Answer:
36 pencils
[tex]Cost = 0.2[/tex]
Step-by-step explanation:
Given
Cost Price = 180
Represent the number of items by x
This implies that the cost of each item is [tex]\frac{x}{180}[/tex]
[tex]Selling\ Price = Cost + Profit[/tex]
[tex]Selling\ Price = \frac{x}{180} + 2[/tex]
Since all but 6 items were sold, the total selling price is:
[tex]Total = (x - 6)(\frac{x}{180} + 2)[/tex]
This amount can be used to buy 30 more items.
So, we have:
[tex](x - 6)(\frac{x}{180} + 2) = x + 30[/tex]
Multiply both sides by 180
[tex]180 * (x - 6)(\frac{x}{180} + 2) =180(x + 30)[/tex]
[tex](x - 6)(x + 360) = 180x + 5400[/tex]
Expand brackets
[tex]x\² + 360x - 6x - 2160 = 180x + 5400[/tex]
[tex]x\² + 354x - 2160 = 180x + 5400[/tex]
Equate to 0
[tex]x\² + 354x - 180x - 2160 - 5400 = 0[/tex]
[tex]x\² + 174x - 7560 = 0[/tex]
Expand
[tex]x\² + 210x - 36x - 7560 = 0[/tex]
[tex]x(x + 210) - 36(x + 210) = 0[/tex]
[tex](x - 36)(x + 210) = 0[/tex]
[tex]x - 36 = 0[/tex] or [tex]x + 210 = 0[/tex]
[tex]x = 36[/tex] or [tex]x = -210[/tex]
Since, number of items can't be negative, we have to discard x = -210.
Hence:
[tex]x = 36[/tex]
We can then conclude that, Mr. Javier purchased 36 pencils
Recall that
[tex]Cost = \frac{x}{180}[/tex]
[tex]Cost = \frac{36}{180}[/tex]
[tex]Cost = 0.2[/tex]
Find the general solution of y''' + 9y'' + y' − 111y = 0 if it is known that y1 = e−6x cos(x) is one solution.
Answer:
[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]
Step-by-step explanation:
The objective of this question is to solve:
[tex]\dfrac{dy(x)}{dx}+ 9\dfrac{d^2y(dx)}{dx^2}+\dfrac{d^3y(x)}{dx^3}-111y(x) = 0 :[/tex]
Suppose the general solution is proportional to [tex]e^{\lambda x}[/tex] for [tex]\lambda[/tex] is constant; Then:
Let's replace [tex]y(x) = e^{\lambda\ x}[/tex] into the above equation:
i.e.
[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )+ 9 \dfrac{d^2}{dx^2}(e ^{\lambda x} ) + \dfrac{d}{dx}(e ^{\lambda x} )- 111 \ e ^{\lambda x} = 0[/tex]
To Replace:
[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )[/tex] with [tex]\lambda^3 e ^{\lambda x }[/tex]
[tex]\dfrac{d^2}{dx^2}(e ^{\lambda x} ) \ with \ \lambda^2 e^{\lambda\ x}[/tex]
[tex]\dfrac{d}{dx}(e ^{\lambda x} ) \ with \ \lambda e ^{\lambda \ x}[/tex]
Thus;
[tex]\lambda^3 e ^{\lambda x }[/tex] + [tex]9 \lambda^2 e^{\lambda\ x}[/tex] + [tex]\lambda e ^{\lambda \ x}[/tex] - 111 [tex]e ^{\lambda \ x}[/tex] = 0
[tex]e ^{\lambda \ x} (\lambda ^3 + 9 \lambda ^2 + \lambda - 111 )= 0[/tex]
∴
In as much as [tex]e^{ \lambda x}\neq 0[/tex] for any finite [tex]\lambda[/tex]; Then:
[tex]\lambda ^3 + 9 \lambda ^2 + 111 = 0[/tex]
By Factorization:
[tex](\lambda - 3) ( \lambda ^2 + 12 \lambda + 37) = 0[/tex]
[tex]\lambda = -6 + i \ or\ \lambda = -6 - i \ or \ \lambda = 3[/tex]
However;
The root [tex]\lambda = -6 \pm i[/tex] yield;
[tex]y_1 = (x) = c_1 e ^ {(-6+i)x}[/tex]
[tex]y_2 (x) = c_2e^{(-6-i)x}[/tex]
The root [tex]\lambda = 3[/tex] yield;
[tex]y_3(x) = c_3 e^{3x}[/tex]
∴
The general solution is:
[tex]y(x) = y_1(x) + y_2(x) + y_3(x) = \dfrac{c_1}{c^{(6-i)}x}+\dfrac{c_2}{c^{(6+i)}x}+ c_3e^{3x}[/tex]
Using Euler's Identity ;
[tex]e^{\alpha+i \beta} = e^\alpha \ cos (\beta ) + i \ e^\alpha \ sin ( \beta)[/tex]
[tex]y(x) = c_1 ( \dfrac{cos (x) }{e^{6x}}+ \dfrac{i \ sin x }{e^{6x} }) + c_2 ( \dfrac{cos (x)}{e^{6x}}- \dfrac{-i \ sin (x)}{e^{6x}})+c_3 e^{3x}[/tex]
[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]
g(x) = -4x + 5 and h(x) = x^2 - 3x + 5 find (g-h) (x)
/~—☆☆☆——☆☆☆——☆☆☆——☆☆☆——☆☆☆—~~
Answer:
−x2+g+3x−5 (I think)
Step-by-step explanation:
If two different integers between 1 and 100 inclusive are chosen at random, what is the probability that the difference of the two numbers is 15
Answer: 17 / 990
Step-by-step explanation:
To obtain the probability of the question above :
Find the count of number pairs whose difference gives is 15 in the range (1 to 100).
Also find the count of all distinct number pair differences
Number pair which have a difference of 15 = 85
Total distinct number pair differences = 4950
Probability = required outcome / Total possible outcomes
P(difference of 15) = 85/4950 = 17/990
the value of x in logx(9/63)=1/2 is
Answer: x = 7/2
Step-by-step explanation: u juss simplify 1/2 x 7 to 7/2 so x = 7/2
The value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
What is a logarithmic equation?
"A logarithmic equation is an equation that involves the logarithm of an expression containing a variable."
Given logarithmic equation
[tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x(\frac{1}{7} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x=\frac{1}{2}({7} )[/tex]
⇒ [tex]log_{10}x=\frac{7}{2}[/tex]
⇒ [tex]x = 10^{\frac{7}{2} }[/tex]
⇒ [tex]x = 10^{3+\frac{1}{2} }[/tex]
⇒ [tex]x = 10^{3}[/tex] × [tex]10^{\frac{1}{2} }[/tex]
⇒ [tex]x = 1000\sqrt{10}[/tex]
The value of [tex]x = 1000\sqrt{10}[/tex]
Hence, the value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
Learn more about logarithmic equation here
https://brainly.com/question/14406114
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The regular admission price for an amusement park is $72. For a group of 15, or more, the admission price is reduce by $25 per person. How many people need to be in a group to save $500?
=========================================
Explanation:
x = number of people
Without the discount, each person pays $72, so the total cost is 72x dollars if x people go through the gate individually.
Now applying the group discount, those x people pay 72-25 = 47 dollars each. Meaning the total cost is now 47x. Keep in mind that [tex]x \ge 15[/tex] in order for the discount to kick in.
Subtracting the two amounts leads to 72x-47x = 25x. It is not a coincidence that we get a coefficient of 25 here.
Set this equal to 500 and solve for x
25x = 500
x = 500/25
x = 20
------------
If x = 20 people attend individually, then they pay 72*x = 72*20 = 1440 dollars.
If 20 people go as one group, they pay 47x = 47*20 = 940 dollars
We have a savings of 1440-940 = 500 dollars. This confirms the answer.
All 20 people must go as one group if they want to save $500.
Rewrite the following using the GCF and Distributive properly ?
63 + 27
The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss, at various temperatures in degrees Celsius:
Temperature (degrees Celsius) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Percent heat loss from beak 35 36 38 28 41 43 55 46 39 54 45 58 60 56 62 67
a. The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: _____ (Use decimal notation. Give your answer to four decimal places.)
b. Use the equation to predict (
±
0.01) beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius.
c. What percent (
±
0.01) of the variation in beak heat loss is explained by the straight-line relationship with temperature?
d. Find the correlation r (
±
0.001) between beak heat loss and temperature.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Temperature (degrees Celsius) : 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Percent heat loss from beak : 35 36 38 28 41 43 55 46 39 54 45 58 60 56 62 67
Using an online regression calculator ; the regression equation obtained is :
ŷ = 2.0927X + 0.6029
X = independent variable
Y = predicted variable
2.0927 = slope
0.6029 = intercept
B.) temperature = 25
ŷ = 2.0927(25) + 0.6029
= 52.9204
C.) the explained variance is the value of the coefficient of determination (R²) which is the square of the correlation Coefficient
0.8785² = 0.7718
D.) the correlation Coefficient r is 0.8785 using the Coefficient of regression calculator
(3+sqrt-16)(6-sqrt-64)
Answer:
12i + 9
Step-by-step explanation:
Since sqrt of negative numbers cannot exist, they are numbers followed by the letter I.
sqrt -16=4i
sqrt -64=8i
3 and 6 cannot be grouped with them, so you would add these two
3+6=9
8i+4i=12
I believe this would be the answer:
12i + 9.
Answer:
18-32i
Step-by-step explanation:
(3+sqrt(16i)(6-sqrt(64i)
= 18-32i
The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient? There are fraction 6 and 1 over 4 two-thirds in fraction 4 and 1 over 6.
a. There are fraction 6 and 1 over 4 five and one-sixths in fraction 2 over 3.
b. There are fraction 8 and 1 over 6 two-thirds in fraction 5 and 1 over 6.
c. There are fraction 8 and 1 over 6 five and one-sixths in fraction 2 over 3.
Answer:
C. D. E. or 3. 4. 5.
Step-by-step explanation:
If a =
3
5
, b = 3, c = 1, d = 5, which equality is true?
A)
d
a
=
b
c
B)
a
b
=
c
d
C)
b
a
=
c
d
D)
a
d
=
b
c
Answer:
could you give a picture of the problem. cause I may be able to help but I cant really understand the question with what you typed
Answer:
D
Step-by-step explanation:
just took this test
A polynomial has a leading coefficient of 1 and the
following factors with multiplicity 1:
X+2
x-√2
What is the factored form of the polynomial?
Answer:
Its A
Step-by-step explanation:
I got it right on EDGE 2021
Answer:
The answer is actually the last one
Step-by-step explanation:
I just did it. The other answer isn't even the right question.
Find 8% of $40 answers with the nearest penny
Answer:
3.20
Step-by-step explanation:
Sorry i had the same question and i asked the teacher if he could help and he did but he sorta juts gave me the answer so cant really give an explanation so sorry.
At Sakaro's Sushi, you can get 18 wraps for $30.06 What is the price for 1 wrap?
Answer: $1.67
Let's make an equation for the problem. To find the price for each sushi roll, divide the price by the number of sushi rolls.
30.06 ÷ 18 = 1.67
State the domain of the relation (1,2,3,3,4,5) (-3,-1,1,2,3)
David has 574 cereal bars that he wants to fit in bags of 10 and bags of 8. The number of bags of 8 is 2 more than the number bags of 10. How many bags of 8 and 10 can david pack the cereal bar into
Answer: lol have the same question
Step-by-step explanation:
A migrating bird flies 688 miles in 16 hours. How many miles does it fly in 5 hours?
Answer:
In 5 hours, the migrating bird will frly 215 miles.
Step-by-step explanation:
Since the bird flys 688 miles in 16 hours we need to find the unit rate. So i divided 16 by the 16 hours which gave me 1, so i also divided 688 by 16 and i got 43. So the bird flys 43 miles in a hour. We are not done yet because we need to find how many miles in 5 hours. So we multiply the 43 miles by 5 and got 215, and i also multiplied the 1 hour bye 5 and got 5. Last but not least, the migrating bird will fly 215 miles in 5 hours. I hope that this will help you out.
At 7:00 one Summer morning Harry and Hermione hopped into their speedy more motorboat and left Hogwarts dock. They arrived at Dumbledore Wharf 35 minutes later. During the busy summer months a car ferry departs from Dumbledore wharf every five minutes. Tourists crowd onto the ferry for the 55 minute ride to Hogswarts dock. If Harry and Hermione followed the route that the car ferries take, how many car ferries did they see on their trip?
9514 1404 393
Answer:
19
Step-by-step explanation:
If we assume that the car ferries start at or before 6:05, and each 5 minutes thereafter, and if we count the ferries at the dock on either end, the total number seen is the number of ferries encountered in ...
55 +35 = 90 . . . minutes
That is, it is the number already in transit when they leave, plus the number that start while they are traveling.
That's 90/5 +1* = 19 ferries.
_____
The attached diagram can give an idea. Each up-sloping line represents a ferry in-transit. The left side is Dumbledore Wharf; the right side is Hogwarts dock. Each horizontal unit represents the distance traveled by a ferry in 5 minutes. Each vertical unit represents a 5-minute interval.
The down-sloping line represents the motorboat travel. The dots at either end of the latter line represent car ferries that are at the dock, just arriving or just-departing. Altogether, there are 17 places where the lines cross, in addition to the boats at the docks.
__
* the +1 is because the number of points defining intervals is 1 more than the number of intervals.
A.(-2,3)
B.(-2,-3)
C.(2,3)
D.(4,3)
3 people take 90mins to water a garden how long does it take 6 people
Answer:
hope it is helpful
Step-by-step explanation:
mark as branlist
^ ^
Find f(5). f(x) = x2 +2x
Answer:
f(5) = 35
Step-by-step explanation:
In any function f(x), x is the input and f(x) is the output
Example:
f(x) = 2x + 3, find f(a)
That means we need to find value of f(x) at x = a, so substitute x by a
f(a) = 2(a) + 3 = 2a + 3
f(a) = 2a + 3
Let us use the same way to solve our question
∵ f(x) = x² + 2x
→ We need to find f(5), so substitute x by 5
∴ f(5) = (5)² + 2(5)
∴ f(5) = 25 + 10
→ Do addition
∴ f(5) = 35
Researchers investigated whether the proportion of American teenagers with some level of hearing loss was diff erent in 2005–2006 than in 1988–1994. They collected data on random samples of American teenagers in those two time periods. Let the symbol π05-06 denote the population proportion of American teenagers with some level of hearing loss in 2005–2006 and similarly for π88-94. A 95% confidence interval for the parameter π05-06 − π88-94 turns out to be (0.0015, 0.0467).
Required:
What is an appropriate conclusion to draw?
Complete Question
Researchers investigated whether the proportion of American teenagers with some level of hearing loss was different in 2005–2006 than in 1988–1994. They collected data on random samples of American teenagers in those two time periods. Let the symbol [tex]\pi __{05-06}}[/tex] denote the population proportion of American teenagers with some level of hearing loss in 2005–2006 and similarly for [tex]\pi__{{88-94}}[/tex]. A 95% confidence interval for the parameter [tex]\pi__{{05-06}} }- \pi__{{88-94}}[/tex] turns out to be (0.0015, 0.0467).
Required:
What is an appropriate conclusion to draw?
Answer:
The appropriate conclusion is
The sample data provide little evidence to doubt that the proportion of American teenagers with hearing loss was the same in 1988-1994 as in 2005-2006
Step-by-step explanation:
Generally the appropriate conclusion is
The sample data provide little evidence to doubt that the proportion of American teenagers with hearing loss was the same in 1988-1994 as in 2005-2006.
This because the confidence intervals are very close to zero , i.e both the upper limit and the lower limit are close to zero and if we are take 0.05 as our level of significance we see that the both values of the confidence level are small to be significant
The length of a table is 110 cm to the nearest cm
Write down the error interval using inequalities.
10 points for right answer
Answer: they didn’t give the exact answer.
Step-by-step explanation: they rounded to the nearest.
What is the image of point (-3,-1) under a reflection in the origin?
Answer:
3,1
Step-by-step explanation:
Please help I would appreciate
Answer:
the 1st 2nd and 5th since if there is even one negative in the fraction it makes the whole fraction negative
Find the value of
5x^2 if x = -3.
Step-by-step explanation:
5x²
If x = 3
Then,
5(3)²
= 5×9
= 45
10) Sarah is 3 years older than her sister Mary.
Together their ages add up to 23. How old is Mary?
Answer:
20
Step-by-step explanation:
20 - 3
Sarah is 3 years older so 23 is going to be subtracted.
I would really appreciate some help. Thanks!
Seth has game and education apps on his tablet. He noticed that he has 5 game apps for every 2 education apps. Which of the following is another way to write this ratio?
A. 2:3
B. 2:5
C. 3:2
D. 5:2
Answer:
D
Step-by-step explanation:
the question says that he has 5 to 2 and if you put it in a fraction you cant reduce it so therefore the answer has to be 5:2
Answer:
D. 5:2
Step-by-step explanation:
He has 5 games so 5: for every 2 school apps so 5:2
Quickkkk!!!!!!!! Help
Answer:
2143
Step-by-step explanation:
A simple index of three socks have opening values on day 1 and day 8 as shown in the table below. What is the rate of change of this simple index over one week? Round your answer to the nearest tenth
Answer: -7.7%
Step-by- A P E X
Text a friend and write a clear set of instructions on how to find a ratios amount
Answer:
Hi ___
A ratio is created from two numbers it can also be a fraction.
To find a ratio you have to have 2 numbers
You can take these 2 numbers and divide them so they are a unit ratio
For example 3:6 can be reduced to 1:3
Step-by-step explanation:
Hope this helps please give brainliest