The height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction 4 pi Over 5 EndFraction (t minus one-half)) + 12. What is the minimum height of the flag?
3 feet
9 feet
12 feet
15 feet
Answers
Answer:
15 feet
Step-by-step explanation:
See the attached graph. [y and x replace h and t in the given equation]
The are two ways to answer the question. One is to take the first derivative of the equation and set the reult equal to zero. The solutions represnet the points at which the slope of the line is 0 (i.e., where the line changes direction - at the top and bottom).
An easier way is to graph the equation and look for the maximum(s). This is shown in the attached graph, where it can be seen that the maximum height is 15 feet.
Related Questions
Triangles pqr and sqt are similar. the dimensions are given in centimeters (cm). the length of pq is 261 cm. what is the length of tq, in centimeters, to the nearest whole number?
Answers
The solution is, the length of TQ, in centimeters, to the nearest whole number is 167cm.
What is the scale factor?
A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
here, we have,
given that,
Triangles PQR and SQT are similar.
so, from the given figure we get,
PR/ST = RQ/TQ
now, we have,
the scale factor = PR/ST
= 75/50
=3/2
= 1.5
so, RQ/TQ = 1.5
or, TQ = RQ/1.5
=250/1.5
=166.66
Hence, The solution is, the length of TQ, in centimeters, to the nearest whole number is 167cm.
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Jobs arriving to a computer server have been found to require CPU
time that can be modeled by an exponential distribution with a mean of 140 ms
(milliseconds). The CPU scheduling discipline is quantum-oriented so that a job not
completed within a quantum of 100ms will be routed back to the tail of the queue of waiting
jobs.
a. What is the probability that an arriving job is forced to wait for a second quantum (that is,
it will be forced to wait for more than 100ms)?
b. What is the probability that the fifth arriving job of a day will be the first one that is
forced to wait for a second quantum (that is, it will be forced to wait for more than
100ms)
Answers
The probability of the fifth job being the first one that is forced to wait for a second quantum is 0.0266.
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability is calculated by taking all possible outcomes into consideration and then dividing the number of favourable outcomes by the total number of possible outcomes.
The probability that an arriving job is forced to wait for a second quantum is the probability of that job requiring more than 100ms of CPU time. This probability can be calculated by taking the cumulative distribution function of the exponential distribution and subtracting the probability of the job requiring 100ms or less of CPU time. The probability of the job requiring more than 100ms of CPU time is 0.6853.
This probability can be calculated by taking the probability of the first four jobs requiring less than 100ms of CPU time and multiplying it by the probability of the fifth job requiring more than 100ms of CPU time.
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Four envelopes contain four different amounts of money. You are allowed to open them one by one, each time deciding whether to keep the amount or discard it and open another envelope. Once an amound is discarded, you are not allowed to go back and get it later. Compute the probability that you get the largest amount under the following different strategies: a) You take the first envelope b) You open the first envelope, note that it contains the amount x, discard it, and take the next amount which is larger than x( if no such amount shows up, you must take the last envelope). c) You open the first two envelopes, cal the amounts x and y, and discard both and take the next amount that is larger than both x and y.
Answers
1. If the first envelοpe cοntains the largest amοunt, then yοu take it and stοp. The prοbability οf this happening is 1/4.
What is prοbability?Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.
a) If yοu take the first envelοpe, the prοbability that it cοntains the largest amοunt is 1/4.
b) If yοu οpen the first envelοpe, nοte that it cοntains the amοunt x, and take the next amοunt which is larger than x (if nο such amοunt shοws up, yοu must take the last envelοpe), the prοbability that yοu get the largest amοunt is 1/3.
Tο see why, cοnsider the fοllοwing cases:
2. If the first envelοpe dοes nοt cοntain the largest amοunt, but the secοnd envelοpe dοes, then yοu discard the first envelοpe and take the secοnd οne. The prοbability οf this happening is (3/4) x (1/3) = 1/4.
3. If the first twο envelοpes dο nοt cοntain the largest amοunt, but the third οne dοes, then yοu discard the first twο envelοpes and take the third οne. The prοbability οf this happening is (3/4) x (2/3) x (1/2) = 1/4.
4. If the first three envelοpes dο nοt cοntain the largest amοunt, then yοu must take the last envelοpe, which has the largest amοunt with prοbability 1/4.
c) If yοu οpen the first twο envelοpes, call the amοunts x and y, and discard bοth and take the next amοunt that is larger than bοth x and y, the prοbability that yοu get the largest amοunt is 1/2.
Tο see why, cοnsider the fοllοwing cases:
1. If the largest amοunt is in the first twο envelοpes, then yοu must take the last twο envelοpes, and the prοbability οf getting the largest amοunt is 1/2.
2. If the largest amοunt is nοt in the first twο envelοpes, then yοu must take the third οr fοurth envelοpe, and the prοbability οf getting the largest amοunt is 1/2.
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If the sixth term of an(AP) is 37 and the sum of the first six terms is 147 find the
I) first term
I) the sum of the first fifteen terms
Answers
As a result, the arithmetic progression's first term is 22 and its first fifteen terms add up to 735. The AP's initial term is 22 and its first fifteen terms add up to 735.
The total of the first seven terms is seventy-five.
The formulae for the nth term and the sum of an arithmetic progression can be used to solve the issue.
We have the following using the nth term formula:
a + 5d = 37\s(6/2)(2a + 5d) = 147
3a + 15d = 147\sa + 5d = 49
We may find a by substituting d into either equation and finding:
a + 5(-3) = 37\sa = 22
Hence, the first term of the arithmetic progression is 22 and the formula for the total of the first fifteen terms is (15/2)(2a + 14d) = 735.
(15/2)(2(22) + 14(-3)) = 735
If we simplify, we get:
15 terms added together is 735
As a result, the AP's first term is 22 and its first fifteen terms add up to 735.
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5.83. the probabilities are 0.40, 0.50, and 0.10 that, in city driving, a certain kind of compact car will average less than 28 miles per gallon, from 28 to 32 miles per gallon, or more than 32 miles per gallon. find the probability that among 10 such cars tested, 3 will average less than 28 miles per gallon, 6 will average from 28 to 32 miles per gallon, and 1 will average more than 32 miles per gallon.
Answers
The probability that among 10 such cars tested, 3 will average less than 28 miles per gallon, 6 will average from 28 to 32 miles per gallon, and 1 will average more than 32 miles per gallon is given by 0.0020125
Let X be the number of cars among ten that averages less than 28 miles per gallon. Let Y be the number of cars among ten that average from 28 to 32 miles per gallon. Let Z be the number of cars among ten that average more than 32 miles per gallon. We are to find P(X = 3, Y = 6, Z = 1).
Firstly, let us find the probability of getting 3 cars among 10 cars that will average less than 28 miles per gallon.
The probability of getting exactly 3 cars among 10 cars that will average less than 28 miles per gallon is given by the probability mass function:
P(X = 3) = (10C3) (0.4)³ (0.6)⁷
= (10 x 9 x 8 / 3 x 2 x 1) (0.064) (0.096)
= 0.23 (approximately)
Similarly, the probability of getting 6 cars among 10 cars that will average from 28 to 32 miles per gallon is given by the probability mass function:
P(Y = 6) = (10C6) (0.5)⁶ (0.5)⁴
= (10 x 9 x 8 x 7 x 6 x 5 / 6 x 5 x 4 x 3 x 2 x 1) (0.156) (0.063)
= 0.25 (approximately)
Finally, the probability of getting 1 car among 10 cars that will average more than 32 miles per gallon is given by the probability mass function:
P(Z = 1) = (10C1) (0.1)¹ (0.9)⁹
= (10) (0.1) (0.348)
= 0.035
Therefore, the answer is:
P(X = 3, Y = 6, Z = 1) = P(X = 3) P(Y = 6) P(Z = 1)
= 0.23 x 0.25 x 0.035
= 0.0020125 (approximately)
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4. (Odds / Ends p. 125 #7) Martha is trying to decide where to go to university. She applied to three schools: UTM, Western, and Queens. UTM is her first choice, Queens is her last choice. So far Martha has only heard back from Western. They are offering her early admission: they’ll admit her but only if she agrees right now to go there (she can’t wait until she finds out if the other two schools will admit her). Based on her grades, Martha knows that if she waits she’ll be admitted to Queens for sure. But her chance of getting into UTM is only 6/10. After thinking about it a while, she can’t decide: a guaranteed spot at Western seems just as good to her as the gamble on UTM vs. Queens. a. If the utility of going to Queens is 5/10 for Martha, and the utility of going to UTM is 9/10, what is the utility of going to Western? b. Martha’s friend is considering York University. Martha didn’t apply to York, but if she had she would be indifferent between these options: - Accept an early-admissions offer from York and go there. - Gamble on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens. How much utility does going to York have for Martha?
Answers
a. The utility of going to Western is 6.4/10
b. The utility of going to York would also be 5.15/10
Define the term decision theory?Decision theory is a branch of mathematics that deals with decision making in the face of uncertainty.
a. If Martha accepts the early admission offer from Western, her utility would be 5/10, since that is the utility of going to Queens.
If Martha waits and gets admitted to Queens, her utility would be 5/10 as well, since that is the utility of going to Queens.
If Martha waits and gets admitted to UTM, her utility would be 9/10.
The probability of getting admitted to Queens is 1, since she is guaranteed admission. The probability of getting admitted to UTM is 6/10. The probability of accepting the early admission offer from Western is 4/10, since it is the complement of the probability of getting admitted to UTM.
Therefore, the expected utility of waiting is ⇒ (1 * 5/10) + (6/10 * 9/10) = 8.4/10. The expected utility of accepting the early admission offer is
⇒ (4/10 * 5/10) = 2/10.
Since Martha is indifferent between the two options, the utility of going to Western is 8.4/10 - 2/10 = 6.4/10
b. If Martha is indifferent between accepting an early-admissions offer from York and gambling on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens, then the utility of going to York must be the same as the expected utility of gambling.
If Martha gambles, her expected utility would be (3/4 * 6.4/10) + (1/4 * 5/10) = 5.15/10.
Therefore, the utility of going to York would also be 5.15/10.
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What is the measure of the major arc?
R
Q
150*
O A. 150°
OB. 220°
O C. 195°
OD. 210°
Answers
Answer:
210°
Step-by-step explanation:
Measure of unknown arc = Measure of full circle - Measure of given arc
= 360° - 150°
= 210° --- Option D
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Thanks.
I drove 175 miles in 5 hours. What was my speed
Answers
The speed at which the driver travelled the 175 miles in 5 hours is 35 miles/hour.
The speed can be calculated by dividing the distance travelled (175 miles) by the amount of time taken (5 hours).
Formula: Speed = Distance/Time
Speed = 175/5 = 35 miles/hour
Therefore, my speed was 35 miles/hour.
To calculate the speed, the formula mentioned above is used. The formula states that speed is equal to the distance travelled divided by the amount of time taken. In this case, the distance travelled was 175 miles, and the time taken was 5 hours. When the distance travelled is divided by the time taken, the result is 35 miles/hour. This is the speed at which the driver travelled the 175 miles in 5 hours.
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The function p(t) = 3(2)* represents the population of a certain type of bacteria
after t days.
What is the population of the bacteria after 5 days?
Answers
The pοpulatiοn οf the bacteria after 5 days is 96.
What is an expοnential functiοn?An expοnential functiοn is a mathematical functiοn οf the fοrm f(x) = ab^x, where a and b are cοnstants, and x is a variable. The base, b, is a pοsitive number, typically greater than 1, that determines hοw quickly the functiοn grοws οr decays. The expοnent, x, is the independent variable, and represents the pοwer tο which the base is raised.
Tο find the pοpulatiοn οf the bacteria after 5 days, we need tο substitute t = 5 intο the given functiοn:
p(5) = 3(2)⁵
Simplifying the expressiοn, we get:
p(5) = 3(32)
p(5) = 96
Therefοre, the pοpulatiοn οf the bacteria after 5 days is 96.
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-7 - 4 is equivalent to?
-11
11
-3
3
Answers
The functionf(x)= x−12x+6,x=1, is one-to-one. Find an equation forf −1(x), the inverse function.f −1(x)=x=2(Simplify your answer. Use integers or fractions for any numbers in the expression.) The domain of the plecewise function is(−[infinity],[infinity]). a. Graph the function. b. Use your graph to determine the function's range.f(x)={ 4x if x≤02 if x>0a. Choose the correct graph below. b. The range off(x)is (Type your answer using interval notation, set notation, and the union operator as need
Answers
Answer:find the inverse of f(x)=3x+2. Inverse functions, in the most ...
Step-by-step explanation:
In a consumer research study, several Meijer and Walmart stores were surveyed at random and the average basket price was recorded for each. You wish to determine if the average basket price for Meijer is different from the average basket price for Walmart. It was found that the average basket price for 25 randomly chosen Meijer stores (group 1) was $60.345 with a standard deviation of $10.8968. Similarly, a random sample of 20 Walmart stores (group 2) had an average basket price of $67.635 with a standard deviation of $12.936. Perform a two independent samples t-test on the hypotheses Null Hypothesis: μ1 = μ2, Alternative Hypothesis: μ1 ≠ μ2. What is the test statistic and p-value of this test? You can assume that the standard deviations of the two populations are statistically similar.
Question 3 options:
1) Test Statistic: -2.052, P-Value: 1.977
2) Test Statistic: -2.052, P-Value: 0.0461
3) Test Statistic: -2.052, P-Value: 0.023
4) Test Statistic: -2.052, P-Value: 0.977
5) Test Statistic: 2.052, P-Value: 0.0461
Answers
From the given data, the test statistic is -2.052 and the p-value is 0.0461. The correct answer is option 5.
To perform a two independent samples t-test, we can use the following formula to calculate the test statistic:
t = (x₁ - x₂) / (s_p × √(1/n₁ + 1/n₂))
where x₁ and x₂ are the sample means, n₁ and n₂ are the sample sizes, s_p is the pooled standard deviation, calculated as:
s_p = √(((n₁ - 1) × s₁² + (n₂ - 1) × s₂²) / (n₁ + n₁ - 2))
Let's calculate the test statistic:
x₁ = 60.345, s₁ = 10.8968, n₁ = 25
x₂ = 67.635, s₂ = 12.936, n₂ = 20
s_p = √(((25 - 1) × 10.8968² + (20 - 1) × 12.936²) / (25 + 20 - 2)) = 11.8074
t = (60.345 - 67.635) / (11.8074 × √(1/25 + 1/20)) = -2.052
The degrees of freedom for the t-distribution can be calculated as:
df = n₁ + n₂ - 2 = 43
Using a two-tailed t-test at a significance level of 0.05, the critical t-value is ±2.016.
The p-value for the test is the probability of obtaining a t-value as extreme or more extreme than the calculated t-value, assuming the null hypothesis is true. Since the calculated t-value is outside the critical region (|t| > 2.016), the p-value is less than 0.05 and we can reject the null hypothesis in favor of the alternative hypothesis.
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The property tax in one town was $6. 95 per $1000 value in the year 2012. The tax increased to $7. 71 per $1,000 value in 2013. What effect did that have on the property tax for a house with a value of $100,000?
a) increase $76
b) decrease $96
c) increase $ 791
d) decrease $695
Answers
The effect of the tax increase from 2012 to 2013 for a house with a value of 100,000 was an increase of 76.
The property tax in one town was 6.95 per 1000 value in the year 2012. In 2013, the property tax increased to 7.71 per 1000 value. This means that in 2013, the property tax for a house with a value of 100,000 would be 771.
To calculate the effect that the tax increase had on the property tax for a house with a value of 100,000, we can use the following formula:
Effect of Tax Increase = (New Tax Rate - Old Tax Rate) x Value of Property
Using this formula, the effect of the tax increase for a house with a value of $100,000 would be:
Effect of Tax Increase = ($7.71 - $6.95) x $100,000
Effect of Tax Increase = $0.76 x $100,000
Effect of Tax Increase = $76
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Anyone know this and can help?
Answers
Answer: A. ; [tex]2x-3=7[/tex]
Step-by-step explanation: We are solving for when the value of x is equal to five. Here is proving that the answer to the first question is correct.
[tex]2x-3=7[/tex]
Add 3 to both sides
[tex]2x=10[/tex]
Divide both sides by 2
[tex]x=5[/tex]
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Answer: A
Step-by-step explanation:
When an equation has a solution for x = some number n, that means the equation is true when you substitute for x=n. In this case, n=5, so we substitute x=5 in all 4 equations. We can notice that A yields 2*5-3=7 -> 10-3=7, which is true. Therefore, A yields a solution for x=5. We can also put in x=5 for the other 3 equations and we can spot that the equation does not hold for x=5 for any of them.
what is the radius if a circle with diameter 3cm
Which diagram shows how to set a pair of compasses to draw a circle with diameter 3cm
Answers
Answer: The radius of a circle is half of its diameter. Therefore, if the diameter of the circle is 3 cm, then the radius is 1.5 cm.
To set a pair of compasses to draw a circle with diameter 3 cm, open the compasses to a distance of 1.5 cm (which is the radius of the circle). The correct diagram in the link provided shows the compasses set to the correct radius.
So its A
The radius of the circle is 1.5cm.
A circle's diameter is divided in half by its radius. Thus, if the circle's diameter is 3 cm, the radius is:
radius = diameter/2 = 3cm/2 = 1.5cm
what is the radius?Any circular object's radius is the measurement from the centre to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.
It is possible to define a circle as the locus of a point travelling on a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its centre. The fixed point is referred to as the centre of the circle.
The distance along a line drawn between two points on a circle and through the centre of the circle is the diameter of the circle. It is equivalent to double the circle's radius. It is typically indicated with a d or a D.
Diameter = 2 x Radius
Or
Radius = diameter / 2.
The circle's longest chord equals its diameter.
Moreover, we may relate a circle's area and circumference to its diameter.
Circle circumference equals (Diameter)
Circle area equals /4 (Diameter[tex])^2.[/tex]
from the question;
A circle's diameter is divided in half by its radius. Thus, if the circle's diameter is 3 cm, the radius is:
radius = diameter/2 = 3cm/2 = 1.5cm
Therefore, the radius of the circle is 1.5cm.
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pls help me this is also due on Saturday!!!!!
Answers
Answer:
u=4
Step-by-step explanation:
u+6/12 = 4+6/12 = 10/12 ÷ 2/2 = 5/6
Answer: u = 4
Step-by-step explanation:
2100 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to reach 5100 dollars?
Answers
Therefore, it will take about 11 years for the account value to reach 5100 dollars.
What is percent?Percent is a way of expressing a quantity as a fraction of 100. The symbol "%" is used to represent percent. For example, if we say that an interest rate is 5%, it means that the interest is 5/100 or 0.05 as a decimal. Percentages are commonly used in finance, economics, and everyday life to express rates, proportions, and changes in quantities.
Here,
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)ⁿˣ
where A is the amount of money in the account after x years, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and x is the time (in years).
We are given that P = 2100, r = 0.05, and we want to find the value of x when A = 5100. Let's assume that the interest is compounded annually (n = 1). Substituting the given values into the formula, we get:
5100 = 2100(1 + 0.05)ˣ
Dividing both sides by 2100, we get:
(1 + 0.05)ˣ = 5100/2100
Simplifying the right-hand side, we get:
(1 + 0.05)ˣ = 2.42857
Taking the natural logarithm of both sides, we get:
ln(1 + 0.05)ˣ = ln 2.42857
Using the power rule of logarithms, we can simplify the left-hand side:
x ln(1 + 0.05) = ln 2.42857
Dividing both sides by ln(1 + 0.05), we get:
x= ln 2.42857 / ln(1 + 0.05)
Using a calculator, we get:
x≈ 11.4
Rounding this to the nearest year, we get:
x ≈ 11 years
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right gets brainliest
Answers
Answer:
C. Dwayne begins with more tickets than Lyla.
Step-by-step explanation:
We can see from the chart and what is given that Dwayne starts with 600 tickets and Lyla starts with 500 tickets.
Dwayne is selling 5 tickets per minutes, just like Lyla; Option A and B are false. You can calculate Dwayne's sell rate using the slope formula.
[tex]\frac{600-580}{8-4} =\frac{20}{4} \\ = 5[/tex]
Choice D. is false because we just said that Dwayne started with 100 more tickets than Lyla.
Need help with this, can anyone help out?
Answers
a) The minimum number of hikers who could have walked between 6 miles and 17 miles is 9.
b) The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
What is meant by minimum and maximum value?When the derivative equals 0, we will rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which will be the point where the maximum or lowest will occur, and this is provided in this answer.
The solution will be put back into the original function to determine the minimum or maximum.
Thus, looking at the given table, minimum number will be 9
Similarly the maximum number will be 15 hikers.
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please i beg you can you help me with this!!!!
Answers
Answer:
it's negative one over five...... -1\5
Si O es el centro de la circunferencia de la figura y el ∡ ABC = 40°, halla la medida del ∡X
Answers
As in the given circle, the measure of the value of ∠X is 115°.
Now, let's look at point X. This point is on the same line as point B and is also on the circle. Since the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circle, we can find the measure of ∠AXB by first finding the measure of arc ACB. Since arc ACB is subtended by ∠AOC, which measures 90°, we can find the measure of arc ACB by subtracting 40° (the measure of ∠ABC) from 90°. Therefore, arc ACB measures 50°. This means that ∠AXB is half the measure of arc ACB, so ∠AXB measures 25°.
Therefore, the measure of ∠X is 180° minus the sum of ∠AXB and ∠ABC, which gives us:
∠X = 180° - (25° + 40°) = 115°.
So, the measure of ∠X is 115°.
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Complete Question:
If O is the center of the circle of the figure and the ∠ABC = 40°, then the measure of ∠X
Select the expression that will calculate how many eighths are in 2 bars? Use the model to help you.
2 equal-sized bars each labeled
A.
2
÷
8
B.
8
÷
2
C.
2
÷
1
8
D.
8
÷
1
2
Answers
Step-by-step explanation:
To know how many eighths you have in two bars, simply divide 2 by 1/8
2/1 ÷ 1/8
Ans 2÷ ⅛
round each number to the nearest hundred
124= 2,311= 48=
Answers
Answer:
124= 100
2,311= 2,300
48= 0
Step-by-step explanation:
Place the two small triangles on top of the square what is the area of the each small triangle
Answers
The area of each small triangle is equal to √(7)/8 times the square of the length of one side of the square.
First, we need to find the area of the larger triangle that is created by placing the two small triangles on top of the square. Let's call the base of the larger triangle "b" and the height of the larger triangle "h".
To find "b", we can use the length of one side of the square since the two small triangles are placed on top of the square. Let's call the length of one side of the square "s".
Since the two small triangles are congruent, we know that the base of each small triangle is equal to half of one side of the square, which is s/2. Therefore, the total base of the larger triangle is equal to the sum of the bases of the two small triangles, which is s/2 + s/2 = s.
To find "h", we need to use the Pythagorean theorem since the larger triangle is a right triangle. Let's call the hypotenuse of the larger triangle "c". Since the hypotenuse is the diagonal of the square, we know that its length is √(2)*s.
Using the Pythagorean theorem, we can find the height of the larger triangle:
h² + (s/2)² = c² h² + (s/2)² = (√(2)s)² h² + s²/4 = 2s² h² = 7s²/4 h = √(7)/2 x s
Now that we have found "b" and "h", we can use the formula for the area of a triangle:
Area = 1/2 x base x height
Area of the larger triangle = 1/2 x s x √(7)/2 x s = √(7)/4 x s²
Finally, we can find the area of each small triangle by dividing the area of the larger triangle by two:
Area of each small triangle = 1/2 x (√(7)/4 x s²) = √(7)/8 x s²
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A small manufacturer makes two types of motors, models A and B. The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes 3 hours of wiring, 2 hours of drilling, and 1. 5 hours of assembly. Each model B must go through 2 hours of wiring, 1 hour of drilling, and 0. 5 hours of assembly. During the next production period, 240 hours of wiring time, 210 hours of drilling time, and 120 hours of assembly time are available. Each model A sold yields a profit of $22. Each model B can be sold for a $15 profit. Assuming that all motors that are assembled can be sold, find the best combination of motors to yield the highest profit
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The maximum profit of $3330 can be obtained by manufacturing 80 model A motors and 70 model B motors.
Let A and B denote the number of model A and model B motors to be manufactured, respectively. The goal is to maximize the total profit, which is given by the expression 22A + 15B
The given constraints imply that [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]
We can solve this problem using linear programming. Let P = 22A + 15B denote the total profit. Then, the optimization problem can be written as follows:
Maximize P = 22A + 15B
Subject to [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]
Using the Simplex Method, we obtain the optimal solution: A = 80, B = 70, and P = 2280 + 1050 = 3330$. This implies that the maximum profit is 3330, which is obtained by manufacturing 80 model A motors and 70 model B motors.
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In an integer programming problem, if it is desired to have variable X be exactly twice the value of variable Y, the constraint that enforces this condition would be written as: A. 2X + Y = 0 B. X + 2Y = 0 C. 2X - Y = 0 D. X - 2Y = 0
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The constraint 2X - Y = 0 states that the difference between variable X and twice variable Y must be equal to 0, meaning that X must be exactly twice the value of Y.The correct answer is C. 2X - Y = 0.
This constraint states that the difference between variable X and twice variable Y must be equal to 0. In other words, the value of variable X must be exactly twice the value of variable Y. This can be mathematically represented as 2X - Y = 0, meaning that 2 multiplied by X minus Y must equal 0. To illustrate this, let us assume that the value of variable X is 10 and the value of variable Y is 5. This means that 2X is equal to 20 and Y is equal to 5. When we subtract Y from 2X, we get 20 - 5 = 15. However, since the constraint states that the difference between X and twice Y must equal 0, the value 15 does not satisfy the condition. Therefore, the values of X and Y must be adjusted until the difference between X and twice Y equals 0. To satisfy the constraint, the value of X must be equal to 20 and the value of Y must be equal to 10. This means that X is exactly twice the value of Y, which satisfies the condition set by the constraint 2X - Y = 0.
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solve this question
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Step-by-step explanation:
(a + 1/a)³ = a³ + 3a + 3/a + 1/a³
We are given that a + 1/a = 4, so we can substitute that into the identity and simplify:
(a + 1/a)³ = (4)³ = 64
a³ + 3a + 3/a + 1/a³ = 64
a³ + 1/a³ + 3(a + 1/a) = 64
a³ + 1/a³ + 3(4) = 64
a³ + 1/a³ = 52
Therefore, we have proved that a³ + 1/a³ = 52 when a + 1/a = 4.
What is the elevation at point b? question 6 options: 700 ft 740 ft 780 ft 800 ft
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The elevation at point B is 740 ft. So, option B is correct.
The elevation is the height above or below a specified reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation.
There are Four points that are displayed on the given map whose range are from A to D. There are few additional lines in between these four places. The height between these points and lines is indicated on the map in feet, and from point A onwards there is an elevation difference of 20 feet. Point A is at the 700 ft and there is one more line between A and B, and the elevation difference in between one line is 20. So the elevation difference at point B is = 700 + 20 +20= 740 ft. So, option answer is B.
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Let f be a one-to-one function. If f(2)=7 and
f-1(-3)=5, determine the following ;
(a). f-1(7)
(b) f(5)
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a) We have f−1(7) = 2.Thus, the value of f-1(7) is 2.
b) We can conclude that f( f−1(−3) ) = f(5) = −3.Thus, the value of f(5) is -3.
(a) Determine f-1(7)Given that f be a one-to-one function and f(2)=7.Since f is one-to-one, there exists a unique inverse function f−1. We have f(2) = 7, hence 2 = f−1(7). Therefore, we have f−1(7) = 2.Thus, the value of f-1(7) is 2.(b) Determine f(5)Given that f be a one-to-one function and f−1(−3) = 5.Since f is one-to-one, there exists a unique inverse function f−1. Hence, f( f−1(x) ) = x and f−1( f(x) ) = x for all x in the domain of f. Also, f(2) = 7, thus f−1(7) = 2. Therefore, we can conclude that f( f−1(−3) ) = f(5) = −3.Thus, the value of f(5) is -3.
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Complete the problem. Let f(x)=(1)/(x) and g(x)=(1)/(x+3). Describe the transformation from f(x) to g(x).
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The transformation from f(x) to g(x) involves a horizontal shift and a change in the slope of the graph.The function g(x) is obtained from the function f(x) by a vertical shift of 3 units to the left.
Specifically, the denominator of g(x), x+3, represents a horizontal shift of 3 units to the left compared to the denominator of f(x), x. As a result, g(x) is shifted to the left relative to f(x). Furthermore, the shift causes the graph of g(x) to be steeper than that of f(x) at x=0. This is because, for small values of x, the difference between (1)/(x) and (1)/(x+3) becomes larger as x gets smaller. Therefore, the transformation from f(x) to g(x) involves a horizontal shift and a change in the slope of the graph.
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