Ashley puts 45 stamps in an album. She puts the same number of stamps on each page,and 3 stamps on the last page. There are 2 more pages in the album than the number of stamps on each page. How many pages are in the album? How many stamps are on each page?

Answers

Answer 1

Answer: 45 pages total
3 on last page
45-3=42
there are 42 on the rest of the pages
on each page, there are 2 more pages in album than then stamps on pages

amount of stamps on pages with equal number of stamps is
A=numberofpgest times number of stamps on pages
number of pages=p
number of stamps per papge=s
a=ps

2 more pages than stamps on pages
p=2+s
total number of stamps per page is s=(45-3)/(p-1)
(what I did is I first got rid of number of stamps on last page, then got rid of the last page)
P=2+s
s=(45-3)/(2+s-1)
s=42/(s+1)
times s+1 both sides
s^2+s=42
minus 42
s^2+s-42=0
factor
(s-6)(s+7)=0
set equal to zero
s-6=0
s=6

s+7=0
s=-7, false, no negative stamps

6 stamps per page

sub
p=2+s
p=2+6
p=8
8 pages

check
last page is 3 so 8-1=7 page left

7*6=42
3+42=45

correct

there are
8 pages in the album
6 stamps per page

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Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

Answers

f(x) = x³ + 4 and g(x) = ∛(x - 4)

so, the first thing the question asks of you is to see that f(g(x)) = x. try it out, plugging g(x) in as the x-variable in the first equation:

f(g(x)) = (∛(x - 4))³ + 4

they were merciful in writing this problem, and thankfully your cube roots cancel out and don't cause you any trouble. continue solving:

f(g(x)) = (∛(x - 4))³ + 4 ... cube root and exponent cancel
f(g(x)) = x - 4 + 4 ... simplify
f(g(x)) = x

so, yep. that one worked. try out the second half of the question: g(f(x)) = x

g(f(x)) = ∛((x³ + 4) - 4) ... simplify inside your radical, cancelling out the 4s
g(f(x)) = ∛(x³) ... the cube root of x³ is x itself, so:
g(f(x)) = x

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A railroad tunnel is shaped like a semiellipseThe height of the tunnel at the center is 58 ft and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.

Answers

y²/58² + x²/b² = 1
(0,58), (-21,29), and (21,29) are points on the ellipse.

29²/58² + 21²/b² = 1
¼ + 21²/b² = 1
21²/b² = ¾
4·21²/3 = b²
b² = 588

y²/3364 + x²/588 = 1

Answer:

Step-by-step explanation:

The equation of ellipse is given as:

$(x^2)/(a^2)+(y^2)/(b^2)=1$ (1)

Now, from the given information, The ellipse passes through (0, 58), (0, -58), (21, 29), thus equation (1) becomes:

$(0)/(a^2)+((58)^2)/(b^2)=1$

⇒ $b^2=(58)^2$

⇒ $b^2=3364$

Also, $((21)^2)/(a^2)+((29)^2)/((58)^2)=1$

⇒ $((21)^2)/(a^2)=1-(841)/(3364)$

⇒ $((21)^2)/(a^2)=(3)/(4)$

⇒ $a^2=(4(441))/(3)$

⇒ $a^2=588$

Now, substituting the values of $a^2 and b^2$ in the equation (1), we have

$(x^2)/(588)+(y^2)/(3364)=1$

which is the required equation for ellipse.

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Answers

$(tan^2x)/(1+cot^2x)+(cot^2x)/(1+tan^2x)=sec^2x\ cosec^2x-3\n\nL=(tan^2x(1+tan^2x)+cot^2x(1+cot^2x))/((1+cot^2x)(1+tan^2x))=(tan^2x+tan^4x+cot^2x+cot^4x)/(1+tan^2x+cot^2x+tanxcotx)\n\n=(tan^2x+cot^2x+tan^4x+cot^4x)/(1+tan^2x+cot^2x+1)=(tan^2x+2+cot^2x+tan^4x-2+cot^4x)/(tan^2x+cot^2x+2)$

$=((tanx+cotx)^2+(tan^2x-cot^2x)^2)/((tanx+cotx)^2)=((tanx+cotx)^2)/((tanx+cotx)^2)+((tan^2x-cot^2x)^2)/((tanx+cotx)^2)\n\n=1+((tanx-cotx)^2(tanx+cotx)^2)/((tanx+cotx)^2)=1+(tanx-cotx)^2\n\n=1+tan^2x-2tanx\ cotx+cot^2x=tan^2x+cot^2x+1-2\n\n=\left((sinx)/(cosx)\right)^2+\left((cosx)/(sinx)\right)^2-1=(sin^2x)/(cos^2x)+(cos^2x)/(sin^2x)-1=(sin^4x+cos^4x)/(sin^2x\ cos^2x)-1$

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Write the standard equation of the circle with the given center that passes through the given point. Center (-2,6); point (-2,10)

Answers

The general form of the equation of a circle is given by:
(x-a)²+(y-b)²=r²
where:
(a,b) is the center
r is the radius
Given that the circle with center (-2,6) and cuts point (-2,10), the equation of the circle will be found as follows:
the radius of the circle will be:
r=√[(x-a)²+(y-b)²]
r=√[(-2-(-2))²+(10-6)²]
r=√[(-2+2)²+4²]
r=√[0+4²]
r=4 units
hence plugging the values to obtain the equation we get:
(x-(-2))²+(y-6)²=4²
simplifying we get:
(x+2)²+(y-6)²=4²

3(x-2)>-3
solve each inequality

Answers

divide each side by the number that does not contain a variable
answer is x>1

Fill in the blank. A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.

Answers

Answer:

A conditional probability of an event is a probability obtained with knowledge that some other event has already occurred.

Step-by-step explanation:

Conditional probability of an event (A) is a probability obtained with knowledge that some other event (B) has already occurred and is denoted as P(A|B).

It satisfies the following equation:

P(A|B)=P(A and B) / P(B)

where P(A and B) is the probability of A and B occurring together.

Conditional probability is applied in many areas of Bayesian statistics and machine learning.

Final answer:

The blank space should be filled with 'conditional'. A conditional probability of an event is a probability calculated with the knowledge that another event has already happened.

Explanation:

The blank space should be filled with 'conditional'. A conditional probability of an event is a probability obtained with knowledge that some other event has already occurred. Suppose you have events A and B from the same sample space. The conditional probability of event A given that event B has occurred, denoted as P(A|B), is computed as P(A and B) divided by P(B), where P(A and B) represents the probability that both events happen, and P(B) is the probability of B happening. This quantity is meaningful as long as P(B) is not zero.

Learn more about Conditional Probability here:

brainly.com/question/32171649

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