Bronson is ordering pizza at a restaurant, and the server tells him that he can have up to three toppings: spinach, bacon, and pepperoni. Since he cannot decide how many of the toppings he wants, he tells the server to surprise him. If the server randomly chooses which toppings to add, what is the probability that Bronson gets just spinach? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

What is the Gaussian method?

The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.

To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:

Machining department: 1200x + 1800y + 3000z = 1050(60)

Inspection department: 2400x + 1200y = 1160(60)

Assembly department: 600x + 3000y = 830(60)

Simplifying these equations, we get:

Machining department: 20x + 30y + 50z = 3150

Inspection department: 8x + 4y = 232

Assembly department: x + 5y = 139

Now we can use the Gaussian method to solve for x, y, and z:

Step 1: Write the augmented matrix:

| 20 30 50 | 3150 |

| 8 4 0 | 232 |

| 1 5 0 | 139 |

Step 2: Use row operations to get the matrix in row echelon form:

R2 → R2 - 4/5 R3

R1 → R1 - 20R3

| 0 -2 50 | 850 |

| 0 2 -4   | -28 |

| 1 5 0     | 139 |

R2→ -1/2 R2

R1 → R1 + R2

| 0 1 -25 | 407 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R1→ R1 - R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R3→ R3 - 5R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R1→ -1/23 R1

| 0 0 1 | -17 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R2 → R2 + 2R3

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 10 | 65 |

R3 → R3 - 10R1

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 0 | 235 |

Step 3: Read off the solution from the row echelon form:

z = -17

y = 96

x = 235

Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

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The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

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Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

Answer:

what grade is thistfgydyfyryhehdhufhf

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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Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

Answer:

the overall mean mortality rate for the two regions is 1524.15

Step-by-step explanation:

Given that;

Summary of Mortality

Group     Count       Mean      Median       Std-Dev  

North         34        1631.59      1631           138.470

South         27       1388.85     1369          151.114

the overall mean mortality rate for the two regions = ?

first we determine number of deaths in the North;

⇒ count × mean = 34 × 1631.59 = 55,474.06

Next,  number of deaths in the South

⇒ count × mean = 27 × 1388.85 = 37,498.95

so, mortality rate for the two region will be;

⇒ (55,474.06 + 37,498.95) / ( 34 + 27 )

= 92,973.01 / 61

= 1,524.1477 ≈ 1524.15

Therefore, the overall mean mortality rate for the two regions is 1524.15

The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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Answer: $240.54

Step-by-step explanation: Basically, what you are doing is multiplying both prices then subscract that value from 800 to see which amount goes to school.

Answer:

  x = 3  or  x = 5

Step-by-step explanation:

The quadratic formula tells the solutions to a quadratic equation based on its coefficients when written in standard form.

The solution to ax² +bx +c = 0 is given by ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

In order to make use of the formula, we need to find the coefficients when the equation is written in standard form. Subtracting 24x from both sides will put it in that form. We can also save a little bit of work by dividing the resulting equation by the common factor of 3.

  3x² -24x +45 = 0 . . . . . . . . subtract 24x

  x² -8x +15 = 0 . . . . . . . . . . divide by 3

This leaves us a standard-form equation with a=1, b=-8, c=15. The formula gives the solutions as ...

  \(x=\dfrac{-(-8)\pm\sqrt{(-8)^2-4(1)(15)}}{2(1)}=\dfrac{8\pm\sqrt{64 -60}}{2}\\\\x=\dfrac{8\pm\sqrt{4}}{2}=4\pm1\\\\ \boxed{x= \{3, 5\}}\)

The solutions to the given quadratic equation are x=3 and x=5.

Answer:

the answer is c because decreased by means the symbol minus so y decreased by 24 will be y-24

Answer:

Rate parameter of \(\mu = 0.5\)

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:  

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

One appearance per two minutes.

This means that \(m = 2\)

Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?

\(\mu = \frac{1}{m} = \frac{1}{2} = 0.5\)

So

Rate parameter of \(\mu = 0.5\)

Answer:

$17.2

Step-by-step explanation:

120 + 16*100 = 120 + 1600 = 1720

The member pays $1720 annually for 100 classes and membership fee combined.

1720/100 = 17.2

The student pays $17.2 per class on average.

Answer:

x = 15

Step-by-step explanation:

create a proportion:   x + 10 = x + x + 10

                                       5               8

cross-multiply:  8(x + 10) = 5(2x + 10)

                          8x + 80 = 10x + 50

                                  80 = 2x + 50

                                  30 = 2x

                                   15 = x

my guess would be c. but id wait for someone else to answer just to be sure

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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14)The sum of the tangent and the sine of the angle is obtained as 1.21.

15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.

16)The angle opposite the largest side is  130°.

The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the  trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.

14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;

a = √2^2 + 3^2

a = √ 4 + 9

a = 3.6

We know that;

tan θ = 2/3 = 0.66

sin θ = 2/3.6 = 0.55

Then;

tan θ + sin θ

0.66 + 0.55

= 1.21

We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.

15)

The area of the segment is obtained as;

Area of the triangle;

1/2r^2 sinθ

r= radius of the circle

θ = angle of inclination

1/2 * (10)^2 * sin 60

= 43.3

Area of the sector;

60/360 * 3.142 * (10)^2

= 52.3

Therefore the area of the triangle is;

43.3 +  52.3 = 95.6 m

b)The perimeter of the segment;

(2πr * θ/360) + 2rsin(θ/2)

(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))

1.047 + 10

= 11.047 m

16)

Using;

c^2 = a^2 + b^2 - 2abcos C

20^2 = 13^2 + 9^2 - 2(13 * 9) cos C

400 = 250 - 234cosC

400 - 250 = - 234cosC

150 =  - 234cosC

Cos C = -(150/234)

C = Cos-1-(150/234)

C = 130°

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Answer:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

Answer:

\(\left \{ {{x=2+3\cos t} \atop {y\:=-1+3\sin t}} \right. => \pi \leq t \leq 5\pi\)

Step-by-step explanation:

The standard equation of a circle centered at (a,b) with radius r would be (x - a)^2 + (y - a)^2 = r^2

This example represents a circle with center (2, - 1) having a radius of 3

The parametric equation of a circle centered at (0,0) would be;

x = r cos t,

y = r sin t

And so when centered at (a, b) we would have;

x = a + r cos t,

y = b + r sin t

In this case x = 2 + 3 cos t, and y = - 1 + 3 cos t

Now if the particle starts at (-1, - 1), correspondent to a start parameter of t = π, we need two revolutions so it should be that t = π + 2 * 2π = 5π.

\(\left \{ {{x=2+3\cos t} \atop {y\:=-1+3\sin t}} \right. => \pi \leq t \leq 5\pi\)

Answer:

\(x = 4\)

Step-by-step explanation:

\(5x + 2 = 22\)

\(5x = 20\)

\(x = 4\)

\(\small\bold{5x + 2 = 22 }\)

Subtract 2 from 22 :

\(\small\bold{ 5x + 2 = 22}\)

\(\small\bold{5x = 22 - 2 }\)

Simplify :

\(\small\bold{5x = 20 }\)

Now , Divide 5x by 20 :

\(\small\bold{ \frac{5x}{20}}\)

\(\small\bold{x = 4 }\)

Sam drove approximately 246 miles.

Let's start by subtracting the base fee from the total amount Sam paid to find the additional fee he incurred for the miles driven:

213.33 - 18.99 = 194.34

We know that the additional fee is 79 cents per mile, so we can set up an equation to find the number of miles Sam drove:

194.34 = 0.79x

where x is the number of miles driven.

To solve for x, we can divide both sides of the equation by 0.79:

x = 194.34 / 0.79 ≈ 246

Therefore, Sam drove approximately 246 miles.

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1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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The amount of money which you must invest today is equal to $68,517.85.

Mathematically, the present value of an investment can be calculated by using this formula:

Present Value, PV = FV/(1 + r)^t

Given the following data:

Time, t = 9 years.

Future value, FA = $190,000.

Interest rate, r = 12% = 0.12.

Substituting the given parameters into the formula, we have;

PV = 190,000/(1 + 0.12)^9

PV = 190,000/(1.12)^9

PV = 190,000/2.7730

PV = $68,517.85.

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The value of the probability is P(Large or Blue) = 7/10

The given parameters are represented on the table

Using the table parameters, we have

P(Large or Blue) = [(Large) + (Blue) - (Large and Blue)]/Total

This gives

P(Large or Blue) = ((17 + 8) + (17 +3) - 17)/(17 + 3 + 8 + 12)

This gives

P(Large or Blue) = 28/40

Simplify

P(Large or Blue) = 7/10

Hence, the value of the probability is P(Large or Blue) = 7/10

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The correct formula for the slope will be:

m = (100 - 50)/(4 - 2) = 50/2 = 25 . Rafael took the reciprocal of the values.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. Δy and Δx are the net changes in the y and x coordinates, respectively.

So,

m = Δy / Δx

Using the slope-intercept form, as illustrated below, we can quickly get the slope for just a given line:

Y = mx + c can be used to represent a line.

For the stated question:

The slope calculated by Rachel is:

m = (4 - 2) / (100 - 50) = 2/50 = 1/25

Which is incorrect .

Thus, the correct formula for the slope will be:

m = (100 - 50)/(4 - 2) = 50/2 = 25

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Answer: B

Step-by-step explanation: