Answer:
[tex] \huge \pi \: units [/tex]
Step-by-step explanation:
[tex]l = \frac{48 \degree}{360 \degree} \times 2\pi \: r \\ \\ = \frac{2}{24} \times 2 \times \pi \times 6 \\ \\ = \frac{24}{24} \times \pi \\ \\ = \pi \: units \\ [/tex]
Cual es la diferencia entre circulo y circunferencia
A solid right pyramid has a square base with an edge length of x cm and a height of y cm.
A solid right pyramid has a square base with an edge length of x centimeters and a height of y centimeters.
Which expression represents the volume of the pyramid?
One-thirdxy cm3
One-thirdx2y cm3
One-halfxy2 cm3
One-halfx2y cm3
Answer:
B
Step-by-step explanation:
One-thirdx2y cm3 i got it right on edg
The volume of the pyramid with a square base of side x and height (y) is (1/3)x²y cm³
How to calculate volume?Volume is the amount of space occupied by a three dimensional shape or object.
The area of the square base = x cm * x cm = x² cm²
The volume of the pyramid = (1/3) * area of square base * height = (1/3) * x² * y = (1/3)x²y cm³
The volume of the pyramid with a square base of side x and height (y) is (1/3)x²y cm³
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Solve the inequality.
x/3-x-1/2≥1 a. x≤-3 b. x≥-3 c. x≤3 d. x≥3
Answer:
x ≤-9/4
Step-by-step explanation:
x/3-x-1/2≥1
Multiply each side by 6 to get rid of the fractions
6(x/3-x-1/2)≥1*6
2x -6x -3≥6
Combine like terms
-4x-3≥6
Add 3 to each side
-4x-3+3≥6+3
-4x ≥9
Divide each side by -4, remembering to flip the inequality
-4x/-4 ≤9/-4
x ≤-9/4
On solving the inequality x/3 - x - 1/2 ≥ 1, we get x ≤ -3. Hence the correct option is A.
Solve the inequality: x/3 - x - 1/2 ≥ 1
Combine like terms: x/3 - (2x + 1)/2 ≥ 1
Get a common denominator: 2x/6 - 3(2x + 1)/6 ≥ 6/6
Simplify the equation: -4x - 3 ≥ 0
Solve for x: x ≤ -3
HELP PLEASE
Find the are of the circle.Leave your answer in terms of pie
A.9pi ft
B.324pi ft
C.18pi ft
D.81 pi ft
Answer:
A = 81 pi ft^2
Step-by-step explanation:
The area of a circle is found by
A = pi r^2
The radius is 9
A = pi 9^2
A = 81 pi ft^2
Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is an ace, or the 2nd a two, or the 3rd a three, or . . . , or the 13th a king, or the 14th an ace, or the 15th a two, and so on, we say that a match occurs. Compute the expected number of matches that occur.
Answer:
Expected number of matches that occur = 4 matches
Step-by-step explanation:
First of all, let X_i be the event that when we turn over card i if it matches the required cards face.
Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.
The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;
The expected number of matches when cards are drawn from a standard 52-card deck is 4.
We define a match for each card position as X_i = 1 if a match occurs, and X_i = 0 otherwise. The expectation E(X_i) for each card is 1/13 because the probability of the ith card being an i-matched card (Ace in the 1st position, Two in the 2nd position, and so on up to King in the 13th, then repeat with Ace) is 1/13.
Given there are 52 cards, each having the same pattern of matching, the expected number of matches is computed as:
E(X) = E(X_1 + X_2 + ... + X_52) = E(X_1) + E(X_2) + ... + E(X_52)
Since E(X_i) = 1/13 for all i:
E(X) = 52 * (1/13) = 4
Therefore, the expected number of matches is 4.
You see that country B can make 60 units of X and no Y at point j, or it can make no X and 30 Y at point f. So, if country B decides to produce point j instead of point f (if can do any point f through j) where it gives up units of Y it gets back X, how many units of X does it gain for each unit of Y given up
Answer:
Country B gaines 2 units of good X , per unit of Good Y sacrifised.
Step-by-step explanation:
Country B's production possibilities in form of goods (X,Y) are :
Point J [Only good X] = (60,0) Pont F [Only good Y] = (0,30)The country can produce 60 units of good X or 30 units of good Y, by complete specialisation in either good & not producing the other good.
The country has more (twice) advantage in producing good X. As, it can produce 2 times more good X, than good Y, from the same available resources.
If it decides to produce at point J, production specialising in Good X: It will produce only good X, no units of Y. This implies that - it gains 2 units of good X per unit of good Y sacrifised, as per their production potential ratio (60:30)
write 0.1 as a fraction in simpliest form
Answer:
1/1000
Step-by-step explanation:
A copy machine makes 36 copies per minute. How many copies does it make in four minutes and 45 seconds?
Answer: The copy machine makes 171 copies in 4 minutes and 45 seconds.
Step-by-step explanation:
Let's dissect the question. The copy machine makes 36 copies per minute.
36 per min.
To see how many copies it makes in 4 minutes and 45 seconds, we multiply 36 * 4.75. 45 seconds is 3/4ths of a minute, or 0.75 of a minute.
[tex]36 * 4.75=171[/tex]
It makes 171 copies in 4 minutes and 45 seconds.
Suppose a company that makes fitness watches samples 15 watches. They know the probability one of their watches fails, within 1 year of purchase, is 0.12. The chance one watch fails is independent of other watches. What type of distribution will best model the number of watches out of the 15 sampled that fail within 1 year
Answer:
Binomial probability distribution.
Step-by-step explanation:
For each watch, there are only two possible outcomes. Either it fails within 1 year of purchase, or it does not. The probability of a watch falling within 1 year of purchase is independent of other watches. So the type of of distribution will best model the number of watches out of the 15 sampled that fail within 1 year is the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
What is the probability of picking A-day that begins with the letter s
Answer:
28 or 29%
Step-by-step explanation:
There are 7 days total, 2 of which start with “S”, divide the 2 by 7 to get your percentage of 28-29%
The probability of picking a day that begins with the letter s is 2/7.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
There are seven days in a week, and two of them start with the letter s: Sunday and Saturday.
Now,
The probability of picking a day that begins with the letter s.
= 2/7
Or,
= 0.2857
Or,
= 0.2857 x 100%
= 28.57%.
Thus,
The probability of picking a day that begins with the letter s is 2/7.
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The average annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5% (Inflationdata). In 1980, the inflation rate was above 13%. If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year
Answer:
2.68% probability that inflation will be above 13% next year
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 3.37, \sigma = 5[/tex]
If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year
This is the pvalue of Z when X = 13. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13 - 3.37}{5}[/tex]
[tex]Z = 1.93[/tex]
[tex]Z = 1.93[/tex] has a pvalue of 0.9732
1 - 0.9732 = 0.0268
2.68% probability that inflation will be above 13% next year
Answer:
[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]
And we can find this probability using the complement rule and the normal standard distirbution table or excel:
[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the annual inflation of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(3.37,5)[/tex]
Where [tex]\mu=3.37[/tex] and [tex]\sigma=5[/tex]
We are interested on this probability
[tex]P(X>13)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]
And we can find this probability using the complement rule and the normal standard distirbution table or excel:
[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]
A die is rolled twice.
What is the probability that the first roll was a 6 and the second roll was an odd number?
Answer:
1/12
Step-by-step explanation:
1/6 * 3/6 (First roll has a one in 6 chance, second 3 in 6)
1*3 / 36 =
3 / 36 =
1/12
covert the units of weight 32IB 12oz = blank IB ? Help please as fast as you can
Answer:
32¾
Step-by-step explanation:
1 pound (lb) = 16 ounces
12 oz = 12/16 = 3/4 lb
32 pounds 12 oz
32 ¾ lb
The number of passengers on coaches travelling along 12 popular scenic routes are 29 42 45 39 36 41 38,37.43,35 and 40 find the mean numbres of passengers on coaches
In a group of 700 people, must there be 2 who have matching first and last initials? Why? (Assume each person has a first and last name.) Correct: Your answer is correct. . Let A be the set of 700 distinct people and let B be the 52 Incorrect: Your answer is incorrect. different unique combinations of first and last initials. If we construct a function from A to B, then by the Correct: Your answer is correct. principle, the function must be Correct: Your answer is correct. . Therefore, in a group of 700 people, it is Correct: Your answer is correct. that no two people have matching first and last initials.
Answer:
Yes, there are only 676 different possibilities, which is less than the number of people in the group.
Step-by-step explanation:
Assuming that the English alphabet has 26 different letters, the number of possible combinations of first and last name initials is:
[tex]n = 26*26\\n=676[/tex]
If we try to assign a different combination to each person in the group, it would only be possible to do it for the first 676 people, while the remaining 24 would have a repeated first and last initial. Therefore, the answer is yes, there must be 2 people who have matching first and last initials.
The Pigeonhole Principle in mathematics implies in a group of 700 people, there must be at least two people who have matching first and last initials.
Explanation:The concept of this problem involves understanding the Pigeonhole Principle in mathematics. Considering the English alphabet has 26 letters, we can have 26 possible first initials and 26 possible last initials. Therefore, there are 26x26=676 unique combinations of first and last initials. However, we have a group of 700 people which is more than 676. The Pigeonhole Principle states that if you try to distribute more items than there are containers, then at least one container must hold more than one item. Therefore, applying this principle, there must be at least two people among the group of 700 who have matching first and last initials because the number of people (700) is greater than the possible unique combinations of first and last initials (676).
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Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams1 shows that B was the most common correct choice, with 90 of the 400 questions having B as the answer. Does this provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely? Show all details of the test. The data are available in APMultipleChoice.
Answer:
Option B is not the most common correct choice.
Step-by-step explanation:
The multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.
The probability that any of these five option is the correct answer is:
[tex]p=\frac{1}{5}=0.20[/tex]
A random sample of 400 multiple-choice questions on Advanced Placement exam are selected.
The results showed that 90 of the 400 questions having B as the answer.
To test the hypothesis that option B is more likely the correct answer for most question, the hypothesis can be defined as:
H₀: All the options are equally probable, i.e. p = 0.20.
Hₐ: Option B is more likely the correct option, i.e. p > 0.20.
Compute the sample proportion as follows:
[tex]\hat p=\frac{90}{400}=0.225[/tex]
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.225-0.20}{\sqrt{\frac{0.20(1-0.20)}{400}}}= 1.25[/tex]
The test statistic is 1.25.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=P(Z>1.25)\\=1-P(Z<1.25)\\=1-0.89435\\=0.10565\\\approx 0.1057[/tex]
*Use a z-table.
The p-value is 0.1057.
The p-value of the test is quite large. Thus, the null hypothesis was failed to rejected.
Hence, it can be concluded that option B is not the most common correct choice.
Testing the hypothesis, it is found that since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.
At the null hypothesis, it is tested if all of them are equally as likely, that is, the proportion of B is [tex]p = \frac{1}{5} = 0.2[/tex]. Thus:
[tex]H_0: p = 0.2[/tex]
At the alternative hypothesis, it is tested if B is more likely, that is, if the proportion of B is more than 0.2. Thus:
[tex]H_1: p > 0.2[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.In this problem, the parameters are: [tex]p = 0.2, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.225 - 0.2}{\sqrt{\frac{0.2(0.8)}{400}}}[/tex]
[tex]z = 1.25[/tex]
The p-value of the test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 1.25.
Looking at the z-table, z = 1.25 has a p-value of 0.8944.
1 - 0.8944 = 0.1056.
Since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.
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Which of the following are like radicals? Check all of the boxes that apply.
Answer:
3x√x²y, –12x√x²y, x√yx², 2√x²y. or on Edge is A,B,D,F
Step-by-step explanation:
Got 100% on edge...
Multiply 2 and 1 half by 3 and 1 third
Answer:
8 1/3
Step-by-step explanation:
2 1/2 * 3 1/3
Change each to an improper fraction
2 1/2 = (2*2 +1)/2 = 5/2
3 1/3 = (3*3+1)/3 = 10/3
5/2 *10/3 = 50/6
Divide the top and bottom by 2
25/3
Change to a mixed number
3 goes into 25 8 times with 1 left over
8 1/3
estimate 1.3 - (-2.5)
Answer:
3.8
Step-by-step explanation:
Can someone please help me solve this
Answer:
30
Step-by-step explanation:
Everything has to add up to 90.
Add EVERYTHING together.
3x + 33
3x + 33 = 90
90 - 33 = 57
57 / 3 = 19
19 = x
19 x 2 = 38
38 - 8 = 30
Answer:
The answer for ∠CDF is 30°.
Step-by-step explanation:
It ia given that complemetary angle is 90° so we can make an expression in terms of x :
It ia given that complemetary angle is 90° so we can make an expression in terms of x :∠AFB + ∠BFC + ∠CFD = 90°
32° + (x+9)° + (2x-8)° = 90°
In order to find ∠CFD, we have to find the value of x first so we have to move all the like-terms to one side :
32° + x + 9° + 2x - 8° = 90°
2x + x = 90° - 32° - 9° + 8°
3x = 57°
Then divide both sides by 3 :
3x ÷ 3 = 57° ÷ 3
x = 19°
We have already found the value of x. Now, the question ask us to find ∠CDF, (2x-8)°. We just have to substitute x value into the expression :
Let x = 19,
∠CDF = 2x - 8
= 2(19) - 8
= 30°
Based on the list, how many different-color pants does Megan have to choose from?
Answer:
Whats on the list?????
Step-by-step explanation:
Consider the following time series data: Month 1 2 3 4 5 6 7 Value 23 14 20 11 19 24 15 (a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place. What is the forecast for month 8? If required, round your answer to one decimal place. Do not round intermediate calculation. (b) Compute MSE using the average of all the data available as the forecast for the next period. If required, round your answer to one decimal place. Do not round intermediate calculation. What is the forecast for month 8? If required, round your answer to one decimal place. (c) Which method appears to provide the better forecast?
Answer:
a) MSE = 61.33
Forecast for 8th month = 15
b) MSE = 34.51
Forecast for 8th month = 18
c) The average method provides a better forecast because of its low MSE
Explanation:
Check the attached file for the solvings.
To answer this two-part question, you'll need to calculate the mean square errors (MSE) using two different forecasting methods: using the most recent value as a forecast and using the average of all data for a forecast. The one with lower MSE is the correct prediction. The forecast for the next month is always based on the previous value or average value depending on the method.
Explanation:To answer this question, you need to understand how mean square error (MSE) and forecasting work. For (a), we use the last value as the forecast for the next value and compute MSE. For (b), we use the average of all data as the forecast for the next value and calculate the MSE. Finally, we compare which method gives a lower MSE, therefore better forecasting.
For (a), the forecast values would be the previous month's data, i.e., forecast for month 2 is 23, month 3 is 14 and so on. To calculate MSE, you subtract each monthly value from its forecast, square the result and find the average of these squares. The forecast for month 8 would be the value of month 7 which is 15.
For (b), you calculate the average of all the data available and use it as a forecast for all the next periods. The MSE and forecast for month 8 can be calculated in a similar manner as in (a).
In step (c), compare the MSE calculated in step (a) and step (b). A lower MSE indicates a better forecast and consequently represents an accurate choice for a predictive model.
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A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the legal 1000-pound limit, and desires σ to be less than 40. Tests were run on a random sample of n = 40 helmets, and the sample mean and variance were found to be equal to 825 pounds and 2350 pounds2 , respectively.Construct a 95% confidence interval for the population variance.
Answer:
Step-by-step explanation:
Hello!
You need to construct a 95% CI for the population variance of the forces the safety helmets transmit to wearers.
The variable of interest is X: Force a helmet transmits its wearer when an external force is applied (pounds)
Assuming this variable has a normal distribution, the manufacturer expects it to have a mean of μ= 800 pounds and a standard deviation of σ= 40 pounds
A test sample of n=40 was taken and the resulting mean and variance are:
X[bar]= 825 pounds
S²= 2350 pounds²
To estimate the population variance per confidence interval you have to use the following statistic:
[tex]X^2= \frac{(n-1)S^2}{Sigma^2} ~~X^2_{n-1}[/tex]
And the CI is calculated as:
[[tex]\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}}[/tex];[tex]\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}}[/tex]]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{39;0.975}= 58.1[/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{39;0.025}= 23.7[/tex]
[[tex]\frac{39*2350}{58.1}[/tex];[tex]\frac{39*2350}{23.7}[/tex]]
[1577.45; 3867.09] pounds²
Using a confidence level of 95% you'd expect that the interval [1577.45; 3867.09] pounds² contains the value of the population variance of the force the safety helmets transmit to their wearers when an external force is applied.
I hope this helps!
Can someone please answer this question I am confused
Answer:
Step-by-step explanation:
what should 2.33 be multiplied by to make a whole number
Answer:
You dont multiply anything, you just round
Step-by-step explanation:
basically, you round the 2.3 to the nearest whole number which is most likely 2 because 3 is under five so it doesnt round up
An agricultural researcher plants 25 plots with a new variety of yellow corn. Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean LaTeX: \mu and standard deviation LaTeX: \sigma = 10 bushels per acre.Q: Which of the following would produce a confidence interval with a smaller margin of error than the 90% confidence interval?A) Plant only 5 plots rather than 25, because 5 are easier to manage and control.B) Plant 10 plots rather than 25, because a smaller sample size will result in a smaller margin of error.C) Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error.D) Plant 100 plots rather than 25, because a larger sample size will result in a smaller margin of error.
Answer:
Correct Answer: CA larger sample size results in a smaller margin error, i.e. with a plant of 100 plots instead of 25, the margin error will be smaller.
Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
An agricultural researcher plants 25 plots with a new variety of yellow corn.
Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean and standard deviation of 10.
We need to find a confidence interval with a smaller margin of error than the 90% confidence interval
n=25, x=150,s=10,a=0.95
Unknown mean u means we use t table.
[tex]150 ± t_{0.975} \frac{10}{\sqrt{25}}[/tex]
150±[tex]t_{0.975}[/tex]×2
Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
Hence, option C is correct. Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error
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A firework rocket is shot upward at a rate of 640ft/sec. Use the projectile formula h= -16t^2 +v0t to determine the times when the height of the firework will be 1,200 feet. Round your answer to the nearest whole number.
Answer:
2 seconds and 38 seconds
Step-by-step explanation:
h=-16t²-vot
1,200=-16t²-640t
turn this into standard form
16t²-640t+1200=0
now plug thes numbers into the quadratice formula
a 16 b -640 c 1200
solve with quadratic formula to get ≅2 and ≅38 seconds
Answer:
t≈2 seconds,t≈38 seconds
Step-by-step explanation:
h=−16t2+ v0t
Step 1. Solve the equation.
1,200= −16t^2+ 640t
We know the velocity, v0, is 640 feet per second.
The height is 1,200 feet. Substitute the values.
This is a quadratic equation. Rewrite it in standard form. Solve the equation using the quadratic formula.
ax^2 + bx + c . = 0
16t^2 −640t + 1,200 = 0
Identify the values of a, b, and c.
a=16, b=−640, c=1,200
Write the quadratic formula.
t=−b± √b2−4ac‾‾‾‾‾‾‾‾
2a
640+ √332,800‾‾‾‾‾‾‾‾ t= √640− √332,800‾‾‾‾‾‾‾
32 32
Rewrite to show two solutions.
t=640+332,800‾‾‾‾‾‾‾‾√32,t=640−332,800‾‾‾‾‾‾‾‾√32
Approximate the answer with a calculator.
t≈2 seconds,t≈38 seconds
Step 2. Check the answer. The check is left to you.
Step 3. Answer the question.
The firework will go up and then fall back down. As the firework goes up, it will reach 1,200 feet after approximately 2 seconds. It will also pass that height on the way down at 38 seconds.
{71.NS.6b and 18.NS.6c} The three points (4,0), (-6,0), and (-6,-4) form three corners of a rectangle. Determine the coordinates of the fourth point.
Answer:
(4,-4)
Step-by-step explanation:
Diagonals of a rectangle share a common midpoint
(4-6)/2 , (0-4)/2 = (-6+x)/2, (0+y)/2
-2 = -6 + x
x = 4
-4 = y
We determined the fourth point of a rectangle by ensuring that the sides of the rectangle are parallel to the axes and the sides are equal in length. The fourth point of the rectangle formed by the points (4,0), (-6,0), and (-6,-4) is (4,-4).
Explanation:The fourth point of the rectangle should have the same x-coordinate as the point (4,0) and the same y-coordinate as the point (-6,-4). Therefore, the fourth point is (4,-4)
To better understand the reasoning, let's consider the points on a plane. We recall that rectangles have sides of equal length and parallel to the axes. Therefore, since the line connecting (4,0) and (-6,0) is parallel to the x-axis, the fourth point's x-coordinate has to be the same as the point on the opposite side of the rectangle, which is 4. Similarly, as the line connecting (-6,0) and (-6,-4) is parallel to the y-axis, the fourth point's y-coordinate has to equal the y-coordinate of the point on the opposite side (-6,-4), which is -4. Hence, the fourth point is (4,-4).
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Dan rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 15
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
The factors of 15 are numbers that can divide even through 15 without any remainders.
These numbers are 1, 3, 5 and 15;
When we roll two fair dice once, there are about 36 possible out comes and this is the sample space of rolling this fair dice.
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
The total that will give a factor of 15;
(1, 2) (2, 3) (1, 4) (2, 1) (3, 2) (4, 1)
Out of the 36 possible outcomes, we have 6 whose sum will give a factor of 15;
Probability of this = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex]
2x + 3y = 12 is an equation in slope intercept form.
True
False