does the system composed of equations 1 and 2 have a unique solution, no solution, or infinitely many solutions?

Answer:

The value of x should be x = 40.

Step-by-step explanation:

Answer:

$6.75

Step-by-step explanation:

You would have to find how much it would cost you to buy 1 can. So you do $9/4= $2.25

now multiply $2.25 and 3

which equals $6.75

6 dollars 75 cents

Hope this helps :)

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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Answer:

Step-by-step explanation:

The equation is V = √(20L).

Solve this equation for L and the result is L = V2/20

Since V = 57 mph, putting this value into the equation, L = (57)2/20 = 162.45 ft should be his skid marks

15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:

400

Step-by-step explanation:

Percentage decrease = 20% × 500

New value = 500 - Percentage decrease

500 - (20% × 500) =

500 - 20% × 500 =

(1 - 20%) × 500 =

(100% - 20%) × 500 =

80% × 500 =

80 ÷ 100 × 500 =

80 × 500 ÷ 100 =

40,000 ÷ 100 =

400

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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y = 2x - 12

Answer:

1,500,000

Step-by-step explanation:

Answer:

44 gallons in tank now

36 more gallons needed

Step-by-step explanation:

55% of 80 = 44

Given that a quadratic equation has two solutions, denoted as α and β, it is possible to determine the pair of numbers (α, β) by examining the coefficients of the quadratic equation.

The explanation in the following paragraph will elaborate on how to find the pair.

Let's consider a quadratic equation in the form of ax^2 + bx + c = 0, where a, b, and c are nonzero real numbers. The solutions of this equation are given by the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, the solutions are α and β.

By comparing the given quadratic equation with the general form, we can determine the values of a, b, and c. Once we have determined these values, we can substitute them into the quadratic formula to find the values of α and β.

Therefore, to find the pair (α, β), it is necessary to provide the specific values of a, b, and c in the given quadratic equation. Without the explicit equation or the values of the coefficients, it is not possible to determine the pair (α, β) in this particular case.

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Answer:

5

Step-by-step explanation:

divide the distance by the rate of speed

5/1=5

Answer:

5 seconds.

Step-by-step explanation:

Answer:

2y +3z -1 = 0

Step-by-step explanation:

The sketch of the plane is in the image :)

The red axis is the x-axis, the green axis is the y-axis, and the blue axis is the z-axis

Answer:

x = 23

y = 7

z = 11

Step-by-step explanation:

Since ∆PRS ≅ ∆CFH, therefore,

m<R = m<F

13y - 1 = 90° (substitution)

Add 1 to both sides

13y - 1 + 1 = 90 + 1

13y = 91

Divide both sides by 13

13y/13 = 91/13

y = 7

Since ∆PRS ≅ ∆CFH, therefore,

PS = CH

2x - 7 = 39 (substitution)

Add 7 to both sides

2x - 7 + 7 = 39 + 7

2x = 46

Divide both sides by 2

2x/2 = 46/2

x = 23

Since ∆PRS ≅ ∆CFH, therefore,

m<S = m<H

Find m<S

m<S = 180 - (m<P + m<R) (sum of ∆)

m<S = 180 - (28 + (13y - 1)) (substitution)

Plug in the value of y

m<S = 180 - (28 + (13)(7) - 1))

m<S = 180 - (28 + 91 - 1)

m<S = 180 - 118

m<S = 62°

Therefore, since m<S = m<H,

62° = 6z - 4 (substitution)

Add 4 to both sides

62 + 4 = 6z - 4 + 4

66 = 6z

Divide both sides by 6

66/6 = 6z/6

11 = z

The values of x, y, and z are;

x = 23

x = 23y = 7

x = 23y = 7z = 11

We are told that triangle PRS is congruent to triangle CFH.

Since both triangles are congruent, by inspection we can see that;

m<R = m<F

m<F is a right angle = 90°. Thus;

13y - 1 = 90

13y = 90 + 1

13y = 91

y = 91/13

y = 7

Also by inspection;

PS = CH

2x - 7 = 39

2x = 39 + 7

2x = 46

x = 46/2

x = 23

Since m<R is 90°, then;

m<S = 180 - (90 + 28)

m<S = 62°

By inspection;

m<S = m<H

Thus;

6z - 4 = 62

6z = 66

z = 66/6

z = 11

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Answer:

B: 90

d: 86

e: 92

Step-by-step explanation:

edg2020

Answer:

  a.  7

  b.  9

  c. 15

Step-by-step explanation:

You want to know the number of binary bits required to represent the unsigned numbers 65, 409, 16385.

N bits can be used to represent an unsigned integer in the range 0 to (2^n)-1. That is, the value 2^n will be greater than the integer being represented by n bits.

We recognize some powers of 2 as ...

  2^6 = 64

  2^8 = 256

  2^14 = 16384

Each of these values is slightly smaller than the number we want to represent, so the number of bits required is ...

  a) 65 ⇒ 7 bits

  b) 409 ⇒ 9 bits

  c) 16385 ⇒ 15 bits

__

Additional comment

The number of bits required is the ceiling of the base-2 logarithm of 1 more than the number being represented. The calculator in the attachment uses ceiling( ) = 1 + floor( ), which will be true for any number having a non-zero fractional part. All of these logarithms do.

The minimum number of binary bits needed to represent each of the following unsigned decimal integers is

2^n.

a. 65
The minimum number of binary bits needed to represent 65 is 7. This is because 2^6 = 64, which is the closest power of 2 that is less than 65. Therefore, 7 bits are needed to represent 65 in binary.
b. 409
The minimum number of binary bits needed to represent 409 is 9. This is because 2^8 = 256, which is the closest power of 2 that is less than 409. Therefore, 9 bits are needed to represent 409 in binary.
c. 16385
The minimum number of binary bits needed to represent 16385 is 14. This is because 2^13 = 8192, which is the closest power of 2 that is less than 16385. Therefore, 14 bits are needed to represent 16385 in binary.

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Answer:

-39x^2 + 17x

Step-by-step explanation:

= 5x - 60x^2 + 3 (4x+7x^2)

= 5x - 60x^2 + 12x + 21x^2

= -39x^2 + 17x

Answer:

-39x^2 + 17x is correct

Step-by-step explanation:

I checked it

Angle of elevation in degrees is \(28.1\)° .

Define angle of elevation.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

According to the question ,

Roof shape = isosceles triangle

base length = 30 m

and two sides each =  17 m.

Let it be in the middle ,such that the two 17 m beams will have the same angle of elevation .

Now , we have to find the angle of elevation such that we can split the roof in half vertically to create a right angled triangle.

The base will now be 15 m, and the hypotenuse will be 17.

Therefore we use a trigonometry function to solve for the angle. We know the hypotenuse and the side adjacent to the angle, so we can use cosine.

Now ,by trignometric formulas :

\(cos(\)Ф\()\)\(= \frac{adjacent side }{hypotenuse}\)

\(cos(\)Ф\()=\frac{15}{17}\)

Ф=cos inverse of \(\frac{15}{17}\)

Ф\(= 28.1\)°

Hence the angle is 28.1° .

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Using the binomial distribution, there is a 0.6328 = 63.28% probability that she wins at most 1 prize.

For each box, there are only two possible outcomes, either it has a prize, or it does not. The probability of a box having a prize is independent of any other box, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

She buys 5 boxes, hence

1 in 4 boxes has a prize, hence

The probability is:

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

Then ,

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

= 0.2373 + 0.3955

= 0.6328

Thus 0.6328 = 63.28% probability that she wins at most 1 prize

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Answer:

I think yes

Step-by-step explanation:

12/4=3

36/12=3

-6/-2=3

and so on

A graph of the linear function y = -2x/3 + 490 in slope-intercept form is shown in the image attached below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Next, we would rearrange and simplify the given given linear equation in slope-intercept form in order to enable us plot it on a graph:

2x + 3y = 1,470

3y = -2x + 1,470

y = -2x/3 + 1,470/3

y = -2x/3 + 490

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Answer:

-5/8

Step-by-step explanation:

First find the least common denominator. It is 8.

1/8- 2/8- 4/8

Hi!

1/8 - 1/4 - 1/2 = 1/8 - 2/8 - 4/8 =

= (1 - 2 - 4)/8 = (-1 - 4)/8 = -5/8

Answer:

C

Step-by-step explanation:

When talking about multiplication two negatives do, in fact, make a positive but if there is only one negative in the equation, the product(answer) will be negative. Therefore, C 31(-10)=-310 is the only problem that is correct.

Answer:

C.\(31\left(-10\right)=-310\)

Step-by-step explanation:

\(31\left(-10\right)\)

\(\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\)

\(=-31\cdot \:10\)

\(\mathrm{Multiply\:the\:numbers:}\:31\cdot \:10=310\)

\(=-310\)

The 16th term of the sequence is `a16 = 141`.

Given that the first term, `a = 6` and common difference, `d = 9`

The nth term of an arithmetic sequence is given by the formula

`an = a + (n - 1)d`.

Substitute `a = 6` and `d = 9` in the above equation

`an = a + (n - 1)d6 + 9(n - 1)`

Simplify

`an = 9n - 3`

Therefore, the nth term of the given sequence is

`9n - 3`.

Now, we have to find the 16th term, that is, `a16`.

`a16 = a + (16 - 1)d`

Substitute `a = 6` and `d = 9` in the above equation.

`a16 = 6 + 15 × 9`

Simplify`a16 = 141`

Therefore, `a16 = 141`.

Thus, the nth term of the arithmetic sequence is given by `an = 9n - 3`.

The 16th term of the sequence is `a16 = 141`.
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It will take approximately 51.25 minutes for the man to get home at his usual speed of 9 kilometers per hour.

Step 1: Convert the given time in minutes to hours
26 minutes = 26/60 hours = 0.4333 hours
10 minutes = 10/60 hours = 0.1667 hours

Step 2: Calculate the distance covered during each time interval
First interval: 6.76 km/h * 0.4333 hours = 2.9276 km
Second interval: 5.55 km/h * 0.1667 hours = 0.9256 km

Step 3: Add the distances together to find the total distance covered
2.9276 km + 0.9256 km = 3.8532 km

Step 4: Calculate the remaining distance to reach home
11.54 km - 3.8532 km = 7.6868 km

Step 5: Calculate the time it takes to cover the remaining distance at the usual speed
Time = Distance / Speed
Time = 7.6868 km / 9 km/h = 0.8541 hours

Step 6: Convert the time in hours back to minutes
0.8541 hours * 60 = 51.246 minutes

So, it will take approximately 51.25 minutes for the man to get home at his usual speed of 9 kilometers per hour.

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Answer and Step-by-step explanation:

First equation:

y = -4x + 9

This equation has a negative slope (a slope that does downwards) and has a positive y-intercept (at (0, 9)).

Second Equation:

y = -4x - 4

This equation is parallel to the first line because it has the same slope. It also has a negative y-intercept (at (0, -4)).

#teamtrees #PAW (Plant And Water)

For the attached image, note that slope is the same thing as gradient.

1) y = 2x + 4

2) Substituting in x = 1 and y = 1,

1 = 4(1) + c

1 = 4 + c

c = -3

So, the equation is y = 4x - 3