Answer:
-5/2 because there is -5y/2 but we have to take coefficient only so -5/2
peter bought 3 suits and 3 pairs of jeans and paid $2397. James bought 8 suits and 11 pairs of jeans and paid $6989. What is the price of each?
Answer:
Therefore each suit cost $600 and each jean cost $199
Step-by-step explanation:
Let x represent the price of each suit and let y represent the price of each jeans.
Since 3 suits and 3 pairs of jeans cost $2397, this can be represented by the equation:
3x + 3y = 2397
Dividing through by 3:
3x/3 + 3y.3 = 2397/3
x + y = 799 (1)
Also, 8 suits and 11 pairs of jeans cost $6989, this can be represented by the equation:
8x + 11y = 6989 (2)
To find x and y, solve equation 1 and 2 simultaneously. Multiply equation 1 by 8 and subtract from equation 2 to get y:
3y = 597
y = $199
Put y = $199 in equation 1:
x + 199 = 799
x = $600
Therefore each suit cost $600 and each jean cost $199.
What is the equation x^2+12x-3=16 written in the form (x-p)^2=q using the method of completing the square ?
Step-by-step explanation:
[tex] {x}^{2} + 12x - 3 = 16[/tex]
[tex] {x}^{2} + 12x = 19[/tex]
[tex] {x}^{2} + 12x + 36 = 19 + 36[/tex]
[tex](x + 6) {}^{2} = 55[/tex]
3+5 plz help will gibe brain
Answer:
8
Step-by-step explanation:
The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 48,637 miles, with a variance of 11,282,880. What is the probability that the sample mean would differ from the population mean by less than 778 miles in a sample of 143 tires if the manager is correct
Answer:
[tex]P(x < -778) = 0[/tex]
Step-by-step explanation:
Given
[tex]\bar x = 48673[/tex]
[tex]\sigma^2 = 11282880[/tex]
[tex]n = 143[/tex]
Required
[tex]P(x <- 778)[/tex]
First, we calculate the z score
[tex]z = \frac{x}{\sqrt{\sigma^2}/n}[/tex]
So, we have:
[tex]z = \frac{-778}{\sqrt{11282880}/143}[/tex]
[tex]z = \frac{-778}{3359.0/143}[/tex]
[tex]z = \frac{-778}{23.49}[/tex]
[tex]z = -33.12[/tex]
So:
[tex]P(x < -778) = P(z < -33.12)[/tex]
From z score probability, we have:
[tex]P(x < -778) = 0[/tex]
Find the equation of the line with Slope = 3 and passing through (4, 10) .write your equation in the form y=mx+b
A jean manufacturer makes three types of jeans, each of which goes through three manufacturing phases: cutting, sewing, and finishing. The number of minutes each type of product requires in each of the three phases is given below:
Jean Cutting Sewing Finishing
I 8 12 4
II 12 18 8
III 18 24 12
There are 5200 minutes of cutting time, 6000 minutes of sewing time, and 2200 minutes of finishing time each day. The company can sell all the jeans it makes and makes a profit of $4 on each Jean I, $4.50 on each Jean II, and 6 on each Jean III.
Required:
a. What number of jeans in each category should be made each day to maximize profits?
b. Formulate a linear programming problem that models the problem given above. Be sure to identify all variables used.
c. Analyze the solution.
Answer:
z ( max) = 2000 $
x₁ = 500 x₂ = 0 x₃ = 0
Step-by-step explanation:
cutting sewing finishing Profit $
Jean1 (x₁ ) 8 12 4 4
Jean2 (x₂ ) 12 18 8 4.5
Jean3 (x₃ ) 18 24 12 6
Time available 5200 6000 2200
b) Formulation of a linear programming problem:
Objective Function z
z = 4*x₁ + 4.5*x₂ + 6*x₃ to maximize
Constrains:
Constrain 1
Available cutting time 5200 minutes
8*x₁ + 12*x₂ + 18*x₃ ≤ 5200
Constrain 2:
Available sewing time 6000 minutes
12*x₁ + 18*x₂ + 24*x₃ ≤ 6000
Constrain 3:
Available finishing time 2200 minutes
4*x₁ + 8*x₂ + 12*x₃ ≤ 2200
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
After 6 iterations the optimal solution is:
z ( max) = 2000 $
x₁ = 500 x₂ = 0 x₃ = 0
We can see in the model that times required to make jean 2 and jean 3
are much bigger than jean 1 and but the price of jean 2 is only 0.5 $ above the price of jean 1 and jean 3 is only 2 $.
HELP!! I don’t know part C or D and I need to know if part A and B are correct
Answer:
Step-by-step explanation:
A and B are correct!
For part C, just multiply the dimensions given to you by four.
For part D, the answer would be 4 x 4 x 4 which is 264
Jayden drives 22.5 miles in 30 minutes. If he drove one hour in total at the same rate, how far did he go? Before you try that problem, answer the question below. How many minutes did Jayden drive in total?
how far did he go in minutes?
Answer:
45 miles in 1 hour
Step-by-step explanation:
1 hour is 60 minutes
22.5 miles / 30 minutes * 2/2 = 45 miles / 60 minutes = 45 miles in 1 hour
Answer:
He drove 22.5 miles in 60 min. He drove 45 miles in 1 hour
Step-by-step explanation:
22.5 miles in 30 min
1 hour= 60 min
30+30=60
22.5+22.5=45 miles
7 + 8/5-2
Could someone help me with this?
Answer:
hope it's helpful for you
Please help!! First person gets award or whatever it is!! Awarding 10 points
10
17 A sequence starts at 300 and 40 is subtracted each timee.
300
260
2200
1800...
The sequence continues in the same way,
What is the first number in the sequence which is less than zerol?
[11]
9514 1404 393
Answer:
-20
Step-by-step explanation:
300/40 = 7.5, so the 8th term will be the last positive term. It will be 300 -7×40 = 20. The 9th term will be 20 -40 = -20.
__
The sequence starts ...
300, 260, 220, 180, 140, 100, 60, 20, -20, ...
The table shows a linear relationship between x and y.
х
у
-20
96
-12
60
-6
33
-2
15
What is the rate of change of y with respect to x?
Answer:
[tex] -\frac{9}{2} [/tex]
Step-by-step explanation:
Rate of change of x and y can be calculated using the following formula and using any two given pair of values from the table:
Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using (-12, 60) and (-6, 33).
Where,
[tex] (-12, 60) = (x_1, y_1) [/tex]
[tex] (-6, 33) = (x_2, y_2) [/tex]
Plug is the values
Rate of change = [tex] \frac{33 - 60}{-6 -(-12)} [/tex]
Rate of change = [tex] \frac{-27}{6} [/tex]
Simplify
Rate of change = [tex] \frac{-9}{2} [/tex]
Rate of change = [tex] -\frac{9}{2} [/tex]
Examine the geometric relationships in the diagram below which option shows the correct value of x and y?
Answer:all of them
Step-by-step explanation:
Here is a trapezium drawn on a centimetre grid (not drawn to scale).
Work out the area of the trapezium, stating the units of your answer.
Answer:
Step-by-step explanation:
equation
area(base1 + base2)
If f(x) is an exponential function where f(-2,5) = 9 and f(7) = 91, then find the value of f(12), to the nearest hundredth.
Answer:
[tex]f(12) = 323.02[/tex]
Step-by-step explanation:
Given
[tex]f(-2.5) = 9[/tex]
[tex]f(7) = 91[/tex]
[tex]f(12) = 16.7 * 1.28^{12[/tex]
Required
[tex]f(12)[/tex]
An exponential function is:
[tex]f(x) = ab^x[/tex]
[tex]f(-2.5) = 9[/tex] implies that:
[tex]9 = ab^{-2.5}[/tex]
[tex]f(7) = 91[/tex] implies that:
[tex]91 = ab^7[/tex]
Divide both equations
[tex]91/9 = ab^7/ab^{-2.5}[/tex]
[tex]91/9 = b^7/b^{-2.5}[/tex]
Apply law of indices
[tex]91/9 = b^{7+2.5}[/tex]
[tex]10.11 = b^{9.5}[/tex]
Take 9,5th root of both sides
[tex]b = 1.28[/tex]
So, we have:
[tex]9 = ab^{-2.5}[/tex]
[tex]9 = a * 1.28^{-2.5}[/tex]
[tex]9 = a * 0.54[/tex]
[tex]a = 9/0.54[/tex]
[tex]a = 16.7[/tex]
f(12) is calculated as:
[tex]f(x) = ab^x[/tex]
[tex]f(12) = 16.7 * 1.28^{12[/tex]
[tex]f(12) = 323.02[/tex]
The probability of rolling a 1 on a 6-sided biased dice is 0.85
The biased dice is rolled twice.
Complete the probability tree diagram.
Answer:
Step-by-step explanation:
If the odds of rolling a 1 is .85 the odds of rolling not a one is
1-.85= .15
The Complete probability tree diagram is
First roll have (0.85, 0.15).
Second Roll have (0.85, 0.85, 0.15, 0.15).
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
The probability of rolling a 1 on a 6-sided biased dice is 0.85.
Now, the probability not rolling 1
= 1- 0.85
= 0.15
So, First roll have (0.85, 0.15).
and, the Second Roll have (0.85, 0.85, 0.15, 0.15).
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please help meeeeeeee
pt 4
Answer:
The answer is
[tex]2 {x}^{2} + 3x - 1 = 0[/tex]
Why? Below I explain
Step-by-step explanation:
That formula has three variables a, b and c.
So, a = 2, b = 3 and c = -1
Because the formula is written like
[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4 \times a \times c} }{2 \times a} [/tex]
First factor out the greatest common factor from each term. Then factor the remaining polynomial.
4x2+4x-80
Can you please help?
Pls help I’ll brainlest
write equation of the line below
Hi there!
We are given two ordered pairs which are:
(0,0)(5,4)If you are curious how do I get these ordered pairs, they come from those two big circles or dots. x and y make relation and can be written as (x,y).
1. Find the slope
Yes, our first step is to find the slope of a graph if you want to find an equation. You may be curious how to find that right? No worries! We have got a special formula for you to find the slope![tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
Since we have two given points, we can substitute them in the formula.
[tex] \large{m = \frac{4 - 0}{5 - 0} } \\ \large \boxed{m = \frac{4}{5} }[/tex]
2. Form an equation.
Since we have finally found, got or evaluated the slope. Next step is to find the y-intercept. Oh! Before we get to form an equation, do you know the slope-intercept form? We will be using that linear equation form since it is commonly used in the topic.[tex] \large \boxed{y = mx + b}[/tex]
Where m = slope and b = y-intercept. We substitute m = 4/5.
[tex] \large{y = \frac{4}{5} x + b}[/tex]
Next thing to remember is that when the graph intersects an origin point, b-term or y-intercept would be 0. Therefore b = 0 since the graph intersects (0,0).
[tex] \large \boxed{y = \frac{4}{5} x}[/tex]
3. Answer
Therefore the equation of the line is y = 4x/5.How many pounds of each type of fruit did she buy? she bought
pounds of limes and pounds of pears.
Pat bought 5 pounds of apples.
(1) 1 pound of pears cost $0.5 more that 1 pound of apples.
If 1 pound of pears cost $1 and 1 pound of apples cost $0.5, then the cost of 5 pounds of apples is 5*0.5=$2.5. For $2.5 we can buy 2.5/1=2.5 pounds of pears.
If 1 pound of pears cost $1.5 and 1 pound of apples cost $1, then the cost of 5 pounds of apples is 5*1=$5. For $5 we can buy 5/1.5=10/3 pounds of pears.
(2) 1 pound of pears cost 1.5 times as much as 1 pound of apples.
The cost of 5 pounds of apples is $5a (where a is the cost of 1 pound of apples). For $5a we can buy 5a/(1.5a)=5/1.5 pounds of pears. Sufficient.
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Given question is incomplete , the complete question is given below ,
Pat bought 5 pounds of apples. How many pounds of pears could he have bought for same amount of money?
(1) 1 pound of pears cost $0.5 more that 1 pound of apples
(2) 1 pound of pears cost 1.5 times as much as 1 pound of apples
Over what interval is the parabola below decreasing?
3<. x. <∞
−∞ <. x. <3
−1<. x. <∞
−∞ < x < −1
Answer:
B. -oo < x < 3
Step-by-step explanation:
since the vertex (3, -1), so, x should be less than 3
-oo < x < 3
HELP AFAP I WILL GIVE BRAINLIST
Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the contingency table. Find the probability that the student preferred afternoon classes given he or she is a junior. Round to the nearest thousandth. Be sure to show and explain your work.
When Do You Prefer to Take Classes?
Freshman
Sophomore
Junior
Senior
Morning
2
9
5
10
Afternoon
8
9
8
8
Evening
9
15
16
3
Answer:
Ok where only looking for junior so heres the stats for that
Morning:5
Afternoon:8
Evening:16
so if we add that up
5+8+16=29
and 8 like after noon so
8/29 as a percent 27.5862%
Hope This Helps!!!
Which inequality models this situation? 3 The company president sets a goal that the percentage of working phones must increase from 30% to at least 80% by the end of the day. 3 8 -> 103 8. 3+% 10+ DONE () Intro
Answer:
3+x/10+x>8/10
need help pls gving brainliest
In the questions below suppose the variable x represents students and represents courses, and:
•M(y): y is a math course F(x): x is a freshman
•B(x): x is a full-time student T(x,y): x is taking
•Write the statement in good English without using variables in your answers.
Answer:
Here the answer is given as follows,
Step-by-step explanation:
The last three parts are coming with a question mark, so can't answer those parts. post the image or write it properly
a) Every student is taking at least one course.
[tex]\forall x \exists y T(x,y)[/tex]
So for all x, there is a y such that T(x,y) is a true will be given by the above statement
b) There is a part-time student who is not taking any math courses.
[tex]\exists x \forall y [A(x) \Lambda (M(y) \rightarrow ~T(x,y))][/tex]
one fourth of a number is 5. find the number
Hope this helps. Please mark brainliest
Answer: 20
let the number be x
1/4 x = 5
x=5*4
x=20
Answer:
x=20
Step-by-step explanation:
[tex]\frac{1}{4}x=5\\x=20[/tex]
divide [tex]\frac{1}{4}[/tex] on both sides, which gives you 20.
Presto Corp. had total variable costs of $180,000, total fixed costs of $110,000, and total revenues of $300,000. Compute the required sales in dollars to break even.
Answer:
$230,000
Step-by-step explanation:
Contribution margin = Sales - Variable costs
=($250,000 - $137,500)
= $112,500
Contribution margin ratio = Contribution margin ÷ Sales
= ($112,500 ÷ $250,000)
= 0.45
Basically
Break-even sales = Fixed expenses ÷ Contribution margin ratio
=($103,500 ÷ 0.45)
= $230,000
The required sales in dollars to break even is $275,000.
Given that, total variable costs of $180,000, total fixed costs of $110,000, and total revenues of $300,000.
What is a total revenue?Total revenue is the total amount of money a company brings in from selling its goods and services. It determines how well a company is bringing in money from its core operations based on demand and price.
The contribution margin ratio = Contribution margin/Sales revenue
= (300,000 - 180,000 = 120,000)/300,000
= 40%
Break-even point in dollars = Fixed cost/Contribution margin ratio
= 110,000/0.40
= $275,000
Therefore, the required sales in dollars to break even is $275,000.
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y = 2x - 3
y = -x + 3 solve for x and y
We are given the system of equations:
[tex] \large{ \begin{cases} y = 2x - 3 \\ y = - x + 3 \end{cases}}[/tex]
Since both are y-isolated equation, we can combine them together.
[tex] \large{2x - 3 = - x + 3}[/tex]
Isolate and solve for x-term.
[tex] \large{2x - 3 + 3 + x = - x + 3 + x + 3} \\ \large{2x + x = 6 \longrightarrow 3x = 6} \\ \large{ \frac{3x}{3} = \frac{6}{3} \longrightarrow \boxed{ \red{x = 2}}}[/tex]
Next, we find the value of y. Simply substitute x = 2 in one of these equations. The less coefficient values, the faster and better. I will substitute x = 2 in y = -x+3. You can substitute x = 2 in y = 2x-3 if you want but the result would be the same.
[tex] \large{y = - x + 3}[/tex]
Substitute x = 2 in the equation.
[tex] \large{y = - 2 + 3} \\ \large \boxed{ \blue{y = 1}}[/tex]
Therefore - when x = 2, y = 1. We can write in coordinate point or ordered pair as (2,1) from (x,y).
Answer
x = 2, y = 1(2,1) --- ordered pairx + 3y = 10
-x + y = 6
Answer:
X= -2. Y= 4.
Step-by-step explanation: