Recall that
d/dx sech(x) = - sech(x) tanh(x)
d/dx tan⁻¹(x) = 1/(1 + x²)
Then by the chain rule,
dy/dx = - sech(x) tanh(x) / (1 + x²)
Maria has a net income of $2,400 per month. She puts $400 into her
savings. What percent of her net income did she put into savings?
Round your answer to the nearest tenth.
Answer:
17%
Find the percentage that 400 is of 2400 (It's quite tricky to explain).
A video store offers two yearly pricing plans: A. $10.00 charge plus $2.50 for each movie rented. B. $4.00 charge (total) for the first 4 movies rented plus $3.00 per movie. How many movies will a person need to rent in order to spend an equal amount of money using either plan?
Answer:
36
Step-by-step explanation:
The cost of renting n movies using Plan A is ...
c = 10 +2.50n
The cost of renting n movies using Plan B is ...
c = 4 +3(n -4) . . . . for n ≥ 4
The two costs are equal when ...
4 +3(n -4) = 10 +2.50n
0.50n = 18 . . . . . . . . . . add 8 -2.50n and simplify
n = 36 . . . . . . . . . . multiply by 2
A person would have to rent 36 movies to spend the same using either plan.
Three cards are dealt from a shuffled standard deck of playing cards. Find the probability that the first card dealt is red, the second is black, and the third is red. (Enter your probability as a fraction.)
There are 52 cards in a deck, half the cards aware red and half the cards are red.
First card being red is 26/52 = 1/2
After the first card is dealt there are 51 cards left and 26 are black so dealing a black card = 26/51
After 2 cards are dealt there are 50 cards left and 25 red ones left. The probability would be 25/50 = 1/2
The probability of all 3 happening = 1/2 x 26/51 x 1/2 = 13/102
Answer: 13/102
The Rahul ages of and pushti are in the ratio 3 ratio 5 four years later the sum of their ages will be 48 what are their present ages
Answer:
Rahul is 15, Pushti is 25Step-by-step explanation:
Rahul age = r, Pushti age = p
Equations according to given info:
r / p = 3 / 5 ⇒ r = 3p/5r + 4 + p + 4 = 48 ⇒ r + p = 40 ⇒ r = 40 - pCompare the two equations and solve for p:
3p/5 = 40 - p3p = 200 - 5p3p + 5p = 2008p = 200p = 200/8p = 25Find the value of r:
r = 40 - 25 r = 15Simplify the expression completely.
Answer: B
Step-by-step explanation: Best way to solve this is to first take the square root of 9 which is 3. Notice in the expression there is an x^4 but once the square root of 9x^4 is taken, you get 3x^2. There is a minus sign in the middle, so answer choice C and D are out. Now, there is answer choice A or B. Now we take the square root of 12 but 12 isn't a perfect square root. But, you can think of 2 numbers that when you multiply give you 12 and one of those numbers is a perfect square root. In this case, it would be 4 because 4 times 3 = 12. Square root of 4 is 2. Again, notice there is an x^2. Once the square root of 4 is taken, you are left with 2x and square root of 3. The square root of 3 isn't a perfect square root. But, you can write the expression in the following way:
2x[tex]\sqrt{3}[/tex] - 3[tex]x^{2}[/tex]
Hope this helps.
There are 14 European cities that Sam would eventually like to visit. On his next vacation, though, he only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)
Answer:
2184 different schedules
Step-by-step explanation:
Sam can make different schedules of the same three cities, so order of cities does matter, but no repetition is allowed. This makes this a permutation without repetition.
When we choose from n items, and we choose r of them, our formula is
n! / (n-r)!. We have 14 things to choose from, and 3 to choose, so our formula becomes
14! / (14-3)! = 14!/11! = 14*13*12 = 2184 different schedules
PLEASE HELP!! DUE SOON!!! WILL GIVE 5 STARS ALONG WITH A HEART!!!
Answer:
8
Step-by-step explanation:
Your utility company charges 14 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below.
a. What is the daily cost of keeping lit a 150-watt light bulb for 8 hours each day?
b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 20 watts of power?
a. The daily cost of keeping lit a 150-watt light bulb for 8 hours each day is $
(Round to three decimal places as needed.)
b. The yearly savings of replacing the 150-watt light bulb with a 20-watt light bulb is
(Round to two decimal places as needed.)
Answer:
P = 150 W * 60 sec/min * 60 min/hr = 540000 W-sec/hr
1 kW = 1000 W * 3600 sec = 3.6E6 W-sec
E (8 hrs) = 8 * .54E6 W-s = 4.32E6 W-sec
or E= 4.32/3.6 = 1.2 kW = .168 $/day
20/150 = .133 as much for a 20-watt bulb
For a LED bulb cost/day = .168 * .133 = $.022/da
Note 1 W = 1 Joule/sec
Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4% interest on the total investment. How much money did he put in each account?
Answer:
600 in the 8% interest and 2400 in the 3% interest.
Step-by-step explanation:
600 + 8% = 48
2400 + 3% = 72
72 + 48 =120
The x-value of the vertex of f(x) = x2 - 10x + 3 is
Answer:
x- coordinate = 5
Step-by-step explanation:
Given a parabola in standard form , f(x) = ax² + bx + c ( a ≠ 0 ) , then
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - 10x + 3 ← is in standard form
with a = 1 , b = - 10 , then x- coordinate of vertex is
x = - [tex]\frac{-10}{2}[/tex] = 5
Helppp meee please !!!
Answer:
why has the speaker come to the earth
Answer:
the two numbers are 3x and -x.
Step-by-step explanation:
product = -3x²
sum = 2x
hope this helps you.
Enter the number that belongs in the green box
Answer:
128 degrees
Step-by-step explanation:
Opposite interior angles
1+ root2x + 1 = root2x + 8
Answer:
14x 2 +9
Step-by-step explanation:
IS IT 60 SOMEONE PLEASE TELL ME THE RIGHT ONE !!!
Answer:
60 is the answer you're welcome
what is 4/3 x 19/6-45 x 7
Answer:
-310.777777778
Step-by-step explanation:
Answer:
The answer is -310.777777778
Step-by-step explanation:
hope its help:)
I’m having a lot of trouble with this question
Answer:
Function C has the greatest initial value
Function B has the greatest rate of change
Step-by-step explanation:
C is greatest for initial value because the line intercepts at 2 and i think B intercepts at -1 then as u can see A intercepts at 0 or origin
B is the greatest rate of change or slope because it goes up by 3 and then A goes up by 5/2 and C goes up by 1/3
rise over run
Hope i helped
please help ill mark brainliest
Answer:
I think it is 8
Step-by-step explanation:
sorry If I'm wrong
Frank rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 76 cents for cach mile driven. Frank had
S152.75 when he returned the truck. For how many miles did he drive the truck?
Answer:
Frank drove 176 miles.
Step-by-step explanation:
Subtract the base fee from the total payment
152.75 - 18.99 = 133.76
divide the remaining amount(price for miles driven) by the cost for each mile
133.76 / .76 = 176
176 miles.
On solving the linear equation in one variable, given that there was a base fee of $18.99, and there was an additional charge of 76 cents for each mile driven, Frank had $152.75 when he returned the truck, the number of miles driven were 176 miles.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable.
Let the number of miles driven be x.
Given in the question,
base fees = $18.99
charge per mile = 76 cents = $0.76
The equation of the total cost becomes :
= base fees + charge per mile * number of miles
= 18.99 + 0.76x
Given the total cost = $152.75
Equating the two values,
= 18.99 + 0.76x = 152.75
= 0.76x = 133.76
= x = 176
Learn more about linear equation here
https://brainly.com/question/32634451
#SPJ2
PLEASE HELP ME!!!
Which expression has a value of 8?
a: 10−(−2)
b: (−10)−(−2)
c:(−2)−(−10)
d: (−2)−10
Answer:
c:(-2)-(-10)
Step-by-step explanation:
When two minus symbols are next to each other in an expression, they become a plus sign.
a: 10-(-2)
10+2
12
b: (-10)-(-2)
-10+2
-8
c: (-2)-(-10)
-2+10
8
d: (-2)-10
-12
C.
-2 - -10= 8
The negative stays the same. The two dashes in between 2 and 10 become pluses.
10 - 2 = 8
The bigger number positive or negative is the dominant passing down their + or - to the value.
Write an equation in slop intercept form with a given slope. Slope: 5/6, y-intercept: 8
y=5/6x+8
...............
Solve for x. Show all work. 2/3 (x+7) =10
Answer:
answer is 8
Step-by-step explanation:
2/3(x+7)=10
2x/3+14/3=10
2x/3=10-14/3==>30-14/3
2x/3=16/3
x=16/3*3/2
x=8
A shuffled deck of cards is placed facedown on the table. It contains 7
hearts, 8 diamonds, 6 clubs and 3 spades. What is the probability that the top two cards are one of the clubs followed by one of the heartS?
Answer:
3/23 x 5/23 = 15/529 = 2.84%
Answer:
First find the total of 7 hearts, 8 diamonds, 6 clubs and 6 spades which is 24 altogether. Therefore we are talking about 4 types of cards. I therefore think the probability will be 2/24
-2(x+1)= -2+5
How you solve that?
[tex]-2(x+1) = -2+5\\\\\implies -2x -2 = 3\\\\\implies -2x = 3 +2 =5\\\\\implies x = - \dfrac 52[/tex]
Add the numbers, then add 2 to both sides of the equation. The solution would be x = - 5/2
7 1/4 -3 3/4= 4 1 /4 - 3/4
Answer:
7/2
Step-by-step explanation:
Tamika ran 90 meters in 16.1 seconds. Enrique ran 90 meters in 17.0 seconds. Who had the fastest time, Tamika or Enrique? A. Enrique B. Tamika
I was absentee and i dont know how to solve it help plz
Answer:
-1/3
i think.
Step-by-step explanation:
if it's to find slope
Answer:
m = -1/3
Step-by-step explanation:
There are two easy ways you can find the slope. The first one is using the rise over run method which is to first count how much you need to go up or down to get to the other point, and then how much you need to go forward. In this case you go down one, and forward three. This means its -1/3. You can also use the slope formula which uses the coordinates of each point. I attached it to this answer. (m representing slope)
A cylinder and a cone both have radius of 6". The height of the cone is 12". The height of the cylinder is 6". Which has the greatest volume?
Answer:
cylinder has greatest volume
Step-by-step explanation:
solution
given,
radius of cylinder(r)=6cm
height of cylinder (h)=6cm
we know,
volume of cylinder=πr^2h
=22÷7×6×6×6
=4752÷7
=678.857cm^3
radius of cone(r)=6cm
height of cone(h)=12cm
we know,
volume of cone=1÷3πr^3
= 1÷3×22÷7×6×6×6
= 4752÷21
=226.2857cm^3
as a result,cylinder has greatest volume
A pair of pants costs $24.60 when it is on sale for 25% off. What was the
original cost of the pants? (still....no labels!)
well, we know the pants are 25% off, that means the current sale price is only 75% of the original price, say the original price is "x" or 100%. So we know that $24.60 is 75%, what is the 100%?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 24.6&75\\ x&100 \end{array}\implies \cfrac{24.6}{x}=\cfrac{75}{100}\implies \cfrac{24.6}{x}=\cfrac{3}{4} \\\\\\ 98.4=3x \implies \cfrac{98.4}{3}=x\implies 32.8=x[/tex]
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
○ A. Zero
○ B. Two
○ C. Infinity many
○ D. One
The area of a triangle is 83 square feet. The base is twice the height. Find the height.
Answer:
166
Step-by-step explanation:
83x2(twice the height)