Answer:
9
Step-by-step explanation:
perfect square sholud be \((a+b)^{2} \)
so (w+3)*(w+3) is perfect square and extention of it is =>w*w+6w+9
If it takes 10 workers 4 days to fence a field how long would it take 8 workers
10 workers - 4 days
8 workers - x days
\(10\cdot4=8x\\8x=40\\x=5\)
5 days.
Erica cut 2/3 yard ribbon into pieces that are 1/6 yard long how many pieces of ribbon did she cut
Answer:
4 pieces
Step-by-step explanation:
To perform the calculation, it's easier for both values to have the same denominator.
2/3 yards is the same as 4/6 yards.
Now we have two values with the same denominator: 4/6 and 1/6.
(4/6) / (1/6) = 4.
What is the value of 9 in
quinary number?
Answer:
14x14x14x14x14=14.5
Step-by-step explanation:
Step-by-step explanation:
hope it is helpful to you
Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement.The mean is the measure of central tendency most likely to be affected by an outlier.
The statement that the mean is most likely to be affected by an outlier, is True.
Why is the mean affected by outliers ?The mean (average) of a set of data can be significantly affected by outliers, or data points that are much higher or lower than the majority of the data. Outliers can greatly influence the mean, pulling it away from the center of the data and making it less representative of the majority of the data.
This can cause the mean to become skewed and can give a false representation of the typical values in the data set. This is why it's important to consider the presence of outliers when calculating the mean and to use other measures of central tendency, such as the median or mode, to get a better understanding of the distribution of data in a set.
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What is the correct order of steps to solve 8 2(-x-5)=26?
Answer:
82(-x-5)=26
-82x-410=26
-410-26=82x
-436/82=x
x=-218/41
Please help! Correct answer only!
In a raffle, one ticket out of 1,000 will win a $870 prize, one ticket will win a $820 prize, and one ticket will win a $740 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
Answer:
" Expected Payoff " ⇒ $ 1.56 ; Type in 1.56
Step-by-step explanation:
Consider the steps below;
\(Tickets That Can Be Entered - 1 Ticket,\\Total Tickets Entered - 1000 Tickets,\\\\Proportion - 1 / 1000,\\Money One ( First Ticket ) = 820 Dollars,\\Money One ( Second Ticket ) = 740 Dollars,\\\\Proportionality ( First ) - 1 / 1000 = x / 820,\\Proportionality ( Second ) - 1 / 1000 = x / 740\\\\1 / 1000 = x / 820,\\1000 * x = 820,\\x = 820 / 1000,\\x = 0.82,\\\\1 / 1000 = x / 740,\\1000 * x = 740,\\x = 740 / 1000,\\x = 0.74\\\\Conclusion ; " Expected Payoff " = 0.82 + 0.74 = 1.56\)
Solution; " Expected Payoff " ⇒ $ 1.56
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California. In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem. PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34. The standard error for the difference in proportions is 0.011.
Researchers want to decrease the margin of error by adjusting the confidence level. Which confidence interval will have the smallest margin of error (MOE)?
a) 90% confidence interval
b) 95% confidence interval
c) 99% confidence interval
90% confidence interval will have the smallest margin of error.
What is global warming?
Long-term changes in temperature and weather patterns are referred to as climate change. These changes may be organic, but since the 1800s, human activity has been the primary cause of climate change. This is primarily because burning fossil fuels, such as coal, oil, and gas, releases gases that trap heat.
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California.
In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem.
PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34.
The standard error for the difference in proportions is 0.011.
The correct option is (a).
As the confidence level decreases margin of error decreases.
So 90% confidence interval will have the smallest margin of error.
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find teh exact value of sin 2x given that sec x = 3/2 and csc y = 3 and x and y are in quadrant 1
The exact value of \(sin 2x\) is \(4√5/9.\)
Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.
In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)
Also, we know that sin \(2x = 2 sin x cos x.\)
Now, we need to find sin x.
Having sec x = 3/2, we can use the Pythagorean identity
\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)
As x is in the first quadrant, it lies between 0° and 90°.
Therefore, x cannot be negative.
Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)
Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)
Therefore, the exact value of sin 2x is 4√5/9.
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Example 4: Oscar receives two job offers. The first job offers a bi-weekly salary of $1200. The
second job offers a semi-monthly salary of $1250. Which job pays more?
Answer:
The bi-weekly job!
Step-by-step explanation:
With a bi-weekly salary, your employer pays you every second week.
Since there are 52 weeks in a year: 52/2 = 26
This means you will get a total of 26 pay checks a year.
26 x 1200 = 31200
Therefore, you earn $31200 a year if you are paid bi weekly.
With a semi-monthly salary your employer pays you twice a month.
Since there are 12 months in a year: 12 x 2 = 24
This means you get a total of 24 pay checks a year.
24 x 1250 = 30000
Therefore, you earn $30000 a year if you are paid semi-monthly.
31200 > 30000
Therefore, you earn more on a bi-weekly salary.
PLZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEEEE
Answer:
D.8
Step-by-step explanation:
A cube's volume is basically the side length multiplied by itself 3 times, so if it was increased by a factor of 2, it would mean 2x2x2 which equals 8.
is the function f a k-to-1 correspondence for some positive integer k? if so, for what value of k? justify your answer
We cannot provide a value for k as requested in the question. Hence, our answer is: No, we cannot determine whether the function f is a k-to-1 correspondence for some positive integer k without having the function f.
justify your answer," we need to first understand what a k-to-1 correspondence is.
A k-to-1 correspondence is a function in which each element in the range has exactly k preimages. In other words, if the function f maps elements from set A to set B, then for each element b in set B, there are exactly k elements in set A that map to b.
In this case, we need to determine if the function f is a k-to-1 correspondence for some positive integer k.Now, let's justify our answer. Since we do not have the function f, we cannot determine whether it is a k-to-1 correspondence or not. Therefore, we cannot provide a value for k as requested in the question. Hence, our answer is: No, we cannot determine whether the function f is a k-to-1 correspondence for some positive integer k without having the function f.
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What is the Equation of Continuity and 2) what are its application(s)? please be descriptive
The Equation of Continuity is a principle in fluid dynamics that states the conservation of mass flow rate in a fluid system.
The Equation of Continuity is a fundamental principle in fluid dynamics that states the conservation of mass flow rate in a fluid system. It states that the mass entering a given volume per unit of time must equal the mass leaving that volume per unit of time.
Mathematically, the equation is expressed as A₁v₁ = A₂v₂, where A represents the cross-sectional area of the flow and v represents the velocity of the fluid at that point.
The Equation of Continuity finds applications in various areas of science and engineering. In fluid mechanics, it is used to analyze fluid flow through pipes, nozzles, and other channels.
It helps determine the relationship between flow velocity and cross-sectional area, aiding in the design and optimization of fluid systems.
The equation is also applied in fields like hydraulics, aerodynamics, and cardiovascular physiology to study and predict fluid behavior and ensure the efficient and safe functioning of fluid-based systems.
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24 is 3/4% of what number
Answer:
32
Step-by-step explanation:
Alright, so think of the "what number" as x in this case. (Or any number/symbol you choose.)
So our simple equation looks something like this:
\(24= x *\frac{3}{4}\)
So, to find out what the "what number" would be we'd flip the fraction around/find the reciprocal and multiply 24 by it. That gives us "x" or the number we're missing.
So: \(24 * \frac{4}{3} = x\)
Doing the simple math we get:
\(24 * \frac{4}{3} = 32\).
32 is your answer.
Hope this helps and have a nice day! Sorry I'm not great at explaining it!
4. (3 marks) A married couple decides that they will continue to have children until they have 3 boys. It is assumed that having a boy or a girl is equally likely. (a) What is the probability that the couple has 5 children until they have 3 boys? (b) How many children does this couple expect to have until they have 3 boys?
This couple can expect to have 3.75 children until they have 3 boys. (a)To calculate the probability that the couple has 5 children until they have 3 boys, we need to consider the possible outcomes that could result in having 3 boys within the first 5 children. One possible outcome is having the first three children be boys and the next two be girls.
Another possible outcome is having the first two children be girls, followed by three boys. Another outcome is having one girl and two boys, followed by two girls and then three boys. There are actually ten different possible outcomes that could result in having 3 boys within the first 5 children. Since each birth has an equal probability of being a boy or girl, each of these outcomes has a probability of 1/2^5 = 1/32. Therefore, the probability that the couple has 5 children until they have 3 boys is the sum of these probabilities, which is 10/32 or 0.3125.
(b) To calculate the expected number of children this couple will have until they have 3 boys, we need to consider the probability of having each possible number of children. Let X be the number of children this couple will have until they have 3 boys. We know that X is at least 3, since it takes at least 3 children to have 3 boys. We can calculate the probability of having X = 3 by having the first three children be boys, which has a probability of 1/2^3 = 1/8. We can calculate the probability of having X = 4 by having the first three children be any combination of boys and girls that does not result in 3 boys, followed by a fourth boy, which has a probability of 1/2^4 * 1/2 = 1/16. We can calculate the probability of having X = 5 by using the calculation from part (a), which is 10/32. We can calculate the probability of having X = 6 by having the first five children be any combination of boys and girls that does not result in 3 boys, followed by a sixth boy, which has a probability of 1/2^5 * 1/2 = 1/32. Continuing in this way, we can calculate the probability of having any value of X. To calculate the expected value of X, we multiply each possible value of X by its probability and then add up all of these products. Doing so yields:
E(X) = 3*(1/8) + 4*(1/16) + 5*(10/32) + 6*(1/32) + ...
We can simplify this expression by factoring out 1/16 and noticing that the remaining terms form a geometric series with first term 5 and common ratio 1/2. Therefore, we have:
E(X) = 3*(1/8) + 5*(1/16)*(1 + 1/2 + 1/4 + ...) = 3.75
Therefore, this couple can expect to have 3.75 children until they have 3 boys.
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Suppose you are given the function f(x) = 7x and asked for f(-6). This is the same as asking for the value of the function at x = ?
Answer:
the correct answer is -6
cannonball is shot into the air. its height can be described by the equation h = -5t2 + 40t, where h is the height in feet and t is the time is seconds. when will the cannonball hit the ground?
Answer:
Step-by-step explanation:
hello :
the cannonball hit the ground when h=0
-5t² + 40t=0 means : -5t(t- 8)=0
t=8
simplify 8/9/20 please
The value of 8/9/20 could be either 0.04 or 17.77.
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.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and a lower word is called the denominator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
Given the fraction,8/9/20
Case 01)
(8/9)/20 = 0.888/20 = 0.044.
Case 02)
8/(9/20) = 8/0.45 = 17.77.
Hence "The value of 8/9/20 could be either 0.04 or 17.77".
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Two firms producing identical products engage in price competition. Cost of firm 1 is $20 per unit produced and cost of firm 2 is $15 per unit produced. There are no fixed costs. Firms produce only after they learn the quantity demanded. Each firm can choose any real number in the interval [15,25] as its price.
For tie-breaking we will assume that if both firms set the same price, all consumers purchase from firm 2.
The payoff/profit function of firm 1 is:
(p1 - 20)(100 - p1) if p1 is less than or equal to p2,
0 if p1 is greater than p2
The payoff/profit function of firm 2 is:
(p2 - 15)(100 - p2) if p2 is less than p1,
0 if p2 is greater than or equal to p1
Given all of this information, solve the following parts of the problem:
a) is p1 = 20, p2 = 19.50 a Nash Equilibrium?
b) is there a Nash Equilibrium in which Firm 2 makes a positive profit?
c) How many strategies does player 1 have?
d) is p1 = 15, p2 = 15 a Nash Equilibrium?
e) is p1 = 21, p2 = 21 a Nash Equilibrium?
a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.
b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.
c) Player 1 has infinitely many strategies.
d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.
e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.
What is Nash Equilibrium?Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.
Finding Nash Equilibrium
a) Is p1 = 20, p2 = 19.50 a Nash Equilibrium?No. Firm 1 has an incentive to decrease the price to 19.49, thus breaking the tie in its favour. So p1=20, p2=19.5 is not a Nash equilibrium.b) Is there a Nash Equilibrium in which Firm 2 makes a positive profit?Yes. There are several equilibria in which Firm 2 makes a positive profit. One such equilibrium is when both firms charge the same price of 15, at which both firms earn a profit of 375.c) How many strategies does player 1 have?Player 1 has infinitely many strategies to choose from as they can choose any real number in the interval [15,25] as their price.d) Is p1 = 15, p2 = 15 a Nash Equilibrium?Yes. This is a Nash Equilibrium because neither firm has an incentive to change their strategy as they are earning non-zero profits. Both firms earn a profit of 375.e) Is p1 = 21, p2 = 21 Nash Equilibrium?No. If Firm 1 changes its price to 20.99, its profit increases from 405 to 407.99. Therefore, p1=21 and p2=21 is not a Nash Equilibrium.Learn more about Nash equilibrium at
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Consider the function f(x)=2−6x^2, −4 ≤ x ≤ 2, The absolute maximum value is and this occurs at x= ___________
The absolute minimum value is and this occurs at x= __________
The absolute maximum value of the function f(x) = 2 - 6x^2 on the interval [-4, 2] is 2, and it occurs at x = -4. The absolute minimum value is -62 and it occurs at x = 2.
To find the absolute maximum and minimum values of the function f(x) = 2 - 6x^2 on the interval [-4, 2], we need to evaluate the function at the critical points and endpoints of the interval.
First, we find the critical points by taking the derivative of f(x) and setting it equal to zero:
f'(x) = -12x
-12x = 0
x = 0
Next, we evaluate the function at the critical point x = 0 and the endpoints x = -4 and x = 2:
f(-4) = 2 - 6(-4)^2 = 2 - 96 = -94
f(0) = 2 - 6(0)^2 = 2
f(2) = 2 - 6(2)^2 = 2 - 24 = -22
From the above calculations, we see that the absolute maximum value of 2 occurs at x = -4, and the absolute minimum value of -62 occurs at x = 2.
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Help me solve this problem please
Answer: -3
Step-by-step explanation: PLEASE GIVE BRAINLIEST IT HELPS ALOT. THANKYOU.
a sample of 1500 computer chips revealed that 69% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that 72% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.05 level to dispute the company's claim? state the null and alternative hypotheses for the above scenario.
At a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.
What is the null hypothesis in statistics?
The null hypothesis in inferential statistics states that two possibilities are the same. The null hypothesis states that the observed difference is solely due to chance. The likelihood that the null hypothesis is true can be calculated using statistical tests.
Sample size, n =1500
The sample proportion of the chips that do not fail in the first 1000 hrs of their use, \(\hat{p} = 0.69\)
Null Hypothesis, H0: p=0.72
Alternate Hypothesis, \(Ha: p \neq 0.72\)
Test statistic,
\(z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} - \frac{0.69-0.72}{\sqrt{\frac{0.72(1-0.72)}{1500}}} = -2.5877\)
Critical Value,
\(Z_{0.05/2} =\)±1.96
Now, since the absolute value of the test statistic i.e, 2.5877 is greater than the absolute value of the critical value i.e, .1.96, thus we will reject the null hypothesis.
Thus at a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.
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Bags of jelly beans have a mean weight of 353 gm with a standard deviation of 6 gm. Use Chebyshev's Theorem to find a lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm Lower bound bags
Based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.
Chebyshev's Theorem states that for any given number k greater than 1, at least (1 - 1/k²) of the data values in a dataset will fall within k standard deviations of the mean.
In this case, we have a sample size of 225 bags and a mean weight of 353 gm with a standard deviation of 6 gm.
To find a lower bound for the number of bags that weigh between 335 and 371 gm, we need to calculate the range within k standard deviations of the mean.
First, let's find the number of standard deviations for the given range:
Lower range: (335 - 353) / 6 = -3
Upper range: (371 - 353) / 6 = 3
Since we want to find the lower bound, we consider the lower range and use its absolute value: |-3| = 3.
Now, we can use Chebyshev's Theorem to find the lower bound:
(1 - 1/k²) ≤ (1 - 1/3²) = 1 - 1/9 = 8/9
This means that at least 8/9 of the bags will fall within 3 standard deviations of the mean.
To find the lower bound for the number of bags, we multiply this probability by the sample size:
Lower bound = (8/9) * 225 = 200
Therefore, based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.
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seven times a two-digit number is equal to four times the number obtained by reversing the digits. if the difference between the digits is 3. find the number.
The required number is 36 .
Given,
The difference between the digits is 3 .
Let numbers be x at ones place & y at tens place so,
10y+x is the digit.
Reversed digit =10x+y
According to the question,
∴7(10y+x)=4(10x+y)
⇒x=2y⟶(i)
Now,
Given, x-y=3
from equation (i)2y=x substitute in the above equation.
2y-y=3
y=3
So,
x=2y=2×3=6
∴ Required original no: is =10y+x=10×3+6=36.
We can also check that the difference of the digit of 36 is 3 (6-3=3) .
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Prepare a grid with magic number 30. You can choose any set of numbers in sequence but the numbers should not be repeated.
The grid of numbers with a row and column sum of 30 is
3 15 12
17 11 2
10 4 16
How to prepare the grid?The grid in the question has a row sum and column sum of 15
The question implies that we create a similar grid with a row sum and column sum of 30
Represent the grid as follows:
a b c
d e f
g h j
So, we have the following sum of rows
a + b + c = 30
d + e + f = 30
g + h + j = 30
And, we have the following sum of rows
a + d + g = 30
b + e + h = 30
c + f + j = 30
Using trial by error, we have:
3 + 15+ 12 = 30
17 + 11 + 2 = 30
10 + 4 + 16 = 30
When the columns are added, we have
3 + 17 + 10 = 30
15 + 11 + 4 = 30
12 + 2 + 16 = 30
Hence, the grid of numbers is
3 15 12
17 11 2
10 4 16
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Let f(x) = xe^-x+ ce^-x, where c is a positive constant. For what positive value of c does f have an absolute
maximum at x = -5?
Answer:
\(c=6\)
Step-by-step explanation:
The absolute maximum of a continuous function \(f(x)\) is where \(f'(x)=0\). Therefore, we must differentiate the function and then set \(x=-5\) and \(f'(x)=0\) to determine the value of \(c\):
\(f(x)=xe^{-x}+ce^{-x}\)
\(f'(x)=-xe^{-x}+e^{-x}-ce^{-x}\)
\(0=-(-5)e^{-(-5)}+e^{-(-5)}-ce^{-(-5)}\)
\(0=5e^{5}+e^{5}-ce^{5}\)
\(0=e^5(5+1-c)\)
\(0=6-c\)
\(c=6\)
Therefore, when \(c=6\), the absolute maximum of the function is \(x=-5\).
I've attached a graph to help you visually see this.
the velocity function, in feet per second, is given for a particle moving along a straight line, where t is the time in seconds. Findthe displacement andthe total distance that the particle travels over the given interval.
When given a displacement function, its derivative is the velocity function. Vice versa, when given a velocity function, its integral is the displacement function.
So, we need to integrate the given function to find the displacement function.
\(\begin{gathered} \int(t^3-8t^2+15t)dt \\ \\ =\int t^3dt-\int8t^2dt+\int15tdt \\ \\ =\int t^3dt-8\int t^2dt+15\int tdt \\ \\ =\frac{t^4}{4}-8(\frac{t^3}{3})+15(\frac{t^2}{2})+C \\ \\ =\frac{t^4}{4}-\frac{8t^3}{3}+\frac{15t^2}{2}+C \end{gathered}\)To solve for C, we need to have a known displacement. We know that when t = 0, the object has not moved yet. Therefore, it is safe to assume that d must be 0.
\(\begin{gathered} \frac{t^4}{4}-\frac{8t^3}{3}+\frac{15t^2}{2}+C=0 \\ \\ \frac{0^4}{4}-\frac{8(0^3)}{3}+\frac{15(0^2)}{2}+C=0 \\ \\ C=0 \end{gathered}\)So now we know that the displacemnet function is:
\(d(t)=\frac{t^{4}}{4}-\frac{8t^{3}}{3}+\frac{15t^{2}}{2}\)We can now solve for the total displacement when t = 5.
\(\begin{gathered} d(t)=\frac{t^{4}}{4}-\frac{8t^{3}}{3}+\frac{15t^{2}}{2} \\ \\ d(5)=\frac{5^4}{4}-\frac{8(5^3)}{3}+\frac{15(5^2)}{2} \\ \\ d(5)=\frac{625}{4}+\frac{1,000}{3}+\frac{375}{2} \\ \\ d(5)=\frac{8,125}{12}\approx677.083 \end{gathered}\)Therefore, the total displacement is 677.083 feet.
Because the particle is moving along a straight line, then the distance is equal to the displacement.
Point M is the midpoint of line segment CD,
shown below.
What are the coordinates of point M?
C (6,10)
M
D (20, 18)
Answer:
M(13, 14)-------------------------
Each coordinate of the midpoint is the average of endpoints:
x = (6 + 20)/2 = 26/2 = 13y = (10 + 18)/2 = 28/2 = 14Therefore M is (13, 14).
Which graph represents the solution to this inequality?
-1/4 (12x+8) ≤ -2x+11
A. a straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passes through minus 5
B.
A straight line passing from minus 17 to minus 5. A ray with a red line starts at point minus 13 and passes through minus 17
C.
A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5
D.
A straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passes through minus 17
A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.
This graph represents the solution to this inequality.
What is inequality?
An inequality in mathematics is a relation that compares two integers or other mathematical statements in an unequal way. The majority of the time, height comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
Given inequality:
(-1/4)*(12x + 8) < -2x + 11
First, we need to solve it for knowing the value of x,
So,
(-1/4)*(12x + 8) < -2x + 11
Or, -3x - 2 < -2x + 11
Or, -2 - 11 < -2x + 3x
Or, -13 < x
A ray with a red dot at minus 13, and it passes through minus 5.
Hence the correct answer is C; a straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.
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When examining the plots, only one displays a straight line going from -17 to -5 and a ray going from -13 to -5. (indicating that x can be any value greater than or equal to -13) Thus, option C is correct.
What is the inequality?To solve the inequality, we can simplify it by first distributing the -1/4 on the left side:
\(-3x - 2 ≤ -2x + 11\)
Next, we can isolate the variable on one side by subtracting -2x from both sides:
\(-x - 2 ≤ 11\)
Finally, we can isolate the variable by adding 2 to both sides:
\(-x ≤ 13\)
And since we want to solve for x, we need to multiply both sides by -1, which will flip the direction of the inequality:
\(x ≥ -13\)
This means that x can be any value greater than or equal to \(-13\) .
Therefore, Looking at the graphs, the only one that shows a straight line passing from -17 to -5 and a ray starting at -13 and passing through -5 (indicating that x can be any value greater than or equal to -13)
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What is the area of the figure composed of a parallelogram, a square and a rectangle ?
Answer : The area of the figure composed of a parallelogram, a square and a rectangle is 126 in².
Step-by-step explanation :
Area of composed figure = Area of parallelogram + Area of square + Area of rectangle
First we have to calculate the area of parallelogram.
Area of parallelogram = Base × Height
Given:
Base = 10 in
Height = 3.5 in
Area of parallelogram = 10 in × 3.5 in
Area of parallelogram = 35 in²
Now we have to calculate the area of square.
Area of square = (Side)²
Given:
Side = 4 in
Area of square = (4 in)²
Area of square = 16 in²
Now we have to calculate the area of rectangle.
Area of rectangle = Length × Breadth
Given:
Length = 12.5 in
Breadth = 6 in
Area of rectangle = 12.5 in × 6 in
Area of rectangle = 75 in²
Now we have to calculate the composed figure.
Area of composed figure = Area of parallelogram + Area of square + Area of rectangle
Area of composed figure = 35 in² + 16 in² + 75 in²
Area of composed figure = 126 in²
Therefore, the area of the figure composed of a parallelogram, a square and a rectangle is 126 in².
The area of the given figure is 126in²
Composite figuresThe given figure is a composite figure composed of a parallelogram, a square and a rectangle.
Get the area of the square
Area = L²
Area of the square = 4² = 16in²
Area of the rectangle = 6 * 12.5
Area of the rectangle = 75in²
For the parallelogram:
Area of the parallelogram = Base * Height
Area of the parallelogram = 10 * 3.5
Area of the parallelogram = 35 in²
Area of the figure = 75in² + 35in² + 16in²
Area of the figure = 126in²
Hence the area of the figure is 126in²
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What do all of the numbers in the box below have in common 60% 0.57 0.9 120%
Answer:
First of all, the numbers are all positive numbers
They can all be divided by the number 3
They are all rational numbers, this means that they can be expressed as a ratio of two numbers