Answer:
There are 10 students
Step-by-step explanation:
69.55-(5.35*3)= 53.5
53.5/10=5.35 which is what each ticket costed
So the answer is 10 students
Let [tex]\alpha[/tex] be positive real number.
Let f:[tex]\mathbb{R}\to\mathbb{R}[/tex] and g:[tex](\alpha,\infty)\to\mathbb {R}[/tex] be the function defined by
[tex] \rm f(x) = \sin \bigg( \dfrac{\pi x}{12} \bigg ) \: and \: g(x) = \dfrac{2 log_{e}( \sqrt{x} - \sqrt{ \alpha } ) }{ log_{e}( {e}^{ \sqrt{x} } - {e}^{ \sqrt{ \alpha } } ) } [/tex]
Then the value of [tex] \rm \lim_{x \to { \alpha }^ + } f(g(x)) \\ [/tex] is
First, [tex]f(x)[/tex] is continuous on its domain, so
[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = f\left(\lim_{x\to\alpha^+} g(x)\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \sin\left(\frac\pi6 \lim_{x\to\alpha^+} \frac{\ln\left(\sqrt x - \sqrt\alpha\right)}{\ln\left(e^{\sqrt x} - e^{\sqrt\alpha}\right)}\right)[/tex]
As [tex]x\to\alpha^+[/tex], [tex]\sqrt x-\sqrt\alpha\to0[/tex] and [tex]e^{\sqrt x}-e^{\sqrt\alpha}\to0[/tex], so overall we have an indeterminate form ∞/∞. Apply l'Hôpital's rule and simplify.
[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = \sin\left(\frac\pi6 \lim_{x\to\alpha^+} \frac{\frac1{2\sqrt x\left(\sqrt x - \sqrt\alpha\right)}}{\frac{e^{\sqrt x}}{2\sqrt x\left(e^{\sqrt x} - e^{\sqrt\alpha}\right)}}\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \sin\left(-\frac\pi6 \lim_{x\to\alpha^+} \frac{e^{-(\sqrt x-\sqrt\alpha)} - 1}{\sqrt x - \sqrt\alpha}\right)[/tex]
Substitute [tex]y=\sqrt x-\sqrt\alpha[/tex], so that [tex]x\to\alpha^+\implies y\to0^+[/tex].
[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = \sin\left(-\frac\pi6 \lim_{y\to0^+} \frac{e^{-y} - 1}y\right)[/tex]
The remaining limit is the right-derivative of [tex]e^{-y}[/tex] at [tex]y=0[/tex], so
[tex]\displaystyle \lim_{x\to\alpha^+} f(g(x)) = \sin\left(-\frac\pi6\frac{de^{-y}}{dy}\bigg|_{y\to0^+}\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \sin\left(\frac\pi6\right) = \boxed{\frac12}[/tex]
Use the figure and follow the directions below.
A line passes through the point (8,-4) and has a slope of -3/4
Write an equation in slope intercept form for this line.
Answer: y=-3/4x+2
Step-by-step explanation:
y=mx+b
y=-3/4x+b
-4=-3/4(8) +b
-4=-6+b
b=2
y=-3/4x+b
y=-3/4x+2
$2,000 lounge suite was sold under a hire purchase agreement. A deposit of $200 was made. The balance and interest were then paid off in equal monthly instalment of $68 over 3 years.
How much did the lounge suite cost in total?
The Lounge suite price in total is, $2648.
Given that, $2,000 lounge suite was sold under a hire contract. A deposit of $200 was made. The balance and interest were then paid off in equal monthly instalment of $68 over three years.
Under a rent purchase agreement, a purchaser pays an initial deposit and takes the item away. The purchaser makes regular repayments (instalments). The instalments embrace each repayment of the debt and also the interest being charged by the seller. At the top of the amount of the agreement, the purchaser owns the item.
As mentioned, the lounge suite was purchased by paying $200 deposit and also the rest quantity through instalments i.e $68 over three years.
The total price of the lounge suite are going to be,
total price = deposit amount + instalments
= $200 + $68 over 3years
= $200 + $68 (3* 12) ( since, annually has twelve months)
=$200 + $68(36)
=$200 + $2448
=$2648
Therefore the overall price of the lounge suite is, $2648.
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A clothing store buys jeans for $12 and marks them up 200% before selling them to customers. What is the selling price of the jeans? Group of answer choices
Answer:
The selling price = $36
Step-by-step explanation:
The Buying price or Cost (C) = $12Markup = 200%So
Percent Markup on Cost (M) = 200% of 12
= 200/100 × 12
= 2 × 12
= $24
Thus the selling price = Cost (C) + Markup (M)
= $12 + $24
= $36
Therefore, we conclude that:
The selling price = $36
A phone company has two long distance
calling plans. The first plan is $25 per month
for unlimited long distance calling. The second
plan is $10 per month plus $0.05 per minute
of long distance calling. After how many
minutes oflong distance calls will it be cheaper
for a customer to purchase the first plan?
It is cheaper for a customer to purchase the first plan if they make more than 300 minutes of long-distance calls. The answer is (C) 300.
Let's denote the number of minutes of long-distance calls as x. Then, the total cost of the second plan would be:
Cost of Plan 2 = $10 + $0.05x
The total cost of the first plan is always $25, regardless of the number of minutes of long-distance calls.
So we need to find the value of x at which the cost of Plan 2 exceeds the cost of Plan 1, i.e. when:
$10 + $0.05x = $25
Subtracting $10 from both sides, we get:
$0.05x = $15
Dividing both sides by $0.05, we get:
x = 300
So for values of x greater than 300, the cost of Plan 2 will exceed the cost of Plan 1.
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A recipe for punch uses 2 cups of grape
juice and 3 cups of orange juice. How many
cups of orange juice are needed if 6 cups of
grape juice are used?
A 7 cups
B 9 cups
C 15 cups
D 30 cups
Answer:
B 9 cups
Step-by-step explanation:
Grape juice to orange juice ratio is 2:3, for every 2 cups of grape juice 3 cups of orange juice are used.
6/2=3
3 x 3 =9
for every 6 cups of grape juice, 9 cups of orange juice are used
Check for answer by seeing if the ratio matches up.
6:9 simplified is 2:3.
Answer is correct.
What is the point of factoring
Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form, and when we apply the principles of factoring to equations, we yield a lot of useful information. There are a lot of different factoring techniques.
Let X denote the number of cousins of a randomly selected student. Explain the difference between StartSet Upper X equals 2 EndSet and Upper P (Upper X equals 2 ).
A. (X =4) is the event that the student has four cousins: P(X-4) is the probability of the event that the student has four cousins.
B. (X =4) is the frequency that a student has four cousins, P(X-4) is the relative frequency that a student has for cousins.
C. (X =4) is the probability of the event that the student has four cousins, P-4) is the event that the student has four cousins.
D. (X =4) is the relative frequency that a student has four cousins; P(X 4) is the frequency that a student has four cousins.
Answer:
A. (X =4) is the event that the student has four cousins: P(X-4) is the probability of the event that the student has four cousins.
Step-by-step explanation:
An event is an individual outcome or any number of outcomes of a random experiment or trial. An even that contains only one sample point is called a simple event. A compound event contains more than 1 sample point and is formed by the union of simple points.
An event A is said to occur only and if only the outcome of the experiment corresponds to some element of A.
In the given question the first symbolic representation gives an event and the second symbolic representation gives the probability.
The probability of X = 2 or 4 is given by P (X=2) or P (X=4) symbollically.
So A is the best choice.
The relative frequency gives the probability so choice B,C and D are wrong.
help me please with this math problem [(7 + 3) • 5 – 4] ÷ 2 + 2
Answer:
[(7+3).5-4]/2+2
[46]/2+2
23+2
25
Answer: 25
Step-by-step explanation:
Follow the order of operations: PEMDAS
[(7+3) * 5-4] / 2+ 2
[10*5-4]/2+2
[50-4]/2+2
46/2+2
23+2
= 25
HELP the bag of letter tiles include 15 vowels and 25 consonants. What is the probability of selecting two vowels one after another? NEED HELP ASAP
Answer:
Step-by-step explanation:
15 vowels plus 25 consonants is 40
so 15/40 then you take the one vowel out and there is 39 so then it is 14 over 39.
Converse statement. If this month is February then the next month is march
Answer:
If the month is march then the next month is February
Step-by-step explanation:
Explain two attributes that a rectangle and a square have in common.
Answer:
All angles and opposite angle are equal;opposite sides are parallel.
Step-by-step explanation:
Answer:
they both have 4 sides and they both have paralell sides.
Step-by-step explanation:
Can someone help me out?
Answer:
16
Step-by-step explanation:
please mark me brainliest and 5 star
Answer:
16
Step-by-step explanation:
You add all the sides together hope it helps pls mark brainliest
plz help what is the square root of pi
Answer:
Approximately 1.77
To solve it I used a scientific calculator
Answer:The square root of Pi is approximately 1.77245.
Step-by-step explanation:
i hope i got it rigth ....
Let [tex]R[/tex] be the region bounded between the parabola [tex]y=4x-x^2[/tex] and the x-axis. Find [tex]m[/tex] so that the line [tex]y=mx[/tex] divides [tex]R[/tex] into two pieces of equal area.
First, we observe that
[tex]4x-x^2 = x(4-x) = 0 \implies x=0 \text{ or } x = 4[/tex]
and
[tex]4x-x^2 = 4-(x-2)^2 \le 4[/tex]
so that [tex]R[/tex] is in the first quadrant. Any line [tex]y=mx[/tex] that slices this region into two pieces must then have a slope between [tex]m=0[/tex] and [tex]m=4[/tex] (which is the slope of the tangent line to the curve through the origin).
The parabola and line meet at the origin, and again when
[tex]4x - x^2 = mx \\\\ ~~~~ \implies x^2 + (m-4)x = x (x + m - 4) = 0 \\\\ ~~~~\implies x = 4-m[/tex]
with [tex]4x-x^2\ge mx[/tex] for [tex]0\le x\le4-m[/tex].
Now, the total area of [tex]R[/tex] is
[tex]\displaystyle \int_0^4 (4x-x^2) \, dx = \left(2x^2 - \frac{x^3}3\right)\bigg|_0^4 = \frac{32}3[/tex]
so that half the area is 16/3.
The area of the left piece (containing the origin) is
[tex]\displaystyle \int_0^{4-m} ((4x-x^2) - mx) \, dx = \left(\frac{4-m}2 x^2- \frac{x^3}3\right)\bigg|_0^{4-m} = \frac{(4-m)^3}6[/tex]
Solve for [tex]m[/tex].
[tex]\dfrac{(4-m)^3}6 = \dfrac{16}3[/tex]
[tex](4-m)^3 = 32[/tex]
[tex]4 - m = \sqrt[3]{32} = 2\sqrt[3]{4}[/tex]
[tex]\boxed{m = 4 - 2\sqrt[3]{4} \approx 0.825}[/tex]
y is directly proportional to the square of x.
When y= 24, x= 2.
Find the value of y when x=4.
Answer:
y= 48
Step-by-step explanation:
X was doubled so i believe this is correct
Have a great day!!!
5. Jade has $59.87 in her checking account.
She buys his mom a birthday present for $25.98.
How much money is left in her account?
Answer: $33.89
Step-by-step explanation:
$59.87 - $25.98 = $33.89
Answer:
33.89
Step-by-step explanat33.89ion:
$59.87-$25.98
Solve the inequality. Choose the number line that represents the inequality.
n+5<7
Answer:
3
Step-by-step explanation:
3+5 =8>7
Answer:
N<2
Step-by-step explanation:
7th grade math help me please :))
Answer:
no because the absolute value of -7 is 7 which is greater than the absolute value of 6 which is 6.
Simplify 8 over negative 4 ÷ negative 3 over 9 . (5 points)
Answer:
6
Step-by-step explanation:
[tex]-\frac84 divided-\frac39\\-2 divided- \frac13\\-2 \cdot -3\\6[/tex]
Why is a scale factor of 2 the same as 200%?
Answer:
the action of deposing someone, especially a monarch.
Step-by-step explanation:
Geometry. PLS help asap 20 points
Answer:
you need to prove AB=AD
Step-by-step explanation:
Petro was given this system of equations. Negative 14 x minus 2 y = 24. 14 x + 8 y = negative 12. Petro’s work is shown in the table. Where, if anywhere, did Petro first make a mistake? Steps Petro’s Work Step 1 Negative 14 x minus 2 y = 24. 14 x + 8 y = negative 12. 6 y = 12. Step 2 6 y = 12. y = 2. Step 3 Negative 14 (2) minus 2 y = 24. Negative 28 minus 2 y = 24. Negative 2 y = 52. y = negative 26.
step 1
step 2
step 3
no mistake
Answer:
C Step 3
Step-by-step explanation:
Answer:
C: Step 3 is where the mistake was made
Step-by-step explanation:
During a 7-year period, the amounts (in millions of dollars) spent each year on buying new vehicles N and used vehicles U by United States residents are modeled by the equations
N=−0.028t3+0.06t2+0.1t+17
U=−0.38t2+1.5t+42
where t=1 represents the first year in the 7-year period.
a. Write a polynomial that represents the total amount spent each year on buying new and used vehicles in the 7-year period.
b. How much is spent on buying new and used vehicles in the fifth year?
$ ???
Using addition of polynomials, it is found that:
a) The total amount is: T(t) = -0.028t³ - 0.32t² + 1.6t + 59.
b) $55.5 million was spent on buying new and used vehicles in the fifth year.
How do we add polynomials?To add polynomials, we have to combine the like terms, that is, the terms that have t elevated to the same power.
For this problem, the functions are given as follows:
N(t) = -0.028t³ + 0.06t² + 0.1t + 17.U(t) = -0.38t² + 1.5t + 42.Hence the total amount is:
T(t) = N(t) + U(t)
T(t) = -0.028t³ + 0.06t² + 0.1t + 17 - 0.38t² + 1.5t + 42.
T(t) = -0.028t³ + (0.06 - 0.38)t² + (0.1 + 1.5)t + 17 + 42.
T(t) = -0.028t³ - 0.32t² + 1.6t + 59.
For the 5th year, the amount is given by:
T(5) = -0.028(5)³ - 0.32(5)² + 1.6(5) + 59 = 55.5.
$55.5 million was spent on buying new and used vehicles in the fifth year.
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3. 32-(5.23) I need answers quick
Answer:
[tex] \sf \large \: - 31[/tex]
Step-by-step explanation:
3²−5(2³)
=9−5(2³)
=9−(5)(8)
=9−40
=−31
Solve the system
4x+5x= -27
x+9y= 1
Answer:
x=-3, y = 4/9
Step-by-step explanation:
This is in equation form.
Jenna❤️Jenna❤️❤️L’s recipe calls for 1/2 cup of flour she only has 1/4 cup measure which equivalent fraction shows the amount of flowers she could use for the recipe
Answer:
1/2 divided by 1/4
Step-by-step explanation:
so 2
hope this helps :)
A farm has 216 apple trees. The trees were evenly across 8 rows. How many apple trees are there in each row
Answer:
27 in each row
Step-by-step explanation:
216/8=27
Answer:
27 Apple Trees in each row
Step-by-step explanation:
216 divided by 8 gives us 27
The equation is 216/8=27
4(x-1)-2(3x+5) =-3+1
Answer:
x= -8
Step-by-step explanation:
4(x-1)-2(3x+5)=-3+1
4x-4-6x-10=2
-2x-14=2
-2x=16
x= -8