instruction to measure out 8 tbsp. of chocolate sauce and add it to \(2\frac{1}{2}\) cups of milk.

2. Start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. chocolate sauce.

No work is required for this question. It is a simple instruction to start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

3. Add \(3\frac{1}{3}\) tbsp. chocolate sauce to \(1\frac{1}{4}\) cups milk.

No work is required for this question. It is a simple instruction to add  \(3\frac{1}{3}\)tbsp. of chocolate sauce to \(1\frac{1}{4}\) cups of milk.

4. For every 1 cup of milk add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

No work is required for this question. It is a simple instruction to add \(2\frac{1}{2}\) tbsp. of chocolate sauce for every \(1\) cup of milk.

5. Stir \(1\) tbsp. chocolate sauce into \(\frac{2}{3}\) cup milk.

No work is required for this question. It is a simple instruction to stir 1 tbsp. of chocolate sauce into \(\frac{2}{3}\) cup of milk.

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Answer:

1.6

So one whole orange and a sixth of another orange

Step-by-step explanation:

Nominal wage changes have no impact on the economy's output in the long run. The long-run equilibrium output is determined by factors such as technology, productivity, and the availability of resources. Nominal wages alone do not directly affect the economy's output in the long run.

In the long run, the economy reaches a state of equilibrium where the aggregate price level and real GDP stabilize. The long-run aggregate supply (LRAS) curve represents the level of output that can be sustained without causing inflationary or deflationary pressures. It is determined by factors such as the available resources, technology, and productivity.

Nominal wages refer to the wages stated in current dollars, without adjusting for inflation. While changes in nominal wages can affect the distribution of income and purchasing power in the short run, they do not impact the economy's output in the long run. This is because nominal wage changes do not alter the underlying factors that determine the economy's productive capacity and potential output.

Therefore, the correct answer is that nominal wages have no impact on output in the long run. The long-run equilibrium level of output is determined by factors beyond nominal wage changes, such as technology, productivity, and the availability of resources.

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Answer:

 distance divided by rate = time aka D/R=T

Step-by-step explanation:

this is what i learned at least hope it helps

The equation that represents the distance traveled by the car is equal to d = 50 x t.

To calculate the speed of an object, it is necessary to relate the distance traveled and the time required to travel that distance, so that:

                                                \(V = \frac{d}t}\)

Thus, as we are given the value of a velocity and if we are asked for the expression that represents the distance traveled depending on the time, we have:

                                        \(50 miles/hour = \frac{d}{t}\)

                                             \(d = 50 \times t\)

So, the equation that represents the distance traveled by the car is equal to d = 50 x t.

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There are 8.0658 × \(10^{67}\) more form to shuffle a deck of cards than atoms.

What is the factorial?

Factorial is an important function, which is used to find how many ways things can be arranged or the ordered set of numbers.The factorial of a whole number is the function that multiplies the number by  number below it.

The number of ways to shuffle a deck of cards is astronomically large, far greater than the estimated number of atoms in the observable universe.

A standard deck of 52 playing cards can be arranged in 52 factorial ways, denoted as 52!. This means multiplying all the positive integers from 1 to 52 together:

52! = 52 × 51 × 50 × ... × 3 × 2 × 1=8.0658 × \(10^{67}\).

Therefore,the exact value of 52! is an  large number, approximately equal to 8.0658×\(10^{67}\).

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