Answer:
5
Step-by-step explanation:
8 quizzes / 2 weeks = 20 quizzes / x weeks
Cross multiply:
8x = 40
Divide:
x = 5
Harold will have to attend 5 weeks.
The radius of a right circular cylinder is increasing at the rate of 6 in./s, while the height is decreasing at the rateof 3 in./s. At what rate is the volume of the cylinder changing when the radius is 5 in. and the height is 11 in.?
The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is
[tex]V=\pi r^2h[/tex]
Differentiate both sides with respect to time:
[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dr}{\mathrm dt}+\pi r^2\dfrac{\mathrm dh}{\mathrm dt}[/tex]
We're given that
[tex]\dfrac{\mathrm dr}{\mathrm dt}=6\dfrac{\rm in}{\rm s}[/tex]
[tex]\dfrac{\mathrm dh}{\mathrm dt}=-3\dfrac{\rm in}{\rm s}[/tex]
so that at the point when [tex]r=5\,\rm in[/tex] and [tex]h=11\,\rm in[/tex], the volume is undergoing a total change of
[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi(5\,\mathrm{in})(11\,\mathrm{in})\left(6\dfrac{\rm in}{\rm s}\right)+\pi(5\,\mathrm{in})^2\left(-3\dfrac{\rm in}{\rm s}\right)[/tex]
[tex]\boxed{\dfrac{\mathrm dV}{\mathrm dt}=585\pi\dfrac{\mathrm{in}^3}{\rm s}}[/tex]
The volume of the right circular cylinder is changing at a rate of 255π cubic inches/sec with the radius increasing at 6 in./s and height decreasing at 3 in./s.
Explanation:The question involves the application of calculus concepts particularly related to volume flow rate. The volume (V) of a right circular cylinder is given by V = πr²h, where r is the radius and h is the height. We can take the derivative in respect to time (t) of both sides, which will result in dV/dt = πrh(dr/dt) + πr²(dh/dt).
According to the problem, dr/dt = 6 in./s and dh/dt = -3 in./s. The volume is changing when the radius (r) is 5 in. and the height (h) is 11 in. Substituting all these values into the formula, we get: dV/dt = π(5)(11)(6) + π(5)²(-3). This equals 330π - 75π = 255π cubic inches/sec.
Thus, the volume of the cylinder is changing at a rate of 255π cubic inches/sec.
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What are the coordinates of p?
A.(0,5)
B.0,7
C.7,0
D.5,0
Answer:
(5,0)
Step-by-step explanation:
Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)
Answer:
(5,0)
Step-by-step explanation:
Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)
Need help!
What is the area of this triangle?
Enter your answer as a decimal in the box round only your final answer to the nearest tenth.
The answer is:
The area of the triangle is:
[tex]Area=13.2cm^{2}[/tex]
Why?We can solve the problem using the Side-Angle-Side (SAS) method, to calculate the area of a triangle given two sides and a single angle.
The SAS method to calculate the area of a triangle is given by the following the equation:
[tex]Area=\frac{abSinC}{2}[/tex]
Where,
a and b are the known sides.
C is the known angle
Now, we are given a triangle with the following dimension:
[tex]Side_{a}=7cm\\Side_{b}=8cm\\\alpha=28\°[/tex]
Then, using the information and solving we have:
[tex]Area=\frac{7cm*8cm*Sin(28\°)}{2}[/tex]
[tex]Area=\frac{56cm^{2}*Sin(28\°)}{2}\\\\Area=\frac{56cm^{2}*0.47}{2}\\\\Area=\frac{26.32cm^{2}}{2}\\\\Area=13.16cm^{2}[/tex]
Hence, the area of the triangle, rounded to the nearest tenth is:
[tex]Area=13.2cm^{2}[/tex]
Have a nice day!
Sammy likes to mix and match her 4 necklaces, 2 bracelets, and 3 hats. The colors are listed in the table. On monday, she randomly picks a bracelet, a necklace, and a hat. What is the probability of sammy choosing a red necklace and yellow bracelet?
URGENT BRAINLIEST
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
In calculating probability, remember that "AND" means "MULTIPLICATION" and "OR" means "ADDITION".
Since we want the probability of red necklace AND yellow bracelet, we calculate individual probabilities and "MULTIPLY" them.
Probability of red necklace:
There are 4 necklaces and 1 of them is red, hence probability of red necklace is 1/4
Probability of Yellow bracelet:
There are 2 bracelet and 1 of them is yellow, hence probability of yellow bracelet is 1/2
Now, we multiply both to get our answer.
1/4 * 1/2 = 1/8
Answer:
1/8
Step-by-step explanation:
Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
Answer:
Step-by-step explanation:
I'm sure you want your functions to appear as perfectly formed as possible so that others can help you. f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation: f(x) = 4(2)^x
f(b) - f(a)
The formula for "average rate of change" is a.r.c. = --------------
b - a
change in function value
This is equivalent to ---------------------------------------
change in x value
For Section A: x changes from 1 to 2 and the function changes from 4(2)^1 to 4(2)^2: 8 to 16. Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2. Thus, in this Section, the a.r.c. is:
8
------ = 8 units (Section A)
1
Section B: x changes from 3 to 4, a net change of 1 unit: f(x) changes from
4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units. Thus, the a.r.c. is
224 units
----------------- = 224 units (Section B)
1 unit
The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.
This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").
Answer:
Part A: Section A- 8, Section B- 32.
Part B: 4 times.
Step-by-step explanation:
The function is given by .
Section A is from x = 1 to x = 2.
Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16
Again, section B is from x = 3 to x = 4.
Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64
Part A:
In section A, the average rate of change is = 8
And in section B, the average rate of change is = 32
Part B:
Therefore, the average rate of change of section B is greater than section A is (32 / 8 = 4)
Benito runs 1/10 of a mile each day. Which shows how to find the number of days it will take for Benito to run 3/5 of a mile?
A. divide 1/10 by 3/5
B. divide 1/10 by 5/3
C. divide 3/5 by 1/10
D. divide 3/5 by 10/1
D is most likely right. Basically, I would turn them into decimals and divide using a graphing calculator.
Answer:
D
Step-by-step explanation:
which are the correct reprsentives of the inequality -3(2x-5)<5(2-x)check all that apply x<5
Answer:
x > 5Step-by-step explanation:
[tex]-3(2x-5)<5(2-x)\qquad\text{use the distributive property}\\\\(-3)(2x)+(-3)(-5)<(5)(2)+(5)(-x)\\\\-6x+15<10-5x\qquad\text{subtract 15 from both sides}\\\\-6x<-5-5x\qquad\text{add 5x to both sides}\\\\-x<-5\qquad\text{change the signs}\\\\x>5[/tex]
The population of a town is decreasing at a rate of 1% per year in 2000 there were 1300 people write an exponential decay function to model this situation then find the population in 2008.
A.) 1200 people
B.) 1300 people
C.) 1500 people
D.) 1100 people
Answer:
b
Step-by-step explanation:
Based on the rate at which the population is decreasing, we can calculate that population in 2008 is A. 1,200 people
The population after a certain number of years is:
= Population now x (1 - rate) ^ number of years
The number of years is:
= 2008 - 2000
= 8 years
The population in 2008 is therefore:
= 1,300 x ( 1 - 1%)⁸
= 1,199.57
= 1,200 people
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Find the exact circumference of a circle with an approximate area of 78.5 square feet.
Answer:
31.41ft
Step-by-step explanation:
the area A of a circle is πr² = 78.5 square feet
3.1416* r² = 78.5
r² =78.5/3.1416 = 24.987
r = √24.987 = 4.999ft
the circumference C of a circle is 2πr
C = 2* 3.1416 * 4.999 = 31.41ft
Given the the table of values below which of the following ordered pairs are found on the graph of the inverse function?
Answer:
C
Step-by-step explanation:
From the table we see that
[tex]f(-2)=12\\ \\f(-1)=10\\ \\f(0)=8\\ \\f(1)=6\\ \\f(2)=4[/tex]
Thus, the inverse function has the rule
[tex]f^{-1}(12)=-2\\ \\f^{-1}(10)=-1\\ \\f^{-1}(8)=0\\ \\f^{-1}(6)=1\\ \\f^{-1}(4)=2[/tex]
This gives us that ordered pairs
[tex](12,-2),\ (10,-1),\ (8,0),\ (6,1),\ (4,2)[/tex]
are on the graph of the inverse function
Answer:
it is c
Step-by-step explanation:
yep
Marcy is making a hooked circle-shaped rug for her mother. The circumference of the circle-shaped rug is 56.52 inches.
What is the area of the rug? Use = 3.14.
Answer:
The area is
[tex]A=254.34\ in^2[/tex]
Step-by-step explanation:
The circumference of a circle is given by a following formula:
[tex]C = 2\pi r[/tex]
Where r is the radius of the circumference.
In this case we know that
[tex]C = 2\pi r=56.52\ in[/tex]
We solve the equation for r
[tex]C = 2\pi r=56.52\ in[/tex]
[tex]2\pi r=56.52\\\\r=\frac{56.52}{2\pi}\\\\r=9\ in[/tex]
The area of a circumference is given by the following formula
[tex]A=\pi r^2[/tex]
Now we substitute the value of r in the equation to find the area
[tex]A=\pi (9)^2[/tex]
[tex]A=3.14* (9)^2[/tex]
[tex]A=254.34\ in^2[/tex]
6 more than 3 times what number squares is 81
Eli is filling up gift bags each bag will have a 3 baseball cards which number sentence would Eli use to find how many bags he can feel if he has 21 cards?
21-3=18
21÷3=7
21+3=24
21x3=63
If Eli has a total of 21 baseball cards, and wants each bag to have 3 cards, you would divide the number of total cards by the amount you want in each group. Dividing is like grouping.
So, the equation he'd use is: 21 / 3 = 7
I hope that helped.
Answer:
21÷3=7
Step-by-step explanation:
Dividing the number of available cards by the quantity in each bag will tell Eli how many bags he can fill.
___
Division can be thought of as "repeated subtraction" with the quotient telling you how many times the divisor can be subtracted from the dividend. One way Eli can do this repeated subtraction is to put the cards into piles of 3:
ccc . ccc . ccc . ccc . ccc . ccc . ccc
He will run out of cards when he has made 7 piles.
This system of equations has an infinite number of solutions. Define the solutions algebraically, and allow z to represent all real numbers.
3x − 4y + 4z = 7
x − y − 2z = 2
2x − 3y + 6z = 5
x =
y =
z = all real numbers
Answer:
x = 12z + 1 and y = 10z - 1
Step-by-step explanation:
To solve the system of equations, we can use the substitution method
If we call
3x - 4y + 4z = 7 I
x - y - 2z = 2 II
2x - 3y + 6z = 5 III
Clearing II x = 2 + y + 2z
Now, replacing II in III
2(2 + y + 2z) - 3y +6z = 5
4 + 2y + 4z - 3y + 6z = 5
10z - y = 1 from here y = 10z - 1
Finally, replacing y in I
3x - 4(10z - 1) + 4z = 7
3x -40z + 4 + 4z = 7
3x - 36z = 3
3x = 36z + 3
x = 12z + 1
Done
URGENT!!!!!!!!!
A bird drops a stick to the ground from a height of 80 ft. The function h = -16t^2 = 80 gives the stick's approximate height h above the ground, in feet, after t seconds. Graph the function. At about what time does the stick hit the ground?
Please show all the work and steps and if you cant graph the function the can you please give the points and I will graph it then
Answer:
1:7 2:9
Step-by-step explanation:
Which statement describes the graph of function g?
Answer:
The graph of G is 3 units to the left of graph F
Step-by-step explanation:
I used Desmos graphing calculator to check my answer, but generally you can use this formula.
a(x + or - h) + or - k = y
h is vertical movement and k is horizontal movement.
Answer: Never mind that answer was incorrect it is not B!!
Step-by-step explanation:
6. The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to
the temperature of the gas. If the pressure is 6 pounds per square inch when the temperature is 440° F,find
the pressure exerted when the temperature of the gas is 380°F.
(SHOW WORK)
Answer: 5.18 pounds
Step-by-step explanation:
Given: The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas.
Let 'p' denote the pressure exerted on the walls and 't' denotes temperature of the gas.
Then the equation is given by :-
[tex]p=ct[/tex], where c is the proportionality constant.
Also, the pressure is 6 pounds per square inch when the temperature is 440° F.
[tex]\Rightarrow\ 6=440c\\\\\Rightarrow\ c=\dfrac{6}{440}=\dfrac{3}{220}[/tex]
Then, the final equation to calculate pressure becomes :-
[tex]p=\dfrac{3}{220}t[/tex]
Now, the pressure exerted when the temperature of the gas is 380°F is given by :-
[tex]p=\dfrac{3}{220}\times380=5.181818\approx5.18\text{ pounds}[/tex]
a cylinder-shaped water tank is 160 cm tall and measures 87.92 cm around. what is the volume if the water tank? enter your answer as a decimal in the box. use 3.14 for pi.
Answer:
The volume is equal to [tex]98,470.4\ cm^{3}[/tex]
Step-by-step explanation:
step 1
Find the radius of the base of cylinder
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=87.92\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]87.92=2(3.14)r[/tex]
[tex]r=87.92/[2(3.14)]=14\ cm[/tex]
step 2
Find the volume of the water tank (cylinder)
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=14\ cm[/tex]
[tex]h=160\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=(3.14)(14)^{2} (160)[/tex]
[tex]V=98,470.4\ cm^{3}[/tex]
Answer:
The answer is 98470.4
Step-by-step explanation:
Help me please i have been on this problem for a while and my teachers aren't really helping!
Answer:
106 m²
Step-by-step explanation:
Imagine this shape was a square, it's area would be 120 m².
Now imagine the little rectangle with 7 m as the side, you will have to work out the area of that so
Side = 7
4 + 4 + ? = 10
8 + ? = 10
? = 2
So the area of the little rectangle is 14 m²
Now we minus both of the areas : 120 - 14 = 106
What is the value of x in the trangle? Enter your answer in the box. Round your final answer to the nearest hundredth.
Use trigonometry.
cos(18°) = x/25
Multiply both sides by 25.
cos(18°)25 = x
23.7764129074 = x
We round off to the nearest hundredth. This means to round off to two decimal places.
Doing so, we get 23,78 cm = x.
What is the equation of a line, in general form, with a slope of -2 and a y-intercept of 8?
A.x + 2y - 8 = 0
B.2x + y - 8 = 0
C.2x - y + 8 = 0
Answer:
B. 2x + y -8 = 0
Step-by-step explanation:
2x + y -8 = 0
2x - 8 = -y
Divide both sides by negative one
-2x + 8 = y
Answer:
B. 2x + y - 8 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope m = -2 and the y-intercept b = 8. Substitute:
[tex]y=-2x+8[/tex]
The general form of an equation of a line:
[tex]Ax+By+C=0[/tex]
Convert:
[tex]y=-2x+8[/tex] add 2x to both sides
[tex]2x+y=8[/tex] subtract 8 from both sides
[tex]2x+y-8=0[/tex]
Find the midpoint between A and C.
(1, 1)
(5, -7)
(-5, 7)
(0.5, 0.5)
Answer:
(0.5, 0.5)Step-by-step explanation:
The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):
[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
From the graph we have the points A(-2, 4) and C(3, -3).
Substitute:
[tex]M_{AC}(x,\ y)\\\\x=\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\y=\dfrac{4+(-3)}{2}=\dfrac{1}{2}=0.5[/tex]
Answer:
0.5 0.5
Step-by-step explanation:
because it is logically correct now deal with it! hehehe have a grate day un like me!;)
A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.04x^2+9.1x+11.9, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from it’s starting point will the rocket land?
Answer:
228.8 meters
Step-by-step explanation:
y = -0.04 x² + 9.1 x + 11.9
When the rocket lands, y = 0:
0 = -0.04 x² + 9.1 x + 11.9
Solving for x, start by multiplying by -1:
0 = 0.04 x² - 9.1 x - 11.9
Multiply by 100:
0 = 4x² - 910 x - 1190
Solve with quadratic formula:
x = [ -b ± √(b² - 4ac) ] / 2a
x = [ 910 ± √((-910)² - 4(4)(-1190)) ] / 2(4)
x = [ 910 ± √(847140) ] / 8
x ≈ -1.3, 228.8
Since x can't be negative, x = 228.8 meters.
Answer:
The rocket will land at 208.02 m. Hence, if you are on the same connexus assignment, your answer will be A.
Hope this helps! :D
if you are trying to choose a committee which of the following is the best sampling method?
A. simple random sampling
B. systematic random sampling
C. stratified random sampling
D. Cluster sampling
Answer:
The best answer would be B. systematic random sampling
Step-by-step explanation:
The best sampling method for choosing a committee is Cluster Sampling.
What are different types of sampling?Simple random sampling - Simple random sampling is a sort of probability sampling in which a researcher selects a subset of a population at random.
Systematic random sampling A probability sampling approach in which a random sample of a bigger population is selected with a defined periodic interval.
Stratified random sampling A form of sampling known as stratified random sampling includes dividing a population into smaller sub-groups known as strata.
Cluster Sampling The population is divided into groups first. Every member of some of the groupings is included in the total sample. The teams are chosen at random.
If we are trying to choose a committee, cluster sampling method would be the best as there should be representatives of every group of the society in that committee and the representative from each group should be chosen completely randomly.
Hence the cluster sampling method is the best way to choose a committee.
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Convert 27/40 to a decimal using long division.
Answer:
Step-by-step explanation:
\frac{27}{40} in a decimal is 0.675
I’ve attached a picture of my work!!
what is 5 1/4 in decimal form
5 1/4 in decimal form is 5.25 because 25 is 1/4 of 100.
The mixed fraction 5 1/4 is equivalent to 5.25 in decimal form. The fraction 1/4 is converted to decimal by dividing 1 by 4 to get 0.25 and then added to the whole number 5.
Explanation:To convert the mixed fraction 5 1/4 to decimal form, you need to divide the numerator by the denominator for the fractional part and then add that result to the whole number part. In this case, 1 divided by 4 equals 0.25. Adding this result to the whole number 5 gives you 5.25, which is 5 1/4 in decimal form.
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help
B= °
b=
c=
it has something to do with sin cos or tan I'm not sure
Answer:
Actually it does relate to sin, cos and tan.
* tan50° = 16/b
=> b = 16/tan50° ≈ 13.426
* sin50° = 16/c
=> c = 16/sin50° ≈ 20.887
*cos∠B = 16/c = 16/20.887
=> m∠B ≈ 40.002
If –1 is a root of f(x), which of the following must be true?
Answer:
(x + 1) is a factor of f(x).
Step-by-step explanation:
Please share the answer choices. Thank you.
If –1 is a root of f(x), which of the following must be true?
(x + 1) is a factor of f(x).
On a piece of paper, graph y-3>2x+2. Then determine which answer choice matches the graph you drew
ANSWER
Option C
EXPLANATION
The given inequality is
[tex]y - 3 \: > \: 2x + 2[/tex]
We add 3 to both sides to get,
[tex]y \: > \: 2x + 2 + 3[/tex]
[tex]y \: > \: 2x +5[/tex]
The corresponding linear equation is
[tex]y = 2x + 5[/tex]
This becomes the dashed boundary line of the inequality.
We test the origin to determine which half plane to shade.
[tex]0\: > \: 2(0)+5[/tex]
[tex]0\: > \: 5[/tex]
This is false.
Hence we shade the upper half plane.
The correct answer is C
The graphs of f(x) and g(x) are shown below:
graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 5, 0.
If f(x) = (x + 7)2, which of the following is g(x) based on the translation?
g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x − 9)2
g(x) = (x − 5)2
the translation should make the equation
g(x)= (x+5)2
Answer:
b
Step-by-step explanation: