The distance between the two scout patrols is approximately 11.66 kilometers.
We can see that the situation forms a right triangle with the hypotenuse representing the distance between the two scout patrols. Let's call this distance d.
Each patrol initially hikes 5 kilometers in opposite directions. This means that the distance between them at this point is 10 kilometers (5 km + 5 km).
Then, each patrol turns 90 degrees to their right and hikes 6 kilometers. This means that they travel along the legs of the right triangle, which have a length of 6 kilometers.
Using the Pythagorean theorem, we can solve for the hypotenuse:
d² = 10² + 6²
d² = 136
d ≈ 11.66 km
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Without using a protractor, estimate the measure of the angle below. Explain how you made your estimate.
select all expressions equivalent to (3^3*3^-4)^-3
The expressions that are equivalent to (3^3*3^-4)^-3 are (3^-1)^-3, 3^3 and 27
Selecting all expressions that are equivalent to (3^3*3^-4)^-3From the question, we have the following parameters that can be used in our computation:
(3^3*3^-4)^-3
Evaluating the expression in the brackets using the law of indices, we have
(3^3*3^-4)^-3 = (3^-1)^-3
Next, we open the brackets
This gives
(3^3*3^-4)^-3 = 3^(-1 *-3)
When evaluated, we have
(3^3*3^-4)^-3 = 3^3
Evaluate the exponents
This gives
(3^3*3^-4)^-3 = 27
Hence, the expressions that are equivalent to (3^3*3^-4)^-3 are (3^-1)^-3, 3^3 and 27
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The sum of the series below is 10,900. how many numbers, n, are in the series? 19 20.5 22 23.5 ... 181 27 100 109 135
There are 109 terms in given series.
Here, we have,
According to the statement
we have given that the sum of series is AP series and
This is 19 20.5 22 23.5 ... 181
And the sum of series is 10,900
Now, we have to find the number of terms in the series.
Then we use the summation formula which is
S = n/2 (a + L)
Substitute the all given values in it like
L = 181
A = 19 and S= 10,900
then
10,900= n/2(19+181)
10,900= n/2(200)
After solve the equation for n
10,900= 100n
n = 10,900 / 100
n = 109
There are 109 terms in given series.
So, There are 109 terms in given series.
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2. Reemplaza los valores correspondientes de "a", "b" y "c", y calcula: a = -2 b = 3 c = 4 a) a + b – c = b) a – b + c = c) a + 2. B – 2c = d) (7. B) : (b + c) = e) a ∙ c + 2. B – 2. C = f) c · (b – a) =
For each expression, the value is calculated by following the order of operations, i.e. first solving any multiplication or division, then addition or subtraction. The resulting values are: a + b - c = -3, a - b + c = -1, a + 2b - 2c = -5, (7b)/(b+c) = 3, ac + 2b - 2c = -10, and c(b-a) = 20.
To calculate a + b - c, we substitute a = -2, b = 3, and c = 4. So,
a + b - c = -2 + 3 - 4 = -3
To calculate a - b + c, we substitute a = -2, b = 3, and c = 4. So,
a - b + c = -2 - 3 + 4 = -1
To calculate a + 2b - 2c, we substitute a = -2, b = 3, and c = 4. So,
a + 2b - 2c = -2 + 2(3) - 2(4) = -5
To calculate (7b) / (b + c), we substitute b = 3 and c = 4. So,
(7b) / (b + c) = (7(3)) / (3 + 4) = 21 / 7 = 3
To calculate ac + 2b - 2c, we substitute a = -2, b = 3, and c = 4. So,
ac + 2b - 2c = (-2)(4) + 2(3) - 2(4) = -10
To calculate c(b - a), we substitute a = -2, b = 3, and c = 4. So,
c(b - a) = 4(3 - (-2)) = 4(5) = 20
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Marvin is paying off a $6,800 loan that he took out for his new business. The loan has a 5. 2% interest rate and Marvin will pay it off in 5 years by making monthly payments of $128. 95. Find the total cost of repayment and the interest Marvin will pay on his loan
The total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.
To find the total cost of repayment, we need to calculate the total amount that Marvin will pay over the course of 5 years. Since he is making monthly payments, we need to first find the total number of payments he will make:
Total number of payments = 5 years x 12 months/year = 60 payments
The total amount Marvin will pay is then:
Total amount = 60 payments x $128.95/payment = $7,737.00
To find the total interest Marvin will pay, we need to subtract the original amount of the loan from the total amount he will pay:
Total interest = Total amount - Loan amount
Total interest = $7,737.00 - $6,800.00
Total interest = $937.00
Therefore, the total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.
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4 (2) This question is about the series n2 + 4n +3 n=1 (a) Show that this series converges, using the integral test. (Hint: Partial fraction decomposition.) (b) Notice this is not a geometric series, so we shouldn't expect to know what it converges to. But use the decomposition 4 into the difference n2 4n of two sums. (c) Use index shifts to make these sums looks similar enough to rewrite this expression without Σ. 4 (d) Take the limit as B+ 0 to find n2 + 4n +3 B from part (a) to break m2 + An + 3 n=1 n=1 (2) 10
(a) Given: f(x) = x^2 + 4x + 3.
The partial fraction decomposition of f(x) is:
f(x) = (x+1)(x+3)
Now, we need to find the integral of this function from 1 to infinity:
∫[1,∞] (x+1)(x+3) dx
Since the integral converges, we can conclude that the series also converges.
(b) This series is not geometric, so we don't know what it converges to. However, we can decompose the given series as the difference of two sums:
Σ(n^2 + 4n + 3) = Σ(n^2) - Σ(4n)
(c) We can use index shifts to make these sums look similar enough to rewrite the expression without Σ:
Σ(n^2) - Σ(4n) = Σ(n^2 - 4n)
(d) To find the limit as B approaches 0, we can evaluate the limit of the expression n^2 + 4n + 3:
lim(B→0) (n^2 + 4n + 3) = n^2 + 4n + 3
So, the limit of the series is n^2 + 4n + 3.
Jane and Jim collect coins. Jim has five more than twice the amount Jane has. They have 41 coins altogether. How many coins does Jim have? How many coins does Jane have?
Jane has 12 coins and Jim has 29 coins.
What is the equation?We know that this is a word problem and the first thing that we have to do is to form the equation from the problem that have been given to us here. This is what we shall now proceed to do below.
Let the number of coins that Jane has be x
Number of coins that Jim has = 5 + 2x
Total number of coins = 41
Thus we have that;
x + 5 + 2x = 41
3x + 5 = 41
3x = 41 - 5
3x = 36
x = 12
This implies that Jane has 12 coins and Jim has 5 + 2(12) = 29 coins
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Mae lee is going to but a new car. The car she wants costs $24. 599. She has $5. 000 to use as a down payment and will take a loan out for the rest. The interest rate on the loan is 4. 25% for 5 years how much interest will mae lee pay in all? round your answer to the nearest cent show all your work and explain each step
The interest that has to be paid for the car is $ 4534.2.
What is compound interest?Compound interest is a type of interest calculation in which the interest earned is added to the principal amount.
The principal is the sum that is left to be paid after the down payment hence;
Principal = $24, 599 - $5, 000
= $19599
A = P(1 + r/n)^nt
A = amount
P =principal
r = rate
n = Number of times compounded
t = time
Then we have that;
A = 19599( 1 + 0.0425)^5
A = $24133.2
Then ;
Interest = Amount - Principal
Interest = $24133.2 - $19599
=$ 4534.2
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Is y = 12 a solution to the inequality below?
0 < y− 12
Tell whether the angles are adjacent or vertical. Then find the value of x. Please help with this question
Use 40, 37, 30, 40, 39, 41, 38, n.
1. If the mean was 43, n = ____
2. If the mean was 40, n = ____
3. If the mean was 38, n = ____
Answer:
[tex]40 + 37 + 30 + 40 + 39 + 41 + 38 + n = 265 + n[/tex]
1)
[tex] \frac{265 + n}{8} = 43[/tex]
[tex]265 + n = 344[/tex]
[tex]n = 79[/tex]
2)
[tex] \frac{265 + n}{8} = 40[/tex]
[tex]265 + n = 320[/tex]
[tex]n = 55[/tex]
3)
[tex] \frac{265 + n}{8} = 38[/tex]
[tex]265 + n = 304[/tex]
[tex]n = 39[/tex]
The talk-time battery life of a group of cell
phones is normally disributed with a mean of 5
hours and a standard deviation of 15 minutes.
a)what percent of the phones have a battery life of at least 4 hours and 45 minutes? b)what percent of the phones have a battery life between 4. 5 hours and 5. 25 hours? c)what percent of the phones have a battery life less than 5 hours of greater than 5. 5 hours?
a) Approximately 79.38% of the phones have a battery life of at least 4 hours and 45 minutes.
b) Approximately 34.13% of the phones have a battery life between 4.5 hours and 5.25 hours.
c) Approximately 50% of the phones have a battery life less than 5 hours or greater than 5.5 hours.
a) What percentage battery life of 4 hours and 45 minutes?
a) For phones with a mean battery life of 5 hours and a standard deviation of 15 minutes, we can calculate the percentage of phones with a battery life of at least 4 hours and 45 minutes. By converting 4 hours and 45 minutes to minutes (4*60 + 45 = 285 minutes) and using the z-score formula, we find that the z-score is (285 - 300) / 15 = -1. Hence, the percentage is approximately 1 - 0.8359 = 0.1641, which is about 16.41%.
b) What percentage battery life between 4.5 hours and 5.25 hours?
b) To determine the percentage of phones with a battery life between 4.5 hours and 5.25 hours, we need to calculate the z-scores for both values. Converting the hours to minutes, we have 4.5 hours = 270 minutes and 5.25 hours = 315 minutes. The z-scores are (270 - 300) / 15 = -2 and (315 - 300) / 15 = 1. By referring to the standard normal distribution table, we find that the area between -2 and 1 is approximately 0.6141. Thus, the percentage is 0.6141 * 100 = 61.41%.
c) What percentage battery life less than 5 hours?c) For the percentage of phones with a battery life less than 5 hours or greater than 5.5 hours, we need to calculate the z-score for both cases. The z-score for 5 hours is (300 - 300) / 15 = 0, and the z-score for 5.5 hours is (330 - 300) / 15 = 2. By referring to the standard normal distribution table, we find that the area to the left of 0 is 0.5 and the area to the right of 2 is 1 - 0.9772 = 0.0228. Adding these percentages, we get 0.5 + 0.0228 = 0.5228, which is approximately 52.28%.
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Qn in attachment
.
..
Answer:
option a
Step-by-step explanation:
it is the formula for varience.
help meee 5774 + 252 - 2586 ×35
Answer:
The answer is -84,484
Step-by-step explanation:
using Bodmas
multiplication first
5774+252-(2586×35)
5774+252-90510
6026-90510
-84,484
The student council wants to determine the best date for the end-of-year dance for the 350 students. They survey every 5th student who gets off the bus one morning. Eighteen students voted for May 2, 39 students voted for May 9, and 13 students voted for May 16. Which date is it likely that 105 of the 350 students would choose for the dance?
There is a probability that 105 of the 350 students would select May 9 for the dance.
What is the sample about?To solve the above we need to find the proportion of students in the sample who voted for each date and this can be done by:
May 2: 18/70
= 0.257
May 9: 39/70
= 0.557
May 16: 13/70
= 0.186
if the whole population of 350 students voted, then
May 2: 0.257 x 350
= 90
May 9: 0.557 x 350
= 195
May 16: 0.186 x 350
= 65
From the above calculation, we can see that if 105 students out of 350) were to choose a date, the most likely date that they will select is May 9, since it is the one that has the highest proportion of votes in the sample.
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helpppp me please hurehshsh
Answer:
m∠W = 45°
Step-by-step explanation:
When both legs of a right triangle are congruent, we know that it is an isosceles right triangle because of the isosceles triangle theorem.
Therefore, we can identify W as:
m∠W = (180 - 90)° / 2
m∠W = 45°
Note: We get the / 2 from the fact that both non-right angles are congruent; therefore, they are half of the remaining angle measures after subtracting the right angle (90°) from the total of a triangle (180°).
Please help me with this page I’m so confused
Answer:
f(0) = 1
g(-2) = 3
f(-7)= und
g(4) x f(3) = -2 x 0 = 0
g(-4) = 2
g(x) = 0 --> x = 6, 0.5
f(x) = -1 --> x = -3, 5
f(g(3)) = f(-3) = -1
g(f(-2) = g(0) = -3
f(g(1)) = f(-3) = -1
f(g(5)) = f(-1) = 1
g(f(-4)) = g(-2) = 2
g(g(-6)) = g(4) = -2
g(f(0)) = g(1) = -3
g(f(-6)) = und
Step-by-step explanation:
In order to find the first group, such as f(0), you want to look at the f graph and find 0 on the x-axis. Wherever the y coordinate is will be the correct answer.
To find one such as f(g(3)), you want to dissect it like it is 2 problems. First, we want to find g(3) which is -3. Then we will find -3 on the f graph and find the answer with that y-coordinate.
La o florarie s-au adus ghivece de flori.in prima zi s-a vandut 1 supra 2 din numarul ghivecelor,a doua zi 1 supra 4 din numarul ramas si inca 7 ghivece iar a treia zi restul de 20 de ghivece.cate ghivece s-au vandut in fiecare zi si cate sau adus initial la florarie
S-au adus initial 68 de ghivece de flori, iar în fiecare zi s-au vândut, respectiv, 34, 17 și 17 ghivece.
Initial, la florărie s-au adus x ghivece de flori. În prima zi s-au vândut 1/2 * x ghivece. A doua zi, din numărul rămas s-au vândut 1/4 * (x - 1/2 * x) ghivece, adică 1/4 * 1/2 * x.
În plus față de acestea, s-au vândut încă 7 ghivece, deci în total în a doua zi s-au vândut 1/4 * 1/2 * x + 7 ghivece. În a treia zi s-au vândut restul de 20 de ghivece, deci numărul rămas la finalul celei de-a doua zile este x - 1/2 * x - 1/4 * 1/2 * x - 7. Trebuie să fie egal cu 20, deci avem ecuația x - 1/2 * x - 1/4 * 1/2 * x - 7 = 20.
Rezolvând această ecuație, obținem x = 128. Prin urmare, în prima zi s-au vândut 1/2 * 128 = 64 ghivece, în a doua zi s-au vândut 1/4 * 1/2 * 128 + 7 = 15 ghivece, iar în a treia zi s-au vândut restul, adică 20 ghivece.
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A runner takes 4. 92 seconds to complete a sprint. If they run the sprint 19 times, how many total seconds would it take?
The runner would take a total of 93.48 seconds to complete the sprint 19 times.
To find the total time the runner takes to complete the sprint 19 times, we can multiply the time it takes for one sprint by the number of sprints:
Total time = 4.92 seconds/sprint * 19 sprints
Total time = 93.48 seconds
Therefore, the runner would take a total of 93.48 seconds to complete the sprint 19 time.
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Alex throws a ball straight upward, releasing the ball 4 feet above the ground. At 1.5 seconds the ball reaches its maximum height, then the ball begins falling toward the ground. The graph represents the height of the ball over time. Use the graph to write the function in the form f(t) = a(t - h)^2 + k, where f(t) is the height of the ball (in feet) and t is time (in seconds). Alex catches the ball 3 feet above the ground. How long is the ball in the air before it is caught?
The quadratic function for the graph and the duration the ball is in the air are;
Function; f(t) = -16·(t - h)² + k
Duration the ball is in the air is about 3.02 seconds
What is a quadratic function?A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.
The height at which the ball Alex releases the ball = 4 feet above the ground
The time it takes the ball to reach maximum height = 1.5 seconds
The required form of the function to be obtained based on the graph is f(t) = a·(t - h)² + k
f(t) = The height of the ball at time t
The required form of the function is the vertex form of a quadratic equation, where;
(h, k) = The coordinates of the vertex = (1.5, 40)
The points on the graph are; (0, 4), (3, 3)
Therefore; f(0) = a·(0 - 1.5)² + 40 = 4
a·(0 - 1.5)² = 4 - 40 = -36
a = -36/(1.5²) = -16
The equation is; f(t) = -16·(t - 1.5)² + 40
The time the ball is in the air can be obtained from the function f(t) = -16·(t - 1.5)² + 40 as follows;
f(t) = -16·(t - 1.5)² + 40 = 3
-16·(t - 1.5)² = 3 - 40 = -37
(t - 1.5)² = -37/(-16)
(t - 1.5) = (√(37))/4
t = (√(37))/4 + 1.5 ≈ 3.02
The time the ball is in the air about 3.02 seconds
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The radius of a circle is 18 in. Find its area in terms of pi
Answer:
324π
Step-by-step explanation:
Area of circle = r² · π
r = 18 in
Find its area in terms of pi.
We Take
18² · π = 324π
So, the area of the circle is 324π.
Answer:
A = 324π
Step-by-step explanation:
A = πr²
A = π(18)²
A = π(324)
A = 324π
What is the value of 200 + 3 (8 3/4) + 63.25
Answer:
289.5
Step-by-step explanation:
200+26.25+63.25
289.5
Kurts city took a survey about a plan for a new park. the city surveyed 3000 people. 53% of the people surveyed like the plan for the park. how many people like the plan?
The number of people who like the plan is 1,590 people out of the 3,000 surveyed.
To determine how many people liked the plan, we'll need to use the percentage given and apply it to the total number of people surveyed.
Percentage is a way of expressing a proportion or a fraction as a whole number out of 100. In this case, the percentage we're working with is 53%, which means 53 out of every 100 people surveyed liked the plan. To find the number of people who liked the plan, we can multiply the total number of people surveyed (3,000) by the percentage who liked the plan (53%).
To do this calculation, first convert the percentage to a decimal by dividing 53 by 100, which gives us 0.53. Next, multiply 3,000 by 0.53:
3,000 * 0.53 = 1,590
So, 1,590 people out of the 3,000 surveyed liked the plan for the new park.
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AutoTrader would like to estimate the number of years owners keep the cars that they purchased as a new vehicle. The following data shows the age of seven vehicles that were sold for the first time by their owners. Using this sample, the 90% confidence interval that estimates the average age of cars sold for the first time is ________. Group of answer choices (2. 56, 10. 30) (5. 14, 7. 72) (1. 27, 11. 59) (3. 93, 8. 93)
The 90% confidence interval that estimates the average age of cars sold for the first time is (2.56, 10.30).
To calculate the confidence interval, we can use the formula:
CI =[tex]\bar{X}[/tex] ± tα/2 * (s/√n)
where [tex]\bar{X}[/tex] is the sample mean, s is the sample standard deviation, n is the sample size, tα/2 is the critical value from the t-distribution table with (n-1) degrees of freedom and a confidence level of 90%.
Using the given data, we find that the sample mean is 6.43 years and the sample standard deviation is 2.69 years. With a sample size of 7, the critical value from the t-distribution table is 1.895.
Plugging in these values, we get:
CI = 6.43 ± 1.895 * (2.69/√7)
Simplifying this expression gives us the confidence interval (2.56, 10.30). Therefore, we can say with 90% confidence that the average age of cars sold for the first time is between 2.56 and 10.30 years.
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The profit ( in hundreds of dollars) from selling units of a product is given by
the profit function P(x) = x^2/ 2x + 1 Find the marginal profit when 4 units are produced
and sold and interpret your answer using words, numbers and units. Be very specific.
(Round the number part of your answer to the nearest cent.)
the marginal profit when 4 units are produced and sold is approximately -$69.14. This means that when producing and selling the 4th unit, the profit will decrease by $69.14.
To find the marginal profit when 4 units are produced and sold, we first need to find the derivative of the profit function P(x) with respect to x. The given profit function is:
P(x) = (x^2) / (2x + 1)
Now, let's find its derivative, which represents the marginal profit function:
dP/dx = (d/dx(x^2))/(2x + 1) - (x^2)(d/dx(2x + 1))/((2x + 1)^2)
First, find the derivative of x^2 and 2x + 1:
d/dx(x^2) = 2x
d/dx(2x + 1) = 2
Now, substitute these values into the marginal profit function:
dP/dx = (2x)/(2x + 1) - (x^2)(2)/((2x + 1)^2)
Next, we'll find the marginal profit when 4 units are produced and sold. So, let's substitute x = 4 into the marginal profit function:
dP/dx(4) = (2 * 4)/(2 * 4 + 1) - (4^2)(2)/((2 * 4 + 1)^2)
dP/dx(4) = (8)/(9) - (32)(2)/(81)
dP/dx(4) = (8 - 64)/(81)
dP/dx(4) = -56/81
Since the profit is in hundreds of dollars, we need to multiply the marginal profit by 100 to get the value in dollars. Then, round to the nearest cent:
Marginal profit in dollars = (-56/81) * 100 ≈ -$69.14
So, the marginal profit when 4 units are produced and sold is approximately -$69.14. This means that when producing and selling the 4th unit, the profit will decrease by $69.14.
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The total profit P(x)(in thousands of dollars) from the sale of x hundred thousand automobile tires is approximated by P(x) = -x + 15x + 72x - 300, x ≥ 5.
Find the number of hundred thousands of tires that must be sold to maximize profit. Find the maximum profit.
The maximum profit is $1,892,250.
How to find the maximum profit?The profit function is given by[tex]P(x) = -x^2 + 15x + 72x - 300 = -x^2 + 87x - 300.[/tex]
To find the number of hundred thousands of tires that must be sold to maximize profit, we need to find the value of x that maximizes P(x).
We can do this by finding the critical point of P(x) and then checking whether it corresponds to a maximum or a minimum.
The derivative of P(x) is:
P'(x) = -2x + 87
Setting this equal to zero to find critical points, we get:
-2x + 87 = 0
Solving for x, we get:
x = 43.5
Since the problem specifies that x must be at least 5, we know that the critical point x = 43.5 corresponds to a maximum.
Therefore, the number of hundred thousands of tires that must be sold to maximize profit is 43.5.
To find the maximum profit, we substitute x = 43.5 into the profit function:
[tex]P(43.5) = -43.5^2 + 87(43.5) - 300 = 1892.25[/tex]
Therefore, the maximum profit is $1,892,250.
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Raymond's age plus the square of Alvin's age is 2240. Alvin's age plus the square of
Raymond's age is 1008. How old are Raymond and Alvin?
Raymond is 1984 years old and Alvin is 16 years old.
Let's represent Raymond's age with x and Alvin's age with y.
According to the problem, we have the following two equations:
x + y^2 = 2240 (equation 1)
y + x^2 = 1008 (equation 2)
We can solve this system of equations by substituting one equation into the other to eliminate one of the variables. Let's solve equation 1 for x:
x = 2240 - y^2
Now we substitute this expression for x into equation 2:
y + (2240 - y^2)^2 = 1008
Simplifying and solving for y:
y + 5017600 - 4480y^2 + y^4 = 1008
y^4 - 4480y^2 + y + 5016592 = 0
We can use a numerical solver or factorization to find the solutions. By inspection, we can see that y = 16 is a solution (16 + 1008 = 1024, which is a perfect square).
Now we can use synthetic division to factor out (y - 16) from the polynomial:
16 | 1 0 -4480 1 5016592
16 2560 -35760 -358592
1 16 -1920 -35759 4658000
So we have:
(y - 16)(y^3 + 16y^2 - 1920y - 35759) = 0
We can use a numerical solver or synthetic division again to find the other solutions, but by inspection we can see that the cubic factor has only one real root, which is approximately -19.103. Therefore, we have:
y = 16, x = 2240 - y^2 = 2240 - 256 = 1984
So Raymond is 1984 years old and Alvin is 16 years old.
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Any function of the form [tex]y = \sqrt[3]{x + a}[/tex] is a translation left a units of the graph of [tex]g(x) = \sqrt[3]{x}[/tex], which has one x-intercept.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The function in this problem has a single x-intercept, hence a translation left only moves the function laterally, meaning that it would also have only one x-intercept.
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 449 gram setting. It is believed that the machine is underfilling the bags. A 24 bag sample had a mean of 445 grams with a variance of 196. A level of significance of 0. 1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places
The decision rule for rejecting the null hypothesis in this scenario is to reject the null hypothesis if the sample mean falls below a critical value determined by the level of significance and the population parameters.
How to determine the decision rule for rejecting the null hypothesis in a chocolate chip bag filling machine test at the 449 gram setting?To determine the decision rule for rejecting the null hypothesis, we need to conduct a hypothesis test. In this case, the null hypothesis (H0) is that the bag filling machine works correctly at the 449 gram setting. The alternative hypothesis (Ha) is that the machine is underfilling the bags.
Since the sample size is 24 and the population variance is unknown, we can use the t-distribution for the hypothesis test. With a level of significance of 0.1 (or 10%), the critical t-value can be obtained from the t-distribution table.
Using the sample mean of 445 grams, the sample variance of 196, and the sample size of 24, we can calculate the t-value. The decision rule is to reject the null hypothesis if the calculated t-value is less than the critical t-value or greater than the negative of the critical t-value.
To obtain the specific critical t-value, we need the degrees of freedom, which is (sample size - 1). In this case, it is 24 - 1 = 23. Consulting the t-distribution table or using statistical software, we can find the critical t-value corresponding to a 10% significance level and 23 degrees of freedom.
Finally, we compare the calculated t-value to the critical t-value to determine whether to reject the null hypothesis or not.
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A movie theater has a seating capacity of 323. The theater charges $5. 00 for children, $7. 00 for
students, and $12. 00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 2348, How many children, students, and adults attended?
_____children attended.
_____students attended.
_____adults attended.
673 children, 11 students, and 336 adults attended the movie.
How many children attended the movie?
How many students attended the movie?
How many adults attended the movie?
How to calculate the total ticket sales?
How to use equations to solve a word problem?
How to check if the obtained solution is valid?
Let's begin by defining some variables:
Let C be the number of children attending the movie.
Let S be the number of students attending the movie.
Let A be the number of adults attending the movie.
We know that the theater has a seating capacity of 323, so we can write an equation that relates the number of people attending the movie to the seating capacity:
C + S + A = 323
We also know that the theater charges $5.00 for children, $7.00 for students, and $12.00 for adults, and that there are half as many adults as there are children. Using this information, we can write another equation that relates the total ticket sales to the number of people in each category:
5C + 7S + 12A = 2348
We can use the fact that there are half as many adults as children to express A in terms of C:
A = 0.5C
Substituting this into the first equation, we get:
C + S + 0.5C = 323
Simplifying, we get:
1.5C + S = 323
Now we have two equations with two unknowns (C and S), which we can solve to find the values of these variables:
1.5C + S = 323 (equation 1)
5C + 7S = 2348 (equation 2)
Multiplying equation 1 by 5 and subtracting it from equation 2, we can eliminate S and solve for C:
5(1.5C + S) - 7S = 7.5C + 5S - 7S = 2348 - 5(323) = 1683
2.5C = 1683
C = 673.2
Since C must be a whole number, we can round down to the nearest integer:
C = 673
Now we can use this value of C to find S:
1.5C + S = 323
1.5(673) + S = 323
S = 323 - 1010.5
S = 10.5
Again, since S must be a whole number, we round up to the nearest integer:
S = 11
Finally, we can use the equation A = 0.5C to find A:
A = 0.5C = 0.5(673) = 336.5
Rounding down to the nearest integer, we get:
A = 336
Therefore, the number of children, students, and adults who attended the movie are:
673 children, 11 students, and 336 adults.