(625 • (a4)) + 22b4
54a4 + 22b4
Final result :
625a4 + 4b4
The intersection of plane A and plane S will be
The intersection of lines n and k is
Point X is the intersection of
Answer:
bjbjbfbdvdjbfv
Step-by-step explanation:
fdbfdvbdjv
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Answer:
[tex]p = 2[/tex] if given vectors must be linearly independent.
Step-by-step explanation:
A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:
[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]
In other words, the following system of equations must be satisfied:
[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)
[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)
[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)
By Eq. 1:
[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]
Eq. 1 in Eqs. 2-3:
[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]
[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]
[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)
[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)
By Eq. 3b:
[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]
Eq. 3b in Eq. 2b:
[tex](p-2)\cdot \alpha_{2} = 0[/tex]
If [tex]p = 2[/tex] if given vectors must be linearly independent.
How many terms of the series 2 + 5 + 8 + … must be taken if their sum is 155
9514 1404 393
Answer:
10
Step-by-step explanation:
The sum of terms of an arithmetic series is ...
Sn = (2a +d(n -1))·n/2 = (2an +dn^2 -dn)/2
For the series with first term 2 and common difference 3, the sum is 155 for n terms, where ...
155 = (3n^2 +n(2·2 -3))/2
Multiplying by 2, we have ...
3n^2 +n -310 = 0 . . . . . arranged in standard form
Using the quadratic formula, the positive solution is ...
n = (-1 +√(1 -4(3)(-310)))/(2(3)) = (-1 +√3721)/6 = (61 -1)/6 = 10
10 terms of the series will have a sum of 155.
Step-by-step explanation:
[tex]\displaystyle \ \Large \boldsymbol{} S_n=\frac{2a_1+d(n-1)}{2} \cdot n =155 \\\\ \frac{4+3(n-1)}{2} \cdot n =155 \\\\\\ 4n+3n^2-3n=310 \\\\ 3n^2+n-310=0 \\\\D=1+3720=3721=61^2\\\\n_1=\frac{61-1}{6} =\boxed{10} \\\\\\n_2=\frac{-61-1}{3} \ \ \o[/tex]
In a survey of 15000 students of different schools, 40% of them were found to have tuition before the see examination. Among them 50% studied only mathematics ,30% only science and 10% studied others subject. how many student studied mathematics as well as science.
Answer:
600
Step-by-step explanation:
first, 40% of 15000 is 6000,
10% of 6000, which is the number of students studying mathematics as well as science, 600
Answer:
•600 students studied both the subject.
Find the sum. 31.25 + 9.38
Answer:
40.63
Step-by-step explanation:
31.25+9.38= 40.63
Hope this helps
Answer: 40.63
Look at the image for shown work.
A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?
Emily and Kate were at a cheerleading competition this fall.They cheered 12 rounds. Each round lasted 8.24 minutes. Calculate the total number of minutes, Emily cheered and the total number of minutes Kate cheered at the competition
Answer:
98.88
Step-by-step explanation:
Given: They cheered 12 rounds. Each round = 8.24
To find the total number, multiply how much one round is with the total number of rounds.
8.24
× 12
-----------
1648
+ 8240
----------
98.88
Each girl cheered 98.88 minutes. If you need this estimated, the answer would be 99 minutes.
WORTH 30 POINTS PLEASE HELP!!!!! WILL GIVE POINTS
Answer:
2/3 and 4/6
Step-by-step explanation:
In a random sample of people, the mean driving distance to work was miles and the standard deviation was miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a % confidence interval for the population mean . Interpret the results. Identify the margin of error.
Complete Question
In a random sample of ten people, the mean driving distance to work was 23.1 miles and the standard deviation was 6.6 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 99% confidence interval for the population mean Interpret the results. Identify the margin of error.
Answer:
The 99% confidence interval is [tex]16.32< \mu <29.88[/tex]
The interpretation is that there is 99% confidence that the true mean lies within the limits
The margin of error is [tex]E = 6.783[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 23.1[/tex]
The standard deviation is [tex]\sigma = 6.6 \ miles[/tex]
The sample size is n = 10
Generally the degree of freedom is mathematically represented as
[tex]df = n-1[/tex]
=> [tex]df = 10-1[/tex]
=> [tex]df =9[/tex]
Given that the confidence level is 99% , the n the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha =1\%[/tex]
[tex]\alpha =0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] with a df of 9 from from the student t-distribution table the value is
[tex]t _{\frac{\alpha }{2} , df } = 3.250[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , df } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 3.250 * \frac{6.6 }{\sqrt{10} }[/tex]
[tex]E = 6.783[/tex]
The 99% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]23.1 - 6.78 < \mu <23.1 + 6.78[/tex]
=> [tex]16.32< \mu <29.88[/tex]
The interpretation is that there is 99% confidence that the true mean lies within the limits
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. Suppose you wish to test the claim that , the mean value of the differences d for a population of paired data, is greater than 0. Given a sample of n15 and a significance level of 0.01, what criterion would be used for rejecting the null hypothesis?
Answer:
reject null hypothesis if calculated t value > 2.624
Step-by-step explanation:
n = 15
To calculate degree of freedom, n -1 = 14
The claim says ud>0
The decision rule would be to reject this null hypothesis if the test statistics turns out to be greater than the critical value.
With df =14
Confidence level = 0.01
Critical value = 2.624 (for a one tailed test)
If the t value calculated is > 2.624, we reject null hypothesis.
Using the t-distribution and it's critical values, the decision rule is:
t < 2.624: Do not reject the null hypothesis.t > 2.624: Reject the null hypothesis.At the null hypothesis, we test if the mean is not greater than 0, that is:
[tex]H_0: \mu \leq 0[/tex]
At the alternative hypothesis, we test if the mean is greater than 0, that is:
[tex]H_1: \mu > 0[/tex].
We then have to find the critical value for a right-tailed test(test if the mean is more than a value), with 15 - 1 = 14 df and a significance level of 0.01. Using a t-distribution calculator, it is [tex]t^{\ast} = 2.624[/tex].
Hence, the decision rule is, according to the test statistic t:
t < 2.624: Do not reject the null hypothesis.t > 2.624: Reject the null hypothesis.A similar problem is given at https://brainly.com/question/13949450
A cupboard costing Rs.16800 is depreciated at the rate of 15% per year. What will be the cost of the cupboard after 2 years.
Answer:
Rs. 11132
Step-by-step explanation:
formula for depriciation= P(1-R/100)^T
p= principal, r=rate, t=time
Answer:
15162
Step-by-step explanation:
after 1 year= 16800*95%= 15960
after 2 year= 15960*95%= 15162
If we were to make a poset of the form (A, |), where is the symbol for divisibility, which of the following sets A would yield a poset that is a total ordering?
I. A- (1, 4, 16, 64)
II. A- (1.2,3, 4, 6, 12)
III. A 1,2,3, 4, 6, 12, 18, 24)
IV. A+{1 , 2, 3, 6, 12)
Answer:
IV. A+{1, 2, 3, 6, 12}
Step-by-step explanation:
The set of natural numbers form a poset number under relation of > or =. The discrete variables are used to form a poset. The symbols for divisibility in poset form are when an integer is divided by the variable without integer. The correct answer is therefore 4th option.
9sin(Θ)-7=0. Solve the trigonometric equation
Step-by-step explanation:
here's the answer to your question
For real numbers x and y, what is the largest possible value of [tex]5 - (x-3)^2[/tex]?
Answer:
5
Step-by-step explanation:
Anything other than making x - 3 = 0 will make x - 3 have a value. No matter what happens (x - 3)^2 is positive. There is a minus sign outside the brackets which makes (x - 3)^2 negative.
That means that something is always taken away from 5 unless x = 3. Try and find any value that will make a number bigger than or equal to five that isn't x = 3.
By the way, I'm assuming the question is y = 5 - (x - 3)^2
Find the area of the figure.
A =
Is it m, m2, or m3
Answer:
348 m^2
Step-by-step explanation:
The figure is made up of a rectangle 24 m by 12 m, and a triangle with a 24 m base and a 5 m height.
A = LW + bh/2
A = 24 m * 12 m + (24 m)(5 m)/2
A = 288 m^2 + 60 m^2
A = 348 m^2
football team, won 35 out of 39 games over a period of 4 years. if they keep winning pace, predict how many games you would expect them to win over the next 78 football games
Answer:
70
Step-by-step explanation:
If the team continues with same pace, they expected wins as per previous ratio:
35/39*78 = 70Expected wins 70 out of 78 games
A sample of a radioactive substance decayed 11% over the course of 3 weeks. How many grams were in the sample originally if 30.26 grams of the substance were remaining after the 3 weeks?
Answer:
34 grams
Step-by-step explanation:
If the remaining sample has 30.26 grams of radioactive substance, and 11% of it decayed, that means that 30.26 grams is 89% of the original. Let the original be x.
30.26=0.89x
Multiply both by one hundred
3026=89x
Divide both by 89
34=x
x=original, so the original was 34 grams.
Subtract 2x^2 -9x - 7 from 8x^2 -5x + 9.
Answer:
-6x² -4x -16
Step-by-step explanation:
be watchful of signs to avoid making errors
If a person earns $8.74 per hour, estimate how much the person would earn per year. Assume a person works 40 hours per week and 50 weeks per year.
Answer:
$17,480 per year.
Step-by-step explanation:
Amount earned per hour = $8.74
If a person works for 40 hours every week for 50 weeks in a year, number of hours worked in a year = [tex] 40hrs*50weeks = 2000 hrs [/tex]
Estimated amount earned per year by the person = [tex] 2000hrs * 8.74 dollars [/tex]
= $17,480 per year.
Identify each x-value at which the slope of the tangent line to the function f(x) = 0.2x^2 + 5x − 12 belongs to the interval (-1, 1).
Answer:
Step-by-step explanation:
Hello, the slope of the tangent is the value of the derivative.
f'(x) = 2*0.2x + 5 = 0.4x + 5
So we are looking for
[tex]-1\leq f'(x) \leq 1 \\ \\<=> -1\leq 0.4x+5 \leq 1 \\ \\<=> -1-5=-6\leq 0.4x \leq 1-5=-4 \\ \\<=> \dfrac{-6}{0.4}\leq 0.4x \leq \dfrac{-4}{0.4} \\\\<=> \boxed{-15 \leq x\leq -10}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).
What is the slope of the tangent line to a function f(x) at point x = x_0?It is given by the derivative at x = x_0, that is:
m = f'(x_0)
In this problem, the function is:
f(x) = 0.2x^2 + 5x − 12
Hence the derivative is:
f'(x) = 0.4x + 5
For a slope of -1, we have that,
0.4x + 5 = -1
0.4x = -6
x = -15.
For a slope of 1, we have that,
0.4x + 5 = 1.
0.4x = -4
x = -10
Hence it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).
More can be learned about derivatives and tangent lines at;
brainly.com/question/8174665
#SPJ2
xThe closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $18 and $28 per share. What is the probability that the stock price will be: More than $20? (Round your answer to 4 decimal places.)
Answer:
The probability is [tex]P(X > 20 ) = 0.8[/tex]
Step-by-step explanation:
From the question we are told that
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $18 and $28 per share.
Given that the stock is uniformly distributed then the probability that the stock price will be more than $20 is mathematically evaluated as
[tex]P(X > 20 ) = 1 - P(X < 20 )[/tex]
Since it is uniformly distribute between $18 and $28 per share then we can solve is as follows
=> [tex]P(X > 20 ) = 1 - [\frac{ 20 - 18 }{28 -18} ][/tex]
=> [tex]P(X > 20 ) = 0.8[/tex]
List the angles in order from the largest to the smallest for ABC.
AB= 14, AC = 15, BC = 16
Answer:
B. ∠A, ∠B, ∠C
Step-by-step explanation:
1. Draw a model with AB as the shortest line and BC as the longest line.
∠A connects the two shortest lines, making it the largest angle.
∠B connects the shortest and the longest lines, making it the second largest angle.
∠C connects the two longest lines, making it the smallest angle.
Answer:
A > B > C
Step-by-step explanation:
Ypu probably wouldn't think about it unless someone pointed it out, but if you look at a triangle of any type you can see that the sizes of the sides are directly related to the sizes of the angles opposed to them.
By this I mean, the largest side will have the largest angle across from it and the smallest side will have the smallest angle.
Based off of my drawing, it looks like the order is angle A, then B, then, and then C.
Find the least whole number that can replace
to make the statement true.
110< =47
Answer:
it is false
Step-by-step explanation:i cant explain but trust
A human factor expert recommends that there be atleast 9 square ft of floor space in a classroom for every student in the class. Find the min space required for 49 students
If In (x) = 3.53, what is the value of x ?
what number has 7 ten thousands, 1 thousand, 1 hundred, and no ones?
Answer:
[tex]71,100[/tex]
Step-by-step explanation:
If you are trying to find a number that is written in word form, we can just use place values to find what goes where.
A number is broken down into this:
Ten thousands, thousands, hundreds, tens, ones.
If they have 7 ten thousands, the first digit will be a 7.
If they have 1 thousand, the second digit will be a 1.
If they have 1 hundred, the third digit will be a 1.
Since nothing is stated about tens, we assume it's value is 0.
And since there are no ones, it's value is 0.
So:
71,100.
Hope this helped!
Which statements are true about triangle QRS?
Select
three options.
Answer:
The side opposite <Q is RS
The hypothenuse is QR
The side adjacent to <Q is QS
Step-by-step explanation:
Side RS is directly opposite <Q. The first statement provided in the options is correct.
The side that is opposite to <R is QS. The second statement in the options is not correct.
The longer leg of a right triangle is always the hypotenuse. Side QR in ∆QRS is the hypotenuse. The third statement given in the options is correct.
The side adjacent to <R is not SQ. RS is the side adjacent to <R. The fourth statement in the given options is not correct.
Side QS is adjacent to <Q. The fifth option is correct.
Answer:
A, C, E
Step-by-step explanation:
on edge! hope this helps!!~ （‐＾▽＾‐）
Joseph is 33 years old. Five years ago, He was twice as old as Ann. How old will Ann be in 5 years time?
Answer:
19 years oldStep-by-step explanation:
[tex]Joseph = 33 \:years \:old\\ \\Let \: ann's \:age be x\\\\33-5 = 2x\\\\28 = 2x\\\\Divide \:both \:sides \:of \:the \:equation \: by \:2\\\\\frac{2x}{2} = \frac{28}{2} \\\\x = 14\\\\Ann's \:present \:age \:= 14\\\\In \:5 \:years \:time ; \\\\14+5 = 19\\[/tex]
In 2004, 50 out of every 100 drivers at the National Trucking Company passed their driver's license exam on their first try. In 2005, 62 of the drivers passed on their first attempt. What was the percent increase in the passing rate?
Answer:
I believe it's a 12 percent increase.
Step-by-step explanation:
50/100= 50%
62/100= 62%
62%-50%=12%
The sum of four
consecutive odd number is 8o. Find the number
Answer:
The sum of 4 consecutive odd number is 80
Let X be the first of these numbers
Then the next odd number is X+2
The third is X+4The fourth is X+6
All of these add up to 80
(X) + (X+2) + (X+4) + (X+6) = 80
Using the commutative and associative laws, let's transform this equation into
(X + X + X + X) + (2 + 4 + 6) = 804X + 12 = 80
Subtract 12 from both sides of the equation gives4X = 68
Divide both sides by 4 gives
X = 17
Going back to the original question:What are the 4 consecutive odd numbers: 17, 19, 21, 23Checking our answer:17 + 19 + 21 + 23 = 80 Correct!