Answer:
The volume of the metal used to make the pipe is [tex]\mathbf{1,680\pi\ cm^3}[/tex]
Step-by-step explanation:
The Volume of a Cylinder
Given a right cylinder of base radius r and height h, the volume is calculated as follows:
[tex]V=\pi r^2h[/tex]
We are given the dimensions of a cylindrical metallic pipe whose external diameter is de=12 cm and the internal diameter is di=8 cm. The height is h=21 cm.
The volume of the metal used in making the pipe is the difference between the external volume and the internal volume.
Calculating the external volume:
[tex]V_e=\pi r_e^2h[/tex]
[tex]V_e=\pi 12^2*21[/tex]
[tex]V_e=3,024\pi\ cm^3[/tex]
Calculating the internal volume:
[tex]V_i=\pi r_i^2h[/tex]
[tex]V_i=\pi 8^2*21[/tex]
[tex]V_i=1,344\pi\ cm^3[/tex]
The volume of metal is:
[tex]V_m=V_e-V_i=3,024\pi\ cm^3-1,344\pi\ cm^3[/tex]
[tex]V_m=1,680\pi\ cm^3[/tex]
The volume of the metal used to make the pipe is [tex]\mathbf{1,680\pi\ cm^3}[/tex]
Complete the equation by rewriting 2 12/20
Answer:
52/20
Step-by-step explanation:
Common sense and simple math
The table shows the number of songs and the length of the playlist on an iPad. Each song is the same leng
Answer:4 minutes
Step-by-step explanation:
16/4 is 4
36/9 is 4
64/16 is 4
josephin is going on a run around the lake. she knows the distance around the lake. but she would like to complete her run in a certain amount of time. josephine knows she can use the formula d= rt.
which equation correctly rearranges the formula to find the time it will take her to run around the lake?
look at picture and tell me if it is a, b, c, or d.
Answer:
A. [tex]t = \frac{d}{r}[/tex]
Step-by-step explanation:
Given
[tex]d = rt[/tex]
Required
Determine the time
From the question, we understand that:
[tex]d = distance[/tex]
[tex]r = rate[/tex]
[tex]t = time[/tex]
This question implies that we make t the subject of formula.
[tex]d = rt[/tex]
Divide both sides by r
[tex]\frac{d}{r} = \frac{rt}{r}[/tex]
The equation becomes:
[tex]\frac{d}{r} = t[/tex]
Reorder the equation.
[tex]t = \frac{d}{r}[/tex]
The correct option is (a) [tex]t = \frac{d}{r}[/tex]
If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
OmZA = 15° and mZC = 35°
mZA = 25° and mZC = 25°
OmZA = 20° and mZC = 30°
OmZA + m ZB = 155° and mZC = 60°
Answer:
m∠A = 25° and m∠C = 25°
Step-by-step explanation:
The sum of all three angles in a triangle must add up to 180°. Since the measure of angle B is 130°, the sum of the other two angles have to be 50°.
Also, the triangle is isosceles, meaning two of the sides are equal in length. For those sides, their corresponding angles must also be equivalent. In this case, it's the two smaller angles. Since we have 50° between the two angles, A and C, divide 50 by 2 to get 25° for both angle measurements.
The statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°
GeometryFrom the question, we are to determine which of the statements must be true
From the given information,
m ∠B = 130°
Since the triangle is an isosceles triangle, the base angles must be equal
That is,
m ∠A = m ∠C
But, angles in a triangle sum up to 180°
Then,
∠A + ∠B + ∠C = 180°
This becomes
2 × ∠A + 130° = 180°
2 × ∠A = 180° - 130°
2 × ∠A = 50°
∠A = 50° ÷ 2
∠A = 25°
Since ∠A = ∠C
Therefore,
∠C = 25°
Hence, the statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°
Learn more on Geometry here: https://brainly.com/question/14440001
Plz help fast. What is the value of x?
Answer is 7.b because of the angles
where does -3/4 go on a number line
Answer:
Va entre-3y-4
Step-by-step explanation:
Step-by-step explanation:
split the area between -1 and 0 into four parts
it'll be the part closest to -1
Hello can someone help me with this please
Answer:
well there are eight total red cookies and there been two that had been bitten out of already that makes the ration 2:8
A business bought 500 lamps for $10,000. They want to mark them up 25%. What is the retail price of each lamp?
Answer:
$25 a lamp
Step-by-step explanation:
First divide $10,000 by 500 lamps to find how much one of them cost
That is $20 a lamp so then multiply .25 *20 or 1/4 *20
you get 5 than add 20 +5=25
b. 3 ice cream cones cost $8.25. At this rate, how much do 2 ice cream cones cost? Explain how you know.
Solve the proportion
fraction numerator 15 t over denominator 5 end fraction equals fraction numerator 2 t plus 3 over denominator 6 end fraction
Answer:
t = 3/16
Step-by-step explanation:
Solve the proportion fraction numerator 15 t over denominator 5 end fraction equals fraction numerator 2 t plus 3 over denominator 6 end fraction
From the above question, we are to solve for t
The above expression is written Mathematically as:
15t/5 = 2t + 3/6
We cross Multiply
15t(6) = 5(2t + 3)
90t = 10t + 15
Collect like terms
90t - 10t = 15
80t = 15
t = 15/80
t = 3/16
PLEASE HELPPPPPPPPP! 44 POINTS
Answer:
#6-
1. 9x30=(9x10)+(9x10)+(9x10)
2. 9x30=9(10+10+10)
3. 9x30=270
#7-
1. 7x50=7x(10+10+10+10+10)
2. 7x50=7x(25+25)
3. 7x50=350
#8-
1. 2x90=(2x45)+(2x45)
2. 2x90=90+90
3. 2x90=180
Step-by-step explanation:
Hope this helps!
A population of 2,000 mosquitos grows at a rate of 15% per month. Which equation models the population, p(t), of the mosquitos after t months?
For what value of x is quadrilateral CDEF a parallelogram?
с C
x + 1
F
2X-3
D
N
E
X=
Answer:
[tex] x = 4 [/tex]
Step-by-step explanation:
Since the diagonals of a parallelogram bisects each other, therefore:
[tex] x + 1 = 2x - 3 [/tex]
Collect like terms
[tex] x - 2x = -1 - 3 [/tex]
[tex] -x = -4 [/tex]
Divide both sides by -1
[tex] x = 4 [/tex]
need an answer thanks in advance!
Answer:
1806 seats.
Step-by-step explanation:
From the question given above, the following data were obtained:
Row 1 = 24 seats
Row 2 = 27 seats
Row 3 = 30 seats
Total roll = 28
Total number of seat =?
From the above data, we can liken the roll to be in arithmetic progress.
Also, we are asked to determine the total number of seats in the theater.
Thus the sum of the sequence can be written as:
Roll 1 + Roll 2 + Roll 3 +... + Roll 28 i.e
24 + 27 + 30 +...
Thus, we can obtain obtained the total number of seats in the theater by applying the sum of arithmetic progress formula. This can be obtained as follow:
First term (a) = 24
Common difference (d) = 2nd term – 1st term
Common difference (d) = 27 – 24 = 3
Number of term (n) = 28
Sum of the 28th term (S₂₈) =?
Sₙ = n/2 [2a + (n –1)d]
S₂₈ = 28/2 [2×24 + (28 –1)3]
S₂₈ = 14 [48 + 27×3]
S₂₈ = 14 [48 + 81]
S₂₈ = 14 [129]
S₂₈ = 1806
Thus, the number of seats in the theater is 1806.
Help please
Sarah's rectangular dining table has a area of 9000 sq ft and the length is 20 in less then four time the width find the length and width
Given that,
The area of a rectangular dining table = 9000 sq ft
Solution,
Let the width is b ft. Length is 20 less then four time the width.
Length = (4b-20) ft
The formula for the area of a rectangle is given by :
A = lb
Substitute all the values,
[tex]9000=b(4b-20)\\\\4b^2-20b-9000=0\\\\\text{It is a quadratic equation, when we solve it we get :}\\\\b=50,-45\ feet[/tex]
Neglecting negative value, b = 50 ft
Length, l = (4(50)-20)
l = 180 ft
So, the length is 180 ft and width is 50 ft.
What is i raised to the 5th power?
Complex numbers algebra
Best way to learnMath
Answer:
ramrari focus and concentration garnu. Ani lightly linu SABAI problems haru .
Answer:
the best way to learn maths is by regular hard work and by practicing of maths daily
Two ships leave the port at 12 noon. Ship A is traveling at the bearing of 146 at 20 miles per hour, and ship B travels at a bearing of N32 E at 28 miles per hour. Approximate how far apart ships are at 3 PM. At what bearing ship A is from ship B at 3 PM.
Answer: [tex]d = 103.23 miles[/tex] apart.
Step-by-step explanation:
given data:
ship a = 20miles. = 60miles
ship b = 28miles. = 84miles
time interval = 3hrs.
θ = 90
[tex]d = \sqrt{a^{2}+b^{2}-2ab (cos90) }[/tex]
[tex]d = \sqrt{60^{2}+84^{2}-2(60)(84) *(cos90) }[/tex]
[tex]d = \sqrt{3600+7056-10080*(cos90) }[/tex]
[tex]d = \sqrt{10656-10080*(cos90) }[/tex]
[tex]d = \sqrt{10656-0[/tex]
[tex]d = \sqrt{10656[/tex]
[tex]d = 103.23 miles[/tex]
find the measure of a line EC
9514 1404 393
Answer:
41
Step-by-step explanation:
The product of segment lengths from the point of intersection to the circle is the same for both chords.
QC·QE = QD·QF
2x(21) = (x+4)(30)
14x = 10(x +4) . . . . . divide by 3
4x = 40 . . . . . . . . . . subtract 10x
x = 10 . . . . . . . . . . . .divide by 4
2x +21 = EC = 2(10) +21 . . . . . find EC
EC = 41
50 students live in a dormitory. The parking lot has the capacity for 30 cars. Each student has a car with probability 12 , independently from other students. Use the CLT (with continuity correction) to find the probability that there won't be enough parking spaces for all the cars.
Answer:
P(X is greater than 30) = 0.06
Step-by-step explanation:
Given that:
Sample proportion (p) = 0.5
Sample size = 30
The Binomial can be approximated to normal with:
[tex]\mu = np = 50 \times 0.5 \\ \\ \mu= 25[/tex]
[tex]\sigma = \sqrt{np(1-p) } \\ \\ \sigma = \sqrt{50 \times (0.5)(1-0.5) } \\ \\ \sigma = 3.536[/tex]
To find:
P(X> 30)
So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 30 lies between 29.5 and 30.5
Normal distribution:
x = 30.5, [tex]\mu[/tex] = 25, [tex]\sigma[/tex] = 3.536
Using the z test statistics;
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]z = \dfrac{30.5 - 25}{3.536}[/tex]
[tex]z = \dfrac{5.5}{3.536}[/tex]
z = 1.555
The p-value for P(X>30) = P(Z > 1.555)
The p-value for P(X>30) = 1 - P (Z< 1.555)
From the z tables;
P(X> 30) = 1 - 0.9400
Thus;
P(X is greater than 30) = 0.06
What is a real life word problem for (-7) + (7). Solve problem. Can you help?
Answer:
Step-by-step explanation:
Sally owes 7 dollars to Matthew. She opens her piggy bank and takes out 7 dollars. Now, how much money does she owe to Matthew?
-7 + 7 = 0
-7 + 7 is the same as 7 - 7
You can clearly see that 7-7 is 0.
Answer:
You are in debt of $7. You pay the bank $7. How many money do you owe now?
1. The waiting times (in minutes) of customers at a certain bank is given below. 5.5 6.5 6.7 7.2 6.4 7.3 (a) Construct a 95% confidence interval for the mean waiting time of all customers at the bank. (b) Based on the confidence interval in (a), will the bank manager be satisfied if she wishes the average waiting time in her bank to be less than 7 minutes
Answer:
The 95% confidence interval is
[tex] 5.92 < \mu < 7.284 [/tex]
Step-by-step explanation:
From the question we are told that
The data is 6.5 6.7 7.2 6.4 7.3
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{\sum x }{n}[/tex]
=> [tex]\= x = \frac{ 5.5 + 6.5 + \cdot 7.3 }{ 6}[/tex]
=> [tex]\= x = 6.6[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \frac{ \sum (x_i - \= x )^2 }{ n-1} }[/tex]
=> [tex]\sigma = \sqrt{ \frac{ (5.5 - 6.6 )^2 +(6.5 - 6.6 )^2 + \cdot + (7.3 - 6.6 )^2 }{ 6-1} }[/tex]
=> [tex]\sigma = 0.6512[/tex]
Gnerally the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 6 -1[/tex]
=> [tex]df = 5[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]t_{\frac{\alpha }{2} , 5 } = 2.571 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2}, 5 } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.571 * \frac{0.6512}{\sqrt{6} }[/tex]
=> [tex]E = 0.6835 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]6.6 - 0.6835 < \mu < 6.6 + 0.6835[/tex]
=> [tex] 5.92 < \mu < 7.284 [/tex]
PLEASE HELP IF UR GOOD AT MATH!!!
there are 18 boys and 46 girls in a class. 87.5% of the students in the class take the bus to school. How many students do nnot take the bus to school?
On Monday, Cody bought 414141 cherries. On Tuesday, Cody ate 191919 cherries. Now, she wants to divide the remaining cherries into bags of 444 cherries each.
Estimate how many bags of 444 cherries Cody can make.
Choose 1 answer:
Answer:
5 bags
Step-by-step explanation:
Answer this question if cool
Answer:
The answer to your question is given below
Step-by-step explanation:
From the question given above, the mean score is 23.
Thus, we can obtain the distance from the mean (absolute deviation) by using the following formula:
Mean deviation = | mean – Score |
Mean = 23
For Score 21:
Mean deviation = | mean – Score |
Mean deviation = | 23 – 21 | = 2
For Score 22:
Mean deviation = | mean – Score |
Mean deviation = | 23 – 22 | = 1
For Score 28:
Mean deviation = | mean – Score |
Mean deviation = | 23 – 28 | = 5
For Score 29:
Mean deviation = | mean – Score |
Mean deviation = | 23 – 29 | = 6
SUMMARY:
Score >> Mean >> Absolute deviation
21 >>>>> 23 >>>>> 2
21 >>>>> 23 >>>>> 2
21 >>>>> 23 >>>>> 2
22 >>>>> 23 >>>>> 1
22 >>>>> 23 >>>>> 1
22 >>>>> 23 >>>>> 1
22 >>>>> 23 >>>>> 1
22 >>>>> 23 >>>>> 1
28 >>>>> 23 >>>>> 5
29 >>>>> 23 >>>>> 6
It is suspected that calcium in blood platelets may be related to blood pressure. As part of a study of this relationship, researchers recruited 30 subjects whose blood pressure was normal (i.e., not abnormally elevated). For each subject two measurements were made: pressure (average of systolic and diastolic measurements) and calcium concentration in the blood platelets. The sample size is n = 30, and the sample correlation is r = 0.4. Is there evidence that blood pressure and platelet calcium are linearly related? State the hypothesis and test it at 5% level of significance. What is your conclusion?
Answer:
Step-by-step explanation:
The null and the alternative hypothesis are:
[tex]\mathbf{ H_o: \rho = 0} \\ \\ \mathbf{H_1: \rho \ne 0}[/tex]
The test statistics is as follows:
[tex]t = \dfrac{r\sqrt{n-2} }{\sqrt{1-r^2}}[/tex]
[tex]t = \dfrac{0.4 \sqrt{30-2} }{\sqrt{1-0.4^2}}[/tex]
[tex]t = \dfrac{0.4 \sqrt{28} }{\sqrt{0.84}}[/tex]
t = 2.3094
The critical value
[tex]t_{\alpha/df} = t_\ \{0.05/2 \ , \ 30-2 \} } \\ \\ = t_{0.025,28} = \pm 2.048 ( from \ the \ t-tables)[/tex]
Decision rule:
To reject [tex]H_o[/tex] if t > [tex]t_{\alpha/df}[/tex].
So since t > [tex]t_{\alpha/df}[/tex]. we reject [tex]H_o[/tex] at ∝ = 0.05
Conclusion: There is sufficient evidence to conclude that blood pressure and patient calcium are linearly related.
Marbleslides: Lines
Answer:
ok
Step-by-step explanation:
In the diagram below qs and pt are altitudes and m r=55 what is m poq
Answer: POQ = 125
Step-by-step explanation: If you don’t want to read my long explanation, I drew a diagram of my work. :>
First we need to establish that POQ is a vertical angle to SOT, this makes the angles equal. We also need to establish that because the definition of an altitude, that T And S both form right angles. (An altitude is a perpendicular segment from a vertex of a triangle to the opposite side.) Now let’s take a look at the quadrilateral that is formed inside the triangle, the quadrilateral being RSOT. Luckily we know the measure of three of the angles, R=55, T=90, and S=90. If you didn’t know beforehand all angles of a quadrilateral add up to 360, so we can add up the angles we’ve already found to find the missing angle O/ SOT. When we add the angles, and then subtract that from 360 we get 125, so SOT=125. Remember that we established that SOT and POQ are vertical angles, so if SOT=125 then POQ=125.
I really hoped my explanation was good, this was my first time giving an answer. Also I’m sorry if my method of finding the answer wasn’t helpful, but this was the only way I could think of.
I accidentally gave myself a one star rating, that sucks.
Suppose that y varies inversely with x and y = 3 when x=10 find y when x=5
Answer:
y=1.5
Step-by-step explanation:
if (y = 3) is (x = 10) and (y = ?) is (x = 5) we see that x is half of the first equation in the second. This means we divide both variables in the first equation by half to get the second. [(x = 10) / 2 = (x = 5)] therefor, [(y = 3) / 2 = (y = 1.5)]. Making your answer 1.5.
Hope this helps :)