Can someone please help me with my algebra fraction homework Page's 8,9 and 10. Thank You!

Answer:

Given Function is an even function

Step-by-step explanation:

Explanation:-

Even function :-

A function f is even if the graph of f is symmetric with respective to the y - axis.

Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f.

Odd function : -

A function f is odd if the graph of f is symmetric with respective to the origin

Algebraically, f is odd if and only if f(-x) = - f(x) for all x in the domain of f.

given function is [tex]f(x) = 3 x^2-1[/tex]

[tex]f(-x) = 3 (-x)^2-1=3 x^2 -1 = f(x)[/tex]

therefore f(-x) = f(x)

given function is an even function.

To maximize profit, the art club should find the combination of small and large greeting cards that satisfies the given constraints and generates the highest total profit. The optimal solution will provide the number of boxes of small and large cards that should be bought to maximize profit while staying within the given constraints.

To maximize profit, the art club should find the combination of small and large greeting cards that satisfies the given constraints and generates the highest total profit. Let's assume the art club buys x boxes of small cards and y boxes of large cards. The constraints are:

The objective is to maximize profit, given by:

52.20x + 85y

We need to solve this linear programming problem to find the values of x and y that maximize profit. The optimal solution will provide the number of boxes of small and large cards that should be bought to maximize profit while staying within the given constraints.

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Answer:

1 is the positive number for which the sum of it and its reciprocal is the smallest.

Step-by-step explanation:

Let x be the positive number.

Then, the sum of number and its reciprocal is given by:

[tex]V(x) = x + \dfrac{1}{x}[/tex]

First, we differentiate V(x) with respect to x, to get,

[tex]\frac{d(V(x))}{dx} = \frac{d(x+\frac{1}{x})}{dx} = 1-\dfrac{1}{x^2}[/tex]

Equating the first derivative to zero, we get,

[tex]\frac{d(V(x))}{dx} = 0\\\\1-\dfrac{1}{x^2}= 0[/tex]

Solving, we get,

[tex]x^2 = 1\\x= \pm 1[/tex]

Since x is a positive number x = 1.

Again differentiation V(x), with respect to x, we get,

[tex]\frac{d^2(V(x))}{dx^2} = \dfrac{2}{x^3}[/tex]

At x = 1

[tex]\frac{d^2(V(x))}{dx^2} > 0[/tex]

Thus, by double derivative test minima occurs for V(x) at x = 1.

Thus, smallest possible sum of a number and its reciprocal is

[tex]V(1) = 1 + \dfrac{1}{1} = 2[/tex]

Thus, 1 is the positive number for which the sum of it and its reciprocal is the smallest.

Answer:

Option A. 0.4 of an orange

Step-by-step explanation:

Formula to calculate the opportunity cost is

Opportunity cost = [tex]\frac{\text{Sacrificed}}{\text{Gained}}[/tex]

In this question for the high yield, sacrificed thing is 100 tubs of grapes and gain is to produce 250 tubs oranges.

Opportunity cost = [tex]\frac{100}{250}=0.4[/tex] of an orange

Therefore, Option A. 0.4 of an orange, will be the answer.

Answer: The answer is 7shirts

Step-by-step explanation:

100¢ = $1

$5 * 100 = 500¢

First shirt = 50¢

500¢-50¢ = 450¢

Pay increase to 75¢ after the first shirt.

Number of shirts ironed for 450¢ = 450/75 = 6shirts

Therefore, 6shirts for 450¢ and 1 shirt for 50¢ total 7 shirts for 500¢ = $5

The statement 'there is a positive integer that is not the sum of three squares' can be defined mathematically, using predicates, quantifiers, logical connectives, and operators as: ∃ ∈ : ¬(∃,, ∈ : = ² + ² + ²).

In order to express the statement that there is a positive integer that is not the sum of three squares, we use predicates, quantifiers, logical connectives, and mathematical operators. Consider the domain of discourse being the set of positive integers. You can express the statement as follows:

∃ ∈ : ¬(∃,, ∈ : = ² + ² + ²)

Overall, this statement corresponds to the claim that there exists some number in the set of positive integers such that no three squares in that set can sum to equal it.

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Answer:

if a triangle had two right angles it would not be complete as to make it a triangle all corners have to meet while a 2 right angled triangle does not meet that.

i believe this is the answer

Answer:

After evaluating we get [tex]b^2-4ac = 52[/tex].

Step-by-step explanation:

Given:

[tex]b^2-4ac[/tex]

We need to evaluate the expression with a =3, b =8 and c= 1

Solution:

To evaluate the expression we will first substitute the values of a,b and c in the expression we get;

[tex]b^2-4ac = 8^2-4\times3\times1[/tex]

Now by using PEDMAS which states first operation needs to perform here is the exponent function.

so we get;

[tex]b^2-4ac = 64-4\times3\times1[/tex]

Now next operation to be performed is multiplication.

[tex]b^2-4ac = 64-12[/tex]

And finally we will perform subtraction operation.

[tex]b^2-4ac = 52[/tex]

Hence After evaluating we get [tex]b^2-4ac = 52[/tex].

Answer:

  a. a║b

  b. c║d

  c. AB║CD

  d. none

Step-by-step explanation:

a. If distinct lines in a plane are perpendicular to the same line, then they are parallel.

__

b. If same-side interior angles are supplementary where a transversal crosses two lines in the same plane, then those two lines are parallel.

__

c. If alternate interior angles are congruent where a transversal crosses two lines in the same plane, then those two lines are parallel. (Here, the measure of the upper angle at A is 180°-78°-67° = 35°, congruent with the lower angle at C. Those two angles are alternate interior angles with respect to lines AB and CD and transversal AC.)

__

d. The marked angles are unrelated to each other, so define nothing about the relationship between lines a and b, or between lines c and d. However, they do mean that if a║b, then c║d.

Parallelism between lines can be determined by applying geometrical principles or postulates via if-then statements, such as the Corresponding Angles Postulate, Alternate Interior Angles Theorem, or the Converse of the Same-Side Interior Angles Theorem, establishing congruity or supplementarity in the context of lines intersected by a transversal.

To determine which lines are parallel, you must look for certain geometrical properties or postulates. If-then statements or direct applications of properties such as the corresponding angles postulate, alternate interior angles theorem, or the converse of the same-side interior angles theorem can be used to identify parallel lines.

If two lines are cut by a transversal and the corresponding angles are equal, then the lines must be parallel (Corresponding Angles Postulate). If the alternate interior angles are congruent when two lines are cut by a transversal, then the two lines are parallel (Alternate Interior Angles Theorem). If two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel (Converse of the Same-Side Interior Angles Theorem). Each of these statements is an application of 'if-then' logic.

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Answer:

f(t)/g(t) represents the average cost of producing a unit of commodity between the time frame 0-t.

Step-by-step explanation:

f(t) is cost in dollar while g(t) is in unit.  f(t)/g(t) will be cost per unit.

In other words  f(t)/g(t) is the total cost spent in time t divided by the amount of commodity produced in units produced in time t.

Answer:

1) 5

2) 5

Step-by-step explanation:

Data provided in the question:

(3²⁷)(5¹⁰)(z) = (5⁸)(9¹⁴)([tex]x^y[/tex])

Now,

on simplifying the above equation

⇒ (3²⁷)(5¹⁰)(z) = (5⁸)((3²)¹⁴)([tex]x^y[/tex])

or

⇒  (3²⁷)(5¹⁰)(z) = (5⁸)(3²⁸)([tex]x^y[/tex])

or

⇒ [tex](\frac{3^{27}}{3^{28}})(\frac{5^{10}}{5^8})z=x^y[/tex]

or

⇒[tex](\frac{5^2}{3})z=x^y[/tex]

or

⇒[tex]\frac{5^2}{3}=\frac{x^y}{z}[/tex]

we can say

x = 5, y = 2 and, z = 3

Now,

(1) y is prime

since, 2 is a prime number,

we can have

x = 5

2) x is prime

since 5 is also a prime number

therefore,

x = 5

Answer: 10√17

Step-by-step explanation:

The movement of the boat takes the shape of a trapezium as shown in the attached photo.

The distance of the boat from its starting point is represented by x kilometers.

To determine the distance, x, we would apply Pythagoras theorem on the right angle triangle ABC formed. It is expressed as

Hypotenuse² = opposite side² + adjacent side². It becomes

x² = 40² + 10² = 1600 + 100

x² = 1700

x = √1700 = √100 × √17

x = 10√17

Answer:the charge for admission is $6 and the cost of a ride is $2

Step-by-step explanation:

Let x represent the charge for admission.

Let y represent the cost of a ride.

An amusement park charges admission plus a fee for each ride. Admission plus two rides costs $10. This means that

x + 2y = 10 - - - - - - - - - - - - - 1

Admission plus five rides cost $16. This means that

x + 5y = 16 - - - - - - - - - - -- - -2

Subtracting equation 2 from equation 1, it becomes

- 3y = - 6

y = - 6/- 3

y = 2

Substituting y = 2 into equation 1, it becomes

x + 2×2 = 10

x = 10 - 4 = 6

Answer:

l(n) = 80n + 520

Step-by-step explanation:

From the information given in the  question, there is a relationship between the number of new policy sold, n, and earning, I

           For 3 new policies, he earned $760

           For 5 new policies, he earned $920.

The rate of change of IIya's earning with respect to number of new policy sales is

             [tex]m = \frac{dI}{dn}[/tex]

             [tex]m = \frac{920 - 760}{5 - 3}[/tex]

             m = $160 / 2 policies

             m = $80 / policy

The linear equation for the relationship is;

             l(n) = mn + b

I(n) is Ilya’s weekly income which is a function of the number of new policies, n

m is the rate of change of I with respect to n

n is the number of new policies,

b is the intial function which is IIya's income when n equals zero

Recall, Ilya earns a commission of $80 for each policy sold during the week. (m = $80 per policy)

                 l(n) = 80n + b

To complete the relationship l, we need to calculate the initial value b.

For 3 new policies, he earned $760,

             760 = 80(3) + b

             760 = 240 + b

             b = 760 - 520

             b = 520

The final equation is l(n) = 80n + 520

From the final equation, we can deduce that Ilya’s weekly salary is $520 and he earns an additional $80 commission for each new policy sold.

Final answer:

Ilya's weekly income I(n) can be determined by constructing an equation from the two given points of data, namely I(3) = $760 and I(5) = $920. By solving the system of linear equations, we find that Ilya's base salary is $520 and his commission per policy is $80. The income equation is I(n) = $520 + $80n.

Explanation:

To determine the equation for Ilya's weekly income I(n), we need to establish the relationship between the number of policies sold (n) and the total income (I). Given that Ilya earned $760 for selling 3 policies and $920 for selling 5 policies, we can set up the following two equations based on the formula I(n) = base salary + (commission per policy × n):

1) 760 = base salary + (commission per policy × 3)
2) 920 = base salary + (commission per policy × 5)

To solve this system of equations, we use the method of elimination or substitution. By subtracting the first equation from the second, we can find the commission per policy. Then, we can substitute that value back into either equation to find the base salary. Once we have both values, we can express the equation for Ilya's weekly income as I(n) = base salary + (commission per policy × n).

Step-by-step solution:

Therefore, Ilya's weekly income depends on the base salary of $520 and an additional commission of $80 per new policy sold. The income equation I(n) is both the total of these two components and represents how Ilya's income scales with the number of policies he sells.

Answer:19.3

Step-by-step explanation:

96+28=124

6x+8=124

124-8=116

6x=116

116/6

x=19.3

Question is not proper; Proper question is given below;

D'Angelo needs 100 lb of garden soil to landscape a building. In the company’s storage area, he finds 2 cases holding 24 3/4 lb of garden soil each, and a third case holding 19 3/8 lb. How much gardening soil does D'Angelo still need in order to do the job?

Answer:

D'Angelo required [tex]31 \frac{1}{8}\ lb[/tex] more garden soil to do the job.

Step-by-step explanation:

Given:

Total Amount of garden soil needed to do job = 100 lb

Amount of garden soil in 1st case = [tex]24\frac{3}{4}\ lb[/tex]

[tex]24\frac{3}{4}\ lb[/tex] can be rewritten as [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 1st case =  [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 2nd case = [tex]24\frac{3}{4}\ lb[/tex]

[tex]24\frac{3}{4}\ lb[/tex] can be rewritten as [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 2nd case =  [tex]\frac{99}{4}\ lb[/tex]

Amount of garden soil in 3rd case = [tex]19\frac{3}{8}\ lb[/tex]

[tex]19\frac{3}{8}\ lb[/tex] can be rewritten as [tex]\frac{155}{8}\ lb[/tex]

Amount of garden soil in 3rd case =  [tex]\frac{155}{8}\ lb[/tex]

We need to find Amount of garden soil required more.

Solution:

Now we can say that;

Amount of garden soil required more can be calculated by subtracting sum of Amount of garden soil in 1st case and Amount of garden soil in 2nd case  and Amount of garden soil in 3rd case from Total Amount of garden soil needed to do job.

framing in equation form we get;

Amount of garden soil required more = [tex]100-\frac{99}{4}-\frac{99}{4}-\frac{155}{8}[/tex]

To solve the fraction we will make the denominator common using LCM.

Amount of garden soil required more = [tex]\frac{100\times8}{8}-\frac{99\times2}{4\times2}-\frac{99\times2}{4\times2}-\frac{155\times1}{8\times1}= \frac{800}{8}-\frac{198}{8}-\frac{198}{8}-\frac{155}{8}[/tex]

Now denominators are common so we will solve the numerator.

Amount of garden soil required more = [tex]\frac{800-198-198-155}{8}=\frac{249}{8}\ lb \ \ OR \ \ 31 \frac{1}{8}\ lb[/tex]

Hence D'Angelo required [tex]31 \frac{1}{8}\ lb[/tex] more garden soil to do the job.

Answer:

Option B

Step-by-step explanation:

P(B|A) is pronounce as the probability of event B given the event A. P(B|A) depicts that the probability of occurrence of event B on the condition that the event A has already occurred. It is also known as conditional probability. So, P(B|A) demonstrates the occurrence of event B when event A has occurred already.

Final answer:

The notation P(B|A) represents the probability of event B occurring, given that event A has already occurred. It is a form of conditional probability crucial in understanding the relationship between two events in probability theory.

Explanation:

The notation P(B|A) represents the probability of event B occurring, given that event A has already occurred. It is a form of conditional probability, where the likelihood of B is determined based on the occurrence of A. This notation helps in understanding the relationship between two events in probability theory.

Answer:

a) Sample size = 822

b) Margin of error = 0.03407          

Step-by-step explanation:

We are given the following in the question:

p = 74% = 0.74

a) Sample size is required to obtain margin of error of 0.03

Formula:

[tex]\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

Putting values, we get,

[tex]0.03 = 1.96\times \sqrt{\dfrac{0.74(1-0.74)}{n}}\\\\n = (\dfrac{1.96}{0.03})^2(0.74)(1-0.74)\\\\n = 821.24 \approx 822[/tex]

Thus, the sample size must be approximately 822  to obtain a 95% confidence interval with an approximate margin of error of 0.03

b) Margin of error for the 95% confidence interval

p = 54% = 0.54

Formula:

[tex]\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

Putting values, we get,

[tex]\text{Margin of error} = 1.96\times \sqrt{\dfrac{0.54(1-0.54)}{822}}\\\\=0.03407[/tex]

The margin of error now will be 0.03407.

Based on the sampling information given, the sample size will be 822.

The margin of error is given as 0.03. Therefore, the sampling size will be:

= (1.96/0.03)² × 0.74 × (1 - 0.74)

= 822

The margin of error for a 95% confidence interval will be:

= 1.96 × ✓0.54 × ✓0.46 × ✓822

= 0.3407

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Answer: Probability that the first card dealt is black,the second red and the third black is O.127

Step-by-step explanation: Total number of cards=52

Total number of black cards =26

Total number of red cards=26

Probability of pulling black=26/52

Probability of pulling red=26/51

Probability of pulling a mother black=25/50

Probability of pulling 3 cards =26/52×26/51×25/50

16900/132600

=0.127

The probability that the first card dealt is black, the second is red, and the third is black is 13/102.

To find the probability that the first card dealt is black, the second is red, and the third is black, we need to consider the total number of possible outcomes and the number of favorable outcomes. Since we are drawing without replacement, we need to calculate the probabilities for each card.

To find the overall probability, we multiply the probabilities of each event together.

(1/2) * (26/51) * (1/2) = 13/102

Therefore, the probability that the first card dealt is black, the second is red, and the third is black is 13/102.

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Answer no she does not have enough:

Step-by-step explanation:

2(1.25) = 2.5

2.75

2.5+2.75 =5.25

Time to go to the store!

Answer: The baker doesn't have enough butter.

Step-by-step explanation:

Total number of pounds of butter that the baker needs for the recipe is 6 pounds.

She found 2 portions. One of them weighs 1 1/4 pounds. Converting 1 1/4 pounds to improper fraction, it becomes 5/4 pounds.

The other portion weighs 2 3/4 pounds. Converting 2 3/4 to improper fraction, it becomes 11/4 pounds.

Total amount of butter that the baker has would be

5/4 + 11/4 = 16/4 = 4 pounds.

Therefore, the baker doesn't have enough butter.

Answer:

7.27 min

Step-by-step explanation:

Given: Isaiah pick 3 apple in one minute.

           Juanita pick 5 apple in two minutes.

           They need to pick 40 apples.

Now, finding number of apple picked by Juanita in one minutes.

As given, Juanita pick 5 apple in two minutes.

⇒ Number of apple picked by Juanita in one minutes= [tex]\frac{5}{2} = 2.5 \ apples[/tex]

∴ Total number of apples picked by Isaiah and Juanita in one minute= [tex]3+2.5[/tex]

Hence, Total 5.5 apples picked by Isaiah and Juanita in one minute.

Next finding time taken to pick total 40 apples for a pie.

⇒ Time to pick 40 apples= [tex]\frac{40}{5.5} = 7.27 \min[/tex]

Hence, 7.27 minutes taken to pick 40 apples.

Answer:

Option 1) 10 sides

Step-by-step explanation:

We are given a regular polygon. The sum of interior angles measure upto 1440 degrees.

Since it is a regular polygon, it satisfies the following properties:

Let the regular polygon have n sides.

Then, the sum of interior angle is given by:

[tex](n-2)\times 180^\circ[/tex]

Putting the values, we get,

[tex](n-2)\times 180 = 1440\\\\n-2 = \dfrac{1440}{180}\\\\n-2 = 8\\n = 8 + 2\\n =10[/tex]

Thus, there are 10 sides. The regular polygon is a regular decagon.

Answer:
Decagon

Step-by-step explanation:

Found other sources saying the same thing

Answer: the speed of the plane with no wind is 500 miles per hour.

the speed of the wind is 100 miles per hour.

Step-by-step explanation:

Let x represent the speed of the plane.

Let y represent the speed of the wind.

Traveling with the wind, a plane takes 2 1/2 = 2.5 hours to fly a distance of 1500 miles. The total speed would be x + y

Distance = speed × time

It means that

1500 = 2.5(x + y)

1500 = 2.5x + 2.5y - - - - - - - - - 1

The return trip of 1500 miles against the same wind speed, takes 3 hours. The total speed is x - y

It means that

1500 = 3(x - y)

1500 = 3x - 3y - - - - - - - - - - - - 2

Multiplying equation 1 by 3 and equation 2 by 2, it becomes

4500 = 7.5x + 7.5y

3000 = 7.5x - 7.5y

Adding both equations, it becomes

7500 = 15x

x = 7500 /15 = 500

Substituting x = 500 into equation 1, it becomes

1500 = 2.5 × 500 + 2.5y

1500 = 1250 + 2.5y

2.5y = 1500 - 1250 = 250

y = 250/2.5 = 100

Answer:

Step-by-step explanation:

The value of the total mass will be equal to 13.189x10³ kg.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Calculate weight,

B₁ = ρVg

B₁ = (1027) x (4/3Π(1.3)³ x (9.8)

B₁ = 92.622\ kN

Calculate weight,

B₂ = ( 1027 ) x ( 5 x 2.6 x 2.8) x  (9.8)

B₂ = 366.35\ kN

The total mass will be,

B₁ + B₂ = mg

m = ( B₁ + B₂ ) / g

m = ( 36635 + 36635 ) / 9.8

m = 13.189 x 10³ kg

Therefore, the value of the total mass will be equal to 13.189x10³ kg.

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Answer:

Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.            

Step-by-step explanation:

We are given the following in the question:

The distribution of systolic blood pressure of other women is a bell shaped distribution that is a normal distribution.

z-score = 1.50

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

Let x be the Gina's systolic blood pressure.

Thus, we can write:

[tex]1.50 = \displaystyle\frac{x-\mu}{\sigma}\\\\x = 1.5\sigma + \mu \\\text{where }\sigma \text{ is the standard deviation and }\\\mu \text{ is the mean for the given distribution of blood pressure.}[/tex]

Thus, we can write Gina's blood pressure  is 1.50 standard deviations above the average systolic blood pressure of women her age.

Option b) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.

Gina's z-score of 1.50 indicates that her systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.

The best interpretation of Gina's standardized score (z-score) of 1.50 is option B: Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age. Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.

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Answer:

Probability of either getting a B but neither gets a C = 0.6

Step-by-step explanation:

Probability of sought event = At least one gets a B but neither gets a C

Let

P = Probability of either getting a B but neither gets a C

P(JA)= The probability of getting an A by John

P(JB) = The probability of getting a B by John

P(JC) = The probability of getting a C by John

P(MA) = The probability of getting an A by Mary

P(MB) = The probability of getting a B by Mary

P(MC) = The probability of getting a C by Mary

Desired event = P(MA)×P(JB) + P(MB)× P(JB) + P(MB)× P(JA)

The probability of Mary having a grade is

P(MA) + P(MB) + P(MC) = 1 and P(JA) + P(JB) + P(JC) = 1

Rearranging

P(MA) = 1- ( P(MB) + P(MC) ) and P(JA) = 1 - ( P(JB) + P(JC) )

P = ( 1- ( P(MB) + P(MC) ) ) × P(JB) + P(MB)× P(JB) + ( 1 - ( P(JB) + P(JC) ) ) × P(MB)

P = P(JB) - P(JB)×P(MB) - P(JB)×P(MC) + P(MB)×P(JB) + P(MB) - P(JB)×P(MB) - P(MB)×P(JC)

P= P(JB)+ P(MB)-( P(JB)× P(MC)+ P(MB)×P(JB)+ P(MB)×P(JC))

We are told that the probability that neither gets an A but at least one gets B is

0.1 = P(JB)×P(MC) + P(JB)× P(MB) + P(JC)×P(MB)

Therefore the probability that at least one gets a B but neither gets a C

P = 0.3+0.4 - 0.1 = 0.6

Ans 0.6

The probability of either John or Mary getting a 'B' but none of them getting a 'C' is 0.6.

The probability of a scenario where neither John nor Mary gets a 'C' is contingent on the possibilities where they get 'A's', 'B's' or both. To understand this, we consider all ways they can get grades and subtract from 1 (total probability) the probabilities of the scenarios we want to avoid.

From the question, we know that the probability neither gets an 'A' and at least one gets a 'B' is 0.1.

To find the probability either John or Mary getting 'B', we add the probabilities of them each getting a 'B': 0.3 + 0.4 = 0.7. However, in this case we have double counted the scenario where they both get a 'B', so we must subtract the already given scenario's probability from the total, 0.7 - 0.1 = 0.6.

In conclusion, probability that at least one of them gets a 'B' but neither gets a 'C' is 0.6.

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Answer:

The rain barrel an hold [tex]3\frac{1}{5}\ gallons[/tex] of water more.

Step-by-step explanation:

Given:

Amount of water barrel can hold = 12 gallons

Amount of water in the barrel before storm = [tex]2\frac{1}{5}\ gallons[/tex]

[tex]2\frac{1}{5}\ gallons[/tex] can be Rewritten as [tex]\frac{11}{5}\ gallons[/tex]

Amount of water in the barrel before storm =  [tex]\frac{11}{5}\ gallons[/tex]

Amount of water storm added = [tex]6\frac{3}{5}\ gallons.[/tex]

[tex]6\frac{3}{5}\ gallons.[/tex] can be Rewritten as [tex]\frac{33}{5}\ gallons.[/tex]

Amount of water storm added = [tex]\frac{33}{5}\ gallons.[/tex]

we need to find the amount of water barrel can hold more.

Solution:

Now we can say that;

the amount of water barrel can hold more can be calculated by Subtracting the sum of Amount of water in the barrel before storm and Amount of water storm added from Amount of water barrel can hold.

framing in equation form we get;

the amount of water barrel can hold more = [tex]12-(\frac{11}{5}+\frac{33}{5})= 12-\frac{11+33}{5}= 12- \frac{44}{5}[/tex]

Now we can see that 1 number is whole number and other is fraction.

So we will make the whole number into fraction by multiplying the numerator and denominator with the number in the denominator of the fraction.

so we can say that;

the amount of water barrel can hold more = [tex]\frac{12\times5}{5}-\frac{44}{5} = \frac{60}{5}-\frac{44}{5}[/tex]

Now we can see that denominator is common so we can subtract the numerator.

the amount of water barrel can hold more = [tex]\frac{60-44}{5}=\frac{16}{5}\ gallons \ OR \ \ 3\frac{1}{5}\ gallons[/tex]

Hence The rain barrel an hold [tex]3\frac{1}{5}\ gallons[/tex] of water more.

Final answer:

To find out how many more gallons of water the barrel can hold, subtract the total current water in the barrel from its maximum capacity.

Explanation:

In the question, it is asked how much more water a rain barrel can hold after it has been partially filled. To find this, we need to subtract the amount of water already in the barrel from its total capacity. Initially, the barrel contains 2 1/5 gallons, and the storm adds another 6 3/5 gallons.

We first convert these to improper fractions to make the addition easier.

The rain barrel can hold 12 gallons of water.

Before the storm, there were 2 1/5 gallons in the barrel.

The storm added 6 3/5 gallons of water to the barrel.

To find out how many more gallons of water can the barrel hold, we need to calculate: 12 - (2 1/5 + 6 3/5).

12 - (2 1/5 + 6 3/5) = 12 - (2.2 + 6.6) = 12 - 8.8 = 3.2 gallons.

Answer:

The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].

Alyssa purchased 4 Americana chickens and 8  Delaware chickens.

Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.

Step-by-step explanation:

Given:

Let the number of Americana chickens be 'x'.

Let the number of Delaware chickens be 'y'.

Number of chickens purchased = 12

Now we know that;

Number of chickens purchased is equal to sum of the number of Americana chickens and the number of Delaware chickens.

framing in equation form we get;

[tex]x+y =12 \ \ \ \ equation\ 1[/tex]

Also Given:

Cost of Americana chickens = $3.75

Cost of Delaware chickens = $2.50

Total amount spent = $35

Now we know that;

Total amount spent is equal to sum of the number of Americana chickens multiplied by Cost of Americana chickens and the number of Delaware chickens multiplied Cost of Delaware chickens.

framing in equation form we get;

[tex]3.75x+2.5y =35 \ \ \ \ equation\ 2[/tex]

Hence The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].

Now to find the number of each type of chickens she purchased we will solve the above equation.

First we will multiply equation 1 with 2.5 we get;

[tex]2.5(x+y)=12\times2.5\\\\2.5x.+2.5y = 30 \ \ \ \ equation \ 3[/tex]

Now we will subtract equation 3 from equation 2 we get;

[tex]3.75x+2.5y-(2.5x+2.5y)=35-30\\\\3.75x+2.5y-2.5x-2.5y=5\\\\1.25x=5[/tex]

Now Dividing both side by 1.25 we get;

[tex]\frac{1.25x}{1.25}=\frac{5}{1.25}\\\\x= 4[/tex]

Now we will substitute the value of 'x' in equation 1 we get;

[tex]x+y=12\\\\4+y=12\\\\y=12-4 = 8[/tex]

Hence Alyssa purchased 4 Americana chickens and 8  Delaware chickens.

Now Given:

Number of eggs laid by American chicken per day = 2 eggs

Number of eggs laid by Delaware chicken per day = 1 egg

Cost of 12 eggs = $2.5

Total number of days = 7

Now first we will find the Total number of eggs laid by both the chickens.

Total number of eggs laid per day = [tex]4\times2 + 8\times 1= 8 +8 =16\ eggs[/tex]

Total number of eggs laid in week = [tex]16\times7= 112[/tex] eggs

12 eggs = $2.5

112 eggs = Cost of 112 eggs.

By cross multiplication we get;

Cost of 112 eggs = [tex]\frac{2.5 \times 112}{12} = \$23.33[/tex]

Hence Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.

The system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased are as follows;

A + D = 12

3.75A + 2.50D = 35

Alyssa purchased 4 Americans chicken and 8 Delaware chickens.

She is expected to take in $22.5 at the end of the first week with her 12 chickens.

number of Americana chickens  = A

number of Delaware chickens = D

Therefore,

A + D = 12

3.75A + 2.50D = 35

A  = 12 - D

3.75(12 - D) + 2.50D = 35

45 - 3.75D + 2.50D = 35

-1.25D  = -10

D = -10 / -1.25

D = 8

A = 12 - 8 = 4

A = 4

Therefore, Alyssa bought 4 Americans chickens and 8 Delaware chickens.

Each American chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day.

She only sells the egg in full dozen for $2.50.

The amount of money she expects to take in at the end of the first week with her 12 chickens is calculated as follows.

1 week = 7 days

Number of American chicken eggs(first week) = 7 × 4 × 2 = 56 eggs

Number of Delaware chicken eggs(first week) = 1 × 7  × 8 = 56 eggs

Total eggs =  56 + 56 = 112 eggs.

She can only sell full dozen of eggs. Therefore,

112 / 12 = 9.333

1 dozen = $2.50

9 dozen =

cross multiply

Amount made from the eggs = 9 × 2.50  = $22.5

learn more about system of equation: https://brainly.com/question/15319423?referrer=searchResults

Final answer:

To find the mean speed for the entire trip, calculate the total distance traveled (465 miles) and the total time spent (12 hours). The mean speed is then determined to be 38.8 mph when rounded to one decimal place.

Explanation:

To find the mean speed for the entire trip, we need to first calculate the total distance traveled and the total time spent driving. This can then be used to calculate the mean speed using the formula: Mean Speed = Total Distance / Total Time.

On the highway: 5 hours at 50 mph = 250 miles

Through the city: 2 hours at 20 mph = 40 miles

On a county road: 5 hours at 35 mph = 175 miles

The total distance traveled is 250 miles + 40 miles + 175 miles = 465 miles. The total time spent driving is 5 hours + 2 hours + 5 hours = 12 hours.

Thus, the mean speed for the entire trip is 465 miles / 12 hours = 38.75 mph. Rounded to one decimal place, the mean speed is 38.8 mph.