Answer:
2396
Step-by-step explanation:
Let the diameter = d
Let the height = h
Formula
Metric Tons = k * d^4 / h^2
Solution
Metric Tons = 64
d = 2
h = 9
k = ?
(You can't do the second part by not using a ratio unless you put k in and solve for it)
64 = 2^4 k / 9^2
64 = 8 *k / 81
64 * 81 / 8 = k
5184 / 8 = k
k = 648
Solve for the second example
Metric Tons = d^4 * k / h^2
Metric Tons = ?
d = 5
h = 13
k = 648
Metric Tons = 5^4 * 648 / 13^2
Metric Tons = 625 * 648 / 169
Metric Tons = 2396 rounded.
A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 10 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.
Answer:
127.53 liters left after 10 minutes
Step-by-step explanation:
Let
[tex]A \to Amount[/tex]
[tex]t \to time[/tex]
Given
[tex]A(0) = 200[/tex] --- initial
[tex]A(5) = 200 * (1 - 20\%) = 160[/tex] --- the amount left, after 5 minutes
Required
[tex]A(10)[/tex] --- amount left after 5 minutes
To do this, we make use of:
[tex]A(t) = A(0) * e^{kt}[/tex]
[tex]A(5) = 160[/tex] implies that:
[tex]160 = 200 * e^{k*5}[/tex]
Divide both sides by 200
[tex]0.80 = e^{k*5}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.80) = \ln(e^{k*5})[/tex]
[tex]\ln(0.80) = \ln(e^{5k})[/tex]
[tex]\ln(0.80) = 5k\ln(e)[/tex]
So, we have:
[tex]-0.223 = 5k[/tex]
Divide by 5
[tex]k = -0.045[/tex]
So, the function is:
[tex]A(t) = A(0) * e^{kt}[/tex]
[tex]A(t) = 200 * e^{-0.045t}[/tex]
The amount after 10 minutes is:
[tex]A(10) = 200 * e^{-0.045*10}[/tex]
[tex]A(10) = 200 * e^{-0.45}[/tex]
[tex]A(10) = 127.53[/tex]
When a coin is tossed it is either heads or tails. Suppose heads has a point value of 1 and tails a point value of -1. if the sum of the point value after 50 tosses is 14. How many of the tosses must have been heads?
Answer:
32
Step-by-step explanation:
Totally there are 50 tosses.
Let the number of tosses which resulted head be x.
Therefore the number of tosses which resulted tail is 50−x.
We get x×1+(50−x)×(−1)=14
x−(50−x)=14
x−50+x=14
x=32
Find the value of x . PLEASE ANSWER QUICK ILL MARK BRAINLIEST
Answer:
x = 30°
Step-by-step explanation:
(3x) = 90
[tex](3x)/3=90/3[/tex]
x [tex]=[/tex] 30
Hence, x = 30°
4)
5 + 15x
42x + 4
-
A) -2
C) -10
B) 3
D) -8
Answer:
answer is --10 pls make me brainlest
Identify factors that influence the significance level and power of a hypothesis test. Which of the following statements is FALSE?
a. Alpha (a) is equal to the probability of making a Type I error.
b. A smaller sample size would increase the effectiveness of a hypothesis test.
c. The probability of rejecting the null hypothesis when the null hypothesis is true is called a Type 1 Error.
d. The power of a hypothesis test is the probability of not making a Type Il error.
Answer:
b. A smaller sample size would increase the effectiveness of a hypothesis test.
Step-by-step explanation:
A hypothesis test is an important procedure in the field of statistics. It evaluates any two mutually exclusive statements about a population that determines and tells which statement made best supports to the sample data provided.
Now we know that an increase in the sample size makes the hypothesis test more effective and sensitive and it is more likely to reject the null hypothesis.
The probability of making a type I error is known as the Alpha while the probability of making type II error is called Beta.
Thus the correct option is (b).
Answer:
A smaller sample size would increase the effectiveness of a hypothesis test
Step-by-step explanation:
Determine the distance between points (x1, y1) and point (x2, y2), and assign the result to point Distance. The calculation is:
Given:
The two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
To find:
The distance between given points.
Solution:
Plot the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] randomly randomly on a coordinate plane, then form a right angle triangle as shown in the below figure.
Now, the hypotenuse is the distance between the two points.
[tex]\text{Perpendicular}=y_2-y_1[/tex]
[tex]\text{Base}=x_2-x_1[/tex]
Using Pythagoras theorem,
[tex]\text{Hypotenuse}^2=\text{Base}^2+\text{Perpendicular}^2[/tex]
[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Taking square root on both sides, we get
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] [Distance is always positive]
Therefore, the distance between the two points is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]. It is also known as distance formula.
If a distribution for a quantitative variable is thought to be nearly symmetric with very little variation,and a box and whisker plot is created for this distribution,which of the following is true?
A) The box will be quite wide but the whisker will be very short.
B) The left and right-hand edges of the box will be approximately equal distance from the median.
C) The whiskers should be about half as long as the box is wide.
D) The upper whisker will be much longer than the lower whisker.
Answer:
B). The left and right-hand edges of the box will be approximately equal distances from the median.
Step-by-step explanation:
The 'symmetry' si described as a 'satisfying arrangement of a balanced distribution of the elements of the whole' while a 'symmetry group' is characterized as a group whose elements are all the transformations under which a given object remains invariant and whose group operation is function composition.
As per the given conditions, the second statement asserts a true claim regarding the keeping of edges of left, as well as, right-hand side's boxes at equal intervals from the median. This will help in making the arrangement fulfilling while keeping a little scope for the variation. Thus, option B is the correct answer.
if f(x)=x+2 and g(x)=3x^2+7x find (f x g)(x)
Answer:
3x³ + 13x² + 14x
Step-by-step explanation:
(f × g)(x)
= f(x) × g(x)
= (x + 2)(3x² + 7x)
= x(3x² + 7x) + 2(3x² + 7x) ← distribute parenthesis
= 3x³ + 7x² + 6x² + 14x ← collect like terms
= 3x³ + 13x² + 14x
What is the result when the number 84 is decreased by 50%?
Answer:
42
Step-by-step explanation:
Answer:
42
84 ×50%by100 =42. 84-42= 42. hope helpful answerwhat type of triangle measuring 60cm, 100 cm, 40 cm
Answer:
Not a triangle
Step-by-step explanation:
Not a triangle.
The sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
40 + 60 is not greater than 100
therefor it is not a triangle
Due today.. I'm Stuck and need help please). The table shows the test scores and the sleep averages of several students. A) Write the least squares regression equation that models the data. Let x = the test score and y = average sleep. B) Use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. Show Your Work. ( Will Mark Brainliest but no Links or nonsense answers please). Answer A and Answer B.
Answer:
Y = -0.3587+0.09118X
92 %
Step-by-step explanation:
Using technology to fit the data between the variables, test score and hours of sleep; we obtain the linear model :
Ŷ = -0.3587+0.09118X
Where, x = test score ; y = hours of sleep
To obtain the test score of a student who sleep foe 8 hours using the model :
Y = 8
Ŷ = -0.3587+0.09118X
8 = -0.3587+0.09118X
8 + 0.3587 =0.09118X
8.3587 = 0.09118X
X = 8.3587 / 0.09118
X = 91.672515
X = 92 ( approximately)
Express the percent as a decimal.
41%
Answer:
0.41
Step-by-step explanation:
41/100
0.41
hope it helps
Answer:
0.41
Step-by-step explanation:
Percentages, fractions, and decimals are tightly connected.
When breaking the meaning of "percent" down, you get "per" (for each) and "cent" ("hundred" in French), so a percent is always a number over 100.A fraction is one number divided by another, a part of a whole.A decimal is a number expressed with the base-ten system of counting.This being said, if you get 41%, remember that you can write it as a fraction of the number over 100, which would be [tex]\frac{41}{100}[/tex]. You can then turn it into a decimal*, which would be 0.41.
*when you have a two-digit whole number as the numerator of a fraction with denominator 100, the decimal form would just be 0. the numerator and the percent would be the numerator %. If the numerator is a whole one-digit number and the denominator is 100, the decimal form would be 0.0 the numerator, and the percent would still be just the numerator %.
e.g. for a fraction of [tex]\frac{17}{100}[/tex], the decimal is 0.17 and the percent is 17%.e.g. for a fraction of [tex]\frac{3}{100}[/tex], the decimal is 0.03 and the percent is 3%.What is the slope between the two points (2,8) ;(3,12)
Answer:
4
Step-by-step explanation:
If we have two points we can find the slope
m = ( y2-y1)/(x2-x1)
= (12-8)/(3-2)
= 4/1
= 4
how much does a customer save for buying a sound system marked $1,200 at a discount of 15%
Answer:
Step-by-step explanation:
Mp=$1200
Let sp be x
SP=MP-discount% of MP
x=1200-15/100 * 1200
x=120000-18000/100
x=102000/100
x=1020
the amount of money person saves=MP-SP
=$1200-$1020
=$180
therefore he saves $180
HELPPPPPPPPPPPPPPPP!!!!!!
Answer:
70.2 degrees
Step-by-step explanation:
[tex]\arccos \left(\frac{19}{56}\right)=1.22463\ = \quad \begin{pmatrix}\mathrm{Degrees:}&70.17^{\circ \:}\end{pmatrix}[/tex]
Convert to scientific notation: 0.000112
Answer:
Answer is=112power -4
please make me brainlest pls
Answer:
[tex]10^{-4}[/tex]x 1.12
Step-by-step explanation:
4 times to the right
Choose 3 values that would make this inequality true. n - 3 ≤ 10
14
15
5
10
22
13
30
Answer:
5, 10 and 13
Step-by-step explanation:
5 - 3 = 2 < 10
10 - 3 = 7 < 10
13 - 3 = 10 = 10
Two buses leave towns 520 kilometers apart at the same time and travel toward each other. One bus travels 16 km/h slower than the other. If they meet in 2 hours, what is the rate of each bus?
Answer:
122 km/h
138 km/h
Step-by-step explanation:
distance = speed * time
One bus travels 16 km/h slower than the other
(s * 2) + (s - 16)2 = 520
2s + 2s - 32 = 520
4s = 552
s = 552/4
s = 138 km/h
s - 16 = 122 km/h
One of the legs of a right triangle measures 16 cm and the other leg measures 8 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
17.9
Step-by-step explanation:
Use the Pythagorean theorem, c²= a² + b². We can rewrite it as c = √(a² + b²), a=16 and b=8. Plug it in as c = √(16² + 8²) then simplify.
c = √(16² + 8²)
c = √(256 + 64)
c = √320
c≈17.9 (rounded to the nearest tenth)
Megan worked 20 hours last week. This
week she worked 80% more hours. How
many more hours did she work this week 2
Answer:
16 more hours for a total of 36 hours.
Step-by-step explanation:
C= 20 × .8
C= 16
T= 20 + C
T = 20 + 16
T = 36
Which is the better value for money 250g of coffee R12,35 or 450g of the same coffee at R21,95
Answer:
450g coffee or 21.95$ coffee
Step-by-step explanation:
again, divide whichever pair you want to and you still have the same answer whether it is less or more: 450/250 is math would be 9/5 and 21.95/12.35 is 1.77732793522. so if we find the true value of 9/5, which is 1.8, and since it is more that the original price that means the more coffe you get, the cheaper it gets (basically all of life is like this), so the 450 g coffee is worth alot less than and is bigger than the 250 g coffee
Please answer this I am to lazy to think right now
QUESTION:- WHICH FRACTION IS THE RECIPROCAL OF [tex] \frac{4}{3}[/tex]
[tex]RECIPROCAL = \frac{3}{4} [/tex]
what is the answer to this question
Answer: Your Answer to this question is C. Can you mark me as Brainliest and a thanks plss!!
A small country had a population of 7.1 x 10° in 1990. Since then, the original population has doubled, and an additional 7.7 x 1010 people have immigrated into the country. What is the population of the country now? The population is A x 10 where
Answer:
[tex]21.9 * 10^{10}[/tex] Population of the Country Now .
Step-by-step explanation:
According to the Question,
Given, A small country had a population of [tex]7.1 * 10^{10}[/tex] in 1990. Since then, the original population has doubled Thus The Population as of Now is [tex]2*7.1 * 10^{10} =[/tex] [tex]14.2 * 10^{10}[/tex] And [tex]7.7 * 10^{10}[/tex] people have immigrated into the country Thus, The New Population of the Country is [tex]14.2 * 10^{10} + 7.7 * 10^{10} =[/tex] [tex]21.9 * 10^{10}[/tex] .23
1 Which of the following numbers makes
the inequality below true?
2.5p < 14
Ap=5
Bp=6
cp=7
Dp = 8
lo What is the value of n in the countion
Answer:
A. p=5
Step-by-step explanation:
2.5x5=12.5
The rest are over 14
Hope this helps! :)
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
Answer:
B. 489.8 ft²
Step-by-step explanation:
Lateral surface of the cylinder = 2πrh
Where,
radius (r) = 6 ft
height (h) = 13 ft
Let π = 3.14
Plug in the values into the formula
Lateral surface of the cylinder = 2*3.14*6*13
Lateral surface of the cylinder = 489.8 ft²
salma is 1.45 meters tall. at 3p.m she measures the length of a tree's shadow to 29.35 meters. she stands 24.3 meters away from the tree, so that the tip of her shadow meets the tip of the treels shadow. find the height of the tree to the nearest hundreth of a meter.
Answer:
23.67
Step-by-step explanation:
Answer:
kimjnuhbygvtcfrdxe
Step-by-step explanation:
How do you do an explicit formula for a geometric problem
Answer:
State the initial term.
Find the common ratio by dividing any term by the preceding term.
Substitute the common ratio into the recursive formula for a geometric sequence.
Click on the measure of the gangle.
Answer:
34
Step-by-step explanation:
The bottom line is at 180
The top line is at 146
180-146 =34
Suppose 56% of recent college graduates plan on pursuing a graduate degree. Twelve recent college graduates are randomly selected.
a. What is the probability that no more than three of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
b. What is the probability that exactly eight of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)
c. What is the probability that at least six but no more than ten of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)