John sold a generator and made a profit o $98, which is equal to 4 1/4 percent of the cost price.What was the cost of the Generator?​

Think about this. If we were to align the coefficients with their solutions to form this matrix, it would be the following -

[tex]\begin{bmatrix}2&-6&-2&|&1\\ 0&3&-2&|&-5\\ 0&2&2&|&-3\end{bmatrix}[/tex]

Now this is one way to assign the coefficients. As you can see, 2, - 6, - 2 are present as the coefficients for the first row. Similarly 0, 3, - 2 are present as the coefficients for the second row - ( as one term is missing from this row, it is replaced with a " 0 " ). The same applies for the third row. The end values of the system of equation is present as the last column.

The options are assigned in a manner with which the coefficients and variables are present in two columns, while the end values of the system of equation given, is present as the last column. Knowing the arrangement of both the coefficients and the end values of the system of equation, all we have to do is add these " variables " as one column -

Solution = Option B

Answer:

Selected option is correct

Step-by-step explanation:

Triangle BDE and BAC are similar because of the two pairs of equal angles (AA)

1. angle B

2. angle BDE = angle BAC

Answer: 205 and 1/7

Step-by-step explanation:

Hope this helped!

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Answer:

triangle pythagora

Step-by-step explanation:

the pythagora is made by someone special names albert and you ahve to amke three sides a b and c

Answer:

£1.53 per litre

Step-by-step explanation:

original = 1.02

if it is increased by 2/3 then we do 1.02 / (2/3) =£1.53 per litre

[tex]50/20=20/x\implies50x=400\implies\boxed{x=8\mathrm{ft}}[/tex]

Hope this helps.

The length of the shadow cast by the flag pole is 6.4 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that;

Height of building= 50 foot

Shadow= 20foot

Now,

Let x be the length of the shadow cast by the flag pole. Then we have:

2050​=x20​

Cross-multiplying, we get:

50x=20×20

Dividing both sides by 50, we get:

x=5020×20​

Simplifying, we get:

x=58​×4

Multiplying, we get:

x=6.4

Therefore, by the proportion the answer will be 6.4 feet.

More can be learned about proportions at;

brainly.com/question/24372153

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Answer: C. y ≤ 2/3x + 1/5

Step-by-step explanation: From 1/5 on the y coordinate plane go up 2 and right 3 and it perfectly matches, so it would be C. 100% on Edge2020.

Answer:

C

Step-by-step explanation:

just did the test.

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

Answer: A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈  $1388.89

Answer:  A) 0.5

Step-by-step explanation:

The denominator should be in the form 1 + e sin θ

Currently the denominator is: 2 + 1 sin θ

Divide the denominator by 2 to get:  1 + 0.5 sin θ

Thus, e = 0.5

Answer:

C.  (x - 9)(x^2 + 9x + 81).

Step-by-step explanation:

The cube identities are

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Checking against the list the one that fits is the difference formula:

x^2 - 9^2 = (x - 9)(x^2 + 9x + 81).

a=1, b = 9, ab = 1 *9 = 9.

Answer:

Tan<C=2.4

Step-by-step explanation:

Opp=36

Adj=15

Tan<C=opp/adj

Tan<C=36/15

Tan<C=2.4

Hope this helps :) ❤

Answer: 6p^3+29p^2+22p-21

Answer:

B.90°counterclockwise

Answer: B

Step-by-step explanation:

A. If you rotate a figure in the first quadrant 180 degrees clockwise it will end up in the third quadrant so the answer can't be A.

B. If you rotate a figure in the first quadrant 90 degrees counterclockwise it will end up in the second quadrant because you will rotate it backwards and as you could see A prime is in the second quadrant.

C.If you rotate a figure in the first quadrant 180 counterclockwise it will end up in the third quadrant. SO the answer can't be it C.

D.If your rotate a figure in the first quadrant 270 counterclockwise it will end up in the fourth quadrant. So the answer can't be D.

Answer:

Step-by-step explanation:

Since 15 liters of water flow through a water pipe and enter a tank within 4.5 minutes, the same amount of water would flow through a similar pipe at the same time. Therefore, if two similar water pipes are used, the volume of water that would flow into the tank in 4.5 minutes is 15 × 2 = 30 liters

Therefore, the time it will take to pump 727.5 liters of water into a water tank using 2 similar water pipes is

(727.5 × 4.5)/30 = 109.125 minutes

Answer:

Check the answers to the questions below

Step-by-step explanation:

a) If [tex]\mu_1[/tex] is the average learning rate of the 6th graders without background noise level and [tex]\mu_2[/tex] is the average learning rate of the 6th graders with background noise level

The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.

Null hypothesis, [tex]H_0: \mu_1 = \mu_2[/tex]

b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.

Alternative hypothesis, [tex]H_a: \mu_1 \neq \mu_2[/tex]

c) Assumptions that must be met about the data before she can correctly use independent t-test

There must be random selection of the 6th graders

That the two groups are normally similar in their learning abilities

The division of students into the two groups should be at random

d) She has to  make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.

She can still get accurate results if she include some bias in the selection to prove a particular result.

Given Information:

Annual interest rate = r = 10%

Accumulated amount = A = $6380.00

Semi-annual compounding = n = 2

Number of years = t = 38/12 = 19/6  

Required Information

Principle amount= P = ?

Answer:

Principle amount= P = $4,684.05

Step-by-step explanation:

The principal amounts in terms of compound interest is given by  

[tex]$ P = \frac{A}{(1 + i)^N} $[/tex]

Where  

i = r/n

i = 0.10/2

i = 0.05

N = n*t

N = 2*19/6

N = 19/3

So, the principal amount is

[tex]P = \frac{6380.00}{(1 + 0.05)^{19/3}} \\\\P= \$4,684.05 \\\\[/tex]

Therefore, you need to invest $4,684.05 at 10% compounded semiannually for 38 months to get $6380.00 in savings.

Answer:

5676039

Step-by-step explanation:

-14² + 5675843

Solve for exponent.

196 + 56758

Add the numbers.

= 5676039

Answer:

B

Step-by-step explanation:

the hotpotuse is always the biggest

the rest is pretty easy to determine

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry. A right-angled triangle is a triangle having one of its angles with a measure of 90°. The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

If one of the angle is of 90°  then the triangle is right angled triangle.

We can see that the Hypotenuse is always the biggest side among all the sides.

Then the perpendicular side BC is the second biggest and then the base of the triangle.

Therefore, the order must be AB > BC > AC.

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

Learn  more about  right angled triangle here:

https://brainly.com/question/27190025

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Answer:

cot(A-B) = 3/19

Step-by-step explanation:

The formula for cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A)

we know that cot A = 1/ Tan A

Given

tan A=2/3

therefore cot A = 1/ tan A = 1/2/3 = 3/2

tan B= -3/5  

cot B = 1/ tan B = 1/-3/5 = -5/3

Thus,

(Cot A Cot B + 1 ) = (3/2)*(-5/3 )+ 1 = -5/2 +1 = (-5+2)/2 = -3/2

(Cot B - Cot A) = -5/3 -3/2 = (-5*2) + (-3*3) / 2 = -10 -9/2 = -19/2

Thus,

cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A) = -3/2  / -19/2 = 3/19

Thus,

cot(A-B) = 3/19

Answer:

15

Step-by-step explanation:

Answer: 15

Step-by-step explanation: (9-6) + 12

                                              (3) + 12

                                              15

Answer:

1057

Step-by-step explanation:

tower is 60 feet high.

angle of 3.25 degrees.

3.25/360 * 2 * pi * r = the arc length of this angle.

that would be equal to 0.0567232007* r

if we assume the arc length and the height of the tower are approximately equal, then 0.0567232007 * r = 60

solving for r, we get r = 60/0.0567232007 = 1057.768237 feet.

that's about how far the tower is from the observer.

since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 1057.768237 meters is going to be a little less than the actual distance.

Answer:

≈ 1058 ft

Step-by-step explanation:

Use of arc formula: s=rθ

Given:

r= s/θ= 60/0.0567 ≈ 1058 ft

Answer: The box with three shaded squares and one non-shaded square

Step-by-step explanation:

You are trying to find the representation of the shaded region.

The scale shows point A at 0.75, and the scale can range from 0 to 1.

0.75 is equal to 3/4 of 1

3 of the 4 squares are shaded

So, the common ratio is 3:4 or 3/4

Answer:

The car travels 83 1/3 meters in 3 seconds.

Step-by-step explanation:

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Lets find speed of car in Meters/second

speed of car in m/sec = 100*1000 m/3600 second

here we have taken 1000 for km and 3600 for hour

speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

speed of car in m/sec = 250/9  m per sec

We know that

distance = speed*time

speed = 250/9  m per sec

time =3 second

distance = 250/9 * 3 meters = 250/3 meters = 83 1/3 meters.

Thus, car travels 83 1/3 meters in 3 seconds.

Answer:

b

Step-by-step explanation:

The slope is 3/4 and the y-intercept is y(0,2)

The slope is what we multiply by the variable ( here t) and the y-intercept is the number we add

Answer:

All angles in any quadrilateral adds up to 360°

Step-by-step explanation:

We can prove this by using 180(n - 2)

n = 4 for a quadrilateral

180(4 - 2)

180(2)

360°

So, 360 - (125 + 67 + 80) = 88°

Answer:

See below

Step-by-step explanation:

The interior angles of a quadrilateral (having 4 sides) add up to 360 degrees.

=> So, to find x, we'll simply subtract the rest if the angles from 360

So,

=> x = 360-125-67-80

=> x = 88 degrees

Answer:

(1) A Normal approximation to binomial can be applied for population 1, if n = 100.

(2) A Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.

(3) A Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.

Step-by-step explanation:

Consider a random variable X following a Binomial distribution with parameters n and p.

If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

The three populations has the following proportions:

p₁ = 0.10

p₂ = 0.30

p₃ = 0.50

(1)

Check the Normal approximation conditions for population 1, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.10=1<10\\\\n_{b}p_{1}=100\times 0.10=10=10\\\\n_{c}p_{1}=50\times 0.10=5<10\\\\n_{d}p_{1}=40\times 0.10=4<10\\\\n_{e}p_{1}=20\times 0.10=2<10[/tex]

Thus, a Normal approximation to binomial can be applied for population 1, if n = 100.

(2)

Check the Normal approximation conditions for population 2, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.30=3<10\\\\n_{b}p_{1}=100\times 0.30=30>10\\\\n_{c}p_{1}=50\times 0.30=15>10\\\\n_{d}p_{1}=40\times 0.10=12>10\\\\n_{e}p_{1}=20\times 0.10=6<10[/tex]

Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.

(3)

Check the Normal approximation conditions for population 3, for all the provided n as follows:

[tex]n_{a}p_{1}=10\times 0.50=5<10\\\\n_{b}p_{1}=100\times 0.50=50>10\\\\n_{c}p_{1}=50\times 0.50=25>10\\\\n_{d}p_{1}=40\times 0.50=20>10\\\\n_{e}p_{1}=20\times 0.10=10=10[/tex]

Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.

Answer: x=48°

Step-by-step explanation:

The 3 angles of the triangle add up to 180°. We can set the angles to 180 and solve.

47+85+x=180               [combine like terms]

132+x=180                    [subtract both sides by 132]

x=48

Answer:

x=48

Step-by-step explanation:

Total sum of angles in a triangle =180

47+85+x=180

132+x=180

x=180-132

x=48

Answer:

Option (4)

Step-by-step explanation:

Surface area of a prism = 2B + P×h

where B = Area of the triangular base

P = perimeter of the triangular base

h = height of the prism

B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]

Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]

(20)² = (12)² + (Leg 2)²

Leg 2 = [tex]\sqrt{400-144}[/tex]

          = 16 units

Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]

                     = 96 units²

P = 12 + 16 + 20

P = 48 units

h = 7.5 units

Surface area of the prism = 2(96) + (48×7.5)

                                           = 192 + 360

                                           = 552 units²

Therefore, surface area of the given triangular prism = 552 units²

Option (4) will be the answer.

They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value.  The answer is A.

Answer:

A

Step-by-step explanation: