Answer:
160
Step-by-step explanation:
(3a+4b) = 16
ab = 4
Square (3a+4b)
(3a+4b)(3a+4b) = 16^2
9a^2 + 12ab+12ab+16b^2 = =256
9a^2 +16b^2 +24ab=256
9a^2 +16b^2 +24ab - 24 ab=256 -24ab
9a^2 +16b^2 =256- 24ab
We know ab = 4
9a^2 +16b^2 =256- 24*4
9a^2 +16b^2 =256- 96
9a^2 +16b^2 =160
Practice Exercise 3.1 Fill in the blanks: (i) The factors of 12 are (ii) The least non-zero multiples of any number is (iii) ......... is a factor of every number. ing with Numbers
Answer:
i.)1,2,3,4,6,12
ii).the number itself
iii.)1
A researcher wants to better understand the health benefits of eating vegetables. In a study he finds 300 adults aged 45-60 who eat at least 3 servings of vegetables a day on average. He finds another 200 adults who eat less than 3 servings of vegetables a day on average. The researcher looks at rates of cancer and heart disease in each group and compares both groups. In another study, the researcher finds 500 adults aged 45-60 who eat less than 3 servings of vegetables a day on average, and are willing to participate in a study. The researcher randomly assigns 250 of these adults to a diet which includes 4 servings of vegetables a day. The other 250 continue their usual habits. After 4 years, the rates of cancer and heart disease between the two groups are compared
Identify the statement that correctly states the reason for considering the first study as an observational study and second study as an experiment.
a. In the first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on the subjects.
b. In the first study, the treatment is not imposed on every subject, whereas in the second study the treatment is imposed on every subject.
c. In the first study, the subjects were not randomly chosen, whereas in the second study the subjects were randomly assigned.
Answer:
a. In first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on subjects.
Step-by-step explanation:
In the first study, observation are made on 300 adults who eat 3 servings of vegetables a day on average. The second study has further intensified the research which imposed treatment on the subjects. The random samples of adults are observed in both studies.
If you deposit $500 dollars “Each Month!” Into an account paying 3% interest, compounded monthly, how much would be in said account after 4 years.
Please show proper work and give a good explanation in regards as to how you got your answer
Answer:
26029.26
Step-by-step explanation:
Assuming we are investing the 500 at the end of the period and starting with 500 in the account
[ P(1+r/n)^(nt) ]+PMT × {[(1 + r/n)^(nt) - 1] / (r/n)}
PMT = the monthly payment
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time in years
[ 500(1 + .03/12)^(4*12) ]+500 × {[(1 + .03/12)^(4*12) - 1] / .03/12)}
[ 500(1 + .0025)^(48) ]+500 × {[(1 + .0025)^(48) - 1] / .0025)}
563.66 +25465.60
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“””” HELP PLEASE “”””
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9514 1404 393
Answer:
x = 14 cm
Step-by-step explanation:
We can only solve for x if the triangles are similar. The arrows on the left and right legs say those are parallel. Since alternate interior angles at each of the transversals are congruent, the triangles are AA similar.
ΔABC ~ ΔDEC, so we have ...
EC/ED = BC/BA
x/(18 cm) = (35 cm)/(45 cm)
x = (18 cm)(7/9) = 14 cm
Find f(-1) given f(x) = –2x^3 + 3x^2 – 22
[tex]\\ \sf\longmapsto f(-1)[/tex]
[tex]\\ \sf\longmapsto -2x^3+3x^2-22[/tex]
[tex]\\ \sf\longmapsto -2(-1)^3+3(-1)^2-22[/tex]
[tex]\\ \sf\longmapsto -2(-1)+3(1)-22[/tex]
[tex]\\ \sf\longmapsto 2+3-22[/tex]
[tex]\\ \sf\longmapsto 5-22[/tex]
[tex]\\ \sf\longmapsto -17[/tex]
Plz help
Need answers ASAP
Answer:
1. cube
2. square pyramid
4. cone
5. cube
What is the equation of a horizontal line passing through the point (-7,5)?
Oy = 5
Oy = -7
Ox=5
Ox= - 7
Answer:
1st option, y = 5
Step-by-step explanation:
when the line is horizontal, it's parallel to the x axis
Answer:
y = 5
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (- 7, 5 ) with y- coordinate 5 , then
y = 5 ← is the equation of the line
What is the area of the pool ?
Answer:
https://brainly.com/question/24258518
Step-by-step explanation:
The median age (in years) of the U.S. population over the decades from 1960 through 2010 is given by
f(t) = −0.2176t3 + 1.962t2 − 2.833t + 29.4 (0 ≤ t ≤ 5)
where t is measured in decades, with t = 0 corresponding to 1960.
(a) What was the median age of the population in the year 1970?
(b) At what rate was the median age of the population changing in the year 1970?
(c) Calculate f ''(1).
Considering the given function, we have that:
a) 28.31 years.
b) 0.3382 years a decade.
c) 2.6184.
What is the function?The median age of the U.S. population in t decades after 1960 is:
f(t) = -0.2176t³ + 1.962t² - 2.833t + 29.4.
1970 is one decade after 1960, hence the median was:
f(1) = -0.2176 x 1³ + 1.962 x 1² - 2.833 x 1 + 29.4 = 28.31 years.
The rate of change was is the derivative when t = 1, hence:
f'(t) = -0.6528t² + 3.924t - 2.933
f'(1) = -0.6528 x 1² + 3.924 x 1 - 2.933 = 0.3382 years a decade.
The second derivative is:
f''(t) = -1.3056t + 3.924
Hence:
f''(1) = -1.3056 x 1 + 3.924 = 2.6184.
More can be learned about functions at https://brainly.com/question/25537936
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37. The trip between 2 towns is exactly 90 miles. You have gone 40% of this distance. How far have
you gone?
Answer:
36 miles
Step-by-step explanation:
We want to find 40% of 90 miles
40% * 90
.40 * 90
36 miles
We have to find travelled distance inorder to find this we have to find 40℅ of 90miles
[tex]\\ \Large\sf\longmapsto 90\times 40\℅[/tex]
[tex]\\ \Large\sf\longmapsto 90\times \dfrac{40}{100}[/tex]
[tex]\\ \Large\sf\longmapsto 9\times 4[/tex]
[tex]\\ \Large\sf\longmapsto 36miles [/tex]
find the missing side lengths
this is a special triangle so v = 17
u = 17√2
Answer:
v = 17
u = 17[tex]\sqrt{2}[/tex]
Step-by-step explanation:
If v = 17 (it is because it is a right triangle, so the pythagorean theorum works, and triangles are 180 degrees, so 180 - 90 = 90, so the other two angles are 45 degrees, meaning that v is the same length as 17.) then
17 ^ 2 = u ^2
289 = u^2
17 root to 2
GIVING BRAINLIEST!!!!! AND ALL POINTS!!!!!!!!!!!!!!!!!!!
A right rectangular prism is packed with cubes of side length fraction 1 over 4 inch. If the prism is packed with 12 cubes along the length, 8 cubes along the width, and 5 cubes along the height, what is the volume of the prism?
fraction 2 and 3 over 4 cubic inches
fraction 3 and 3 over 4 cubic inches
fraction 7 and 1 over 4 cubic inches
fraction 7 and 1 over 2 cubic inches
Answer:
7 and 1 over 2 cubic inches ( 7 1/2 in³
Step-by-step explanation:
The height = 1/4 * 5 = 1 1/4 = 1.25
The width = 1/4 * 8 = 2
The length = 1/4 * 12 = 3
Volume = 1.25 * 2 * 3 = 2.5 * 3 = 7.5
0.5 is represented as 1/2
So answer : fraction 7 and 1 over 2 cubic inches or 7 1/2 in³
if my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Determine the maturity value of a 45-day note for $1,250 dated May 23 and bearing interest 8%.
The maturity value of a 45-day note for $1,250 dated May 23 and bearing interest 8% is $1,262.5
Using this formula
Maturity value=Principal amount+ Interest
Let plug in the formula
Maturity value=$1,250+($1,250*8%*45 days/360 days)
Maturity value=$1,250+$12.5
Maturity value=$1,262.5
Inconclusion the maturity value is $1,262.5
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A math professor is wondering if students today are better or worse than in the past. He has given the same final to this year's class that he gave ten years ago. Compute mean, median, and mode for both classes and write a paragraph summarizing the differences.
This Year
35 45 65 75 87
80 69 71 53 90
99 95 70 82 73
93 67 61 57 74
72 77 71 81 83
Ten Years Ago
56 77 75 76 59
74 51 89 55 79
67 77 69 91 68
90 65 79 69 79
87 86 98 91 95
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following data:
This year :
35, 45, 53, 57, 61, 65, 67, 69, 70, 71, 71, 72, 73, 74, 75, 77, 80, 81, 82, 83, 87, 90, 93, 95, 99
Mean = ΣX / n = 1825 / 25 = 73
The mode = 71 ( most frequently occurring)
Median = 1/2(n+1)th term = 1/(26) = 13th term
Median = 73
10 years ago :
51, 55, 56, 59, 65, 67, 68, 69, 69, 74, 75, 76, 77, 77, 79, 79, 79, 86, 87, 89, 90, 91, 91, 95, 98
Mean = ΣX / n = 1902 / 25 = 76.08
The mode = 79 ( most frequently occurring)
Median = 1/2(n+1)th term = 1/(26) = 13th term
Median = 77
According to the computed statistics, we can conclude that, today is worse than the past as the average score which is almost similar to the median value is higher 10 years ago and the modal score is better 10 years ago as well.
10. What is the multiple zero and multiplicity of f(x) = (x - 3)(x - 3)(x + 5)?
Multiple zero is -3; multiplicity is 2
Multiple zero is 5; multiplicity is 1
Multiple zero is -5; multiplicity is 1
Multiple zero is 3; multiplicity is 2
Answer:
x=3, multiplicity of 2
x=-5, multiplicity of 1
Step-by-step explanation:
f(x) = (x - 3)(x - 3)(x + 5)
Rewriting
f(x) = (x - 3)^2(x + 5)
Setting equal to zero
0 = (x - 3)^2(x + 5)
Using the zero product property
(x-3)^2 = 0 x+5 = 0
x-3 = 0 x= -5
x=3 x-5
Since x-3 was squared, the multiplicity is 2
Answer:
x=3, multiplicity of 2
x=-5, multiplicity of 1
Step-by-step explanation
2sin^2(2x) + 1 = 3sin(2x) Solve for x with exact answers. The domain is 0 ≤ x ≤ π
Answer:
x = π/12 and x = π/4.
Step-by-step explanation:
2sin^2(2x) + 1 = 3sin(2x)
2sin^2(2x) - 3sin(2x) + 1 = 0
(2sin(2x) - 1)(sin(2x) - 1) = 0
2sin(2x) - 1 = 0
2sin(2x) = 1
sin(2x) = 1/2
When there is a variable n = π/6, sin(π/6) = 1/2 [refer to the unit circle].
2x = π/6
x = π/12
sin(2x) - 1 = 0
sin(2x) = 1
When there is a variable n = π/2, sin(π/2) = 1 [refer to the unit circle].
2x = π/2
x = π/4
Hope this helps!
According to the American Academy of Cosmetic Dentistry, 75% of adults believe that an unattractive smile hurts career success. Suppose that 25 adults are randomly selected. What is the probability that 15 or more of them would agree with the claim?
Answer:
0.9703 = 97.03% probability that 15 or more of them would agree with the claim.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they agree with the claim, or they do not. The probability of an adult agreeing with the claim is independent of any other adult, which means that the binomial probability distribution is used to solve this question.
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.
75% of adults believe that an unattractive smile hurts career success.
This means that [tex]p = 0.75[/tex]
Suppose that 25 adults are randomly selected.
This means that [tex]n = 25[/tex]
What is the probability that 15 or more of them would agree with the claim?
This is:
[tex]P(X \geq 15) = 1 - P(X < 15)[/tex]
In which:
[tex]P(X < 15) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 13) + P(X = 14)[/tex]
14 is below the mean, so we start below and go until the probability is 0. Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 14) = C_{25,14}.(0.75)^{14}.(0.25)^{11} = 0.0189[/tex]
[tex]P(X = 13) = C_{25,13}.(0.75)^{13}.(0.25)^{12} = 0.0074[/tex]
[tex]P(X = 12) = C_{25,12}.(0.75)^{12}.(0.25)^{13} = 0.0025[/tex]
[tex]P(X = 11) = C_{25,11}.(0.75)^{11}.(0.25)^{14} = 0.0007[/tex]
[tex]P(X = 10) = C_{25,10}.(0.75)^{10}.(0.25)^{15} = 0.0002[/tex]
[tex]P(X = 9) = C_{25,9}.(0.75)^{9}.(0.25)^{16} \approx 0[/tex]
Then
[tex]P(X < 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0002 + 0.0007 + 0.0025 + 0.0074 + 0.0189 = 0.0297[/tex]
And
[tex]P(X \geq 15) = 1 - P(X < 15) = 1 - 0.0297 = 0.9703[/tex]
0.9703 = 97.03% probability that 15 or more of them would agree with the claim.
Given the arc, name the central angle.
FG
A. ∠GQJ
B. ∠FQG
C. ∠GQI
D. ∠HQI
Answer:
B
Step-by-step explanation:
Given arc FG then the central angle is the angle at the centre subtended by FG , that is
central angle = ∠ FQG
The central angle is B i.e ∠FQG
What is central angle?A central angle exists an angle whose vertex stands present at the center of a circle created by the two radii as the sides of the angle.
In Mathematics, an “arc” exists as a smooth curve joining two endpoints. In general, an arc exists one of the portions of a circle. It is essentially a part of the circumference of a circle. Arc exists as a part of a curve. An arc can be a portion of some other curved constitutions like an ellipse but mostly guides to a circle.
The angle substended by the arc would be ∠FQG.
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What is the largest value of A according to the division operation given above?
A)300 B)314 C)400 D)450
Answer:
Hello,
Answer B
Step-by-step explanation:
Since A=15*20+B and B<15
The max for B is 14
==> 300+14=314
A translation T maps point B(-2,4) onto point B (3,-1). What is the translation T?
HELP PLSS!!!!
A- (x+5, y-5)
B- (x+5, y+5)
C- (x-5, y+5)
D- (x-5, y-5)
Answer:
(x+5, y-5) is the correct answer
Step-by-step explanation:
first, take -2 and 3 on x value; when you jump from -2 to 3, your answer is positive 5
second, take 4 and -1 on y value; when you jump from 4 to -1, your answer is negative 5
hence your answer for this question is a- (x+5, y-5)
i need help and thx you freinds
Answer:
Below
Step-by-step explanation:
Find the areas of the triangles on the sides
A = bh / 2
= (3)(5) / 2
= 7.5
There are 2 of these so it would just be 15
Now for the square
A = lw
= (5)(6)
= 30
Add em all up
Total area = 15 + 30
= 45 cm^2
Hope this helps!
The stem-and-leaf plot lists the ages of customers in a bookstore.
How many customers are 19 or younger?
Enter your answer in the box.
Answer:
Step-by-step explanation:
1 calculate the weight of a dog on the earth and on the moon if it has a mass of 28kg
To solve the problem.
W=m×g
W=28×10
W=280.
The weight of a dog on the surface of earth is 280N.
Answer:
274.68N and 45.36N respectively
Step-by-step explanation:
Weight of any object is the mass in kilograms(kg) multiplied by the gravity in meter per square second(m/s^2). The gravity on earth is 9.81m/s^2 and on moon is 1.62m/s^2...so since the gravity varies the weight of the dog will also vary. The wight on earth would be 28kg multiplied by 9.81m/s^2 which would be 274.68N and the weight on moon would be 28kg multiplied by 1.62m/s^2 which would be 45.36N.
Which ordered pair is a solution to the system of inequalities? y > 2x
y > 7
A. (0, 0) B. (4, 8) C. (3, 7) D. (1, 9)
Answer:
D( 1,9)
Step-by-step explanation:
First y must be greater than 7 which eliminates A and C
y must be greater than 2 times the x value
2*4 = 8 so B is eliminated
2*1 = 2 which is less than 9 Choice D is a solution
Question 1 and 2 plz explain
Answer:
1.D
2.B
Step-by-step explanation:
1. The x intercept is the value of x when y is zero. We know that the x intercept is 0.5 so we must find a value of k that will make our rational function equal zero when x=0.5
[tex]y = \frac{k}{x + 1} - 2[/tex]
Substitute x=0.5 and y=0.
[tex]0 = \frac{k}{0.5 + 1} - 2[/tex]
[tex]0= \frac{k}{1.5} - 2[/tex]
[tex]2 = \frac{k}{1.5} [/tex]
[tex]3 = k[/tex]
D is the Answer.
2. We need to consider the function
[tex] \frac{2x}{1 - {x}^{2} } [/tex]
Since the numerator is a linear term, it will have one zero to the equation using fundamental Theorem of Algebra so C is wrong.
This is a rational function because we are dividing two polynomials by each other and q(x) or the denominator isnt zero. So D is wrong.
The denominator is a quadratic term so it will have two vertical asymptote according to the fundamental Theorem of Algebra So A is Wrong.
B is Right, the equation isnt defined at x=0 because when we plug 0 into the denominator, it doesn't equate to zero.
About 12.5% of restaurant bills are incorrect. If 200 bills are selected at ran- dom, find the probability that at least 22 will contain an error. Is this likely or unlikely to occur
Answer:
0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
About 12.5% of restaurant bills are incorrect.
This means that [tex]p = 0.125[/tex]
200 bills are selected at random
This means that [tex]n = 200[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.125 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.125*0.875} = 4.677[/tex]
Find the probability that at least 22 will contain an error.
Using continuity correction, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 25}{4.677}[/tex]
[tex]Z = -0.75[/tex]
[tex]Z = -0.75[/tex] has a p-value of 0.2266.
1 - 0.2266 = 0.7734
0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.
Find COS Instructions: Find the value of the trigonometric ratio. Make sure to simplify the If needed
Answer:
Sin A = 15 / 17
Step-by-step explanation:
Given a right angled triangle, we are to obtain the Sin of the angle A ;
Using trigonometry, the sin of the angle A, Sin A is the ratio of the angle opposite A to the hypotenus of the right angle triangle.
Hence. Sin A = opposite / hypotenus
Opposite = 15 ; hypotenus = 17
Sin A = 15 / 17
need help asap (giving brainliest)
Answer:
hhhhjhgbbbjjhjjjjjkkkkkkkk
Answer:
Step-by-step explanation:
Q1. Sobey's is the best deal
In Food Basics, having the two loaves of bread costing 4.88 would mean that (4.88 / 2) one would cost 2.44.
To find out how much three would cost, multiply 2.44 by three, and the result is 7.32, which is higher than the three loves of bread that costs 7.20 in Sobey's, which Sobey's has a better deal. 7.20 / 3 = 2.40, yet Food Basics does cost higher by 4 cents for just one.
I am not too sure about question 2, but I do hope the above question helps!
[{66 +1} 2-6].7
I need help ASAP please due Monday pre-algebra show work
Ans; 7× [2-6 { 1+66}] —> 7× [2 - 6 { 67} ] —> 7× [2-402] —> 7×[- 400] —> = – 2800
I hope I helped you ^_^
Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
O A. 1
ОВ. о
C. infinitely many
O D. cannot be determined
SURAT
Answer:
C. infinitely many
Step-by-step explanation:
If two equations in slope-intercept form have the same slope and y-intercept they must be the same line. Additionally, the solutions of a system of equations are wherever the two lines intersect. Since the lines are the same they must intersect at every point. Therefore, there are infinitely many solutions.
