Answer:
9x³−3x²−2x+7
Step-by-step explanation:
Mang Efren is now 5 times as old as his son. Four years ago, the product of their ages was 52. Find Mang Efren's present age in years. (Just type in the numerical value of your answer)
Mang Efren's present age is 30 years.
Let's assume the present age of Mang Efren's son is x years.
Mang Efren is presently 5 times as old as his son.
So, Mang Efren's present age = 5x years
Four years ago,
Mang Efren's son's age = x - 4 years.
Mang Efren's age = 5x - 4 years
According to the question, four years ago, the product of their ages was 52.
From this information, we will create an equation.
(x - 4)(5x - 4) = 52
5x² - 4x - 20x + 16 = 52
5x² - 24x + 16 - 52 = 0
5x² - 24x - 36 = 0
Solving the quadratic equation to obtain the value of x,
5x² - 30x + 6x - 36 = 0
5x(x -6) + 6(x - 6) = 0
(5x - 6)(x - 6) = 0
x = 6
So, Mang Efren's present age is 5 × 6 = 30 years.
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How do you write 6% as a fraction or mixed number?
Answer:
As a fraction: 3/50
It cannot be turned into a mixed number
an elementary school is offering 3 language classes: one in spanish, one in french, and one in german. the classes are open to any of the 100 students in the school. there are 28 students in the spanish class, 26 in the french class, and 16 in the german class. there are 12 students that are in both spanish and french, 4 that are in both spanish and german, and 6 that are in both french and german. in addition, there are 2 students taking all 3 classes.
Using Venn diagram, if a student is chosen randomly, (a) the probability that he or she is not in any of the language classes is 0.5, (b) the probability that he or she is taking exactly one language class is 0.32, and (c) if 2 students are chosen randomly, the probability that at least 1 is taking a language class is 0.753.
Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)
Let A = students in the Spanish class = 28
B = students in the French class = 26
C = students in the German class = 16
Hence, the probability of each class is:
P(A) = 28/100 = 0.28
P(B) = 26/100 = 0.26
P(C) = 16/100 = 0.16
P(A ∩ B) = 12/100 = 0.12
P(B ∩ C) = 6/100 = 0.06
P(A ∩ C) = 4/100 = 0.04
P(A ∩ B ∩ C) = 2/100 = 0.02
(a) P(not A, B, C) = 1 - P(A ∪ B ∪ C)
P(not A, B, C) = 1 - [P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]
P(not A, B, C) = 1 - (0.28 + 0.26 + 0.16 - 0.12 - 0.06 - 0.04 + 0.02)
P(not A, B, C) = 1 - 0.5
P(not A, B, C) = 0.5
(b) P(A, B, C only) = P(A only) + P(B only) + P(c only)
P(A, B, C only) = [P(A) - P(A ∩ B) - P(A ∩ C) + P(A ∩ B ∩ C)] + [P(B) - P(A ∩ B) - P(B ∩ C) + P(A ∩ B ∩ C)] + [P(C) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]
P(A, B, C only) = (0.28 - 0.12 - 0.04 + 0.02) + (0.26 - 0.12 - 0.06 + 0.02) + (0.16 - 0.06 - 0.04 + 0.02)
P(A, B, C only) = 0.14 + 0.10 + 0.08
P(A, B, C only) = 0.32
(c) P = 1 - (50/100 x 49/99)
P = 1 - (49/198)
P = 149/198
P = 0.753
To complete the problem, here are the questions:
(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
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Growing linearly, the balance owed on your credit card triples from $500 to $1500 in 9 months. If the balance were growing according to the exponential function f(x)=500(1+0.13)x where x represents the number of months, what would the balance be after 9 months? Round your answer to the nearest cent.
If the balance were growing according to the exponential function, the balance owed on your credit card after 9 months is equal to $1,502.02.
What is an exponential function?In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of an argument.
From the information provided, an exponential function that models or represents the rate at which the balance owed on your credit card triples is given by:
f(x) = 500(1 + 0.13)^x
Where:
f(x) represents the balance owed on your credit card.x represents the number of months.After 9 months, the balance owed on your credit card would be calculated by substituting the value of x with 9 as follows:
Balance owed, f(x) = 500(1 + 0.13)^9
Balance owed, f(x) = 500(1.13)^9
Balance owed, f(x) = 500 × 3.0040419380
Balance owed, f(x) = $1,502.02.
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Complete Question:
Growing linearly, the balance owed on your credit card triples from $500 to $1500 in 9 months. If the balance were growing according to the exponential function f(x) = 500(1 + 0.13)^x, where x represents the number of months, what would the balance be after 9 months? Round your answer to the nearest cent.
Answer:
$1502.02
Step-by-step explanation:
f(x)=500(1+0.13)^x
f(9) = 500(1.13)^9
f(9) = 500(3.004041938)
f(9) = 1502.02
Answer: $1502.02
Find all values for x that will make this expression equal to 0.
3x(x+6)
Answer:
3x(x+6)
=(3x)(x+6)
=(3x)(x)+(3x)(6)
=3x2+18x
Step-by-step explanation:
(Laws of Exponents with Integer Exponents LC) Simplify (34)−1. one over three raised to the fourth power one over three raised to the power of negative four −34 33
The simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
In the question ,
the expression is given as (3⁴)⁻¹ ,
the rule of law of exponents states that a⁻ⁿ = 1/aⁿ .
Using the above mentioned law of indices , the expression (3⁴)⁻¹ can be written as ,
(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴
which can be expressed in words as one over three raised to the fourth power .
Therefore , the simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
The given question is incomplete , the complete question is
The Simplified value of (3⁴)⁻¹ is
(a) one over three raised to the fourth power
(b) one over three raised to the power of negative four
(c) −3 to the power of 4
(d) 3 to the power of 3
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Evaluate the expression for x=-1,0, 1, 2
-3x + 4
X=0
X=-1
x = 1
X=2
Answer:
-3(-1) + 4 = 3 + 4 = 7
-3(0) + 4 = 0 + 4 = 4
-3(1) + 4 = -3 + 4 = 1
-3(2) + 4 = -6 + 4 = -2
Clay is flying a helicopter at an altitude of 400 feet in the air. Jason is diving 200 feet below the surface.
How far apart are Clay and Jason?
Explain how to show the distance between Clay and Jason using absolute value.
Clay and Jason are 600 feet far apart.
When an object goes above the surface, the altitude is measured as +ve and when an object goes below the surface, the altitude is measured as -ve.
Since Clay is flying a helicopter at an altitude of 400 feet in the air,
The Value of altitude of Clay = +400
Since, Jason is diving 200 feet below the surface,
The Value of altitude of Jason = -200
The the distance between Clay and Jason = (The Value of altitude of Clay) - (The Value of altitude of Jason)
= +400 - (-200)
= 400 + 200
= 600 feet
Therefore, the distance between Clay and Jason is 600 feet.
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HELP!!!! HELP HELP HELP HELP
The matchings are:
3x - y = -5 ⇒ table C.
x - 3y = 12 ⇒ table A.
3x - y = -2 ⇒ table D.
2x - 3y = 9 ⇒ table B.
How to match each equation to the correspondent table?The first equation we have is:
3x - y = -5
Evaluating in x = 0, we have:
3*0 - y = - 5
y = 5
So we have the point (0, 5).
Evaluating in x = -2 we get:
3*-2 - y = -5
6 + y = 5
y = 5 - 6 = -1
So we have the point (-2, -1)
The only table with that point is table C, so we conclude that it is the correct option.
2) The second equation is:
x - 3y = 12
Evaluating in x = 0 we get:
0 - 3y = 12
y = 12/-3 = -4
So we have the point (0, -4)
if x = 3 we have:
3 - 3*y = 12
-3*y = 12 - 3 = 9
y = 9/-3 = -3
So we have the point (3, -3)
The only table with these two points is table A, so that is the correct one.
3) The next equation is:
3x - y = -2
The tables left are B and D.
Now, let's evalaute this equation in x = 3.
3*3 - y = -2
9 - y = -2
9 + 2 = y
11 = y
So we have the point (3, 11)
Notice that on table B,the value associated to x = 3 is y = -1, so we discard table B, and we conclude that this equation relates to table D.
Trivially, the last equation:
2x - 3y = 9
Matches table B.
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HELP I’LL MARK BRAINLIEST AND ITS 100 POINTS
p: a month begins with the letter M; q: it has 31 days
match the statements
1) conditional
2) converse
3) inverse
4) contrapositive
if a month does not begin with the letter M then it does not have 31 days
if a month does not have 31 days then it does not begin with the letter
if a month begins with the letter M then it has 31 days if a month has 31 days then it begins with the letter M
Answer:
1) Conditional
If a month begins with letter M, then it has 31 days.
2) Converse
If a month has 31 days, then it begins with letter M.
3) Inverse
If a month does not begin with the letter M, then it does not have 31 days.
4) Contrapositive
If a month does not have 31 days, then it does not begin with the letter M.
Step-by-step explanation:
1) Conditional
If a month begins with letter M, then it has 31 days.
2) Converse
If a month has 31 days, then it begins with letter M.
3) Inverse
If a month does not begin with the letter M, then it does not have 31 days.
4) Contrapositive
If a month does not have 31 days, then it does not begin with the letter M.
Conditional statement states the original statement. If 'p' , then 'q'
Converse statement switch positions in the original if --then statement. If 'q', then 'p'
Inverse statement states the opposite of the original statement. If not 'p', then not 'q'.
Contrapositive if not 'q' , then not 'q'.
Which of the following situations can be modeled by the equation?
answer = a
formula; a(1 + r)^x
a = the initial amount - 7.71 [answer cannot be b or d]
! i think it's a as the decay factor is < 1, therefore, 100-.933333
I need help with this assignment
Answer:
8800000 or 88x 10^5
Step-by-step explanation:
4x2200000=8800000
your pulse reflects the rate at which your heart beats. a healthy resting pulse rate in adults is between 60 and 100 beats per minute. in which of these two settings is a binomial distribution more likely to be at least approximately correct? explain your answer. (a) you select at random 10 times in the next 24-hour period to take your pulse. you then go about your usual activities, including exercising and sleep. the random variable ???? is the number of measurements that are less than 100 beats per minute. (b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.
The situation in which the binomial distribution can be approximated to the normal distribution is given by:
(b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The binomial distribution can be approximated to the normal distribution if there are at least 10 failures and 10 successes on the experiment, that is:
np ≥ 10, n(1 - p) ≥ 10.
Meaning that a large number of trials is usually required for the approximation.
In the context of this problem, to achieve the large number of trials needed for the approximation, multiple days are needed to take the observations, hence option b is correct.
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How much hours does it take the robot to complete one task
Answer:
0.41
Step-by-step explanation:
Please help. I would appreciate it! Will mark brainlyest if you remind me and if someone replies just remind me!
In the picture there is a prism with measures. The surface area of prism is 156.
Given that,
In the picture there is a prism with measures.
We have to find the surface area of prism.
The surface area of prism=(2×base area)+(Base perimeter×height)
The base is trapezoid
So, the area of trapezoid is (a+b)/2×h
=(6+12)/2×4
=18/2×4
=9×4
=36
Here base area we got is 36.
Now, we find the perimeter of trapezoid is a+b+c+d
=6+12+5+5
=18+10
=28
Here, base perimeter we got is 28.
Now surface area of prism is
=(2×36)+(28×3)
=72+84
=156
Therefore, the surface area of prism is 156.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The answer is not D
Answer:
b
Step-by-step explanation:
Thực hiện phép tính -7x^2(3x-4y)
Answer: -21x^3 + 28x^2 y
what is the value of n?
Answer: Sorry for the late answer, I was already answering it by the time someone else answered
Step-by-step explanation:
Since two angles on a straight line add up to 180, I used the angles given to find the adjacent angles to it by subtracting those angles from 180. Then, since the angles of a triangle add up to 180, I used the angles I just solved for to find the angle that is adjacent to n. I did the same thing I did to the first two angles by subtracting it from 180 to find n, which was 69 degrees
I need help..........
Answer:
y=1.34x-3.22
Step-by-step explanation:
y=mx+b
find m/ gradient:
[tex]m = \frac{-3.94 - 2.4}{-4.75 - 0}[/tex]
∴[tex]m=1.34[/tex]
find b/ y-intercept:
sub (2.4,0)
0= 1.34 (2.4) +b
b=0-3.216
b= -3.216
∴ b=-3.22(2.d.p)
linear equation:
∴1.34x-3.22
Could you guys help a sista out? I’m struggling
if u know this please help
Answer:
alternate angles and corresponding angles.
and vertical opposite angles
Step-by-step explanation:
#G o o g l e
what two numbers multiply to 2400 and add up to -16?
Based on the fact that the two numbers multiply to 2,400 and add up to -16, the numbers are undefined.
How to find the numbers?Assume that one of the numbers is x and the other number is y, the system of equations to represent this is given that the two numbers add up to -16 and multiplying to 2,400:
x + y = -16
xy = 2,400
Expressing y in terms of x :
xy = 2,400
y = 2,400 / x
Solving for x gives:
x + y = -16
x + (2,400 / x) = -16
x = 0
y = 0
The problem given in the question is wrong because the results of x and y are undefined.
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If Maggie corrected her mistake, what would be the correct answer for x?
correct value of x will 9 if Maggie corrected her mistake.
WHAT IS LINEAR EQUATION ?When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0. The variables x and A in this situation are variables, whereas B is a constant.
CALCULATIONApplying the parallel line theorem
alternate angles are always equal -
therefore ,
4x + 2 = 7x - 25
27 = 3x
x = 9
so , the correct value of x will be 9 if maggie corrected her mistake
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Melissa rented a Segway, a stand up scooter, in downtown Austin, Tx. The store charges a $3.25 initial charge plus $2.50 per mile. Which equation can be used to find y, the total cost of the rental, if x represents the number of miles Melissa rode on the Segway?
pls it has to be like "y=mx+b"
Answer:
y = x(2.50)+3.25
Step-by-step explanation:
y (total cost )= x (miles rode) * 2.50 (cost per mile) + 3.25 (initial cost)
Ella walks to the art store at 2mph, but returns home at 4 mph. If her total walking time is 1/2 an hour, how far away is the art store? Express your answer as a fraction.
The distance of art store from Ella's house is 2/3 miles or 0.67 miles.
It is a question of time, speed and distance.
It is given in the question that Ella walks to the art store at 2mph, but returns home at 4 mph.
Also, the total time taken by Ella to cover the journey is 1/2 an hour.
We have to find the distance of art store from Ella's house.
Let the distance from Ella's house to art store be d miles.
We know that,
Speed = distance/time
Time = distance/speed
Hence, we can write,
time = d/2 (walking to the art store from from)
Also,
time = d/4 (walking to home from the art store)
Hence,
d/2 + d/4 = 1/2
3d/4 = 1/2
d = 2/3 miles or 0.67 miles.
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Solve 7x − 2(x + 1) = 6x + 14
A. x = −12
B. x = 12
C. x = −16
D. x = 16
I don't know what to do here.
Answer: C, x = -16
Step-by-step explanation:
1. Distribute
7x-2(x+1)=6x+14
7x-2x-2=6x+14
2. Combine like terms
7x-2x-2=6x+14
5x-2=6x+14
3. Add 2 to both sides
5x-2+2=6x+14+2
4. Simplify
Add the numbers
5x=6x+16
5. Subtract 6x from both sides
5x-6x=6x+16-6x
6. Simplify
Combine like terms
-x=16
7. Divide both sides by the same factor
-x/-1=16/-1
8. Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
The price of a math textbook can be modeled by the equation:
y = 2x + 76, where x is time in years and y is the price of
the textbook. This equation tells us that the textbook originally
cost $76 and each year the cost went up $2. How many years
will it take for the textbook to cost $100?
Please answer all questions. I really need help! Thank you
For the quadratic equation:
x^2 + 7x = 8x + 12
The two solutions are:
x = 4
x = -3
How to find the zeros of the quadratic equation?I'm only solving the first question, as it is how the guidelines say.
Here we have the quadratic equation:
x^2 + 7x = 8x + 12
First, we can rewrite this equation as:
x^2 + 7x - 8x - 12 = 0
x^2 - x - 12 = 0.
Using Quadratic formula we can see that the solutions (or zeros of the quadratic) are:
x = (1 ± √( (-1)^2 - 4*1*-12))/(2*1)
x = (1 ± 7)/2
Then the two solutions are:
x = (1 + 7)/2 = 4
x = (1 - 7)/2 = -3
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The Jules Server Scholarship Fund gives a graduation award of
$250.00 to a graduating senior at North End High School. Currently the
fund has a balance of $8300.00 in an account that pays 2.2% interest
compounded annually. Will the amount earned in annual interest be enough
to pay for the award?
The compound interest of $182.60 will not be enough to pay for the award.
What is compounding?Compounding is the process by which interest is added to both the principal balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns to interest are magnified over time, or the so-called "miracle of compounding." For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest.So, annual interest will be sufficient to serve the award:
Compound interest of $83020.00 at the annual interest of 2.2% for 1 year will be $182.60.The total amount after 1 year will be $8482.60.(Refer to the compound chart given below)
Interest will be $182.6 and the graduation award is $250.00, so the interest will not be enough to pay for the award.Therefore, the compound interest of $182.60 will not be enough to pay for the award.
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12. Adam didn't sleep well the night before a big trip. He only slept 4 ½ hours. This is 3/5
of what he usually sleeps. How many hours does he usually sleep?
Answer:
seven and a half hours
Step-by-step explanation:
aa