Answer:
The answer is below
Step-by-step explanation:
From the diagram of the flask attached, the diameter of the cylinder is 1 inch and its height (h) is 3 inches. The radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch
The volume of the cylinder = πr²h = π(0.5)² × 3 = 2.36 in³
While for the sphere the diameter is 4.5 in. The radius of the sphere R = diameter / 2 = 4.5/2 = 2.25
The volume of the sphere = 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³
Volume of the flask = The volume of the cylinder + The volume of the sphere = 2.36 + 47.71 = 50.07 in³
If the sphere and the cylinder are dilated by a scale factor of 2. For the cylinder its height (h') = 3/2 = 1.5 inch and its radius (r') = 0.5/2 = 0.025
The new volume of the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³
While for the sphere The radius of the sphere R' = 2.25 / 2 = 1.125
The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³
New Volume of the flask = The new volume of the cylinder + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³
The ratio of the new volume to original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125
The resulting volume would be 0.125 times the original volume
Answer:
50.07 and 8 times
Step-by-step explanation:
1) Calculate volume of each figure using according formulas.
You should get:
Sphere: 47.71in^3
Cylinder: 2.36in^3
Now let's add, and you should get 50.07.
2) Let's dilate the dimensions/flask by 2 (multiply by 2)
4.5 * 2 = 9
1 * 2 = 2
3 * 2 = 6
Now with these dimensions you should get:
Sphere: 381.7in^3
Cylinder: 18.85in^3
This should add up to 400.55in^3
Divide new by original. 400.55 / 50.07 = 8
So it is 8 times larger.
49*32’55” + 37*27’15” = ?
Answer:
87°10''
Step-by-step explanation:
In 49°32'55'', we convert 32' to degrees. So. 32/60 = 8/15. We also convert 55'' to degrees. So, 55 × 1/60 × 1/60 = 55/3600 = 11/720
In 37°27'15'', we convert 27' to degrees. So. 27/60 = 9/20. We also convert 15'' to degrees. So, 15 × 1/60 × 1/60 = 15/3600 = 1/240
We now add the fractional parts plus the whole part of the angles together.
So,
49 + 8/15 + 11/720 + 37 + 9/20 + 1/240 = 49 + 37 + 8/15 + 9/20 + 11/720 + 1/240 = 86 + 59/60 + 7/360.
We now convert the fractional parts 59/60 to minutes by multiplying by 60 and convert 7/360 to seconds by multiplying by 3600
86° + 59/60 × 60 + 7/360 × 3600 = 86° + 59' + 7 × 10 =86° + 59' + 70'' = 86 + 59' + 1' + 10''= 86 + 60' + 10'' = 86 + 1° + 10'' = 87° 10''
So, 49°32'55'' + 37°27'15'' = 87°10''
The Three Stooges are having a pie eating contest. In 3 hours, Moe can eat 36 pies, Larry can eat 30, and Curly can eat 60. How many hours does it take them to eat 126 pies?
Answer:
3 hours
the information states in 3 hours they eat 36+30+60 = 126 pies.
Answer:
Altogether, the three stooges will consume 126 pies in three hours.
Step-by-step explanation:
1. In one hour, the three stooges can eat their total divided by three: Moe can eat 12 in one hour, Larry can eat 10 in one hour, and Curly can eat 20 in one hour. Therefore, the three stooges can eat 42 pies in one hour altogether. So, we have the equation 126 = 42h where h = the number of hours. Solving for 126 gives us 126/42 = h. h = 3. The three stooges can eat 126 pies in three hours.
Need help ASAP!!!! THX
Answer:
C
Step-by-step explanation:
f(x) = x - 2
f(2) = (2) - 2
f(2) = 0
A + B are wrong cuz..
f(-2) = -2 - 2
f(-2) = -4
The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.a. Suppose you learn that 5% of American households spend less than $1000 for dailytransportation. What is the standard deviation of the amount spent?b. What is the probability that a household spends between $4000 and $6000?c. What is the range of spending for the 3% of households with the highest daily transportationcost?
Answer:
(a) The standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
Step-by-step explanation:
We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.
(a) It is stated that 5% of American households spend less than $1000 for daily transportation.
Let X = the amount spent on daily transportation
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312
[tex]\sigma[/tex] = standard deviation
Now, 5% of American households spend less than $1000 on daily transportation means that;
P(X < $1,000) = 0.05
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;
[tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]
[tex]\sigma=\frac{-\$5312}{-1.645}[/tex] = 3229.18
So, the standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)
P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)
P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)
= 1 - 0.5359 = 0.4641
P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$4000-\$6312}{\$3229.18}[/tex] ) = P(Z [tex]\leq[/tex] -0.72) = 1 - P(Z < 0.72)
= 1 - 0.7642 = 0.2358
Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is given by;
P(X > x) = 0.03 {where x is the required range}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;
[tex]\frac{x-\$6312}{3229.18}=1.88[/tex]
[tex]{x-\$6312}=1.88\times 3229.18[/tex]
x = $6312 + 6070.86 = $12382.86
So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
HELPPP MEEE
Ying was planning how to seat guests at a dinner. There were between 50 and 100 people coming. Ying noticed that they could be seated with 8 people to a table and no seats left empty. She also noticed that they could be seated with 12 people to a table with no seats left empty. How many people were coming?
Answer:
96 people were coming
Step-by-step explanation:
In this question, we want to determine the number of people who were coming to the party.
First of all, we were made to know that this number is between 50 and 100. So whatever figure we will be giving as answer will be something within that range.
We were told that if 8 or 12 people sat at a table, there would be no remainder left. So basically what we need to do here is to calculate the highest multiple of 8 and 12 which is between 50 and 100.
we could have 24, 48 and 96 as multiples of both. But that multiple that sits between 50 and 100 is 96. So therefore, our answer is 96.
A line passes through the point (–1,–2) and is perpendicular to the line with the equation y= –x – 1. What's the equation of the line?
Question 16 options:
A)
y = x – 5
B)
y = –x + 3
C)
y = –x + 7
D)
y = x – 1
Answer:
D) y = x - 1
Step-by-step explanation:
First we need the general equation of point slope form:
(y - y0) = m(x - x0)
Where y0 is the y coordinate and x0 is the x coordinate and m is the slope.
For the line to be perpendicular, we need the slope to be the negated opposite of the other equation. So the negated opposite of -1 is 1.
So our m = 1, y0 = -2, and x0 = -1. Now let's plug this into the equation and reform the equation into slope-intercept form
(y - (-2)) = 1 (x - (-1))
y + 2 = 1 (x + 1)
y + 2 = x + 1
y = x - 1
So the equation of the line that goes through the point (-1,-2) and is perpendicular to the line y = -x -1, is y = x - 1.
Cheers.
Answer:
B) y = -x - 3
Step-by-step explanation:
slope = -1
y = mx + b
-2 = -1(-1) + b
-3 = b
y = -x - 3
answer it answer it answer it.
Answer:
C. p = 3/q
Step-by-step explanation:
An inverse proportion has the form:
y = k/x
Your problem uses p and q, so you need the form
p = k/q
Answer: C. p = 3/q
The time required to drive a fixed distance varies inversely as the speed. It takes 2 hr at a speed of 200 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 80 km/h?
Answer:
5 hours
Step-by-step explanation:
From the question, we are told that:
Time required to drive a fixed distance varies inversely as the Speed
T ∝ 1/S
k = proportionality constant hence,
T =k × 1/S
T = k/S
Step 1
Find k
It takes 2 hr at a speed of 200 km/h to drive a fixed distance
T = 2 hours, S = 200km/h
T = k/S
2 = k / 200
k = 2 × 200
k = 400
Step 2
How long will it take to drive the same distance at a speed of 80 km/h?
S = 80km/h
T = k/S
k = 400
T = 400/80
T = 5
Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr
Which of the binomials below is a factor of this trinomial? URGENT!!!
Answer:
C
Step-by-step explanation:
10×-28=-280
35-8=27
35×(-8)=-280
10x²+27x-28
=10x²+(35-8) x-28
=10x²+35x-8x-28
=5x(2x+7)-4(2x+7)
=(2x+7)(5x-4)
=========================================================
Explanation:
One way we can factor is through use the of the quadratic formula.
Let [tex]10x^2+27x-28 = 0[/tex]
For now, the goal is to find the two roots of that equation.
Plug a = 10, b = 27, c = -28 into the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(27)\pm\sqrt{(27)^2-4(10)(-28)}}{2(10)}\\\\x = \frac{-27\pm\sqrt{1849}}{20}\\\\x = \frac{-27\pm43}{20}\\\\x = \frac{-27+43}{20} \ \text{ or } \ x = \frac{-27-43}{20}\\\\x = \frac{16}{20} \ \text{ or } \ x = \frac{-70}{20}\\\\x = \frac{4}{5} \ \text{ or } \ x = -\frac{7}{2}\\\\[/tex]
The two roots are x = 4/5 and x = -7/2
For each root, rearrange the equation so we have 0 on the right hand side, and it's ideal to get rid of the fractions
x = 4/5
5x = 4
5x-4 = 0 gives us one factor
and
x = -7/2
2x = -7
2x+7 = 0 gives the other factor
The two factors are 5x-4 and 2x+7
Note how (5x-4)(2x+7) = 0 leads to the two separate equations of 5x-4 = 0 and 2x+7 = 0 due to the zero product property. Solving each individual equation leads to the two roots we found earlier.
Alternative methods to solve this problem are the AC factoring method (which leads to factor by grouping), using the box method, or you could use guess and check.
HHHHEEEEELLLLLPPPPPPP PLEASEEE ANSWER #1 AND #2
Answer:
37 = -3 + 5(k +6)
37 = -3 + 5k + 30
37 = 27 + 5k
10 = 5k
k = 2
-2 = -(w - 8)
-2 = -w + 8
-10 = -w
w = 10
Answer:
37=-3+5(k+6)
37=-3+5k+30
37=27+5k
37-27=5k
5k=10
k=10/2
k=5
***********************************************************************************
-2= -(w-8)-2=-w+8
-2-8=-w
-w=-10
w=10
Find the value of x. A. 53–√ m B. 241−−√ m C. 6 m D. 6+35–√ m
Answer:
x = 2√41 mStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
a² = b² + c²
where a is the hypotenuse
From the question x is the hypotenuse
So we have
[tex] {x}^{2} = {8}^{2} + {10}^{2} [/tex][tex] {x}^{2} = 64 + 100[/tex][tex] {x}^{2} = 164[/tex]Find the square root of both sides
We have the final answer as
x = 2√41 mHope this helps you
Answer:
2 sqrt(41) =c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 10^2 = c^2
64+ 100 = c^2
164 = c^2
take the square root of each side
sqrt(164) = sqrt(c^2)
sqrt(4*41) = c
2 sqrt(41) =c
A landscaper is designing a wall of white bricks . The pattern consists of 130 white bricks in the bottom row , 110 white bricks in the second row , and 90 white bricks in the third row . How meany white bricks will the 6th row have
Answer:
30 Bricks in the 6th row
Step-by-step explanation:
i found the answer online
Answer:
b: 30
Step-by-step explanation:
took test
Sams building a suspension bridge for the playground at the elementary school I needed some chain-link and some rope he bought a total of 80 feet of materials and The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135 how much of each did he buy
Answer:
Amount of material for chain link = 30 feet
Amount of material for rope = 50 feet
Step-by-step explanation:
Let the amount of chain link = X
The amount of rope be represented by Y
He bought a total of 80 feet of materials
Hence we have:
X + Y = 80 ....... Equation 1
Y = 80 - X
The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135
X × $2 + Y × $1.50 = $135
2X + 1.5Y = 135 ......Equation 2
Substitute 80 - X for Y in Equation 2
2X + 1.5(80 - X) = 135
2X + 120 - 1.5X = 135
Collect like terms
2X - 1.5X = 135 - 120
0.5X = 15
X = 15/0.5
X = 30 feet
Substitute 30 feet for X in Equation 1
X + Y = 80 ....... Equation 1
30 + Y = 80
Y = 80 - 30
Y = 50 feet
Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet
A bag contains 2
2
blue marbles, 2
2
red marbles, and 2
2
yellow marbles.
If Jenna randomly draws a marble from the bag (and puts it back) 15
15
times, how many times should she expect to pull a yellow marble?
Answer:
5 times
Step-by-step explanation:
Jenna wil most likely pull a yellow marble 1/3 of the time, because the total number of marbles is 6, and there are 2 yellow marbles, 2/6 which is 1/3. 1/3 times 15 is 5. So Jenna will most likely pull a yellow marble 5 times.
I WILL GIVE BRAINLIEST!
80 patients gave information about how long they waited to see the doctor.
1. Work out an estimate of the mean time that the patients waited.
2. The doctor says, “70% of our patients wait less than 30 minutes to be seen.” Is she correct?
Answer:
No, 68.75% waited less than 30mins
I don't really know about the other one, but i tried my best, soooo sorry
soz
Hope that helped!!! k
[tex] {x}^{3} - {x}^{2} \div x[/tex]
Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?
This question is incomplete because the options are missing; here is the complete question:
Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?
A. He can randomly survey 50 boys in the school.
B. He can survey 30 students in the school band.
C. He can randomly survey 50 6th graders in the school.
D. He can survey 20 friends from his neighborhood.
The correct answer is C. He can randomly survey 50 6th graders in the school.
Explanation:
A representative sample is a portion of a population that shows the characteristics of all the population. In this context, for a sample to be representative it needs to include only individuals of the population that is studied. Also, ideally, individuals should be selected randomly as this guarantees the sample is not influenced by the researcher. According to this, option C is the best as this is the only one that focuses on the target population (6th graders) and the sample is random, which contributes to the sample being objective and representing the behavior of 6th-graders.
Answer:
He can randomly survey 50 sixth-graders in the school.
Step-by-step explanation:
the difference between y and 3/8 is 3/4. workout the possible values of y
Answer:
y-3/8 =3/4y=3/4-3/8y=3/8Please give me the correct answer
Answer:
Step-by-step explanation:
slant height = l = 15 mm
radius = r = 7 mm
Surface area of cone = πr (l + r) square units
= 3.14 * 7 *(15 + 7)
= 3.14 * 7 * 22
= 483.56 square mm
Find the volume of the given shapes. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
5.
volume=l×w×h=8×6×7=336 mi³
6.
diameter=16 yd
radius=16/2=8 yd
[tex]volume=\frac{4}{3} \pi \times 8^3=\frac{2048}{3} \pi \approx 2144.67 \approx 2144.7 yd^3[/tex]
[tex]2x + x { }^{2} + x[/tex]
Answer:
[tex]\huge \boxed{x(x+3)}[/tex]
Step-by-step explanation:
[tex]2x+x^2 +x[/tex]
Combine like terms.
[tex]x^2 +(2x+x)[/tex]
[tex]x^2 +3x[/tex]
Factor out [tex]x[/tex] from the expression.
[tex]x(x+3)[/tex]
The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70
[tex] d \propto v^2[/tex]
$\implies d=kv^2$
substitute the given values, $5=k(10)^2\implies k=\frac1{20}$
now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$
A big blunder from my side, now fixed!
Solve for x: 3(x + 1) = -2(x - 1) + 6. (1 point)
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1
First: distribute 3(x+1)= -2(x-1)+6
3x+3=2(x-1)+6
Then you have too distribute again
3x+3=2(x-1)+6
3x+3= -2x+2+6
Third: add the numbers
3x+3= -2x+2+6
3x+3= -2x+8
Fourth: add the same term to both sides of the equation
3x+3= -2x+8
3x+3-3= -2x+8-3
Fifth: Simplify 3x= -2x+5
Sixth: add same term to both sides of the equation
3x= -2x+5
3x+2x= -2x+5+2x
Seventh: simplify again
5x =5
Eigth: divide both sides of the equation by the same term
5x=5
5x/5 =5/5
Last: Simplify
X=1
how do you solve 6 – 5c = -29
Answer: C = 7
Step-by-step explanation:
6 -5c = -29 make the variable be by itself by subtracting 6 on both sides.
-5c = -35 divide -5 on both sides, when dividing if both numbers are negative they become positive.
c = 7
29. A painter leans a ladder against the side of a
house that is 3 feet from the base. If the top
of the ladder reaches 16 feet, how long is the
ladder ?
HELP! answer if you can!
Answer:
16.2788 feet
Step-by-step explanation:
a²+b²=c²
3²+16²=c²
9+256=c²
265=c²
c=√265
c=16.2788 feet
If the ladder is 3 feet from the base of the house and the top is 16 feet from the base then the length of ladder is approximately 16.2788 feet long.
What is pythagoras theorem?Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to the sum of squares of base and perpendicular of that respective triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex] where H is hypotenuse, P is perpendicular, B is base of triangle.
How to find length of ladder?If a painter leans a ladder against a wall then it forms a right angled triangle so in this we will apply pythagoras theorem to find the length of ladder.
let the length of ladder be h so,
[tex]h^{2} =3^{2} +16^{2}[/tex]
[tex]h^{2} =9+256[/tex]
[tex]h^{2} =265[/tex]
h=[tex]\sqrt{265}[/tex]
h=16.2788 feet.
Hence the length of ladder is 16.2788 feet.
Learn more about pythagoras theorem at https://brainly.com/question/343682
#SPJ2
An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.H0: The product does not change the height of the plant.Ha: The product makes the plant grow taller.Is the following an example of a type I or type II error?The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.a) Type Ib) Type II
Answer:
The error made here is a Type I error.
Step-by-step explanation:
A Type I error is the rejection of a null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.
A Type II error is failing to discard a null hypothesis when indeed the null hypothesis is false. It is symbolized by β.
The hypothesis in this case is defined as follows:
H₀: The product does not change the height of the plant.
Hₐ: The product makes the plant grow taller.
The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.
So, the sample suggests to reject the null hypothesis when in fact the null hypothesis is true.
Thus, the error made here is a Type I error.
what is the answer to (x+1)(3x+2)
hey gouys I need help on this to plz help mee
Answer:
d. 3√6 = 7.348
Step-by-step explanation:
1. simplify each expression
a. √150 / 2 = 6.124
b. π + 4 = 7.142
c. 2π = 6.283
d. 3√6 = 7.348
the largest number will be the closest to 8. therefore, point W is expression D.
Which formula would you use to calculate the total enclosed space of Firm 1’s structure. Explain your choice.
What is the total enclosed space of Firm 1’s structure
Answer:
Total enclosed space = 6597.35 ft³
Step-by-step explanation:
Firm 1's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,
Volume = πr²h
where r = radius of the structure
h = height of the Firm
By substituting the values of 'r' and 'h' in the given formula,
V = [tex]\pi (\frac{70}{2})^{2}(60)[/tex]
= [tex]\pi (35)\times 60[/tex]
= 6597.345
≈ 6597.35 cubic feet
Total enclosed space of Firm 1 is 6597.35 cubic feet.
Answer:
pi*r sqrq
Step-by-step explanation:
bc its a cirlce
total SA=10445.8 units sqrt
ur welcome
Please show your work. I will give brainliest to the right answer!
Answer:
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
Step-by-step explanation:
Given:
Focus of parabola: (-4, 6)
Directrix: y = 2
Required:
Equation for the parabola
SOLUTION:Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.
Where,
a = -4
b = 6
k = 2
Plug these values into the equation formula
[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]
[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
