The maximum concentration is greatest at; t = 4.926 hours
How to find the time at maximum concentration?We are given the equation that represents the concentration as;
C = (3t² + t)/(50 + t³)
The maximum value of C is obtained when the slope of C' is zero (can be a local maxima too). So we are going to find solutions of C'.
C' = (-3t⁴ - 2t³ + 300t + 50)/(50 + t³)
At C' = 0, we have;
-3t⁴ - 2t³ + 300t + 50 = 0
Using online polynomial root calculator, the only valid root of this is;
t = 4.926 hours
Thus, the maximum concentration is greatest at t = 4.926 hours
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among 175 students 100 study math 70 study phisycs 46 study chemistry 30 study math and phisycs 28 study math and chemistry 23 study phisycs and chemistry and 18 study all three how many study only one subject
The number of people that studied only one subject is 108.
What is a set?A set is a collection of well-defined objects.
Objects in a set are called elements or members of a set.
Set notation or the use of Venn diagrams are the methods used to solve set problems.
Analysis:
let P = physics
C = chemistry
M = mathematics
n(P) = 70
n(C) = 46
n(M) = 100
n(M n P n C) = 18
n(M n P) = 30
n(M n P n C') = 30 - 18 = 12
n(M n C) = 28
n(M n C n P') = 28 - 18 = 10
n(P n C ) = 23
n(P n C n M') = 23 - 18 = 5
n(P n C' n M') = 70-(12+18+5) = 70 - 35 = 35
n(P' n C n M') = 46-(18+5+10) = 46-23 = 13
n(P' n C' n M) = 100 - (10+18+12) = 100 - 40 = 60
people that studied only one subject are = 35 + 13 + 60 = 108
In conclusion 108 students studied only one type of subject.
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Choose the equation for the graph.
V
1
a) y = 2x - 3| +1
b) y = −2|x - 3| +1
c) y = 2x - 3|-1
d) y = −2|x + 3| − 1
e) y = 2x + 3| +1
Answer: e
Step-by-step explanation:
The vertex is at (-3, 1).
The x coordinate being -3 eliminates a, b, and c.The y coordinate being 1 eliminates d.This leaves e.
A line with a slope of 3 passes through the points (-10, z) and (-8, 8). What is the value of
z?
Z=?
Answer:
z=2
Step-by-step explanation:
We are given that a line has a slope of 3.
The line passes through the points (-10, z) and (-8, 8)
We want to find the value of z.
To do that, we can calculate the slope.
The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
Even though we already have 2 points, let's label their values to avoid any confusion.
[tex]x_1=-10\\y_1=z\\x_2=-8\\y_2=8[/tex]
Now substitute those values into the formula, and set it equal to 3. Remember that the formula uses subtraction.
[tex]\frac{8-z}{-8--10}[/tex] = 3
We can simplify this first.
[tex]\frac{8-z}{-8+10}[/tex] = 3
[tex]\frac{8-z}{2}[/tex] = 3
We can multiply both sides by 2 to clear the fraction and make it easier to calculate.
2([tex]\frac{8-z}{2}[/tex]) = 2(3)
Multiply.
8 - z = 6
Subtract 8 from both sides
-z = - 2
Multiply both sides by -1.
-1(-z) = -1(-2)
Multiply.
z = 2
find the volume of the sphere
Answer:
523.6
Step-by-step explanation:
Volume of sphere= 4/3πr^3
V=4/3π(5^3)
V=523.6 (correct to 1 dp)
You and your classmates create 18 watercolor paintings to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the watercolor paintings, you need to sell each of the watercolor paintings for $2.25. When transporting the watercolor paintings to the auction, one of your parents accidentally drops four of the watercolor paintings in the street and they are run over by a garbage truck. What is the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials?
Using proportions, it is found that the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials is of $2.89.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To pay for the materials, you need to sell 18 paintings at $2.25 each, hence the total is:
T = 18 x 2.25 = $40.5.
If you lose four paintings, you will sell 14, and still need to make $40.5, hence the price will be of:
P = $40.5/14 = $2.89.
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Please help!!!! Consider the region shaded in yellow. Which inequality does the shaded region correspond to?
Answer:
y-x-1 < 0
Step-by-step explanation:
according to the graph (0,1) and (-1,0) lies on the doted line,
equation of the dotted line is y-x-1=0
shaded region = y-x-1 < 0
Find the least common multiple (LCM) of the polynomials z² + 5z + 6 and zx + 2x − 8z-16
Answer:
(z+2)(z+3)(x-8)
Step-by-step explanation:
z² + 5z + 6 can be factored into (z+3)(z+2)
zx + 2x − 8z-16 can be factored into (x-8)(z+2)
the LCM would be (z+2)(z+3)(x-8)
if you were to multiply the two expressions together, you would multiply (z+2)^2, which is not necessary for LCM, which is why you factor them first
Simplify the following expression.
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
Let's start by crossing everything out!
12/3 can be crossed out to 4.
a^3/a^2 can be crossed out to a.
b^6/b^4 can be crossed out into b^2.
c^5/c^5 is just 1.
So which the results we got, we can multiply them, so that it is 4ab^2.
4ab^2 is our final answer!
A. In 2000, the population of a country was approximately 5.89 million and by 2050 it is projected to grow to 10 million.
Use the exponential growth model A = Ao ekt, in which t is the number of years after 2000 and Ao is in millions, to find
an exponential growth function that models the data.
B. By which year will the population be 11 million?
A. The exponential growth function that models the data is: [tex]A(t) = 5.89{0.0106t}[/tex]
B. Using the function, the population will be 11 million by 2059.
What is the exponential growth function for the population?The function is given by:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the population in 2000.k is the exponential growth rate, as a decimal.t is the number of years after 2000.Item a:
We have that:
A(0) = 5.89, A(50) = 10.
We use this to find k, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]10 = 5.89e^{50k}[/tex]
[tex]e^{50k} = \frac{10}{5.89}[/tex]
[tex]\ln{e^{50k}} = \ln{\frac{10}{5.89}}[/tex]
[tex]50k = \ln{\frac{10}{5.89}}[/tex]
[tex]k = \frac{\ln{\frac{10}{5.89}}}{50}[/tex]
k = 0.0106.
Hence the equation is:
[tex]A(t) = 5.89{0.0106t}[/tex]
Item b:
We have to solve for t when A(t) = 11, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]11 = 5.89e^{0.0106t}[/tex]
[tex]e^{0.0106t} = \frac{11}{5.89}[/tex]
[tex]\ln{e^{0.0106t}} = \ln{\frac{11}{5.89}}[/tex]
[tex]0.0106t = \ln{\frac{11}{5.89}}[/tex]
[tex]t = \frac{\ln{\frac{11}{5.89}}}{0.0106}[/tex]
t = 58.9
Rounding up, the population will be of 11 million in 2059.
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Kenji earned the test scores below in English class
79, 91, 93, 85, 86, and 88
After his next test, his Mean and Median scores both change to 88.
How much does he earn on this test?
Please help me!!
The mean is 87 and median is 86.
What is mean and median?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
The median is the middle value in a list ordered from smallest to largest.
Given:
79, 91, 93, 85, 86, and 88
So,
79+85+86+88+91+93/6 = 87
and, the median
79, 85, 86, 88, 91, 93
median = 86
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find x
pls help !!!
Answer: Sorry If I'm wrong but if you are asking for the missing angle on the bottom, I think it is 30 degrees.
Step-by-step explanation: All the angles in a triangle add up to 180 degrees. we already know that one is 50 degrees. The 2nd angle is a bit wider than a 90 degree angle, and the third angle is 30 degrees, so 50 degrees + 100 degrees + 30 degrees add up to 180. So, I think your answer would be 30 degrees.
Answer:
x = 25
Step-by-step explanation:
I added a drawing down below to guide you through!
First, we should remember, that if a line crosses two parallel lines, then the adjacent angles will have the same value. Since Line D and Line E are parallel and line BC is crossing it, angles ABC and 105 will be the same.
Now that we know one of the missing angles, we can find x easily!
All angles in a triangle add up to 180, so in this case, the equation will be: 50 + 105 + x = 180.
155 + x = 180
x = 25.
So x will equal to 25 degrees!
Choose what the expressions below best represent within the context of the word problem.
The tens digit of a number is twice the ones digit. The sum of the digits in the number is 12. What is the number?
x represents
the tens
digit
2x represents
the tens
digit
By solving a system of equations we will see that the two-digit number is 84.
Which expression best represents the word problem?
"The tens digit of a number is twice the ones digit"
"The sum of the digits is 12".
A two-digit number can be written as:
a*10 + b
Where a is the tens digit and b is the ones digit.
The word problem can then be written as:
a = 2*b
a + b = 12
So we have a system of equations.
To find the number we need to solve these, if we replace the first equation into the second one:
a + b = 12
(2b) + b = 12
3b = 12
b = 12/3 = 4
Then:
a = 2b = 2*4 = 8
So the two-digit number is 84.
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Edward Nigma is installing square tiles in his bathroom. The blueprint above is a scaled drawing of the tile pattern to be used. If the total area of the shaded region is 22 ft^2, what is the total floor area of the bathroom?
Answer:
H. 99 ft²
Step-by-step explanation:
Area is proportional to the number of tiles.
ProportionThe total area of the bathroom is 6×9 = 54 tiles. Of these, 12 are shaded. The proportion can be written as ...
total area / shaded area = total tiles / shaded tiles
total area / (22 ft²) = 54/12 . . . . . use given numbers
total area = (22 ft²)×(54/12) = 99 ft² . . . . . multiply by 22 ft²
The total floor area of the bathroom is 99 square feet.
What is the 25th term given a₁ = 8 and r = 2?
Answer:
134217728
Step-by-step explanation:
The geometric sequence formula is:
[tex]\displaystyle{a_n = a_1r^{n-1}}[/tex]
We know that [tex]\displaystyle{a_1=8}[/tex] and [tex]\displaystyle{r=2}[/tex], we also want to find the 25th term, substitute n = 25:
[tex]\displaystyle{a_{25}=8\cdot 2^{25-1}}\\\\\displaystyle{a_{25}=8\cdot 2^{24}}\\\\\displaystyle{a_{25}=134217728}[/tex]
Therefore, the 25th term of sequence is 134217728
2/5 of the pupils in Year 9 say
their favourite colour is red.
There are 75 pupils in Year 9
How many students said red is
their favourite colour?
Answer:
30 pupils
Step-by-step explanation:
first you divide 75 and 2.5 to get 30.
Answer:
30 prefer red
Step-by-step explanation:
Multiply the fraction by the number of students:
[tex]75(\frac{2}{5})=\frac{(75)(2)}{5} =\frac{150}{5} =30[/tex]
Hope this helps
Which of the following is a characteristic of all parallelograms?
A. All pairs of consecutive angles are complementary.
B. Both pairs of opposite sides are parallel.
C. The diagonals are congruent.
D. The diagonals are perpendicular.
which of the following ordered pairs satisfies the following linear pairs? 3x+2y=-2 x+2y=2
Answer:
-2
Step-by-step explanation:
you will group the like terms and add and subtract the remaining digits
Please give answer to this problem
The two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals
Conjugate of a radicalThe conjugate of a radical is the value which when multiplied with the radical expression clears the radical. Conjugates have the same numbers but the opposite sign in the middle.
The given roots are
[tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex]
They have the same numbers but opposite signs in the middle.
Hence, the two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals
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Can I please get a full answer? Thanks a bunch!
32) The cost of mailing a first-class letter is $.22 for the first ounce and $.17 for each additional ounce or fraction
thereof. What is the cost of mailing a 7.4-ounce letter?
Oa.) $1.56
Ob.) $1.36
Oc.) $1.41
A supermarket purchases chickens wholesale from a farm for $4 each. The store then marks up the chickens 50%. After 10:00 p.m., the supermarket marks down the price of the chickens by 50% to make sure they all sell before the store closes. Which statements are true about the price of a chicken?
The true statements are:
The marked up price of chicken before 10pm is $6
The 50% mark down is taken off the marked up price
What are the true statements?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Price after the mark up= (1 + mark up) x initial price
1.50 x 4 = $6
Price after the mark down = (1 - percentage mark down) x price after mark up
0.50 x $6 = $3
Here are the options:
The marked up price of chicken before 10pm is 6
The 50% mark down is taken off the marked up price
The chickens sell for $4 after 10pm
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You want to put in a new concrete patio behind your house. You want it to be 12 ft wide by 14 ft long and it needs to be eight inches thick. You know that an 80 lb. bag of concrete yields 0.60 cubic feet. How many 80 lb. bags of concrete will you need for your patio? (round to the nearest whole number , if needed )
Considering the volume of the rectangular prism, you will need 2240 bags will be needed for the patio.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, the dimensions are:
l = 14 ft, w = 12 ft, h = 8 ft.
Hence the volume is:
V = 14 x 12 x 8 = 1344 ft³
Each bag yields 0.6 ft³, hence the number of bags is:
n = 1344/0.6 = 2240 bags.
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Which inequality is equivalent to 2/3 X-5 < 11
Answer:
2/3 x - 5 < 11
2/3 x < 16 (add 5 to both sides)
x < 16 * 3/2 (multiply both sides by 3/2)
x < 24
Step-by-step explanation:
Which number line represents the solutions to -21x1 = -6?
+
+
-8-7-6-5-4-3 -2 -1 0 1
-8-7-6-5-4-3-2-1
0
++ +
-8-7 -6 -5 -4 -3 -2 -1 0
-8-7-6 -5 -4 -3 -2 -1 0
1
2 3
2
2
3
4
FR
+3
64
2 3 4
5
6 7
5 6
5 6
+4
8
5 6
+ +
7 8
7 8
7
8
Answer + Step-by-step explanation:
-2|x| = -6
⇔ 2|x| = 6
⇔ |x| = 3
⇔ x = 3 or x = -3
Determine the period.
Using it's concept, it is found that the period of the function is of 20 units.
What is the period of a function?The period of a function is given by the distance between it's repetitions.
Looking at the graph, the distance between the repetitions is of 20 units, which is the period of the function.
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I'm comfused on this
Answer:
Step-by-step explanation:
can you show part a nd b for a better understanding of the question
in a survey of 200 students 120 were taking mathematics and 50 were taking speech what is the least number of students who could have been taking both courses.
Elaine had StartFraction 5 Over 8 EndFraction of a pizza left after lunch. She told 5 of her friends that they could share the rest. What fraction of the pizza did each of her friends get if they split it evenly?
The fraction of pizza each of her friends get if they split it evenly is 1/8
Division of fractionQuantity of pizza Elaine has = 5/8Number of Elaine friends = 5Number of pizza each friend gets = Quantity of pizza Elaine has ÷ Number of Elaine friends
= 5/8 ÷ 5
= 5/8 × 1/5
= (5 × 1) / (8 × 5)
= 5/40
= 1/8
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15/16-4/6=
please help I could do this but I’m too lazy so please
Estimate the decimal 61.33 + 53.482 by first rounding each number to nearest whole number
Answer:
it's
answer
is
32.36
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