The average weekly allowance of a 5th grade student as calculated using direct variation with the information provided by Fidelity Investment Vision Magazine is 5.367 dollars per week.
The question given is a direct variation problem:
Let:
• Average weekly allowance = [tex]a[/tex]
• Grade level = [tex]g[/tex]
If Average weekly allowance varies directly as grade level , then , then the direct variation between the variables can be expressed as :
[tex]a = k * g[/tex]
Where , [tex]k[/tex] = constant of proportionality
We can obtain the value of k from the given values of a and g
[tex]9.66 = k * 9\\9.66 = 9k\\k = 9.66/9[/tex]
Our equation becomes:
[tex]a = (9.66/9) * g[/tex]
[tex]a = (9.66/9) * 5\\a = 5.367[/tex] (rounded to 3 decimal places)
Hence, using proportional relationship, the average weekly allowance for a 5th grade student is [tex]5.367[/tex] per week
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find the solution to the system of equations.
y= -7x + 3
y= -x - 3
Answer:
x = 1 y = -4
Step-by-step explanation:
-7x + 3 = -x - 3
-7x = -x - 6
-6x = -6
x = 1
y = - (1) - 3
y = -1 - 3
y = -4
Please help! Thank you.
Answer:
B at -1 minus we go to - ∞
at -1 plus we to + ∞
Step-by-step explanation:
x^2 -x
g(x) = ---------
x+1
Factor out x
x(x-1)
g(x) = ---------
x+1
As x is to the left of -1
x is negative (x-1) is negative
x+1 will be slightly negative
g(-1 minus) = -*-/ - = - and we know that the denominator is very close to zero we are close to infinity so we go to - ∞
As x is to the right of -1
x is negative (x-1) is negative
x+1 will be slightly positive
g(-1 plus) = -*-/ + = + and we know that the denominator is very close to zero we are close to infinity so we go to ∞
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!
Which equation can she use as statement 5? 60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)
Find the missing side round your answer to the nearest tenth
Answer:
x=13.2
Step-by-step explanation:
cos(43)=x/18
x=18×cos(43)
x=13.2
Answered by GAUTHMATH
Which of the following pairs of functions are inverses of each other?
A. f(x) = 5 + x and g(x) = 5 - x
B. f(x) = 2x -9 and g(x)=x+9/2
C. f(x) = 3-6 and g(x)=x+6/2
D. f(x)= x/3+4 and g(x) = 3x - 4
The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's analyze the given options:
A. f(x) = 5 + x and g(x) = 5 - x
To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.
B. f(x) = 2x - 9 and g(x) = x + 9/2
By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.
C. f(x) = 3 - 6 and g(x) = x + 6/2
Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.
D. f(x) = x/3 + 4 and g(x) = 3x - 4
After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.
In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
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If a person invested half of her money at 9% and half at 7% and received $160 interest, find the total amount of money invested.
Answer:
$2000
Step-by-step explanation:
let x be the money she invested
lets assume this was for 1 year
0.09(x/2) + 0.07(x/2) = 160
multiply each side by 2 to cancel the denominators:
0.09x + 0.07x = 320
0.16x = 320
x = 2000
Answer: $2000
Let the amount of money she invested be x
Lets assume the time of investment as 1 year
ATQ
0.09(x/2) + 0.07(x/2) = 160
0.09x + 0.07x = 320
0.16x = 320
x = 2000
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What are the zeros of the polynomial function f(x)=x3-7x2+8x+16
Answer: x=4, -1
Step-by-step explanation:
Assuming you meant [tex]x^3-7x^2+8x+16[/tex], the zeros of the question are x = 4 and -1.
Step 1. Replace f(x) with y.
[tex]y = x^3-7x^2+8x+16[/tex]
Step 2. To find the roots of the equation, replace y with 0 and solve.
[tex]0 = x^3-7x^2+8x+16[/tex]
Step 3. Factor the left side of the equation.
[tex](x-4)^2 (x+1)=0[/tex]
Step 4. Set x-4 equal to 0 and solve for x.
[tex]x-4=0[/tex]
Step 5. Set [tex]x+1[/tex] equal to 0 and solve for x.
[tex]x=-1[/tex]
The solution is the result of [tex]x-4=0[/tex] and [tex]x+1=0[/tex].
[tex]x=4,-1[/tex]
Is the relationship shown by the data linear? If so, model the data with an equation.
Answer:
4th option
Step-by-step explanation:
The relationship is linear,
putting the value of x in the right side of the equation of option 4, you'll get the value of the left side
putting, x=1
y+4=-1/2(x-1)
y=-1/2(1-1)-4
y=-4
putting, x=7
y+4=-1/2(7-1)
y=-1/2(6)-4
y=-6/2-4
y=-3-4
y=-7
If P is (-5, 4) and Q is (7, -5), what is 2/3 of that?
Answer: 10
Step-by-step explanation:
Sqrt (7- -5)^2+(-5-4)^2 =
Sqrt (12)^2+(-9)^2 =
Sqrt 225 = 15
2/3 * 15 = 30/3 = 10
A local school board member randomly sampled private and public high school teachers in his district to compare the proportions of National Board Certified (NBC) teachers in the faculty. The results were:
Answer:
0.025 ;
(-0.7198 ; 0.7698)
Step-by-step explanation:
From the table :
_____________ private schls ___ public schls
Sample size, n _____ 80 __________ 520
P, NBC teachers ___ 0.175 ________ 0.150
P1 = P of private school teachers
P2 = P of public school teachers
Difference in proportion :
P1 - P12 = 0.175 - 0.150.= 0.025
The 90% confidence interval for 2 - sample proportion :
C.I = (p1-p2) ± [Zcritical * √(p1(1-p1)/n1 + (p2(1-p2)/n2)]
Zcritical at 90% = 1.645
C.I = 0.025 ± [1.645 * √((0.175*0.825)/80 + (0.150*0.850)/520)]
C.I = 0.025 ± [1.645 * √(0.0018046875 + 0.0002451)]
C.I = 0.025 ± 1.645 * 0.0452755
C.I = 0.025 ± 0.07448
C.I = (-0.7198 ; 0.7698)
What is the difference between squaring and cubing a value?
Answer:
squaring a number is multiplying it by itself twice and cubing a number is multiplying the number three times itself
Step-by-step explanation:
for example 2²=2×2
=4
and 2³=2×2×2
=8
I NEED HELP THANK YOU!!
Answer:
rt3/2
Step-by-step explanation:
first off cosine is the x coordinate
now if you do't want to use a calculator, you can use use the unit circle.
360 - 330 = 30 (360 degrees is a whole circle)
a 30 60 90 triangle is made, then use the law for 30 60 90 triangles:
if the shortest leg is x, the other leg is x*rt3 and the hypotenuse is 2x.
Answer:
D
Step-by-step explanation:
cos 330 = cos (360-330)
= cos 30
= √3 /2
f=((-1,1),(1,-2),(3,-4)) g=((5,0),(-3,4),(1,1),(-4,1)) find (f/g)(1)
9514 1404 393
Answer:
-2
Step-by-step explanation:
(f/g)(1) = f(1)/g(1) = -2/1 = -2
__
The value of f(1) is the second number in the ordered pair (1, -2) that is part of the definition of function f. Similarly, for g, we look for the ordered pair that has 1 as its first value. The second value is g(1).
Given the triangle below, what is the length of the third side, rounded to the nearest whole number?
Answer:
Step-by-step explanation:
You need the Law of Cosines for this, namely:
[tex]x^2=21^2+14^2-2(21)(14)cos58[/tex] where x is the missing side.
[tex]x^2=441+196-311.5925[/tex] and
[tex]x^2=325.4075[/tex] so
x = 18.0 or just 18
Ivan invests $5,000 into an account with a 3.5% interest that is compounded semi-annually.
How much money will he have in this account if he keeps it for 15 years?
9514 1404 393
Answer:
$8414
Step-by-step explanation:
The compound interest formula is useful for this.
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years. A is the ending balance.
A = $5000(1 +0.035/2)^(2·15) = $5000·1.0175^30 ≈ $8414.00
Ivan will have $8414 in his account after 15 years.
Tay–Sachs Disease Tay–Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the probability that their offspring will develop the disease is approximately .25. Suppose a husband and wife are both carriers of the disease and the wife is pregnant on three different occasions. If the occurrence of Tay–Sachs in any one offspring is independent of the occurrence in any other, what are the probabilities ofthese events?
a. All three children will develop Tay–Sachs disease.
b. Only one child will develop Tay–Sachs disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Answer:
a) 0.0156 = 1.56% probability that all children will develop the disease.
b) 0.4219 = 42.19% probability that only one child will develop the disease.
c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, 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.
The probability that their offspring will develop the disease is approximately .25.
This means that [tex]p = 0.25[/tex]
Three children:
This means that [tex]n = 3[/tex]
Question a:
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]
0.0156 = 1.56% probability that all children will develop the disease.
Question b:
This is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.25)^{1}.(0.75)^{2} = 0.4219[/tex]
0.4219 = 42.19% probability that only one child will develop the disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Third independent of the first two, so just multiply the probabilities.
First two do not develop, each with 0.75 probability.
Third develops, which 0.25 probability. So
[tex]p = 0.75*0.75*0.25 = 0.1406[/tex]
0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
Determine what type of transformation is represented.
A. none of these
B. reflection
C. dilation
D. rotation
Answer:
The answer is "Option D"
Step-by-step explanation:
In a rotation, an item is rotated around with a known location. Clockwise or anticlockwise spinning is possible. Rotation centers are spherical geometry in space where rotation occurs. The direction of inclination is the indicator of the total rotation made. Rotary point refers to that part point of a figure around which it is revolved.
7(a-1)=45 what is the answer to that equation????
Answer: a = 52/7
Step-by-step explanation:
remove the parentheses, move the constant to the right, calculate, then divide both sides
Answer:
The answer is, a = 52/7, or a = 7.42 in decimal form
Follow the steps below for better explanation:
What is force? How is it measured? Write any two effects of force
Answer: Please refer to:
- A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. ... Forces only exist as a result of an interaction.
- Force is a vector quantity, with both direction and magnitude. It is defined as Mass x Acceleration = Force.
+ The SI unit of force is the newton (N); defined as the unit of force which would give to a mass of one kilogram an acceleration of 1 meter per second squared.
- two effects of force:
+ It can change the state of movement of the body on which force is applied, i.e. it can move a stationary object or stop a moving object.
+ It can change the shape and size of an object.
Step-by-step explanation:
I'm not sure but hope it helps.
16)dry air is trapped in a narrow uniform glass tube by a mercury pellet of length 25cm .when the tube is placed vertical with the open end um long.what is the external pressure if the column of air becomes 40 cm in length when inverted ? . ( required answer = 74cm hg )
Step-by-step explanation:
Ru Tu yulyryosuyyyhlsgjpcbmb kvjvlcykxnlvdlbvhck
chgkbhlxyovk m.
chchhlzixhvkh
what percent is 50cent of 50cent
what
Step-by-step explanation:
pretty sure its 25 percent
Answer:
25%
Step-by-step explanation:
if you take half of 50 it is 25 so all of it is used or 25%
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Using your textbook, solve the problems below. Show your work.
Solve for y:
y + 8 = 2
Answer:
i dont know lol
Step-by-step explanation:
Point A lies outside of plane P. How many planes can be drawn that pass through point A?
A. 0
B. an infinite number
C. 2
D. 1
Answer:
D.
Step-by-step explanation:
.
The number of planes that can be drawn that pass through point A is 1.
How to estimate the number of planes that can be drawn that pass through point A?
A perpendicular line creates an angle of 90° with a line or a plane. If a line exists to be drawn from a point to a line or a plane it can only be one. In this case, a line exists to be drawn through a point A to a plane P. If the line stands to be perpendicular, then it exists only one.
Therefore, the correct answer is option D. 1.
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A survey is sent out to 500 people asking questions related to the link between religion and sexual behavior at a young age. The survey does not have any tracking device, and the results are sent to a database that gives no indication of who or where the results came from. However, the database is posted online for religion and human behavior researchers to freely conduct statistical analyses. The responses to this survey are
a. both confidential and anonymous.
b. confidential only.
c. anonymous only.
d. neither confidential nor anonymous.
Answer:
c
Step-by-step explanation:
Since the the identities of the survey takers were kept secret, it would be anonymous. If it wasn't anonymous, then people would know who took the survey.
Since the survey results were released online for analyses, it is not confidential. If it were to be confidential, then the survey distributors would have kept the results to themseles.
The distribution of SAT scores is approximately normal with a mean of 1500.
If 1628 is the 90th percentile, what is the standard deviation?
Answer:
Hello,
Answer
[tex]\sigma=457,95...[/tex]
Step-by-step explanation:
p(z<a)=0.9
p(z<1.29)=0.9015
p(z<1.28)=0.8997
using linear interpolation: with 4 decimals
p(z<1.282)<0.9
[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]
ko dung may tinh hay so sanh
3√7 vs 7√3
Answer:
what this makes bi sense haha
Step-by-step explanation:
but ok
letter A represents the decimal
Answer:
answer is 0.4
Step-by-step explanation:
Is this a function graph
HELP ME OUT ASAPPP PLSSS
Answer:
https://linksharing.samsungcloud.com/ul5cX9oOmhzt
