The dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.
In the question,
The function is [tex]B(x) = 0. 06x^2 - 0. 2x^3[/tex]
To find the maximum or minimum, take the derivative and set it equal to zero.
⇒ [tex]B'(x) = 2(0. 06)x - 3(0. 2)x^{2}[/tex]
Setting it equal to zero, we get
⇒ [tex]0.12x - 0.6x^{2}=0[/tex]
⇒ 0.6x (0.2-x) = 0
⇒ x = 0 or x = 0.2
Now substitute x = 0.2 in B(x), we get
⇒ [tex]B(0.2) = 0. 06(0.2)^{2} - 0. 2(0.2)^{3}[/tex]
⇒ B(0.2) = 0.0024 - 0.0016
⇒ B(0.2) = 0.0008
To know B(0.2) is maximum, let us find the values for x = 1 and x = 0.01.
For x = 1,
⇒ [tex]B(1) = 0. 06(1)^{2} - 0. 2(1)^{3}[/tex]
⇒ B(1) = 0.06-0.2
⇒ B(1) = -1.04
For x = 0.01,
⇒ [tex]B(0.01) = 0. 06(0.01)^{2} - 0. 2(0.01)^{3}[/tex]
⇒ B(0.01) = 0.000006 - 0.0000002
⇒ B(0.01) = 0.0000058
Thus, x = 0.2 is the maximum.
Hence we can conclude that the dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.
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Full factor of 32a^3+ 12a^2
Answer:
4a²*(9a + 3)
Step-by-step explanation:
Factorize:Prime factorize 32 and 12. Then find GCF.
32a³ = 2 * 2 * 2 * 2 * 2 * a³
12a² = 2 * 2 * 3 * a²
GCF = 2 * 2 * a² = 4a²
32a³ + 12a² = (4a²*9a) + (4a²*3)
=4a²*(9a + 3)
You are out to dinner with 10 friends (meaning there are 11 of you). The bill total is $110. You all want to split the bill evenly. How would you write this as an improper fraction?
A 110/10
B 10/111
C 11/110
D 110/11
Answer:
110/11
A
Step-by-step explanation:
divide the bill by 11 people.
Answer:
D. 110/11
Step-by-step explanation:
110 Dollars
11 people to split it with
110/11 to find the total for each person
A shopkeeper has $680 in the denominations of $50, $20, $10 and $5 notes. The number of notes of each denomination is equal. What is the total number of notes?
The total number of notes is 32
The number of notes
Let the number of notes be x
$50 = x
$20 = x
$10 = x
$5 = x
Total number of notes = 4x
Let's find 'x'
50x + 20x + 10x + 5x = 680
85x = 680
x = 680/ 85
x = 8
We know that;
Total number of notes = 4x = 4 × 8 = 32 notes
Thus, the total number of notes is 32
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(06.04 MC)
Find the perimeter of the image below:
Answer: 39 units
Step-by-step explanation:
Using the distance formula, we get that:
[tex]PT=\sqrt{10^2 + 4^2}=\sqrt{116}\\\\TS=\sqrt{7^2 + 0^2}=7\\\\SR=\sqrt{7^2 + 1^2}=\sqrt{50}\\\\RQ=\sqrt{6^2 + 5^2}=\sqrt{61}\\\\PQ=\sqrt{2^2 + 6^2}=\sqrt{40}[/tex]
So, the perimeter is
[tex]\sqrt{116}+7+\sqrt{50}+\sqrt{61}+\sqrt{40} \approx 39[/tex]
20 PIONTSSS TO WHOEVER ANDWER THIS QUESTION !!!
Answer:
The answer would be 36cm².
Step-by-step explanation:
⇒ Two prisms are similar.
⇒ Scale factor = 3:8
⇒ The ratio of the surface area is 9:64.
⇒ So S₁ : S₂ = 9:64
⇒ S₁ : 256 = 9:64
⇒ S₁ = 36cm²
This would mean that the answer is 36 centimeters ² (squared).
Solve for x in the equation: 8a = 2xy + b.
Step-by-step explanation:
Simplifying 8a = 2xy + b
Reorder the terms: 8a = b + 2xy
Solving 8a = b + 2xy
Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.
Divide each side by '8'. a = 0.125b + 0.25xy
Simplifying a = 0.125b + 0.25xy
Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called
Stratified random sampling is used to subdivided into groups by volume of sales.
According to the statements
Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.
Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.
Thus, Stratified random sampling is used to subdivided into groups by volume of sales.
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Describe how the graph of the function g(x) = -5x²-2 is related to the graph of
the function f(x) = 5x².
(A) reflection of f(x) = 5x² across the x-axis and translated left 2 units
(B) translation of f(x) = 5x² down 2 units
(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units
(D) reflection of f(x) = 5x² right 2 units
Answer:
(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units
i need help with this page
9a). The measure of segment GH from the given information can be evaluated as one-fourth of the perimeter; 48/4 = 12 cm.
9b). The measure of <EJF is 90° as the angle EJF is a right angle made at the intersection of the rhombus diagonals.
9c). The measure of <EHG is 60° as the opposite angles in a rhombus are congruent and <EHG = 2 × <EHJ = 2 × 30 = 60°.
10a). The sides labelled in the rectangle are congruent by the rectangle diagonal congruence concept; it therefore follows that the required value of x is; 9x+ 20 = 10x +8; and x = 12.
10b). The angle measures as labelled in the rhombus are congruent as this follows from the fact that the diagonal is an angle bisector. Hence, 2x +15 = 5x +3; and x = 4.
What is congruence?The concept of congruence describes a similarly between 2 or more geometric figures or elements.
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waheda purchased 8 textbooks each costing rupees 12 and 4 story books each question rupees 9 find the ratio of amounts she spent on the two types of books .
Answer:
8/3 or 2(2/3) Textbooks to storybooks
Step-by-step explanation:
Textbooks: (8 books)*(12 rupees/book) = 96 rupees
Storybooks: (4 books)*(9 rupees/book) = 36 rupees
Total is 132 rupees
Ratio: Textbook/Storybook = 96/36
96/36 = 8/3 or 2(2/3) Textbooks to storybooks
Find the missing value so that the two points have a slope of 1/2.
(9, 1) and (3, y)
Please explain
Answer: -2
Step-by-step explanation:
Substituting into the slope formula,
[tex]\frac{y-1}{3-9}=\frac{1}{2}\\\\y-1=-3\\\\y=-2[/tex]
Pls help me on 103 :((
Answer:
J) [tex]18cm^2[/tex]
Step-by-step explanation:
a square inscribed in a circle means that the radius of the circle is the same thing as a line drawn from the center of the square to a corner.
this will give you the side measurements for a triangle (look at the attached picture). now use the Pythagorean theorem to find the hypotenuse aka the side length of the square. then multiply it by itself.
Answer: H
Step-by-step explanation:
Finding the DiameterIf we draw a line through a diagonal of the square, two triangles are formed. The angle opposite the diagonal is 90°, as all angles are 90° in a square. One of the properties of a circle state that the angle in a semicircle is always 90°, which means that the diagonal formed a semi-circle.
A semi-circle only forms when a diameter is drawn in a circle, making the diagonal a diameter. This will be useful information, as we can calculate the side length of a square using the length of its diagonal.
A diameter is just twice the length of a radius, so the diagonal of the square would be 6 cm.
[tex]2*3=6[/tex]
Finding the Length of One SideThe diagonal also splits the square into two 45-45-90 triangles. These triangles have a special property that their hypotenuse is √2 times each leg, and all legs are the same length.
Therefore, we can calculate the length of a leg by dividing the hypotenuse by √2.
[tex]\frac{6}{\sqrt{3}}[/tex]
The length of one side of the square is [tex]\frac{6}{\sqrt{3}}[/tex]
Finding the AreaAs we already know the length of one side, we can just square it to get the area.
[tex](\frac{6}{\sqrt{3}})^2[/tex]
[tex]\frac{6^2}{(\sqrt{3})^2}[/tex] [Properties of Exponents]
[tex]\frac{36}{3}[/tex]
[tex]12[/tex]
Hence, the area of the square is 12 cm².
Simplify (5√3 − 2√5) the whole square
Answer:
95 - 20[tex]\sqrt{15}[/tex]
Step-by-step explanation:
(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²
= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )
each term in the second factor is multiplied by each term in the first factor, that is
5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis
= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms
= 95 - 20[tex]\sqrt{15}[/tex]
Answer:
95 - 20√15
Step-by-step explanation:
I assume the expression is (5√3 − 2√5)^2 (?).
(5√3 − 2√5)*(5√3 − 2√5)
25√3^2 - 20√15 + 4√5^2
25*3 - 20√15 +4*5
75 - 20√15 +20
95 - 20√15
Next, you will make a scatterplot. Name a point that will be on your scatterplot and describe what it represents.
The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius
How to make a scatter plot?To do this, we make use of the following points
(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)
Where x represents the number of hours and y represents temperature
See attachment for the scatter plot.
The description of a pointTo do this, we make use of the point (12, 190)
This means that the temperature after 12 hours is 190 degrees Celsius
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If a line that passes through the
points (8, 10) and (4, -6) also passes through the point (b, 2b), then find the value of b?
A school system is reducing the amount of dumpster loads of trash removed each week. in week 5, there were 60 dumpster loads of waste removed. in week 10, there were 40 dumpster loads removed. assume that the reduction in the amount of waste each week is linear. write an equation in function form to show the amount of trash removed each week. f(x) = −4x 60 f(x) = 4x 60 f(x) = −4x 80 f(x) = 4x 80
The equation in function form is f(x)=-4x+80.
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
We can find the equation in function form as shown below:
We have given two points (5,60) and (10,40)
Slope of line
m = (40-60)/ (10-5)
m=-20/5
m=-4
Equation in slope intercept form
(y-y1) =m(x-x1)
(y-60) =-4(x-5)
y-60=-4x+20
y=-4x+20+60
y=-4x+80
y=f(x)
f(x)=-4x+80
Hence, the equation in function form is f(x)=-4x+80.
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C = 75h + 125
The equation above gives the amount C, in dollars, an electrician charges for a job that takes h hours. Ms. Sanchez and Mr. Roland each hired this electrician. The electrician worked 2 hours longer on Ms. Sanchez's job than on Mr. Roland's job. How much more did the electrician charge Ms. Sanchez than Mr. Roland?
Ms. Sanchez paid 150 dollars more than Mr. Roland.
How much more did the electrician charge Ms. Sanchez than Mr. Roland?Let's say that the electrician worked for x hours in Mr. Roland's home, then worked for (x + 2) hours in Ms. Sanchez home.
Then we need to find the difference between the linear equations:
C(x + 2) - C(x) = (75*(x + 2) + 125) - (75*x + 125)
If we simplify that, we get:
75*x + 75*2 + 125 - 75*x - 125
= 75*2 = 150
This means that Ms. Sanchez paid 150 dollars more than Mr. Roland.
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 i need help putting it in expanded form and solving it
Answer:
4x^04x^04x^04x^1 which equals 256
Step-by-step explanation:
The 4 outside of the parentheses says take what you have outside of the parentheses and multiply it by itself that may times.
x raised to the zero is 1, so you are just left with 4x4x4x4 or 256
there are five chemistry instructors and six physics instructors at a college. if a committee of four instructors is selected,
The probability of at least one of them being a physics instructor is 120 ways to form the committee.
Probability of Independent Events: The 'At Least One' Rule?Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.
Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.
6 select 2; 8 select 3
15×56 =840
We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.
(9) = 20 options for selecting the professors. 3
(3) = 6 options for selecting the professors.
(9) (¹) = 20 × 6 = 120 ways.
Therefore, 120 ways to form the committee.
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Complete question:
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?
find the area of the following
Answer:
24000 ft²
Step-by-step explanation:
Triangle PRS:b = base = PR = 240 ft
2AS = 240 ft
[tex]\sf AS = \dfrac{240}{2}\\\\ AS = 120 \ ft[/tex]
h = height = AS = 120 ft
[tex]\sf \boxed{\bf \ Area \ of \ triangle = \dfrac{1}{2}b*h}[/tex]
[tex]\sf =\dfrac{1}{2}*240*120\\\\ = 120 * 120\\\\ = 14400 \ ft^2[/tex]
Triangle PRQ:b = PR = 240 ft
3BQ = 240 ft
[tex]\sf BQ = \dfrac{240}{3}\\\\ BQ = 80 \ ft[/tex]
[tex]\sf Area \ of \ triangle \ PRQ = \dfrac{1}{2}*240*80[/tex]
= 120 * 80
= 9600 ft²
Area of the quadrilateral PQRS = area of ΔPRS + area of ΔPRQ
= 14400 + 9600
= 24000 ft²
Which of these statements is true for f(x) = 2.3*?
OA. The y-intercept is (0, 1).
OB. The domain is x > 0.
OC. The y-intercept is (0, 2).
OD. It is always decreasing.
The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).
How to determine the true statement?The function is given as:
f(x) = 2(3)^x
Set x = 0 to determine the y-intercept
f(0) = 2(3)^0
Evaluate
f(0) = 2
This means that the y-intercept of f(x) = 2(3)^x is (0,2)
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Question 5 of 10
Suppose f(x) = x² and g(x)= (1x)
graph of g(x) with the graph of f(x)?
Which statement best compares the
A. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 4.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 4.
C. The graph of g(x) is the graph of f(x) shifted units right.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 4.
Answer: A
Step-by-step explanation:
See attached image.
Which is the graph of the linear inequality 2x-3y < 12?
Answer:
First, transform the given equation into the slope-intercept form, y = mx + b.
2x - 3y < 12
3y > 2x - 12
y > [tex]\frac{2}{3}[/tex]x - 4
Since the equation is y > [tex]\frac{2}{3}[/tex]x - 4, first draw the graph of y = [tex]\frac{2}{3}[/tex]x - 4 with a dotted line (because it is >, not ≥) and shade the area above the dotted line.
To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem.
Quadrilateral W X Y Z is shown. A diagonal is drawn from point W to point Y. Sides W Z and X Y are parallel and congruent.
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
WY ≅ WY by the reflexive property.
∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.
WX ≅ ZY by definition of a parallelogram.
WZ ≅ XY by the given.
The reasons Travis can use to prove both triangles are congruent by the SAS congruency theorem are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.What is the SAS Congruency Theorem?The SAS congruency theorem states that two triangles are congruent when they both have two pairs of corresponding congruent sides and a pair of corresponding congruent included angles.
Given the image below, we have the following proof with the statement and reasons in bracket:
WZ ≅ XY [given]
WY ≅ WY [reflexive property]
∠ZWY ≅ ∠XYW [by the alternate interior ∠s theorem]
△WZY ≅ △YXW [by the SAS congruency theorem]
Therefore, the reasons Travis can use are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.Learn more about the SAS congruency theorem on:
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Answer:
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem;
B. WY ≅ WY by the reflexive property; & E. WZ ≅ XY by the given.
Step-by-step explanation: Trust Me! Answer is correct on Edge.
Good Luck! :)
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem B. WY ≅ WY by the reflexive property E. WZ ≅ XY by the given
omg please help me!!!
area = pi * r^2
here, the radius is 2 as its the diameter/2.
so the area is 4pi.
circumference = 2*pi*r.
so the circumference is 4pi as well.
help me please im in a rush
Answer:
The answers are in the image
Step-by-step explanation:
The solutions are in the image
The planner needs a clearance of 9 feet under the arch has the planner met the minimum
Yes, the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of the arc is 9.6 feet
How to explain the information?As we can see that at the mid value, for x=4, the value of f(x)=9.4
It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.
It means that the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of arc is 9.6 feet
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Please help me solve this random answers will be removed
Answer:
AB-46 cm
Step-by-step explanation:
Use law of cosines
AB^2 = 24^2 + 26^2 - 2 (24)(26)cos 134
AB= 46 cm
find the value in the figure
Which explains how to show that
X=-8/3
is a root of
9×^2+48×+64=0?
a. Graph
9x^2 + 48x + 64 = 0
to show that
x=-8/3
is where the parabola crosses the y axis.
b. Graph
9x^2 + 48x +64 = 0
to show that the parabola's vertex is just above the value
x=-8/3
c. Substitute
x=-8/3
back into
9x^2 + 48x + 64 =0
and simplify to show that a true statement
results.
d. Substitute
x=-8/3
back into
9x^2 + 48x + 64 = 0
and simplify to show the values of
a
c
remain perfect squares.
Answer:
c. Substitute
Step-by-step explanation:
A graph of the function on the left shows the parabola touches the x-axis at x = -8/3. That is, the vertex is on the x-axis. It crosses the y-axis at y = 64.
Show a value is a rootA given solution to an equation can be verified by substituting that value into the equation an showing the result is a true statement. Here, the value x=-8/3 is a root of the given equation because that value makes the equation true.
[tex]9\left(-\dfrac{8}{3}\right)^2+48\left(-\dfrac{8}{3}\right)+64=0\\\\9\left(\dfrac{64}{9}\right)-\left(\dfrac{48\cdot8}{3}\right)+64=0\\\\64-\dfrac{3\cdot2\cdot8\cdot8}{3}+64=0\\\\64-2\cdot64+64=0\\\\0=0\qquad\text{True}[/tex]