The function of the number of penguins is an exponential function
The penguins are going to find a new home in 2015
How to determine the yearThe equation of the function is given as:
[tex]P(t) = 24(1.231)^t[/tex]
When there are 70 penguins, the equation becomes
[tex]24(1.231)^t =70[/tex]
Divide both sides by 24
[tex]1.231^t =2.917[/tex]
Take the logarithm of both sides
[tex]t\log(1.231) =\log(2.917)[/tex]
Divide both sides by log(1.231)
[tex]t =5[/tex]
The time is 5 years from 2010.
So, we have
Year = 2010 + 5
Year = 2015
Hence, the penguins are going to find a new home in 2015
Read more about exponential functions at:
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write 105/20 as a decimal
Answer:
5.25
Step-by-step explanation:
Answer: 105/20 in decimal = 5.25
Step-by-step explanation: The fraction bar means "divided by" in the fraction 105/20, where 105 is the numerator and 20 is the denominator. As a result, the fraction 105/20 can be written as "105 divided by 20" or "105 20."
We discovered that 105/20 in decimal form is: 105 20 = 5.25 when we divided 105 by 20.
As a result, 105/20 has a decimal form of 5.25.
Hope this helps.
which statement is true about the graphs shown
Only graph A represents a proportional relationshi
Golygraph represents a proportional relationship
Graph A and graph both represent a proportional relationship
Graph and goh both representa non proportional relationships
[tex] \rm \: If \: y = {e}^{x} - \frac{1}{x} + { log_{e}x } \: \: find \: \frac{dy}{dx} [/tex]
Thanks!!
We are given with a function y and need to find dy/dx or the first Derivative of y w.r.t.x , but let's recall
[tex]{\boxed{\bf{\dfrac{d}{dx}\{f(x)\pm g(x)\pm h(x)\pm \cdots =\dfrac{d}{dx}\{f(x)\}\pm \dfrac{d}{dx}\{g(x)\}\pm \dfrac{d}{dx}\{h(x)\}\pm \cdots}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}(log_{e}x)=\dfrac{1}{x}}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}(e^x)=e^{x}}}}[/tex]Now consider :
[tex]{:\implies \quad \sf y=e^{x}-\dfrac{1}{x}+log_{e}x}[/tex]
Differentiating both sides w.r.t.x
[tex]{:\implies \quad \sf \dfrac{d}{dx}(y)=\dfrac{d}{dx}\bigg\{e^{x}-\dfrac{1}{x}+log_{e}x\bigg\}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=\dfrac{d}{dx}(e^x)-\dfrac{d}{dx}\left(\dfrac{1}{x}\right)+\dfrac{d}{dx}(log_{e}x)}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}-\dfrac{d}{dx}(x^{-1})+\dfrac{1}{x}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}-(-1)(x)^{-1-1}+\dfrac{1}{x}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}+(x)^{-2}+\dfrac{1}{x}}[/tex]
[tex]{:\implies \quad \sf \dfrac{dy}{dx}=e^{x}+\dfrac{1}{x^{2}}+\dfrac{1}{x}}[/tex]
Simplifying will yield
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\dfrac{dy}{dx}=\dfrac{e^{x}x^{2}+x^{2}+x}{x^{2}}}}}[/tex]
This is the required answer
If w = 10 units, x = 5 units, and y = 6 units, what is the surface area of the figure? Round your answer to the nearest tenth.
Figure is composed of a right square pyramid on top of a square prism. The sides of the square pyramid are equal to the sides of the square prism, the length and width of the square prism is w, the height of the square prism is x, and the height of the square pyramid, which forms a right angle with the center, is y.
A) 656.2 units2
B) 400 units2
C) 256.2 units2
D) 456.2 units2
Answer:
456.2 units², so answer d
Step-by-step explanation:
The area of the square base is ...
base area = w² = (10 units)² = 100 units²
The lateral area is 4 times the area of one rectangular face:
lateral area = 4wx = 4(10 units)(5 units) = 200 units²
The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:
h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²
h = √61 units
So, the area of 4 triangles is ...
area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²
Now we have the areas of the parts, so we can add them together to get the total surface area:
surface area = base area + lateral area + area of triangular faces
= 100 units² + 200 units² + 156.2 units²
surface area = 456.2 units²
What is the value of x in this triangle
someone help!! 18 pts + brainlest !!!! ASAP
Answer:
33.22 square inches
Step-by-step explanation:
Diameter to Radius: [tex]\frac{1}{2}d = r[/tex]
Area of Circle: [tex]\pi r^2[/tex]
We are given the diameter of a pancake as 4.6 inches, so the radius is 2.3 inches. Next, we have to apply the area of circle formula with pi as 3.14 and the radius as 2.3
[tex]3.14 * 2.3^2[/tex] [tex]3.14 * 5.29[/tex] [tex]16.6106[/tex]Next, since there's two pancakes, we double 16.6106.
[tex]16.6106 * 2[/tex] [tex]33.2212[/tex]Lastly, we round to the nearest hundredth.
33.2212 ≈ 33.22 square inchesTherefore, the answer is 33.22 square inches.
A company manufactures 16-oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0. 15 oz, the production is stopped. What is the range of acceptable values for production to continue? 15. 15 oz to 16. 00 oz 15. 85 oz to 16. 00 oz 15. 85 oz to 16. 15 oz 16. 15 oz to 16. 45 oz.
The range of acceptable values for production to continue working of the company without stoppage is 15.85 to 16.15.
What is the range of acceptable values?Range is the area of fluctuation between the upper and lower limit. The range of the acceptable values is all the values between the upper and lower limit.
Here, a company manufactures 16-oz boxes of cereal. Now, this boxes are randomly weighted to ensure the correct amount.
As the discrepancy in weight is more than 0.15 oz then the production of the company is stopped.
To proper functioning of the company without stoppage, the limit of the production should be with in 0.15 oz.
The company produce, 16-oz boxes of cereal and the disperancy is 0.15 oz. Thus the value of the lower limit will be,
[tex]L=16-0.15\\L=15.85\rm \; oz[/tex]
The value of the upper limit will be,
[tex]U=16+0.15\\U=16.15\rm \; oz[/tex]
Thus, the range will be {15.85-16.15 oz}
Hence, the range of acceptable values for production to continue working of the company without stoppage is 15.85 to 16.15.
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−28.3= -3.3+b/0.1 solve for b
Answer:
b=negative 5/2
Step-by-step explanation:
first, convert the decimal into a fraction
−28.3= -3.3+b/1/10
simplify the complex fraction
-28.3=-3.3+10b
add 3.3 to both sides
-25=10x
divide each side by 10
x=negative 5/2 or x=negative 2.5
help for brainlist :)
Answer:
y = - [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
6x - 3y = - 7 → (1)
2x + 3y = - 9 → (2)
multiplying (2) by - 3 and adding to (1) will eliminate x
- 6x - 9y = 27 → (3)
add (1) and (3) term by term to eliminate x
0 - 12y = 20
- 12y = 20 ( divide both sides by - 12 )
y = [tex]\frac{20}{-12}[/tex] = - [tex]\frac{5}{3}[/tex]
7-20. The two triangles below are congruent. Write a congruence statement relating the triangles. Describe a sequence of transformations that maps one onto the other. N E 10 10 8 .
Step-by-step explanation:
m ( < E ) = m ( < N )
m ( < H ) = m ( < J )
m ( < A ) = m ( < O )
NH = EJ
NA = EO
AH = JO
PLS HELP IM GIVING 25 POINTS
The figure shows Triangle ABC and some of its transformed images on a coordinate grid:
Which of the four triangles was formed by a translation of Triangle ABC?
1
2
3
4
Answer: Triangle 4
The specific translation or shifting is "move 9 units to the right and 4 units down".
We can prove this by looking at something like point A(-10,2) and note how it moves to (-4,-2). Going from (-10,2) to (-4,-2) is exactly 9 right and 4 down.
In terms of x,y notation the translation rule is [tex](x,y) \to (x+9,y-4)[/tex]
volume of cone with 18mi height and 18mi diameter
Answer:
4580.442
Step-by-step explanation:
the closest answer I can fight
Work out the percentage increase from 320 to 388
Answer:
21%
Step-by-step explanation:
388-320=68 then divide 68 by 320 which is 0.21 then divide that by 100 or you could move the decimal 2 times to the right which makes it 21%
hope this helped!
also please tell me if I'm wrong
A dozen of eggs was brought at N2000. If each egg was sold at N60, find the profit or loss
A dozen = 12
Multiply the prices they were sold for by 12:
12 x 60 = 720
By selling the 12 eggs they made 720
Since they bought it for 2000 they lost money.
2000 - 720 = 1280 loss
help this is literally due tomorrow
This is a trick question. They eat 1/3 of the gallons given. Multiply
1/3 * 1/3 = 1/9 gallons or 0.111 gallons
Answer: Aye aye, cap'in
Step-by-step explanation:
So we start off with our base value, 1/3 gallons.
We are trying to find how many gallons we have eaten, so we do 1/3*1/3, since we need to find what is 1/3rd of that gallon.
For reference, if you wanted to find how much is left over, we multiply by 2/3 since 1-1/3 = 2/3, so there are 2/3 of the 1/3rd gallons left. Not important for solving this problem, but it might help you understand why we decided to multiply by 1/3.
1/3 * 1/3 = 1/9
Our answer is 1/9.
Can someone help me with b please??
Answer:
1) 0.25
2)4
Step-by-step explanation:
1) 12 divided by 48 is 0.25
2) 48 divided by 12 is 4
hope this helps
If a sprinkler waters 1 over 8 of a lawn in 1 over 2 hours, how much time will it take to water the entire lawn?
2 hours
4 hours
10 hours
16 hours
I am in middle school.
Answer:16
Step-by-step explanation:
For 1/8 of the lawn it takes 2 hours
So, for the entire lawn it will take 2/(1/8) = 16
So, your final answer is 16 hoursHope this helps!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.
Answer:
For the 2 first exponents you multiply for the last 2 you add the powers
Step-by-step explanation:
-2x4=-8=4^-8
2x-1=-2 4^-2
2+6= 4^8
5-3=2 4^2
h^3+4h-25h-100
factor by grouping
show steps please
Answer:
h³-21h-100
Step-by-step explanation:
You only have to subtract 25h from 4h.
EXPRESS angles X IN TERMS OF Y
Answer:
y = [tex]\frac{1}{2}[/tex] x
Step-by-step explanation:
the inscribed angle y is half the measure of the central angle x
y = [tex]\frac{1}{2}[/tex] x
A metal bar weighs 7 Kg. 93% of the bar is Silver. How many Kgs of silver is there in the bar?
From the given data
93% of the bar is silver :
[tex]\small\bold{ → 93\% \: \: of \: \: 7kg}[/tex]
[tex]\small \bold{→\frac{93}{100} \times 7 }[/tex]
[tex]\small \bold{→ \frac{651}{100} }[/tex]
[tex]\small \bold{→ 6.51 \: kg }[/tex]
Therefore, 6.51 Kg of Silver is there in the bar.
» A metal bar weighs 7 Kg. 93% of the bar is Silver. How many Kgs of silver is there in the bar?
[tex] \mathbb{ANSWER:}[/tex]6.51 kilogram (kg) of Silver is there in the bar.— — — — — — —
[tex] \mathbb{SOLUTION:}[/tex][tex] \bold{ 93\% \: of \: 7 \: kg \: \: so, }\\ \\ \tt \: \: \: \: \: \: \: \: \: \: \: \: \: = 93/100*7 \\ \tt = \frac{651}{100} \\ \: \: \: \: \: \: \: \: \: \: \tt= \underline{ \boxed{ \purple{ \tt 6.51 \: kg}} }\\ [/tex]Therefore, 6.51 kg of Silver is there in the bar.
_______________❦︎_______________
Help me about this
10 POINTS!
Answer:
a. 16; b. mean = 43.75; median = 43; mode = none
Step-by-step explanation:
Put all the numbers in order:
36, 38, 40, 41, 45, 48, 50, 52
a. Range:
52 - 36
= 16
b. Mean:
(36 + 38 + 40 + 41 + 45 + 48 + 50 + 52) /8
= 43.75
Median:
36, 38, 40, 41, 45, 48, 50, 52
=> (41 + 45) / 2
= 43
Mode: None (no numbers come again)
On the map below, all numbered streets run parallel to each other. Both 3rd and 4th streets are intersected by King Avenue.
A delivery driver is driving around town and has noticed that every time he turns, it creates an angle. What are the measures of Angles X, Y, and Z on the map?
In your answer, give the measures of angles X, Y, and Z, and explain how you calculated each one.
Answer:
ok
Step-by-step explanation:
x:
X is adjacent to the 75 angle so x + 75 need to be 180.
180 - 75 = 105
x = 105
z:
Z is on opposite across outside corners from X so it will be the same thing.
z = 105
y:
Y is adjacent to Z so Y + Z must equal 180.
Z = 105
y + 105 = 180
y = 75
HELP PLEASE FOR BRAINLEST
Answer:
3/13
Step-by-step explanation:
Put the total number that tapped the ground AND 5/10 worms (which is 3) over the total number which is 13
so 3/13 which doesn't simplify
hope this helped :)
Carys is taking 3 biscuits to eat. George steals 2. How many biscuits does Carys eat at the end?
I will give BRAINILEST
Answer:
i think it is 24
i think it is Step-by-step explanation:
Answer:
The players club is playing with the players
Step-by-step explanation:
give me a good Answer to my Question
What is the scale factor of this dilation? a:1/2 b:2/3 c:3/4 d:3/2
For the pair of similar triangles, find the value of x.
Answer: 26
Step-by-step explanation:
If the ratio of boys to girls is 3 : 11 and there are 66 girls in the play, how many students are boys?
Answer:
18 boys
Step-by-step explanation:
boys/girls = 3/11 = b/66
3/11 = b/66
11b = 3 × 66
b = 3 × 6
b = 18
There are 18 boys.
97 is what percent of 837? Round to the nearest whole #
if we take 837 as the 100%, what is 97 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 837&100\\ 97&x \end{array}\implies \cfrac{837}{97}=\cfrac{100}{x}\implies 837x=9700 \\\\\\ x=\cfrac{9700}{837}\implies x\approx 11.59[/tex]
PLEASE HELP asap. Thank you so much to anyone that helps:)
to find radius; 8.4/2,
therefore 2×22/7×8.4/2×10.9=1079.76Answer:
398.5
Step-by-step explanation:
a (surface area) = 2πrh + 2π[tex]r^{2}[/tex]
r (radius) = 8.4/2
r = 2.4
a = 2π (4.2 x 10.9) + 2π (4.2 x 4.2)
a = 2π x 45.78 + 2π x 17.64
a = 287.64 + 110.83
a = 398.5