Answer:
The number of liters for container R = x = 0.5 liters
The number of liters for container S = y = 1.5 liters.
Step-by-step explanation:
Let the number of liters of container R = x
Let the number of liters of container S = y
We are told in the question : that
Container R holds a solution that is 20% alcohol
= 20% × x = 0.20x
Container S holds a solution that is 60% alcohol.
= 60% × y = 0.60y
How many liters of solution from each container should be used to create 2 liters of solution that is 50% alcohol?
Hence;
x + y = 2 ....... Equation 1
x = 2 - y
0.20x + 0.60y = 2 × 50%
0.20x + 0.60y = 1........ Equation 2
Substitute
2-y for x in Equation 3
0.20(2 - y) + 0.60y = 1
0.40 - 0.20y + 0.60y = 1
Collect like terms
0.40y = 1 - 0.40
0.40y = 0.60
y = 0.60/0.40
y = 1.5 liters
Note that :
x = 2 - y
x = 2 - 1.5
x = 0.5 liters
Therefore,
the number of liters for container R = x = 0.5 liters
the number of liters for container S = y = 1.5 liters.
determine if the function f(x)=3^(2x-3) is exponential
An exponential function gives a variable raised to the power of x, where the variable is a positive real number
Yes, [tex]\underline{f(x) = 3 ^{(2 \cdot x - 3)}}[/tex] is an exponential function
Reason:
An exponential function is a function that can be written in the form;
f(x) = eˣ
Where;
e = Euler's number, which is the number approximately 2.71828
In the general form, an exponential number is a number given in the form;
f(x) = a·bˣ
Where;
b = A positive real number
The given function; [tex]f(x) = 3 ^{(2 \cdot x - 3)} = \dfrac{3^{2\cdot x}}{3^3} = \dfrac{1}{27} \times 9^x[/tex] is an exponential function
Where;
a = [tex]\dfrac{1}{27}[/tex]b = 9Therefore, the correct response is; Yes, [tex]f(x) = 3 ^{(2 \cdot x - 3)}[/tex] is an exponential function
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A rectangular prism has a square base with side length s units. It also has the curious property that the numerical value of the sum of its edge lengths (in units) is equal to the numerical value of its surface area (in square units).
If one edge of the prism has length 8 units and s 6= 8, then s can be written in the form a + √b, where a and b are integers. Find a + b.
A construction company requires 25,400 bricks
for a job. If it allows 2% more bricks for breakage, how
many bricks must it order?
How do you simplify
x2+2x-8
x2+6x+8
Answer:
x4+8x
Step-by-step explanation:
x2+x2=x4
2x+6x=8x
(-8)+8=0
You cant add x4 and 8x so thats your final answer
If the slope of a line is -1 and two points on the line are (-9, 3) and (-10, r), what is the value of r?
Answer:
[tex]r=4[/tex]
Step-by-step explanation:
We know that the slope of the line is -1.
We also know that the line passes through (-9, 3) and (-10, r).
We want to find the value of r.
First, let's figure out the equation of our line. We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's substitute -1 for m. Since we know the point (-9, 3), let's use this for (x₁, y₁).
Substitute:
[tex]y-(3)=-1(x-(-9))[/tex]
Simplify:
[tex]y-3=-(x+9)[/tex]
Distribute:
[tex]y-3=-x-9[/tex]
Add 3 to both sides. So, our equation is:
[tex]y=-x-6[/tex]
It passes through (-10, r) and we want to find the value of r. So, let's substitute -10 for x and r for y, since -10 is our x and r is our y. So:
[tex]r=-(-10)-6[/tex]
Evaluate for r. Distribute:
[tex]r=10-6[/tex]
Subtract:
[tex]r=4[/tex]
So, the value of r is 4.
And we're done!
3. Give the domain of y= √6-X using set builder notation.
Answer:
{x | x ≤ 6}
Step-by-step explanation:
Given
y = √(6 - x)
Required
Determine the domain
We start by setting 6 - x to ≥ 0.
i.e.
6 - x ≥ 0
Add x to both sides
6 - x + x ≥ 0 + x
6 ≥ x
This can be rewritten as
x ≤ 6
Using set builder, the above van be represented as: {x | x ≤ 6}
While jumping rope, Juan jumped 24 times in 30 seconds. At this rate, how many times will he jump in 50 seconds?
Answer:
40
Step-by-step explanation:
In 50 times Juan will jump 40 times.
What is unitary method ?Unitary method is first finding the value of a single unit and then deriving the required units from the given data.
For example - : A can eat 2 bananas in 2 seconds.So he can eat one banana in 1 second.From this we can calculate how many bananas he can eat in any given time.
According to the given question Juan jumped 24 times in 30 seconds.
∴ In 1 sec Juan will jump 24/30 times which is
= 4/5 times.
So, in 50 secs Juan will jump ( 4/5 × 50 ) = 40 times.
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On which interval are both the sine and cosine functions increasing?
A (3pi/2, 2pi)
B (pi/2, pi)
C (0, pi)
D (pi, 3pi/2)
Answer: It’s A
Step-by-step explanation:
On the interval (3π/2, 2π), both the sine and cosine functions are increasing.
What are the values of sine and cosine functions at (0, π/2, π, 3π/2, 2π)?The values of sine and cosine functions at (0, π/2, π, 3π/2, 2π) are as follows:
sin (0) = 0; cos (0) = 1
sin (π/2) = 1; cos (π/2) = 0;
sin (π) = 0; cos (π) = - 1
sin (3π/2) = - 1; cos (3π/2) = 0
sin (2π) = 0; cos (2π) = 1
Therefore, it is clear from the above values of sine and cosine that on the interval (3π/2, 2π), both the sine and cosine functions are increasing.
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Use the drop-down menus to complete the sentences:
The terminal ray of an angle measuring -10/9pie at lies in the
quadrant.
This angle measures
Answer:
1. second
2. -200
Step-by-step explanation:
Just did it on e2020
What number is 272 less than 2,744?
Answer: 2472
Step-by-step explanation: It is just 2744 minus 272
Answer:
2472 okay that is your answer, you just subtract 272 from 2744. you can use a calculator to solve of paper
pls help plz pls plz
Answer: c
i’m pretty sure it’s c
Answer:
B
Step-by-step explanation:
15 rows with 7 cookies is just multiplying, 15*7, to get how many cookies that's in the tray. There's also 9 trays, so we multiply (15*7) by 9
A candy store makes 6 1/2 pounds of fudge in 1/4 hr how many pounds of fudge can the store make in 1 hr
Answer:
26 lbs
Step-by-step explanation:
there are four 1/4 hours in an hour 1/4 x4=1 hour
6 1/2 x4= 26 lbs in an hour
1,052.785 rounded to the nearest hundredths place
Hello! The correct answer is 1,052.79.
You may remember the rounding rule..0-4 goes down, 5-9 goes up..
✨ You underline the "8" in "1,052.785". ✨
We can see, the number behind it is "5", which means 8 goes up once.
**ONLY** the 8 goes up, everything stays.
⌨ Which makes it 1,052.79! ⌨
Therefore, your answer is 1,052.79, I hope this helps you.
✔ Please give me brainiest!! ✔
®
can you help me find the answer please
Answer:
Its B (4.69 * 10^8)
Step-by-step explanation:
if u add them all together thats what you get I typed it into a calculator
Is 45/60 equal to 75/100?
Answer:
Yes the both simplify into 3/4
Step-by-step explanation:
Answer: yes they are both 15 apart
Step-by-step explanation:
Solve for n. 2 (4 + n) = 28
Answer:
n = 10
Step-by-step explanation:
=> 2(4 + n) = 28
=> 2(4) + 2(n) = 28
=> 8 + 2n = 28
=> 2n = 28 - 8
=> 2n = 20
=> n = 20/2
=> n = 10
Answer:
n = 10
Step-by-step explanation:
2(4 + n) = 28
Distribute:
(8 + 2n) = 28
Eliminate Parenthesis:
8 + 2n = 28
Cancel Out:
2n = 20
Divide:
n = 10
1,826.5 divided by what equals 18265
Answer:
33361022.5
Step-by-step explanation:
62+(3·4)−24
PLS HELP MEEEEEEEE
Answer:
50
Step-by-step explanation:
62+(3·4)−24
62+12-24
Final Answer: 50
Answer:
50
Step-by-step explanation: :D
which number line model represents the expression -2+ (- 7/2)
Answer: -5.5
Step-by-step explanation:
(; -2= 7/2
-5+ 7 =12
12/2=5
Richard and Gloria ran a 10-kilometer race. Gloria gave Richard a head start by letting him begin 2.2 kilometers in front of the start line. The distances of Richard and Gloria past the start line as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Whose time was faster, and by how much?
Richard’s Distance Past the Start Line
Time (minutes)
5
10
15
20
25
Distance (kilometers)
2.8
3.4
4.0
4.6
5.2
A graph titled Gloria's Distance Past the Start Line has time (minutes) on the x-axis and Distance (kilometers) on the y-axis. A line goes through points (5, 0.8), (10, 1.6), (15, 2.4), (20, 3.2) and (25, 4).
Gloria’s time was 0.5 minutes faster.
Richard’s time was 0.5 minutes faster.
Gloria’s time was 2.5 minutes faster.
Richard’s time was 2.5 minutes faster.
Answer:
Gloria's time was 2.5 minutes faster
Step-by-step explanation:
The assets (in billions of dollars) of the four wealthiest people in a particular country are 47, 30, 28, 18. Assume that samples of size n=2 are randomly selected with replacement from this population of four values. a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined.
Step-by-step explanation:
The 16 possible permutations and their means are:
47, 47: μ = 47
47, 30: μ = 38.5
47, 28: μ = 37.5
47, 18: μ = 32.5
30, 47: μ = 38.5
30, 30: μ = 30
30, 28: μ = 29
30, 18: μ = 24
28, 47: μ = 37.5
28, 30: μ = 29
28, 28: μ = 28
28, 18: μ = 23
18, 47: μ = 32.5
18, 30: μ = 24
18, 28: μ = 23
18, 18: μ = 18
So the frequency distribution of the sample means is:
[tex]\left[\begin{array}{cc}Mean&Frequency\\18&1\\23&2\\24&2\\28&1\\29&2\\30&1\\32.5&2\\37.5&2\\38.5&2\\47&1\end{array}\right][/tex]
The mean of a dataset is the average value of the dataset.
The dataset is given as:
47, 30, 28 and 18
From the above dataset, we can see that the data elements are 4
The sample size is given as:
n = 2
So, the number of different samples is:
[tex]Samples = 4^2[/tex]
[tex]Samples = 16[/tex]
The 16 samples are: {(47,47), (47,30), (47,28), (47,18),(30,47), (30,30), (30,28), (30,18),(28,47), (28,30), (28,28), (28,18),(18,47), (18,30), (18,28), (18,18)}
The mean values of the above samples are: {47, 38.5, 37.5 , 32.5 , 38.5 , 30 , 29 , 24 , 37.5 , 29 , 28 , 23 , 32.5 , 24 , 23 , 18}
Rearrange in ascending order
18, 23, 23, 24, 24, 28, 29,29, 30, 32.5, 32.5, 37.5, 37.5, 38.5, 38.5, 47
So, the table of the sample means is:
Mean Frequency
18 1
23 2
24 2
28 1
29 2
30 1
32.5 2
37.5 2
38.5 2
47 1
Total 16
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2/4 = y/10 what is y?
Answer:
5
Step-by-step explanation:
2/4=y/10
=> 2x10=yx4
=> 20=yx4
=>y=5
Which answer choice shows these three expressions in order from least to greatest?
Answer:
Option D.
Step-by-step explanation:
Convert each to a decimal.
pie + 8 = 11.14
5 and the square root of 20 = 22.36
10/ the square root of 3 = 5.77
Now put them in order from least to greatest.
10/ the square root of 3, pie + 8, 5 and the square root of 20.
Option D is your answer!
The distance between 4 and 17 is
Question 9 of 10 What is the scale factor of ABC to DEF?
Let p: x = 4
Let q: y = -2
Which represents "If x = 4, then y=-2
At its highest point, the elevation of a county is feet above sea level. At its lowest point, the elevation of the county is feet below sea level. Answer parts a through c.
Answer: There is no photo, I cannot see
-5(x+2)+3x= Which expression can be written in the box on the other side of the equation
Answer:
O-2(x+5)
Step-by-step explanation:
I have to much time on my hands
Answer:
-2x-10
Step-by-step explanation:
-5(x+2)+3x=
Distribute
-5x-10 +3x
Combine like terms
-2x-10
Select the locations on the number line to plot the points 5, 3, and −2
Answer:
To find the points, remember the definition of distance or difference.
First, the 5 is easy to find, is in the extreme right.
Now, the next number is 3.
The difference between 3 and 5 is:
3 - 5 = - 2
This means that the place of the 3 will be 2 units at the left of the 5.
The next number is -2
The difference between -2 and 5 is:
-2 - 5 = -7
This means that the -2 is located 7 units at the left of the 5.
Below is an image of the located points in a number line.
explain how polygon A is congruent to polygon B
Answer:
polygon B is just polygon B flipped to the side
Step-by-step explanation:
polygon B is just polygon B flipped to the side
