Mathematics High School
Answers
Answer 1
Answer: 34.78 gallon
Step-by-step explanation:
Exponential equation for decay:
[tex]A=P(1-r)^t[/tex] , where p = initial amount, r= rate of decay , t= taime
As per given,
r= 8% = 0.08
For days 1 , i.e. at t= 0 , P= 32 gallons
[tex]1=32(1-0.08)^t\\\\\Rightarrow\ \dfrac{1}{32}=(1-0.08)^t \\\\\Rightarrow\ \ln \left(\frac{1}{32}\right)=t\log (0.92)\\\\\Rightarrow\ t=-\frac{5\ln \left(2\right)}{\ln \left(0.92\right)}=41.5\approx42[/tex]
Total water = [tex]\dfrac{a(1-r^n)}{1-r}=\dfrac{32(1-0.08^{42})}{1-0.08}=34.782[/tex]
hence, the the total number of gallons of water that leaked from the tank = 34.78 gallon approx.
Related Questions
y=x^2+9x+3 write graph form
Answers
That’s the graph for this equation
i really really need help
Answers
Answer:
with what? i can help you more than likely if you tell me what you need help with.
Step-by-step explanation:
i can help as well with anything
An animal reserve has 24,000 elks. The population increases by 12% a year. How long until the population is equal to 96,000,000
Answers
Answer:33,325,000
Step-by-step explanation:95,976,000÷2.88=33,325,000
The ratio of students who made
the honor roll to the total number
of students is 1:50. If there are
500 students in total, how many
made the honor roll?
Answers
Answer:
10 is the answer. 1:50 is 10:500 simplified
Step-by-step explanation:
500÷50=10.
Use the distributive property
to expand -4(-2/5+3x)
Which is an equivalent expression?
Answers
Answer:
8/5-12x
Step-by-step explanation:
-4(-2/5+3x)
Multiply each term inside the parentheses by -4
-4 * -2/5 + -4 * 3x
8/5-12x
Answer:
-1.6+12x
Step-by-step explanation:
First you do -4*2/5 + -4*3x. Which will give you -1.6+ 12x
PROBLEM 1
Peter has many socks, all the same except that they are in three different colours. He is leaving to catch an early train to go on a business trip, and he does not want to wake his wife, so he packs in the
dark. He needs eleven pairs of socks, each sock in each pair the same colour. How many socks must he take from his drawer to be sure of achieving this?
Answers
Answer:
24 socks
Step-by-step explanation:
The given parameters are;
The number of different colors of socks = 3
Therefore, we have the worst case, the first three socks are different colors, since there are three different colors, the fourth socks is first pair in the worst case scenario
After which, every other two socks makes a pair in the worst case process, the number of socks he must take to make sure he has eleven pairs are given by the pairing table
Number of socks123456789101112131415161718192021222324
Number of pairs000112233445566778899101011
Therefore, he must take 24 socks to make sue he has 11 pairs of the same color.
Five times the sum of a number n and seven
Hint- you need parenthesis
Answers
5(n + 7) is the equation
The equation of the problem is [tex]5(n+7)[/tex]
The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.
Which point is an example of a y intercept?
A. (-2, 8) B. (3, 4)
C. (0, -4)
D. (5,0)
Answers
(0, -4)
this would be the y intercept because its lining up to the y axis of the plane.
Ron was able to run a mile in 7 minutes . Fred was only able to run 4,985 feet in 7 minutes . How much further did Ron run than Fred ?
Answers
Ron ran 295 feet more than Fred.
1 mile= 5,280 feet
5,280 - 4,985 = 295
Therefore, Rob ran 295 feet more than Fred.
Please reply quickly and explain if you can thanks
Answers
Answer:
36
Step-by-step explanation:
k(6)= (6)²
I think the answer is 36. If I’m right, it’s saying that k(6)= 6^2
-2/5x=-5 What is this?
Answers
Answer:
25/2 or 12 1/2 or 12.5
Step-by-step explanation:
*
ate: Find 8% of 40.
nt)
Answers
The answer is 3.2.
8 percent of 40 is 3.2
Sarah arrives at the bus station at 8:25 and can catch either bus A or B. How long does she wait for the next bus?
Bus A runs every 6 mins
Bus B runs every 8 mins
What bus can she catch and what time?
Answers
Answer:
every 8 mins
Step-by-step explanation:
bus b
sum n=3 ^ infty (2n+5)
find the series shown
Answers
Answer: Choice C) 11 + 13 + 15 + 17 + ...
=====================================================
Explanation:
We're adding terms in the form (2n+5)
The first term is when n = 3, so
2n+5 = 2*3+5 = 6+5 = 11
The next term is when n = 4, so
2n+5 = 2*4+5 = 8+5 = 13
The next term is when n = 5, so
2n+5 = 2*5+5 = 10+5 = 15
And so on
This means,
[tex]\displaystyle \sum_{n=3}^{\infty} (2n+5) = 11+13+15+17+\ldots[/tex]
which matches with choice C. The three dots indicates the pattern goes on forever.
-------------------
Choice B does not have these dots, so that's why choice B is not the answer. If we replaced the infinity symbol with 7, then choice B would be the answer.
I.e,
[tex]\displaystyle \sum_{n=3}^{7} (2n+5) = 11+13+15+17+19[/tex]
The right triangle ABC, shown below is reflected over the line y = -x. Where will the point C' be located?
Answers
Answer:
(4, -3)
Step-by-step explanation:
It says my answers need to be at least 20 characters long so I had to write this.
Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y Z and Y Z X are congruent. Consider isosceles ΔXYZ. What is the value of n? What is the measure of leg XY? ft What is the measure of leg XZ? ft
Answers
Answer:
[tex]n = 3[/tex]
[tex]XY = 39[/tex]
[tex]XZ = 39[/tex]
Step-by-step explanation:
Given
[tex]XY = 9n + 12[/tex]
[tex]XZ = 15n - 6[/tex]
[tex]<XYZ = <YZX[/tex]
Solving (a): n
To solve for n;
We make use of
[tex]XY = XZ[/tex]
Substitute values for XY and XZ
[tex]9n + 12 = 15n - 6[/tex]
[tex]9n - 15n = -12 - 6[/tex]
[tex]-6n = -18[/tex]
Divide through by -6
[tex]n = 3[/tex]
Solving (b) XY
[tex]XY = 9n + 12[/tex]
Substitute 3 for n
[tex]XY = 9 * 3 + 12[/tex]
[tex]XY = 27 + 12[/tex]
[tex]XY = 39[/tex]
Solving (c): XZ
[tex]XZ = XY[/tex]
[tex]XZ = 39[/tex]
The value of n is 3, the measure of leg XY is 39 ft, and the measure of XZ is 39 ft and this can be determined by using the properties of an isosceles triangle.
Given :
Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y Z and Y Z X are congruent. Consider isosceles ΔXYZ.
Given that the angle XYZ and angle YZX are congruent to each other and triangle XYZ is an isosceles triangle.
From the above statement, it can be concluded that the side length of XY and the side length of XZ is also congruent to each other, that is:
XY = XZ
9n + 12 = 15n - 6
Simplify the above expression in order to determine the value of 'n'.
18 = 6n
n = 3 ft
The measure of leg XY is given by:
XY = 9(3) + 12 = 39 ft
The measure of leg XZ is given by:
XZ = 15(3) - 6 = 39 ft
For more information, refer to the link given below:
https://brainly.com/question/19237987
Alice drove 170 miles in 2.5 hours. At this rate, how far will she drive in 4 hours? miles
Answers
Answer:
She will drive 272 miles in 4 hours.
Step-by-step explanation:
What is 7/8 x 4/5 divided by 7/20
Answers
Answer: 2
Step-by-step explanation: First, multiply 7/8 by 4/5 which equals to 7/10. Then, divide 7/10 by 7/20. Finally, you should end up with a result of 2.
4/10 would be your answer to your question
Chloe was given a box of assorted chocolates for her birthday. Each night, Chloe treated herself to some chocolates. There were originally 30 chocolates in the box and after 2 nights, there were 24 chocolates remaining in the box. Write an equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Chloe's birthday.
Answers
Answer:
C=-3t+30
Step-by-step explanation:
a mercury thermometer records a temperature of 8 degrees fahrenheit at 10 a.m. if the temperature drops by 3 degrees fahrenheit every hour what will be the temperature by 2 p.m. of the same day
Answers
Answer:
-4 Degrees Fahrenheit
Step-by-step explanation:
Given
[tex]Initial\ Temperature = 8[/tex] ---- at 10am
[tex]Difference = -3[/tex]
Required
Determine the final temperature at 2pm
First, we need to determine the hour from 10am to 2pm (Both inclusive)
[tex]Interval = 2pm - 10am + 1hr[/tex]
[tex]Interval = 4hr + 1hr[/tex]
[tex]Interval = 5hr[/tex]
To solve further, we make use of the following Arithmetic Progression formula:
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]a = 8[/tex] --- Initial
[tex]d = -3[/tex] --- difference
[tex]n = 5[/tex] -- 5th term
[tex]T_n[/tex] --- Final temperature at 2pm
So: we have:
[tex]T_n = 8 + (5 - 1) * -3[/tex]
[tex]T_n = 8 + (4) * -3[/tex]
[tex]T_n = 8 + 4 * -3[/tex]
[tex]T_n = 8 -12[/tex]
[tex]T_n = -4[/tex]
Hence:
The temperature is -4 Degrees Fahrenheit
How do you workout the fraction 3/4 + 1/8
Answers
Answer:
The LCM for 4 and 8 is 8. Add both numerator and rewrite it in a single form. By using LCM method, 7/8 is the equivalent fraction by adding 3/4 and 1/8.
Hope This Helps!!! Have a great day!
<3<3
Answer:
[tex]\frac{7}{8}[/tex] or [tex]\mathrm{Decimal:\ }\:0.875[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}+\frac{1}{8}[/tex]
lcm of 4 and 8 is 8
adjust the fraction base on the lcm
[tex]=\frac{6}{8}+\frac{1}{8}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:[/tex][tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]
[tex]\mathrm{Add\:the\:numbers:}\:6+1=7[/tex]
[tex]=\frac{7}{8}[/tex]
Carlos buys a box of frozen flavored ice sticks. 2/5 of the ice sticks are blue raspberry. Of the remaining ice sticks, 1/3 are grape, and the rest are cherry. If there are 48 blue raspberry and cherry flavored ice sticks altogether, how many ice sticks total are in the box?
Answers
Given:
[tex]\dfrac{2}{5}[/tex] of the ice sticks are blue raspberry.
Of the remaining ice sticks, [tex]\dfrac{1}{3}[/tex] are grape, and the rest are cherry.
There are 48 blue raspberry and cherry flavored ice sticks altogether.
To find:
The total number of ice sticks.
Solution:
Let x be the total number of ice sticks.
[tex]\dfrac{2}{5}[/tex] of the ice sticks are blue raspberry.
Blue raspberry [tex]=\dfrac{2}{5}x[/tex]
Remaining raspberry [tex]=x-\dfrac{2}{5}x[/tex]
[tex]=\dfrac{3}{5}x[/tex]
Of the remaining ice sticks, [tex]\dfrac{1}{3}[/tex] are grape, and the rest are cherry.
Grape [tex]=\dfrac{1}{3}\times \dfrac{3}{5}x[/tex]
[tex]=\dfrac{1}{5}x[/tex]
Cherry [tex]=\dfrac{3}{5}x-\dfrac{1}{5}x[/tex]
[tex]=\dfrac{2}{5}x[/tex]
There are 48 blue raspberry and cherry flavored ice sticks altogether.
[tex]\dfrac{2}{5}x+\dfrac{2}{5}x=48[/tex]
[tex]\dfrac{4}{5}x=48[/tex]
[tex]x=48\times \dfrac{5}{4}[/tex]
[tex]x=60[/tex]
Therefore, the total number of ice sticks is 60.
Six students are working to simplify the expression shown 4y+13x-5+6y-x
Answers
Answer:12x+10y-5
Step-by-step explanation:
Answer:
Step-by-step explanation:
GIVING BRAINLIST SO PLZZZ HELP PLZZZ
A weather station on the top of a mountain reports that the temperature is currently 0℃ and has been falling at a constant rate of 3 ℃ per hour. If it continues to fall at this rate, fill in each indicated temperature below.
The temperature will be _____ 0 in half an hour.
Answers
Answer:
5.c hope this help - shelby
Step-by-step explanation:
Answer:
I’m confused
Step-by-step explanation:
Given the perimeter of a rectangle and either the length or width, find the unknown measurement using the appropriate formula.
The perimeter is 70ft . and the width is 16ft .
Answers
Answer:
Step-by-step explanation:
Givens
P = 2*L + 2*W
P = 70
w = 16
Solution
70 = 2L + 2*16
70 = 2L + 32
70-32 = 2L
38 = 2L
38/2 = 2L/2
L = 19
HELP ASAP DUE TOMORROW!!!
On a family outing, Tyler bought 5 cups of hot cocoa (x)
and 4 pretzels (y) for $18.40. Some of his family members
would like a second serving, so he went back to the same
food stand and bought another 2 cups of hot cocoa (x) and
4 pretzels (y) for $11.20.
Answers
Answers:
x = 2.40
y = 1.60
This means 1 hot cocoa costs $2.40 and 1 pretzel costs $1.60
=======================================
Work Shown:
x = cost of 1 cup of hot cocoa
y = cost of 1 pretzel
5x = cost of 5 cocoas
4y = cost of 4 pretzels
5x+4y = cost of 5 cocoas+4 pretzels
5x+4y = 18.40
----------------
2x = cost of 2 cocoas
4y = cost of 4 pretzels
2x+4y = cost of 2 cocoas+4 pretzels
2x+4y = 11.20
----------------
The system of equations we have is
[tex]\begin{cases}5x+4y = 18.40\\2x+4y = 11.20\end{cases}[/tex]
Note how 4y shows up twice. This is handy to be able to get rid of the y terms completely.
How? By subtracting the equations straight down
The x terms subtract to 5x-2x = 3x
The y terms subtract to 4y-4y = 0y = 0 and they go away
The right hand sides subtract to 18.40 - 11.20 = 7.20
After those three separate subtractions, we have this new equation:
3x = 7.20
Divide both sides by 3 to isolate x
3x/3 = 7.20/3
x = 2.40
Each hot cocoa costs $2.40
Now use this x value to find y. You can pick any equation you want as long as it has x,y in it. I'll pick the first equation
5x+4y = 18.40
5(2.40)+4y = 18.40
12+4y = 18.40
4y = 18.40-12
4y = 6.40
y = 6.40/4
y = 1.60
Each pretzel costs $1.60
If we picked on the second equation, we should get the same y value
Let's find out
2x+4y = 11.20
2(2.40)+4y = 11.20
4.80+4y = 11.20
4y = 11.20-4.80
4y = 6.40
y = 6.40/4
y = 1.60
We get the same result as before.
To check the answers, you need to plug those values back into the two original equations and simplify. You should get the same thing on both sides.
What is the slope of this line?
Enter your answer as a fraction, formatted like this: 42/53
Or, if the slope is undefined, enter a lowercase letter "u," like this: u
Please help me and I will give you brianlyeist
Answers
Answer:
2, 4
Step-by-step explanation:
The radius of the red circle is 7 units and the distance between the two circles is 3 units.
What is the diameter of the red circle?
A 8 units
B 12 units
C 14 units
D 20 units
Answers
Answer:
14
Step-by-step explanation:
The diameter is always the same as 2*the radius, so if the radius is 7, the diameter is 14. Most of the information presented is unrelated.
how many times 92 go in too 100
Answers
Answer:
5
Step-by-step explanation:
Answer:
1 time
Step-by-step explanation:
Help please I’lol really appreciate it
Answers
Answer:
j+z+12
Step-by-step explanation:
