Coefficient of 'x'= 5a
Coefficient of 'x square'= -17
Constant term = 14a
Robert must read a few books from his home library. He read any 4 out of 6 books from the top shelf, and then any 2 out of 3 books from the middle shelf and then any 3 out of 6 books from the bottom shelf. In how many ways can Robert read the books, if different orders in which the books will be read count as different ways
Answer:
Robert can read the books in 129,600 different ways.
Step-by-step explanation:
The order in which the book are read is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Top shelf:
4 books from a set of 6. So
[tex]P_{(6,4)} = \frac{6!}{2!} = 360[/tex]
Middle shelf:
2 books from a set of 3. So
[tex]P_{(3,2)} = \frac{3!}{2!} = 3[/tex]
Bottom shelf:
3 books from a set of 6. So
[tex]P_{(6,3)} = \frac{6!}{3!} = 120[/tex]
Total:
360*3*120 = 129,600
Robert can read the books in 129,600 different ways.
Helppp me quick !!!!!!!!!!!!!!!!!!
Answer:
Look at explanation
Step-by-step explanation:
For a) It is TRUE
For b) it is TRUE
For c) it is FALSE
Hope this helps!! :)
Answer:
okay, the answer to this question is listed below;
for a it says that half pupils choose maths.
And as you can see the results in the circle that it is true.
for the question c it says most pupils choose science that PE, as you can see the the circle that PE is a little more than science, so this Answer is false
Over the past year, the vice president of human resources at a large medical center conducted a series of three-month workshops aimed at increasing worker motivation and performance. As a check of effectiveness, she selected 7 employees from the personnel files and recorded their most recent annual performance ratings along with the ratings attained prior to attending the workshops. At a 5% level of significance, before after. is there evidence that the workshops increased performance ratings?
Take the differences =
Before After
72 59
74 72
62 89
74 67
78 81
88 92
71 81
Take the differences before-after. Order the data smallest to largest, ignoring the negative signs. Rank the data from 1 to 7
Observation 5 had the values Before = 81 and After 78. What is the difference before - after of these values?
What rank will observation 5 receive?
Add up all the ranks that have a negative difference, T . What is the value of T?
Add up all the ranks that have a positive difference,, T+. What is the value of T+?
What is the test statistic, T?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Before _After_ diff ___rank
72 ______ 59 __13 __ 2
74 _______ 72 _ 2 __ 7
62 _____ 89 __ - 27 _ 1
74 _______ 67 __ 7 __4
78 ______ 81 __ - 3 __ 6
88 ______ 92 __ - 4 __5
71 _______ 81 __ - 10 __3
Ranking the data:
27, 13, 10, 7, 4, 3, 2
Observation 5 :
Before = 78 ; After = 81
Difference ; 78 - 81 - 3
Observation 5 = Rank 6
Ranks with negative difference, T = 6 + 5 + 3 + 1 = 12
Ranks with negative difference T+ = (2 + 7 + 4) = 13
Write an expression without brackets that is equivalent to (2x)2
Answer:
[tex]4 {x}^{2} [/tex]Step-by-step explanation:
As,
[tex] {(ax)}^{2} = a \times a \times x \times x[/tex]
Hence,
[tex] {(2x)}^{2} [/tex]
= 2×2×x×x
[tex] = 4 {x}^{2} (ans)(without \: brackets)[/tex]
if the sum of any two number is 20 and difference is 10 find the numbers
"The sum of two numbers is 20" can be translated mathematically into the equation:
x + y = 20.
"... and their difference is 10" can be translated mathematically as:
x - y = 10
We can now find the two unknown numbers, x and y, because we now have a system of two equations in two unknowns, x and y. We'll use the Addition-Subtraction Method, also know as the Elimination Method, to solve this system of equations for x and y by first eliminating one of the variables, y, by adding the second equation to the first equation to get a third equation in just one unknown, x, as follows:
Adding the two equations will eliminate the variable y:
x + y = 20
x - y = 10
-----------
2x + 0 = 30
2x = 30
(2x)/2 = 30/2
(2/2)x = 15
(1)x = 15
x = 15
Now, substitute x = 15 back into one of the two original equations. Let's use the equation showing the sum of x and y as follows (Note: We could have used the other equation instead):
x + y = 20
15 + y = 20
15 - 15 + y = 20 - 15
0 + y = 5
y = 5
CHECK:
In order for x = 15 and y = 5 to be the solution to our original system of two linear equations in two unknowns, x and y, this pair of numbers must satisfy BOTH equations as follows:
x + y = 20 x - y = 10
15 + 5 = 20 15 - 5 = 10
20 = 20 10 = 10
Therefore, x = 15 and y = 5 is indeed the solution to our original system of two linear equations in two unknowns, x and y, and the product of the two numbers x = 15 and y = 5 is:
xy = 15(5)
xy = 75
surface area and volume word problem above show work pls
Answer:
Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.
Step-by-step explanation:
Answer:
SA = 2(Area of Trapezoid) + 2(Area of Rectangle) + Area of Base + Area of Top
SA = 2 ( 10cm + 6cm)(7cm) + 2(16cm x 8cm) + (16cm x 10cm) + (16cm x 8cm)
2
SA = 112 cm2 + 256 cm2 + 160 cm2 + 128 cm2
SA = 656 cm2 wrapping paper you need
In the diagram below of triangle PQR, S is the midpoint of PR and T is the
midpoint of QR. If ST = -32 + 9x, and PQ = -53 +28, what is the measure
of ST?
Answer: ST=?
Answer:
ST = 4
Step-by-step explanation:
A segment joining the midpoints of 2 sides of a triangle is half the length of the third side.
ST = [tex]\frac{1}{2}[/tex] PQ substitute values
- 32 + 9x = [tex]\frac{1}{2}[/tex] (- 5x + 28) ← multiply both sides by 2 to clear the fraction
- 64 + 18x = - 5x + 28 (add 5x to both sides )
- 64 + 23x = 28 ( add 64 to both sides )
23x = 92 ( divide both sides by 23 )
x = 4
Then
ST = - 32 + 9x = - 32 + 9(4) = - 32 + 36 = 4
Review the graph of function g(x).
For which value of a does lim g(x) not exist?
X-
O-6
0-3
0 0
2-
Answer:
0-6 de correct answer okay.
At x→ -3 the value of the limit of function g(x) does not exist because the left-hand limit and right-hand limit are not equal an option second is correct.
What is the limit?A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have a graph of function g(x)
[tex]\rm \lim_{x \to a}g(x)[/tex]
Let's check at x = -3
Finding the left-hand limit and right-hand limit.
[tex]\rm \lim_{x \to -3^{-1}}g(x) = -2[/tex]
[tex]\rm \lim_{x \to -3^{+1}}g(x) = -4[/tex]
Since the left-hand limit and right-hand limit are not equal then at x = -3 the limit does not exist.
Thus, at x→ -3 the value of the limit of function g(x) does not exist because the left-hand limit and right-hand limit are not equal an option second is correct.
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A right triangle has one angle that measures 36°. What is the measure of the other acute angle?
Answer:
54 degrees
Step-by-step explanation:
The total degree of a triangle is 180. Since it is a right angle, one of the angles is 90 degrees. The equation is, 36+90+x=180. You should then get 54 degrees.
Write a definition of area that includes all the information
that you think is important.
Answer:
In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units such as square centimteres, square feet, square inches, etc.
TULI
Spinner A
Spinner
025
05
Tim has two spinners, spinner A and Spinner B.
Each spinner can only land on red or bloe.
The probability that spinner A will land on red is 0.5
The probability that spinner will land on red is 0.6
The tree diagram shows this information
Tim spins spinner A once and he
spins spinner Bonce
He does this a number of times.
The number of times both spinners 0.5
land on red is 84.
Work out an estimate for the
number of times both spinners land on blue.
red
05
blu
blue
So we would expect both spinners to land on blue once, approximately.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. The closer the probability is to 1, the more likely the event is to occur, while the closer it is to 0, the less likely it is to occur.
Here,
To solve this problem, we can use the multiplication rule of probability, which states that the probability of two independent events A and B occurring together is equal to the product of their individual probabilities:
P(A and B) = P(A) × P(B)
In this case, we want to find the number of times both spinners land on blue, which is equivalent to the probability that spinner A lands on blue (0.5) multiplied by the probability that spinner B lands on blue (0.4), because the events are assumed to be independent. Therefore:
P(both blue) = P(A blue) × P(B blue) = 0.5 × 0.4 = 0.2
This means that the probability of both spinners landing on blue is 0.2, or 20%.
To estimate the number of times both spinners land on blue out of a certain number of trials, we can use the expected value of a binomial distribution, which is given by:
E(X) = n × p
where X is the random variable representing the number of successes (in this case, both spinners landing on blue), n is the number of trials, and p is the probability of success (0.2 in this case).
We are given that the number of times both spinners land on red is 84, which is equivalent to the number of trials minus the number of times both spinners land on blue. Let's denote the number of trials as n. Then we have:
n - 84 = number of times both spinners land on blue
Substituting the values we have found, we get:
n - 84 = 0.2n
Simplifying and solving for n, we get:
0.8n = 84
n = 105
Therefore, the estimated number of times both spinners land on blue out of 105 trials is: number of times both spinners land on blue
= 0.2 × 105 - 84 ≈ 1
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In 2016, there were approximately 4.46 x 10 people in Asia. On average, a person takes
8.4 x 10 breaths per year. Using this data, what was the number of breaths of all the people
in Asia in 2016? Expressing your answer in scientific notation in the form a < 10', what are
the values of a and b?
Answer:
The answer for A is A- 3.75
And the answer for B is B- 16
What are the answers?
Answer:
20.5 , 30.4 , 5.3
Step-by-step explanation:
SOHCAHTOA
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
tanθ = opposite / adjacent
10. tan64° = 42 / x ; x = 42 / tan64° ; x = 20.48476872
12. sin54° = BD / 20 ; BD = 20 * sin54° ; BD = 16.18033989 ;
tan28° = BD / DC ; DC = BD / tan28° ; DC = 30.43079344
13. tan51° = JL / 14 ; JL = 14 * tan51° ; JL = 17.28856019 ;
cos72° = KL / JL ; KL = JL * cos72° ; KL = 5.342458907
1/8 times 5/8 in simplest form
Answer:
5/64
Step-by-step explanation:
numerators 1 time 5 is 5 and denominators 8 times 8 is 64; 5/64
helppppp! how do I find this?
Answer:
y=3x-6
Step-by-step explanation:
(2,0). y=mx+b or 0=3 × 2+b, or solving for b: b=0-(3)(2). b=-6.
(3,3). y=mx+b or 3=3 × 3+b, or solving for b: b=3-(3)(3). b=-6.
Plugging in the two points from the graph.
Hence, y=3x-6
What is the radius and center for 2+4+4+2=43?
Answer:
im sorry
i still dont know the answer tho
The table displays the amount of money Stephen has in his piggy bank.
Stephen's Piggy Bank
Types of Coins Amount ($)
Quarters 7.50
Dimes 6.00
Nickels 5.50
Pennies 3.00
Which answer choice does NOT accurately approximate a comparison between the value of
the dimes in the piggy bank and the total value of Stephen’s coins?
A. 6%
B. 3/11
C.6/22
D. 27%
Answer:
A.6% Is the correct answer... #:Carry on Learning... ^_^Answer:
A. 6%
Step-by-step explanation:
The is no step by step explanation sadly
Please answer this question needed ASAP !!
Angle F should be 46 degrees
Solve for X.Enter the solutions from least to greatest.
Round to two decimal places.
(x + 7)^2– 11 = 0
lesser x =
greater x =
Answer:
lesser x= -10.32
greater x= -3.68
Step-by-step explanation:
[tex] - 7 + \sqrt{11} = - 3.68[/tex]
[tex] - 7 - \sqrt{11} = - 10.32[/tex]
Answer:
Lesser x: -10.31 Greater X:-3.68
Step-by-step explanation:
Sally has 3 yards of yarn. She will use 6 inches per bracelet. How many bracelets can she make?
3 feet in a yard... 12x3 = 36...... 36+36+36 =108 inches
108 divided by 6 is 18 bracelets
I need the answer pls answer fast
Answer:
A = 846 in²
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ( d₁ and d₂ are the diagonals ) , then
A = [tex]\frac{1}{2}[/tex] × 36 × 47 = 18 × 47 = 846 in²
Answer:
846
Step-by-step explanation:
area of a rhombus is [tex]\frac{pq}{2}[/tex] where p and q are the two diagonals ..
so [tex]A=\frac{36*47}{2}[/tex]
A=846
A nickel and a quarter are tossed once. What is the probability that both lands on tails? show work
Answer:
1/4
Step-by-step explanation:
1/2 x 1/2 = 1/4
which is greater? 0.04 or 0.39
Answer:
0.39
Step-by-step explanation:
think about it this way, if you take away the decimal it would be 39 and 04. 04 is another way to write 4 and 4 is less than 39. so 0.04 is less than 0.39
Answer:
0.04 > - 0.39
Step-by-step explanation:
0.04 > - 0.39
Hows your day doing this is not a thing for math but just wandering
Help!!!!!!!!!!!!!!!!!
Please help!! Math
What is the missing value of the missing angle?
A. 43*
B. 133*
C. 90*
D. 47*
Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean’s weekly income is approximately normal with mean $225 and standard deviation $25. The distribution of Evan’s weekly income is approximately normal with mean $240 and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?
a. 0.67
b. 0.700
c. 0.227
d. 0.303
e. 0.354
Answer:
d. 0.303
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
In this question:
We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.
Distribution of the difference between Sean's and Evan's income:
Sean has mean 225, Evan 240. So
[tex]\mu = 225 - 240 = -15[/tex]
Sean's standard deviation is of 25, Evan's of 15. So
[tex]\sigma = \sqrt{25^2+15^2} = 29.15[/tex]
Probability that Sean will have a greater income than Evan in a randomly selected week:
Probability of the subtraction being greater than 0, which is 1 subtracted by the pvalue of Z when X = 0. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-15)}{29.15}[/tex]
[tex]Z = 0.51[/tex]
[tex]Z = 0.51[/tex] has a pvalue of 0.695
1 - 0.695 = 0.305.
Closest to 0.303, option d.
In the figure, lines ℓ and m are parallel. Describe ∠1 and ∠2.
∠1 and ∠2 are equal angles as the lie on same side of transversal, are on parallel lines and are corresponding to each other
thank you
What is a decimal that is equivalent to the fraction 82/100
Answer:
0.82
Step-by-step explanation:
100 has 2 zeros so you move the decimal 2 places to the left.
82.
8.2
0.82
Answer:
0.82
Step-by-step explanation:
Decimals are out of 100, this fraction, 82/100, is also out of one hundred; this makes the question much easier to solve. Just take the numerator and put it as a decimal, so in this case, the numerator is 82. We take that numerator and make it a decimal: 0.82.
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