Is the ordered pair (4,1) a solution of the system of linear equations:
-x + y = -3
x + 3y = 6
a. yes
b. no

The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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Answer:

27

Step-by-step explanation:

a and c is the answer.

as you have studied in lower standard.

Answer:

X=87.5 and the equation is 0.40/x=35

Step-by-step explanation:

To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

The equations that represent the relationship between the two angles is:

x = 2(y + z) - 60

x = 2z + 20

We are given the parameters as:

x is the largest angle.

y is the next largest angle

z is the smallest angle.

The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles. Thus:

x = 2(y + z) - 60

The largest angle is twice the smaller angle plus 20 degrees. Thus:

x = 2z + 20

x + y + z = 180

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Answer:

10 or 5

Step-by-step explanation:

I think 10

Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

⭐What is the Pythagoras' Theorem?

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

\((C)^2 = (A)^2 + (B)^2\)

\(26^2 = 24^2 + B^2\)

\(676 = 576 + B^2\)

\(100 = B^2\)

\(\sqrt{100} = \sqrt{(B)^2}\)

\(10 = B\)

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

Answer:

Just input sin(9), sin(30), sin(81), etc.

For this set, you need a scientific calculator or else, you won't be able to answer that. There is a way but that is already obsolete now.

The value of the missing length to the nearest tenth are;

a. x = 7.5

b. x = 7.8

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore ;

c² = a²+b²

a. x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = 7.5 ( nearest tenth)

b. using Pythagoras theorem also!

x² = 6²+5²

x² = 36+25

x² = 61

x = √61

x = 7.8( nearest tenth).

Therefore the value of the missing values are 7.5 and 7.8

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\(x^{2} +x^{2} =9^{2} \iff 2x^{2} = 81\)

\(x^{2} = \dfrac{81}{2} \iff x = \sqrt{\dfrac{81}{2}} \iff x = \dfrac{9}{\sqrt{2} }\\\)

\(\implies x = \dfrac{9\sqrt{2} }{2}\\\)

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

The median is the average of the two middle values: (334 + 448) / 2 = 391.

the third quartile is 391 lb.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.

To find the first and third quartile, we need to first arrange the data in ascending order:

132, 183, 191, 237, 251, 277, 279, 334, 448, 599

The median of the entire data set is the value that separates the lower 50% of the data from the upper 50% of the data. In this case, the median is the average of the two middle values:

(251 + 277) / 2 = 264

Next, we need to find the median of the lower half of the data set (also known as the first quartile). We can see that the lower half of the data set is:

132, 183, 191, 237, 251

The median of this data set is the value that separates the lower 50% of this half of the data from the upper 50% of this half of the data. In this case, the median is the average of the two middle values:

(191 + 237) / 2 = 214

So the first quartile is 214 lb.

Finally, we need to find the median of the upper half of the data set (also known as the third quartile). We can see that the upper half of the data set is:

277, 279, 334, 448, 599

The median of this data set is the value that separates the lower 50% of this half of the data from the upper 50% of this half of the data. In this case, the median is the average of the two middle values:

(334 + 448) / 2 = 391

So the third quartile is 391 lb.

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Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

f'(x) = 4 + 80x³

General Formulas and Concepts:

Calculus

The definition of a derivative is the slope of the tangent line.

We can take the derivative/distribute it over addition and subtraction.

Basic Power Rule:  

Step-by-step explanation:

Step 1: Define function

f(x) = 4x + 20x⁴

Step 2: Find 1st derivative

The surface area of the object is 280 square inches.

To find the surface area of this object, we need to find the area of each of its faces and add them up. Since the object has different dimensions for each face, we need to calculate each face's area separately.

First, we identify the dimensions of each face:

Face 1: 6 in x 6 in

Face 2: 8 in x 8 in

Face 3: 2 in x 6 in

Face 4: 9 in x 8 in

Face 5: 2 in x 6 in

Face 6: 9 in x 6 in

Face 7: 5 in x 6 in

Then, we calculate the area of each face:

Face 1: 6 in x 6 in = 36 sq in

Face 2: 8 in x 8 in = 64 sq in

Face 3: 2 in x 6 in = 12 sq in

Face 4: 9 in x 8 in = 72 sq in

Face 5: 2 in x 6 in = 12 sq in

Face 6: 9 in x 6 in = 54 sq in

Face 7: 5 in x 6 in = 30 sq in

Finally, we add up the areas of all seven faces:

36 + 64 + 12 + 72 + 12 + 54 + 30 = 280 sq in

Therefore, the surface area of the object is 280 square inches.

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A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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Answer:

124

Step-by-step explanation:

A supplementary angle is 180

180-56=124

Answer:

d

Step-by-step explanation:

Any 3 digit number can be expressed in the form of:

\((a*100)+(b*10)+(c*1)\)

Where \(a, b, c\) represent any natural number from 0 to 9.

We are told the hundreds number (this means \(a*100\) in the expression above) is equal to the value of 40 tens, 40 tens is 400. Then, we know the digit in the tens is greater then 6, this means \(b>6\) in the expression above.

So, there are multiple numbers the room number could be, namely:

\(400+(b*10)+(c*1)\\\)

where \(b\) can be 7, 8, or 9; and \(c\) can be  0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So, there's 30 possible room numbers Lydia may be.

Given statement solution is :- The manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

To determine if the manager will have enough funds to cover the nightly payroll for the next four weeks, we need to calculate the total cost for four weeks and compare it to the amount set aside.

The nightly payroll has a mean of $2200 and a standard deviation of $300. Since there are seven nights in a week, the weekly payroll can be calculated as:

Weekly Payroll = Nightly Payroll * Number of Nights in a Week

= $2200 * 7

= $15,400

To calculate the total cost for four weeks, we multiply the weekly payroll by four:

Total Cost for Four Weeks = Weekly Payroll * Number of Weeks

= $15,400 * 4

= $61,600

Now, let's calculate the z-score using the formula:

z = (X - μ) / σ

Where:

X = Total Cost for Four Weeks

μ = Mean of the distribution

σ = Standard deviation of the distribution

z = ($61,600 - $2200) / $300

z = $59,400 / $300

z ≈ 198

To determine if the manager will have enough funds to cover the payroll, we need to find the proportion of the distribution that is less than or equal to the z-score. This can be done by consulting a standard normal distribution table or using statistical software.

For a z-score of 198, the proportion in the tail of the distribution is essentially 1 (or 100%). This means that the manager is virtually guaranteed to have enough funds to cover the payroll for the next four weeks.

Since the manager has set aside $10,000, which is less than the calculated total cost of $61,600, he will indeed have enough funds to cover the payroll.

Therefore, the manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

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Answer:-1/6

Step-by-step explanation:

Draw a line out in the 2nd quadrant.

Your y=\(\sqrt{35}\)    hypotenuse=6  use pythagorean theorem to solve for x

6² = 35 + x²

x=1

so

cosΘ = -1/6

Answer:

The ratio of the width to the length is;

Explanation:

Given that the cell phone has the dimension;

The ratio of the width to the length is;

Therefore, the ratio of the width to the length is;

Answer:

B. 8 x 12

Step-by-step explanation:

First of all, it has an area of 96

So lets find the multiplication pair that equals 96.

10 x 10 = 100        NO

6 x 16 = 96           YES

8 x 12 = 96           YES

Now we have two equations: 8 x 12 and 6 x 16

Perimeter of 40 means:

2(a+b) = 40

Lets input the two equations:

2(8+12) = 2 x 20 = 40

2(6+16) = 2 x 22 = 44

So the dimensions that works is 8 x 12

If my answer is incorrect, pls correct me!

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-Chetan K

To calculate the total surface area of a triangular prism, we need to find the area of each face and add them up.

The triangular faces have base 5cm and height 12cm, so each one has an area of:

(1/2) x 5cm x 12cm = 30cm²

There are two of these faces, so their combined area is:

2 x 30cm² = 60cm²

The rectangular faces have dimensions 5cm x 10cm and 5cm x 13cm, so their areas are:

5cm x 10cm = 50cm²

5cm x 13cm = 65cm²

Again, there are two of these faces, so their combined area is:

2 x (50cm² + 65cm²) = 230cm²

Finally, we add up the areas of all the faces to get the total surface area:

60cm² + 230cm² = 290cm²

Therefore, the total surface area of this triangular prism is 290cm².

Answer:

705.81 and 705.810

Step-by-step explanation:

700 + 5 + 0.8 + 0.01 = 705.81

Answers:

705.810

705.81

Answer:

The differences become smaller

Step-by-step explanation:

Normally, we use the t-distribution table rather than the normal distribution when the population standard deviation is unknown and when the sample size is small i.e. less than 30.

Now, as the sample size gets bigger, we will be getting closer to the point where we have to use the normal distribution.

This means that as the sample size increases, the values of the t-distribution will be getting close to that of the normal distribution because normal distribution is used when sample is more than 30.

For example the t-value for a sample of 25 people would be closer to the normal distribution value for a sample of 35 people while a t-value for a sample of 15 people will be far away from the normal distribution value for a sample of 35 people.

Thus, as the sample size increases, the differences between the t-distribution and standard normal distribution becomes smaller.

1. <C= 90 degree

AC =  13.25 unit

<B= 60 degree

2.  <C= 90 degree

AC =  13.

<B= 60 degree

1. Using Sine law

sin C/4 = sin 30/2 = sin B/ AC

so, sin C/4 = 1/4

sin C = 1

C= 90 degree

and, <B= 180 - 30- 90= 60 degree

So, sin 30/2 = sin 60/ AC

1/4 AC = √3/2

AC = 2√3

2. Using Sine law

sin 30/ 7.65 = sin B / 15.3

1/15.3 = sin B/15.3

sin B= 1

B = 90 degree

and, <C= 180 - 90 - 30 = 60

So, 1/15.3 = sin 60/ C

C = 13.25

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\(p(t)=1650e^{0.11t}\implies \stackrel{p(t)}{2479}=1650e^{0.11t}\implies \cfrac{2479}{1650}=e^{0.11t} \\\\\\ \log_e\left( \cfrac{2479}{1650} \right)=\log_e\left( e^{0.11t} \right)\implies \log_e\left( \cfrac{2479}{1650} \right)=0.11t \\\\\\ \ln\left( \cfrac{2479}{1650} \right)=0.11t\implies \cfrac{ ~~ \ln\left( \frac{2479}{1650} \right) ~~ }{0.11}=t\implies 3.7\approx t\)

at that moment, the population will reach 2479, and right after that, it'll exceed it.