Which value of the variable is the solution of the equation?
a + $5.92 = $12.29
a = $5.37, $5.47, $6.37, $6.27
Enter your answer in the box.
$

Answer:

r=-1

Step-by-step explanation:

- 3 ( 1 + 6 r ) = 14 - r

-3-18r=14-r

-3-18r+r=14

-3-17r=14

-17r=14+3

-17r=17

r=-1

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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By using the unitary method and dividing the time into equal intervals, the number of bacteria doubled every 3 hours, the final total of 32,000 bacteria after 14 hours.

Unitary method involves dividing the time interval into equal parts, and calculating the growth for each unit of time before adding them all up to get the total growth.

To start, let's divide the 14 hours into 3 hour intervals. We have

=> 14 hours / 3 hours = 4 intervals.

Next, we need to calculate the growth in each 3 hour interval. Since the number of bacteria doubles every 3 hours, we can find the growth by multiplying the initial number of bacteria by 2.

Starting with the first interval, we have 2000 bacteria * 2 = 4000 bacteria.

We can now repeat this calculation for each interval, multiplying the previous total by 2 each time.

For the second interval, we have 4000 bacteria * 2 = 8000 bacteria.

For the third interval, we have 8000 bacteria * 2 = 16,000 bacteria.

Finally, for the fourth interval, we have 16,000 bacteria * 2 = 32,000 bacteria.

So, at the end of 14 hours, there will be 32,000 bacteria in the culture.

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Answer:  The correct answer is b = √13 or b = −√13

Step-by-step explanation:

When factoring squared variables or numbers, use the square root

b^2 = 13

Take the square root of both sides

√b^2 = √13

b = √13 or b = −√13

111.51 is the probability of the random sample of 15 people that 4 of them are left-handed.

P(exactly x out of n) = (n! ÷ (x! × (n - x)!)) × \(p^{x}\) × \((1 - p)^{n - x}\).

where n = number of trials = 15.

p = probability of selecting one lefty in one trial = 10% or 0.1

x = probability which needs to be deduced = 4.

P(exactly 4 out of 10) = (10! ÷ (4! × (10 - 4)!)) × \(1^{4}\) × \((1 - 0.1)^{10 - 4}\).

P(exactly 4 out of 10) = (10! ÷ (4! × 6!)) × \(1^{4}\) × \((0.9)^{6}\).

P(exactly 4 out of 10) = 210 × \(1^{4}\) × \((0.9)^{6}\).

P(exactly 4 out of 10) = 210 × 1 ×0.531

P(exactly 4 out of 10) = 111.51

The probability that 4 of them are left-handed is 111.51.

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Answer:

8.33

Step-by-step explanation:

1hr=60 minutes

?hr = 500 minutes

To find how many hours, divide 500 by 60

500/60 = 8.33

500 minutes = 8.33 hours

Answer:

8

Step-by-step explanation:

Therefore, the solution to the given system of linear equations is: x = 2y - 4 = 2(5/3) - 4 = -2/3 y = 5/3 z = 8/3

The given system of linear equations is, 2x - 5y + z = -9 (i) x + 4y - 6z = 2 (ii)

3x - 4y - 2z = -10 (iii)

Let's solve this system using the elimination method. From equations (i) and (iii), we have:

2x - 5y + z = -9 ........(i)

3x - 4y - 2z = -10.......(iii)

We can eliminate z from these equations by multiplying equation (i) by 2 and adding it to equation (iii) as shown:4x - 10y + 2z = -18 (2i)3x - 4y - 2z = -10........(iii)

7x - 14y = -28............(iv)

Divide equation (iv) by 7, and we get

x - 2y = -4....................(v)

Now let's eliminate z from equations (ii) and (iii). We can do this by multiplying equation (ii) by 2 and adding it to equation (iii) as shown:

x + 4y - 6z = 2.......(ii)

3x - 4y - 2z = -10.......(iii)

2x + 8y - 12z = 4.......(ii)

3x - 4y - 2z = -10.......(iii)

5x + 4y - 14z = -6.......(vi)

Now, let's eliminate y from equations (v) and (vi). To do this, we can multiply equation (v) by 4 and add it to equation (vi) as shown:

4x - 8y = -16..........(v)

5x + 4y - 14z = -6.......(vi)

9x - 14z = -22.........(vii)

We can now solve for z by substituting equation (vii) into equation (iv). Therefore:

9x - 14z = -22 (vii)

x - 2y = -4 (v)

Solve equation (v) for x as follows:x = 2y - 4Substitute this into equation (vii) to get:

9(2y - 4) - 14z = -22

Simplify and solve for z as follows:

18y - 36 - 14z = -22 18y - 14z = 14 9y - 7z = 7

Now, we can substitute the values we have obtained for x and z into equation (ii) to solve for y as follows:

x + 4y - 6z = 2 (ii)2y - 4 + 4y - 6z = 2 6y - 7z = 3 6y - 7(1) = 3 6y - 7 = 3 6y = 10 y = 5/3

Now we can substitute x = 2y - 4 and y = 5/3 into any of the three original equations to solve for z. Using equation (i), we get:

2x - 5y + z = -9 2(2y - 4) - 5y + z = -9 4y - 8 - 5y + z = -9 -y + z = 1 z = y + 1 = 5/3 + 1 = 8/3.

Hence, the main answer is

x = -2/3, y = 5/3, z = 8/3.

Therefore, the solution to the given system of linear equations is: x = 2y - 4 = 2(5/3) - 4 = -2/3 y = 5/3 z = 8/3.

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Answer:

-59

Step-by-step explanation:

(-6) (8) + (-11)

(-48) + (-11)

-48 -11

-59

Answer:

a = 40 + root(7) , b = 5 root(7)

Step-by-step explanation:

\(49 + \sqrt{7} - \sqrt{81} + \sqrt{-175}\\ = 49+\sqrt{7}-9+5\sqrt{7}i\\ = 40+\sqrt{7} + 5\sqrt{7}i\)

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

here we go~

\(\qquad \sf  \dashrightarrow \: 4x {}^{2} - 25y {}^{2} \)

[ identity : a² - b² = (a + b)(a - b) ]

\(\qquad \sf  \dashrightarrow \: (2x) {}^{2} - (5y) {}^{2} \)

\(\qquad \sf  \dashrightarrow \: (2x + 5y)(2x - 5y)\)

Answer:

(0. - 11 )

Step-by-step explanation:

To find the y- intercept let x = 0 and solve for y, that is

y = - 3(0)² - 7(0) - 11 = 0 - 0 - 11 = - 11

y- intercept = (0, - 11 )

The appropriate simulation applet to calculate an approximate p-value is 0.0077.

The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.

Delay or no delay, answer: the number of words remembered

The mean distance between words remembered with and without delay over time is null, or zero.

Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.

Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.

The mean distance in words remembered is 1.85.

1)0.0077 as the p-value

2)Strong data suggests that a brief delay impairs memorization.

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Answer:

X=8

Step-by-step explanation:

48+22=70

4×8=48

so X is 8

Answer: 1 tire would cost 68$

Step-by-step explanation:

can I have brainliest pls <3

Answer:

here we've been given the cost of 4 tires. and we've to find the cost of one tire.

in such a situation , we usually divide the cost of " n " number of tires by " n " ( where , n = number of tires )

so , here we go -

_____________________________

\(\bold{cost \: of \: 4 \: tires = 272 \: dollars }\\ \\ cost \: of \: 1 \: tire = \frac{272}{4} \: dollars \\ \\ \dashrightarrow \: 68 \: dollars\)

_____________________________

hope helpful :D

There are 176,851 ways for the 100 pages to be assigned to the four printers if there are no restrictions on how many pages a printer can print.

The question asks to find the number of ways in which the 100 pages can be assigned to the four printers if there are no restrictions on how many pages a printer can print.

To find the number of ways, we need to solve this problem using the "Stars and Bars" technique.

Here, stars represent pages and bars represent the partitions between different printers.

Here, we have 2 pages for printer 1, 3 pages for printer 2, 5 pages for printer 3, and 4 pages for printer 4.

The number of stars before the first bar represents the number of pages assigned to printer 1, the number of stars between the first and second bar represents the number of pages assigned to printer 2, and so on.

Therefore, the problem reduces to counting the number of ways of arranging two bars and 100 stars, i.e., 102 objects, where bars and stars are treated as indistinguishable.

The number of ways can be found using the formula, (n+k-1)C(k-1),

where n is the number of stars and k is the number of bars.

For this problem, n=100 and k=4.

Hence, the number of ways is(100+4-1)C(4-1) = 103C3 = 176,851.

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When P is true, and Q is false, the proposition P ⊃ Q is false. Therefore, the answer is TFTT. The correct answer is option d. TFTT.

The given truth table for the compound proposition P ⊃ Q is: P Q P⊃QT T T T T F FT F T T F

The conditional P ⊃ Q implies that whenever the antecedent P is true, then the consequent Q is true as well.

This implies that the only time the conditional P ⊃ Q is false is when the antecedent is true, but the consequent is false.

Since we see in the truth table that when P is true, and Q is true, the proposition P ⊃ Q is also true.

However, when P is true, and Q is false, the proposition P ⊃ Q is false. Therefore, the answer is TFTT.

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The curve with polar equation r = 10sin(θ)cos(θ) can be expressed in Cartesian coordinates as \(x^2 + y^2 - 10xy = 0\)

To derive the Cartesian equation, we can use the identities x = r cos(θ) and y = r sin(θ) to substitute for r in the polar equation:

\(x^2 + y^2 = (10sin(\theta)cos(\theta))^{2}\)

Simplifying, we get:

\(x^2 + y^2 = 25x^{2}y^{2}\)

Rearranging, we obtain the final Cartesian equation:

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

This equation represents a special type of conic section known as a hyperbola. It has two branches that are symmetric about the line y = x/2. To visualize the curve, we can plot several points using the polar equation and convert them to Cartesian coordinates.

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The domain of the function is `R` and the y-intercept is `(0, -3)`

Given, `y = log4(2x + 1) - 3`.

To determine the domain of the function,

we should look for all values of `x` that would make the given function undefined.

There are no real values of `x` that would make the function undefined.

Therefore, the domain of the function is all real numbers or `R`.

To determine the y-intercept, substitute `x = 0` in the given function.`

y = log4(2(0) + 1) - 3 = log4(1) - 3 = 0 - 3 = -3`

Therefore, the y-intercept of the function is `(0, -3)`.

Hence, the domain of the function is `R` and the y-intercept is `(0, -3)`.

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The number οf triangles that can be fοrmed is C(5,3)C(10,3) = 10120 = 1200.

In mathematics, cοmbinatiοns refer tο the number οf ways yοu can chοοse a specific number οf items frοm a larger set οf items, where the οrder in which yοu chοοse the items dοes nοt matter.

1. a) 9!/7! = 9*8 = 72

b) The questiοn seems tο be incοmplete. Please prοvide additiοnal infοrmatiοn.

c) P stands fοr permutatiοn, which is the number οf ways tο arrange οbjects in a specific οrder. A Stands fοr cοmbinatiοn, which is the number οf ways tο select οbjects withοut regard tο their οrder.

2. a) There are 6 ways tο chοοse οne apple frοm the basket.

b) There are 6 ways tο chοοse οne apple and 9 ways tο chοοse οne pear, sο there are 6*9 = 54 ways tο chοοse οne apple and οne pear.

c) There are 15 ways tο chοοse either οne apple οr οne pear (6 apples + 9 pears - 0 cοmmοn fruits).

d) There are 698 = 432 ways tο chοοse οne fruit οf οne variety and twο fruits οf anοther variety.

3. a) There are 6 subjects tο be studied and exactly οne lessοn is planned fοr each subject. Therefοre, there are 6! = 720 ways tο make a list οf lessοns fοr this day.

b) There are 6 chοices fοr the first digit, 5 chοices fοr the secοnd digit, 4 chοices fοr the third digit, and 3 chοices fοr the fοurth digit. Therefοre, there are 654*3 = 360 different fοur-digit numbers that can be fοrmed frοm the given digits.

c) There are 8 peοple and we need tο chοοse a cοmmittee οf 4 peοple. Therefοre, there are C(8,4) = 70 ways tο chοοse a cοmmittee οf fοur peοple.

3. Let n be the number οf members in the aerοbics grοup. Each member can shake hands with n-1 οther members. Since each handshake invοlves twο peοple, the tοtal number οf handshakes is n(n-1)/2. We are given that this tοtal is 66, sο we can sοlve fοr n as fοllοws:

\($ \frac{n(n-1)}{2} = 66\)

\(n(n-1) = 132\)

\(n^2 - n - 132 = 0\)

\((n-12)(n+11) = 0\)

Since n must be positive, the only possible value is n=12. Therefore, there are 12 members in the aerobics group.

4. There are 5 points on line a and 10 points on line b. Any three points on different lines can form a triangle, as long as they are not collinear.

Therefore, the number of triangles that can be formed is C(5,3)C(10,3) = 10120 = 1200.

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Answer:

Look Down

Step-by-step explanation:

1) x=9

2) x=12

3) x=12

4) x=12

5) x=11

6) x=11

The solutions for the equation \(y=-4(x-2)^2+6\) are as follows \(x = 2 + \sqrt{(6 - Y) / 4}\) or \(x = 2 - \sqrt{(6 - Y) / 4}\).

The given equation is in standard form for a quadratic equation, where the coefficient of \(x^2\) is negative. This means the graph of the equation is a downward-opening parabola, and the vertex of the parabola is (2, 6).

To solve the equation, we can first isolate the variable Y on one side:

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

Then we can divide both sides by -4:

\((Y - 6) / -4 = (x - 2)^2\)

Next, we can take the square root of both sides:

\(\sqrt{[(Y - 6) / -4] }= x - 2\)

\(\pm \sqrt{(Y - 6) / -4}= x - 2\)

So the solutions are:

\(x = 2 + \sqrt{(6 - Y) / 4}\) or \(x = 2 - \sqrt{(6 - Y) / 4}\)

These equations give the x-coordinates of the points on the graph of the equation for a given value of Y.

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Answer:

x > 15

Step-by-step explanation:

Try to get x on a side by itself...

3x - 42 > 3

3x > 45

x > 15

1) Find the perimeters of the square and the triangle.

Suppose you divide the wire into 2 pieces that measure x and y. x is used to make the square and y is used to make the triangle, according to the figure:

x is the perimeter of the square;

y is the perimeter of the triangle.

Since the total wire is 30 inches long:

x + y = 30 (equation 1).

2) Find the area of the geometric figures.

Square:

Since a square has 4 equal sides, each side will measure x/4 (4*x/4=x)

And, since the area (As) of a square whose side measures a is:

The area of the square is:

Equilateral Triangle:

Since an equilateral triangle has 3 equal sides, each side will measure y/3 (3*y/3 = y).

And, since the area (At) of an equilateral triangle whose side measures b is:

The area of the triangle is:

3) Find the total area.

The total area (A) is the sum of the areas:

4) Isolate y in equation 1 and substitute in the equation for the area.

x + y = 30

y = 30 - x

5) The maximum or minimum value of A happens at x when dA/dx = 0.

So, derivate A:

And do dA/dx = 0 to find x.

Then, isolate x:

6) Evaluate the equation for x at the exremes x = 0; y = 30, and at x = 13.

For x = 0

For x = 30

And for x =13

7) Compare the results:

As you can see in step 6, when x = 13, the area is minimized, while the area is maximized when x = 30.

The greatest area will be reached when x = 30. That means y = 0 (x + y =30).

Answer:

The greatest area is reached when all the wire is used to make the square.

To make the 2 figures, we wire should be cut as nearest as possible to 30, and the greatest piece should be used to make the square.

Since

The pattern is that once a number is divided by 1/10. It is equivalent to multiplying the number by 10.

Thus we find that;

Thus 18 / (1/10) = 180

By square root 5 this we get the value √5 = 2.2360…Or √5 ≈ 2.24 with correct two decimal number fraction .

1. First, the number 5 can be expressed as 5.00000000, or 5 = 5.00 00 00 00.

2.Take the number whose square is less than five. The perfect square of the number 2 is 4, which comes after the number 5.

3..Enter 2 in both the divisor and quotient places so that it may be multiplied by 2 to get the answer 4. Add 4 to 5 to obtain the answer, which is 1.

4.Write two zeros after one and add them to the quotient. Add the decimal point after the first zero.

5.Now multiply by 2 to make 4 in the divisor. Pick a number that will go next to 4, ensuring that the result of multiplying the combination with that number will be less than or equal to 100. In order to make 42 times 2 equal 84, which is less than 100, we shall use 2 in this instance. To get the remainder, take 100 out of it immediately. The remainder is therefore 16.

6.Repetition of Step 5 up to 4 places of decimals with the addition of two more zeros.

7.Ultimately, you arrive at the quotient value, which is 2.2360, or around 1.236.

In light of this, the value of root 5 is, √5 = 2.2360… Or √5 ≈ 2.24

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Answer: she must sell 6 large photos and 6 small photos

Step-by-step explanation: and how I knew that is I multiplied 6 40 times and that gives you 240 and if you multiply 6 ten times that gives you 60 so 240 plus 60 is $300

Answer:

14 cents or $0.14

Step-by-step explanation:

Let each stick cost be x

25x=3.5

x=0.14

Answer:

each sticker = $0.14

Step-by-step explanation:

25 stickers =$3.50

1 sticker =3.50/25

1 sticker= 0.14