Answer:
Step-by-step explanation:
We first need to come up with a system of equations that models this situation. Let's call apple pies "a" and lemon pies "L". Then we look to each individual involved in selling these pies and come up with an equation for each. Scott sold 3 apple and 12 lemon pies. The combination of this number of these 2 types of pies grossed him $141. In equation form, the combination of this number of these 2 types of pies is an addition thing. Namely,
3a + 12L = 141
For Paul, his combination was 2 apple and 5 lemon for a total of $64. His equation is
2a + 5L = 64
We need to solve this system either by substitution or elimination/addition to come up with the cost of both types of pies. I chose elimination/addition because I think in this case it is easier, and easier is good.
Setting up for elimination/addition:
3a + 12L = 141
2a + 5L = 64
Let's first eliminate the a terms. That means that the coefficient on each a has to be the same but with different signs. The LCM of both 3 and 2 is 6, so we will multiply the top equation by 2 and the bottom equation by -3 (we could also have chosen to eliminate the L's first; we also could have chosen to eliminate the a's first but made the 2 negative instead of the 3. As long as you do the math correctly, you'll get the same answer regardless of how you choose to do it). Multiplying the first equation by 2 and the second by -3 gives us a new system:
6a + 24L = 282
-6a - 15L = -192
The reason this is called the elimination or addition method is because the goal is to eliminate, but you do that by adding the columns together. As you can see, 6a - 6a eliminates the a terms, right? What you're left with then is
9L = 90 and
L = 10
Now that we know the cost of a lemon pie, we can back sub in to solve for the cost of an apple pie. It doesn't matter which equation you back sub into, as long as it has both an L and an a in it. I'll choose the first equation we wrote when we took on this nightmare:
3a + 12L = 141. Subbing in 10 for L gives us
3a + 12(10) = 141 and
3a + 120 = 141 and
3a = 21 so
a = 7
That means that lemon pies cost 10 each and apple pies cost 7 dollars each.
what are the values of the coefficient and constant term of 0 = 4 - 7 x^2 + x in standard form? a= b= c=
Step-by-step explanation:
0 = 4 - 7 x^2 + x
0= (-7)x^2 + (1)x + 4
a= -7
b = 1
c= 4
basil asks 40 students how many books they bought last year. the chart shows information about the number of books they each bought.
a) what is the percentage of those students who bought 20 or more books?
b) work out an estimate for the mean number of books bought.
please show the full working out.
Number of students who bought 0-4 books= 9
number of students who bought 5-9 books= 10
number of studenst who bought 10-14 books= 13
number of students who bought 15-19 books= 2
number of studenst who bought 20-24 books= 6
please show the full working out
Answer:
a) 15% b) 10.25Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = number of expected outcome/total outcome.
a)Total number of student is the total outcome = 40
Expected number of outcome is the number of students who bought 20 or more books = 6 (number of students who bought 20-24 books)
Probability of those students who bought 20 or more books = 6/40 = 0.15
Expressing as percentage = 0.15 * 100 = 15%
This means that 15% of the total students bought 20 or more books
b) Mean is calculated using the formula [tex]\overline x =\frac{\sum fx}{N}[/tex]
f is the frequency
x is the midpoint of the class interval
N is the total number of students.
Check the attachment for the frequency table.
[tex]\overline x = \frac{410}{40}\\ \overline x = 10.25[/tex]
Mean number of books bought is 10.25
Please help! Correct answer only please! I need to finish this assignment by today.
On a residential single lane road there was a wreck that backed up traffic for 4 miles. 70% of the traffic consists of cars and 30% of the traffic consists of trucks. the average distance between vehicles is 3 feet. the average length of a car is 13.5 feet and the average length of a truck is 20 feet. estimate how many vehicles are stuck in the traffic jam.
(hint: there are 5280 feet in 1 mile)
A) 276
B) 896
C) 1172
D) 1412
what types of solutions does this equation have?
Answer:
Two imaginary solutions.
Step-by-step explanation:
In order to simplify the equation, we square root both sides. As the argument (value in the root) is negative, and we know that the square root function's domain is only positive numbers, we would have two imaginary solutions.
This would be positive/negative [tex]3i\sqrt{5}[/tex].
Another way to visualize this is by looking at the parabola's graph. Through algebraic manipulation, we know that the parabola is z^2 + 45. This parabola never crosses the x-axis. Therefore there are two solutions that are imaginary.
I hope this helps!
Which polynomial is in standard form?
Answer:
B
Step-by-step explanation:
Standard form is just descending powers.
Highest power in the polynomial is 5,
Second highest is 2,
Third Highest is 1 (x^1 = 9x)
Lowest is x^0 (the 12 is actually 12*x^0 = 12*1)
:-)
The question is above please help
Answer:
10x³ - 6x² - 9x + 12
Extra information:
★ Cubic polynomial: A polynomial of degree three is called cubic polynomial.
It is of the form P ( x ) = ax³ + bx² + cx + d [ Where a,b,c,d are real numbers and a is not equal to 0 . ]
plz help, if your answer is correct I will give it a brainiest, plzzzzz help
sorry I don't want to give you the wrong answer
Answer:
42 units²
Step-by-step explanation:
It can be split in two parts:
rectangle with sides of 1 and 12 units and
a right triangle with base (6-1)= 5 units and the height of 12 units.
then the area:
A= 1*12 + 1/2*5*12= 12+ 30= 42 units²Write the fraction as a percent. Round to the nearest tenth of a percent if necessary.
17/40
Plsss help !!
Answer:42.5%
Step-by-step explanation:
Answer:
the answer is 42.5%
Step-by-step explanation:
you multiply both 40 and 17 by 2.5 to get 42.5/100 which is the percent in fraction form
Shelley sells 5 bone-shaped treats for $3.50. How much should she charge for a package of 12 treats? Which proportion is needed to solve the problem? StartFraction 5 over 12 EndFraction = StartFraction x over 3.5 EndFraction StartFraction 12 over 3.5 EndFraction = StartFraction 5 over x EndFraction StartFraction 3.5 over 12 EndFraction = StartFraction 5 over x EndFraction StartFraction 5 over 3.5 EndFraction = StartFraction 12 over x EndFraction
Answer:
StartFraction 5 over 3.5 EndFraction = StartFraction 12 over x EndFraction
or [tex]\frac{5}{3.5}[/tex] = [tex]\frac{12}{x}[/tex]
Step-by-step explanation:
Answer:
it’s D
Step-by-step explanation:
Which verbal expression shows 4-n?
Answer:
are there answer choices because if there is i can help you
If a conditional statement is “If the sun shines, people will be in good moods”, what is the statement “If the sun does not shine, people will not be in good moods.” A. converse B.conditional C. inverse D. contrapositive
Answer:
C. Inverse
Step-by-step explanation:
The second statement is the inverse, because in an inverse, the hypothesis and the conclusion are both negated. In this case, the sun doesnt shine and the people wont be in a good mood, as opposed to the sun will shine, and the people will be in a good mood.
Answer:
Inverse
Step-by-step explanation:
Lisa sees a dress in a sale .The normal price of the dress is $45 the price that she reduced by 12% in a sale work out the price of the dress in the sale
Answer:
$39.6
Step-by-step explanation:
If (2 − √3) is a zero of a quadratic polynomial then the other zero is __________.
Answer:
(2+sqrt3)
Step-by-step explanation:
Assertion(A): (2-√3) is one zero of the quadratic polynomial then the other zero will be (2+√3).
Reason (R): Irrational zeros (roots) always occurs in pairs.
What is the other zero of the polynomial if one zero of the quadratic polynomial?Since the given polynomial is a quadratic so it has only two zeros. Let other zero be x. Hence, the other zero is (2 -√3).
What is one zero of the quadratic polynomial?Polynomials that have only one zero mean both values of the variable are the same. This is the case of equal zeros of a quadratic equation. Let x be the variable of a quadratic equation and both zeroes of the quadratic equation are 2, i.e., equal roots.
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I run a book club with $n$ people, not including myself. Every day, for $365$ days, I invite five members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of five members over all $365$ days?
Answer:
Step-by-step explanation:
if we have n people and we want to do groups of 5, the total number of different combinations is:
[tex]c = \frac{n!}{(n - 5)!5!}[/tex]
find the smallest n such c > 365.
let's do it by brute force:
if n = 5, we have:
[tex]c = 5C_5 = 5[/tex]
if n = 6
[tex]c =6C_5 =6[/tex]
if n = 7
[tex]c = 7C_ 5= 21[/tex]
if n = 8
[tex]c = 8C_5 = 56[/tex]
if n = 9
[tex]C = 9!/(4!*5!) = 126[/tex]
so 9 is not enough, let's see N = 10
C = 10!/(5!*5!) = 252
10 is not enough, let's see with 11.
C = 11!/(6!*5!) = 462
So you need at least 11 members in the club.
Then the minimum number of members such we have more than 365 combinations is 11 members
Client need al least 11 members in the club.
Permutation and CombinationAccording to the question,
Group of five members, the combination will be:
→ [tex]c = \frac{n!}{(n-5)! \ 5!}[/tex]
By using Brute force,
If n = 5,
c = 5,
C₅ = 5
If n = 6,
c = 6,
C₅ = 6
If n = 7,
c = 7,
C₅ = 21
If n = 8,
c = 8,
C₅ = 56
Now,
If n = 9,
→ C = [tex]\frac{9!}{(4!\times 5!)}[/tex]
= 126
and, If n = 10,
→ C = [tex]\frac{10!}{(5!\times 5!)}[/tex]
= 252
and, If n = 11,
→ C = [tex]\frac{11!}{(6!\times 5!)}[/tex]
= 462
Then perhaps the minimal number of individuals required to have more than 365 possible combinations seems to be 11.
Thus the response above is correct.
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The cost of a ticket increases by 10% to £18.15
Work out the original cost.
Answer:
£16.50
Step-by-step explanation:
[tex]x \times (1+\frac{10}{100} )=18.15[/tex]
[tex]x \times \frac{110}{100} =18.15[/tex]
[tex]\frac{110}{100} x=18.15[/tex]
[tex]1.1x=18.15[/tex]
[tex]\frac{1.1x}{1.1}=\frac{18.15}{1.1}[/tex]
[tex]x=16.5[/tex]
Answer: £16.50
Step-by-step explanation:
Let the original cost be x
x + 10/100x = 18.15
1.1x = 18.15
x = 16.50
If sin 2X = COS ZY and m2X = 72°, what is the measure of ZY?
18°
072°
90°
108°
Answer:
18°
Step-by-step explanation:
sin 2x=cos zy
m(2x)=72°
cos(π/2-a)=sin a
cos(π/2-72°)=sin72°
cos18°=sin72°
=>m(zy)=18°
IS ANYONE GOOD AT CALCULUS? PLEASE HELP!!! The rate at which a certain radioactive isotope decays is given by = negative 0.0032 y, where y is the amount of the isotope after t days. After approximately how many days would the amount of this isotope in a sample reach 75% of its original amount?
Answer:
90 days.
Step-by-step explanation:
dy/dt = - 0.0032y
dy = -0.0032y dt
dy/y = -0.0032 dt
Integrating:
ln y = -0.0032t + c where c is some constant
y = e^(-0032t) + e^c
y = A e^(-0032t) where A is a constant.
At time 0 we can let y = 1 so in that case A = 1
When there is 0.75 of y left:
0.75 = e^-0032t
ln 0,75 = -0032 t
t = ln 0.75 / -0032
t = 90.
Answer:
B. 90 days
Step-by-step explanation:
Edge 2022
plz help me, brainliest to be given
Answer:
4%
Step-by-step explanation:
R=INTEREST X 100% / TIME X PRINCIPAL
r=40 x 100=4000
4000/500 x 2=1000
4000/1000=4%
The length of a rectangular park is 20 feet longer than the width of the park.If the length of the park is 36 feet,what is the width of the park?
Answer: width = 16 ft.
Step-by-step explanation:
let width be w
Length is w + 20
Given
w + 20 = 36
w = 36 - 20
w = 16
Answer:
16 ft
Step-by-step explanation:
l= w+20
36= w+20
w= 36-20
w=16 ft
The chair of the meeting collects $2702 from 28 people.Whats the unit rate?
Answer:
$96.50
Step-by-step explanation:
She needs to build a line of dominoes 21 and 1/4 in a long with each domino spaced 1 and 1/4 in. apart. How many will she need?
Answer:
17 dominoes
Step-by-step explanation:
21 and 1/4 in divided by how far they need to be spaced apart, 1 and 1/4 in, is equal to 17 dominoes.
Solve for x. I WILL MARK BRAINLIEST.
Answer:
73 degreesStep-by-step explanation:
We all know that the inner degrees of a pentagon add up to 540°
thus we can use the following equation to solve for x:
33+140+2x+x+x+75=540
173+4x+75=540
248+4x=540
4x=540-248
4x=292
x=292/4
x=73
Thus, the answer is 73 degrees
Answer:
[tex]x=73[/tex]
Step-by-step explanation:
The sum of all interior angles of a pentagon is 540°.
[tex]33+140+2x+x+x+75=540[/tex]
Add all like terms.
[tex]33+140+4x+75=540[/tex]
[tex]4x+248=540[/tex]
Subtract 248 on both sides.
[tex]4x=540-248[/tex]
[tex]4x=292[/tex]
Divide 4 on both sides.
[tex]x=292/4[/tex]
[tex]x=73[/tex]
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
-1/5
Step-by-step explanation:
h(0) is 5, and h^-1 is 1/h, so 1/-5 is -1/5.
A triangle has two sides of lengths 5 and 12 what value could be the third side check all that apply
A)11 B)9 C)17 D)5 E)17 F)19
Answer:
9 and 11
Step-by-step explanation:
A dilation is given by the transformation (x, y) - (.75x, 75y). What type of dilation is this
A -enlargement
B- it is not a dilation
C- reduction
A square tile has a width of 1 foot. How many tiles will fit end-to-end along a
4-foot wall?
Answer:
4
Step-by-step explanation:
Starting at the left end of the wall, you'll find that you can set four (4) tiles end to end along this wall.
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
x+5
Step-by-step explanation:
Side is equal to sqrt area
= sqrt x^2 +10x + 25
= x+5
So one side of the square is x+5 metres
Answer:
(x+5) meters long
Step-by-step explanation:
x^2 + 10x+25
We recognize that this is a perfect square trinomial
a^2 + 2ab+b^2 = (a+b)^2
x^2+2*5*x+5^2 = (x+5)^2
Since this is a square
A = s^2 where s is the side length
(x+5) ^2 =s^2
Each side is (x+5)
The population of Greenbow, Alabama in 1995 was 200 people. Since then, the population has grown 2% per year. Model this situation with the proper equation and use that equation to predict the population of Greenbow in 2020.
Answer:
Equation is;
P = I(1 + r)^n
The population is 328
Step-by-step explanation:
Here we want to model the situation and use the modeled equation to predict population.
This follows an exponential pattern with similarity to the amount paid on a compound interest
Mathematically, we can have the equation as;
P = I(1 + r)^n
Where P is the population we want to calculate
I is the initial population in 1995 = 200 people
r is the rate of increase = 2% = 2/100 = 0.02
n is the difference in the number of years = 2020-1995 = 25
Thus the population would be;
P = 200(1 + 0.02)^25
P = 200(1.02)^25
P = 328.12
which is 328 approximately
which of the following rational functions is graphed below
Answer:
D.
Step-by-step explanation:
The simplest and fastest way to answer this question is to graph the equations given. Once you do so, then you should see that D is the correct answer.
On a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.
Time (x)
Height (y)
0 10
2 24
16 10
How high was the ball after 8 seconds?
Answer:
42
Step-by-step explanation:
