suppose that p(n) is a propositional function. determine for which positive integers n the statement p(n) must be true, and justify your answer, if

Answer:

0.8r

Step-by-step explanation:

r - 0.2r = 1r - 0.2r = (1 - 0.2)r = 0.8r

Answer:

0.8r

Step-by-step ex

took test

I don't know for certain if you are trying to write this in standard form, graph it, or so forth. However, here is the standard form.

Standard Form:

\((x+2)^2+(y-2)^2=36\\\)

Hope this helps you!

Answer:

below

Step-by-step explanation:

A triangle can only be a triangle if the two shortest sides add up to be greater than the longest side.

For example on the first one, the segments 1 2 and 3 will not make a triangle as 1 + 2 = 3 and if the two smallest sides of a triangle are equal to the longest side it will not be a triangle at all.

So to make this easy, out of the three numbers given: add the two smallest numbers. This number has to be greater than the third number given, and it cannot be equal.

For question three: 3+9 = 12

And 12 is greater than 11, therefore this can make a triangle.

The percent error of the measurement, to the nearest tenth of a percent, is 5.6.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

John measured a line to be 1.7 inches long.

The actual length of the line is 1.8 inches.

The amount of error = 1.8 - 1.7

The amount of error = 0.1

Let 1 - n be the required percentage of error.

Then applying the percentage formula,

1.8 x n /100 = 1.7

Applying cross multiplication,

we get,

1.8n = 170

n = 170/1.8

n = 94.4

So, 1 - n = 100 - 94.4 = 5.6

Therefore, the percentage is 5.6.

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A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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Point D is the centroid of ΔABC, since we know that A.F, BC, and CE are all medians.

A median of a triangle is the line segment that connects the vertex of a triangle to the midpoint of the opposite side. There are usually three medians of a triangle.

The point where the three medians of a triangle intersect each other or meet at is referred to as the centroid of the triangle.

The diagram shows a triangle with three medians that meets at point D in the triangle. Therefore, point D is the centroid of the tringle because lines A.F, BC, and CE are all medians of the given triangle.

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The solution to lim h→0 (9 + h)−1 − 9−1 h is -1/9.

To find the solution to lim h→0 (9 + h)−1 − 9−1 h, we can simplify the expression first.

Starting with (9 + h)−1, we can use the formula for the difference of squares to get:

\((9 + h)-1 = (9 + h - 9) / ((9 + h)(9 - 9)) = h / (9h + h^2)\)
Substituting this back into the original expression gives:

\((9 + h)-1 -9-1 h = h / (9h + h^2) - 1 / 9h\)

We can combine the two fractions by finding a common denominator of 9h(9 + h), giving:

(9h - (9 + h)) / (9h(9 + h)) = -1 / (9 + h)

Now we can take the limit as h approaches 0:

lim h→0 (9 + h)−1 − 9−1 h = lim h→0 -1 / (9 + h) = -1 / 9

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Answer:

(9,36)

Step-by-step explanation:

Substitute the 4x for the y in second equation.

Basically setting them equal to each other because the both have 'y='

4x = 8x - 36

-4x  = -36 (subtract 8x from both sides)

x = 9         (divide by -4, both sides)

y = 4(9)     (Substitute the x value into first equation)

y = 36

Answer:

c+10+2c+c=220

Step by step Explanation:

Let, a= number of adult's tickets sold

s= number of senior's tickets sold

c= number of children's tickets sold

a=c+10

and, s=2c

Now, a+ s+ c=220

c+10+2c+c=220

4c=210

c=52.5

Note: If there were 222 tickets the answer will be 53

We conclude that less than 30% of teen girls smoke to stay thin.

Let p be the percentage of teen girls who smoke to stay thin.

So, the Null Hypothesis,(\(H_{0}\)):

p≥ 30%

This means that at least 30% of teen girls smoke to stay thin

Alternate Hypothesis,(\(H_{A}\)) :

p < 30%

This means that less than 30% of teen girls smoke to stay thin.

The test statistics that would be used here

One sample z proportion statistics:

T.S = p' - p/ \(\sqrt{p'(1-p')/n}\) ≈N( 0,1)

Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231

n = number of sample of teen girls = 273

Now putting these values we have:

Test statistics = 0.231 - 0.30/ \(\sqrt{0.231( 1- 0.231)/ 273}\)

                      = -2.705

So we get the value of z-test statistics as - 2.705.

As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.

As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore we get that less than 30% of teen girls smoke to stay thin.

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Answer:

(a) Let x be the number of weeks and let y be the total amount in their savings accounts. Then, the system of equations that represents the scenario is:

Kevin: y = 25x + 500

Janet: y = 50x + 250

(b) To determine after how many weeks Kevin and Janet will have the same amount of savings, we need to solve the system of equations by setting them equal to each other:

25x + 500 = 50x + 250

Subtracting 25x and 250 from both sides, we get:

250 = 25x

Dividing both sides by 25, we get:

x = 10

Therefore, Kevin and Janet will have the same amount of savings after 10 weeks. To find out what that amount is, we can substitute x = 10 into either equation:

y = 25x + 500

y = 25(10) + 500

y = 750

So after 10 weeks, both Kevin and Janet will have $750 in their savings accounts.

Step-by-step explanation: explained it in the answer

Answer:

LCD = 24

Equivalent Fractions with the LCD

1 1/2

=

36/24

3/8

=

9/24

5/6

=

20/24

3

=

72/24

Answer:

x > -2

Step-by-step explanation:

Answer:

Please see the attached image below for explanation.

The area of the sector is evaluated to be equal to 9π square meters

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For the area of circle 72π m²;

πr² = 72π m²

r² = 72 m²

hence the area of the sector is calculated as follows:

area of the sector = (45°/360°) × π × 72 m²

we simplify by multiplication and division

area of the sector = 1/8 × π × 72 m²

area of the sector = π × 9 m²

area of the sector = 9π m².

Therefore, the area of the sector is evaluated to be equal to 9π square meters

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Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

Step-by-step explanation:

The line representing the equation 7x1 + 4x2 = 28 goes through the points (4,0) and (0,7).

The mass of the wire is \($\frac{\pi}{2}$\)

Given the equation of the wire as \($x^2 + y^2 = 4$\) and the radius of the semicircle as 2, with \($\sigma$\) representing the density of the wire (given by y), we need to find the mass of the wire using integration. The formula for mass is given by:

\(\[ \text{Mass} = \int_{b}^{a} \sigma(x, y) \, ds \]\)

We can parameterize the semicircle as follows:

\(\[ x = 2 \cos(t) \quad y = 2 \sin(t) \quad \text{where } t \in [0, \frac{\pi}{2}] \]\)

The element of arc length, $ds$, can be calculated as:

\(\[ ds = \sqrt{dx^2 + dy^2} = \sqrt{\sin^2(t) + \cos^2(t)} \, dt = 1 \, dt \]\)

Therefore, the mass of the wire can be calculated as:

\(\[ \int_{0}^{\frac{\pi}{2}} \sigma(x, y) \, ds = \int_{0}^{\frac{\pi}{2}} y \sqrt{\sin^2(t) + \cos^2(t)} \, dt = \int_{0}^{\frac{\pi}{2}} 2 \sin(t) \sqrt{\sin^2(t) + \cos^2(t)} \, dt \]\)

Now, let's substitute \($\sin^2(t)$\) by\($1 - \cos^2(t)$:\)

\(\[ \int_{0}^{\frac{\pi}{2}} 2 \sin(t) \sqrt{1 - \cos^2(t)} \, dt \]\)

Next, let's substitute \($\cos(t)$\) by u, which implies \($dt = -\sin(t) \, du$\). When t = 0, \($u = \cos(0) = 1$\), and when \($t = \frac{\pi}{2}$\), \($u = \cos(\frac{\pi}{2}) = 0$\).

So, the limits change from 0 to\($\frac{\pi}{2}$\) to 1 to 0 respectively:

\(\[ \int_{1}^{0} 2 (1 - u^2)^{\frac{1}{2}} (-du) = 2 \int_{0}^{1} (1 - u^2)^{\frac{1}{2}} \, du = 2 \left[ \frac{1}{2} \sin^{-1}(u) \right]_{0}^{1} = \frac{\pi}{2} \]\)

Hence, the mass of the wire is\($\frac{\pi}{2}$\).

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1. The frequency of the second harmonic is twice that of the fundamental frequency. The frequency of the second harmonic is, therefore, 120 Hz.

2. The 3rd, 9th, and 15th harmonics are triplen harmonics. Triplen harmonics are so-called because they are three times the fundamental frequency (50Hz). They are multiples of the third harmonic (150Hz) and are considered triplen harmonics.
3. A positive-rotating harmonic would be more damaging to an induction motor. Harmonics that rotate in the opposite direction to the fundamental frequency are referred to as negative-rotating harmonics. Positive-rotating harmonics are harmonics that rotate in the same direction as the fundamental frequency. Negative-sequence currents are created by negative-rotating harmonics, which cause a rotating magnetic field that rotates in the opposite direction to the fundamental frequency's magnetic field. This causes stator windings to heat up, which can cause a great deal of damage to an induction motor.
4. An ammeter should be used to determine what harmonics are present in a power system. An ammeter is used to determine the presence and quantity of current harmonics. It can also be used to compare the percentage of current distortion in the system with the maximum allowable percentage of current distortion, which is determined by the nature of the load.
5. The transformer's rating should be derated to avoid overheating. If an ammeter that indicates peak current is used instead of a true-RMS ammeter, the current reading is multiplied by 1.414 (the peak of the sine wave). The true-RMS current, on the other hand, is what creates heat in the transformer. The transformer should be derated to compensate for the current difference between the two meters. The derating factor can be found using the following equation:

true-RMS current/Peak reading x 100%. 94 A/204 A x 100%

= 46%.

The transformer should be derated by 46%.

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Answer:

2√30

Step-by-step explanation:

Since we have a right triangle, we first need to find the base of the big triangle, which is also the hypo of the smaller triangle.

We apply A²+B²=C²

We plug values in that we have

15²+B²=19²

Simplify

B²=136

B=√136=√2x2x2x2x17=4√17

Now that we have the hypo for the small triangle we apply the same formula to get X

4²+X²=√136

16+X²=136

X²=120

X=√120=√2x2x2x3x5=2√30

Answer:

11.0 mm (3sf)

Step-by-step explanation:

Let length of hypotenuse of smaller triangle be H mm. (this is referring to the only unlabelled length in the picture)

by the Pythagorean theorem (larger triangle),

19² = 15² + H²

H² = 361 - 225

H² = 136

by the Pythagorean theorem (smaller triangle),

H² = 4² + x²

136 = 16 + x²

x² = 120

x = 11.0 mm (3sf)

hope this helps!

Brandon is currently 6 81 years old.

Let M be Michael's age and B be Brandon's age.

We are given that Michael is 3 33 times as old as Brandon. This means that M = 3 33 × B

We are also given that 18 1818 years ago, Michael was 9 99 times as old as Brandon. This means that M - 18 1818 = 9 99 × (B - 18 1818).

We can combine these two equations to solve for Brandon's current age:

3 33 × B = (9 99 × B) + 18 1818

2 66 × B = 18 1818

B = 18 1818 / 2 66 = 6 81.

Therefore, Brandon is currently 6 81 years old.

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Answer: 12/8

Step-by-step explanation:

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

I hope this helps!

The amount of the remittance from ABC is $1,960.

The given information states that merchandise is sold for $2,000 with terms of 2/10, n/30 to ABC. The terms 2/10, n/30 imply a 2% discount if payment is made within 10 days, with the full amount due within 30 days.

Since ABC sends a remittance on Dec. 26, it means the payment is made after the discount period but within the credit period. Therefore, ABC is not eligible for the discount of 2%.

To calculate the amount of the remittance, we simply subtract the discount from the total amount. In this case, the discount is $2,000 * 2% = $40. Thus, the remittance amount is $2,000 - $40 = $1,960.

In conclusion, the amount of the remittance from ABC is $1,960, as they did not qualify for the early payment discount.

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Answer:

1673

Step-by-step explanation:

multiply the volume value by 100

Answer:

1673

Step-by-step explanation:

since your liter to centiliter you just multiple you number by 100 for example:

10.30l x 100 = 1030

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Blake needs to now at least 17 lawns in order to earn at least $200 to buy a new stereo system.

To solve this problem, we can set up an inequality that represents the situation. Let's let x be the number of lawns that Blake needs to mow. The inequality will be:
12x >= 200

This inequality states that the amount of money Blake earns from mowing lawns (12x) must be greater than or equal to the amount of money he wants to earn ($200).

To solve for x, we can divide both sides of the inequality by 12:
x >= 200/12

Simplifying the right side of the inequality gives us:
x >= 16.67

Since Blake cannot mow a fraction of a lawn, we need to round up to the next whole number. This means that Blake needs to now at least 17 lawns in order to earn at least $200 to buy a new stereo system.

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Answer: 19

Step-by-step explanation: when you add a post it be with a negative you're basically gonna subtract them

Answer:

-150

Step-by-step explanation:

25×(-6)=-150 because I multiplied

*see attachment below for the dot plots

Answer:

A. The number of snacks grabbed for Class A has less variability than the number of snacks grabbed for Class B.

Step-by-step explanation:

The extent of variability of the data represented on a dot plot can be determined by the range value.

Range is the difference between maximum value of the data set and the minimum value of the data set.

The larger the range, the more the data has more variability, while the smaller the range, the less the variability of the data.

Range for Class A = 37 - 15 = 22

Range for Class B = 45 - 12 = 33

Therefore, class B has more variability in the number of snacks grabbed compared to Class A.

Correct statement is: "The number of snacks grabbed for Class A has less variability than the number of snacks grabbed for Class B."