Find the measure of the exterior angle​

Answer:No Solution

Step-by-step explanation: the explanation can be found in the attached picture

The given system of linear equations does not have a unique solution, as one equation is a multiple of another. Therefore, this is a dependent system and the solution can be expressed in terms of a parameter satisfying all equations.

In order to solve a system of linear equations, one can use a variety of methods such as substitution, elimination, or matrix method. Let's use the elimination method here. The given system of equations is:

a) x + 2y - 7z = -8, b) 2x + y + z = 23 and c) 3x + 9y - 36z = -63. It is seen that equation c) is simply 3 times equation a), hence these equations are dependent and will not provide any unique solution. The system of equations is therefore dependent and does not have a unique solution. It can be expressed in terms of a parameter which will satisfy all given equations. The solution cannot be expressed in terms of x, y and z.

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Answer:

Ratio of the increase in value to the original value will be 1 : 5

Step-by-step explanation:

This question is incomplete; Here is the complete question.

A house with an original value to $150,000 increased in value to $180,000 in 5 years. what is the ratio of the increase in value to the original value of the house?

Original value of the house = $150000

Value of the house after 5 years = $180000

Appreciation in value of the house after 5 years = $180000 - $150000

= $30000

Now the ratio of the increase in value to the original value = [tex]\frac{\text{Increased value}}{\text{Original value}}[/tex]

= [tex]\frac{30000}{150000}[/tex]

= [tex]\frac{1}{5}[/tex] or 1 : 5

Therefore, ratio of the increase in value to the original value of the house is 1 : 5

Final answer:

To find the ratio of the increase in house value to the original value, subtract the original price from the increased price, then divide by the original price. For a house purchased at $200,000 and increased to $250,000, the ratio would be 0.25, or a 25% increase from the original value.

Explanation:

To calculate the ratio of the increase in value to the original value of a house, you must take the difference between the final value and the original value, then divide this by the original value. Suppose a house was bought for $200,000 and is now worth $250,000, this would be an increase of $250,000 - $200,000 = $50,000. The ratio of increase to original value would thus be $50,000 / $200,000 = 0.25 or 1:4. This indicates that, for every dollar of the original value, the house increased in value by 25 cents. If we wanted to express this as a percentage, we would multiply by 100, giving us a 25% increase in value. However, it's important to remember other factors such as transaction costs, market conditions, and loan repayment when considering the rate of return on a house.

The two numbers are 8,13.

Step-by-step explanation:

Let,

smaller number = x

Larger number = x+5

According to given statement;

Smaller number + Bigger number = 3x-3

[tex]x+(x+5)=3x-3\\x+x+5=3x-3\\2x+5+3=3x\\8 = 3x-2x\\8=x\\x=8[/tex]

Smaller number = 8

Larger number = 8+5 = 13

The two numbers are 8,13.

Keywords: algebraic equation, addition

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Answer:

The two numbers are 8,13.

Answer:

(5,-3) , (10, -2), (7,-8)

Step-by-step explanation:

The new triangle will be

(5,-3) , (10, -2), (7,-8) by mapping

(x,y) => (x +3, y-5)

Answer:

AB = 14 units

Step-by-step explanation:

Given:

A triangle GHJ with the following aspects:

A, B, C are midpoints of sides GH, HJ and GJ respectively.

AB = [tex]3x+8[/tex]

GJ = [tex]2x+24[/tex]

Midsegment Theorem:

The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and the length of the midsegment is one-half of the length of the third side.

Therefore, AB is the midsegment of sides GH and HJ and thus, is parallel to GJ and equal to one-half the length of GJ.

[tex]\therefore AB=\frac{1}{2}\times\ GJ[/tex]

Now, plug in the values of AB and Gj and solve for 'x'.

This gives,

[tex]3x+8=\frac{1}{2}(2x+24)\\\\3x+8=x+12\\\\3x-x=12-8\\\\2x=4\\\\x=\frac{4}{2}=2[/tex]

Now, the length of AB is given by plugging in 2 for 'x'.

[tex]AB=3\times2+8=6+8=14[/tex]

Therefore, the length of midsegment AB is 14 units.

Answer:

14 Units

Step-by-step explanation:

The length of midsegment AB is equal to one-half the length of side GJ. In this case, AB is given by the expression 3x + 8 and GJ is given by the expression 2x + 24.

To find the value of x, we can set the expressions for AB and GJ equal to each other and solve for x.

3x + 8 = 1/2(2x + 24)

We can simplify this equation by distributing the 1/2 to the terms inside the parentheses:

3x + 8 = x + 12

Next, we can subtract x from both sides to isolate the x term:

3x - x + 8 = 12

2x + 8 = 12

Then, we can subtract 8 from both sides:

2x = 4

Finally, we can solve for x by dividing both sides by 2:

x = 2

Now that we have the value of x, we can substitute it back into the expression for AB:

AB = 3(2) + 8

AB = 6 + 8

AB = 14

Therefore, the length of midsegment AB is 14 units.

Answer:

$600

Step-by-step explanation:

Let the random variable [tex]X[/tex] denote the damage in $ incurred in a certain type of accident during a given year. The probability distribution of [tex]X[/tex] is given by

                        [tex]X : \begin{pmatrix}0 & 1000 & 5000 & 10\; 000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]

A company offers a $500 deductible policy and it wishes its expected profit to be $100. The premium function is given by

                    [tex]F(x) = \left \{ {{X+100, \quad \quad \quad \quad \quad \text{for} \; X = 0 } \atop {X-500+100} , \quad \text{for} \; X = 500,4500,9500} \right.[/tex]

For [tex]X = 0[/tex],  we have

                              [tex]F(X) = 0+100 = 100[/tex]

For [tex]X = 500[/tex],

                             [tex]F(X) = 500-500+100 = 100[/tex]

For [tex]X = 4500[/tex],

                            [tex]F(X) = 4500-500+100 = 4100[/tex]

For [tex]X = 9500[/tex],

                            [tex]F(X) = 9500-500+100 = 9100[/tex]

Therefore, the probability distribution of [tex]F[/tex] is given by

                           [tex]F : \begin{pmatrix} 100 & 100 & 41000 & 91000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]

To determine the premium amount that the company should charge, we need to calculate the expected value of [tex]F.[/tex]

[tex]E(F(X)) = \sum \limits_{i=1}^{4} f(x_i) \cdot p_i = 100 \cdot 0.81 + 100 \cdot 0.09 + 4100 \cdot 0.08 + 9100 \cdot 0.02[/tex]

Therefore,

                             [tex]E(F) = 81+9+328+182 = 600[/tex]

which means the $600 is the amount the should be charged.

Answer:

3/4

Step-by-step explanation:

Step-by-step explanation:

the sum of angles in a triangle is 180°. so if a triangle is equivalent, each degree will be 180/3 = 60°

Answer:

Therefore, area under the curve is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

We have to find the area under curve y = x³ from 0 to 1 as limit.

Since Area 'A' = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x[/tex]

The given function is f(x) = x³

Since [tex]x_{i}=a+\triangle x.i[/tex]

Here a = 0 and [tex]\triangle x=\frac{1-0}{n}=\frac{1}{n}[/tex]

[tex]f(x_{i})=(\frac{i}{n})^{3}[/tex]

Now A = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x= \lim_{n \to \infty}\sum_{i=1}^{n}(\frac{i}{n})^{3}(\frac{1}{n})[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}\sum_{i=1}^{n}i^{3}[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}( \frac{n(n+1)}{2})^{2}[/tex]    Since 1³ + 2³ + 3³..............n³ = [tex][\frac{n(n+1)}{2}]^{2}[/tex]

[tex]= \lim_{n \to \infty}\frac{n^{2}(n+1)^{2}}{4n^{4}}[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{4}(1+\frac{1}{n})^{2}[/tex]

[tex]=\frac{1}{4}(1+0)[/tex]

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

Therefore, area under the curve is [tex]\frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

A continuous function is one that has a set of unique solutions. a function is also said to be continuous if at every interval, there exist no sudden change in the assumed values otherwise the function will be discontinuous.

for example, the sine and cosine function are continuous over a set of real integers.

from the question, any assumed expression of x and integrating over the interval x and infinity will render the function continuous.

Assumed f(x) = cuberoot of x

Integrating and evaluating will prove that the function is continuous, as such a defined function is always a continuous function and not necessarily lipschitz.

Answer:11.38

Step-by-step explanation:

290-257=33 /290=.11379 x 100=11.37  =11.38

Final answer:

To find the percentage of racers who did not complete the marathon, we add those who gave up and those who were disqualified, a total of 31 racers. The percentage is then calculated using the formula for percentage, resulting in 10.7% of racers not completing the marathon.

Explanation:

To find the percentage of racers who did not complete the marathon, we first need to determine the total number of racers who did not finish. This includes those who gave up and those who were disqualified. In this case, 27 racers gave up, and 4 were disqualified, giving us a total of 31 racers who did not complete the marathon.

To calculate the percentage, we use the formula:

Percentage = (Number of racers who did not complete / Total number of racers) × 100%

Plugging the numbers into the formula gives us:

Percentage = (31 / 290) × 100% = 0.1069 × 100% = 10.69%

Rounding to the nearest tenth of a percent, 10.7% of racers did not complete the marathon.

Answer:

The Teenagers spend $172.05 billion dollars in 2001.

Step-by-step explanation:

Given:

Number of billion dollars spent by teenagers in 2000 = $155

Percentage amount increase in 2001 = 11%

We need to find how many billions of dollars did teenagers spend in 2001.

Solution:

First we will find the Number of billion dollar increase in 2001.

Number of billion dollar increase in 2001 can be calculated by Percentage amount increase in 2001 multiplied by Number of billion dollar spent by teenagers in 2000 and then divided by 100.

framing in equation form we get;

Number of billion dollar  increase in 2001 = [tex]\frac{11}{100}\times 155 = \$17.05[/tex]

So no number of billion dollars teenagers spend in 2001 is equal to Number of billion dollars spent by teenagers in 2000 plus Number of billion dollar  increase in 2001 .

framing in equation form we get;

number of billion dollars teenagers spend in 2001 = [tex]\$155+\$17.05 = \$172.05[/tex]

Hence The Teenagers spend $172.05 billion dollars in 2001.

Answer:

See below.

Step-by-step explanation:

x < 2   f(x) = |x|.

x ≥ 2   f(x) =  3.

Answer:

Casandra will run 8 miles on the 9th Day.

Step-by-step explanation:

Given:

Casandra on first day of training  she runs 4 miles

So we can say that;

[tex]a_1=4\ miles[/tex]

Also Given:

each day after that she adds on 0.5 mile.

So we can say that;

Common difference [tex]d=0.5\ miles[/tex]

We need to find on what day she will run 8 miles.

So we can say that;

[tex]T_n = 8[/tex]

Let the number of the day be denoted by 'n'

Solution:

Now By using the formula of Arithmetic Progression we get;

[tex]T_n= a_1+(n-1)d[/tex]

Now substituting the values we get;

[tex]8=4+(n-1)0.5[/tex]

Now by using distributive property we get;

[tex]8 =4+0.5n-0.5\\\\8=3.5+0.5n[/tex]

Now subtracting both side by 3.5 we get;

[tex]8-3.5=3.5+0.5n-3.5\\\\4.5=0.5n[/tex]

Dividing both side by 0.5 we get;

[tex]\frac{4.5}{0.5}=\frac{0.5n}{0.5}\\\\9=n[/tex]

Hence Casandra will run 8 miles on the 9th Day.

The transformation type may be identified by understanding each option: reflection would flip the figure across an axis, translation would slide it, and a 90° counter-clockwise rotation would pivot it around the origin. The right choice depends on the specific positioning of ABCD and A'B'C'D'.

The student's question revolves around identifying the type of transformation that maps quadrilateral ABCD to A'B'C'D'. Without the specific coordinates or a visual representation it's difficult to provide the exact transformation.

However, the choices given are reflections across the X-axis or the Y-axis, translation, or a 90° counter-clockwise rotation.

Reflecting across the X-axis would mean to move every point of ABCD to the opposite side vertically, while the Y-axis reflection would be a horizontal flip. A translation involves sliding the figure in any direction without altering its orientation or shape.

But, the 90° counter-clockwise rotation is a pivot of every point at a 90-degree angle around the origin in the counter-clockwise direction, which appears to be the action described in the subsequent figures and discussion of the merry-go-round example.

The three types of descriptions involving the positive x direction, vertically upward, and horizontally to the right side can be related to the translation movement in the coordinate system.

Answer:

Malcolm is showing evidence of gambler's fallacy.

This is the tendency to think previous results can affect future performance of an event that is fundamentally random.

Step-by-step explanation:

Since each round of the roulette-style game is independent of each other. The probability that 8 will come up at any time remains the same, equal to the probability of each number from 1 to 10 coming up. That it has not come up in the last 15 minutes does not increase or decrease the probability that it would come up afterwards.

Answer:

8.

Step-by-step explanation:

5, 10, 12, 4, 6, 11, 13, 5

Arrange in ascending order:

4, 5, 5, 6, 10, 11, 12, 13.

The median is the mean of the 2 middle numbers:

= (6 + 10) / 2

= 8.

Answer:

See explanation!

Step-by-step explanation:

We know that the maximum miles allowed before oil change is 5,000miles (thus Kaci can drive less or up to 5,000 miles but not more).

Kaci has already driven 3,450miles since last oil change.

Inequalities are typically employed to show a relating or comparative relationship between expressions and can be identified by the sybolism of less, more or/and equal to (i.e. [tex]<[/tex] , [tex]>[/tex] , [tex]\leq[/tex], [tex]\geq[/tex] ).

Let us denote the miles Kaci can drive before oil changing again by [tex]x[/tex], then we can write the following inequality:

[tex]3450+x\leq 5000[/tex]

solving for the remaining miles [tex]x[/tex] allowed

[tex]3450+x\leq 5000\\x\leq 5000-3450\\x\leq 1550[/tex]

Thus Kaci can drive up to and including 1550 miles before chaging car oil again.

Final answer:

Kaci can drive up to 1550 more miles before needing an oil change, based on the advice not to exceed 5000 miles between oil changes and the fact she has already driven 3450 miles.

Explanation:

The question asks us to write and solve an inequality that will help determine how many more miles Kaci can drive before needing an oil change. It is given that her car has already been driven 3450 miles since the last oil change, and she has been advised not to exceed 5000 miles between oil changes.

To solve this, let x represent the number of miles Kaci can still drive before reaching the 5000-mile limit. The inequality that represents this situation would be:

3450 + x ≤ 5000

To find the value of x, we subtract 3450 from both sides of the inequality:

x ≤ 5000 - 3450

x ≤ 1550

Therefore, Kaci can drive up to 1550 more miles before needing her oil changed again.

Answer:

The population of city is 7 million in 2015.

Step-by-step explanation:

It is given that the population of a city, P, in millions, is a function of t, the number of years since 2010.

It means, P = f(t).  

We need to explain the meaning of the statement f(5) = 7 in terms of the population of this city.

f(5) = 7 means the population is 7 millions at t=5.

t = 5 means 5 years after 2010, i.e., 2010+5 = 2015

Therefore, the population of city is 7 million in 2015.

Answer:

  OT, OU, OR

Step-by-step explanation:

Point O is the center of the circle, so will be one end of any radius. Segments are shown from point O to points T, U, and R on the circle. Each of those segments is a radius:

  OT, OU, OR . . . . are radii

_____

OS would also be a radius, but no segment is shown there, and it doesn't show in any answer choice.

Answer:

A) g(x)= 1/2(x-8)^2-8.   The vertex is (8, -8).

Step-by-step explanation:

A. g(x)= 1/2(x-8)^2-8 is the vertex form of the function.

In general it can be written as

f(x) = a(x - h)^2 + k       where (h, k) is the vertex.

Here the vertex is (8, -8)

For given function g(x), vertex = (8, -8)

The correct answer is option (A)

"The graph of the quadratic function is shaped like a parabola. The form of this quadratic function is called vertex form."

"The vertex of the graph of a quadratic function is the highest or lowest possible output for that function. "

For given example,

We have been given three equivalent forms of a quadratic function g.

[tex]g(x) = \frac{1}{2} (x-8)^2-8\\\\g(x) = \frac{1}{2}(x-12)(x-4)\\\\g(x) = \frac{1}{2}x^2-8x+24[/tex]

In general the vertex form of a function can be written as

f(x) = a(x - h)^2 + k,

where (h, k) is the vertex.

From these functions the function g(x)= 1/2(x-8)^2-8 is vertex type function.

Comparing with the general equation,

we have h = 8 and k = -8

So, the vertex are (8, -8).

The correct answer is option (A)

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Final answer:

A chemist cannot achieve a 34% concentration by mixing 20% and 30% acid solutions, as it is outside the possible range of concentrations achievable by combining these two solutions, option no 4.

Explanation:

When a chemist is mixing two acid solutions, one with a 20% concentration and the other with a 30% concentration, they can obtain a range of concentrations between the two provided percentages by varying the proportions of each solution mixed. The concentrations that could not be obtained would be any value outside of the 20% to 30% range because the resulting mixture cannot exceed the concentration of the higher concentrated solution or be lower than the concentration of the less concentrated solution. Therefore, a 34% concentration could not be obtained by mixing a 20% solution with a 30% concentration.

Answer:

The answer to your question is below

Step-by-step explanation:

Data

∠1 = 105°

Process

a)

∠2 = 180 - 105 = 75°          supplementary angles

∠3 = ∠2 = 75°                     supplementary angles

∠4 = 105°                            vertical angles

∠5 = 105°                            corresponding angles

∠6 = 180 - 105 = 75°           alternate interior angles

∠7 = ∠6 = 75°                      supplementary angles

∠8 = 105°                             alternate interior angles

b)

∠3 = 80°

∠1 = 180 - 80 = 100°           supplementary angles

∠2 = 80°                              vertical angles

∠4 = 100°                              supplementary angles

∠5 = 100°                             supplementary angles

∠6 = 80°                               alternate interior angles

∠7 = 80°                               corresponding angles

∠8 = 100°                              supplementary angles

Answer: -3

Step-by-step explanation: using the mathematical process

4-(4/4)-6=

4-1-6= -3

Answer:

Actually there are two answers: -3 and 0, depending on how the expression is written.

Step-by-step explanation:

If the rational expression is x - 4/x - 6, we have:

x - 4/x - 6

= 4 - 4/4 - 6

= 4 - 1 - 6 = 4 - 7 = -3

If the rational expression is (x - 4)/(x - 6), we have:

(x - 4)/(x - 6)

= (4 - 4)/(4 - 6)

= 0/-2 = 0

Answer:

the answer is 9/8 or 1 and 1/8

Step-by-step explanation:

divide 3/4 by 2 to get 3/8 and then multiply 3/8 by 3 (since its tripling) to get 9/8 which can also be written as 1 1/8. Hope this helps!

Answer:

Voters can select their members in 10possible ways

Step-by-step explanation:

According to the question, the voters are to elect 3members out of 5 candidates, this means they are to select any 3 candidates of their choice from a pool of 5 candidates. Since "combination" has to do with selection, we use the combination formula.

To select 'r' objects from 'n' pool of objects, we have;

nCr = n!/(n-r)!r!

5C3 = 5!/(5-3)!3!

5C3 = 5!/2!3!

5C3 = 5×4×3×2×1/2×3×2

= 120/12

5C3 = 10

Candidates can therefore vote in 10 possible ways

Answer:

She would earn in a week (six days) 1482 cents.

Step-by-step explanation:

Given:

Mrs. Hall went to work for the shirt factory.

She earned nineteen cents per hour.

She worked thirteen hours per day.

Now, to find the money she earn in a week (six days).

Money she earned per hour = 19 cents.

As she she worked 13 hours per day.

So, money she earned per day = [tex]19\times 13=247.[/tex]

Now, to get the total money she earned in a week (six days) we multiply 6 by money earned in per day:

[tex]6\times 247[/tex]

[tex]=1482\ cents.[/tex]

Therefore, she would earn in a week (six days) 1482 cents.

Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%

Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz

b=1.2 oz

Let S be the volume of randomly selected soda bottles

Y-score: S-a/b

For S=32 oz

Substitute the values of S,a and b into the equation

Y=32-32.3/1.2

Y=-0.25

Probability of bottles that have a volume less than 32 oz is

P(S<32)=P(Y<-025)= 0.40129

Percentage of bottles that have volume less than 32 oz will be

0.40127×100%=40.13%

Answer:

[tex]P(16.6 < \bar X < 22.6) = P(\frac{16.6-19}{3} <Z< \frac{22.6-19}{3})= P(-0.8 < Z < 1.2)[/tex]

[tex]P(16.6 < \bar X < 22.6) =P(-0.8<Z<1.2) = P(Z<1.2)-P(Z<-0.8) = 0.88493- 0.211855= 0.673[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(19,6)[/tex]  

Where [tex]\mu=19[/tex] and [tex]\sigma=6[/tex]

And we select n =4 fish. For this case we want to find this probability:

[tex] P(16.6 < \bar x < 22.6) [/tex]

And since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}=3)[/tex]

And the z score is given by:

[tex]z = \frac{\bar x -\mu}{\sigma_{\bar x}}[/tex]

And if we apply this formula we got:

[tex]P(16.6 < \bar X < 22.6) = P(\frac{16.6-19}{3} <Z< \frac{22.6-19}{3})= P(-0.8 < Z < 1.2)[/tex]

And we can find this probability with this operation using the normal standard table or excel:

[tex] =P(-0.8<Z<1.2) = P(Z<1.2)-P(Z<-0.8) = 0.88493- 0.211855= 0.673[/tex]

To find the probability that the mean weight of four randomly selected fish will be between 16.6 and 22.6 pounds, we can use the Central Limit Theorem. The probability is 0.7556.

To find the probability that the mean weight of four randomly selected fish will be between 16.6 and 22.6 pounds, we can use the Central Limit Theorem. The Central Limit Theorem states that if we take multiple samples from a population with any distribution, the distribution of the sample means will approach a normal distribution. In this case, we have a normally distributed population with a mean of 19 pounds and a standard deviation of 6 pounds.

To calculate the probability, we need to standardize the range of weights using the formula for the standard error of the mean:

Standard error of the mean (SE) = Standard deviation / sqrt(sample size)

We will use the formula:

Z = (X - mean) / SE

Where X is the upper and lower bounds of the range, mean is the population mean, and SE is the standard error of the mean.

First, let's calculate the standard error of the mean:

SE = 6 / sqrt(4) = 3

Then, we can calculate the z-scores for the upper and lower bounds:

Z_upper = (22.6 - 19) / 3 = 1.2

Z_lower = (16.6 - 19) / 3 = -1.1333

Since the z-scores are in standard deviation units, we can look up the corresponding probabilities in the standard normal distribution table:

P(16.6 < X < 22.6) = P(-1.1333 < Z < 1.2)

Using the table, we can find the probabilities:

P(Z < -1.1333) = 0.1293

P(Z < 1.2) = 0.8849

Finally, we can calculate the probability between the two bounds:

P(16.6 < X < 22.6) = P(Z < 1.2) - P(Z < -1.1333) = 0.8849 - 0.1293 = 0.7556

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Answer:

There were 116 jelly beans in the bag to start with

Explanation:

a. Let's start with Carries brother and his friends.

We are given that Carrie's brother ate 4 jelly beans,  the first teammate ate 6, the second teammate ate 8 and so on.

Noticing the pattern, we can see that each teammate ate 2 jelly beans more that the one preceding him.

We are also given that Carrie's brother has 8 teammates.

This means that:

Carrie's brother ate 4 jelly beans

First teammate ate 4 + 2 = 6 jelly beans

Second teammate ate 6 + 2 = 8 jelly beans

Third teammate ate 8 + 2 = 10 jelly beans

Fourth teammate ate 10 + 2 = 12 jelly beans

Fifth teammate ate 12 + 2 = 14 jelly beans

Sixth teammate ate 14 + 2 = 16 jelly beans

Seventh teammate ate 16 + 2 = 18 jelly beans

Eighth teammate ate 18 + 2 = 20 jelly beans

Now, we calculate the total number of jelly beans eaten by Carrie's brother and his teammates

Total jelly beans = 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 108 jelly beans

b. Next, we move to Carrie:

We are given that Carrie ate 5 jelly beans

Adding that to the total number of jelly beans from part a, we get the total number of eaten jelly beans

Therefore:

Total number of eaten jelly beans = 108 + 5 = 113 jelly beans

c. Getting the number of jelly beans that were in the bag to start with:

We are given that the remaining number of jelly beans in the bag after all has eaten was 3 jelly beans

This means that, if we added the number of eaten jelly beans to the number of remaining jelly beans, we will get the total number of jelly beans that were in the bag to start with

Therefore:

Total number of jelly beans in the bag to start with = 113 + 3 = 116 jelly beans

Hope this helps :)

Final answer:

By calculating the total number of jelly beans eaten and adding the three left in the bag, we find that there were originally 119 jelly beans in Carrie's bag.

Explanation:

To figure out how many jelly beans were in the bag initially, we need to work backwards from the information given. Carrie ate 5 beans and then her brother ate 4. Combining that with the 3 beans left at the end, we have a subtotal of 12 beans (5+4+3). We're told that each of Carrie's brother's teammates ate an increasing number of beans, starting with 6 and increasing by 2 each time.

Let's find the total number of beans eaten by the teammates. Since there are 8 teammates and the number of jelly beans increases by 2 for each subsequent teammate, starting at 6, we have an arithmetic sequence.

To find the total beans eaten by teammates, we sum the arithmetic sequence: T = (n/2) * (first term + last term). Here, n=8, the first term is 6, and the last term is 6 + 2*(8-1) = 20 (since the increase is by 2 for each of the 7 teammates after the first).

T = (8/2) * (6 + 20) = 4 * 26 = 104 beans eaten by all teammates combined.

Adding Carrie's and her brother's consumption to the teammates' total gives us: 12 beans (Carrie and her brother) + 104 beans (teammates) = 116 beans. Therefore, there were 116 + 3 (left in the bag) = 119 jelly beans in the bag to start with.