Which event has theoretical probability of exactly 1/5 select three options

Answer: -2 and 4

Step-by-step explanation:

\(f(x) = \frac{-2x+2}{2x+4}\)            g(x) = -2x+8

Question asks what the domain is if we had f(x) ÷ g(x)

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4}\)  ÷                  >When dividing fractions, keep the first

                                                      Change the sign, flip the second fraction

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4} * \frac{1}{-2x+8}\)        

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{(2x+4)(-2x+8)}\)          

> you can never get a 0 on the bottom of division so that is where the exception of what x cannot be.

2x+4 = 0

2x= -4

x =  -2

and

-2x+8 = =

-2x = -8

x = 4

So x cannot be -2 and 4

If l and m are parallel, this means that the angles I'm going to show you in red must be equal:

So what I'm saying is that:

Also, since the angle under alpha and the angle (5x+19) are supplementary:

And, as you can see, beta and alpha are supplementary too, so:

From the second equation we clear beta:

And we replace it in the equation of beta and alpha. Also, we have to replace alpha with the expression in the first equation:

And then, we just clear the x:

I'll take the parenthesis out.

We group the x and add up the constants:

166 goes to the other side as a substraction and the 2 goes dividing:

Finally, the value of x is:

The computed mean expenses of the XYZ Corporation based on the given information are 9,911.22.

The mean refers to the average value.

The mean is computed as the quotient that results from dividing the total value of the data set by the number of items in the set.

Name                      Total Sales      Total Expenses

Quezon City            14,950.00             4,933.50

Caloocan City         18,290.00             6,035.70

Marikina City          37,200.00           12,276.00

Cebu City                18,900.00            6,237.00

Davao City             45,000.00          14,850.00

Mandaluyong City 23,000.00           7,590.00

Cavite                     22,000.00          7,260.00

Laguna                    21,000.00          6,930.00

Manila                    66,000.00         21,780.00

Iloilo                       34,000.00          11,220.00

Total                                                  99,112.20

Mean Expenses = 9,911.22 (99,112.20 ÷ 10)

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Answer: y = -x - 8

Step-by-step explanation: check the pic attached and lemme know if u dont get it :)

Using the least common factor, it is found that it will take 120 days until all four buses return to the terminal on the same day.

To find their least common factor, we factor each number by prime numbers, hence:

6 - 8 - 10 - 15|2

3 - 4 - 5 - 15|2

3 - 2 - 5 - 15|2

3 - 1 - 5 - 15|3

1 - 1 - 5 - 5|5

1 - 1 - 1 - 1

Hence, lcm(6, 8, 10, 15) = 2³ x 3 x 5 = 8 x 15 = 120.

It will take 120 days until all four buses return to the terminal on the same day.

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Answer:

1.2kg

Step-by-step explanation:

6 identical toys weigh 1.8kg.

1 toy would weigh:

1.8/6 = 0.3

0.3 kg.

Multiply 0.3 with 4 to find how much 4 identical toys would weigh.

0.3 × 4 = 1.2

4 identical toys would weigh 1.2kg

Answer:

\(1.2kg\)

Step-by-step explanation:

6 identical toys weigh = 1.8kg

Let's find the weight of 1 toy ,

\(1.8 \div 6 = 0.3\)

Now, lets find the weigh of 6 toys,

\(0.3 \times 4 = 1.2kg\)

Answer:

The answer is 1/6

Step-by-step explanation:

This is the answer due to the fact that a dice has 6 sides meaning there is a 1 in 6 chance of rolling the different numbers

Answer:

\(the \: proberbility \: is \: \frac{2}{6} = \frac{1}{3} \)

As per the perimeter the length of the shorter side is 10.5 feet and the length of the longer side is 73.5 feet.

The perimeter of a rectangle is the sum of the lengths of all its sides. If we know the perimeter of a rectangle and some information about the relationship between its sides, we can use that information to find the lengths of the sides.

Let's call the length of the shorter side "x".

The other side is seven times as long, so it is 7x.

The perimeter of the rectangle is 168 feet, so we have

=> 2x + 14x = 168.

Simplifying the equation, we have

=> 16x = 168.

Dividing both sides of the equation by 16, we find

=> x = 10.5.

So, the length of the shorter side is 10.5 feet and the length of the longer side is

=> 7x = 7 * 10.5 = 73.5 feet.

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Answer:

ज्ध्ध्द्न्द्

Step-by-step explanation:

क्क्न्क्

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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The measure of angle a is 70 degrees

The angle in a semicircle is a right angle.

This means that:

a + d = 90

Where O is the center of the circle

From the figure, we have:

Angle d and the angle with a measure of 20 degrees are corresponding angles

This means that

d = 20

Substitute d = 20 in a + d = 90

a + 20 = 90

Subtract 20 from both sides of the equation

a = 70

Hence, the measure of angle a is 70 degrees

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Answer:

125 percent

Step-by-step explanation:

25 percent *500.00 =

(25:100)*500.00 =

(25*500.00):100 =

12500:100 = 125

Now we have: 25 percent of 500.00 = 125

Question: What is 25 percent of 500.00?

Percentage solution with steps:

Step 1: Our output value is 500.00.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$500.00=100\%$.

Step 4: Similarly, $x=25\%$.

Step 5: This results in a pair of simple equations:

$500.00=100\%(1)$.

$x=25\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{500.00}{x}=\frac{100\%}{25\%}$

Step 7: Again, the reciprocal of both sides gives

{x}/{500.00}={25}/{100}$

$Rightarrow x=125$

Therefore, $25\%$ of $500.00$ is $125$

The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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The required greatest common factor of 48 and 168 is 24.

Given that,
To determine  the greatest common factor of 48 and 168

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.

Here,
GCF
48  and 168
24× 2 and 24 × 7
GCF = 24

Thus,  the required greatest common factor of 48 and 168 is 24.

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Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

Answer:

  x = 6

Step-by-step explanation:

We assume your functions are ...

In general, mixed polynomial and exponential functions have no algebraic solution. That means we need to solve f(x) = g(x) using a table of values, or by graphing.

__

Attached is a graphical solution. It shows the largest value of x for which f(x) = g(x) is x=6.

Check: f(6) = 1/2(2^6) = 32 = g(6) = 5(6) +2

__

Additional comment

We can start with f(x) = g(x) and subtract g(x) from both sides of the equation. This gives ...

  f(x) -g(x) = 0

Many graphing calculators readily identify the zeros of a function or expression. We have used that fact to find the two values of x where these functions are equal: ≈0.32 and 6.

For x>6, the exponential function increases without bound, so the graphs never cross again. Likewise, for x < -0.32, the linear function decreases without bound, so the graphs never cross again.

The lower value of x where the graphs cross is an irrational number near −0.319886722135.

Answer:

135 because if you put it in a caluclator that is what you get

The rental cost in dollars per square foot is $11,00

Cost of renting 1.250 square feet = $13, 750 per month

Rental cost per square foot = Total renting cost / total renting area

= $13, 750 per month / 1.250 square feet

= $11,000

Hence, $11,000 is the rental cost in dollars per square foot.

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As a result, the company produced number of rods are **56** rods.

What exactly is radius?

A radius is a section of a straight line in geometry that connects a circle's or sphere's center to its edge or surface Its length is divided by the circle's diameter by two.

Each rod has a diameter of 6 centimeters, hence the radius is 3 centimeters. Each rod has a 20-centimeter height.

The following formula can be used to determine a cylinder's volume:

V = πr²h

where V stands for volume, r for radius, which is equal to half of the diameter, and h for height.

Adding these values to the formula yields the following results:

V = π(3)²(20) (20)

V = 180π

The volume of each rod is therefore 180 cubic centimeters.

30520.8 cubic centimeters of steel were used to make how many rods?

To find out,

divide the total volume of steel by the volume of each rod:

30520.8 / (180π) ≈ **56** rods

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Answer:

What is the normal rate of return?

Normal rate of return . ' means the average rate of return that a firm would receive in an industry when conditions of perfect competition prevail.

Step-by-step explanation:

Answer:

9x+1

Step-by-step explanation:

2x+1+7x

2x+7x+1

9x+1

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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As a result, the likelihood that 7 out of every 10 people will develop Huntington's illness is 0.9375, or almost 93.75%.

The probability is typically stated to be the proportion of favorable events to every other result in the sample. The likelihood of an occurrence P(E) = (Number of favorable outcomes) is how it is stated (Sample space).

The binomial likelihood formula must be used to determine the likelihood that precisely seven out of ten people will develop Huntington's disease:

\(P(X = k) = (n choose k)\) × \(p^k (1 - p)^(n - k)\)

where the likelihood of obtaining k successes is P(X = k).

The number of trials is n.

The binomial coefficient, n pick k, denotes the number of possible methods to select k successes from n trials, where p is the success rate in each trial.

In this instance, n = 10 (since there are 10 people)

As we are interested in the likelihood that exactly 7 persons will have Huntington's illness, we set k = 7.

p = 0.5 (because there is a 50% chance that each person will inherit the gene)

(n choose k) = 10 select 7 = 120 (since there are 120 ways to choose 7 people from 10)

Given these numbers, we can get the probability using the formula below:

\(P(X = 7) = (10 choose 7)\)× \(0.5^7\) × \((1 - 0.5)^(10 - 7)\)

= 120 × \(0.5^7\) × \(0.5^3\)

= 120 × 0.0078125

= 0.9375

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Therefore, the surface area of the sphere is 324π square feet.

In mathematics, volume is the measure of the amount of three-dimensional space occupied by a solid object. It is typically expressed in cubic units, such as cubic meters, cubic feet, or cubic centimeters. Volumes are used in many areas of mathematics and science, including geometry, calculus, physics, and engineering. They are also used in everyday life, such as determining the amount of liquid that can be held in a container, calculating the amount of space needed to store items, or measuring the capacity of a vehicle.

Here,

We can use the formulas for the volume and surface area of a sphere to solve this problem.

The formula for the volume of a sphere is:

V = (4/3)πr³

where V is the volume and r is the radius of the sphere.

We are given that the volume of the sphere is 972πft³, so we can write:

972π = (4/3)πr³

Simplifying this equation, we get:

r³ = (3/4)(972)

r³ = 729

Taking the cube root of both sides, we get:

r = 9

So the radius of the sphere is 9 feet.

Now we can use the formula for the surface area of a sphere:

A = 4πr²

where A is the surface area and r is the radius.

Substituting r = 9, we get:

A = 4π(9)²

A = 4π(81)

A = 324π

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

a.    \(\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)\)

b.    the expected amount spent by Amy is $1144.47

c.    the expected amount that Brenda is going to spend is $1749.37

Step-by-step explanation:

(a)

From the regression output; the equation for the regression model can be written as:

\(\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)\)

From the information given in the question;

(b)

Amy does not own a home but rent; the variables given also stated that ;

Own Home = 1 if customer owns home, 0 if renting

So for Amy ; Own Home = 0 (since it is rented)

Close = Yes(1)

Salary = $60,000

Catalogs = 12

Therefore;

the mean amount spent by Amy is by using the regression model is  ;

\(\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 1) +(0.02216 * 60000) + (42.62 * 12)\)

\(\hat{amount} \ \hat{ spent} = -91.67 -0-604.90 +1329.6 + 511.44\)

\(\hat{amount} \ \hat{ spent} =1144.47\)

Thus;  the expected amount spent by Amy is $1144.47

(c)

If Brenda has the same characteristics as Amy but does not live close to store with similar merchandise.

Then the Close for Brenda will be = No (0)

Thus; the amount spent by Brenda will be:

\(\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 0) +(0.02216 * 60000) + (42.62 * 12)\)

\(\hat{amount} \ \hat{ spent} = -91.67 -0-0 +1329.6 + 511.44\)

\(\hat{amount} \ \hat{ spent} = 1749.37\)

Thus, the expected amount that Brenda is going to spend is $1749.37

Answer: See solution and explanations in the attached documents

Step-by-step explanation:

See explanations in the attached documents

Answer:

K.E = 1/2mv²

Kinetic energy