Answer:
Tracy must buy 4 apple pies, 4 banana pies, and 8 chocolate pies.
Step-by-step explanation:
The complete question would be:
"Tracy wants to buy some pies for her sisters and she has a budget of $82 to spend on $5 apple pies, $4.5 banana pies, and $5.5 chocolate pies. She wants 16 pies for her sisters and must buy as many chocolate pies as apple pies and banana pies combined. How many of each item should she buy?
Write a system of equations of this problem."
Then, we will write a system of equations according to the information given in the problem:
We must consider each type of pie as an unknown, so:
x: the amount of apple pies
y: the amount of banana pies
z: the amount of chocolate pies
As she has a budget of $82, the amount of each pie must be multiplied by its price and the total sum must be 82:
5x + 4.5y + 5.5z =82 (1)
The total amount of pies must be 16:
x + y + z = 16 (2)
And the amount of chocolate pies must be equal to the quantity of apple pies and banana pies combined:
z= x + y (3)
System of equations:
(1) 5x + 4.5y + 5.5z =82
(2) x + y + z = 16
(3) z= x + y
First, we subtract x and y on 3 on both sides:
z - (x + y )= x + y - (x + y)
-x -y +z = 0
Then, we add 2 and 3:
(2) x + y + z = 16
(3) -x -y +z = 0
2 z=16
z=8
We replace the value of z on 3 and substract x on both sides:
x + y =8
y=8 - x
We use this on equation 1:
5x + 4.5y + 5.5z =82
5x + 4.5×(8-x) + 5.5×8=82
5x + 36 - 4.5x + 44 = 82
0.5x + 80 =82
0.5x=82-80
0.5x=2
x=2/0.5
x=4
We replace the values of x and z on equation 2:
x + y + z = 16
4 + y + 8 = 16
y + 12 = 16
y=16-12
y= 4
Tracy must buy 4 apple pies, 4 banana pies, and 8 chocolate pies.
Which statement best describes the graph of 2c - 5y=-25 and the graph of y= +5?
Answer:
To easily compare the two linear equations just by looking at the equation, let's rearrange this into the slope-intercept formula: y = mx + b, where m is the slope and b is the y-intercept.
2x - 5y = -25
(-5y = -25x - 2x)-1
5y = 25/5 +2x/5
y = (2/5)x + 5
Thus, the slope is 2/5 and the y-intercept is 5.
y=52x + 5
The slope is 52 and the y-intercept is 5.
Thus, we can say that the two linear equations have the same y-intercept. This is the point in the y=-axis in which the two lines intersect. They must intersect at (0,5).
Step-by-step explanation:
Mrs. Olen wants to join a gym. Francis Lewis Gym charges a new member fee of $150 plus $10 each month. Clintonville Gym charges a new member fee of $50 plus $35 each month.
Answer:Step-by-step explanation:
a. Let x = number of months
Amount charged by Francis Lewis Gym = 150 + 10x
Amount charged by Clintonville Gym = 50 + 35x
Set each expression equal to the other to generate an equation to use in finding the number of months for which the cost of membership will be the same at both months
150 + 10x = 50 + 35x
Collect like terms
150 - 50 = -10x + 35x
100 = 25x
Divide both sides by 25
100/25 = x
4 = x
Answer: 4 months
b. Substitute x = 2 into each if the expression of the amount charged by each gym. The one that gives the lowest amount should be the one Mrs. Open should should join.
Amount charged by Francis Lewis Gym = 150 + 10x
= 150 + 10(2)
= 150 + 20
= $170
Amount charged by Clintonville Gym = 50 + 35x
= 50 + 35(2)
= 50 + 70
= $120
She should join the Clintonville Gym if she plans to join a gym for 2 months.
Answer: Clintonville Gym
Help me ...again please n ty
Answer: Number 5 is 60%
Step-by-step explanation:
Polynomial A: 4z + 724 - 7y+7
Polynomial B: 2.c + 12y - 12z - 7
What will be the coefficients for x, y, and z in the resulting sum?
Select all that apply.
-8
-5
-5
2
5
9
Asse
16
Sect
GO BACK
SUBMIT AND CONTINUE
284691-1307
Answer:
-8z +724 + 5y +2c
Step-by-step explanation:
Combine like terms
Help plz I need it ASAP give poinys
Answer:
1 4/5
Step-by-step explanation:
Download photogmath
Answer:
1 7/8
Step-by-step explanation:
9÷4 4/5
=9÷24
=9/1×5/24
=
9×5
-----------
1×24
=45/2
15/8=1 7/8
In 1-3, match each description with the correct graph. Not all graphs will be used.
1.
My graph is non-proportional with a negative y-intercept.
2.
My graph is proportional with a negative slope.
3.
My graph is non-proportional with a positive slope
Answer:
1. d
2. b
3. a
Step-by-step explanation:
1. d => "my graph is non-proportional with a negative y-intercept."
Rationale: it is non-proportional because it does not pass through the point of origin, (0, 0). And also, the line intercepts the y-axis at a point where the value of y is below the point of origin, 0. That gives us a negative y-intercept value.
2. b => "My graph is proportional with a negative slope."
Rationale: it is proportional because the straight line cuts through the point of origin, (0, 0). And also, the line slants downward from left to the right, thus, such downward slope gives us a negative slope value.
3. a => "My graph is non-proportional with a positive slope".
Rationale: it is does not cut across the point of origin, and also the slope slants upward from left to the right. Therefore, it is a non-proportional graph with a positive slope.
ill give brainiest bros
how are we supposed to make a line plot
Answer:
Pic BelowStep-by-step explanation:
Hope this helps! <3
Complete the equation of the line whose y-intercept is (0,6) and slope is 3
Answer:
y= 3x+6
Step-by-step explanation:
the equation to use for this problem is y= mx+b
m is the slope (3) and b is the y-intercept (0,6)
let's plug those numbers into the equation.
y= 3x+6
Hope this helps!
Help! Whats the answer
Answer:
its c
Step-by-step explanation:
The average customer for a certain utility company pays $120 per month for utilities. The company plans to decrease utility bills by 3% each year for the next five years. Which of the following can be used to determine the total amount an average customer will pay for utilities during the next five years? an arithmetic series a geometric series a series that is neither arithmetic nor geometric a series that is both arithmetic and geometric
an arithmetic series
a geometric series
a series that is neither arithmetic nor geometric
a series that is both arithmetic and geometric
Answer:
a geometric series
Step-by-step explanation:
At a sale this week, a suit is being sold for $306 . This is a 15% discount from the original price.
What is the original price?
Answer:
260.1
Step-by-step explanation:15% of 306=45.9
306-45.9=260.1
Answer:
351.9
Step-by-step explanation:
x/306=15/100. then I cross multiplied. And when I do I get 100x/100=4590/100.
I cross out the 100/100 and I leave with x, then I divide 4590 with 100 and get 45.9. So x=45.9.
Then I added the price it was sold..=306+45.9=351.9
The sum of three consecutive odd integers is 18 less than five times the middle number fimd the three integers
Answer:
7, 9, 11
Step-by-step explanation:
x+x+2+x+4=5(x+2)-18
3x+6=5x+10-18
3x+6=5x+-8
3x=5x+-14
-2x=-14
x=7
A part manufactured by plastic injection molding has a historical mean of 100 and a historical standard deviation of 8. Find the value of the mean thickness required to make the probability of exceeding 101 less than 8%.
Answer:
The probability of thickness exceeding 101 is 0.4483.
Step-by-step explanation:
Let X denote the thickness of the part manufactured by plastic injection molding.
Assume that X follows a normal distribution with mean, μ = 100 and standard deviation, σ = 8.
Compute the probability of thickness exceeding 101 as follows:
[tex]P(X>101)=P(\frac{X-\mu}{\sigma}>\frac{101-100}{8})[/tex]
[tex]=P(Z>0.125)\\\\=1-P(Z<0.125)\\\\=1-0.55172\\\\=0.44828\\\\\approx 0.4483[/tex]
Thus, the probability of thickness exceeding 101 is 0.4483.
In an inequality, -2.5 is the lesser number. What is the position of the other number on the horizontal number line in relation to -2.5?
Answer:
It would be to the right of -2.5.
Step-by-step explanation:
if 1 apple cost 3 dollars how much would 5 cost?
Answer:
It would be 15
Step-by-step explanation:
because 5x3 equals 15.
Answer:
15 dollars
Step-by-step explanation:
because you have to multiply how many apples there are to how much each one cost. So the answer would be 5 x 3 equals 15 dollars
Use a calculator to find a value of θ between 0° and 90° that satisfies the statement. Write your answer in degrees and minutes rounded to the nearest minute.
csc(theta)= 4.1191
Answer:
[tex]\theta = 14.1\ degrees[/tex]
[tex]846\ minutes[/tex]
Step-by-step explanation:
Given
[tex]csc(\theta) = 4.1191[/tex]
Required
Solve for [tex]\theta[/tex]
[tex]csc(\theta) = 4.1191[/tex]
[tex]csc(\theta) = \frac{1}{sin(\theta)}[/tex]
So, we have:
[tex]\frac{1}{sin(\theta)} = 4.1191[/tex]
Invert both sides
[tex]sin(\theta) = \frac{1}{4.1191}[/tex]
[tex]sin(\theta) = 0.2428[/tex]
Take [tex]sin^{-1}[/tex] of both sides
[tex]sin^{-1} sin(\theta) = sin^{-1}0.2428[/tex]
[tex]\theta = sin^{-1}0.2428[/tex]
[tex]\theta = 14.0518577574[/tex]
[tex]\theta = 14.1\ degrees[/tex] --- approximated
Convert to minutes:
[tex]1\ degree = 60\ minutes[/tex]
So:
[tex]14.1\ degrees = 14.1 * 60\ minutes[/tex]
[tex]14.1\ degrees = 846\ minutes[/tex]
Find the total amount of water that will leak in the first 24 hours if the leak is not fixed. Use the formula sn=a1-rn1-r and round to the nearest whole milliliter.
77+(1/2)^n-1
whats the formula?
Step-by-step explanation:
Suppose that minor errors occur on a computer in a space station, which will require re-calculation. Assume the occurrence of errors follows a Poisson process with a rate of 1/2 per hour. (a) Find the probability that no errors occur during a day. (b) Suppose that the system cannot correct more than 25 minor errors in a day, in which case a critical error will arise. What is the probability that a critical error occurs since the start of a day? Keep up to the 6th decimal place in your answer. (c) Suppose the error correction protocols reset themselves so long as there are no more than five minor errors occurring within a 2 hour window. The system just started up and an error occurred. What is the probability the next reset will occur within 2 hours?
Answer:
a
[tex] P(X = 0) = 0.6065 [/tex]
b
[tex]P(x < 25 ) = 1.18 *10^{-33} [/tex]
c
[tex] P(x \le 5 ) = 0.9994 [/tex]
Step-by-step explanation:
From the question we are told that
The rate is [tex]\lambda = \frac{1}{2}\ hr^{-1}[/tex] = 0.5 / hr
Generally Poisson distribution formula is mathematically represented as
[tex]P(X = x) = \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]
Generally the probability that no error occurred during a day is mathematically represented as
Here t = 1 hour according to question a
So
[tex]P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}[/tex]
Hence
[tex][tex]P(X = 0) = \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}[/tex]
=> [tex] P(X = 0) = 0.6065 [/tex]
Generally the probability that a critical error occurs since the start of a day is mathematically represented as
Here t = 1 hour according to question a
So
[tex]P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}[/tex]
Hence
[tex]P(x \ge 25 ) = 1 - P(x < 25 )[/tex]
Here
[tex]P(x < 25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}[/tex]
=> [tex]P(x < 25 ) = \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}[/tex]
[tex]P(x < 25 ) = 0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}[/tex]
[tex]P(x < 25 ) = 0.6065 + \cdots + 6.0*10^{-32}[/tex]
[tex]P(x < 25 ) = 1.18 *10^{-33} [/tex]
Considering question c
Here t = 2
Gnerally given that the system just started up and an error occurred the probability the next reset will occur within 2 hours
[tex]P(x \le 5 ) = \sum_{n=0}^{5} \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]
=> [tex]P(x \le 5 ) = \frac{(0.5 * 2) ^ 0 e^{- 0.5 * 2 }}{0!} + \cdots + \frac{(0.5 * 2) ^ 5 e^{- 0.5 * 2 }}{5!}[/tex]
=> [tex]P(x \le 5 ) = \frac{1* 2.7183 }{1 } + \cdots + \frac{1 *2.7183 }{120}[/tex]
=> [tex]P(x \le 5 ) = 2.7183 + \cdots + 0.0226525[/tex]
[tex] P(x \le 5 ) = 0.9994 [/tex]
The water level of a lake rose by 1 2/3 in. during a 3 1/3 week-long wet spell. Simplify the complex
fraction below to find the average rate at which the water level changed every week.
Given that,
The water level of a lake rose by 1 2/3 in. during a 3 1/3 week-long wet spell. We need to find the average rate at which the water level changed every week. It is a problem based on the concept of ratio. So,
[tex]R=\dfrac{1\dfrac{2}{3}}{3\dfrac{1}{3}}\\\\=\dfrac{\dfrac{5}{3}}{\dfrac{10}{3}}\\\\=\dfrac{5}{3}\times \dfrac{3}{10}\\\\=\dfrac{1}{2}[/tex]
So, the average rate at which the water level changed every week is 1/2 inches/week.
I got this wrong can someone, please help me with this.
You found the correct slope for Line 1, but Line 2 has a slope of (3 - 2)/(6-3) = 1/3.
If 2 lines are parallel, their slopes are the same; perpendicular and their slopes are opposite reciprocals (change the sign of the first slope, then divide 1 by it and you get the perpendicular line's slope). 1/3 is NOT the opposite reciprocal of 3 (because they have the same sign) and 1/3 is NOT equal to 3, so that makes the answer neither.
The slope for Line 3 is (3 - 1)/(1 - (-1)) = 2/2 = 1
The slope of Line 4 is (1 - (-1))/(4 - 2) = 2/2 = 1
1 = 1, so these lines are parallel
I need a scale drawing of a house,2 inches:5 feet. The actual kitchen of the house will be 17 feet long. How long will the drawing of the kitchen be?
Answer:
8.5
Step-by-step explanation:
1 2/3 multiplied by -3 1/2
Answer: -5 5/6
Step-by-step explanation:
Convert each number into. 1 2/3 = 5/3 (1=3/3, so 3/3 + 2/3) and -3 1/2 = - 7/2
Then multiply the numbers
5/3 x -7/2 = -35/6 (5x7= 35 and 3x2= 6, negative because a negative times a positive is a negative)
Then simplify....6 goes into 35 5 times with 5 remaining, so -35/6 = -5 5/6
please help 25 point asap
Answer:
B
Step-by-step explanation:
Answer:
b) B,A,C
Step-by-step explanation:
A store owner discounted some canoes from $76 to $38. What is the discount, as a percentage?
Answer:
50.00%
Step-by-step explanation:
Graph the linear function
f(x)=3-6x
Answer:
The best thing to use is Desmos the graphing calculator then just take a screenshot.
Step-by-step explanation:
Hope this helps and have a great day!
A line that divides a circle into two equal halves is the?
Answer:
A bisector or angle
Step-by-step explanation:
An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The interior or internal bisector of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles.
k. 3 kg 924 g - 1 kg 893 g
Converting to grams:
Converting these values to grams will make them easier to subtract
3 kg 924 grams OR 3.924 kg = 3924 grams
1kg 893 grams OR 1.893 kg = 1893 grams
Subtracting:
Now that we have the values in grams, we will put them in their initial order and subtract them
3924 - 1893 = 2031 grams = 2.031 kg OR 2 kg 31 grams
One-half of a number x is equal to the sum of two and
the same number & . Find the value of x.
Answer:
x=-4
Step-by-step explanation:
This is the equation you can write (assuming you meant "the same number x"):
1/2x=2+x
x=4+2x
-x=4
x=-4
Y = 3x + 4 Y = 3x + 7
Answer:
y-7/ 12y+3
Step-by-step explanation:
please help
Which values of k would cause this system of equations to have no solution? Check all that apply.
6x + 4y = 14,
3x + 2y = k
-2
5
7
10
21
Answer:
a , b , d , e
Step-by-step explanation: