Answer:
150
Step-by-step explanation:
Given the following parameters;
Time, T = 150mins
Cooker setting, H = 7
Since the time for a pot of water to boil is inversely proportional to the cooker setting;
[tex]T * 1/H[/tex]
[tex]T = K/H[/tex] ........equation 1
Where, K is the constant of proportionality.
Substituting the parameters into the equation 1, we have;
150 = K/7
K = 150*7
K = 1050
To find the cooker setting at 7mins;
[tex]T = K/H[/tex]
H = K/T
H = 1050 ÷ 7
H = 150.
Hence, the cooker setting must be at 150.
Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model:
P(t) =
d
1 + ke−ct
where c, d, and k are positive constants. For a certain fish population in a small pond d = 1400, k = 13, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0.
(a) How many fish were originally put in the pond?
Correct: Your answer is correct.
fish
(b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.)
10 years Fish
20 years fish
30 years fish
Answer:
a) 19,600 fishes were originally put in the pond.
b) Population of fishes after 10 years = 3,863
Population of fishes after 20 years = 1,733
Population of fishes after 30 years = 1,403
Step-by-step explanation:
The population follows a logistic model
P(t) = d (1 + ke⁻ᶜᵗ)
For a fish pond,
d = 1400, k = 13, c = 0.2
Inserting the values of these constants
P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)
a) How many fish were originally put in the pond?
At the start of the whole thing, t = 0
P(t=0) = 1400 (1 + 13 e⁰) = 1400 × 14 = 19,600
Hence, 19,600 fishes were originally put in the pond.
b) Find the population after 10, 20, and 30 years.
P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)
At t = 10, 0.2t = 0.2 × 10 = 2
P(t=10) = 1400 (1 + 13e⁻²) = 1400 (1 + 1.759) = 3,863.1 = 3,863
At t = 20, 0.2t = 0.2 × 20 = 4
P(t=20) = 1400 (1 + 13e⁻⁴) = 1400 (1 + 0.238) = 1,733.3 = 1,733
At t = 30, 0.2t = 0.2 × 30 = 6
P(t = 30) = 1400 (1 + 13e⁻⁶) = 1400 (1 + 0.00248) = 1,403.47 = 1,403
Hope this Helps!!
20 POINTS A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situation?
A.2 x minus y = negative 6 and 3 x minus y = negative 5
B.2 x minus y = negative 3 and 3 x minus y = negative 5
C.2 x minus y = negative 6 and x minus 3 y = 5
D.2 x minus y = negative 3 and x minus 3 y = 5
Answer:
A.2 x minus y = negative 6 and 3 x minus y = negative 5
Step-by-step explanation:
A ) 2x-y=-6, and 3x-y=-5
Consider the provided information.
First convert the statement into mathematical representation.Consider the smaller number is x and the larger number is y.
y, is equal to twice the sum of a smaller number and 3.
This information can be written as: y=2(x+3)
The larger number is also equal to 5 more than 3 times the smaller number.
This information can be written as: y=5+3x
Answer:
A ) 2x-y=-6, and 3x-y=-5
Step-by-step explanation:
ABC
ABCD ]````````````````````` .```````````````````[
Answer:
B then C
Step-by-step explanation:
First screenshot:
Shape B because the net has a square base.
Second screenshot:
It is C
C does not make a cube
PLS HELP 20 POINTS
Find the volume of a pyramid with a square base, where the perimeter of the base is
19.8 m and the height of the pyramid is 24.2 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:197.7m^3
Step-by-step explanation:
Area of base:
B=24.5025
h=24.2
V=1/3(24.5025)(24.2)
197.6535
V≈197.7m^3
Answer:
197.7m
Step-by-step explanation:
Please help! Correct answer only, please! The cafeteria manager at a middle school wanted to keep track of how many student breakfast and lunches were sold on a Monday. A. B. C. D.
Answer:
Hello There Again. The Correct answer is C.
Explanation: Because it shows that the numbers need to be least median then greater of the breakfast lunch.
Hope It Helps! :)
A particular group of men have heights with a mean of 181 cm and a standard deviation of 6 cm. Earl had a height of 196 cm. a. What is the positive difference between Earl's height and the mean? b. How many standard deviations is that [the difference found in part (a)]? c. Convert Earl's height to a z score. d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Earl's height usual or unusual?
Answer:
a. 15
b. based on the result of part a, 15 standard deviation above the mean.
c. 2.5
d. Earl's height is unusual
Step-by-step explanation:
We have that "x" would be the height of Earl = 196, the mean m = equals 181 and the standard deviation (sd) = 6, now:
a. the positive difference between the mean and Earl's height:
D = x - m
D = 196 - 181 = 15
b. based on the result of part a, 15 standard deviation above the mean.
c. The z value is given by:
z = x - m / sd
replacing:
z = (196 - 181) / 6
z = 2.5
d. the z-score is unusual since the value of z is 2.5 which is a value greater than than 2 standard deviations above the mean, which means that Earl's height is unusual
The distance traveled varies directly with the time spent in motion wh
If d represents the distance traveled and t represents time, which eq
If you travel 150 miles in 4 hours, what is the constant of variation?
If you continue traveling at a constant speed, how long will it take to
an hour.
about
hours
*
Step-by-step explanation:
The distance traveled varies directly with the time spent in motion. If d is distance and t is time taken. Then,
[tex]d\propto t[/tex]
or
[tex]d=kt[/tex]
k is the constant of variation
If d = 150 miles and t = 4 hours
[tex]k=\dfrac{d}{t}\\\\k=\dfrac{150}{4}\\\\k=37.5\ mph[/tex]
In ΔKLM, the measure of ∠M=90°, MK = 2.7 feet, and KL = 6.6 feet. Find the measure of ∠L to the nearest degree.
Answer:
24.15° = 24° to the nearest degree
Step-by-step explanation:
If we draw the triangle we would see that the KL is the longest side and the hypothenus;
Also MK would-be the height and ML is the base of the triangle.
Since L and M are the angles at the base;
From Trigonometry Sin L = MK/ KL
= 2.7/6.6
L = Sin^{-1} (2.7/6.6)
L = Sin^{-1} (0.4091)
=24.15°
Note : sin a = height/ longest side
= Opposite/hypothenus
Select four statements from the invertible matrix theorem and show that all four statements are true or false
This learning module introduced the invertible matrix theorem. This theorem is a collection of 12 equivalent statements. This means that when one statement in the theorem is true, all statements in the theorem are true. Similarly, when one statement in the theorem is false, all statements are false. For your initial post, propose a specific n x n matrix A, where n >= 3. Select four statements from the invertible matrix theorem and show that all four statements are true or false, depending on the matrix you selected. Make sure to clearly explain and justify your work. Also, make sure to label your statements using the notation used in the notes (e.g., part (a), part (f), etc.).
Theorem (The Invertible Matrix Theorem): Let A be an n x n matrix. Then the following statements are equivalent:
A is an invertible matrix.
A is row equivalent to the n x n identity matrix.
A has n pivot positions.
The equation Ax = 0 has only the trivial solution.
The columns of A form a linearly independent set.
The linear transformation x à Ax is one-to-one.
There is an n x n matrix C such that CA = I.
There is an n x n matrix D such that AD = I.AT is an invertible matrix.
Answer:
A) A is an invertible matrix ( TRUE )
B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )
C ) The equation Ax = 0 has only the trivial solution ( TRUE )
D ) The columns of A form a linearly independent set ( TRUE )
Step-by-step explanation:
Assuming a matrix A
[tex]\left[\begin{array}{ccc}1&2&1\\-1&0&3\\4&1&5\end{array}\right][/tex]
det A = 1 [ 0 -3 ] + 2 [12 + 5 ] + 1[-1]
= -3 + 34 -1 = 30 ≠ 0
THEREFORE det A = 30 ≠ 0
Attached is the detailed solution of the given statements above
A large game cube with a three inch side length is wrapped with shrink wrap. How many square centimeters of shrink wrap will be used to wrap ten game cubes?
Answer:
see below
Step-by-step explanation:
cube has 6 square faces so 6*s*s
s =3 in =3*2.54 cm = 7.62 cm
1 in = 2.54 cm
1 cube needs 6*7.62² = 348.3864 cm²
10 cubes = 10*348.3864 =3483.864 cm²
Factor 24g - 36h. Remember that your answer needs to be factored completely.
Answer:
The completed factor is [tex]=12(2g- 3h)[/tex]Step-by-step explanation:
To factor the expression we need to look for a value that is unique to both terms in the expression.
Given the expression
[tex]24g - 36h[/tex]
The available factors common to both terms are 2,3,4,6,8,12. but since we are expected to factor the expression completely we will use the greatest common factor (gcf) to find the solution
The greatest but common factor is 12, hence we have
[tex]=12(2g- 3h)[/tex]
A vertical right circular cylindrical tank measures 20 ft high and 12 ft in diameter. It is full of liquid weighing 62.4 lb divided by ft cubed. How much work does it take to pump the liquid to the level of the top of the tank?
Answer:
Step-by-step explanation:
Work done is given as the product of force and distance.
The liquid in the cylindrical tank weighs 62.4 lb/ft^3.
This means that each ft^3 of the tank has 62.4 lb of the liquid.
To find the wight of the liquid in the entire tank, we multiply 62.4 by the volume of the cylindrical tank.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r is its radius and h is its height
The radius of the tank is 6 ft (since its diameter is 12 ft) and its height is 20 ft.
Therefore, the weight of the liquid in the tank is given as:
[tex]V = \pi * 6^2 * 20 = 2261.95 lb[/tex]
This weight is a force.
The height of the tank is 20 ft.
Therefore, the work done in pumping the liquid to the top of the tank is:
W = 2261.95 * 20 = 45239 ft.lb
Given the functions f(x) = 7x + 13 and g(x) = x + 2, which of the following functions represents f[g(x)] correctly?
Answer:
f[g(x)]= 7x + 27
Step-by-step explanation:
g(x) = x + 2,
f(x) = 7x + 13,
f[g(x)] means you substitute the value of g(x) into the variable of f(x);
Which is 7( x+2) + 13 = 7x +14 +13
= 7x + 27
Whats the answer according to the image ?
A company that produces fine crystal knows from experience that 17% of its goblets have cosmetic flaws and must be classified as "seconds." (Round your answers to four decimal places.)(a)Among seven randomly selected goblets, how likely is it that only one is a second
Answer:
0.3891 = 38.91% probability that only one is a second
Step-by-step explanation:
For each globet, there are only two possible outcoes. Either they have cosmetic flaws, or they do not. The probability of a goblet having a cosmetic flaw is independent of other globets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
17% of its goblets have cosmetic flaws and must be classified as "seconds."
This means that [tex]p = 0.17[/tex]
Among seven randomly selected goblets, how likely is it that only one is a second
This is P(X = 1) when n = 7. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{7,1}.(0.17)^{1}.(0.83)^{6} = 0.3891[/tex]
0.3891 = 38.91% probability that only one is a second
In circle Qwith the measure of minor arc PR= 70°, find m/PSR.
Answer: 290 degrees
Step-by-step explanation:
subtract the minor arc's measure from 360 to get the major arc's measure
If your customers are satisfied 11 out of 15 times how many are satisfied If 350 people come in on Black Friday
Answer:
257 people are satisfied
Step-by-step explanation:
11/15 is the fraction that are satisfied
11/15 * 350 =256.6(repeating)
Rounding to the nearest whole person
257 people are satisfied
The total surface area of a right circular cylinder is 84 pie cm square and the altitude is 11 cm .find the radius of the base
Answer:
r = 3cm
Step-by-step explanation:
Use the formula for the surface area of a cylinder and solve to obtain r=3cm
Hence radius of base is 3 cm of right circular cylinder.
What is a right circular cylinder?The cylinder is known as a right circular cylinder when the axis (one of the rectangle's sides) is perpendicular to the radius ((r)). The base and top of the right circular cylinder are both round and parallel to one another. The general formula for the total surface area of a cylinder is T. S. A. =[tex]2\pi rh+2\pi r^{2} .[/tex]
How to solve?Given total surface area of right circular cylinder =84[tex]\pi cm^{2}[/tex]
Using formula for right circular cyinder =.[tex]2\pi rh+2\pi r^{2} .[/tex]=84
and height=11 cm
[tex]2\pi r11+2\pi r^{2} =84.\pi[/tex]
⇒[tex]11r+ r^{2} =84/2[/tex]
⇒[tex]11r+ r^{2} =42[/tex]
⇒[tex]r^{2} +11r-42=0[/tex]
⇒r = [tex]\frac{-11+-\sqrt{11^{2}-4(1)42 } }{2}[/tex]
⇒r=[tex]\frac{-11+-17}{2}[/tex]
⇒r=3,-1
Hence radius of base is 3 cm as value can't be negative .
Learn more about surface area of cylinder https://brainly.com/question/12763699
#SPJ2
The domain of a function is
Answer:
The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
Step-by-step explanation:
I hope this helped ;)
if sin B=8/17 WHAT IS TAN B?
Answer:
In first quadrant, [tex]\tan B=\frac{8}{15}[/tex]
In second quadrant, [tex]\tan B=\frac{-8}{15}[/tex]
Step-by-step explanation:
Given: [tex]\sin B=\frac{8}{17}[/tex]
To find: [tex]\tan B[/tex]
Solution:
Trigonometry explains the relationship between the sides and the angles of the triangle.
Here,
[tex]\sin B=\frac{8}{17}[/tex]
So, B can be in first or second quadrant as sine is positive both first and second quadrants.
Cosine and tangent are positive in first quadrant but negative in second quadrant.
In first quadrant:
[tex]\cos B=\sqrt{1-\sin ^2B}=\sqrt{1-\left ( \frac{8}{17} \right )^2}=\sqrt{1-\frac{64}{289}}=\sqrt{\frac{225}{289}}=\frac{15}{17}[/tex]
So, [tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{15}{17}}=\frac{8}{15}[/tex]
In second quadrant:
[tex]\cos B=-\sqrt{1-\sin ^2B}=-\sqrt{1-\left ( \frac{8}{17} \right )^2}=-\sqrt{1-\frac{64}{289}}=-\sqrt{\frac{225}{289}}=\frac{-15}{17}[/tex]
[tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{-15}{17}}=\frac{-8}{15}[/tex]
Michael is making a big batch of granola bars to bring to his soccer game. The oats in the granola bars contain 568.7 grams of carbohydrates.
A 2-column table with 3 rows titled Nutritional Facts Oats (1 cup). Column 1 has entries Calories, Carbohydrates, Protein. Column 2 has entries 607, 103.4 grams, 26.3 grams.
How many cups of oats did Michael use in his recipe?
0.415 cups
0.55 cups
4.15 cups
5.5 cups
Answer:
5.5
Step-by-step explanation:
From the table; one cup of oat contains 103.4 carbohydrates.
568.7/103.4 = 5.5 cups
The baseball team ordered 140 T-shirts to sell at the school fair. Of those T-shirts, 50% are white, 20% are blue, 15% are green, 10% are red, and 5% are black. How many black T-shirts did the baseball team order? How many red T-shirts?
Answer:
The team ordered 7 black T-shirts.
The team ordered 14 red T-shirts.
Step-by-step explanation:
The team ordered 140 T-shirts.
How many black T-shirts did the baseball team order?
Of those, 5% are black.
0.05*140 = 7
The team ordered 7 black T-shirts.
How many red T-shirts?
Of those, 10% are red.
0.1*140 = 14
The team ordered 14 red T-shirts.
how much of other chemicals must be evaporated from 400grams of a hand sanitizer that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? correct your answer to the nearest whole number
Answer:
llolololol
Step-by-step explanation:
Answer:80 grams
Step-by-step explanation:
Which is the solution to the linear equation? 2/3 x-1/2=1/3+5/6x
Answer: X = -5
Step-by-step explanation:
1) Multiply both sides by 6, which is 4x - 3 = 2 + 5x
2) Move the terms, 4x - 5x = 2 + 3
3) Combine like terms, -x = 5
4) Multiply both sides by -1, x = -5
A distribution consists of three components with frequencies 200,250 and 300 having means 25,10,and 15 and standard deviations 3,4, and 5 respectively.Calculate the mean and standard deviation.
Answer:
The mean and standard deviation of the combined distribution is 16 and 7.192 respectively.
Step-by-step explanation:
We have given that a distribution consists of three components with frequencies 200, 250, and 300 having means 25, 10, and 15 and standard deviations 3, 4, and 5 respectively.
And we have to find the mean and standard deviation of the combined distribution.
Firstly let us represent some symbols;
[tex]n_1[/tex] = 200 [tex]\bar X_1[/tex] = 25 [tex]\sigma_1[/tex] = 3
[tex]n_2[/tex] = 250 [tex]\bar X_2[/tex] = 10 [tex]\sigma_2[/tex] = 4
[tex]n_3[/tex] = 300 [tex]\bar X_3[/tex] = 15 [tex]\sigma_3[/tex] = 5
Here, [tex]\bar X_1, \bar X_2 , \bar X_3[/tex] represent the means and [tex]\sigma_1,\sigma_2,\sigma_3[/tex] represent the standard deviations.
Now, as we know that Mean of the combined distribution is given by;
[tex]\bar X = \frac{n_1 \times \bar X_1+n_2 \times \bar X_2+n_3 \times \bar X_3}{n_1+n_2+n_3}[/tex]
Putting the above values in the formula we get;
[tex]\bar X = \frac{200 \times 25+250 \times 10+300 \times 15}{200+250+300}[/tex]
[tex]\bar X = \frac{5000+2500 +4500}{750}[/tex]
[tex]\bar X = \frac{12000}{750}[/tex] = 16
Similarly, the formula for combined standard deviation is given by;
[tex]\sigma = \sqrt{\frac{n_1\sigma_1^{2} + n_1(\bar X_1-\bar X)^{2}+n_2\sigma_2^{2} + n_2(\bar X_2-\bar X)^{2}+n_3\sigma_3^{2} + n_3(\bar X_3-\bar X)^{2} }{n_1+n_2+n_3} }[/tex]
[tex]\sigma = \sqrt{\frac{(200 \times 3^{2}) + 200 \times (25-16)^{2}+(250 \times 4^{2}) + 250 \times (10-16)^{2}+(300 \times 5^{2}) + 300 \times (15-16)^{2} }{200+250+300} }[/tex]
[tex]\sigma = \sqrt{\frac{1800 + (200 \times 81)+4000 + (250 \times 36)+7500 +( 300 \times 1) }{750} }[/tex]
[tex]\sigma = \sqrt{\frac{1800 + 16200+4000 + 9000+7500 +300 }{750} }[/tex]
[tex]\sigma = \sqrt{\frac{38800 }{750} }[/tex] = 7.192
Hence, the mean and standard deviation of the combined distribution is 16 and 7.192 respectively.
Evaluate Combination (6,6)
Answer:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
On this case n =6 and x =6 we got:
[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]
Step-by-step explanation:
The utility for the combination formula is in order to find the number of ways to order a set of elements
For this case we want to find the following expression:
[tex] 6C6[/tex]
And the general formula for combination is given by:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
On this case n =6 and x =6 we got:
[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]
wirk out the values of 5x-2y when x=-2 and y = -2
Step-by-step explanation:
5x - 2y
5(-2) - 2(-2)
-10 + 4
= - 6
The diameter of the container is 13 centimeters and
its height is 24 centimeters. Determine, in terms of
I, the volume of the ovlinder, in cubie centimeters,
Please answer this correctly
Answer:
3769.57
Step-by-step explanation:
the perimeter of semicircle is
P = d + πd/2
251.86 = d + (3.14d/2)
multiply both side with 2
503.72 = 2d + 3.14d
503.72 = 5.14 d
d = 98 miles
d is diameter, then the radius is 98 : 2 = 49
Area of semicircle
A = ½ π r²
A = 0.5 x 3.14 x 49²
A = 3769.57 miles²
Answer: 3769.57 miles²
Step-by-step explanation:
The perimeter of the semi circle is the sum of the curve and the diameter.
Perimeter of curve
[tex]\dfrac{1}{2}C=\dfrac{1}{2}2\pi r\\\\\\.\quad =\pi r\\[/tex]
Diameter of the semi circle = 2r
[tex]P = \pi r+2r\\\\\\251.86=r(\pi +2)\\\\\\\dfrac{251.86}{\pi +2}=r\\\\\\\dfrac{251.86}{5.14}=r\\\\\\49=r[/tex]
Area of the curve
[tex]\dfrac{1}{2}A=\dfrac{1}{2}\pi r^2\\\\\\.\quad =\dfrac{1}{2}(3.14)(49)^2\\\\\\.\quad =\large\boxed{3769.57}[/tex]
What is the conjugate
√8-√9
Answer:
[tex]\frac{-1}{(\sqrt{8}+\sqrt{9} )}[/tex]
Answer:
the water here is wet.
Step-by-step explanation: