Using proportions, it is found that the expression that shows the total height of Grandma Maude’s cake is:
[tex]t = 12x^5 + 5x^3 - 2x[/tex]
This question is solved by proportions, using a rule of three.The measure of one layer, in cm, was of [tex]2 + 3x^2[/tex]. In total, there were [tex]4x^3 - x[/tex] layers.The rule of three is:
1 layer - [tex]2 + 3x^2[/tex] cm
[tex]4x^3 - x[/tex] layers - t cm
Applying cross multiplication:
[tex]t = (4x^3 - x)(2 + 3x^2) = 12x^5 + 5x^3 - 2x[/tex]
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Answer:
12x5 + 5x3 – 2x cm
Step-by-step explanation:
Here are the ingredients for a cake. 0.225 kg butter 225 g sugar 225 g flour 0.2 kg eggs 250 g berries How much do the ingredients weigh altogether?
Answer:
1125.
Step-by-step explanation:
I'm going to work out the answer is grams.
1kg = 1000g
0.225kg of butter = 225g, 225g of sugar, 225g of flour, 0.2kg of eggs = 200g, 250g of berries.
225 + 225 + 225 + 200 +250 = 1125.
Hope that helps. x
Answer:
1.125kg or 1125g
Step-by-step explanation:
1kg: 1000g
Butter: 0.225kg or 225g
Sugar: 225g or 0.225kg
Flour: 225g or 0.225kg
Eggs: 0.2kg or 200g
Berries: 250g or 0.25kg
In kg: 0.225 + 0.225 + 0.225 + 0.2 + 0.25 = 1.125
In g: 225 + 225 + 225 + 200 + 250 = 1125
The plans for a shed call for a rectangular floor with a perimeter of 186 ft. The length is two times the width. Find the length and width.
Answer:
length: 62 ft
width: 31 ft
Step-by-step explanation:
Let w represent the width. Then the length is 2w and the perimeter is ...
P = 2(L+W)
186 = 2(2w +w)
31 = w . . . . . . . . . divide by 6
2w = 2(31) = 62
The length of the shed is 62 feet; its width is 31 feet.
Cassidy is selling popcorn for a fundraiser sale at the price shown. he purchases a total of 150 containers of popcorn to sell. after he sells 25 containers, he will make a total profit, after his upfront costs, of $5.50 cassidy's profit, after upfront costs, can be modeled by a linear function in the form of y=mx+b.
C. Will the function be discrete or continuous? Explain.
D. Write the function that models Cassidy's profit.
E. What is the domain of the function?
F. What is Cassidy's profit or loss if he does not sell any popcorn?
G. What is cassidy's profit if he sells all the popcorn?
H. What is the range of the function?
The domain and the range of the function describes the possible profit or
loss from the sale of popcorn and the number of popcorn units.
The correct responses are;
C. The function is discreteD. The function is; y = 1.5·x - 32E. The domain is; 0 ≤ x ≤ 150F. The loss when non of the popcorn is sold is $-32G. The profit is $193H. The range is; -32 ≤ y ≤ 193Reasons:
The question parameters are;
The price of a popcorn = $1.5
Number of popcorn he purchases = 150
Total profit made = $5.50
The number of containers sold = 25
Therefore;
C. Given that the number of containers sole is countable, the function will be discrete.
D. Cost of the containers = Revenue - Profit
Which gives;
Cost of the containers = 1.5 × 25 - 5.5 = 32
The given function is therefore;
y = 1.5·x - 32
E. The domain is the 150 containers which gives;
The domain = 0 ≤ x ≤ 150
F. When no popcorn is sold, we have;
x = 0, which gives;
y = 1.5 × 0 - 32 = -32
If he does not sell any popcorn, the loss is $32
G. If all the popcorn are sold, we have;
x = 150
Therefore;
y = 1.5 × 150 - 32 = 193
The profit if all the popcorn are sold = $193
H. The range of the function are the possible y values, which is the possible profit or loss, which gives;
The range = -32 ≤ y ≤ 193
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Suppose a worker makes $286.08 in one week. If he is paid $5.96 an hour for the first 36 hours he works and then $8.94 an hour in overtime pay for each additional hour, how many hours did he work overtime
Answer:
5.96 x 36 = 214.56.
286.08 - 214.56 = 71.52
71.52 divided by 8.94 = 8.
He worked 8 additional hours.
Answer:
The worker worked about 8 hours overtime.
Step-by-step
First we figure out how much they made without overtime.
Multiply 5.96 x 36 and you would get 214.56
Then we figure out how many hours he worked overtime
Multiply 8.94 times 8 and you would get 71.52
Then take 214.56 and add 71.52, you would get 286.08, the answer is 8 hours overtime.
There are eight swans swimming on a pond and four of those swans are
black. What fraction of the swans are black?
Answer: A. (4/8)
Step-by-step explanation: If there is 4 black swans and 8 swans in total you could see it's 4 black swan out of 8 total swans. You could do
8/8 - 4/8 = 4/8 to find out the answer too.
3. A rectangular deck has an area of 24 square yards. The length of the deck is shown in the figure. What is the width of the deck in yards? Enter your answer in the box.
Answer:
can you please send the picture as well because for this
(The length of the deck is shown in the figure.=??)
figure is needed ..
There is an array under. what is the last number?
1 2 4 7 13 24 ?
Answer:
Here's one possible solution
Step-by-step explanation:
Double the number and subtract the corresponding value from the sequence
0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5...
1 + 1 - 0 = 2
2 + 2 - 0 = 4
4 + 4 - 1 = 7
7 + 7 - 1 = 13
13 + 13 - 2 = 24
24 + 24 - 2 = 46 ←←←
46 + 46 - 3 = 89
89 + 89 - 3 = 175
175 + 175 - 4 = 346
SOMEBODY HELP ME NO LINKS PLEASE
Find f ′(x) for f(x) = ln(x^4 + e^(2x)).
[tex]\text{Given that,}\\\\\\f(x) = \ln(x^4 +e^{2x})\\\\\\f'(x) = \dfrac{1}{x^4 + e^{2x}} \left(4x^3+2e^{2x}\right) = \dfrac{2(2x^3+e^{2x})}{x^4 + e^{2x}}~~~~;[\text{Chain rule}]\\\\\\\text{Note:}\\\\\dfrac{d}{dx} \ln x = \dfrac 1x\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} e^{mx} = m e^{mx}[/tex]
After solving the given equation, the value obtained is equal to [tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex].
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given data in the question,
f(x) = ln (x⁴ + e²ˣ)
[tex]f'(x)=\frac{1}{x^4+e^2^x}(4x^3+2e^2^x)[/tex]
Now, use the chain rule,
[tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex]
Also, note some points,
d/dx ln (x) = 1/x
[tex]\frac{d}{dx}x^n=nx^n^-^1[/tex]
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prove the identity.
(1-sin^2x)tanx=cosxsinx
Note that each Statement must be based on a Rule
[tex](1-\sin^2 x) \tan x \\\\=\cos^2 x \cdot \dfrac{\sin x}{\cos x}\\\\=\cos x \sin x[/tex]
in the pediatric unit of a hospital has 165 beds how many are there if each room holds 3 beds
Answer:
There are 55 rooms
Step-by-step explanation:
There are 165 beds in the hospital. Each room contains 3 beds. In order to find the number of beds per room, take the total number of beds and divide it by the number of rooms in each bed. 165/3=55. There are 55 rooms in the hospital, all containing 3 beds.
Hope this helps!
A man walks 10 km, then travels a certain distance by train and then by bus as far as twice by the train. If the whole journey is of 70km, how far did he travel by train?
Answer:
The man traveled 20km by train.
Step-by-step explanation:
If x is the distance he traveled by train, you can write this equation to represent the situation:
[tex]10+x+2x=70[/tex]
Then, you can simply solve for x:
[tex]10+3x=70\\3x=60\\x=20[/tex]
The man traveled 20km by train.
[tex]10+(20)+2(20)=70\\10+20+40=70\\70=70[/tex]
9. Sofija buys a bracelet for $14.50 plus 8% tax.
Momoka buys a necklace for $12 plus 8% tax.
Enter the sum, in dollars, that Sofija and
Momoka paid, including tax.
Answer:
$12.96
Step-by-step explanation:
Before Tax Price: $12.00
Sale Tax: 8.00% or $0.96
After Tax Price: $12.96
A cruise ship is traveling northwest so that it makes a 45-degree angle with the east-west line. If it has traveled 35 miles from its starting point, what are the components of the vector s formed by the ship's path?
Answer:
Step-by-step explanation:
Answer:
(17.5√2 miles west, 17.5√2 miles north)
Step-by-step explanation:
The distance in the west direction will be ...
35cos(45°) = 17.5√2 . . . . miles west
The distance in the north direction will be ...
35sin(45°) = 17.5√2 . . . . miles north
The vector components are ...
(17.5√2 miles west, 17.5√2 miles north)
_____
Additional comment
When a map with the usual "north is up" orientation is overlaid on an x-y coordinate grid, the (x, y) ordered pair directions correspond to (east, north). Using that coordinate meaning for the vector components here, they would be ...
(-24.7, 24.7) miles
The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.
Answer:
width(w)= 20inches
Step-by-step explanation:
solution,
given,
perimeter of a rectangle (P)=68inches
length of rectangle= 14 inches
we know,
perimeter of a rectangle=2L + 2W
or,68=2×14+2×w
or,68-28=2w
or,40=2w
or,w=40÷2
or,w=20inches.
how to make chicken, with rice ....
Answer:
put rice with chicken
Step-by-step explanation:
find the following right triangle, find the side length x
Answer:
x=41
Step-by-step explanation:
9²+40²=x²
81+1600=x²
1681=x²
√1681=√x²
41=x
Rectangle J′K′L′M′ shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.
Rectangle JKLM is drawn on the grid with vertices J at negative 7, negative 6. K is at negative 4, negative 6. L is at negative 4, negative 2. M is at negative 7, negative 2. Rectangle J prime K prime L prime M prime is drawn with vertices J at prime 6, negative 9. K prime is at 9, negative 9. L prime 9, negative 5. M prime is at 6, negative 5. Trapezoid STUV is drawn with vertices at S 3, 2. T is at 5, 5. U is at 2, 6. V is at 1, 4.
What will be the location of T′ in the image trapezoid S′T′U′V′?
(18, −2)
(18, 2)
(15, −2)
(15, 2)
The transformed figure has the opposite orientation (A'B'C'D' is counterclockwise, whereas ABCD is clockwise), so a reflection is involved. The segment C'D' is still at the bottom, as is CD, so the reflection must be across a vertical line.
In the attached, the light-blue figure A''B''C''D'' shows the reflection of ABCD across the y-axis. It is easy to see that figure A'B'C'D' is a translation of that 5 units downward.
The appropriate choice is the 2nd one ...
... Reflection over the y-axis followed by a translation down by 5 units. droiyhjfgmdp[ytijkmrdo[ijy[hjmpoiujhokmonj-oimog[fujyjh[opifj[yuj'hkm[ofidyjhoijpofyijh[foist[Yaj[hkmcf[oiyjnjc[city[huff[pay[Pj[ifcjty[ijh[fjotijyh[Hj[fogyish[coif[t0yju[pick[fujph[fj0yh-hifcj[oijhpoijcoijhpouihughdxoiuhtoutpgoindxhouthughxdiurht09uhdxpjrtnhiuhdxiourth8iuthojucfptui9yhufchouihgcifuygtidhiougocdiudrhtudxhfogiurhtiohgcdoiuhoiuxdrhtoiughoiutdgr8uhseoiuhtdiuhroiuiudxdhgioudhugtoirugiudghxtiugdifurtyioudfxhriuytoduyhxotuyotiugoiutyoiuhrtuoihesoitughedugyhoiduhrtouhoiguhoidruthuihgdoiuhrtouighdoiurhtghoidutrhourthiuhdcoiutrioduhtgoiuhoitdrhgiouhoiuhderytgiudyhi8yetgiydhrugterudsoseoysrtgoivdxuht8ygfodushty8ugf9d8sythuygsd9e8tgoyfsdgtofidugsyt8g9s8ewgutiyges8tgiueysg7iygterysgt8t6yoesut
Evaluate each of the following limits.
a. lim 8(2 + h) – g(2)
if gt) = VI + 7
h
h→0
How do you solve this?
Answer:
lim = 1/6
Step-by-step explanation:
Apparently, we have ...
[tex]g(t)=\sqrt{t+7}[/tex]
It often works well to multiply by the conjugate of a difference that approaches zero.
[tex]\displaystyle\lim_{h\to 0}{\frac{g(2+h)-g(2)}{h}}=\lim_{h\to 0}{\frac{\sqrt{(2+h)+7}-\sqrt{2+7}}{h}}\\\\=\lim_{h\to 0}\frac{(\sqrt{9+h}-\sqrt{9})(\sqrt{9+h}+\sqrt{9})}{h(\sqrt{9+h}+\sqrt{9})}=\lim_{h\to 0}{\frac{(9+h)-9}{h(\sqrt{9+h}+\sqrt{9})}}\\\\=\lim_{h\to0}{\frac{h}{h(\sqrt{9+h}+3)}}=\left.\frac{1}{\sqrt{9+h}+3}\right|_{h=0}=\boxed{\frac{1}{6}}[/tex]
57846*3746 help please
Answer:216691116
Step-by-step explanation:
Answer:
216,691,116
Step-by-step explanation:
2. Dominique baked 4 dozen muffins. She wants to put the muffins in packages of 6.
How many packages will she have?
A 6
(B 8
© 10
0 24
E 288
Answer:
24 packages
Step-by-step explanation:
One dozen is 12, so 4 x 12 = 24
h=-16t^2+72t+100 solve for t
Answer:0
Step-by-step explanation:
hey i'm in the six grade i'm not sure but pls try it
The position of a large fish relative to the water surface was −17 1/3 feet. It suddenly dove straight down and increased its depth by 6 1/2 feet. What is the position of the fish now relative to the water surface? Enter your answer as a mixed number, in simplified form, in the box.
PLEASE HELP ME please
Answer:
C
Step-by-step explanation:
There isnt rly a lot of information from this question but my best guess would be C. It says "1 drop in each eye bid every 10 days", so assuming that 1 drop equals 1 ml and knowing we have to do it in "each eye bid" we could assume 2ml of eye drops would be used every 10 days.
Sorry if im wrong but i hope this helps have a great day and happy holidays (｢•-•)｢
Based on the scatterplot, what is the best prediction of the amount of $ in sales when the temperature is at 21°C?
Answer:
Between 400$ and 500$
Step-by-step explanation:
Draw a straight line that follows the scatterplot - either by guesstimating (best choice) or by applying any known method to extrapolate a line. Then it's just a matter of reading the y value corresponding to that x. Hardly a perfect image, but close enough since it's a prediction
Solve by completing the square 2x^2+x-4=0
Answer:
x=-1±[65]
________
8
Step-by-step explanation:
solve the equation for xby finding a,b, and come of the quadratic then applying the quadratic formula
Help help help math math
Answer: -1 = (-3/3)
Step-by-step explanation
You go from one point to another, i started from 3,1 and went to 3,0. I got down -3 which is my rise and right 3 for the run. Tell me if this is correct
hellooo merry christmas !
can someone please help mee? ik its a lot but even just a little help would be very mich appreciated :))
Answer:
.....
Step-by-step explanation:
merry Christmas to you too
Which theorem explains why the circumcenter is equidistance
0.15% of what number is 10.5
Answer:
70
Step-by-step explanation:
10.5/0.15 = 70
Check:
70 · 0.15 = 10.5