Answer: [tex]| x - \frac{15}{3} | = 120[/tex] or [tex]\frac{1}{3}| 3 x - 15|= 120[/tex] or [tex]| 3x - 15| = 360[/tex] or [tex]| x - 5 | = 120[/tex]
Step-by-step explanation:
Since, According to the question,
For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive $3.
And, If a contestant weighing x pounds received $15
Then the guessed weight of contestant = [tex]| x - \frac{15}{3} |[/tex]
But, Again according to the question,
The guessed weight is 120 pounds,
Thus, [tex]| x - \frac{15}{3}|= 120[/tex]
⇒ [tex]\frac{1}{3}| 3 x - 15|= 120[/tex]
⇒ [tex]| 3x - 15|= 3\times 120[/tex] (by multiplying 3 on both sides)
⇒ [tex]| 3x - 15|= 360[/tex]
⇒ [tex]3| x - 5|= 360[/tex]
⇒ [tex]| x - 5|= 120[/tex] ( On dividing both sides by 3 )
Answer:
3|x-120|=15
Step-by-step explanation:
what's that?
your welcome ;)
Please help me!!!!!!
Answer: 243, 729
Step-by-step explanation:
1, 3, 9, 27, 81 is a geometric sequence where r = 3
a₁ = 1
a₂ = 1 x 3 = 3
a₃ = 3 x 3 = 9
a₄ = 9 x 3 = 27
a₅ = 27 x 3 = 81
To find the next two terms, multiply the previous term by 3:
a₆ = 81 x 3 = 243
a₇ = 243 x 3 = 729
Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years.
1) Write an inequality that can be used to represent this situation.
2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.
Answer:
1) [tex]2s+s\leq18[/tex]
2) 6 years old
Step-by-step explanation:
Let Hannah's age be [tex]h[/tex] and her sister's age be [tex]s[/tex]
Hannah is 2 times her sister’s age:It means [tex]h=2s[/tex]
The sum of their ages is no more than 18 years:It means the sum is LESS THAN or EQUAL TO 18. So we can write:
[tex]h+s\leq18[/tex]
1. We can substitute first equation into second equation to get our desired inequality of the situation. Thus,
[tex]h+s\leq18\\2s+s\leq18[/tex]
2. To find MAXIMUM age of Hannah's sister, let's further simplify the inequality from number 1. So,
[tex]2s+s\leq18\\3s\leq18\\s\leq\frac{18}{3}\\s\leq6[/tex]
Hence, Hannah's sister's age is LESS THAN OR EQUAL TO 6. So maximum age of her sister is 6.
Could I get some help on this question?
Answer:
The triangles are similar, because the angles are congruent and the sides are proportional.
Step-by-step explanation:
The first step to see if the triangles are similar is to see if the angles are the same.
The third angle in the large triangle is
30 + 65+ unknown = 180
95 + unknown = 180
Subtract 95 from each side
unknown = 180-95
unknown = 85
So the angles are the same.
Lets check the ratio of the the sides
14 10
------ = ----------
7 5
Both simplify to 2/1 so the ratio's are the same.
The triangles are similar because the angles are congruent and the sides are proportional.
23/50 of Zanders friends prefer to stay home on Friday night what percent of Xander's friends prefer to stay home on Friday nights
Answer:
46% of Xander's friends prefer to stay home on Friday nights.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
[tex]\frac{23}{50}\ of\ Zanders\ friends\ prefer\ to\ stay\ home\ on\ Friday\ night.[/tex]
i.e
Zanders friends prefer to stay home on Friday night = 23
Total numbers of Zanders friends are 50.
Part value = 23
Total value = 50
Put in the formula
[tex]Percentage = \frac{23\times 100}{50}[/tex]
[tex]Percentage = \frac{2300}{50}[/tex]
Percentage = 46%
Therefore 46% of Xander's friends prefer to stay home on Friday nights.
Answer:
wasdd ada
Step-by-step explanation:
PLEASE HELP ASAP WILL MARK BRAINLIST
The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.
Which function equation represents the population of the city after t years?
f(t)=451,400(0.968)t
f(t)=451,400(0.032)t
f(t)=451,400(1.032)t
f(t)=451,400(3.2)t
2.The ordered pairs model an exponential function, where j is the function name and e is the input variable.
{(1, 10), (2, 50), (3, 250), (4, 1250)}
What is the function equation in sequence notation?
Enter your answer in the box.
Answer:
f(t) = 451,400(0.968)^t
Step-by-step explanation:
Exponential Decay Function:
y = b (1-r) ^t
where
b is the initial amountr is the rate of changet is timef(t)= 451,400 ( 1 - 0.032) ^t
f(t) = 451,400 (0.968) ^t
Answer:
This was the correct answer, I even provided proof from my own test. Hope this helps!
Step-by-step explanation:
Please answer this question! 25 points and brainliest!
Answer:
a -5/2 <=x
Step-by-step explanation:
5(x-2) <= 9x
Distribute the 5
5x -5*2 <= 9x
5x-10 <= 9x
Subtract 5x from each side
5x-5x-10 <= 9x-5x
-10 <= 4x
Divide by 4 on each side
-10/4 <=4x/4
-5/2 <=x
Kyle has 125 marbles. Fifty of these marbles are red and the reat are other colors. What is the ratio of the nunber of red marbles to the total of marbles expressed in simplest terms?
Answer:
The required simplest form is: [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
We have been given Kyle has 125 marbles.
And 50 out of total 125 are red and rest of them are other colours
that means other colour marble are 125-50=75
we need to find ratio of the number of red marbles to the total of marbles
The rat io is: [tex]\frac{50}{125}=\frac{2}{5}[/tex]
The required simplest form is: [tex]\frac{2}{5}[/tex]
Answer:
Step-by-step explanation:
2/5
The perimeter of a rectangle is 26 meters. The difference between the length and the width is 5 meters. Find the width
l - lenght
w - width
l - w = 5 → l = 5 + w
26 m - perimeter
l + l + w + w = 2l + 2w - perimeter
substitute l = 5 + w:
2(5 + w) + 2w = (2)(5) + (2)(w) + 2w = 10 + 2w + 2w = 10 + 4w
The equation:
10 + 4w = 26 subtract 10 from both sides
4w = 16 divide both sides by 4
w = 6
Answer: The width = 6 m.Find tan θ if sec θ = √26/5 and sin θ < 0.
Answer:
Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0 = tan θ = -1/5
Step-by-step explanation:
cos θ = 5/√26
opposite side = s
s^2 = 26-25 = 1
s = -1
tan θ = -1/5
The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 152. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 12. Ten more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.
Answer:
Number of restaurant-purchased meals eaten in a restaurant = 70
Number of restaurant-purchased meals eaten in a car = 22
Number of restaurant-purchased meals eaten in a home = 60
Step-by-step explanation:
Let the number of people that will eat in a restaurant be R.
Let the number of people that will eat in a car be C.
Let the number of people that will eat in a home be H.
From the information given in the problem we have,
R+C+H = 152 ____equation (1)
C+H-R = 12 ____equation (2)
R = H+10 ____equation (3)
1) Plugging in R=H+10 from equation 3 into the equation 2, we get
C+H-R=12
=> C+H-(H+10)=12
=> C+H-H-10=12
2) Cancelling out +H and -H, we get
C-10=12
3) Add 10 to both sides
C-10+10=12+10
4) Cancelling out -10 and +10, we get
C=22
5) Plugin C=22 in equation 1, we have
R+C+H = 152
=> R+22+H=152
Subtract 22 from both sides,
R+22+H-22=152-22
Cancelling out +22 and -22 from the left side, we get
R+H=130 ____let it be equation (4)
6) Plugin C=22 in equation 2, we have
C+H-R = 12
22+H-R = 12
Subtracting 22 from both the sides, we get
22+H-R-22 = 12-22
Cancelling out +22 and -22 from the left side,
H-R = -10 ____let it be equation (5)
7) Adding equation 4 and equation 5, we get
(R+H)+(H-R) = 130 + (-10)
=> R+H+H-R = 130-10
8) Cancelling out R and -R from the left side, we get
2H = 120
9) Dividing both sides by 2, we get
[tex]\frac{2H}{2} = \frac{120}{2}[/tex]
10) Cancelling out the 2's from the left side, we have
H=60
11) Plugging in C=22 and H=60 in the equation 1, we have
R+C+H = 152
=> R+22+60=152
=> R + 82 = 152
12) Subtracting 82 from both the sides, we get
R + 82 -82 = 152 -82
13) Cancelling out +82 and -82 from the left side, we get
R = 70
So, C=22, H=60, R=70
35 POINT QUESTION, WILL MARK BRAINLIEST. Which of the following options is a 3rd degree polynomial with exactly 1 real root?
Answer:
A. F(x) = x^3+9x^2+27x+27
Step-by-step explanation:
I am not 100% sure but I think this is right.
I found the root for this equation: x=-3
Hope this helps!
Answer:
The correct option is D.
Step-by-step explanation:
In option A,
The given function is
[tex]F(x)=x^3+9x^2+27x+27[/tex]
[tex]F(x)=x^3+3(3)x^2+3(3^2)x+3^3[/tex]
[tex]F(x)=(x+3)^3[/tex] [tex][\because (a+b)^3=a^3+3a^2b+3ab^2+b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x-3)=0\Rigtharrow x=-3[/tex]
The real root of this function is -3 with multiplicity 3. It means this function has 3 real roots.
In option B,
The given function is
[tex]F(x)=x^3+3x^2-9x-27[/tex]
[tex]F(x)=x^2(x+3)-9(x-3)[/tex]
[tex]F(x)=(x^2-9)(x+3)[/tex]
[tex]F(x)=(x+3)(x-3)(x+3)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x+3)=0\Rigtharrow x=-3,3,-3[/tex]
Therefore, this function has 3 real roots.
In option C,
The given function is
[tex]F(x)=x^3-9x^2+27x-27[/tex]
[tex]F(x)=x^3-3(3)x^2+3(3^2)x-3^3[/tex]
[tex]F(x)=(x-3)^3[/tex] [tex][\because (a-b)^3=a^3-3a^2b+3ab^2-b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x-3)(x-3)(x-3)=0\Rigtharrow x=3[/tex]
The real root of this function is 3 with multiplicity 3. It means this function has 3 real roots.
In option D,
[tex]F(x)=x^3+3x^2+9x+27[/tex]
[tex]F(x)=x^2(x+3)+9(x+3)[/tex]
[tex]F(x)=(x+3)(x^2+9)[/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x^2+9)=0[/tex]
[tex]x+3=0\Rightarrow x=-3[/tex]
[tex]x^2+9=0\Rightarrow x^2=-9\Rightarrow x=\pm 3i(Imaginary)[/tex]
The roots of this functions are -3, 3i and -3i. Since this function has exactly one real root, therefore option D is correct.
Sammy bought a new car. The depreciation equation is given by f(x) = 30,000(.85)x, where x represents the number of years since the purchase of the car, and f(x) represents the value of the car. By what percent does Sammy's car depreciate each year?
In a depreciation equation, you multiply the value of the car by the percent of depreciation minus 1.
In the given equation you are multiplying the value of the car by (.85)
This means the percent of depreciation would be 1 - 0.85 =0.15 which is 15%
The car depreciates by 15% every year.
Answer:
The car depreciates by 15% every year.
Step-by-step explanation:
Choose which of the following functions has a domain of all real numbers. Select all that apply. y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, y = 3 - x^2.
Answer:
all of the above
Step-by-step explanation:
Every one of these functions is defined for all values of x.
All the provided functions: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, have a domain of all real numbers. This means any real value can be input into these functions to get a real output.
Explanation:The domain of a function is the set of all possible input values (usually represented by x) that will give an output value. In this case, we are asked to identify which of the provided functions have a domain of all real numbers. For the functions given: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, all of them have a domain of all real numbers. This is because no matter what value of x you choose, these functions will always provide a valid output of y. In other words, you can input any real number into these functions and get a real number out.
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Use substitution to find the solution to the system of equations. 5x+7y=-29 y=x+1
Answer:
(x, y) = (- 3, - 2)
Step-by-step explanation:
given the 2 equations
5x + 7y = - 29 → (1)
y = x + 1 → (2)
substitute y = x + 1 into (1)
5x + 7(x + 1) = - 29 ( distribute and simplify left side )
5x + 7x + 7 = - 29
12x + 7 = - 29 ( subtract 7 from both sides )
12x = - 36 ( divide both sides by 12 )
x = - 3
substitute x = - 3 into (2)
y = - 3 + 1 = - 2
solution is (- 3, - 2 )
Answer:
(-3,-2)
Step-by-step explanation:
If $a$, $b$, $c$, and $d$ are replaced by four different digits from $1$ to $9$, inclusive, then what's the largest possible value for $a.Bc + 0.D$ ?
The largest possible value for (a.bc + 0.d) is (10.56).
The largest possible value for (a.bc + 0.d) when (a), (b), (c), and (d) are replaced by four different digits from 1 to 9, inclusive, can be found by selecting the largest digits for (a), (b), and (c), and the smallest digit for (d).
This results in the number (9.86 + 0.7), which equals (10.56).
Therefore, the largest possible value for (a.bc + 0.d) is (10.56).
Complete question:
If a,b,c,d are replaced by four different digits from 1 to 9, inclusive, then what's the largest possible value for a.bc + 0.d ?
Which of the following ordered pairs represents the solution to the system given below?
x − 4y = 7
5x + 9y = 6
Answer:
The solution to the system would be (3, -1)
Step-by-step explanation:
You can find the solution to this system by using the elimination method. To do that, start by multiplying the top equation by -5 and then adding it through.
-5x + 20y = -35
5x + 9y = 6
-----------------
29y = -29
y = -1
Now that we have the value of y, we can plug it into either equation and find the x value.
x - 4y = 7
x - 4(-1) = 7
x + 4 = 7
x = 3
Final answer:
The solution to the given system of equations is the ordered pair (3, -1).
Explanation:
To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
1. Solve the first equation for x:
x = 7 + 4y
2. Substitute this value of x into the second equation:
5(7 + 4y) + 9y = 6
3. Simplify and solve for y:
35 + 20y + 9y = 6
29y = -29
y = -1
4. Substitute the value of y back into the first equation to find x:
x = 7 + 4(-1)
x = 3
Therefore, the solution to the system is the ordered pair (3, -1).
PLEASE PLEASE HELP PLEASE
Answer:
arc ≈ 25.13 feet
Step-by-step explanation:
arc length = circumference × fraction of circle
= 2 πr × [tex]\frac{\frac{4\pi }{3} }{2\pi }[/tex] ← cancel 2π
= 6 × [tex]\frac{4\pi }{3}[/tex] = 8π ≈ 25.13 feet
A total of 60 60 children signed up for hockey. There were 3 3 boys for every 1 1 girl who signed up. How many of the children who signed up for hockey were girls?
Answer: 15
Step-by-step explanation:
Boys : Girls
3x + 1x = 60
4x = 60
x = 15
Girls (1x) = 1(15) = 15
Answer:
The answer is 15
hey please help me with this
Answer:
Two real solutions
Step-by-step explanation:
z=-1.45
z=0.45
Answer:
ANSWER: Two real solutions
Step-by-step explanation:
its z=-1.45
its z=0.45
Martha estimated there were 89 marbles in a jar for a contest. The actual number of marbles in the jar was 111. What was the percent error of Martha's estimation?
Answer:
18.91 percent
Step-by-step explanation:
Percent error equation: Difference or Difference/Actual
Actual
The difference is the greater amount minus the smaller.
111 - 89 = 22
The actual is 111.
Now divide 22/111.
22/111 = 0.189 repeating
0.189 repeating = about 18.91 percent
Simplify f+g / f-g when f(x)= x-6 / x+7 and g(x)= x-7 / x+6
Answer:
C. 2x^2 - 85 / 13
At the beginning of the week Fayez writes drown the mileage of his limousine - 2529 At the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during the week. The handbook states that the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limousine used 1 gallon of petrol for every 20 miles this week 1 gallon = 4.54 litres Did his limo use 1 gallon of petrol for every 20 miles that week? Explain answer in full Please help!!
Antonio earns $5 an hour for raking leaves. He also has $35 in savings. Which equation shows the amount of money, m, Antonio will have after raking leaves for a number of hours, h?
Answer:
35 + 5h = m
Step-by-step explanation:
please help? i honestly don't know
a population of bacteria doubles every 15 hours, initially the population of bacterica is 40. what is the population of the bacteria after 40 houra?
Answer:
the bacteria's population is 120
Step-by-step explanation:
Answer:
After 40 hrs it is 213.333 bacterias
Approximately 213 bacterias
Step-by-step explanation:
Initial population of bacteria is 40
And it doubles every 15 hrs
If 15 hrs is double
1 hrs is 0.13333
Then 10 hrs is 1.3333
So the first 15 hrs
It multiplies to 40*2= 80
The second 15 hrs it multiplies by 80*2=160
The next 10 hrs it multiplies by
160*1.33333= 213.333
A mayoral candidate would like to know her residents’ views on a public open space before the mayoral debates. She asks only the people in her office. Her co-workers are an example of a ______.
census
population
convenience sample
simple random sample
Answer:
convenience sample
Step-by-step explanation:
Answer: Convenience Sample
Step-by-step explanation: Biased sample–Parts of the population are favored over others. She only asked people in her office
Melanie's trip was 500 miles long. She drove the same number of miles each day for 3 days. How many miles did she drive each day? Write the answer as a mixed number
Melanie drove a total of 500 miles over three days. To determine how many miles she drove each day, we divided total miles by total days. This gives us 166.67 miles or 166 2/3 miles as a mixed number.
Explanation:The subject of the provided question is related to simple division. Here, Melanie has traveled 500 miles in total over the course of three days, and she drove the same distance each day. Mathematically speaking, to find out how many miles Melanie drove each day, we need to divide the total distance by the number of days. Hence, we divide 500 miles by 3 days.
This comes out to be 166.67 miles, which is the decimal format of the distance traveled by Melanie each day. However, the question asks for the answer to be written as a mixed number. Therefore, 166.67 miles can be expressed as 166 2/3 miles per day, as a mixed number. This is calculated by expressing the decimal .67 as a fraction.
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Help me with this please
4.42×10^34 molecules/min
Step-by-step explanation:Multiply the various factors, along with the unit conversion (60 s/min).
... (3.35×10^25 molecules/L) × (2.2×10^7 L/s) × (60 s/min)
... = (3.35×2.2×60)×10^(25+7) molecules/min
... = 442.2×10^32 molecules/min
... ≈ 4.42×10^34 molecules/min
_____
Comment on scientific notation problems
Your scientific or graphing calculator will allow you to enter and display numbers in scientific notation.
It takes layla 2/5 hour to swim 1/2 mile what is the unit rate of miles that layla can swim per hour
Good Morning!
Distance = rate x time
1/2 mile = R x 2/5 hour
1/2=2/5R
/2/5 /2/5
R=1/2 x 5/2
R=1 1/4
She can swim 1 1/4 per hour.
I hope this helps! :)
Answer:
1 1/4
Step-by-step explanation:
i think it is a check my answer?
What function equation is represented by the graph?
f(x)= 4 x +4
f(x)= 4 x +5
f(x)= 3 x +5
f(x)= 3 x +4
Answer:
I am 99% sure the answer is f(x)= 4x + 5
Step-by-step explanation:
That is because the line intercepts y at 5 and every 4 cubes the line hits a corner...
Answer:
F(x)=4x +5
Step-by-step explanation:
A summer camp has 32 campers. A total of 22 of them swim, 20 play softball, and 5 do not swim or play softball. Which values complete the table?
a = 15, b = 10, c = 7, d = 5, e = 12
a = 15, b = 7, c = 5, d = 10, e = 12
a = 14, b = 7, c = 5, d = 12, e = 10
a = 14, b = 12, c = 7, d = 5, e = 10
Answer:
a = 15, b = 7, c = 5, d = 10, e = 12
Step-by-step explanation:
You only need to find d.
22+d=32, d=10
Only one choice has d=10
Don't waste time checking the others.
Answer:
It’s B
Step-by-step explanation: