At a certain school, intro to economics and intro to calculus meet at the same time, so it is impossible for a student take both classes. If the probability that a student takes intro to economics is 0.57, and the probability that a student takes intro to calculus 0.17, what is the probability that a student takes intro to economics or into to calculus?

Answer:

The point of intersection [tex]P\left(\dfrac{1133}{122},\dfrac{149}{122},\dfrac{699}{122}\right)[/tex]

Step-by-step explanation:

Equation of line:

[tex]x=7+9t[/tex]

[tex]y=3-7t[/tex]

[tex]z=7-5t[/tex]

Equation of plane:

[tex]5x-6y-7z=-1[/tex]

We need to find the point of intersection of line and plane.

Point of intersection: When both line and plane meet at single point.

So, put the value of x, y and z into plane.

[tex]5(7+9t)-6(3-7t)-7(7-5t)=-1[/tex]

[tex]35+45t-18+42t-49+35t=-1[/tex]

[tex]122t=-1+32[/tex]

[tex]t=\dfrac{31}{122}[/tex]

Substitute the value of t into x, y and z

[tex]x=7+9\cdot \dfrac{31}{122}=\dfrac{1133}{122}[/tex]

[tex]y=3-7\cdot \dfrac{31}{122}=\dfrac{149}{122}[/tex]

[tex]z=7-5\cdot \dfrac{31}{122}=\dfrac{699}{122}[/tex]

Point of intersection:

[tex]\left(\dfrac{1133}{122},\dfrac{149}{122},\dfrac{699}{122}\right)[/tex]

Hence, The point of intersection [tex]P\left(\dfrac{1133}{122},\dfrac{149}{122},\dfrac{699}{122}\right)[/tex]

Answer:

3/5

Step-by-step explanation:

Total tossed : 30

# of times landed on tails : 18

Experimental probability of tails = 18/30 = 3/5

Answer:

  1763 ft²

Step-by-step explanation:

Using the given conversion factor, ...

  (164 m²)(1 ft/(.305 m))² = 165/.093025 ft² ≈ 1763 ft²

_____

The exact conversion factor is 1/0.3048, so the area is closer to 1765 ft². For a 4-significant digit answer, you need to use a conversion factor accurate to 4 significant digits.

To convert square meters to square feet, you must square the feet to meter conversion factor, resulting in approximately 10.764 sq ft/sq m. You then multiply this by the square meter measurement to get the equivalent in square feet. Therefore, the house's area, which was provided as 164 square meters, translates to approximately 1765.736 square feet.

The measure of the area in square feet can be derived using the conversion factor for feet to meters, 1 ft = 0.305 m. However, when you deal with areas, you must square the conversion factor. We then apply the conversion factor to the known area in reference, which in our case is 164 square meters.

So our conversion factor becomes (1/0.305)² sq ft/sq m = 10.764 sq ft/sq m.

To use the conversion factor, we multiply it by the metric unit measurement, like this: 164 m²*(10.764 ft²/m²) = 1765.736 square feet.

So, the house's area is approximately 1765.736 square feet.

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Final answer:

The problem requires formulating a linear programming model to maximize the profit function Z = 9x + 7y with constraints on machine time for product A and B (2x + 3y ≤ 6 for machine M and 4y ≤ 8 for machine L) and the non-negativity restrictions (x, y ≥ 0).

Explanation:

The linear programming problem can be stated in mathematical terms with an objective function and constraints for a firm making products A and B. The objective is to maximize profit, which is the sum of 9 dollars per unit of product A and 7 dollars per unit of product B. Let the number of products A and B produced be represented by variables x and y, respectively.

The objective function to maximize is Z = 9x + 7y.

Constraints:

Answer:

  $16,479

Step-by-step explanation:

The table tells you Ed's tax is ...

  14,138.50 + 0.31×(70,000 -62,450) = 16,479 . . . . dollars

Answer:

5 units

Step-by-step explanation:

This is a circle with a center of (0, 0).  The square root of 25 represents the radius of the circle which is 5.  The radius represents the distance that the outside of the circle is from the center.

Answer:

  $5036.34

Step-by-step explanation:

Each year, 8% of the existing balance is added to the existing balance, effectively multiplying the amount by 1.08. If that is done for 12 years, the effective multiplier is 1.08^12 ≈ 2.51817. The the amount in the bank at the end of that time is ...

  $2000×2.51817 = $5036.34

The amount in the bank after 12 years with an annual interest rate of 8% on a principal amount of 2000 dollars, compounded annually, will be approximately $5025.90.

This is a compound interest problem. The formula used to solve this type of problem is A = P(1 + r/n)^(nt), where:

In this case, P = $2000, r = 8% or 0.08, t = 12 years and n = 1 (as interest is compounded annually). Substituting these values in the equation, we get:

A = 2000(1 + 0.08/1)^(1*12)

.

The resulting Amount A after 12 years will be approximately $5025.90.

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Answer:

The solution is 22.98.

Step-by-step explanation:

Here, the given equation,

[tex]5 + 69\times 0.96^t = 32[/tex],

Let [tex]f(t) = 5 + 69\times 0.96^t[/tex]

And, [tex]f(t) = 32[/tex]

Where, t represents x-axis and f(t) represents y-axis,

Since, [tex]f(t) = 5 + 69\times 0.96^t[/tex] is an exponential decay function having y-intercept (0,74).

Also, f(t) = 32 is the line, parallel to x-axis,

Thus, after plotting the graph of the above functions,

We found that they are intersecting at (22.984, 32)

Hence, the solution of the given equation = x-coordinate of the intersecting point = 22.984 ≈ 22.98

To solve the given equation, 5 + 69 × 0.96t = 32, you start by subtracting 5 from both sides, then divide by 69. Then, divide both sides by 0.96 to solve for t. The solution is t ≈ 0.41 (rounded to two decimal places).

To solve the equation 5 + 69 × 0.96t = 32 using the crossing-graphs method, we first simplify the equation:

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Answer:

14.6328% , $5836.03

Step-by-step explanation:

Here we are going to use the formula

[tex]A_{0}(1-r)^n = A_{n}[/tex]

[tex]A_{0}[/tex] = 39000

r=?

[tex]A_{8}[/tex] = 11000

n=8

Hence

[tex]39000(1-r)^8 = 11000[/tex]

[tex](1-r)^8 = \frac{11000}{39000}[/tex]

[tex](1-r)^8 = 0.2820[/tex]

[tex](1-r) = 0.2820^{\frac{1}{8}[/tex]

[tex](1-r) = 0.2820^{0.125}[/tex]

[tex](1-r) = 0.8536[/tex]

[tex](1-0.8536=r[/tex]

[tex]r = 0.1463[/tex]

Hence r= 0.1463

In percentage form r = 14.63%

Now let us see calculate the value of car in 2003 that is after 12 years

we use the main formula again

[tex]A_{0}(1-r)^n = A_{n}[/tex]

[tex]A_{0}[/tex] = 39000

r=0.1463

[tex]A_{12}[/tex] = ?

n=12

[tex]39000(1-0.14634)^{(12} = A_{12}[/tex]

[tex]39000(0.8536)^{12} = A_{12}[/tex]

[tex]39000*0.1497 = A_{12}[/tex]

[tex]A_{12}=5840.34[/tex]

Hence the car's value will be depreciated to $5840.34 (approx) by 2003.

The annual rate of change between 1995 and 2003 is -0.1463

The annual rate of change between 1995 and 2003 is -14.63%

The value of the car in 2007 would be $5,844.24

The value of the car decreases as the years go by. This is referred to as depreciation. Depreciation is the decline in value of an asset as a result of wear and tear.

In order to determine the annual rate of change, use this formula:

g = [tex](FV / PV) ^{\frac{1}{n} } - 1[/tex]

Where:

g = depreciation rate

FV = value of the car in 2003 = $11,000

PV = value of the car in 1995 = $39,000

n = number of years = 2003 - 1995 = 8

[tex](11,000 / 39,00)^{\frac{1}{8} } - 1[/tex] = -0.1463 = -14.63%

The value of car in 7 years can be determined using this formula:

FV = P (1 + g)^n

$39,000 x (1 - 0.1463)^12

$39,000 x 0.8537^12 = $5,844.24

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Answer:

[tex]\large\boxed{x=6\pm3\sqrt{10}}[/tex]

Step-by-step explanation:

[tex]x^2-12x+36=90\\\\x^2-2(x)(6)+6^2=90\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-6)^2=90\iff x-6=\pm\sqrt{90}\\\\x-6=\pm\sqrt{9\cdot10}\\\\x-6=\pm\sqrt9\cdot\sqrt{10}\\\\x-6=\pm3\sqrt{10}\qquad\text{add 6 to both sides}\\\\x=6\pm3\sqrt{10}[/tex]

Answer:

A

Step-by-step explanation:

Volume varies directly with the square of the radius, so:

V = k r²

When V = 80, r = 4.

80 = k (4)²

k = 5

V = 5r²

When r = 3:

V = 5 (3)²

V = 45

The flow is 45 L/min.

Answer:

The probability of the sample mean foot length less than 23 cm is 0.120

Step-by-step explanation:

* Lets explain the information in the problem

- The eighth-graders asked to measure the length of their right foot at

  the beginning of the school year, as part of a science project

- The foot length is approximately Normally distributed, with a mean of

 23.4 cm

∴ μ = 23.4 cm

- The standard deviation of 1.7

∴ σ = 1.7 cm

- 25 eighth-graders from this population are randomly selected

∴ n  = 25

- To find the probability of the sample mean foot length less than 23

∴ The sample mean x = 23, find the standard deviation σx

- The rule to find σx is σx = σ/√n

∵ σ = 1.7 and n = 25

∴ σx = 1.7/√25 = 1.7/5 = 0.34

- Now lets find the z-score using the rule z-score = (x - μ)/σx

∵ x = 23 , μ = 23.4 , σx = 0.34

∴ z-score = (23 - 23.4)/0.34 = -1.17647 ≅ -1.18

- Use the table of the normal distribution to find P(x < 23)

- We will search in the raw of -1.1 and look to the column of 0.08

∴ P(X < 23) = 0.119 ≅ 0.120

* The probability of the sample mean foot length less than 23 cm is 0.120

Answer:

  450 km

Step-by-step explanation:

Equations

We can define 3 variables: a, b, d. Let "a" and "b" represent the speeds of the cars leaving cities A and B, respectively. Let "d" represent the distance between the two cities. We can write three equations in these three variables:

1. The relation between "a" and "b":

  a = b -10 . . . . . . . the speed of car A is 10 kph less than that of car B

2. The relation between speed and distance when the cars leave at the same time:

  d = (a +b)·5 . . . . . . distance = speed × time

3. Note that the time it takes car B to travel 150 km to the meeting point is (150/b). (time = distance/speed) The total distance covered is ...

  distance covered by car A in 4 1/2 hours + distance covered by both cars (after car B leaves) = total distance

  4.5a + (150/b)(a +b) = d

__

Solution

Substituting for d, we have ...

  4.5a + 150/b(a +b) = 5(a +b)

  4.5ab +150a +150b = 5ab +5b^2 . . . . . . multiply by b, eliminate parentheses

  5b^2 +0.5ab -150(a +b) = 0 . . . . . . . . . . subtract the left side

Now, we can substitute for "a" and solve for b.

  5b^2 + 0.5b(b-10) -150(b -10 +b) = 0

  5.5b^2 -5b -300b +1500 = 0 . . . . . . . . eliminate parentheses

  11b^2 -610b +3000 = 0 . . . . . . . . . . . . . multiply by 2

  (11b -60)(b -50) = 0 . . . . . . . . . . . . . . . . factor

The solutions to this equation are ...

  b = 60/11 = 5 5/11 . . . and . . . b = 50

Since b must be greater than 10, the first solution is extraneous, and the values of the variables are ...

The distance between A and B is 450 km.

_____

Check

When the cars leave at the same time, their speed of closure is the sum of their speeds. They will cover 450 km in ...

  (450 km)/(40 km/h +50 km/h) = 450/90 h = 5 h

__

When car A leaves 4 1/2 hours early, it covers a distance of ...

  (4.5 h)(40 km/h) = 180 km

before car B leaves. The distance remaining to be covered is ...

  450 km - 180 km = 270 km

When car B leaves, the two cars are closing at (40 +50) km/h = 90 km/h, so will cover that 270 km in ...

  (270 km)/(90 km/h) = 3 h

In that time, car B has traveled (3 h)(50 km/h) = 150 km away from city B, as required.

Answer:

450km

Step-by-step explanation:

Take it that each automobile travels at 30 km an hour, for 150 km, meaning it will be 450 km apart.

Answer:

(g-h)=x^2+5-8-x

=x^2-x-3

(g-h)(-9) means x= -9

x^2-x-3

=(-9)^2-(-9)-3

=81+9-3

=90-3

=87

Answer: (a) 0.37

Step-by-step explanation:

Given: The speed of cars on a stretch of road is normally distributed with an average 48 miles per hour with a standard deviation of 5.9 miles per hour.

i.e. Mean : [tex]\mu = 48\text{ miles per hour} [/tex]

Standard deviation : [tex]\sigma = 5.9\text{ miles per hour}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For the probability that a randomly selected car is violating the speed limit of 50 miles per hour (X≥ 50).

For x= 80

[tex]z=\dfrac{50-48}{5.9}=0.338983050847\approx0.34[/tex]

The P Value =[tex]P(z>0.34)=1-P(z<0.34)=1-0.6330717\approx0.3669283\approx0.37[/tex]

Hence,  the probability that a randomly selected car is violating the speed limit of 50 miles per hour =0.37

Answer:

b. (-1,3)

Step-by-step explanation:

the  image of the point (x ; y)  by symmetry about x-axis is : ( x ;-  y)

so the answer "b" : (-1,3)

Answer:

218.75 miles / 12.5 hours

437.5 miles / 25 hours

656.25 miles / 37.5 hours

Step-by-step explanation:

35 miles / 2 hours = 87.5 miles / 5 hours

This is the  ratio of 2.5. So, the other proportions are

87.5 x 2.5 miles / 5 x 2.5 hours = 218.75 miles / 12.5 hours

87.5 x 5 miles / 5 x 5 hours = 437.5 miles / 25 hours

87.5 x 7.5 miles / 5 x 7.5 hours = 656.25 miles / 37.5 hours

Answer:

  sin(2θ) = 0.96

Step-by-step explanation:

In the third quadrant, both sin(θ) and cos(θ) are negative. Then the double-angle trig identity tells us ...

  sin(2θ) = 2·sin(θ)·cos(θ) = -2cos(θ)√(1 -cos(θ)²) . . . . using the negative root

Filling in the given value, we have

  sin(2θ) = -2·(-0.6)(√(1-(-0.6)²) = 2·0.6·0.8 = 0.96

Answer:

[tex]\large\boxed{A=153\ cm^2}[/tex]

Step-by-step explanation:

Look at the picture.

We have

square with side length a = 9

trapezoid with base lengths b₁ = 9 and b₂ = 6 and the height length h = 6

right triangle with legs lengths l₁ = 3 + 6 = 9 and l₂ = 6

The formula of an area of a square

[tex]A=a^2[/tex]

Substitute:

[tex]A_I=9^2=81\ cm^2[/tex]

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

Substitute:

[tex]A_{II}=\dfrac{9+6}{2}\cdot6=\dfrac{15}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3=(15)(3)=45\ cm^2[/tex]

The formula of an area of a right triangle:

[tex]A=\dfrac{l_1l_2}{2}[/tex]

Substitute:

[tex]A_{III}=\dfrac{(9)(6)}{2}=\dfrac{54}{2}=27\ cm^2[/tex]

The area of the shape:

[tex]A=A_I+A_{II}+A_{III}\\\\A=81+45+27=153\ cm^2[/tex]

Answer: The mean and the standard error of the distribution of the sample mean are 200 and 2.

Step-by-step explanation:

Given: Sample size : n= 81

Mean of infinite population : [tex]\mu=200[/tex]

We know that the mean of the distribution of the sample mean is same as the mean of the population.

i.e. [tex]\mu_x=\mu=200[/tex]

The standard error of the distribution of the sample mean is given by :-

[tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\Rightarrow\ S.E.=\dfrac{18}{\sqrt{81}}=\dfrac{18}{9}=2[/tex]

Hence, the mean and the standard error of the distribution of the sample mean are 200 and 2.

The mean of the sample mean distribution for a random sample of size 81 from a population with a mean of 200 and a standard deviation of 18 is 200, and the standard error is 2.

The question is about determining the mean and the standard error of the distribution of the sample mean. According to the Central Limit Theorem, regardless of the distribution of the original population, the distribution of the sample mean tends to form a normal distribution as the sample size increases. In this case, the mean of the sample mean distribution is the same as the population mean, which is 200.

The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size. So, the standard error in this scenario would be 18/√81 = 2.

Therefore, in a random sample of size 81 taken from an infinite population with a mean of 200 and a standard deviation of 18, the mean of the sample mean distribution is 200, and the standard error is 2.

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Answer:

x = -1 and y = -4

Step-by-step explanation:

It is given that,

3x - 2y = 5     ----(1)

-2x - 3y = 14 ------(2)

To find the solution of equations

(1) * 2 ⇒

6x - 4y = 10  -----(3)

(2) * 3 ⇒

-6x - 9y =  42   ----(4)

eq(3) + eq(4) ⇒

6x - 4y = 10  -----(3)

-6x - 9y =  42  ----(4)

 0   - 13y = 52

y = 52/(-13) = -4

Substitute the value of y in eq(1)

3x - 2y = 5     ----(1)

3x - (2 * -4) = 5

3x  +8 = 5

3x = 5 - 8 = -3

x = -3/3 = -1

Therefore x = -1 and y = -4

Answer:

The solution is:

[tex](-1, -4)[/tex]

Step-by-step explanation:

We have the following equations

[tex]3x - 2y =5[/tex]

[tex]-2x - 3y = 14[/tex]

To solve the system multiply by [tex]\frac{3}{2}[/tex] the second equation and add it to the first equation

[tex]-2*\frac{3}{2}x - 3\frac{3}{2}y = 14\frac{3}{2}[/tex]

[tex]-3x - \frac{9}{2}y = 21[/tex]

[tex]3x - 2y =5[/tex]

---------------------------------------

[tex]-\frac{13}{2}y=26[/tex]

[tex]y=-26*\frac{2}{13}[/tex]

[tex]y=-4[/tex]

Now substitute the value of y in any of the two equations and solve for x

[tex]-2x - 3(-4) = 14[/tex]

[tex]-2x +12 = 14[/tex]

[tex]-2x= 14-12[/tex]

[tex]-2x=2[/tex]

[tex]x=-1[/tex]

The solution is:

[tex](-1, -4)[/tex]

Answer:

  b = 1.098

Step-by-step explanation:

Each year, the GDP is 9.8% higher than the year before, so the multiplier each year is 1 + 9.8% = 1.098. This is the value of b.

  b = 1.098

Answer:

The volume of the prism is 27√3/2

Step-by-step explanation:

* Lets revise the triangular prism properties

- The triangular prism has five faces

- Two bases and three side faces

- The two bases are triangles

- The three side faces are rectangles

- The rule of its volume is Area of its base × its height

* Lets solve the problem

- The triangular prism has two bases which are equilateral triangles

- The length of each side of the triangular base is 3"

- The height of the prism is 6"

∵ The volume of the prism = area of the base × its height

∵ The base is equilateral triangle of side length 3"

- The area of any equilateral triangle is √3/4 s²

∴ The area of the base of the prism = √3/4 × (3)² = 9√3/4

∵ The length of the height of the prism is 6"

∴ The volume of the prism = 9√3/4 × 6 = 27√3/2

* The volume of the prism is 27√3/2

Answer:

Step-by-step explanation:

The 2 numbers that are not in the domain of the function are the 2 numbers that cause the denominator of the function to equal 0.  In order to find those 2 numbers, we have to factor the quadratic that is in the denominator. When you factor, you get x = 2.79 and x = -1.79

Those are the values of x that cause the denominator to equal 0, which of course is NEVER allowed in math!

Answer:

Step-by-step explanation:

The answer above this answer is correct

Answer:

C. 106

Step-by-step explanation:

Angles 2 and 6 are corresponding angles so they're both 74. So you just subtract 74 from 180 to get 106.

Answer:

C. 106 is the answer

Step-by-step explanation:

angle 3 = angle 2 (vertically opp. angle)

angle 3+ angle 5 = 180

74+ angle 5 = 180

angle 5 = 106

Answer: The probability that 3 or more belong to the ruling clique is 0.34.

Step-by-step explanation:

Since we have given that

Number of total members = 50

Number of belonging to ruling clique = 10

Number of belonging to second class member = 40

We need to find the probability that 3 or more belong to the ruling clique.

Let X be the number of outcomes belong to ruling clique.

So, it becomes,

P(X≥3)=1-P(X<3)

[tex]P(X\geq 3)=1-P(X=1)-P(X=2)\\\\P(X\geq 3)=1-\dfrac{^{10}C_1\times ^{40}C_5}{^{50}C_6}-\dfrac{^{10}C_2\times ^{40}C_4}{^{50}C_6}\\\\P(X\geq 3)=1-0.41-0.25\\\\P(X\geq 3)=0.34[/tex]

Hence, the probability that 3 or more belong to the ruling clique is 0.34.

The probability of selecting 3 or more members from the ruling clique when choosing 6 members randomly from a club of 50 members (10 in ruling clique, 40 second-class) is 8.56%.

This probability problem can be solved using the concepts of Combinations and Binomial Theorem. You need to determine the number of ways to choose 3, 4, 5, or 6 members from the ruling clique (10 members) and the remaining from the second-class members (40 members). For each case, divide by the total number of ways to choose 6 members from all 50 members to get the probability. Sum up all the probabilities for each case to get the total probability of having 3 or more from the ruling clique.

1. Number of ways of choosing 3 from the ruling clique and 3 from the second class: C(10,3)*C(40,3) = 120*9880 = 1,185,600 ways

2. Number of ways of choosing 4 from the ruling clique and 2 from the second class: C(10,4)*C(40,2) = 210*780 = 163,800 ways

3. Number of ways of choosing 5 from the ruling clique and 1 from the second class: C(10,5)*C(40,1) = 252*40 = 10,080 ways

4. Number of ways of choosing 6 from the ruling clique and 0 from the second class: C(10,6)*C(40,0) = 210*1 = 210 ways

Total ways to choose 3 or more from the ruling clique: 1,185,600 + 163,800 + 10,080 +210 = 1,359,690 ways

From 50 members, the total ways to choose 6: C(50,6) = 15,890,700 ways

The Probability of 3 or more from the ruling clique = 1,359,690 / 15,890,700 = 0.0856 or 8.56%

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