From base camp, a hiker walks 3.5 miles west and 1.5 miles north. Another hiker walks 2 miles east and 0.5 miles south. To the nearest tenth of a mile how far apart are the hikers
Answers
Answer:
The hikers are 5.9 miles apart.
Step-by-step explanation:
Let O represents the base camp,
Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,
Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.
By making the diagram of this situation,
Let D' is the point in the line AB,
Such that, AD' = CD
In triangle BD'D,
BD' = AB + AD' = 1.5 + 0.5 = 2 miles,
DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,
By Pythagoras theorem,
[tex]BD^2 = BD'^2 + DD'^2[/tex]
[tex]BD = \sqrt{2^2 + 5.5^2}=\sqrt{4+30.25}=\sqrt{34.25}\approx 5.9[/tex]
Hence, the hikers are 5.9 miles apart.
Related Questions
Madison bought an empty lot for $2,000 and later sold it for a 25% profit. How much did Madison sell the lot for? A) $500 B) $1,500 C) $2,500 D) $3,000
Answers
Answer:
C) $2,500
Step-by-step explanation:
Madison's profit is 25% of the $2000 paid, so is ...
0.25 × $2000 = $500
That means the lot was sold for ...
$2000 + 500 = $2500
_____
Profit can also be expressed as a percentage of the selling price. If that were the case here, Madison's initial cost would be 0.75 of the $2666.67 selling price, and the 25% profit would be $666.67. Since that is not among the answer choices, we presume our assumption is correct that Madison's profit is measured as a percentage of cost.
Answer:
c
Step-by-step explanation:
your welcome
The equation [tex]2m^{2}-1m-8=0[/tex] has solutions of the form
M= N +or- sqaure root of D/over M
Solve this equation and find the appropriate values of N,M,and D. Do not worry about simplifying the √D portion of the solution.
N= M= D=
Answers
Answer:
N = 1M = 4D = 65Step-by-step explanation:
The given equation is of the form ...
ax² +bx +c = 0
where a=2, b=-1, c=-8.
The quadratic formula gives the solution to the above equation as ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
So, for your equation, the solution is ...
[tex]m=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(2)(-8)}}{2(2)}=\dfrac{1\pm\sqrt{65}}{4}[/tex]
Comparing this to the form ...
[tex]m=\dfrac{N\pm\sqrt{D}}{M}[/tex]
we see ...
N = 1M = 4D = 65Which of the following illustrates the truth value of the given conjunction?
The number [tex]-\frac{343}{9}[/tex] is an integer, and a rational number.
Answers
The conjunction is false because the number -343/9 is not an integer but is a rational number.
The number [tex]-\frac{343}{9} is an integer, and a rational number.
To determine the truth value of this conjunction, we need to understand that an integer is a whole number like -1, 0, or 1, and a rational number is a ratio of integers like 2/1 or 3/4.
Since the number [tex]-\frac{343}{9} is not an integer and also a rational number (since it can be expressed as -343/9), the conjunction is false.
Pilar used six reusable shopping bags on a recent purchase she made at a grocery store. Each bag decreased the amount she spent by 5 cents. What was the change to the amount Pilar spent at the grocery store by using the reusable bags?
Answers
Pilar will pay 30 cents less from the original amount by using reusable bags.
Step-by-step explanation:
Bags used by Pilar = b = 6
Price decrease per bag = 5 cents
Let x be the total amount paid by Pilar.
Decrease will lessen the amount paid by Pilar, therefore, according to statement;
P(x) = x - 5b
As she used 6 bags, therefore, putting b=6
[tex]P(x)=x-5(6)\\P(x)=x-30[/tex]
Pilar will pay 30 cents less from the original amount by using reusable bags.
Keywords: subtraction, function
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An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume. What is the final pressure of the gas when its temperature returns to its initial value?
Answers
Answer:
The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.
Step-by-step explanation:
Given : An ideal gas is confined within a closed cylinder at a pressure of [tex]2.026\times 10^5[/tex] Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.
To find : What is the final pressure of the gas when its temperature returns to its initial value?
Solution :
Since the temperature is constant .
The relation between P and V is given by,
[tex]P_1\times V_1 = P_2\times V_2[/tex]
[tex]\frac{P_1}{P_2}=\frac{V_2}{V_1}[/tex] ....(1)
The piston moves until the volume of the gas is reduced to one-ninth of the initial volume i.e. [tex]V_2=\frac{V_1}{9}[/tex]
or [tex]\frac{V_2}{V_1}=\frac{1}{9}[/tex]
[tex]P_1=2.026\times 10^5[/tex]
Substitute in equation (1),
[tex]\frac{2.026\times 10^5}{P_2}=\frac{1}{9}[/tex]
[tex]P_2=9\times 2.026\times 10^5[/tex]
[tex]P_2=18.234\times 10^5[/tex]
[tex]P_2=1.8234\times 10^6[/tex]
The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.
I’d appreciate the help!
Answers
Answer:
[tex]\displaystyle 1\frac{119}{250}\:liter[/tex]
[tex]\displaystyle 7,5\:sleps[/tex]
[tex]\displaystyle 37,3\:sleps [/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{119}{250} = \frac{1476}{1000}[/tex]
[tex]\displaystyle 1\frac{1}{13} \times 7 = 7\frac{7}{13} ≈ 7,538461538 ≈ 7,5[/tex]
[tex]\displaystyle \frac{41}{1\frac{1}{10}} = 37\frac{3}{11} ≈ 37,3[/tex]
I am joyous to assist you anytime.
A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?
(A) Between $15,000 and $25,000
(B) Between $30,000 and $50,000
(C) Between $60,000 and $100,000
(D) Between $150,000 and $250,000
(E) Between $300,000 and $500,000
Answers
Answer:
Step-by-step explanation:
We are told the manufacturer expects 0.3% to 0.5% of units to be defected,
So we find 0.3% and 0.5% of the 20,000units
0.3/100 multiplied by 20000 = 60units
0.5/100 multiplied by 20000 = 100units
So we now know from 20000units, between 60units to 100units will be defected
So we find the price of both 60units and 100units knowing that 1unit cost $2,500
60 multiplied by $2,500 equals $150,000
100 multiplied by $2,500 equals $250,000
So the answer is option D, between $150,000 and $250,000
Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone. If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is
a. 0.10
b. 0.90
c. 0.50
d. None of these choices.
Answers
Answer:
Option a, 0.10
Step-by-step explanation:
Given that of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.
i.e. out of 500 customers 50 customers purchased
Hence probability for any random customer to purchase = [tex]\frac{50}{500} =0.10[/tex]
Thus we find that if the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is
Option a)
0.10
This is based on the assumption that the past pattern of purchase determines the probabiltiy
A sample size of n=12 is a simple random sample selected from a normally distributed population. Find the critical value t* corresponding to a 95% confidence level (two-sided).
Answers
For a sample size of n=12, the degrees of freedom (df) would be 11, and the critical t value for a two-tailed 95% confidence interval is typically around 2.201, as determined by a t-distribution table or statistical software.
Explanation:To find the critical t* value corresponding to a 95% confidence level for a sample size of n=12, you must take into account that the degrees of freedom (df) are equal to n - 1, which is 11 in this case. You use a t-distribution, not the z-distribution, because the population standard deviation is unknown. The critical t* value can be found using a t-distribution table or statistical software.
With the degrees of freedom at 11 for a 95% confidence interval (two-sided), the critical t value is typically around 2.201. However, one must look up the exact value using statistical software or a t-distribution table, as the value may vary slightly based on different sources or rounding.
Thus, to answer the student's question: For a two-tailed 95 percent confidence interval and 11 degrees of freedom, the corresponding critical value t* will typically be around 2.201.
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The radius of a cylindrical construction pipe is 3.5 ft. If the pipe is 35 ft long, what is its volume?
Use the value 3.14 for a, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:
Volume = 1346.275 [tex]ft^{3}[/tex]
Step-by-step explanation:
The radius of the pipe is 3.5 ft and height is 35 ft.
The volume of cylinder is found by the formula,
V = (π)([tex]R^{2})(h)[/tex]
(think about the formula as area of individual circles multiplied by the height of cylinder)
taking value of π as 3.14,
Where, the r = radius and h is height of cylinder.
inserting the above values,
[tex]V = (3.14)(3.5^{2})(35)[/tex]
V = 1346.275 [tex]ft^{3}[/tex]
Asked what the central limit theorem says, a student replies, As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal.
Is the student right?
A. No. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample means.
B. Yes. This is exactly what the theorem says
Answers
Answer:
A. No, the student is not right. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample means.
Step-by-step explanation:
No, the student is not right. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample means. The central limit theorem says that if we take a large sample (i.e., a sample of size n > 30) of any distribution with finite mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], then, the sample average is approximately normally distributed with mean [tex]\mu[/tex] and variance [tex]\sigma^2/n[/tex].
Yes. The student is exactly what the theorem says.
True. According to the central limit theorem, as the sample size increases, the sampling distribution of the sample means becomes more Normal.
An example illustrates how from a population with a uniform distribution, as samples are drawn and the means are calculated, the distribution of these means approximates a normal distribution as the sample size increases.
The central limit theorem ensures that regardless of the population's distribution, with sufficiently large samples, the distribution of sample means tends towards a normal distribution.
A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 40 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 80 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked: 10 feet? Answer = 30 feet? Answer =
Answers
The weight rises at the same constant rate of 2ft/s that the worker walks away, regardless of how far the worker has travelled. When the worker walks away, the length of the rope attached to the weight decreases and thus raises the weight. Therefore, at both distances, 10ft and 30ft, the weight will be rising at 2ft/s.
Explanation:This is a physics problem involving related rates under the concept of kinematics. When the worker walks, the total length of the rope (80 ft) remains the same, so as the worker's part of the rope increases, the part attached to the weight decreases causing an upward motion. The rates at which the worker walks away and the weight retracts up are directly related.
When the worker has walked 10 feet, the worker's part of the rope has become 50 ft (original 40ft + 10ft walked), thus the weight's part of the rope is 30ft (80ft total - 50ft). Because the worker is walking at a constant rate of 2ft/s, this means that the weight is also rising at that same constant rate of 2ft/s.
Then, when the worker has walked 30 feet, the worker's part of the rope has become 70ft, thus the weight's part of the rope is 10ft. As previously explained, because the worker has a constant rate of walking away, the weight also has a constant rate of 2ft/s in the upward direction. Regardless of the worker's position, it does not impact the rate of the weight's ascent.
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The weight rises at a constant rate of 1 ft/s regardless of whether the worker has walked 10 feet or 30 feet.
Finding the Rate of the Weight Rising
First, let’s set up the problem with the given data:Distance from the connection point to the ceiling: 40 ft
Worker’s walking speed: 2 ft/s
When the worker is directly next to the weight, the total rope length is 80 ft (rope goes up 40 ft to the pulley, and 40 ft down to the worker).As the worker walks away, the rope is extended, and the weight rises. We need to determine how fast the weight is rising after the worker has walked different distances. Here’s how to do it step-by-step:
Step-by-Step Solution:Let x be the distance the worker has walked away from the initial point. Therefore, the total length of the rope now serves both the height the weight has risen (h) and the horizontal distance the worker has walked (x).
Using the Pythagorean Theorem: the new distance of the rope from the worker to the pulley and down to the weight can be written as:80 ft = 2h + x
Differentiate this equation with respect to time (t):0 = 2(dh/dt) + dx/dt
Given that dx/dt = 2 ft/s (rate the worker walks away), we can solve for dh/dt.2(dh/dt) + 2 = 0
2(dh/dt) = -2
dh/dt = -1 ft/s
Now, we'll analyze the specific cases: when the worker has walked 10 feet and 30 feet respectively.a) For 10 feet: Plugging into the length equation:
2h + 10 = 80
2h = 70
⇒ h = 35 ft
b) For 30 feet: Plugging into the length equation:
2h + 30 = 80
2h = 50
∴ h = 25 ft
The weight rises at a rate of 1 ft/s when the worker has walked either 10 feet or 30 feet because the rate change of height (dh/dt) is constant.
2. A stone is an English measure of weight. There are 14 pounds in 1 stone and 2.2 pounds in 1 kilogram. A certain person weighs 9 stone.
(a) If you wanted to convert the person’s weight to kilograms, what conversion factor should you use? Round the conversion to the nearest hundredth. Show your work.
(b) What is the person’s weight in kilograms rounded to the nearest tenth?
Answers
Answer:
The answer to your question is 57.3 kg
Step-by-step explanation:
a)
[tex]X stones \frac{14 pounds}{1 stone} \frac{1 kilogram}{2.2 pounds}[/tex]
= [tex]\frac{14}{2.2}[/tex]
= 6.36 X stones
b) Weight = 6.36 (x)
x = 9 stones
Weight = 6.36 (9)
= 57.3 kg
Tim and Mia have 8 hours to spend on a mountain hike. They can walk up the trail at an average of 2mph and can walk down at an average of 3 mph. How long should they plan to hike uphill before turning around?
Answers
Answer:
4.8 hours
Step-by-step explanation:
Let the time taken to hike uphill be T
Let the time taken taken to hike downhill = 8 -T
The average speed of walking up = 2 mph
Average speed of walking down = 3mph
Distance hiked uphill = Distance hiked downhill
Speed = distance /time
Distance = Speed * Time
2T = 3(8 -T)
2T = 24 - 3T
2T + 3T = 24
5T = 24
T = 24/5
T= 4.8 hours
Time taken to hike uphill = 4.8hours
Choose the correct product of (5x − 11)^2.
a. 25x^2 − 110x + 121
b. 25x^2 − 121
c. 25x^2 + 121
d. 25x^2 + 110x + 121
Answers
Answer:
A. 25x^2 - 110x + 121
Step-by-step explanation:
(5x - 11)² = (5x)² - 2·5x·11 + (11)² = 25x² - 110x + 121
(a - b)² = a² - 2ab + b²
a. 25x² − 110x + 121
A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?
A. 120
B. 240
C. 480
D. 600
E. 1200
Answers
Answer: E. 1200
Step-by-step explanation:
Given : A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts.
i.e. No. of choices for different salads= 8 -----(1)
No. of choices for different main courses = 5 ----(2)
No. of choices for different desserts = 6
When we choose two different desserts then we use permutation(repeatition not allowed) :
[tex]^6P_2=\dfrac{6!}{(6-2)!}=\dfrac{6\times5\times4!}{4!}=6\times5=30[/tex]----(3)
[∵ No. of ways to choose r things out of n =[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex] ]
If customers choose one salad, one main course and two different desserts for their meal , then By Fundamental principle of counting (Multiply (1) , (2) and (3)), the number of different meals are possible :-
[tex]8\times5\times30\\\\=1200[/tex]
Hence, the correct answer is E. 1200 .
Two bike riders left each other and started to ride in opposite directions. Two hours later they were 54 miles apart. If one of them averaged twice the average rate of the other, what was the rate of each?
Answers
Answer:
The speed of right going rider is 9 mph
The speed of left going rider is 18 mph
Step-by-step explanation:
Given as :
The total distance apart both the riders = 54 miles
Let The speed of right going rider = x mph
and The speed of left going rider = 2 x mph
The Distance cover by right going rider = D miles
The Distance cover by left going rider = 54 - D miles
Total time for both = 2 hours
So, Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]
Or , Distance = speed × Time
For right going rider
D = x × 2
For left going rider
54 - D = 2 x × 2
Or, from first equation
54 - 2 x = 4 x
or, 54 = 4 x + 2 x
or, 6 x = 54
∴ x = [tex]\frac{54}{6}[/tex]
I.e x = 9 mph
So, The speed of right going rider = 9 mph
and The speed of left going rider = 2 × 9 = 18 mph
Hence The speed of right going rider is 9 mph
and The speed of left going rider is 18 mph answer
In a certain carnival game the player selects two balls at random from an urn containing 3 red balls and 9 white balls. The player receives $4 if he draws two red balls and $1 if he draws one red ball. He loses $2 if no red balls are in the sample. Determine the probability distribution for the experiment of playing the game and observing the player's earnings.
The probability to draw two red balls is __, to draw one red ball is __, and to draw zero red balls is __.
Answers
Answer:
The probability to draw two red balls = 1/22
The probability to draw one red ball = 9/22
The probability to draw no red ball = 12/22
Step-by-step explanation:
Number of Red balls = 3
Number of White balls = 9
If the player draws two red balls, he receives $4
If the player draws one red ball, he receives $1
If the player draws no red ball, he looses $2
The total number of balls = 3+9
= 12
Let R represent Red balls
Let W represent White balls
The probability that the player earns $4 by picking two red balls is represented as Pr(R1 n R2)
Pr(R1 n R2) = Pr(R1) * Pr(R2)
Pr(R1) = 3/12
= 1/4
Pr(R2) = 2/11(we assume he draws without replacement)
Pr(R1 n R2) = 1/4*2/11
= 2/44
= 1/22
The probability of earning $4 is 1/22
The probability of drawing one red ball is Pr(R1 n W2) or Pr(W1 n R2)
Pr(R1) = 3/12
= 1/4
Pr(W2) = 9/11
Pr(W1) = 9/12
= 3/4
Pr(R2) = 3/11
Pr(R1 n W2) or Pr(W1 n R2) =
(1/4 * 9/11) + (3/4 * 3/11)
= (9/44) + (9/44)
= 18/44
= 9/22
Therefore, the probability of earning $1 is 9/22
The probability that no red ball is chosen is Pr(W1nW2)
Pr(W1) = 9/12
= 3/4
Pr(W2) = 8/12
Pr(W1nW2) = 3/4 * 8/11
= 24/44
= 12/22
therefore. the probability of loosing $2 is 12/22
The probability to draw two red balls is [tex]\(\frac{1}{22}\)[/tex], to draw one red ball is [tex]\(\frac{9}{22}\)[/tex], and to draw zero red balls is [tex]\(\frac{15}{22}\)[/tex].
To find the probability distribution, we need to calculate the probabilities of drawing two red balls, one red ball, and no red balls from the urn containing 3 red balls and 9 white balls. We use combinations to determine these probabilities.
1. Total Possible Combinations:
The total number of ways to choose 2 balls out of 12 is given by the combination formula:
[tex]\[ \binom{12}{2} = \frac{12!}{2!(12-2)!} = \frac{12 \times 11}{2 \times 1} = 66 \][/tex]
2. Probability of Drawing Two Red Balls:
To draw 2 red balls, we select 2 out of the 3 red balls:
[tex]\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3 \times 2}{2 \times 1} = 3 \][/tex]
The probability is:
[tex]\[ P(\text{2 red balls}) = \frac{\binom{3}{2}}{\binom{12}{2}} = \frac{3}{66} = \frac{1}{22} \][/tex]
3. Probability of Drawing One Red Ball:
To draw 1 red ball and 1 white ball, we select 1 out of the 3 red balls and 1 out of the 9 white balls:
[tex]\[ \binom{3}{1} = 3 \quad \text{and} \quad \binom{9}{1} = 9 \][/tex]
The number of ways to draw 1 red and 1 white ball is:
[tex]\[ \binom{3}{1} \times \binom{9}{1} = 3 \times 9 = 27 \][/tex]
The probability is:
[tex]\[ P(\text{1 red ball}) = \frac{\binom{3}{1} \times \binom{9}{1}}{\binom{12}{2}} = \frac{27}{66} = \frac{9}{22} \][/tex]
4. Probability of Drawing Zero Red Balls:
To draw 0 red balls (i.e., both balls are white), we select 2 out of the 9 white balls:
[tex]\[ \binom{9}{2} = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2 \times 1} = 36 \][/tex]
The probability is:
[tex]\[ P(\text{0 red balls}) = \frac{\binom{9}{2}}{\binom{12}{2}} = \frac{36}{66} = \frac{18}{33} = \frac{6}{11} = \frac{15}{22} \][/tex]
5. Probability Distribution for Earnings:
Now, we summarize the probabilities and corresponding earnings
- Drawing two red balls: [tex]\(\frac{1}{22}\)[/tex], earning $4
- Drawing one red ball: [tex]\(\frac{9}{22}\)[/tex], earning $1
- Drawing zero red balls: [tex]\(\frac{15}{22}\)[/tex], losing $2
Thus, the correct probability distribution for the experiment of playing the game and observing the player's earnings is:
- Probability to draw two red balls: [tex]\(\frac{1}{22}\)[/tex]
- Probability to draw one red ball: [tex]\(\frac{9}{22}\)[/tex]
- Probability to draw zero red balls: [tex]\(\frac{15}{22}\)[/tex]
Help me please! All questions answer. Step by step explain it please....!!!
Answers
Answer:
Part 1) Option A. The graph of g(x) has the lesser y-intercept
Part 2) Option B. (2,4)
Part 3) Option B. 62.5 miles per hour
Part 4) Option A. The functions will intersect at x=-2 and at x=1
Step-by-step explanation:
Part 1)
Let
x ----->the number of years
g(x) ----> the expected value in dollars of televisions
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
In the function g(x)
The slope is
[tex]m=-\$90\ per\ year[/tex] ---> is negative because is a decreasing function
The y-intercept is
[tex]b=\$360[/tex]
substitute
[tex]g(x)=-90x+360[/tex]
Find the x-intercept (value of x when the value of the function is equal to zero)
For g(x)=0
[tex]0=-90x+360[/tex]
[tex]x=4[/tex]
The x-intercept is the point (4,0)
The y-intercept is the point (0,360)
Function f(x)
we have
[tex]f(x)=100(-x+4)[/tex]
[tex]f(x)=-100x+400[/tex]
Find the x-intercept (value of x when the value of the function is equal to zero)
For f(x)=0
[tex]0=-100x+400[/tex]
[tex]x=4[/tex]
The x-intercept is the point (4,0)
The y-intercept is the point (0,400) (value of f(x) when the value of x is zero)
Compare the intercepts both functions
The y-intercept is the same in both functions
The y-intercept is greater in the function f(x)
therefore
The graph of g(x) has the lesser y-intercept
Part 2) we have the equation of the line
[tex]4x-3y=-4[/tex]
Remember that
If a ordered pair is on the given line, then the ordered pair must satisfy the given line
Verify each case
a) (4,4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(4)-3(4)=-4[/tex]
[tex]4=-4[/tex] ---> is not true
so
the ordered pair not satisfy the equation
therefore
the ordered pair is not on the line
b) (2,4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(2)-3(4)=-4[/tex]
[tex]-4=-4[/tex] ---> is true
so
the ordered pair satisfy the equation
therefore
the ordered pair is on the line
c) (2,-4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(2)-3(-4)=-4[/tex]
[tex]20=-4[/tex] ---> is not true
so
the ordered pair not satisfy the equation
therefore
the ordered pair is not on the line
d) (4,-4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(4)-3(-4)=-4[/tex]
[tex]28=-4[/tex] ---> is not true
so
the ordered pair not satisfy the equation
therefore
the ordered pair is not on the line
Part 3) we know that
The formula to calculate the average rate of change using the graph is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this problem we have
[tex]f(a)=f(2)=75\ mi[/tex]
[tex]f(b)=f(4)=200\ mi[/tex]
[tex]a=2\ h[/tex]
[tex]b=4\ h[/tex]
Substitute
[tex]\frac{200-75}{4-2}=125/2=62.5 mi/h[/tex]
Part 4) we know that
The solution of the equation
f(x)=g(x)
are the x-coordinates of the intersection points both graphs
In this problem
If the solutions are x=-2 and x=1
then
The functions will intersect at x=-2 and at x=1
Min collects 334 pounds of aluminum cans on Monday and 124 pounds on Tuesday. Jessica collects 414 pounds on Monday and 314 pounds on Tuesday. How many more pounds does Jessica collect than Min? Enter your answer in the box as a mixed number in simplest form.
Answers
Answer:
270 more pounds of aluminium cans collected by Jessica than Min
Step-by-step explanation:
334 + 124 = 458 (Total pounds of aluminium cans collected by min)
414 + 314 = 728 (Total pounds of aluminium cans collected by Jessica)
728 - 458 = 270 (More pounds Jessica collected than Min)
Final answer:
Jessica collected 270 pounds more of aluminum cans than Min did over the two days. Min collected 458 pounds in total, and Jessica collected 728 pounds in total.
Explanation:
The student's question is asking us to compare the total amount of aluminum cans collected by two individuals, Min and Jessica, over a two-day period and determine how much more Jessica collected compared to Min. To solve this, we need to add the amounts collected by each individual for both days and then subtract Min's total from Jessica's total.
First, we find Min's total collection by adding her collections from Monday and Tuesday: 334 pounds + 124 pounds = 458 pounds.
Next, we find Jessica's total collection by adding her collections from Monday and Tuesday: 414 pounds + 314 pounds = 728 pounds.
Finally, we calculate how much more Jessica collected than Min by subtracting Min's total from Jessica's total: 728 pounds - 458 pounds = 270 pounds. Since the question asks for the answer as a mixed number in simplest form and 270 is already a whole number, our answer is simply 270 pounds. There is no need to convert to a mixed number.
One boat travelling 15 mph goes 47 miles downstream in the same amount of time that another boat going 20 mph goes 40 miles upstream. How fast is the current in mph? (Round your answer to the nearest tenth of miles per hour and enter only the numerical part
Answers
Answer:
3.9 mi/h
Step-by-step explanation:
We assume that the given speeds are the speeds of the boats relative to the water. If c is the speed of the current, we have ...
time = distance/speed
47/(15 +c) = 40/(20 -c)
47(20 -c) = 40(15 +c) . . . . . . multiply by (20-c)(15+c)
940 -600 = 40c +47c . . . . . add 47c-600
340 = 87c . . . . . . . . . . . . . . . simplify; next divide by 87
c = 340/87 ≈ 3.9080 . . . . mi/h
The speed of the current is about 3.9 mi/h.
Given a central angle of 100 in a circle with a radius of 7 in., what is the intercepted arc length of the central angle?
**Use 3.14 for π and round to ONE decimal place.
Answers
Answer:
12.2 inches
Step-by-step explanation:
Write and solve a proportion.
Arc length / circumference = central angle / 360°
x / (2π × 7) = 100° / 360°
x = 12.2
The arc length is 12.2 inches
The owner of a music store received a shipment of stereos at a cost of $160 each. What will the selling price be if he applies a 45% markup? $300 $205 $232 $88
Answers
The selling price will be $232 if he applies a 45% markup.
Step-by-step explanation:
Cost of each stereo = $160
Mark up = 45%
Amount of mark up = [tex]\frac{45}{100}*160[/tex]
Amount of mark up = [tex]\frac{7200}{100} = \$72[/tex]
Selling price = Cost of stereo + mark up
Selling price = 160 + 72 = $232
The selling price will be $232 if he applies a 45% markup.
Keywords: addition, markup
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One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.
Write a differential equation that is satisfied by y
A small town has 3,500 inhabitants. At 8 AM, 280 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round your final answer to one decimal place.)
Answers
Answer:
a) dy/dt = ky(1-y)
b) 3:36pm
Step-by-step explanation:
a) Let the number of people who have heard the rumor = p
Let those who have not heard the rumor= q
Total population = p+q
Fraction of those that heard the rumor = p/p+q = y
Fraction of those who did not hear the rumor = q/p+q = 1-y
The rate at which the rumor spreads = dy/dt
dy/dt varies directly to y(1-y)
dy/dt = ky(1-y) where k is a constant
b) Recall that dy/dt = ky(1-y)
y(t) = y/(y+(1-y) e^-kt)
At 8 am , t= 0
y = p/ p+q
y(0) = 280/3500
y(0) = 0.08
By noon(12pm), t = 4
At this time half of the population has heard the rumor
y(4) = 0.5
Recall that y(t) = y/(y+(1-y) e^-kt)
y(t) = y0/(y0+(1-y0) e^-kt)
y(t) = 0.08/(0.08+(1-0.08) e^-kt)
y(t) = 0.08/(0.08+0 92 e^-kt)
To find k, put y(4) = 0.5 into the equation
y(4) = y/(y+(1-y) e^-4k)
0.5 = 0.08/(0.08+0.92e^-4k)
0.08 + 0.92e^-4k = 0.08/0.5
0.92e^-4k = 0.16 - 0.08
0.92e^-4k = 0.08
e^-4k = 0.08/0.92
e^-4k = 0.087
-4k = ln(0.087)
-4k = -2.422
k = -2.422/ -4
k = 0.611
y(t) = 0.08/(0.08+ 0.92 e^-0.611t)
The time by which 90% of the population would have heard the rumor is
0.9 = 0.08/(0.08+0.92e^-0.611t)
0.08 + 0.92e^-0.611t = 0.08/0.9
0.92e^-0.611t= (0.08/0.9) - 0.08
e^-0.611t = [(0.08/0.9)-0.08] / 0.92
e^-0.611t = 0.00966
-0.611t = ln(0.00966)
-0.611t = -4.640
t = -4.640/ -0.611
t = 7.6hrs
t = 7 hrs + (0.6*60)mins
t= 7 hrs + 36mins
t = 7hrs 36 mins
Therefore 8 am + 7 hrs 36 mins = 3:36pm
The time by which 90% of the rumor spreads = 3:36pm
The differential equation for the spread of a rumor, given the rate is proportional to the product of the fraction of the population who have heard the rumor and the fraction that has not, is dy/dt = k * y * (1 - y). To solve when 90% will have heard it, we find k using initial conditions and integrate to find the time.
Explanation:To create a differential equation for the spread of the rumor we can say that the rate of spread, which is the derivative of the fraction of the population that has heard the rumor with respect to time (dy/dt), is proportional to the product of the fraction of the population that has heard the rumor (y) and the fraction that has not heard the rumor (1 - y). This gives us the differential equation dy/dt = k * y * (1 - y), where k is the proportionality constant.
To solve the problem for when 90% of the population will hear the rumor, we must first find the value of k using the initial conditions provided. At 8 AM, y(0) = 280/3500 and at noon, which is 4 hours later, y(4) = 0.5. Using this information, we can integrate the differential equation to find k and then use it to determine when 90% (i.e., y(t) = 0.9) of the population will have heard the rumor, applying appropriate integration and exponential growth techniques.
raul is 5 years older than twice carlos age. the sum of their ages is 101. how old is carlos?
Answers
Answer:32years old
Step-by-step explanation:
R= 2c+5
R+C= 101
2c+5+c=101
3c+5=101
3c=96
c=32
Answer:
32 years
Step-by-step explanation:
Let the age of Carlos be represented by x
Then the age of Raul can be represented as the sum of twice the age of Carlos and 5.
In other words, Raul's age = 2x + 5
Sum of Carlos and Raul's age is 101
That is, \[x + 2x + 5 = 101\]
Or, \[3x + 5 = 101\]
Or, \[3x = 96\]
Or, \[x = 32\]
Hence, the age of Carlos is 32 years.
Age of Raul on the other hand is 2*32 + 5 = 69 years
Sum of their ages is 32 + 69 = 101 years.
Two jets leave an air base at the same time and travel in opposite directions. One jet travels 100 miles an hour faster than the other. If the two jets are 3924 miles apart after3 hours, what is the rate of each jet?
Answers
Answer: speed of jet A is 704 miles per hour
speed of jet B is 604 miles per hour
Step-by-step explanation:
Let the jets be jet A and jet B
Jet A and Jet B leave an air base at the same time and travel in opposite directions.
Let x = the speed of Jet A
Let y = the speed of jet B
One jet travels 100 miles an hour faster than the other. Let Jet A be the faster Jet. This means that
x = y + 100 - - - - - -1
If the two jets are 3924 miles apart after 3 hours, this means that both Jet A and Jet B travelled a total distance of 3924 miles after 3 hours.
Distance travelled = speed × time
Therefore,
Distance travelled by Jet A in 3 hours will be x × 3 = 3x miles.
Distance travelled by Jet B in 3 hours will be y × 3 = 3y miles.
Therefore, total distance is
3x + 3y = 3924 - - - - - - - -2
Substituting equation 1 into equation 2, it becomes
3(y+100) + 3y = 3924
3y + 300 + 3y = 3924
6y = 3924 - 300 = 3624
y = 3624/6 = 604 miles per hour
x = y + 100 = 604 + 100
x = 704 miles per hour
PLEASE HELP ME!!!!!!! I AM NOT GOOD AT MATH!
Given the function f(x)= \frac{x^2+7x+10}{x^2+9x+20} Describe where the function has a hole and how you found your answer.
Answers
Only hole of function [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex] is at x=(-4)
Step-by-step explanation:
Given the function is [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex]
In order to find holes of any function, you should find when function is becoming undefined or say " infinity"
Given function is polynomial function.
It will become undefined become denominator become zero
[tex]x^{2}+9x+20=0[/tex]
Solving for x value when denominator become zero
[tex]x^{2}+9x+20=0\\x^{2}+5x+4x+20=0\\x(x+5)+4(x+5)=0\\(x+4)(x+5)=0[/tex]
we get possible holes at x=(-4) and x=(-5)
Check whether you can eliminate any holes
Now, Solving for x value when numerator become zero
[tex]x^{2}+7x+10=0\\x^{2}+5x+2x+10=0\\(x+5)(x+2)=0[/tex]
x=(-5) and x=(-2)
x=(-5) is common is both numerator and denominator.
So that, we can eliminate it.
[tex]f(x) = \frac{(x+5)(x+2)}{(x+5)(x+4)}[/tex]
[tex]f(x) = \frac{(x+2)}{(x+4)}[/tex]
Therefore, Only hole of function [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex] is at x=(-4)
The angle measurements in the diagram are represented by the following expressions.
Solve for X then find the measurement of ∠B:
Answers
Answer:
x = 6
∠B = 126
Step-by-step explanation:
∠A = ∠B through alternate interior angles
∠A = ∠B
8x + 78 = 2x + 114
8x - 2x = 114 - 78
6x = 36
x = 36 ÷ 6
x = 6
∠B = 2x + 114
2(6) + 114
12 + 114
= 126
d1 || d2 => ∡A = ∡B
8x + 78° = 2x + 114°
8x - 2x = 114° - 78°
6x = 36°
x = 36° : 6
x = 6°
∡B = 2x + 114°
∡B = 2×6° + 114°
∡B = 12° + 114°
∡B = 126°
A cylinder has a volume of 33 cubic inches. What is the volume of a cone with the same radius and height?
A: 44 cubic inches
B: 33 cubic inches
C: 11 cubic inches
D: 99 cubic inches
Answers
C
Step-by-step explanation:
The volume of a cylinder = πr²h
= 33 cubic inches
The volume of a cone = ¹/3 πr²h
If the cylinder and come share the same radius and height then ‘πr²h’ part of the formulas is the same for both;
It means the difference in proportionality is ¹/3 (because even π is the same across board). The volume of the cone is therefore;
¹/3 (33)
= 11
= 11 cubic inches
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ASAP
What is the area of the rectangle?
Question 1 options:
8 Units
12 Units
20 Units
15 Units
Answers
Answer:
12 units
Step-by-step explanation:
The quickest way to go about this is;
From the figure, when you count the number of full square boxes inside the rectangle, they add up to 7 full square boxes of 1 unit by 1 unit. And the number of half square boxes inside the rectangle add up to 10 which is equal to 5 full square boxes.
So the total number of full square boxes of 1 unit by 1 unit inside the rectangle add up to 12 full square boxes. The area of each full square box is 1 * 1 = 1 units, therefore the area of the rectangle is equal to 1 * 12 = 12 units.