Two friends, Bob and Ben, each buy one ticket for a drawing. They can choose six numbers from a total of one hundred numbers (0 - 99) for their ticket. Bob chooses the numbers 1, 2, 3, 4, 5, 6, and Ben chooses the numbers 39, 45, 66, 72, 74, 89. Who has a higher probability of winning the drawing?

Answer:

\(x>4\)

Step-by-step explanation:

Bring the five to the other side of the equation.

\(-4x<-11-5\)

Add the double negatives.

\(-4x<-16\)

Divide. (flip the sign on account of dividing by a negative number.)

\(x>4\)

Move the constant to the right-hand side and change its sign:

\( - 4x < - 11 - 5\)

Calculate the difference:

\( - 4x < - 16\)

Divide both side of the inequality by -4 and flip the inequality sign:

\(x > 4\)

Answer:

9.48

Step-by-step explanation:

Answer:

The length of the segment is 5

Answer:

Refer to below!

Step-by-step explanation (a):

\(\rightarrow \dfrac{10^{3} \times 10^{4} }{10^{5} } \\\\\\ \rightarrow \dfrac{10^{3 + 4} }{10^{5} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[[\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ] \\\\\\ \rightarrow \dfrac{10^{7} }{10^{5} } \\\\\\\)

\(\rightarrow 10^{7 - 5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}] \\\\\rightarrow 10^{2}\)

Step-by-step explanation (b):

\(\rightarrow \huge{\text{(}{10^{4} \times \dfrac{10^{12} }{10^{7} }\huge{\text{)}\)

\(\rightarrow \huge{\text{(}{10^{4} \times {10^{12 - 7} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]\)

\(\rightarrow \huge{\text{(}{10^{4} \times {10^{5} }\huge{\text{)}\)

\(\rightarrow \huge{\text{(}{10^{4 + 5} }\huge{\text{)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ]\)

\(\rightarrow{10^{9} }\)

Step-by-step explanation (c):

\(\rightarrow \huge{\text{(}\dfrac{10^{5} }{10^{3} } }\huge{\text{)}\)

\(\rightarrow \huge{\text{(}10^{5 - 3} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]\)

\(\rightarrow 10^{2} }\)

Step-by-step explanation (d):

\(\rightarrow \dfrac{10^{4} \times 10^{5} \times 10^{6} }{10^{3} \times 10^{7} }\)

\(\rightarrow \dfrac{10^{4 + 5 + 6} }{10^{3 + 7} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ]\)

\(\rightarrow \dfrac{10^{15} }{10^{10} }\)

\(\rightarrow 10^{15 - 10} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]\)

\(\rightarrow 10^{5} }\)

Step-by-step explanation (e):

\(\rightarrow \dfrac{(10^{5})^{2} }{(10^{2})^{3} }\)

\(\rightarrow \dfrac{10^{5 \times 2} }{10^{2 \times 3} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule: }(a^{2} )^{5} = a^{2 \times 5} = a^{10} ]\)

\(\rightarrow \dfrac{10^{10} }{10^{6} }\)

\(\rightarrow {10^{10 - 6} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}]\)

\(\rightarrow {10^{4}\)

The equation is given as ;

Divide both terms by 5 as;

This will give the following;

Find { b/2}^2 and add it on both sides of the equation where b is the second term in the equation.

{-14/5 / 2 }^2 = {-14/5 * 1/2 }^2 = {-14/10}^2 = {-7/5}^2 = 49/25

Add this on both sides of the equation as;

Factorize as ;

From the above, you notice, a square-root of a negative number will not result to real solutions for a, thus; the equation has no real solution.

Answer:

No real solution

a) the graphs of a equation are parallel

Answer:

About 495 people

Step-by-step explanation:

Divide 7428 by 15 years.

The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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The thirteenth term of this arithmetic progression a + b, 2a, 3a − b, ..... is a₁₃ = 13a - 11b.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 2a - (a + b) = 2a - a - b

Common difference, d = a - b

Substituting the given parameters into the formula, the 13th term of this arithmetic sequence is given by;

a₁₃ = (a + b) + (13 - 1)(a - b)

a₁₃ = (a + b) + (12)(a - b)

a₁₃ = a + b + 12a - 12b

a₁₃ = 13a - 11b.

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The statement that correctly compares -9 and 2 is A. -9 < 2 because 9 is to the left of 2 on a number line.

In arithmetic, a number line is a depiction of a graduated straight line which functions as a graphic representation of real numbers. It is presumed that every number line point and every real number correspond to one another.

Horizontal straight lines termed number lines have integers along them spaced equally apart. All of the numbers in a series can be shown on a number line. This line extends indefinitely at both ends.

In this case, -9 is on the left of a number line since it's negative. In conclusion, the correct option is A

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The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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Simplify

Answer:

\(\boxed{\sf \ \ \ a = 1 \ \ \ }\)

Step-by-step explanation:

Hello,

saying that \(x-\sqrt{a}\) is a factor means that \(\sqrt{a}\) is a zero which means

\(2(\sqrt{a})^4-2a^2(\sqrt{a})^2-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=> 2a^2-2a^3-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=>3-3*\sqrt{a}=0\\\\<=>\sqrt{a}=\dfrac{3}{3}=1\\\\<=> a = 1\)

so the solution is a = 1

Do not hesitate if you have any question

Okay, here we have this:

Considering the provided information, we are going to find the requested equation, so we obtain the following:

Then we can see that we must find the function that represents the total cost, therefore we have

Total cost=Standard charge+ Insurance charge

Replacing:

C=0.50M+15.75+0.25M+5.80

C=(0.50M+0.25M)+(15.75+5.80)

C=0.75M+21.55

Finally we obtain that the equation for the total charge is C=0.75M+21.55

Answer:

see below

Step-by-step explanation:

Remember this definition:

A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.

so if you know only 1 angle, you'll know all of them

because  z is opposite to the given angle 69 so z=69

the other 2 angles are the same = 180 -69 =111

Answer: 0.16

Step-by-step explanation:

Let X be a random variable that represents the heights of women at a large university are approximately bell-shaped, with a mean of 66 inches and standard deviation of 3 inches.

According to the Empirical Rule, for bell-shaped distributions, about 68% of the values fall within 1 standard deviation of the mean.

About 68% woman have height between ( 66-3) inches and (66+3) inches.

i.e. About 68% woman have height between 63 inches and 69 inches.

The percentage of woman have height either less than 69 inches or greater than 69 inches =100% - 68%= 32% [both share equal area on curve.]

The percentage of woman have height  is 69 inches or taller = 32%÷2

= 16%

Hence, the probability that a randomly selected woman from this university is 69 inches or taller =16%=0.16

Answer: 71.57

Step-by-step explanation:

You are going to use SOH CAH TOA to find the angle

because the opposite and adjacent are the sides from the reference angle use TOA (tanΘ=opp/adj)

TanΘ=\(\frac{9}{3}\)

now use that tan^-1 (9/3) on your calculator (make sure your calc is in degree mode)

71.57

Answer:

14 items

Step-by-step explanation:

21-7=14

Answer:

1960 cents

Step-by-step explanation:

98 multiplied by 20

Answer:

if you sell 20 songs that makes you have 1,960 cents

And in total that would make $19.60

Step-by-step explanation:

Hope this helps :)

Answer:

two and a half miles

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The general equation circle is

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

Where r is the radius

Plug in the equation

\( {x}^{2} + {y}^{2} = 16\)

Take the sqr root of 16 tocfind the radius

\( \sqrt{16} = 4\)

Answer:

3.76 is 8% of 47

Step-by-step explanation:

1. We assume, that the number 47 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 47, so we can write it down as 100%=47.

4. We know, that x% equals 3.76 of the output value, so we can write it down as x%=3.76.

5. Now we have two simple equations:

1) 100%=47

2) x%=3.76

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=47/3.76

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 3.76 is what percent of 47

100%/x%=47/3.76

(100/x)*x=(47/3.76)*x       - we multiply both sides of the equation by x

100=12.5*x       - we divide both sides of the equation by (12.5) to get x

100/12.5=x

8=x

x=8

now we have:

3.76 is 8% of 47

Answer:

a) This probability as empirical Probability.

b) This probability is not accurate because this experiment must be repeated a large number of times for empirical probabilities should be accurate.

Step-by-step explanation:

On 6 occasions, of which three times the train was late. that means 3 times the train is on time.

Empirical probability = Number of outcomes satisfying event / No.of trails

                                = 3/6 = 0.5.

a) This probability as empirical Probability.

b) This probability is not accurate because this experiment should be repeated a large number of times for empirical probabilities should be accurate.

The length of side AB is about 5.87 units.

The triangle ABC is a right angle triangle. A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the length AB in the right triangle.

Using trigonometric ratios,

cos 33 = adjacent / hypotenuse

Therefore,

Adjacent side = AB

hypotenuse side = 7 units

cos 33° = AB / 7

cross multiply

AB = 7 cos 33

AB = 7 × 0.83867056794

AB = 5.87069397562

AB = 5.87 units

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Answer:

Therefore, the Panthers had a better overall record for the season, with a total of 212 points earned compared to the Cowboys' total of 173 points.

Step-by-step explanation:

To compare the measures of center, we can calculate the mean and median points earned by each team:

Panthers: Mean = 212/15 = 14.13 points, Median = 14 points

Cowboys: Mean = 173/15 = 11.53 points, Median = 10 points

Based on these calculations, we can see that the Panthers have a larger mean value of about 14.13 points compared to the Cowboys' mean value of about 11.53 points. However, the median value for both teams is less useful for comparison since they are only one point apart. Therefore, we can conclude that the Panthers had the better overall record for the season based on both the total points earned and their larger mean value.

So, the answer is Panthers; they have a larger mean value of about 14.8 points (Option C is incorrect as the mean value of Panthers is approximately 14.13 and not 14.8).

Answer:

b d e a im not fore sure tho

Step-by-step explanation:

Answer:

Lines y and z are Intersecting

Lines y and z are Perpendicular Lines