150 different committees are possible
Solution:Given that a student dance committee is to be formed consisting of 2 boys and 4 girls
The membership is to be chosen from 5 boys and 6 girls
To find : number of different possible committees
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected
The formula for combination is given as:
[tex]n C_{r}=\frac{n !}{(n-r) ! r !}[/tex]
where "n" represents the total number of items, and "r" represents the number of items being chosen at a time
We have to select 2 boys from 5 boys
So here n = 5 and r = 2
[tex]\begin{aligned} 5 C_{2} &=\frac{5 !}{(5-2) ! 2 !}=\frac{5 !}{3 ! 2 !} \\\\ 5 C_{2} &=\frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1 \times 2 \times 1} \\\\ 5 C_{2} &=10 \end{aligned}[/tex]
We have to select 4 girls from 6 girls
Here n = 6 and r = 4
[tex]\begin{aligned} 6 C_{4} &=\frac{6 !}{(6-4) ! 4 !}=\frac{6 !}{2 ! 4 !} \\\\ 6 C_{4} &=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 4 \times 3 \times 2 \times 1}=15 \end{aligned}[/tex]
Committee is to be formed consisting of 2 boys and 4 girls:
So we have to multiply [tex]5 C_{2}[/tex] and [tex]6 C_{4}[/tex]
[tex]5 C_{2} \times 6 C_{4}=10 \times 15=150[/tex]
So 150 different committees are possible
Final answer:
The question is a combinatorial problem in mathematics, where the goal is to calculate the number of different committees that can be formed from 5 boys and 6 girls. To solve this, the combinations formula is applied separately to choose 2 boys from 5 and 4 girls from 6, and the results are multiplied.
Explanation:
The question asks about the number of different committees that can be formed from a group of boys and girls. This is a combinatorial problem involving calculations to find the different possible combinations that can be made using a subset of a larger set. To solve this, you would use the combinations formula which is given by C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes the factorial of a number.
To determine how many different committees are possible, we calculate the number of ways to choose 2 boys from 5, and 4 girls from 6 separately, and then multiply these two results:
The number of ways to choose 2 boys from 5 is C(5, 2)
The number of ways to choose 4 girls from 6 is C(6, 4)
Therefore, the total number of different committees possible is C(5, 2) * C(6, 4).
Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 oz and a standard deviation of 0.11 oz. Find the probability that a single can of Coke has at least 12.19 oz.
Answer:
0.0421
Step-by-step explanation:
Mean(μ) = 12.00 oz
Standard deviation (σ) = 0.11 oz
Z = (x - μ)/σ
Z = (12.19 - 12.00) / 0.11
Z= 0.19/0.11
Z = 1.727
From the normal distribution table, Z = 1.727 = 0.4579
Φ(Z) = 0.4579
Recall that if Z is positive
Pr(x>a) = 0.5 - Φ(Z)
Pr(x > 12.19) = 0.5 - 0.4579
= 0.0421
A survey conducted five years ago by the health center at a university showed that 18% of the students smoked at the time. This year a new survey was conducted on a random sample of 200 students from this university, and it was found that 50 of them smoke. We want to find if these data provide convincing evidence to suggest that the percentage of students who smoke has changed over the last five years. What are the test statistic (Z) and p-value of the test?
Answer:
test statistic (Z) is 2.5767 and p-value of the test is .009975
Step-by-step explanation:
[tex]H_{0}[/tex]: percentage of students who smoke did not change
[tex]H_{a}[/tex]: percentage of students who smoke has changed
z-statistic for the sample proportion can be calculated as follows:
z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where
p(s) is the sample proportion of smoking students ([tex]\frac{50}{200}[/tex] =0.25)p is the proportion of smoking students in the survey conducted five years ago (18% or 0.18)N is the sample size (200)Then, z=[tex]\frac{0.25-0.18}{\sqrt{\frac{0.18*0.82}{200} } }[/tex] ≈ 2.5767
What is being surveyed is if the percentage of students who smoke has changed over the last five years, therefore we need to seek two tailed p-value, which is .009975.
This p value is significant at 99% confidence level. Since .009975 <α/2=0.005, there is significant evidence that the percentage of students who smoke has changed over the last five years
Bill and susan buy 16 oranges at a fruit stand. They make orange juice using 3/4 of the oranges. How many oranges do bill and susan use to make orange juice?
they use 12 oranges
4•4=16-4=12 which is 3 of the 4/4
The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers but the division is not wholly complete.
As per the given,
They make orange juice using 3/4 of the oranges.
3/4 of 16
(3/4)16 = 3 x 4 = 12 oranges
Hence "The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges".
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You formally challenge the classification of information and the classifying agency provides a partial response. What is your responsibility if the classifying agency does not provide a full response within 120 days.
Answer:
I will forward the challenge to the ISCAP.
Step-by-step explanation:
If the classifying agency does not provide a full response within 120 days, then as per my responsibility, I will forward the challenge to the ISCAP.
ISCAP is the Inter agency security classification appeals panel.
ISCAP is a deciding panel that decides on certain classification or declassification issues to its users, with a forum for further review.
Find all functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).
Answer:
[tex]y=Ae^{-2x}[/tex]
Step-by-step explanation:
Given that the functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).
Let (x,y) be any arbitrary point of contract
The tangent line passes through two points (x,y) and (x+2,0)
Slope of tangent line = f'(x) = change in y/change in x= [tex]\frac{-y}{2}[/tex]
i.e. we have
[tex]\frac{dy}{dx} =\frac{-y}{2}[/tex]
Separate the variables
[tex]\frac{dy}{y} =-2x\\lny =-2x+c[/tex]
Raise to power e
[tex]y=Ae^{-2x}[/tex]
Thus the functions would have the above form for various values of A
Find an explicit rule for the nth term of the sequence.
7, -7, 7, -7, ... (5 points)
Select one:
a. an = 7 • (-1)n-1
b. an = 7 • (-1)n
c. an = 7 • 1n-1
d. an = 7 • 1n+1
Answer:
(a) The ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7 \times (-1)^{n-1}\\[/tex].
Step-by-step explanation:
Here, the given sequence is 7, -7, 7, -7, ...
The first term = 7, Second term = -7, Third term =-7 and so on..
Now check the given sequence for each given formula, we get:
(1) [tex]a_n = 7 \times (-1)^{n-1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (-1)^{1-1}\\[/tex]
[tex]= 7 \times (-1)^0 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (-1)^{2-1}\\[/tex]
[tex]= 7 \times (-1)^1 = 7 \times (-1) = -7 \implies a_2 = -7[/tex]
Hence, the given formula satisfies the given sequence.
(2) [tex]a_n = 7 \times (-1)^{n}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (-1)^{1}\\[/tex]
[tex]= 7 \times (-1)^1 = 7 \times (-1) = -7 \implies a_1 = -7[/tex]
But, First term = 7
Hence, the given formula DO NOT satisfy the given sequence.
(3) [tex]a_n = 7 \times (1)^{n-1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (1)^{1-1}\\[/tex]
[tex]= 7 \times (1)^0 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (1)^{2-1}\\[/tex]
[tex]= 7 \times (1)^1 = 7 \times (1) = 7 \implies a_2 = 7[/tex]
But, Second term = -7
Hence, the given formula DO NOT satisfy the given sequence.
(4) [tex]a_n = 7 \times (1)^{n+1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (1)^{1+1}\\[/tex]
[tex]= 7 \times (1)^2 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (1)^{2+1}\\[/tex]
[tex]= 7 \times (1)^3 = 7 \times (1) = 7 \implies a_2 = 7[/tex]
But, Second term = -7
Hence, the given formula DO NOT satisfy the given sequence.
So, the ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7 \times (-1)^{n-1}\\[/tex].
Answer:
an=7•(-1)^n-1
Step-by-step explanation:
A simple random sample of 1200 adult Americans is selected, and each person is asked the following question: "In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?" Only 39% of those responding answered "Yes." This survey ____.
a. is reasonable accurate since it used a large simple random sample.
b. needs to be larger since only about 24 people were drawn from each state.
c. probably understates the percent of people who favor a system of national health insurance.
d. is very inaccurate but neither understates nor overstates the percent of people who favor a system of national health insurance. Because simple random sampling was used, it is unbiased.
e. probably overstates the percent of people who favor a system of national health insurance.
Answer:
c. probably understates the percent of people who favor a system of national health insurance.
Alex and bob are playing 5 chess games. Alex is 3 times more likely to win than bob. What is the probability that both of them will win at least 2 games?
To find the probability of both Alex and Bob winning at least 2 games during their 5 games chess play, principles of geometric probability and the Multiplication rule are used. The equation _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))] is formed considering Alex is 3 times more likely to win than Bob.
Explanation:Calculating Probability of Games
In this scenario, Alex and Bob are playing 5 games with Alex being 3 times more likely to win than Bob. The primary question is to find the probability for both of them winning at least 2 games.
We would utilize the principles of geometric probability to solve this. Geometric probability treats each game as a Bernoulli trial, a game of win or lose. Moreover, we operate with the Multiplication rule in finding the probability of both events, Alex and Bob winning 2 games, happening.
Firstly, we define the probability of Alex winning as p, therefore, the probability of Bob winning is p/3. Bob and Alex must win 2 games each, leaving one game open to any outcome. Since the games are independent, the Multiplication rule applies. Therefore, the probability is calculated by multiplying probabilities for each win and possible combinations of five games taken two at a time. In other words, the equation will look like _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))].
The resulting value will be the probability for both of them winning at least 2 games.
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Help with this question please answer it
correctly and show work please and I am gonna Mark you as a brainliest
Answer:
15.5 yards
They will be picked up at an elevation of 15.5 yards
Step-by-step explanation:
Here we are going to make the ski slope of the mountain as the hypotenuse of a right-angled triangle where the top of the slope and bottom of the slope are two ends of the hypotenuse.
We first have to find the height of the top of the mountain with respect to the bottom.
Here we have been given heights with respect to sea level above and below.
Clearly, sum of the distances above and below sea level will be total elevation with respect to the bottom.
h1 - Height of summit above sea level
h2 - Height of bottom below sea level
Hb - Elevation of top w.r.t bottom
Hb = h1 + h2
Hb = [tex]17\frac{3}{4}+13\frac{1}{4}[/tex]
Hb = 31 yards
Now, the ski lift is picking them up in the middle of the slope (hypotenuse of the triangle).
By midpoint theorem line segment parallel to base joins the midpoints of the other 2 sides.
Thus the elevation will clearly be half of total elevation.
Height at which they are picked up is Hb/2
Therefore,
They will be picked up at an elevation of 15.5 yards
The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm so if the circumference of the inside the ring is 50 mm what is the inner diameter of the rain?
Answer: The inner diameter of the ring is 16 mm.
Step-by-step explanation:
As we know that ,
Circumference of a circle = [tex]\pi d[/tex] , where d = diameter of the circle .
We are given that ,
The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm .
Now , if circumference of the inside the ring is 50 mm, then we have
[tex]50 = \pi d[/tex] , where d= diameter of the inner circle .
Then , [tex]d=\dfrac{50}{\pi}=\dfrac{50}{\dfrac{22}{7}}=\dfrac{50\times7}{22}\approx15.909090909\approx16\text{ mm}[/tex]
Hence , the inner diameter of the ring is 16 mm.
The diameter of the inner ring is 15.92mm
Circumference of a circleThe formula for calculating the circumference of a circle is expressed as:
C = πd
d is the diameter
Given the following parameters
C = 50mm
The diameter of the inner ring is given as:
d = C/π
d = 50/3.14
d = 15.92mm
Hence the diameter of the inner ring is 15.92mm
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Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?
a) 6
b) 9
c) 12
d) 27
e) 48
Answer:
b) 9
Step-by-step explanation:
Given: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in [tex]36[/tex] hours.
To Find: If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled.
Solution:
Let the time taken by one machine to fill a certain production alone be[tex]=\text{x}[/tex]
Time taken when three machine operate independently and simultaneously
[tex]\frac{1}{\text{x}}+\frac{1}{\text{x}}+\frac{1}{\text{x}}=\frac{1}{36}[/tex]
[tex]\frac{3}{\text{x}}=\frac{1}{36}[/tex]
[tex]\text{x}=108[/tex] [tex]\text{hours}[/tex]
Let time taken when one additional machine is used [tex]=\text{y}[/tex]
Time when when one additional machine is used
[tex]\frac{1}{108}+\frac{1}{108}+\frac{1}{108}+\frac{1}{108}=\frac{1}{\text{y}}[/tex]
[tex]\frac{4}{108}=\frac{1}{\text{y}}[/tex]
[tex]\text{y}=27[/tex] [tex]\text{hours}[/tex]
it takes [tex]27[/tex] [tex]\text{hours}[/tex] when one additional machine is used
Now,
fewer hours taken when one additional machine is used
[tex]=\text{number of hours taken when three machines are used}-[/tex][tex]\text{number of hours taken when one additional machine is used}[/tex]
[tex]36-27[/tex]
[tex]9[/tex] [tex]\text{hours}[/tex]
in [tex]9[/tex] fewer hours of simultaneous operation the production order can be filled if one additional machine is used
Hence option b) is correct.
Please help me out with this!!!!!!!!!!
Answer:
C
Step-by-step explanation:
Rearranging x - y ≤ 2
- y ≤ 2 - x ( multiply through by - 1 )
y ≥ - 2 + x ← change direction of inequality symbol
This region is above the yellow line
y ≥ 0 is above the x- axis
x ≥ 0 is to the right of the y- axis
Thus the solution is the indicated blue region
The inequalities from C satisfy the given graph
Priya and Han are biking in the same direction on the same path. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many m miles Han has gone after t hours.
m=16t can be used to determine the distance in miles Han has gone after t hours.
Step-by-step explanation:
Speed of Han = 16 miles per hour
Let,
m be the distance covered by Han in miles;
t be the number of hours Han has been biking,
According to formula,
Distance = Speed*Time
[tex]m=16*t\\m=16t[/tex]
m=16t can be used to determine the distance in miles Han has gone after t hours.
Keywords: distance, speed
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Answer:
y = mx + b ( y = 16t + 0
Step-by-step explanation:
1.) Which domain restrictions apply to the rational expression? 14x-2x / x^2-7x
2.) Sara has 85% so far in math. She wants to increase her grade. So far there have been 1,000 points possible in her class. The expression below represents the percent she’ll have if she earns 100% on her final exam, which is worth x points:
(Picture down below)
3.) Solve for x.
3 / x+2 – 1 / x = 1 / 5x
Answer:
3. [tex]\displaystyle 1\frac{1}{3} = x[/tex]
2C. [tex]\displaystyle III.[/tex]
2B. [tex]\displaystyle I.[/tex]
2A. [tex]\displaystyle II.[/tex]
1. [tex]\displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
Step-by-step explanation:
3. See above.
2C. The keyword is ratio, which signifies division, so you would choose "III.".
2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".
2A. The keyword is total, which signifies addition, so you would choose "II.".
1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:
[tex]\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
I am joyous to assist you anytime.
We found the domain restrictions of a rational expression by checking the values that make the denominator zero. A formula was suggested to calculate Sara's future percentage score. To solve the third equation, a common denominator was found and used to simplify the expression.
Explanation:1. The domain restrictions for the rational expression 14x-2x/x^2-7x are all real numbers except for the numbers which make the denominator zero. Solving the equation x^2-7x=0, we get x=0 or x=7. Therefore, the domain restrictions are x≠0 and x≠7.
2. There is no picture provided but generally, to calculate the future percentage score given the current percentage score, total points possible, and future total points, you would use the formula (current score/current total points) * 100% + (future score/future total points) * 100%.
3. To solve for x in the equation 3 / (x+2) - 1 / x = 1 / (5x), we first need to find a common denominator. In this case, it would be 5x^2 + 10x. Multiplying each term by the common denominator and simplifying would then give the value of x.
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Given: ∆ABC, AB = 12, AC = 17 Area ∆ABC = 65 Find: BC, m∠A, m∠B, m∠C
Answer:
BC = 10.889m∠A = 39.6°m∠B = 95.8°m∠C = 44.6°Step-by-step explanation:
There are at least a couple of ways you could go at this. Here, we'll use an area formula to find m∠A, then use the law of cosines to find BC. Using BC, we can use the law of sines to find another angle.
Area = (1/2)·AB·AC·sin(∠A)
65·2/(12·17) = sin(∠A) ≈ 65/102
∠A = arccos(65/102) ≈ 39.587°
From the law of cosines, ...
BC² = AB² +AC² -2·AB·AC·cos(∠A)
BC² = 12² +17² -2·12·17·cos(39.587°) ≈ 118.5735
BC ≈ √118.5735 ≈ 10.889
Then ∠C can be found from the law of sines:
sin(∠C)/AB = sin(∠A)/BC
∠C = arcsin(AB/BC·sin(∠A)) ≈ 44.609°
The measure of ∠B will be the angle that makes the total be 180°:
39.587° +∠B +44.609° = 180°
∠B = 95.804°
_____
There is actually another solution, in which ∠A is obtuse. We thought the diagram showed an acute triangle, so we didn't investigate the other alternative. The above calculations show the triangle is obtuse in any event.
See the second attachment for the other solution.
determine the intervals on which the function is increasing, decreasing and constant
Answer:
increasing: (-∞, 0)decreasing: (0, ∞)Step-by-step explanation:
The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...
increasing from -∞ to 0 (not including 0)
decreasing from 0 to +∞ (not including 0)
_____
At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.
Find the yy-intercept of each line defined below and compare their values.
Answer:
y-intercept: when x = 0
For Line A:
y = 0 + 7 = 7
For line B:
when x = 0, the value is -5
7 > -5, so y-intercept of line A is greater than line B's.
The nutrition information on the box of cereal says that a one third cup serving provides 80 calories and six grams of dietary fiber. At that rate find how many calories and grams of fiber are in a half cup serving
Answer:
120 calories and 9 grams of fiber.
Step-by-step explanation:
We are told that 1/3 cup serving contains 80 calories and 6 grams of fiber.
Let's multiply everything by 3. So,
1 cup serving has 3*80 = 240 calories and 3*6 = 18 grams of fiber.
But, we want to really know about 1/2 cup. So, now we multiply everything by 1/2.
1/2 cup has (1/2) (240) = 40 calories and (1/2) (18 grams) = 9 grams of fiber.
Answer:
240 calories and 9 grams of fiber
Step-by-step explanation:
A wheelchair ramp is 4.2 m long. It rises 0.7 m. What is it's angle of inclination to the nearest degree?
The inclination angle is 10°
Step-by-step explanation:
The given scenario forms a right angled triangle where the length of ramp is hypotenuse and the rise of ramp is the perpendicular
Given
H = 4.2m
P = 0.7m
We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse
Let x be the angle
then
[tex]sin\ x = \frac{P}{H}\\sin\ x = \frac{0.7}{4.2}\\sin\ x = 0.1666\\x = sin^{-1} (1.666)\\x = 9.59 => 10[/tex]
Hence,
The inclination angle is 10°
Keywords: Trigonometric ratios, Right angled triangle
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The angle of inclination of the wheelchair ramp to the nearest degree is 9 degrees.
[tex]\[ \theta = \arctan\left(\frac{\text{rise}}{\text{run}}\right) \][/tex]
Given the rise of the ramp is 0.7 m and the run (length) is 4.2 m, we can plug these values into the formula:
[tex]\[ \theta = \arctan\left(\frac{0.7}{4.2}\right) \][/tex]
Now, we calculate the value of θ:
[tex]\[ \theta = \arctan\left(\frac{1}{6}\right) \][/tex]
Using a calculator, we find:
[tex]\[ \theta \approx \arctan(0.1667) \] \[ \theta \approx 9.4623 \text{ degrees} \][/tex]
Rounding to the nearest degree, we get:
[tex]\[ \theta \approx 9 \text{ degrees} \][/tex]
Therefore, the angle of inclination of the wheelchair ramp is approximately 9 degrees to the nearest degree.
A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of fluid ounces and the sample standard deviation is fluid ounces. Find a 95% two-sided confidence interval on the mean volume of syrup dispensed. Assume the population is approximately normally distributed.
Answer:
You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.
Step-by-step explanation:
Calculation
M = 0.96
Z = 1.96
sM = √(0.96)^2/25) = 0.19
μ = M ± Z(sM)
μ = 0.96 ± 1.96*0.19
μ = 0.96 ± 0.3763
Result
M = 0.96, 95% CI [0.5837, 1.3363].
You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.
A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at , the average attendance had been 27,000. When ticket prices were lowered to , the average attendance rose to 33,000. (a) Find the demand function, assuming that it is linear. (b) How should ticket prices be set to maximize revenue?
Answer:
$9.50
Step-by-step explanation:
Solution is in the attachment . You can see it.
Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. (Assume the car travels the same distance for each one gallon of gas)
The number of miles traveled varies directly with the number of gallons of gas you use.
a. Write an equation that relates miles traveled to gallons of gas used. (Use any variable you like in the equation.
b. How far can you drive with 3.7 gallons of gas? (Make sure to show the calculations you did to determine this answer)
Answer:
Step-by-step explanation:
Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that
1 gallon of gas would be used to drive 392/14 = 28 miles
a) The number of miles traveled varies directly with the number of gallons of gas used.
Let x =number of gallons of gas you use.
Let y = the number of miles travelled.
Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,
y = kx
If 28 miles will require 1 gallon of gas, it means
28 = 1×k
k = 28
So y = 28x
b) we want to determine how far you can drive with 3.7 gallons of gas.
x = 3.7
y = 28x = 28×3.7
y = 103.6 miles
Manufacture has been selling 1450 television sets a week at $540 each. A market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
a) Find the function representing price as a function of the demand p(x)p(x), where xx is the number of the television sets sold per week and p(x)p(x) is the corresponding price.
Answer:
[tex]p(x)= -\frac{1}{10}x + 685[/tex]
Step-by-step explanation:
Since, Function of demand is the linear function of quantity.
Let x represents the quantity and p represents the price of each unit.
∵ Manufacture has been selling 1450 television sets a week at $540 each,
i.e. [tex](x_1, p_1) = (1450, 540)[/tex]
Also, for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
i.e. [tex](x_2, p_2) = (1580, 527)[/tex]
Thus, the linear equation of the price,
[tex]p-p_1 = \frac{p_2-p_1}{x_2-x_1}(x-x_1)[/tex]
[tex]p-540 = \frac{527 - 540}{1580-1450}(x-1450)[/tex]
[tex]p-540 = -\frac{13}{130}(x-1450)[/tex]
[tex]p-540 = -\frac{1}{10}(x-1450)[/tex]
[tex]p = -\frac{1}{10}x + 145 + 540[/tex]
[tex]\implies p = -\frac{1}{10}x + 685[/tex]
Hence, the function representing price as a function of the demand is,
[tex]p(x)= -\frac{1}{10}x + 685[/tex]
You have family traveling from far away to come to your house for Thanksgiving. If they travel 324 miles and arrive to your house in 6 hours, how fast were they traveling?
Answer: 54 mph
Step-by-step explanation:
Speed x Time = Distance
So, Speed = Distance/Time
Speed = 324 miles/6hrs = 54 mph
Susan wants to make pumpkin bread and zucchini bread for the school bake sale. She has 15 eggs and 16 cups of flour in her pantry. Her recipe for one loaf of pumpkin bread uses 2 eggs and 3 cups of flour. Her recipe for one loaf of zucchini bread uses 3 eggs and 4 cups of flour. She plans to sell pumpkin bread loaves for $5 each and zucchini bread loaves for $4 each. Susan wants to maximize the money raised at the bake sale. Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.What is the objective function for the problem?
A. P = 15x + 16y
B. P = 5x + 7y
C. P = 5x + 4y
D. P = 4x + 5y
Answer:
Option C.
Step-by-step explanation:
Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.
Pumpkin bread zucchini bread Total
Eggs 2 3 15
Flour(cups) 3 4 16
Selling price $5 $4
Susan wants to maximize the money raised at the bake sale.
Objective function :
[tex]P=5x+4y[/tex]
Subject to constraints:
[tex]2x+3y\leq 15[/tex]
[tex]3x+4y\leq 16[/tex]
[tex]x,y \geq 0[/tex]
Since the objective function is P = 5x + 4y, therefore the correct option is C.
Answer:
c
Step-by-step explanation:
i got it correct on edgenunity
A ladder leans against a brick wall. The foot of the ladder is 7 feet from the wall. The ladder reaches a height of 22 feet on the wall. What is the angle the ladder makes with the wall? (to the nearest tenth) A) 15.4° B) 17.7° Eliminate C) 18.6° D) 21.5°
Answer:
the answer is 17.7
Step-by-step explanation:
Apply tanθ =
opposite
adjacent
tanθ =
7
22
θ = tan−1(
7
22
)
θ = 17.7°
The angle the ladder that will make with the wall is 17.7°.
What is tangent of an angle?
Tangent of the angle is the ratio between the opposite side and adjacent side of the angle in the right angle triangle.
So according to the asked question,
the distance between lader foot and the wall is 7feet.
the height of the wall is 22feet.
So in triangle ΔABC ,
the height of the wall =AB=22feet
the distance between lader foot and the wall=BC=7feet
∠ABC=90°
the angle between the ladder and the wall= ∠BAC=θ
So in ΔABC,
tan ∠BAC=tan θ=BC/AB
⇒tan θ=7/22
⇒θ=tan⁻¹(7/22)
⇒θ=17.7⁰
Therefore the angle the ladder that will make with the wall is 17.7°.
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What is the value of x, given that AE || BD
Answer:
x = 7.8
Step-by-step explanation:
If AE is parallel to BD, then you can use the theorem called ratio of sides of parallel line.
AC/AB = EC/ED
x+11/x = 12/5
x=7.8
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the unknown sides will be equal to 7.857 units.
What are Similar Figures?
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
For the two similar triangles, ΔAEC and ΔBDC, the ratio of the sides will be,
11/7 = (11+x)/(5+7)
11/7 = (11+x)/12
(11×12)/7 = 11+x
18.857 - 11 = x
x = 7.857
Hence, the length of the unknown sides will be equal to 7.857 units.
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Select the correct choices that belong in the blank for the system of equations shown below.
24x - 39 = 165
-6x +13y = -51
In order to solve this system by elimination, Stacy ____________ by ______. Then, when she adds the equations together, the x terms will cancel.
Question 4 options:
multiplies the second equation; 4
multiplies the first equation; 4
multiplies the second equation; -4
Answer:
The answer to your question is Stacy multiplies the second equation by 4.
Step-by-step explanation:
24x - 39y = 165 (I)
- 6x + 13y = -51 (II)
Multiply the second equation by 4
24x - 39 y = 165
-24x + 52y = -204
Simplify
0 + 13y = 39
y = 39/ 13
y = 3
Find "x" value 24x - 39(3) = 165
24x - 117 = 165
24x = 165 + 117
24x = 282
x = 282 / 24
x = 47/4
The birth rate of a population is b(t) = 2300e0.024t people per year and the death rate is d(t)= 1450e0.019t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)
To calculate the area between the birth rate and death rate curves for a given time interval, find the net growth rate function by subtracting the death rate from the birth rate, and then integrate this function over the time interval. The result reflects the population surge due to the rates of births and deaths.
Explanation:The student's question involves calculating the area between two exponential growth curves, birth rate and death rate, over a given time interval. To find the area between the curves b(t) = 2300e0.024t and d(t) = 1450e0.019t from t = 0 to t = 10, we need to integrate the difference between them with respect to time over the given interval.Step-by-step Solution:
Subtract the death rate from the birth rate to get the net growth rate function: g(t) = b(t) - d(t) = 2300e0.024t - 1450e0.019t.
Integrate the net growth rate function with respect to t from 0 to 10 to find the total area.
Use a calculator or computer software to perform the integration and round the final answer to the nearest integer.
This computation will give the total number of people added to the population over the 10-year period, which reflects the population surge resulting from the different rates of increase in births and deaths.
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What solid figure has congruent squares on all six sides
Answer:
Cube.
Step-by-step explanation:
We are asked to find the solid figure, which has congruent squares on all six sides.
We know that a solid, whose length, width, and height are equal in measure is known as cube.
Upon looking at our attached file, we can see that length, width, and height for the solid are equal to x units, which makes its each face a square.
We know that a cube is a three dimensional figure, which contains six equal squares of all six sides.
Therefore, cube has congruent squares on all six sides.