Answer:
Number of 7-digit numbers that can be made from the digit is 576
Step-by-step explanation:
Given the data in the question;
digits ⇒ 1, 2, 3, 4, 5, 6, 7
Number of odd numbers in the given digits = 4
Number of even numbers in the given digits = 3
now, we take the odd digits as a single unit.
so, number of ways the odd digits can be arranged with the unit will be 4!.
Now, lets consider the unit of 4 odd digits with 3 even digits.
there are 4 units.
so the number of possible arrangements of these 4 units = 4!
hence, Number of 7-digit numbers that can be made from the digits will be;
⇒ Number of possible arrangements of 4 units × Number of ways in which the odd digits can be arranged within the unit.
⇒ 4! × 4!
⇒ 576
Therefore, Number of 7-digit numbers that can be made from the digit is 576
Find the value of a for which there is no term independent of x in the ezlxpansion of
[tex](1 + ax {}^{2} )( \frac{2}{x} - 3x) {}^{6} [/tex]
"no terms independent of x" basically means there is no constant term, or the coefficient of x ⁰ is zero.
Recall the binomial theorem:
[tex]\displaystyle (a+b)^n=\sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]
So we have
[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 \binom 6k \left(\frac2x\right)^{6-k}(-3x)^k[/tex]
[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}[/tex]
[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}+a\sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-4}[/tex]
The first sum contributes a x ⁰ term for 2k - 6 = 0, or k = 3, while the second sum contributes a x ⁰ term for 2k - 4 = 0, or k = 2. The coefficient of the sum of these terms must be zero:
[tex]2^{6-3}(-3)^3\dbinom 63 + a\times2^{6-2}(-3)^2\dbinom 62 = 0[/tex]
which reduces to
2160a - 4320 = 0
2160a = 4320
a = 2
The function f(x) is shown on the provided graph. Graph the result of the following transformation on f(x). f(x) +6
Answer:
Graph the same exact curve, but move every y value up 6.
Step-by-step explanation:
A transformation to the y-values is outside of the argument of the function. i.e., outside of the parentheses.
Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
1. Find the equation of each of the straight line graphs that passes through the given
points.
(i) (1, 7) (2, 10)
(ii) (3, -1) (-2, 9)
(iii) (4, 3) (8,4)
(iv) (2, -5) (-2, 7
(v) (-1, -8) (3, 12)
(vi) (-5, 1) (10, –5)
(viii) (2, 2) (0, -4)
Answer:
25.987957
Step-by-step explanation:
Ayúdenme con esta multiplicación de polinomio por favor
(2×+3y)(-4ײy-2×y²)
Answer: welcome to brainly
Step-by-step explanation:
Hello there! My name is agenthammerx, a Master Answerer and Engagement Team Member here on Brainly. I am here to welcome you to the site! Thank you for taking initiative to check out Brainly and for posting your first question! The Brainly Community welcomes you. If you have any questions regarding anything about the site, please don’t hesitate to reach out to me! I will try my best to help you and answer your question or check out our help center at https://faq.brainly.com/
In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. If the sample mean is 9 hours, then the 95% confidence interval is
Answer:
(8.608, 9.392)
Step-by-step explanation:
We have the following information
Population standard deviation = 1.8
Sample mean = 9 hours
Sample n = 81
C I = 95%
So level of significance
Alpha = 1-0.95
= 0.05
Z critical at 0.05/2
Z(0.025) = 1.96
The 95% c.i =
9+-(1.96)(1.8/√81)
9+-(1.96)(0.2)
(9-0.392)(9+0.392)
(8.608, 9.392)
This is the confidence interval at 95%.
I hope you find my solution useful. Good luck!!!
Suppose 180 randomly selected people are surveyed to determine whether or not they plan on voting to reelect the current president. Of the 180 surveyed, 36 reported they will not vote to reelect the current president. Identify the values needed to calculate a confidence interval for the proportion that will not vote to reelect the current president at the 99% confidence level. Then find the confidence interval.
Answer:
(0.123 ; 0.277)
Step-by-step explanation:
Given :
Sample size, n = 180
x = 36
Proportion, p = x / n = 36/180 = 0.2
Confidence interval for sample proportion :
Confidence interval :
p ± Zcritical * √p(1 - p) / n
Zcritical at 99% = 2.576
0.2 ± 2.576 * √0.2(1 - 0.2) / 180
0.2 ± 2.576 * 0.0298142
0.2 ± 0.0768013792
(0.123 ; 0.277)
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker plz simple for class 5 pleeease
Answer:
$150
Step-by-step explanation:
discount=60%
let the price=x
(100-60)% of x=$60
40% of x=60
x=60×(100/40)=150
Of 240 stamps that Harry and his sister collected, Harry collected 3 times as many as his sister. How many did each collected.
Answer:
Harry collected 180 stamps
Harry's sister collected 60 stamps
Step-by-step explanation:
Let X be the number of stamps that Harry's sister colleted.
The number of stamps Harry colleted is 3 time as many as his sister's
⇒ 3*X + X = 240
⇒ X = 60
⇒ 240 - 60= 180
Answer:
180 for harry and 60 for his sister
Step-by-step explanation:
Find the intersection of the line and the circle given below
2x+y=-5
x^2+y^2=10
Answer:
There are two intersections.
(-3,1) and (-1,-3)
Step-by-step explanation:
Answer:
They intersect at (-3,1), and also (-1,-3)
Step-by-step explanation:
Graph:
Is there a difference in the number of people who have an Annual pass to Disney World comparing people who live in Florida to those who do not?
Answer:
Fail to reject the null hypothesis.
Step-by-step explanation:
People who live in Florida and also have annual pass to Disney world is 221, sample size selected for group 1 is 350.
People who do not live in Florida and have annual pass to Disney world is 365, sample size selected for Group 2 is 650.
Group 1 sample proportion is : 221 / 350 = 0.6314
Group 2 sample proportion is 365 / 650 = 0.5615
Test statistics is 0.8317
Since test stats value is greater than the sample proportion significance level, we fail to reject the null hypothesis.
A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.
This is the Written equation.
x+6x=56
Solve the equation.
Interpret the results and write the answer in words.
The smaller piece is x = _ in.
The longer piece is _x = _ ( ) = _ in.
The lengths of the two pieces are _ in
and _ in.
Part 1 of 2
_ in
Part 2 of 2
_ in
Answer:
8 inches
48 inches
total 56 inches
Step-by-step explanation:
x+6x = 56
7x = 56
Divide by 7
7x/7 = 56/7
x = 8
The smaller piece is x inches or 8 inches
The larger piece is 6x inches or 6*8 =48 inches
8+48 = 56 inches
The total length is 56 inches
Answer:
8 inches, and 48 inches
Step-by-step explanation:
x+6x=56
Solve the equation.
7x=56
x=8
Interpret the results and write the answer in words.
The smaller piece is x = 8 in.
The longer piece is 6x = 6 (8) = 48 in.
The lengths of the two pieces are 8 in
and 48 in.
A number is multiplied by 5 and the answer when divided by 3 gives 1315 . what is the number ?
Answer:
5×789/3
Step-by-step explanation:
According to the question you could simplify the above numbers .
Answer:
789
Step-by-step explanation:
let the number=x
[tex]\frac{5x}{3}=1315\\5x=1315 \times 3=3945\\x=\frac{3945}{5}=789[/tex]
f(x)=-2x^2+x-5 find f(5)
f(5) = -50
Hope it helps you...
Which expression is equivalent to this polynomial? 9x^2 + 4
A. (3x+2i)(3x-2i)
B. (3x+2)(3x-2)
C. (3x+2i)^2
D. (3x+2)^2
Need answers please offering 30 points
Answer:
yefeihuerijohiftv3ugrhoerfujfy
Step-by-step explanation:
I’m in summer school can y’all plz help me
Answer: Choice A. [tex]-x^2+2x+8[/tex]
Work Shown:
[tex](f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = (2x+1) - (x^2-7)\\\\(f - g)(x) = 2x+1 - x^2+7\\\\(f - g)(x) = -x^2+2x+(1+7)\\\\(f - g)(x) = -x^2+2x+8\\\\[/tex]
which shows the answer is choice A.
Side note: be sure to distribute the negative to every term inside the second set of parenthesis. So you wouldn't say -(x^2-7) = -x^2-7. If you did this error, then you'd get to the wrong answer choice C.
Answer:
hope it helps u plz mark me brainliest mate
Step-by-step explanation:
(f-g)(x)=2x+1-(x^2-7)
(f-g)(x)=2x+1-x^2+7
(f-g)(x)= -x^2+2x+8
this is the correct answer
Consider the following data representing the price of refrigerators (in dollars).14051405, 11211121, 13391339, 10961096, 12991299, 14011401, 11381138, 11491149, 12231223, 10711071, 13991399, 14001400, 12421242, 13181318, 11011101, 10651065, 14281428, 12251225, 13501350, 13581358, 13121312Copy DataPrice of Refrigerators (in Dollars)Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency1049–1118 1119–1188 1189–1258 1259–1328 1329–1398 1399–1468 Step 2 of 7 : Determine the frequency of the fifth class.
Answer:
3
Step-by-step explanation:
Given the data:
1405, 1121, 1339, 1096, 1299, 1401, 1138, 1149, 1223, 1071, 1399, 1400, 1242, 1318, 1101, 1065, 1428, 1225, 1350, 1358, 1312
Using the intervals:
Class interval ___ Frequency
1049–1118 ________ 4
1119–1188 ________ 3
1189–1258 ________3
1259–1328 _______ 3
1329–1398 _______ 3
1399–1468 _______ 5
From the table ; the fifth class is the interval :
1329 - 1398 and it has a frequency of 3
Economists have found that the amount of corruption in a country's government is correlated to the gross domestic product (GDP) per capita of that country. This can be modeled by y=530x−9240 where x is the corruption score and y is GDP per capita in dollars. Corruption scores range from 0 to 100 with 0 being highly corrupt and 100 being least corrupt. what is the slope of the line represent?
A. the GDP per capita of the country with the lowest corruption score
B. the corruption score needed for a GDP per capita of zero
C. the average GDP per capita for every point in the corruption score
D. the increase in GDP per capita for every increase of one in corruption score
Step-by-step explanation:
pandemic times: Potential ... - CAF
have shown evidence that the effect of corruption on real GDP per capita is more pronounced in countries with low levels of8
Answer true or false and explain your answer. If it is important not to reject a true null hypothesis, the hypothesis test should be performed at a small significance level.
Answer: No, The goal when testing a hypothesis is to to guess a large significant level to possibly have the answer correct based upon evidence. False. It needs to be a large significant level
Step-by-step explanation:
Can someone help please
9514 1404 393
Answer:
(b) f(x) = (-x)^(1/2)
Step-by-step explanation:
The square root is only defined for argument values that are non-negative. Hence the domain of ...
f(x) = (-x)^(1/2)
is all values of x less than or equal to zero. This is not "all values of x."
What balance will be in an account that has an initial deposit of $4600 with an APR of
1.8%? The money is compounded quarterly for 30 years.
How much interest has been earned for the entire time period?
Answer:
100$or 20.4 that is the answer
Which of the relations given by the following sets of ordered pairs is a function?
C_{(1,2), (2, 3), (3, 4), (5,6), (2, 1)}
C {( - 2,5), (7,5), ( – 4,0), (3,0), (1, - 6)}
Ċ {(2, – 8), (1, – 4), (0,0), (1, 4), (2,8)}
{(3, – 3), (3,
1), (3, 1), (3, 3), (3,5)}
Submit
Pass
elp
Don't know
answer
14
tv
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The first or second one because a function can't have the x value repeating
1,547,489 which digit is in the thousandsths place
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Starting from right to left...
9 is in the ones place
8 is in the tenths place
4 is in the hundreds place
7 is in the thousands place.
I hope this helps!
Two vectors m and n are defined by 3i+4j and n=2i-j. find the angle between m and n
Answer:
[tex]{ \tt{m.n = |m| |n| \cos( \theta) }} \\ { \tt{ (3 \times 2) + (4 \times - 1) = (5)( \sqrt{5}) \cos( \theta) }} \\ { \tt{ \cos( \theta) = \frac{0.4}{ \sqrt{5} } }} \\ \theta = 79.7 \degree[/tex]
Can someone plz solve this for me
Answer: [tex]y^\frac{1}{8}[/tex]
Step-by-step explanation:
Ok so when taking roots the number in the little corner at the left of the radical sign (if there is one) is the root you take. It could be the 4th root, 6th root, or the x root. You don't have to use the radical sign though, you can use an exponent to write it. All you have to do is take the reciprocal of the number to find what to write for the exponent. So for those examples it would be [tex]\frac{1}{4}, \frac{1}{6} ,\frac{1}{x}[/tex]. The number in the top left of the radical sign is 8 so the answer would be [tex]y^\frac{1}{8}[/tex]
What is the cardinal number of the set {-1,3,7,52,36,19,-6}
Answer:
can you please send me another one
What is the length of Line segment A C? Round to the nearest tenth.
Triangle A B C is shown. Angle A C B is 90 degrees and angle B A C is 55 degrees. The length of C B is 15 meters.
10.5 m
12.3 m
18.3 m
21.4 m
Answer:
10.5
Step-by-step explanation:
In the picture if you think about it, it has to be a number less than 15 since CB is 15. I picked 12.3 and got it wrong therefore it has to be 10.5.
Answer:
A) 10.5
Step-by-step explanation:
Need the answer plz.
Mr. Mason’s class is going on a field trip. There are 27 students. There will be 1 adult for every 9 students. Mr. Mason wants to know how many adults (n) are needed for the field trip. Which of the following equations should he use?
A. 9n + 27
B. 27 – 9n
C. 9n = 27 - 1
D. 9n = 27
Answer:
D. 9n = 27
Step-by-step explanation:
If we need one adult for every 9 students, we can represent that as 9n:
if n is the number of adults.
Because we have 27 students, the equation 9n = 27 works.
A better way of formatting the equation is:
n = 27/9
Because it directly shows what the number of adults is, but with some reformatting, it is clearly the same equation.
