Step-by-step explanation:
30 cookies = 2 cups
1 cookie = 2/30 cups = 1/15 cups
40 cookies = 1/15 × 40 = 8/3 cups
The area of a rectangle is modeled by the graph where y is the area (in square meters) and x is the width (in meters).
What dimensions result in the maximum area?
A rectangle_ meters by_ meters results in the maximum area.
Answer:
The dimensions that result in the maximum area are therefore;
Width = 3.5
Height = 3.5
Step-by-step explanation:
The given parameters are;
The area of the rectangle, y = x × h
Where;
x = The width of the rectangle
h = The height of the rectangle
By examination, we have;
x + h = 7
Therefore, x = 7 - h
Which gives;
y = x × (x - 7) = x² - 7·x
y = x² - 7·x
At x = 0, y = 0
At x = 7, y = 0
However, at x = 1, y = -6
Therefore, the function should be, y = -(x² - 7·x)
The maximum occurs where dy/dx = 0, which gives;
dy/dx = d-(x² - 7·x)/dx = 0
dy/dx = 2·x - 7 = 0
2·x - 7 = 0
x = 7/2 = 3.5
On second derivative, we have;
d²y/dx² = 2, which gives a local minimum
x = 3.5 at maximum height
Which give, the maximum height, [tex]y_{max}[/tex] = -(x² - 7·x) at x = 3.5
∴ [tex]y_{max}[/tex] = -(3.5² - 7×3.5) = 12.25
The maximum height = 12.25
The dimensions that result in the maximum area are therefore;
Width, x = 3.5
Height, h = 7 - x = 7 - 3.5 = 3.5
Height, h = 3.5.
-4/5(-8x+6)=1+7 Please Help
Answer:
x = 2
Step-by-step explanation:
-4/5(-8x + 6) = 1 + 7 (distribute first)
6.4x -4.8 = 8 (add 4.8 on both sides)
6.4x = 12.8 (divide by 6.4)
x = 2
PLUG IN
-4/5(-8(2) + 6) = 1 + 7
-4/5(-16 + 6) = 8
-4/5(-10) = 8
8 = 8
Solve the system of linear equations. 4x + 6y = 12 x + 2y = 10 The solution is
Answer:
x = -18, y = 14
Step-by-step explanation:
4x + 6y = 12
x + 2y = 10
Divide both sides of the first equation by 2. Write the second equation below it.
2x + 3y = 6
x + 2y = 10
Rewrite the first equation. Multiply both sides of the second equation by -2 and write below it. Then add the equations eliminating x.
2x + 3y = 6
(+) -2x - 4y = -20
-------------------------
-y = -14
y = 14
Substitute 14 for y in the second equation and solve for x.
x + 2y = 10
x + 2(14) = 10
x + 28 = 10
x = -18
Solution: x = -18, y = 14
1 9/7 ÷ 5/4 please help me
Answer:
64/35
In mixed number form: 1 29/35
Step-by-step explanation:
Thats my fasted record for solving a division problem hehe :) You're welcome!
Which procedure correctly simplifies the expression? ( 4 x − 3 ) − 2 ( x + 5 ) A. Step 1: 4 x − 2 x − 3 + 5 Step 2: 2 x + 2 B. Step 1: 4 x − 3 − 2 x − 5 Step 2: 2 x − 8 C. Step 1: 4 x − 3 − 2 x − 10 Step 2: 2 x − 13 D. Step 1: 4 x − 3 + 2 x + 10 Step 2: 6 x + 7
Answer:
Step 1: 4 x − 3 − 2 x − 10
Step 2: 2 x − 13
Step-by-step explanation:
Given the expression;
(4 x − 3) − 2 (x + 5)
The following steps/ procedure are to be taken when simplifying the expression.
open the parenthesis
(4 x − 3) − 2 (x + 5)
= 4x-3 -2(x)-2(5)
= 4x-3-2x-10
collect the like terms
= 4x-2x-3-10
simplify the resulting expression
= 2x-13
Hence the procedure that correctly simplifies the expression are:
Step 1: 4 x − 3 − 2 x − 10
Step 2: 2 x − 13
A plumber charges a one-time service fee of $20 in addition to his hourly
rate of $25 per hour. If the plumber went to your house to work on your
bathtub and the bill came to $145.00, how many hours did it take him to
complete the job?
Answer:
Three hundred fifty-five
Answer: 10.5
Step-by-step explanation:
20+25x=282.50
Subtract 20 on both sides
262.50
Divide each side by 25
You get 10.5
The diagram shows a right-angled triangle.
13 cm
24°
hcm
What is the value of h?
qive your answer correct to 1 decimal place.
Answer:
11.9cm
Step-by-step explanation:
cos = adj/hyp
cos 24°= hcm/ 13cm
13 cos 24°= h
11.88= h
11.9 cm
Solve x – 1 – 5 = 2.
Answer:
x = 8
Step-by-step explanation:
Answer:
x=8
Step-by-step explanation:
x-1-5=2
first you add 6 to 2 then you get x=8
Find the 64th term of the arithmetic sequence 2, -3,-8
Answer:
-313
Step-by-step explanation:
a1=2; d=-5
a64=2-5(64-1)=-313
The 64th term of the arithmetic sequence 2, -3, -8 ... will be -313.
What is Arithmetic sequence?
An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.
Given that;
The arithmetic sequence;
⇒ 2 , -3 , -8 ...
Now,
The general equation for nth term of the arithmetic sequence is,
[tex]T_{n} = a + (n - 1) d[/tex]
Where, The term 'a' represent the first term.
And, 'd' represent the difference between each consecutive numbers.
Here, In the arithmetic sequence 2 , -3, -8;
The first term = 2
The difference = -3 - (2) = - 5
So, To find the 64th term of the arithmetic sequence, we can substitute
n = 64 and a = 2 and d = -5 in above formula as;
[tex]T_{n} = a + (n - 1) d[/tex]
[tex]T_{64} = 2 + (64 - 1) (-5)[/tex]
[tex]T_{64} = 2 + (63 * -5)[/tex]
[tex]T_{64} = 2 - 315[/tex]
[tex]T_{64} = -313[/tex]
Thus, The 64th term of the arithmetic sequence 2, -3, -8 ... will be -313.
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Admission to the fair is $8.50 and each ride costs $1.25. He has $40 to spend at the fair. write an inequality to represent the situation. Solve the inequality to determine the maximum number of rides Jaylen can enjoy.
PLSSSSS HELPPP IM TIMED AND I WILL MARK BRAINLIEST AND HELP OUT WITH UR QUESTIONS!!!
Answer:
8.50 divided by 1.25 then when u get the answer subtract 40
Answer:
25
Step-by-step explanation:
so instantly 40-8.50=31.5
The question is very vague because it doesn't state the number of rides he wants to go on in minimum.
if you do 1.25x25=31.25
According to that, he will leave with a change of 0.25 and obv u cannot go on half a ride...
So in about 2 mins i guess it is 25???
Add me on instagram: vnshl
Which of the following equations is nonlinear?
y = 3
y = 8x - 1
y = 5x
y = 5x3
Answer:
D)y=5x³
Answer:
y = 5x^3
Step-by-step explanation:
If there is an exponent other than 1 on a variable, then it is not linear.
Answer: y = 5x^3 since the exponent on x is 3.
There are 12 kittens. If they all average 4.7 pounds, what is the total weight of all 12 kittens
Answer:
56.4 pounds
Step-by-step explanation:
Multiply 12 (kittens) by 4.7(pounds) and you get 56.4 pounds, the total weight of the kittens combined.
Noah ordered 16 cupcakes and paid $40. Jada ordered 52 cupcakes and paid $104. Did they pay the same rate? Use ratio table to help your reason. Explain your reasoning.
Answer:
yes
Step-by-step explanation:
If you travel 235.6 miles on vacation, how many kilometers is this? (1 mile = 1,609 meters)
Answer:
About 379 kilometers
Step-by-step explanation:
1609 meters / mile = 1.609 kilometers / mile
1.609 kilometers / mile * 235.6 miles = 379.0804 kilometers
help pls I really need help can anyone help me
Answer:
you didn't screenshot/take the photo fully...
we can't see it.
Step-by-step explanation:
Four of you go to an arcade. The owner charges you $6 for 2 hours to play and $2 for each
additional hour. If you paid a total of $10, how long did you play?
Answer:
the answer is 4 hours
Answer:
3 hours
Step-by-step explanation:
Since you payed 10 dollars you would take out $6 first then divide 4 by 2 which gives you two so two plus the first hour gives you 3 hours
Whitne bought 10 bagels for brunch last Sunday. 8 of the bagels had raisins. What fraction of the bagels had raisins?
Answer:
8/10 bagels had raisins :)
A club has 800 members. 100 of the members were randomly picked and were asked if the dues should be raised. 6 of the members said that dues should be raised. Based on these results, about how many members in the club would be expected to say that dues should be raised?
Answer:
About 48 members would be expected to say that dues be raised
Step-by-step explanation:
Here, we shall be using a case of a representative sampling to determine the actual.
Out of the 100 selected members, 6 said the dues should be raised;
This represents a percentage of 6/100 = 6%
So out of the 800, the expected number of members that would ask for a dues raising will be;
6/100 * 800 = 48
On a horizontal number line, -7 is located to the right of -10.
Will a non-metal replace a metal?
Yes
No
Answer:
No
Step-by-step explanation:
I think only a metal can replace a metal, not a non-metal replace a metal
The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 7 days. About what percentage of births would be expected to occur within 7 days of the mean pregnancy length
Answer:
68.268%.
Step-by-step explanation:
Let \mu be the mean pregnancy length.
The given standard deviation, [tex]\sigma=7[/tex] days
The z-score:
z=\frac{x-\mu}{\sigma}
where x is any pregnancy length.
The range of x within 7 days of the mean pregnancy length is
[tex]\mu-7<x<\mu+7.[/tex]
z-score for this range is:
[tex]\frac{\mu-7-\mu}{\sigma}<z<\frac{\mu+7-\mu}{\sigma}[/tex]
[tex]\Rightarrow -1<z<1[/tex]
So, the area on the normally distributed curve for the above range of z-score will give the expected percentage of birds to occur within 7 days of the mean pregnancy length.
Now, from the z-score table:
The area from [tex]z = -\infty[/tex] to z=1 is 0.84134
and the area from [tex]z = -\infty[/tex] to z=-1 is 0.15866.
So, the area for -1<z<1
=0.84134 - 0.15866
=0.68268
Hence, the percentage of births would be expected to occur within 7 days of the mean pregnancy length=68.268%.
Help plz. If correct, I follow you or mark brainlist
Answer:
I believe 60 square units in the white rectangle and and 140 square units in the blue. Together would be 200 square units...i think...im sorry if i'm wrong
Step-by-step explanation:
because lxw, 10x6, and lxw, 14x10, add you get 200
What is the slope of the line represented by the equation 5 =10x −15
Answer:
m=2
Step-by-step explanation:
y=mx+b
5y=10x-15 dived all by 5
y=2x-3----------2 is the slope
y=mx+b
If 125 students take a test in psychology and 20 get scores of less than or equal to 50%, then what is the percentile rank of a test score of 50%?
Group of answer choices
12
20
50
16
Answer:
20
Step-by-step explanation:
multiply (2x – 3)(x2 – 5x + 3)
Answer:
(2x2- 10x2+ 6x -3x2 + 15x -9) simplified to (-12x2+21x-9)
Step-by-step explanation:
I could explain but you would just be confused because I did it in my head and I don't do it the way they teach us to if you want to make sure my answer is right you should be able to simplify my simplified version back into the original problem
During spring break, a class of 14 children went to Walt Disney World in Florida. The price for each child’s ticket was $75, while each adult ticket was $85. If the total amount spent on tickets was $1,475, how many adults went on the trip?
Answer:
5 adults went on the trip.
Step-by-step explanation:
There are 14 children ($75 each) and the total was $1475. We need to find out how many adults were there ($85 each)
c is for children and a is for adults
equation: $75c+ $85a = $1475
$75(14)+ $85a= $1475
$1050 + $85a = $1475
-1050 -1050
$85a = $425
85a/85 = 425/85
a = 5
5 adults went on the trip. Hope this helps! :)
There were 5 adults that went on the trip.
What is unitary method ?Unitary method is finding the value for a single unit.
According to the given question During spring break, a class of 14 children went to Walt Disney World in Florida the price for each child’s ticket was 75 dollars.
So, Cost of tickets of 14 children is
= (14 × 75) dollars.
= 1050 dollars.
Total amount spent on tickets for children and adults is 1475 dollars.
∴ Total amount spent for tickets for the adults is
= ( 1475 - 1050 ) dollars.
= 425 dollars.
Given price of one ticket for adult is 85 dollars, So for 425 dollars the no. of tickets will be
= 425/85 dollars.
= 5 tickets which states there were 5 adults.
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what is 48020000 in sintiic notation
Answer:
4.802 x 10^7
Step-by-step explanation:
Hope this helps! :)
If this wasn't what you were looking for please don't hesitate to comment again. Have a nice day/night! :)
Answer:
4.802 x 10 power of 7
Step-by-step explanation:
i did this so i know
|x-1=-3
Solve for x.
Answer:
x-1=3
x=3+1
x=4
Solve for h.
-110 = 13 + 3 (4h - 6)
Answer:
h= -35/4
Step-by-step explanation:
decimal form: -8.75
Mixed number form: -8 3/4
In June, Clarissa used 115 gigabytes of data on her cell phone. Given that June has 30 days, how much data did she use on average per day?
Answer:
She used an average of (115/30) gigabytes of data per day
Step-by-step explanation:
To get the average data usage per day, we simply divide the total data used by the number of days
Mathematically, that will be
115 gigabytes/ 30 days = 3.83 gigabytes per day