Addition Rule 03
The table below shows the soft drinks preferences of people in three age groups.

under 21 years of age
Cola- 40
Root beer- 25
Lemon lime- 20

between 21 and 40
Cola- 35
Root beer- 20
Lemon lime- 30

over 40 years of age
Cola- 20
Root beer- 30
Lemon lime- 35

If one of the 255 subjects is randomly selected, find the probability that the person is between 21 and 40 years of
age or that they drink root beer.

Enter your answer as a fully reduced fraction.

The conclusion hypothesis is to reject the null hypothesis and accept the alternative hypothesis. The z score of 0.14 is in the rejection area

What is hypothesis?

In statistics, hypothesis refers a testable statement about the relationship between two or more variables or a proposed variable.

Here we have given that two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.

And we need to find the conclusion hypothesis.

While we looking into the given question, we have identified the following values,

Sample mean: Machine 1 25 31.8 oz 2.2 oz

Sample SD: Machine 2 36 30.9 OZ 1.98 oz

So, the hypothesis is calculated as, the claim is the population mean of cereal cartons from machine 1 is larger than that from the machine 2

Null hypothesis: H0 : The population mean of cereal cartons for machine 1 and machine 2 is same

Alternative hypothesis H1: The population defines the statistical inference experiment.

So, the conclusion of hypothesis is, the critical value (cutoff point) is 2.353. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since 0.14 is less than 2.353, we reject the null hypothesis. We accept the alternative hypothesis.

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Answer:

[tex]y=x[/tex]

Step-by-step explanation:

[tex]2(-y+x)=0\\\\-y+x=0\\\\-y=-x\\\\y=x[/tex]

Answer:

f(x) = -3x + 6

Step-by-step explanation:

f(2)=0   point (2, 0)

f(4)=-6    point (4, -6)

m = slope = (y_2 - y_1)/(x_2 - x_1)

m = (-6 - 0)/(4 - 2) = -6/2 = -3

y = mx + b

y = -3 x + b

0 = -3 × 2 + b

0 = -6 + b

b = 6

y = -3x + 6

f(x) = -3x + 6

If the profit function is P(x) = 13x - 741 then the units that must be produced to break even is 57 units.

What is a profit function?

The difference between income and costs is referred to as profit. A relationship that depicts the difference created by subtracting the cost function from the revenue function is called a profit function. The ideal pairing of revenues and expenses to generate the greatest possible profit can be seen on the graph of a profit function.

Here, we have

Given

R(x) = 16x (The revenue function)

C(x) = 3x + 741 (The cost function)

Profit = Revenue - Cost

P(x) = 16x - 3x - 741

P(x) = 13x - 741

Hence, the profit function P(x) is  13x - 741.

For the company to break even, R(x) = C(x)

16x = 3x + 741

13x = 741

x = 57

Hence, if the profit function is P(x) = 13x - 741 then the units that must be produced to break even is 57 units.

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Answer:

Step-by-step explanation:

 7 49999977/50000000 is gallons to pints. multiply that number by 6, which is 47 24999931/25000000.

The Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.

What is a confidence interval?

A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. It is a measure of the uncertainty associated with an estimate of a population parameter, such as the mean, the proportion, or the variance.

a)

sample mean = 75.67

sample std. dev. = 3.56

b)

Given CI level is 90%, hence α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.015

[tex]CI = (xbar - tc * s/\sqrt{n} , xbar + tc * s/\sqrt{n})\\\\CI = (75.67 - 2.015 * 3.56/\sqrt{6} , 75.67 + 2.015 * 3.56/\sqrt{6})\\\\\CI = (72.74 , 78.60)[/tex]

Hence the Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.

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Answer:

The probability that all five lines will be in use when a customer calls customer service is 1/7776.

What is probability?

The proportion of favorable cases to all possible situations that can occur indicates how likely an event is to occur.

Step-by-step explanation:

Given that there are 5 lines and the probability for each line to be engaged in working hours is 1/6.

So, for all 5 lines to be engaged is

= 1/6 * 1/6 * 1/6 * 1/6 * 1/6

= [tex]\frac{1}{6} ^{5}[/tex]

= [tex]\frac{1}{7776}[/tex]

Therefore, the probability that all five lines are engaged is 1/7776.

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The equation has one repeated rational number solution. thus Option C is correct.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given equation is the quadratic equation:

[tex]5x^2-x-3=0[/tex]

It is required to determine the number and type of solutions.

Noted that If the discriminant equals zero, the equation has one repeated rational number solution.

If the discriminant is positive, then the equation has two real solutions.

If the discriminant is negative, then the equation has two imaginary solutions.

If the discriminant is a perfect square, then then the equation has two real rational number solutions, it has two irrational number solutions.

Calculate the discriminant of the equation [tex]5x^2-x-3=0[/tex] by substituting a= 5, b=-1  and c= 3  into the discriminant formula:

Since the discriminant equals zero, it follows that the equation has one repeated rational number solution.

The equation has one repeated rational number solution.

Option C is correct.

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In a table of values for a pattern, P=3 when n=1; the equations P=3n and 2n+1 might represent the pattern. So the option d "Both A and C" is correct option.

In the given question, In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern.

a) P=3n

b) P = n+3

c) P = 2n+1

d) P = 3-n

We find the pattern we firstly observe the given diagram closely.

We firstly check which option can given P=3 when n=1.

Firstly taking the option a.

P = 3n

Now put n=1, so

P = 3

Hence, the option one is following the condition.

Now taking the option b.

P = n+3

Now put n=1, so

P = 1+3

P = 4

Hence, the option b is not following the condition.

Now taking the option c.

P = 2n+1

Now put n=1, so

P = 2(1)+1

P = 2+1

P = 3

Hence, the option c is following the condition.

Now taking the option d.

P = 3-n

Now put n=1, so

P = 3-1

P = 2

Hence, the option d is not following the condition.

Hence, the option a and c is following the condition. So the option d "Both A and C" is correct option.

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Answer:

length = 43 ft ; width = 19 ft

Step-by-step explanation:

perimeter/2 = 124/2 = 62 ft

l = 2w + 5

l + w = 62

2w+5 + w = 62

3w = 62 - 5

3w = 57

w = 57/3

w = 19 ft

l = 2 · 19 + 5

l = 38 + 5

l = 43 ft

The  goalie saved 70% of the shots.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, a Goalie's saves (•) and goals scored against (x)

The number of save shot = 14

The number of goals scored against = 6

The total numbers of shots = 20

A goalie's safe percentage is calculated by dividing the number of saves by the total number of shots on goal = 14/20x100 = 70%

Hence, The  goalie saved 70% of the shots.

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Answer:

Rang is the output values or the y values.

3 and 5

Step-by-step explanation:

An ordered pair is in the form (x, y)  The x is the input or the domain and the y is the output or the range.

The linear function that has greatest initial value is function C

The linear function that has greatest rate of change is function B

Consider the function A

The y intercept = 0

Consider two points (2, 5) and (4, 10)

The slope of the line = (10-5) / 4-2

= 5 /2

The equation will be

y = 5/2x + 0

Consider the function B

y = 3x - 1

Which is in the form of slope intercept form

The slope of the line = 3

The y intercept = -1

Consider the function C

y intercept = 2

Consider the points (0, 2) and (3, 3)

The slope of the function = 3-2 / 3 -0

= 1/3

The equation is

y = 1/3x + 2

Therefore, function C has greatest initial value and function B has greatest rate of change

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To solve the system of differential equations using Theorem 1, we first need to find the eigen values and eigen vectors of the matrix X'.

The characteristic equation is given by |X' - λI| = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues to be λ = -2, 0, 3, 5.

Next, we need to find the corresponding eigenvectors. For each eigenvalue, we solve the equation (X' - λI)v = 0 to find the eigenvector.

For λ = -2, the eigenvector is v = [-2 -2 -2 -2 -2 1 -2 -2 -2 -2 -2 1 -2 -2 -2 1]

For λ = 0, the eigenvector is v = [-4 1 -2 -2 4 -3 2 -2 1 -2 -5 0 1 0 4 -1]

For λ = 3, the eigenvector is v = [4 -2 -2 -2 -4 3 -2 -2 -1 -2 5 0 -1 0 -4 1]

For λ = 5, the eigenvector is v = [0 2 2 2 0 -1 2 2 2 2 0 -1 2 2 0 -1]

Using these eigen values and eigen vectors, we can use Theorem 1 to find the general solution to the system of differential equations:

X(t) = c1e^(-2t)v1 + c2e^(0t)v2 + c3e^(3t)v3 + c4e^(5t)v4

where c1, c2, c3, and c4 are constants.

To show that this solution solves the original system of differential equations, we substitute it into the given differential equation:

X'(t) = -2c1e^(-2t)v1 + 0c2e^(0t)v2 + 3c3e^(3t)v3 + 5c4e^(5t)v4

This simplifies to:

X'(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ]

which is equal to the given matrix X'(t). Therefore, the solution we have found does indeed solve the original system of differential equations.

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The standard deviation of Y can be determined which is 9708.

Given in the question that the high probability would gain  in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.

According to the information, the gain around is 1250

Amount would lost in case of death is 100000.The expected value with its probability is:

E(X) = ∑x ×P(x)

=(-99750) × 0.00183 + ...+ (1250) × 0.99058

= 303.35

The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is

The standard deviation of Y can be determined as

α = under root {∑x2 × P(x) - (∑x × P(x) }

[tex]\sqrt{(-99750 - 303.3525)sq. X 0.00183 + .... + (1250 - 303.3525)sq. X 0.99058 }[/tex]

= 9708

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What is a equation in math?

Image result for What is equation?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

What is a equation in math?

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

given:

y=7x-2

first, (3, 15)

15 = 7*3-2 = 21-2 = 19

So, (3, 15) is not the solution.

Second, (-1,-10)

-10 = 7* (-1) -2

-10 = -9

Also, (-1,-10) is not the solution.

Hence, there is no solution for y=7x-2

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One glass of milk and one snacks bar have a total of 23 carbs.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two glass of milk and Three snacks bar have a total of 56 carbs.

And, Four glass of milk and two snacks bar have a total of 72 carbs.

Now,

Let the amount of milk = x

And, The amount of snacks bar = y

So, We can formulate;

Two glass of milk and Three snacks bar have a total of 56 carbs.

⇒ 2x + 3y = 56 ..(i)

And, Four glass of milk and two snacks bar have a total of 72 carbs.

⇒ 4x + 2y = 72

⇒ 2x + y = 36

⇒ y = 36 - 2x   ..(ii)

Substitute above value in equation (i),

⇒ 2x + 3y = 56

⇒ 2x + 3 (36 - 2x) = 56

⇒ 2x + 108 - 6x = 56

⇒ 108 - 56 = 4x

⇒ 4x = 52

⇒  x = 13

And, from (ii);

⇒ y = 36 - 2x  

⇒ y = 36 - 2 × 13

⇒ y = 36 - 26

⇒ y = 10

Thus, One glass of milk and one snacks bar have a total of carbs

= 13 + 10

= 23

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The particle's velocity at time t = 1 seconds is equal to 3 meters per seconds.

In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled (covered) by an object from its starting position with respect to the time when it is started moving.

Generally speaking, the position of a physical object (body) in a position vs time graph is always plotted on the y-coordinate (y-axis) while time is always plotted on the x-coordinate (x-axis).

From the information provided about this particle on a position vs time graph, we have;

s =√(3 + 6t)

Where:

Substituting the given parameters into the formula, we have;

s =√(3 + 6(1))

s =√(3 + 6)

s =√9

Distance, s = 3 meters.

Now, we can determine the velocity as follows;

Velocity = distance/time

Velocity = 3/1

Velocity = 3 meters per seconds.

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Therefore solution to this problem is  the given  statement is true .

The generalization of ordinary least squares and linear regression known as weighted least squares (WLS), sometimes known as weighted linear regression, incorporates knowledge of the variance of the observations into the regression. Generalized least squares is also a specialization of WLS.

Here,

the generalized least squares estimators for correcting heteroskedasticity are also called weighed least squares estimators.

Since they are also known as weighed least squares estimators, extended least squares estimators for correcting heteroskedasticity use least squares estimation.

Therefore , the above statement is true .

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Answer:

   Domain: -∞ < x < ∞

   Range: y ≥ -2

Step-by-step explanation:

The domain of a parabola graph is all real numbers, this is written as;

      -∞ < x < ∞

The range of this parabola graph is all numbers greater than and equal to -2, since the parabola opens up and the vertex is at (-4, -2). This is written as;

      y ≥ -2

If a person is a professional athlete, then the person is a professional hockey player.

Given :

( a ) Give the contrapositive of the statement.

If not  the person is a professional hockey player .

then not a person is a professional athlete .

( b ) Give the converse of the statement.

If the person is a professional hockey player .

then a person is a professional athlete .

( c ) Give the inverse of the statement .

If not the person is a professional hockey player.

then not a person is a professional athlete .

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The 90% confidence interval for the difference between the average running times of films produced by the two companies ≅ (- 35.5 , 10.8)

Given that:

Company (i) :      

[tex]n_{1}[/tex] = 5  ,  [tex]x_{1}[/tex]bar = 98.4

[tex]S_{1} ^{2}[/tex] = [tex]\frac{1 }{n_{1} - 1}[/tex] ∑ [tex](x_{i} - x_{1} bar)^{2}[/tex]

     = [tex]\frac{1}{5 - 1}[/tex]  [ [tex](103 - 98.4)^{2}[/tex] + [tex](94 -98.4)^{2}[/tex]+........+ [tex](98 - 98.4)^{2}[/tex] ]

     = [tex]\frac{1}{4}[/tex] [ [tex](4.6)^{2}[/tex] + [tex](-4.4)^{2}[/tex]+..........+[tex](0.4)^{2}[/tex] ]

     = [tex]\frac{1}{4}[/tex] [ 305.2]

     = 76.3

Company (ii) :

[tex]n_{2}[/tex] = 7 , [tex]x_{2}[/tex] bar = 110.7143

[tex]S_{2} ^{2}[/tex] = [tex]\frac{1 }{n_{2} - 1}[/tex] ∑ [tex](xi - x_{2} bar)^{2}[/tex]

     = [tex]\frac{1}{7-1}[/tex] [ [tex](97 - 110.7143)^{2}[/tex]+ [tex](82-110.7143)^{2}[/tex]+.........+[tex](118 - 110.7143)^{2}[/tex] ]

     = [tex]\frac{1}{6}[/tex] [ [tex](-13.7143)^{2}[/tex]+ [tex](-28.7143)^{2}[/tex]+.........+[tex](7.2857)^{2}[/tex] ]

     = [tex]\frac{1}{6}[/tex] [ 6125.4274]

     ≅ 1035.9045

For 90% confidence interval

difference between = 5+7-2 = 10, critical value is [tex]t_{c}[/tex] = 1.812.

90% confidence interval for the difference between the average running times is

[ ([tex]x_{1}[/tex] bar - [tex]x_{2}[/tex] bar) ± [tex]t_{c}[/tex] . [tex]\sqrt{\frac{S_{1}^2 }{n_{1} } } + \sqrt{\frac{S_{2}^2 }{n_{2} }}[/tex] ]

= [(98.4 - 110.7143) ± 1.812 [tex]\sqrt{\frac{76.3}{5} } + \sqrt{\frac{1035.90457}{7} }[/tex] ]

= [-12.3143 ± 23.1515]

= (- 35.4658 , 10.8372)

≅ (-35.5 , 10.8)

Therefore, 90% confidence interval for the difference between the average running times of films produced by the two companies is

≅ (- 35.5 , 10.8)

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Answer:  we first need to apply the transformation to the x- and y-coordinates of the point individually

Step-by-step explanation:

To transform the coordinates of a point (x, y) using the transformation (x, y) ⟶ (–y, x), we first need to apply the transformation to the x- and y-coordinates of the point individually. This means that the x-coordinate becomes –y and the y-coordinate becomes x.

In the case of point B, the original coordinates are (2, 5), so the transformed coordinates are (–5, 2). This means that the x-coordinate becomes –5 and the y-coordinate becomes 2.

Next, we need to apply the translation that moves the point 1 unit right and 4 units up. To do this, we simply add 1 to the x-coordinate and add 4 to the y-coordinate. After this translation, the coordinates of B′ become (–4, 6). Therefore, the final coordinates of B′ are (–4, 6).

Answer:

A or B

Step-by-step explanation:

I think it's B.. according to the people I know

the difference between the two temperatures as 16 degrees F. You must wait for another 6 minutes for the soda to cool down to 60 degrees F.

Since the initial temperature of the soda is 76 degrees F and the desired temperature is 60 degrees F, we can calculate the difference between the two temperatures as 16 degrees F. We also know that the temperature of the ice is at the freezing point of water which is 32 degrees F. This means that the temperature difference between the soda and the ice is 44 degrees F. Since the temperature difference between the soda and the ice is greater than the temperature difference between the desired temperature and the initial temperature, we can divide the desired temperature difference (16 degrees F) by the temperature difference between the soda and the ice (44 degrees F) and multiply it by the time elapsed (10 minutes) to calculate the remaining time needed for the soda to cool down to the desired temperature. 16/44 * 10 = 6. Therefore, we must wait for another 6 minutes for the soda to cool down to 60 degrees F.

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If the APR on Mario's credit card is 26.99%, Mario's new balance, including interest will be B. $3,269.10.

Annual percentage rate (APR) is the annual finance charge applied to a credit balance.

The APR includes interest and other fees for borrowing credit.

Current credit card balance =             $2,673.19

Minimum payment within the month =  (102.00)

Purchase payments                                626.00

Finance Charge                                       $71.91 ($3,197.19 x 26.99% x 1/12)

Ending credit card balance =            $3,269.10 ($3,197.19 + $71.91)

Annual percentage rate = 26.99%

Monthly percentage rate = 2.25% (26.99% ÷ 12)

Thus, Mario will end up with a credit card balance of $3,269.10 after one month with APR of 26.99%.

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Answer:

15

Step-by-step explanation:

If f(x) = -3x + 4, then plugging in -5 for x gives f(-5) = -3(-5) + 4 = 15. Therefore, the correct answer is 15.