The domain of the function C(m) = 0.05m + 20 is (0, ∞) and the range of the function C(m) = 0.05m + 20 is (20, ∞).
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. The total cost of Haley’s monthly cell phone bill can be expressed by the function
[tex]\rm C(m) = 0.05\ m + 20[/tex]
The domain of the function is from zero to infinity because time can never be negative.
Then the range of the function will be
At m = 0, the value of C(m) will be
C(m) = 0.05(0) + 20
C(m) = 20
At m = ∞, the value of C(m) will be
C(m) = 0.05(∞) + 20
C(m) = ∞
Thus, the domain of the function is (0, ∞) and the range of the function is (20, ∞).
More about the linear system link is given below.
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An adult takes 400mg of vitamin c.
Each hour, the amount of vitamin c in
the person's system decreases by about
29%. How much vitamin c is left after 6
hours?
Answer:
51.24 mg
Step-by-step explanation:
400 x (0.71^6) = 51.24
Answer:
51.24 mg
Step-by-step explanation:
400 x (0.71^6) = 51.24
Find the side labeled x.
help please
Answer:
x=7.51
Step-by-step explanation:
Tangent would be the easiest option here in this problem so to do this set up the proportion
[tex] \frac{ \tan(30) }{1} = \frac{x}{13}[/tex]
Cross multiply to get x=tan30(13)
Multiply tan30 by 13 to get the answer to x which is
x=7.51 rounded to the nearest hundredth
Which equation best models the data shown on the scatter-plot below?
The scatterplot is an illustration of a linear regression.
The equation that best models the scatter plot is y = 4x+ 35
How to determine the equation of the scatterplot?The equation of a linear regression is represented as:
y = mx + b
Where:
m represents the slope
b represents the y-intercept
From the graph, we have the following points on the line of best fit (see attachment)
(x,y) = (10,75) and (20,105)
The equation is then calculated as:
[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})(x -x_1) + y_1[/tex]
This gives
[tex]y = (\frac{105 - 75}{20- 10})(x -10) + 75[/tex]
Evaluate
[tex]y = 4(x -10) + 75[/tex]
Open the bracket
[tex]y = 4x -40 + 75[/tex]
Simplify
[tex]y = 4x+ 35[/tex]
Hence, the equation that best models the scatter plot is y = 4x+ 35
Read more about scatter plots at:
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Manny does not eat 4/9 of his orange at lunch. Josh does not 5/9 of his orange at lunch. How much orange do Manny and Josh have left over?
The amount of orange that Manny and Josh have leftover after eating lunch is 1.
What are fractions?A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below
How much orange is leftover?Oranges Manny has left = 1 - 4/9 = 5/9
Oranges Josh has left = 1 - 5/9 = 4/9
Oranges they both have left = 5/9 + 4/9 = 1
To learn more about subtraction of fractions, please check: https://brainly.com/question/915789
find the surface area of the triangular prism
Answer:
97.79ft
Step-by-step explanation:
Adding the area of every side together gets the surface area of the whole shape.
help again thank you .
Answer:
Left 2, up 1
Step-by-step explanation:
If you use slope, remember rise/run. You go up then left.
Answer: left 2 up 1
Step-by-step explanation: I did it by using the rule rise over run so it goes up then left . Hope it helps
Solve for x.
0.2x – 3.2
= 1.8
1
5
X = ?
Answer:
X = 25
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable
Convert 2.25 to a mixed number and an improper fraction. Write answers in the simplest form.
Answer: Answer in picture
Step-by-step explanation:
Math
Help pls!!!!!!!!!
ddddddddddddddd
Review the work showing the first few steps in writing a partial fraction decomposition.
StartFraction 4 x + 40 Over (x + 2) (x + 6) EndFraction = StartFraction A Over x + 2 EndFraction + StartFraction 16 Over x + 6 EndFraction
4x + 40 = A(x + 6) + B(x + 2)
4x + 40 = Ax + 6A + Bx + 2B
What is the partial fraction decomposition in terms of x?
Answer:
8/(x + 2) - 4/(x + 6)
Step-by-step explanation:
4x + 40 = Ax + 6A + Bx + 2B
Equating coefficients of x
4 = A + B (1)
Equating constant terms:
40 = 6A + 2B (2)
Multiply equation (1) by -2:
-8 = -2A - 2B .. (3)
Add (2) and (3):
32 = 4A
A = 32/4
A = 8.
4 = 8 + B
B = 4 - 8
B = -4.
The decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].
What is partial fraction?The partial fraction is the result of writing a rational expression as the sum of two or more fractions.
According to the given question.
We have a partial fraction
[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A}{(x+2)} +\frac{B}{(x+6)}[/tex]
We have to decompose the above partial fraction in terms of x.
The above partial fraction can be written as
[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A(x+6)+B(x+2)}{(x+2)(x+6)}[/tex]
⇒[tex]4x+40 = A(x+6)+B(x+2)[/tex]
⇒[tex]4x + 40 = Ax + 6A + Bx + 2B[/tex]
⇒[tex]4x + 40 = x(A+B) +6A + 2B...(i)[/tex]
On comparing the coefficient of x and the constant terms.
[tex]A+B = 4..(ii)[/tex]
⇒[tex]A = 4 - B[/tex]
and, [tex]6A+2B = 40..(iii)[/tex]
⇒[tex]2(3A+B) = 40[/tex]
Substitute the value of A in (iii)
⇒[tex]2(3A+B) = 40[/tex]
⇒[tex]3A+B = 20[/tex]
⇒[tex]3(4-B)+B = 20[/tex]
⇒[tex]12 - 3B +B = 20[/tex]
⇒[tex]12 - 2B = 20[/tex]
⇒[tex]-2B = 8[/tex]
⇒[tex]B = -4[/tex]
So, [tex]A = 4-(-4) = 8[/tex]
Substitute the value of A and B in the given partial fraction.
⇒[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex]
Hence, the decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].
Find out the more information about the partial fraction here:
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What is the area of a sector with a central angle of 8π11 radians and a radius of 7. 2 ft? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
The area of the sector will be 59.19 ft². The area of a circle's sector is the portion of the area encompassed inside the sector's perimeter.
What is an area of the sector?The area of a circle's sector is the amount of space encompassed inside the sector's perimeter. The origin of a sector is always the circle's center.
The region of a circle encompassed by its two radii and the arc connecting them is known as the sector of a circle.
The area of a circle is found as;
A = πr²
A = π(7.2 ft)²
A = 162.78 ft²
The area of the sector is the ratio of the provided slope to the angle of the complete circle which is similar to 2π;
[tex]\rm A_S= (162.78 )\times \frac{8\pi }{11 \times 2\pi} = 59.19 \ ft^2[/tex]
Hence the area of the sector will be 59.19 ft².
To learn more about the area of the sector refer to the link;
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3 kitchen assistants can prepare 10 kg of vegetables in 60 minutes. How long would it take 25 assistants to prepare the same amount?
Answer:
App. 83.33 kg
Step-by-step explanation:
10/60=0.167 kg/minute
0.167/3=0.056 kg/minute/person
0.056 x 25 x 60= 83.33...6
Brody rearranged the entertainment room at his house. Before the move, he had his game console plugged into an electrical cord that was 60 inches long. After he moved everything, he had to add an additional cord that was 2 feet long.
How many feet of electrical cord did he use altogether?
Answer:
7 feet
Step-by-step explanation:
60 inches is 5 feet add the 2 feet
Moussa owns a small business selling clothing. He knows that in the last week 92 customers paid cash, 5 customers used a debit card, and 25 customers used a credit card.
If next week, he is expecting 1600 customers, about how many would you expect to pay with cash? Round your answer to the nearest whole number.
Answer:
1207
Step-by-step explanation:
Total number of customers last week: 92 + 5 + 25 = 122
Number of customers who paid cash: 92
Percent of customers who paid cash last week: 92/122 × 100% = 75.4%
Next week:
Total number of customers: 1600
Expected number of customers paying cash:
75.4% of 1600 = 0.754 × 1600 = 1207
Let f(x)=3x-4 and g(x)=x^2-5. Find f(g(3))
Answer:
hello
g (x)= x² - 5
g (3) = 3² - 5 = 9 - 5 = 4
Step-by-step explanation:
Use the right triangular prism to find the total surface area of the prism. Leave label off answer.
Step-by-step explanation:
the total surface area is the sum of the 5 individual areas in the surface :
2 triangle sides (left and right).
1 back rectangle side
1 rectangle floor
1 inclined rectangle front side
to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras
c² = a² + b²
where c is the Hypotenuse (the side opposite of the 90° angle).
c² = 3² + 4² = 9 + 16 = 25
c = 5
so, now, we have everything we need.
the area of a triangle side (since it is right-angled) :
4×3/2 = 6
2 sides, that makes 12
the area of the back side
6×3 = 18
the area of the floor
6×4 = 24
the area of the inclined front side
6×5 = 30
so, the total surface area is
12+18+24+30 = 84
What is the volume of the triangular prism
Answer:
A.
Step-by-step explanation:
hope its help^^
#carry on learning6 , 9 , 12 , . . . 6,9,12,... Find the 34th term. Find the 34th term.
Answer:
105
Step-by-step explanation:
nth term=a+(n-1)d (a=first term,d=difference)
a=6,d=9-6=3
34th term=6+(34-1)3
=6+(33×3)
=6+99=105
If the number of bacteria in a
colony doubles every 25 hours
and there is currently a population
of 10,000 bacteria, what will the
population be 75 hours Trom now?
Answer:
The population of 75 hours from now would be 40,000.
Step-by-step explanation:
The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.
How long will it take Eniola to save $5,000 if she started with $500 and found a rate of 6. 2%? Round to the nearest whole number
Answer:
38.28 years
Step-by-step explanation:
The computation of the time period is shown below:
Given that
RATE = 6.2%
PV = $500
PMT = $0
FV = $5,000
The formula is shown below:
= NPER(RATE;PMT;-PV;FV;TYPE)
After applying the above formula, the time period is 38.28 years
Hence, in order to save $5,000 it would take 38.28 years
The volumes of two similar solids have an 125 : 216 ratio. What is the ratio of their side lengths
Answer:
5:6
Step-by-step explanation:
To find the ratio of side lengths you need to cube root of the ratio of the volumes. The reason you use the cube root is because you are multiplying 3 things together when you find volume.
[tex]\sqrt[3]{\frac{125}{216} } =\frac{5}{6}[/tex]
5 : 6
can someone please help me
Help me with this please I will give you extra points
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Total outcomes in which Billy can get 5 or more : 2 outcomes
Total outcomes = 6
So, the probability of getting 5 or higher is ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{favorable \: outcomes}{total \: outcomes} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2}{6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{3} [/tex]
Therefore, the correct choice is C
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Which ordered pair would form a proportional relationship with the point graphed below?
(–40, 20)
(–10, –20)
(15, –30)
(5, –15)
Answer:
(c) (15, -30)
Step-by-step explanation:
A proportional relationship has the equation ...
y = kx
The value of the constant of proportionality is the ratio of y to x:
k = y/x = 40/-20 = -2
__
The point that is on the line y = -2x is the point (15, -30).
[tex] \binom{4a + 3}{5} - \binom{2a + 3}{3} [/tex]
simplify the fraction
I assume your question was to simplify the following fraction ;
[tex]{:\implies \quad \sf \dfrac{4a+3}{5}-\dfrac{2a+3}{3}}[/tex]
Taking LCM will yield ;
[tex]{:\implies \quad \sf \dfrac{3(4a+3)-5(2a+3)}{15}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12a+9-10a-15}{15}}[/tex]
[tex]{:\implies \quad \boxed{\bf \dfrac{2a-6}{15}}}[/tex]
This is the required answer
What is the value represented by the digit 8 after 7,824 is divided by 10
Answer:
See below.
Step-by-step explanation:
7,824/10=782.4
782.4
|
The 8 is in the tens place. It represents 80.
-hope it helps
Answer:
80
Step-by-step explanation:
7824÷10=782.4
Therfore the 8 is in the tens place meaning that the 8 in this is 80
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP THANKS
For the first question it's 52.99 cm^3 because the formula for volume of a cylinder is V=πr^2h.
The second question is 722.57 or 722 cm^2 because the formula for surface area is A=2πrh+2πr^2.
hope it helps!
Answer:
For question 3: 52.9875 cm^3 or 52.99 cm^3.
For question 4: 1,413 cm^3.
Step-by-step explanation: To find the volume of a cylinder, you need the area of the base times the height. We don't have the area of the base, but we can find out by using the formula 3.14 x r^2 where r is the radius, which is 1.5 for question 3 and 5 for question 4. It should look like this:
For question 3: 3.14 x 1.5^2 = 7.065.
For question 4: 3.14 x 5^2 = 78.5.
When you find the area of the base, you multiply it by the height, which is 7.5 for question 3 and 18 for question 4. It should look like this:
For question 3: 7.065 x 7.5 = 52.9875 or 52.99.
For question 4: 78.5 x 18 = 1,413.
Therefore, 52.9875 cm^3 or 52.99 cm^3 is your answer for question 3 and 1,413 cm^3 is your answer for question 4.
Let me know if this is right! :)
Find the slope of the line containing the following points by using the slope-formula, below: (-3, 6) (5, -9)
Answer:
Step-by-step explanation:
(x₁, y₁) = (-3 , 6) &
(x₂ , y₂) = ( 5 , -9)
[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]=\dfrac{-9-6}{5-[-3]}\\\\\\=\dfrac{-15}{5+3}\\\\\\=\dfrac{-15}{8}[/tex]
The diagonals of quadrilateral EFGH intersect at D(1,3). EFGH has vertices at E(2,6) and F(-4,5). What must be the coordinates of G and H to ensure that EFGH is
a parallelogram?
Answer:
G(0, 0), H(6, 1)Step-by-step explanation:
The diagonals of a parallelogram bisect each other.
Point D is the midpoint of both diagonals.
Endpoint of EG is point G with coordinates (x, y):
(2 + x)/2 = 1 ⇒ 2 + x = 2 ⇒ x = 0(6 + y)/2 = 3 ⇒ 6 + y = 6 ⇒ y = 0G = (0, 0)Endpont of FH is point H with coordinates (x, y):
(-4 + x)/2 = 1 ⇒ - 4 + x = 2 ⇒ x = 4 + 2 ⇒ x = 6(5 + y)/2 = 3 ⇒ 5 + y = 6 ⇒ y = 6 - 5 ⇒ y = 1H = (6, 1)help me please, im struggling
Answer:
8.57
Step-by-step explanation:
Hope it helps.......
Answer:
x = 8.57
Step-by-step explanation:
Hi! So first of all, I attached an image that has my best visual explanation of how the 2 triangles overlap but are indeed two separate triangles!
Since the question states that the triangles are similar, that basically means in simple terms that their sides are proportional or, are all based on the same fraction (proportion)! (An example of this is the triangles with the sides that correlate [in this problem, 11 to 7] would be 1 to 2, 3 to 6, and 4 to 8)
Now, we have to figure out which of our sides correspond, the first one being 11 to 7, and the second one being x + 15 (which I got by adding the small portion I have from the big triangle, and the portion I have from the smaller triangle together because the small triangle is inside of the big one!) to 15.
Next, I have to find out what x is based on the fraction (proportion) I already have which is 11 to 7 or [tex]\frac{11}{7}[/tex]. Then, I compare this by setting this proportion equal to are other proportion with x in it!
[tex]\frac{11}{7} = \frac{x+15}{15}[/tex]
Finally, I have to get x by itself to find what it is equal to, which you can see in the image! (If you have a number in the denominator and a variable in the numerator, and a regular number or fraction without a variable on the other side, you can just multiply both sides by the number in the denominator to cancel out the bottom of said variable fraction!)
So! X is equal to 8.57!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO