Hey there! I'm happy to help!
First, let's find the volume of the cylindrical tank.
To find the volume of a cylinder, take the area of the circle base and multiply it by the height of the cylinder.
To find the area of a circle, you square the radius and multiply it by pi (we will use 3.14).
The diameter is always twice the radius, so we divide by two to find the radius.
1.4/2=0.7
We square this.
0.7²=0.49
And we multiply by 3.14.
0.49×3.14=1.5386
Now that we have the area of the circle, we multiply by the height (length in our case since the cylinder is sideways).
1.5386×4.5=6.9237
Now, we see that we will be losing 1.7 feet every minute. To see how many times 1.7 feet goes into our cylinder, we just divide!
6.9237÷1.7= 4.07276470588
So we see that it will take just over 4 minutes for the tank to empty.
Have a wonderful day and keep on learning! :D
if 2^x > 4^ 15 and x is a positive integer, what is the least possible value of x?
Answer:
x = 31
Step-by-step explanation:
2^x > 4^ 15
Rewrite 4 as 2^2
2^x > 2^2^ 15
We know a^b^c = a^(b*c)
2^x > 2^ (2*15)
2^x > 2^30
Since the bases are the same, the exponents must follow the inequality
x> 30
In the data set below, what is the mean absolute deviation? 9,8,3,2,5 If the answer is a decimal, round it to the nearest tenth. mean absolute deviation (MAD):
Answer:
3
Step-by-step explanation:
9,8,3,2,5
3
3/5=0.6
0.6
Aa dealer bought a laptop for rs 45000 and sold it to retailer again sold it to a customer at 25% profit. how much did the customer pay for the laptop.
Answer:
Rs 56250
Step-by-step explanation:
Given:
Cost price of laptop (CP) = RS 45000
Profit (P) = 24 % = 0.24
The selling price of dealer (SP) = Cost price of customer,
So,
Selling price of dealer = [tex]\tt CP + Profit \:Percentage \:of \:C.P[/tex]
Selling price of dealer = CP(1+ Profit %)
Substituting value
Selling price of dealer = 45000(1+0.24)
Selling price of dealer = 45000*1.24
Selling price of dealer = 56250
Therefore, the Customer paid Rs 56250 for the laptop.
Answer:
Rs 56,250
Step-by-step explanation:
To calculate how much the customer paid for the laptop, we need to determine the total price after the retailer added a 25% profit margin.
If the dealer purchased the laptop for Rs 45,000, then Rs 45,000 is 100%. If the dealer sells it to a customer at 25% profit, it was sold at 125% of its purchase price.
Therefore, to calculate how much the customer paid for the laptop, we need to find 125% of Rs 45,000:
[tex]\begin{aligned}\sf 125\%\;of\;45000&=\sf\dfrac{125}{100} \times 45000\\\\&=\sf\dfrac{125\times 45000}{100} \\\\&=\sf\dfrac{5625000}{100} \\\\&=\sf56250\end{aligned}[/tex]
Therefore, the customer paid Rs 56,250 for the laptop.
Bernard wants to give a book and a CD to Rachel for Rachel's birthday. Bernard has 2 books and 3 CDs. Tell whether the situation involves combinations or permutations. Then give the number of possible outcomes.
Answer:
6, permutation
Step-by-step explanation:
Book 1, CD 1
Book 1, CD 2
Book 1, CD 3
Book 2, CD 1
Book 2, CD 2
Book 2, CD 3
There are 6 permutations.
What action represents the "!" symbol on a TI 84 plus CE calculator for a Statistics problem??
Answer:
The "!" represents a factorial
Step-by-step explanation:
In math, a factorial when there is an ! followed by a number.
For example, 5! = 5 factorial.
To solve factorials, multiply every integer below the number before the factorial, including the number.
5! = 5 x 4 x 3 x 2 x 1 = 120.
Can y’all help me out?
Answer:
Expression is equivalent to (x^1/4 y^16)^1/2 is x^1/8 y^8
PLS ANSWER YA'LL!
A house owner wishes to cover their roof with solar panels. Each solar panel is of the following size.
->The roof section is rectangular 7.2 m by 4.4 m.
->Each solar panel measures 1400 mm by 850 mm.
There needs to be at least a 30 cm gap left at each edge of the roof section. The house owner thinks he can have at least 15 solar panels fitted to the roof section.
Can u agree? If yes, show the working. (Hint: He can rotate the solar panel)
Answer:
Yes
Step-by-step explanation:
The roof is Rectangular :
Dimension of roof section : 7.2 m by 4.4 m
Area of roof = length * width
Area of roof = 7.2 * 4.4 = 31.68 m²
Dimension of solar panels = 1400 mm by 850 mm
Converting to m:
1000mm = 1 m
1400/1000 by 850/1000 = 1.4 m by 0.85 m
Area each solar panel = 1.4 * 0.85 = 1.19 m²
Gap left at each edge :
30cm gap about the 4 edges gives a square with side length 30cm:
30cm = 30/100 = 0.3m
Area of gap left = 0.3² = 0.09 m²
Total area that can be covered = (31.68 - 0.09) m² = 31.59 m²
Maximum number of panels that can be placed on roof section :
Total area that can be covered / area of panel
31.59 m² / 1.19 m²
= 26.54 panels
A running track has two semi-circular ends with radius 27m and two straights of length 90.6m as shown.
Calculate the total distance around the track rounded to 1 DP.
Answer:
350.85
Step-by-step explanation:
90.6*2 = 181.2
27*2 = 54 (diameter)
54*pi = 169.646003294
169.646003294 + 181.2 = 350.846003294
350.846003294 = 350.85
Find the equation of the line that passes through (1,6) and (3,10).
y=2x+4
y=-2x+4
y=-24-4
Oy-23-4
Answer:
m = (y2 - y1) / (x2 - x1) = (10 - 6) / (3 - 1) = 2 slope of line
y = m x + b standard form of straight line
y = 2 x + b where b is the intercept at x = 0
b = y - 2 x
b = 6 - 2 = 4 from our first equation
Also, b = 10 - 6 = 4 check from second equation
y = 2 x + 4 is our equation
Check if y = 6 and x = 1 then
y = 2 * 1 + 4 = 6 verifying the first point given
simplify:-a). (-5a²)²(6ab²)(-3ab²)
Picture is right there pls help
Answer: B
Step-by-step explanation:
Using slope formula, change in y (3) over change in x (2) is 3/2. So the equation would be y=3/2x.
What is the slope of the line shown below?
10
(8,8)
O A. -3
LO
(5,5)
O B. -1
O c. 1
-5
5
10
15
5
O D. 3
-10 1
Answer:
It's C. 1
Step-by-step explanation:
Use slope intercept form.
Solve log2(x + 5) + log2(x − 5) = log211.
Answer:
x = 6
Step-by-step explanation:
log2(x + 5) + log2(x − 5) = log2 11.
We know that loga (b) + log a(c) = log a( bc)
log2(x + 5) (x − 5) = log2(11)
Multiply
log2(x^2 -25) = log2(11)
Raise each side to the power of 2
2^log2(x^2 -25) = 2^log2(11)
x^2 - 25 = 11
Add 25
x^2 -25 +25 = 25+11
x^2 = 36
Taking the square root of each side
x = ±6
But x cannot be negative because then the log would be negative in log2(x-5) and that is not allowed
x = 6
Answer:
x = 6
Step-by-step explanation:
[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] 11
Determined the define range.
[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] (11), x ∈ ( 5, + ∞ )
We know that [tex] log_a ( b ) + log_a ( b ) [/tex] = [tex] log_a( bc) [/tex]
[tex] log_2[/tex] ( x + 5 ) ( x - 5 ) = [tex] log_2[/tex] ( 11).
[tex] log_2[/tex] ( ( x + 5 ) × ( x - 5 ) ) = [tex] log_2[/tex] ( 11).
Use indentity :- ( a + b ) ( a - b ) = a² - b².
[tex] log_2[/tex] ( x² + 25) = [tex] log_2[/tex] ( 11).
Since , the base of the logarithm are the same. set the arguments equal.
x² - 25 = 11.
Move constant to the right-hand side and change their sign.
x² = 11 + 25
x² = 36.
Take square root of each side.
√x² = √36
x = ± 6
x = 6
x = -6, x ∈ ( 5, + ∞ )
Check if the solutions is in determine range.
x = 6
Which of the following is a characteristic of science?
Answer:d
Step-by-step explanation:
Answer:
D
explanation:
i got it right on the test
If log 3=x and log 5=y find the value of log 75
Answer:
Step-by-step explanation:
75 = 5 * 5 * 3
Log3 + log(5) + log(5) = 1.8751
log(75) = 1.87506 which is the same answer we got from adding the logs.
Two exponential functions are shown in the table.
Which conclusion about f(x) and g(x) can be drawn from
the table?
X
Х
f(x)=2*
g(x) =
2
4
1
4
1
O The functions f(x) and g(x) are reflections over the x-
axis.
O The functions f(x) and g(x) are reflections over the y-
axis.
O The function f(x) is a decreasing function, and g(x) is
an increasing function.
The function f(x) has a greater initial value than g(x).
1
2
1
0
-1
1
2
A-NI-
-2
4
Save and Exit
Nex
Submit
Given:
The two exponential functions are shown in the given table.
To find:
The correct conclusion about the functions f(x) and g(x).
Solution:
The given functions are:
[tex]f(x)=2^x[/tex]
[tex]g(x)=\left(\dfrac{1}{2}\right)^x[/tex]
The function g(x) can be written as:
[tex]g(x)=\dfrac{1}{2^x}[/tex]
[tex]g(x)=2^{-x}[/tex]
[tex]g(x)=f(-x)[/tex]
It means the graphs of f(x) and g(x) are reflections over the y-axis. So, option B is correct.
Since [tex]g(x)\neq -f(x)[/tex], therefore the functions f(x) and g(x) are not the reflections over the x-axis. So, option A is incorrect.
The function f(x) is an increasing function because the base of the exponent is [tex]2>1[/tex]. The function g(x) is a decreasing function because the base of the exponent is [tex]\dfrac{1}{2}<1[/tex]. So, option C is incorrect.
At x=0 the value of f(x) is 1 and the value of g(x) is also 1. It means the functions has same initial values. So, option D is incorrect.
Therefore, the correct option is B.
We can conclude that g(x) is a reflection over the y-axis of f(x).
How to find the transformation that relates the two functions?
The two functions are:
f(x) = 2^xg(x) = (1/2)^xYou can see the graph of these functions at the end of the answer.
You can also notice that g(x) can be written as:
g(x) = (1/2)^x = 2^(-x) = f(-x)
Then this is a reflection over the y-axis, thing that you can also see in the graph below.
So the correct option is:
"The functions f(x) and g(x) are reflections over the y-axis."
If you want to learn more about reflections, you can read:
https://brainly.com/question/4289712
Which of the following is the equation of a line in a slope= 5 and y-intercept at (0,-3)?
Answer:y=5x-3
Step-by-step explanation:
Solve the formula for the specified variable.
W=X+Xyz for z
Answer:
z= (w-x)/ xy
Step-by-step explanation:
w= x+xyz solve for z
w= x+xyz, isolate the term that has z by subtracting x from both sides (because is the opposite of adding x to the term xyz we try to isolate)
w-x = xyz, divide both sides by xy assuming that xy≠0 (because is the opposite of multiplying z by xy to solve for z, and xy≠0 because we do not want to divide by 0)
(w-x)/xy = z
What is the solution to the equation?
-9=-10x-5
Answer:
2/5=x
Step-by-step explanation:
-9=-10x-5
Add 5 to each side
-9+5=-10x-5+5
-4 = -10x
Divide by -10
-4/-10 = -10x/-10
2/5 =x
Answer:
0.4
Step-by-step explanation:
you take the -5 to the other side as positive and that is -4 = -10X and then you divide -4 by -10 and that is 0.4 hope that helps
Instructions: Find the measure of the missing angle using the Exterior Angle Sum
Theorem
Answer:
It's an isosceles triangle equal 2 sides so
it will be x+67 ° +67 ° =180° ( sum of angle in triangle)
x+134 °=180 °
x =180 - 134
x = 46 °
The measurement of the missing angles in the given triangle is 67.
Use the concept of isosceles triangle defined as:
A triangle with two equal-length sides is said to be isosceles.
An isosceles triangle has equal angles on either side of its equal sides.
In the given figure,
One angle is 67 degrees
And two sides are equal.
Let the missing angle is x°
Since the two sides of this triangle are equal,
So this is an isosceles triangle.
Then two opposite angles must be equal.
For a triangle,
The sum of interior angles = 180°
Therefore,
67° + 67° + x° = 180°
x° = 46°
Hence,
The measurement of the missing angle is 46°
To learn more about the triangle visit;
brainly.com/question/1058720
SPJ4
Does (x, y) satisfy an equation?
Answer:
Yeah
Step-by-step explanation:
A researcher decides to find out whether giving students positive
reinforcement improves or impairs their grades. The researcher's sample
group consists of the following 8 students:
0 Jack
1 Tucker
2 Susie
3 Jill
4 Charianna
5 Trey
6 Ashton
7 Jordan
52197 66082 97867 49397 47924 78900 59414 64755 48733
Which of the following represents a 5-person group selected for the
treatment group using the first number in the line from a table of random
numbers above?
A. Charianna, Tucker, Jack, nobody, Ashton
B. Tucker, Susie, Trey, Ashton, Jordan
C. Trey, Susie, Tucker, Jordan, Ashton
D. Charianna, Tucker, Jack, Ashton, Trey
Answer: C. Trey, Susie, Tucker, Jordan, Ashton
========================================================
Explanation:
The random sub-sequence 52197 66082 helps directly determine who we pick.
The digit 5 is first of that sequence, so we pick Trey first (as he's the 5th student). Then we pick student #2 next, who is Susie.
Up next is student #1, and that would be Tucker
Up next is student #9, but the list only goes high as 7. So we skip over 9
Jordan is next up since 7 is the next digit
Finally, the last selection is Ashton because 6 follows after.
--------------
In other words, the sequence 52197 6 will lead to these selections in the order provided.
5 = Trey2 = Susie1 = Tucker9 = skip, since it's not on the list7 = Jordan6 = AshtonSide note: if we wanted a 6th student, then we'd have to skip over the next 6 since we cannot pick Ashton twice. The 6th selection would be Jack since he's student #0
An acute angle of a right triangle measures 30°, and the length of the triangle's hypotenuse is 10 ft. Find the missing angle measure and side lengths.
Answer:
missing angle <60 and side lengths 5, 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
we understand from the given information that the triangle in question is a special right triangle
and since this is a special triangle the side lengths follows :
the side length that sees <90 is represented by 2x
the side length that sees <60 is represented by x[tex]\sqrt{3}[/tex]
and the side length that sees <30 is represented by x
2x = 10 so x = 5 and x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex]
(x + 6): x= 5:2 Work out the value of x.
Answer:
x is 4
Step-by-step explanation:
[tex]{ \bf{(x + 6) : x = 5 :2 }} \\ { \tt{ \frac{(x + 6)}{x} = \frac{5}{2} }} \\ \\ { \tt{5x = 2(x + 6)}} \\ { \tt{5x = 2x + 12}} \\ { \tt{3x = 12}} \\ { \tt{x = 4}}[/tex]
Answer: x = 4 :)
(x + 6): x= 5:2
x : x + 6 : x = 5 : 2
1 + 6:x = 2,5
6:x = 2,5 - 1
6:x = 1,5
x = 6: 1,5
x= 4
Have a nice day:)
Banks and other financial institutions offer incentives for people to keep their money in a savings account.
True or False?
it's true because it gives interset or compensation amount to the individuals or organizations which motivates people to save their money in a saving account
Evaluate:
18 (5n - 4) = [?]
Answer:
90n-72=0
Step-by-step explanation:
18×5n-18×4=0
asap answer pls ----------------
Answer:
C
Step-by-step explanation:
Which of the following is the best definition of the sample space of a
probability event?
A. The number of successful outcomes
B. The measure of how likely an event is to occur
O O O O
C. The set of all possible outcomes
D. The most likely outcome
Answer:
C:The set of all possible outcomes
Can help me with on this quick
Answer:
18
Step-by-step explanation:
Graph the inequality.
1
Answer:
hope it helps
Step-by-step explanation:
