Answer:
radius r = 47/π in
length l = 23.5 in
Step-by-step explanation:
Let us recall that:
Volume of a cylinder = [tex]\pi r^2 h[/tex] --- (1)
The girth g = [tex]2 \pi r + h[/tex] ----- (2)
Given that:
height (h) + girth (g) = 141
Then g = 141 - h ----- (3)
Equating equation (2) and (3), we have:
141 - h = 2πr + h
2h = 141 - 2πr
h = 70.5 - πr ------ (4)
From, here now, we can now replace the value of h into equation (1)
i.e.
V = πr²(70.5 - πr)
V = 70.5πr² - π²r³
Taking the differential of the above equation with respect to r, we have:
[tex]\dfrac{dv}{dr} = 141 \pi r- 3\pi ^2 r^2[/tex]
By further differentiation:
[tex]\dfrac{d^2v}{dr^2} = 141 \pi - 6\pi ^2 r[/tex]
Let set [tex]\dfrac{dv}{dr}= 0[/tex], Then:
141πr - 3π²r² = 0
141πr = 3π²r²
Divide both sides by πr
141 = 3πr
r = 141/3π
r = 47/π in
Replacing the value of r = 47/π into equation (4), we have:
h = 70.5 - πr
h = 70.5 - π(47/π)
h = 70.5 - 47
h = 23.5 in
From equation (3);
h + g = 141
23.5 + g = 141
g = 141 - 23.5
g = 117.5 in
Volume = πr²h
V = π × (47/π )² × 23.5
V = 16523.94 in³
Find each quotient.
494 ÷ 95 =
136.8 ÷ 24 =
96.9 ÷ 19 =
43.2 ÷ 8 =
Answer:
1. 5.2
2. 5.7
3. 5.1
4. 5.425 or 5.4
Step-by-step explanation:
hope this helps :)
Answer:
1. 5.2
2. 5.7
3. 5.1
4. 5.4
Step-by-step explanation:
you can use the app photo math, you just take a picture of the problem and it will give you the answer and explain the steps.
Which of the following CANNOT be true for a triangle?
A. A triangle can be equilateral and obtuse at the same time.
B. A triangle can be equilateral and equiangular at the same time.
C. A triangle can be isosceles and right at the same time.
D. A triangle can be scalene and obtuse at the same time.
Answer:
A. A triangle can be equilateral and obtuse at the same time
Step-by-step explanation:
All angles in an equilateral triangle are 60° therefore they cannot be above 90° and less than 180°
what is the equivlalent expression of 4 plus 4 plus 4 plus 4 plus 4 plus 4 plus 4
Answer:
4x7
Step-by-step explanation:
4x7=28
4+4+4+4+4+4+4=28
--Answer--
4 x 7 = 28
4 + 4 = 8 <- x 3 + 4 = 28
or splitting it up in some way.
pls help ASAP!! person with correct answer will be marked brainliest
Answer:
41.8°
Step-by-step explanation:
Opposite angles are equal.
Answer:
41.8 degrees
Step-by-step explanation:
They are vertical angles, meaning they are the same, just opposite one another.
2) Use the law of sines to find the length of SR
sin(A)/a=sin(B)/b=sin(C)/c
Answer:
take 28 degree as reference angle
using sine angle
sin28=p/h
0.46=10/h
0.46h=10
h=10/0.46
h=21.73
therefore hypotenuse =21.73
again using sine rule
take 25 degree as reference angle
sin 25=p/h
0.42=SR/21.73
0.42*21.73=SR
9.12=SR
9.1=SR
Step-by-step explanation:
A distance of 400 km is represented in the map by 3 cm. What is the distance between two towns if they are 7.5 cm apart in the map?
Answer:
The distance between the two towns is of 1000 km.
Step-by-step explanation:
This question is solved by proportions, using a rule of three.
We have that:
3 cm represents a distance of 400 km.
What is the distance represented by 7.5 cm?
3 cm - 400 km
7.5 cm - x km
Applying cross multiplication:
[tex]3x = 400*7.5[/tex]
[tex]x = \frac{400*7.5}{3}[/tex]
[tex]x = 1000[/tex]
The distance between the two towns is of 1000 km.
A store has two different coupons that customers can use. One coupon gives the customer $35 off their purchase, and the other coupon gives the customer 35% off of their purchase. Suppose they let a customer use both coupons and choose which coupon gets applied first. For this context, ignore sales tax.
Let f be the function that inputs a cost in dollars) and outputs the cost after applying the "$35 off" coupon, and let g be the function that inputs a cost in dollars) and outputs the cost after applying the "30% off" coupon.
Required:
What is correctly represents the fact that the cost of purchasing $190 worth of goods is $98 when the "30% oft" coupon is applied first followed by the "$35 off" coupon?
Answer:
h(x)=f[g(x)]=0.7x-35
Step-by-step explanation:
In this case function f, which inputs a cost and outputs the cost after applying the $35 off coupon looks like this:
f(x)=x-35
where x is the cost of the purchase. In this case we are subtracting the $35 from the cost x.
Function g, which inputs a cost and outputs the cost after applying the 30% off coupon looks like this:
g(x)=x-0.3x
g(x)=0.7x
in this case we are subtracting 30 percent of the cost from the cost of the purchase.
So in order to find a function that represents the cost of the purchase when first applying the 30% coupon and then the $35 coupon we will need to get a composite function f(g(x)). Which means we need to substitute function g(x) into the f(x) function so we get:
h(x)=f[g(x)]=(0.7x)-35
or:
h(x)=0.7x-35
We can prove this function works when plugging x=$190 in so we get:
h(190)=0.7(190)-35
h(190)=133-35
h(190)=98
A teacher is comparing the quarter grades between two of her classes. She takes a random sample of 8 students from each class and lists the grades as shown. Find the mean for Class A.
Class A: 80, 83, 74, 91, 76, 87, 93, 72
Class B: 90, 75, 82, 86, 73, 85, 79, 94
A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10.2 hours per week. Is the amount of time greater than that for this year
Answer:
mu = the population true mean time spent by teenagers playing computer game this year
Step-by-step explanation:
Dear student, there is no much information given to answer this question but we will try as much as possible to explain (what is the parameter) of the true mean.
In 1990s;
μ = 10.2 hours/week
From the information given,we understand that the parameter is linked to the population, and we're looking for the population average time spent playing computer games by teens in the current situation.
In this situation, the population parameter is the population true mean mu = the population true mean.
Assets Liabilities
Checking and Savings $275
Owe $415 on graduation items
Rare Baseball Cards $210 Borrowed $50 from mom
Check for work done for a neighbor $19
This is a list of Karen's assets and liabilities.
What is her net worth?
$1
$39
$275
$294
Answer:
Step-by-step explanation:
$39
The net worth should be considered as the $39.
Calculation of the net worth;We know that
Net worth = Total assets - total liabilities
here,
total assets = checking & savings + baseball card + check for work done
= $275 + $210 + $19
= $504
And, the total liabilities = owe + borrowed
= $415 + $50
= $465
So, the net worth be
= $504 - $465
= $39
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Ive been stuck on this problem for an hour, help pleaseee.
The graph of the function is given below. Give all y-intercepts and x-intercepts shown.
Answer:
y intercept: [tex]y = 1[/tex]
x intercept: [tex]x = -1[/tex] and [tex]x = -3[/tex]
Step-by-step explanation:
Given
The attached graph
Solving (a): The y intercepts
This is the point where [tex]x = 0[/tex]
From the attached graph, [tex]x = 0[/tex] when
[tex]y = 1[/tex]
Hence, the y intercept is 1
Solving (b): The x intercepts
This is the point where [tex]y = 0[/tex]
From the attached graph, [tex]y = 0[/tex] when
[tex]x = -1[/tex] and [tex]x = -3[/tex]
Hence, the x intercept are -1 and -3
Determine the length of CD.
Question 13 options:
A)
10.77 units
B)
3.74 units
C)
6.32 units
D)
9.17 units
Answer:
The answer is 6.32
Step-by-step explanation:
According to the Altitude Geometric Mean Theorem, the length of the altitude of a triangle is the geometric mean of the lengths of the 2 segments is divides the hypotenuse into.
CD= Altitude
CD^2= 4 times 10
or
CD= The square root of 4 times 10
Square root of 4 times 10 is 6.3245553203
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of CD is 6.32 units. The correct option is C.
What are Similar figures?Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
In ΔBDC and ΔABC, the two angles are given,
∠D = ∠C = 90°
∠B = ∠B {Common}
Therefore, the two triangles are similar triangles, thus, the ratio of the sides can be written as,
CB / AB = CD / AC = DB / CB
Now, the ratio can be solved as,
CB / AB = DB / CB
CB / 14 = 10 / CB
CB² = 14 × 10
CB = √140
Further, in triangle ABC using the Pythagorean theorem, we can write,
AB² = CB² + AC²
14² = (√140)² + AC²
196 - 140 = AC²
AC = √56
Again, using the ratio of the similar triangle, we can write,
CD / AC = DB / CB
CD / √56 = 10 / √140
CD = (√56 × 10)/√140
CD = 6.32 units
Hence, the length of CD is 6.32 units.
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Plz help me well mark brainliest if correct
all of the above which is e
Find the area of each figure. Round to the nearest tenth if necessary.
Answer:
Solution given:
1.
diameter(d)=6mm
base(b)=8mm
height (h)=5mm
Area of figure=area of parallelogram +area of semi circle
base*height+½π(d/2)²8*5+½*π×(6/2)²40+14.1454.4mm²Area :54.14mm²2.
for triangle
base[b]=6ft
height(h)=9ft
for square
length[l]=9ft
Area of figure=area of square +area of triangle
=l²+½*b*h=9²+½*6*9=81+27=108ft²Area: 108ft²please help asap!!!!
Answer:
Hello! answer: 585
Step-by-step explanation:
This polygon can be split into 6 triangles so all you have to do is find the area of 1 then multiply by 6 to get the whole things area so...
15 × 13 = 195 195 ÷ 2 = 97.5 97.5 × 6 = 585 therefore the area is 585 hope that helps you!
solve the following equation 4 x + 10 = 66
-> 4x= 66-10
-> 4x= 56
-> x= 56/4
-> x= 14
mark me brainliestttt plsss :)))
Answer:
x = 14.
Step-by-step explanation:
4x + 10 = 66
4x + 10 - 10 = 66 - 10
4x = 56
x = 56/4 = 14.
In a small metropolitan area, annual losses due to storm, fire, andtheft are assumed to be independent, exponentially distributed random variableswith respective means 1.0, 1.5, 2.4. Determine the probability that the maximumof these losses exceeds 3.
Answer:
[tex]0.4138[/tex]
Step-by-step explanation:
Given
[tex]x \to storm[/tex]
[tex]\mu_x = 1.0[/tex]
[tex]y \to fire[/tex]
[tex]\mu_y = 1.5[/tex]
[tex]z \to theft[/tex]
[tex]\mu_z = 2.4[/tex]
Let the event that the above three factors is greater than 3 be represented as:
[tex]P(A > 3)[/tex]
Using complement rule, we have:
[tex]P(A > 3) = 1 - P(A \le 3)[/tex]
This gives:
[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]
-----------------------------------------------------------------------------------------------------------
The exponential distribution formula of each is:
[tex]P(x \le k) = 1 - e^{-\frac{k}{\mu}}[/tex]
So, we have:
[tex]k = 3; \mu_x = 1[/tex]
[tex]P(x \le 3) = 1 - e^{-\frac{3}{1}} = 1 - e^{-3} = 0.9502[/tex]
[tex]k=3; \mu_y = 1.5[/tex]
[tex]P(y \le 3) = 1 - e^{-\frac{3}{1.5}} = 1 - e^{-2} = 0.8647[/tex]
[tex]k = 3; \mu_z = 2.4[/tex]
[tex]P(z \le 3) = 1 - e^{-\frac{3}{2.4}} = 1 - e^{-1.25} = 0.7135[/tex]
-----------------------------------------------------------------------------------------------------------
[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]
[tex]P(A > 3) = 1 - (0.9502 * 0.8647 *0.7135)[/tex]
[tex]P(A > 3) = 1 - 0.5862[/tex]
[tex]P(A > 3) = 0.4138[/tex]
Move the values to the boxes to complete the inequality statement.
5<____<7<____<9____<11
Helppp
Answers:
first blank = not sure (see explanation below)second blank = 3*sqrt(6)third blank = 3pi============================================================
Explanation:
Use your calculator to compute 3*sqrt(6) = 7.348469 which is approximate.
We can see that 3*sqrt(6), aka 7.348469, is between 7 and 9
Do the same for 3pi to get 3pi = 9.424778 approximately. So this goes between 9 and 11
As for the first blank, between 5 and 7, it seems like an answer choice is missing. So I would ask your teacher about that. If your teacher meant it to be left blank, then just ignore it.
Last Question Plz Help
Answer:
this is good looking nice photo but li can't give you answer of that sorry.
Step-by-step e this https://www.commonlit.org/en/students/student_lesson_activities
What are the main properties of a parallelogram?
use the parallelogram (ABEF) to help you
Answer:
It must be number 2.
1 and 3 number is wrong as parallelogram don't need have right angle
write an equivalent expression for 3/5x + 2/5 + 3/5x
please i will give brainliest
Answer:
= 3/5(x) + 3/5(x) + 2/5
= 6/5(x) + 2/5
= 2/5 (3x+1)
Step-by-step explanation:
Answer: [tex]\frac{6}{5}x + \frac{2}{5}[/tex]
This is the same as writing (6/5)x + 2/5
===================================================
Explanation:
Ignore the fraction [tex]\frac{2}{5}[/tex] for now.
The other terms will combine together since they are like terms. We'll add those terms to get:
[tex]\frac{3}{5}x+\frac{3}{5}x\\\\\left(\frac{3}{5}+\frac{3}{5}\right)x\\\\\frac{3+3}{5}x\\\\\frac{6}{5}x\\\\[/tex]
Then we tack on the [tex]\frac{2}{5}[/tex] we ignored earlier to get the final answer of [tex]\frac{6}{5}x+\frac{2}{5}[/tex]
(CHILL REMINDER) I know it's difficult right now, and I know you want to give up, but now isn't the time to give up. *Everything is going to be okay, I promise.*
We are here to help you...
Join Pastel Wardrobe on Roxxxblox to enter our virtual cruise and giveaways!
Answer:
thanx for the reminder
Step-by-step explanation:
have a wonderful day :)
In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed. What is the expected frequency of West Campus and failed
Answer:
57.5
Step-by-step explanation:
The expected frequency of West Campus and Failed :
Let :
Failed = F
East Campus = C
West Campus = W
Passed = P
Frequency of FnW :
[(FnE) + (FnW) * (PnW) + (FnW)] / total samples
[(52 + 63) * (63 + 37)] / 200
[(115 * 100)] / 200
11500 / 200
= 57.5
n(Failed n East campus)
Answer:
57.5
Step-by-step explanation:
Got it right on the test.
In a year study found that the 7 billion people in the world 6 billion have cell phones how many people live without access for that year
Answer:
1 billion
Step-by-step explanation:
there are 7 billion people and out of that 7 billion , only 6 billion have cell phones and the remaining people don't have cellphones.
Working out:
7 -6=1
ellus
Find the surface area of the composite figure.
2 cm
7 cm
2 cm
12 cm
12 cm
7 cm
7 cm
SA = [?] cm2
Answer:
SA = 484 cm²
Step-by-step explanation:
Surface area of the composite figure = surface area of the larger rectangular prism + (surface area of the smaller rectangular prism - base area of the smaller rectangular prism)
✔️Surface are of the larger rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 7 cm
H = 12 cm
S.A = 2(7*7 + 7*12 + 7*12) = 434 cm²
✔️Surface are of the smaller rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 2 cm
H = 2 cm
S.A = 2(7*2 + 7*2 + 2*2) = 64 cm²
✔️Base area of the smaller rectangular prism = L*W
L = 7 cm
W = 2 cm
Area = 7*2 = 14 cm²
✅Surface area of the composite figure = 434 + (64 - 14)
= 434 + 50
= 484 cm²
Mr. Poplin asked his students to write the following expression: "Two to the fifth power plus seven squared" Which answer choice shows this expression? A 52 - 27 B (2-5) + (7.2) © 25-74 D 2572
Answer:
B
Step-by-step explanation:
they rest The two by five and separate the square
brainliest for answer
Answer:
what is the question?
Step-by-step explanation:
Answer:
i answered
Step-by-step explanation:
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 55 minutes and the variance of the waiting time is 11. Find the probability that a person will wait for more than 33 minutes. Round your answer to four decimal places.
Answer:
1 = 100% probability that a person will wait for more than 33 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean waiting time is 55 minutes and the variance of the waiting time is 11.
This means that [tex]\mu = 55, \sigma = \sqrt{11}[/tex]
Find the probability that a person will wait for more than 33 minutes.
This is 1 subtracted by the p-value of Z when X = 33. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33 - 55}{\sqrt{11}}[/tex]
[tex]Z = -6.63[/tex]
[tex]Z = -6.63[/tex] has a p-value of 0.
1 - 0 = 1
1 = 100% probability that a person will wait for more than 33 minutes.
Choose the correct name for the polygon.
VRUST
SRVUT
SRTUV
RSVUT
The name of polygon is SRVUT.
What is Polygon?In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).
Given:
Usually while naming the polygon we have to focus on the letter to which each vertex is allotted.
and, the name of any geometrical shape should be in a flow, it should be like which letter come after the previous in clockwise or anticlockwise order.
Here, the polygon will have name:
VRSTU
RSTUV
STUVR
TUVRS
UTVRS
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Need help with it I don’t know how to do it