A positive integer from one to six is to be chosen by casting a die. Thus the elements c of the sample space C are 1, 2, 3, 4, 5, 6. Suppose C1 = {1, 2, 3, 4} and C2 = {3, 4, 5, 6}. If the probability set function P assigns a probability of 1 6 to each of the elements of C, compute P(C1), P(C2), P(C1 ∩ C2), and P(C1 ∪ C2).

Answer:

  b: elimination

Step-by-step explanation:

My vote is for elimination, though any of these methods (and some not listed) will get an answer quickly.

Subtracting the second equation from twice the first gives ...

  2(9x +8y) -(18x -15y) = 2(7) -(14)

  31y = 0 . . . simplify

  y = 0 . . . . . divide by 31 (or invoke the zero-product rule)

Then the value of x can be found from the first equation:

  9x = 7

  x = 7/9

__

I like this method because it tells you that y=0 in one step. (Graphing does the same.) For the numbers here, you can do it mentally. Once you recognize that the x-coefficients and the constants are related by the same factor, and that factor is different for the y-coefficients, it becomes apparent that elimination will immediately tell you that y=0.

1. 14 can be divided by 7 ( 14/7 = 2) so 7/14 reduces to 1/2

2. Both 6 and 9 can be divided by 3: 6/9 reduces to 2/3

3. 3/8 cannot be reduced, they do not have a common multiple, so this stays 3/8

4. Both 16 and 20 can be divided by 4, so this reduces to 4/5

Answer:

Part 1) m∠DBC=25°

Part 2) m∠DCB=65°

Part 3) m∠CDB=90°

Part 4) m∠ACD=25°

Part 5) m∠ADC=90°

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle DBC

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

In the right triangle ABC

m∠A+m∠B+m∠C=180° ----> equation A

we have

m∠A=65° ----> given problem

m∠C=90° ----> given problem

Substitute the given values in the equation A and solve for m∠B

65°+m∠B+90°=180°

m∠B+155°=180°

m∠B=180°-155°

m∠B=25°

Remember that the measure of Angle B is equal to say the measure of angle DBC

so

m∠B=m∠DBC

therefore

m∠DBC=25°

step 2

Find the measure of angle DCB and angle CDB

In the right triangle DBC

The sum of the interior angles of a triangle must be equal to 180 degrees

m∠DBC+m∠DCB+m∠CDB=180°

we have

m∠DBC=25°

m∠CDB=90° ----> is a right angle (CD is the height to AB)

substitute the values and solve for m∠DCB

25°+m∠DCB+90°=180°

m∠DCB+115°=180°

m∠DCB=180°-115°=65°

step 3

Find the measure of angle ACD

we know that

m∠ACD+m∠DCB=90° -----> by complementary angles

we have

m∠DCB=65°

substitute the value

m∠ACD+65°=90°

m∠ACD=90°-65°=25°

step 4

Find the measure of angle ADC

m∠ADC=90° ----> is a right angle (CD is the height to AB)

Answer:

Sheila is 0.61 meters taller than her son.

Step-by-step explanation:

First, you would convert 109 cm into meters. Once converted, Sheila's son would be 1.09. Then you would subtract 1.09 from 1.7 to find your answer!

Explanation:

A "common denominator" is the least common multiple (LCM) of the denominators of the rational expressions involved. As such it can be found as the product of the unique factors of those denominators, each to its highest power.

For example, the common denominator for fractions with denominators of 20 and 25 will be 100. It can be found by considering the factors ...

  20 = 2² × 5

  25 = 5²

The unique factors here are 2 and 5, each with a highest power of 2. The product of these unique factors to their highest powers is ...

  2²·5² = 4·25 = 100.

___

Using this method of finding the LCM, it is essential that we know the factors of the numbers.

The LCM can also be found as the product of the numbers, divided by their greatest common factor (GCF). For this method, too, you need to know factors of the numbers involved--or, at least, the greatest common factor.

For the above example numbers, the GCF is 5, so their LCM is ...

  20·25/5 = 500/5 = 100

Factors can help you find a common denominator by revealing common multiples. By multiplying the denominators of the fractions together, you can often find a common multiple that can be used as a common denominator. Simplify the resulting fraction by canceling out any common factors.

Finding a common denominator involves identifying a common multiple of the denominators of the fractions you are working with. Factors can help you find a common denominator by revealing common multiples. By multiplying the denominators of the fractions together, you can often find a common multiple that can be used as a common denominator. It's important to simplify the resulting fraction by canceling out any common factors.

https://brainly.com/question/29048802

#SPJ12

Answer with Step-by-step explanation:

The exponential growth function is given by

[tex]N(t)=N_oe^{mt}[/tex]

where

[tex]N(t)[/tex] is the population of the bacteria at any time 't'

[tex]N_o[/tex] is the population of the bacteria at any time 't = 0'

'm' is a constant and 't' is time after 7.00 a.m in hours

Assuming we start our measurement at 7.00 a.m as reference time  t = 0

Thus we get[tex]N(0)=N_oe^{m\times 0}\\\\12=N_o[/tex]

Now since it is given after 5 hours the population becomes 14 mg thus from the above relation we get

[tex]12\times e^{m\times 5}=14\\\\e^{5m}=\frac{14}{12}\\\\m=\frac{1}{5}\cdot ln(\frac{14}{12})\\\\m=0.031[/tex]

Thus the population of bacteria at any time 't' is given by

[tex]N(t)=12e^{0.031t}[/tex]

Part a)

Population of bacteria after another 5 hours equals the population after 10 hours from start

[tex]N(10)=12e^{0.031\times 10}=16.361mg[/tex]

Part b)

Population of bacteria at 7:00 p.m is mass after 12 hours

[tex]N(1)=12e^{0.031\times 12}=17.41mg[/tex]

Part c)

Population of bacteria at 8:00 p.m is mass after 1 hour

[tex]N(1)=12e^{0.031\times 1}=12.3378mg[/tex]

Part d)

Differentiating the relation of population with respect to time we get

[tex]N'(t)=\frac{d(12\cdot e^{0.031t})}{dt}\\\\N'(t)=12\times 0.031=0.372e^{0.031t}[/tex]

Thus we can see that the percentage increase varies with time initially the percentage increase is 37.2% but this percentage increase increases with increase in time

Part 4)

Since there are 24 hours in 1 day thus the percentage increase in the population is

[tex]\frac{N(24)-N_o}{N_o}\times 100\\\\=\frac{25.25-12}{12}\times 100=110.42[/tex]

Thus there is an increase of 110.42% in the population each day.

Answer:

Length = 128.3

Step-by-step explanation:

The 3 sides of a regular triangle are the same, the 2 sides that are in terms of x are equal:

5x + 40 = 8x - 13

40 + 13 = 8x - 5x

53 = 3x

17.7 = x

The length of a side = 5(17.7) + 40 = 128.3

Answer:

f(- 3) = 5

Step-by-step explanation:

The absolute value always returns a positive value, that is

| - a | = | a | = a

Given

f(x) = | x - 2 |

To evaluate f(- 3) substitute x = - 3 into f(x)

f(- 3) = | - 3 - 2 | = | - 5 | = 5

Answer:

y= 2/3x + 3

Step-by-step explanation: I suggest to look up slope intercept calculator it really helps.

Answer:

y = [tex]\frac{2}{3}[/tex] x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange - 2x + 3y = 9 into this form

Add 2x to both sides

3y = 2x + 9 ( divide all 3 terms by 3 )

y = [tex]\frac{2}{3}[/tex] x + 3 ← in slope- intercept form

On solving the equation -(6x+7)+8=19, we get value of x = -3.

To solve the equation -(6x+7)+8=19, we will first simplify each side of the equation and then solve for x. Here's how to do it step-by-step:

Distribute the negative sign across the parenthesis: -6x - 7 + 8 = 19.

Combine like terms on the left side: -6x + 1 = 19.

Subtract 1 from both sides: -6x = 18.

Divide both sides by -6 to find the value of x: x = -3.

Answer:

Probability of winning on one try : 1.16060875e-8

Step-by-step explanation:

For the first first 4 numbers.

Probability is 1/46 for the first number. Since the numbers are different, and it doesnt matter the order, the second number has a probability now of 1/45, the third has a probability of 1/44 and the last one a probability of 1/43.

Since the probability is dependan of the results of hitting the other number the probability of the first for numbers is the multiple of the 4 probabilities.

So it is 1/46 * 1/45 * 1/44 * 1/43 = 1 / 3916440

And that number is then multiplied by the probabilty of hitting the last number. 1/22

So the final probability is :

1/86161680   = 1.16060875e-8

Answer:

The probability of winning the jackpot on one try is 2.78 * 10^-7

Step-by-step explanation:

There are 46 balls in total  (46-1)+1 = 46 . (b-a)+1 is the formula for number of elements between a and b included.

We need to find the number of combinations possible of 4 balls ( as order doesn't matter - 1234 is the sames as 2341) . So the number of possible combinations of 4 balls taken from 1 - 46  is given by

C= n!/(r!(n-r)!) where n is the number of possible balls = 46 and r the size of combination = 4 and ! is factorial ( ex 3! = 3*2*1) This gives for this case

C= n!/(r!(n-r)!) = 46!/(4!(46-4)!)= 163,185 combinations.

But as there is a fifth ball with (22-1)+1   = 22 posible options each combination must be multiplied by 22( for example 1234 22 is one but also 1234 10 is other)

163,185*22= 3,590,070  possibilities.

The probability of winning is 1 in  3,590,070  possibilities. or

p = 1/ 3,590,070= 2.78 * 10^-7

Answer:

The probability that a particular death is due to an automobile accident is 2.72%

Step-by-step explanation:

The probability can be calculated as the percentage of each particular death.

The formula for this case is:

P(car accident) =  (Number of death due a car accident / Total of deaths) * 100

P(car accident) = (24/883)100 = 2.72%

Probabilities of each particular death:

Automobile accident = (24/883)100 = 2.72%

Cancer = (182/883)*100 = 20.61%

Heart disease = (333/883) * 100 = 37.71%

Answer:

Option 3 is the best option that compares the pair of intersecting rays with the angle

Step-by-step explanation:

The definition of angle says that an angle is a shape that is produced by the intersection of two rays that have a common end point.

A ray is a line segment that has only one end point and is extended infinitely in a unique direction

So Yeah. :) Hope I've helped

Answer:

  see the attachment

Step-by-step explanation:

(8, -3) is added to each of the preimage coordinates to get the coordinates of the image. For example, ...

  X' = X + (8, -3) = (-2, 5) + (8, -3) = (-2+8, 5-3)

  X' = (6, 2)

Final answer:

Explanation of how to find the preimage and image of a triangle under a translation along specified vector.

Explanation:

Translation is a transformation that moves all points of a figure the same distance in the same direction. Given a translation along (8, -3), we can find the preimage and image of the triangle with the given vertices by shifting each point 8 units to the right and 3 units down.

Preimage: X'(-2+8, 5-3) = X(6, 2), Y'(-3+8, 2-3) = Y(5, -1), Z'(-6+8, 6-3) = Z(2, 3).

Image: Triangle XYZ under the translation along (8, -3) has vertices X'(6, 2), Y'(5, -1), Z'(2, 3).

Final answer:

When Mike increased the size of his truck tires from the original P215/60R16 to the larger P235/70R16 without recalibrating his speedometer, the actual speed he was going on the new tires when his speedometer showed 60 mph was approximately 54.2 mph.

Explanation:

When Mike increased the size of his truck tires without recalibrating his speedometer, his speedometer reading would be inaccurate. To determine how fast he is going on the new tires when his speedometer shows 60 mph, we can use the concept of tire revolutions per mile.

The original tire size, P215/60R16, has a diameter of approximately 25.7 inches, while the larger tire size, P235/70R16, has a diameter of approximately 29.0 inches. The new tires cover a greater distance in one revolution compared to the original tires.

To calculate the actual speed, we can use the equation:

Actual Speed = Speedometer Reading * (Original Tire Diameter / New Tire Diameter)

Substituting the given values:

60 mph * (25.7 inches / 29.0 inches)

By simplifying this calculation, the actual speed is approximately 54.2 mph. Therefore, the correct answer is A. 54.2 mph.

Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.

Calculate the difference in tire circumference:

Original circumference: 2 * π * radius = 2 * π * (215 mm / 25.4 mm/inch) * (60 + 30%) = 79.3 inches (assuming 30% aspect ratio)

New circumference: 2 * π * (235 mm / 25.4 mm/inch) * (70 + 30%) = 85.1 inches

Difference: 85.1 inches - 79.3 inches = 5.8 inches

Calculate the percentage increase in circumference:

(5.8 inches / 79.3 inches) * 100% = 7.3%

Apply the percentage increase to the speedometer reading:

Actual speed = Speedometer reading * (1 + % increase)

Actual speed = 60 mph * (1 + 7.3%) = 60 mph * 1.073

Actual speed ≈ 64.4 mph

Therefore, when the speedometer shows 60 mph, Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.

Answer:

h(- 8) = - 8

Step-by-step explanation:

To evaluate h(- 8) substitute x = - 8 into h(x), that is

h(- 8) = [tex]\frac{(-8)^2+3(-8)}{4(-8)+27}[/tex]

        = [tex]\frac{64-24}{-32+27}[/tex]

       = [tex]\frac{40}{-5}[/tex] = - 8

Answer:

Perimeter = 120 m

Step-by-step explanation:

Perimeter = (24+36)*2 = 120 m

The data obtained from both questions is qualitative and discrete. The highest level of measurement for the data is ordinal.

The data obtained from the first question, "What has been your experience with American products?", is qualitative as it involves responses categorized into below average, average, above average, and good to excellent. The data from the second question, where a supervisor gives a summary evaluation rating, is also qualitative, with choices ranging from poor to excellent.

Both sets of data are discrete since they are categorized into distinct choices. The highest level of measurement for these data is ordinal since the choices have a specific order but do not have equal intervals between them.

To determine the size of Dylan's collection, we multiply Jayden's collection (800 cards) by 1/10. The result is that Dylan has 80 baseball cards in his collection.

In this problem, Jayden has a collection of 800 baseball cards. His brother Dylan has a collection that is 1/10 as large. To find out how many cards Dylan has, we perform a simple multiplication problem: we multiply Jayden's collection (800 cards) by the fraction representing Dylan's collection size (1/10).

Therefore, Dylan has 800 * 1/10 = 80 baseball cards.

https://brainly.com/question/35502092

#SPJ2

Step-by-step explanation:

3y-x-5=0

3y=x+5

y=(x+5)/3

y= (1/3)*x + (5/3)

The general equation of y is:

y=mx+b

where:

slope=m

b= y intercept

so, slope is (1/3) and y intercept is (5/3)

and x intercept=0, when you star to graphic you can see that the only option for have y=(5/3) is necessary that the value of x=0. Or:

y intercept= (1/3)*x +(5/3) =(5/3)

(5/3)-(5/3)=(1/3)x

0=(1/3)*x

0/(1/3)=x

x=0.

Answer:

y = 3x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = [tex]\frac{2+4}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3

Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4

y = 3x - 4 ← equation of line

In the equation, x represents the number of balloons. We say that 25 cents per balloon becomes 0.25x.

Jimmy also purchased a chocolate cake. This is the PLUS sign in the equation.

The total for everything purchased is $35.

Balloons x at 25 cents each = 0.25x plus a chocolate cake for $10 together equals $35.

Answer:

Remember that if you want the area on a rectangle you have to think, lengh x width. In this case, the correct answer is C.

Step-by-step explanation:

There is something wrong in this, because 20 is not 2 meters than its width.

Answer:

Step-by-step explanation:

There are two parts to this problem:

As you can learn from any speed limit sign, speed is in units of distance per time--miles per hour in the US. To compute speed, you divide distance by time.

If we were to use the given numbers directly, dividing distance in miles by time in seconds, our speed would have units of miles per second. In order to change the units to the ones asked for by the problem statement, we need to make one of two conversions.

For the first part, we need to convert miles to feet, so our speed is in feet per second instead of miles per second. For the second part, we need to convert seconds to hours, so the speed is in miles per hour.

__

Any units conversion can be done using a conversion factor that is a fraction that has a value of 1. That is, its numerator is equal to its denominator.

For the conversion from miles to feet, we want to cancel units of miles and leave units of feet. The operation on units looks like ...

  [tex]\dfrac{miles}{second}\times\dfrac{feet}{mile}=\dfrac{feet}{second}[/tex]

The units of miles in the numerator cancel the units of miles in the denominator, so we're left with feet per second, as we want. In order to make the conversion factor have a value of 1, it must be ...

  (5280 ft)/(1 mi) . . . . . . numerator equal to denominator

(a) Express the speed in ft/s:

(2.5 mi)/(37.895 s) × (5280 ft)/(1 mi) = 2.5·5280/37.895 ft/s ≈ 348.331 ft/s

__

(b) For the conversion to miles per hour from miles per second, we need to cancel the units of seconds in the denominator and replace them with hours. The conversion factor for that is ...

  (3600 s)/(1 h) . . . . . . numerator equal to denominator

(2.5 mi)/(37.895 s) × (3600 s)/(1 h) = 2.5·3600/37.895 mi/h ≈ 237.498 mi/h

Answer:

[tex]\dfrac{x}{4}[/tex]

C is correct.

Step-by-step explanation:

At a picnic,

Number of adults is 3 times as number of children.

Number of women is twice as number of men.

Total number of men, women and children at the picnic be x

Let number of children be c

Let number of men be m

Let number of women be w

# Number of women is twice as number of men, w = 2m

# Number of adults is 3 times as number of children, w + m = 3c

      2m + m = 3c     (∴  w=2m )

                c = m

Total number of men, women and children at the picnic be x

∵       c + m + w = x

     m + m + 2m = x

                    4m = x

Number of men, [tex]m=\dfrac{x}{4}[/tex]

Hence, The total number of men will be  [tex]\dfrac{x}{4}[/tex]

Answer:

4

Step-by-step explanation:

(16*1/2)*1/2

((16*1)/2)*1/2

(16/2)*1/2

8*1/2

8/2

4

or

16*1/2*1/2

16*(1/4)

16/4

4

Answer:

C is your answer

Step-by-step explanation:

Judy Clark will pay back $7,993.03 on January 20 for her loan of $7,800 at a 6.5% interest rate, with the interest being calculated for 140 days.

To calculate the amount Judy Clark will repay for a loan of $7,800 borrowed from Reel Bank at an ordinary interest rate of 6.5%, we need to determine the amount of interest accumulated by the loan from September 2 to January 20. This involves calculating the time period for the loan, applying the ordinary interest formula, and then adding the interest to the principal amount to find the total repayment amount.

We first calculate the number of days between September 2 and January 20. Without knowing the year of the loan, we can use an approximate count and consider a non-leap year for this example, which would be 140 days (30 days for September after the 2nd, 31 for October, 30 for November, 31 for December, and 18 for January).

Using the formula I = PRT, where P is the principal ($7,800), R is the annual interest rate (0.065), and T is the time in years (140/365), we can calculate the interest:

I = 7,800 × 0.065 × (140/365) = $193.03 (rounded to two decimal places).

To find the total repayment amount, we add the interest to the principal: $7,800 + $193.03 = $7,993.03.

Therefore, Judy Clark will pay back $7,993.03 on January 20.

so the area A is no more than 10, namely A ⩽ 10 , it could be 10 or less, but no more than that.

let's recall the area of a triangle is A = (1/2)bh

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=4\\ h=2x-3 \end{cases}\implies A=\cfrac{1}{2}(4)(2x-3) \\\\[-0.35em] ~\dotfill\\\\ A\leqslant 10\implies \cfrac{1}{2}(4)(2x-3)\leqslant 10\implies 2(2x-3)\leqslant 10\implies 4x-6\leqslant 10 \\\\\\ 4x\leqslant 16\implies x\leqslant \cfrac{16}{4}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{maximum height of the triangle}}{2(4)-3}\implies 8-3\implies 5[/tex]

when x = 4 is the maximum height, since x ⩽ 4, so it could be 4 at most, could be less than 4 or equals but never higher.

Answer:

31

Step-by-step explanation:

Let number of ten dollar bills be x .

So, number of five dollar bills = 2 x

Total amount of money in the cash register = 620 dollars

Amount of money in total cash as a result of  five dollar bills = 2 x × 5 = 10 x  dollars

Amount of money in total cash as a result of  ten dollar bills =  x × 10 = 10 x dollars

According to question ,

Total amount of money in the cash register = Amount of money in total cash as a result of  five dollar bills +  Amount of money in total cash as a result of  ten dollar bills

⇒ 620 = 10 x + 10 x

⇒ 620 = 20 x

⇒ x = [tex]\frac{620}{20}[/tex] = 31

So, number of ten dollar bills = 31

Final answer:

By setting up an algebraic equation based on the information provided, we can determine there are 31 ten dollar bills in the cash register.

Explanation:

To solve the question: A cash register contains only five dollar and ten dollar bills. It contains twice as many five's as ten's and the total amount of money in the cash register is 620 dollars. How many ten's are in the cash register? we need to use algebra.

Let's let x represent the number of ten dollar bills. Since the register contains twice as many five dollar bills as ten dollar bills, we can represent the number of five dollar bills as 2x.

The value of the ten dollar bills is 10x dollars, and the value of the five dollar bills is 5(2x) = 10x dollars. The total amount of money in the cash register is the sum of these values, which equals 620 dollars. So, we have the equation:

10x + 10x = 620

Simplifying, this becomes 20x = 620. Dividing both sides by 20 gives us x = 31.

Therefore, there are 31 ten dollar bills in the cash register.