Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
Find the volume of the figure. Express answers in terms of t, then round to the nearest whole number
Please help :)
Answer:
729π ft³
Step-by-step explanation:
Applying,
Volume of a cone
V = πr²h/3.............. Equation 1
Where r = radius of the base, h = height, π = pie
From the question,
Given: r = 9 ft, h = 27 ft
Substitite these values into equation 1
V = π(9²)(27)/3
V = 729π ft³
Hence the volume of the figure in terms of π is 729π ft³
Which of the following is a like radical to cube rt of 7x
Answer:
[tex]\sqrt[3]{7x}[/tex]
Step-by-step explanation:
Given
[tex]7x[/tex]
Required
The radical statement
Cube root is represented as:
[tex]\sqrt[3]{}[/tex]
Considering [tex]7x[/tex], the expression is:
[tex]\sqrt[3]{7x}[/tex]
I need help nowww!! 16 points
Answer:
A: x = 0
B: x = All real numbers
Step-by-step explanation:
A.
Any number to the power of (0) equals one. This applies true for the given situation; one is given an expression which is as follows;
[tex](6^2)^x=1[/tex]
Simplifying that will result in;
[tex]36^x=1[/tex]
As stated above, any number to the power of (0) equals (1), thus (x) must equal (0) for this equation to hold true.
[tex]36^0=1\\x=0[/tex]
B.
As stated in part (A), any number to the power (0) equals (1). Therefore, when given the following expression;
[tex](6^0)^x=1[/tex]
One can simplify that;
[tex]1^x=1[/tex]
However, (1) to any degree still equals (1). Thus, (x) can be any value, and the equation will still hold true.
[tex]x=All\ real \ numbers[/tex]
HELP HELP HELP MATH⚠️⚠️⚠️⚠️⚠️
Find four consecutive integers with the sum of 2021
Answer:
This problem has not solution
Step-by-step explanation:
lets the integers be:
x
x+1
x+2
x+3
so:
x+(x+1)+(x+2)+(x+3)=2021
x+x+x+x+1+2+3=2021
4x+6=2021
4x=2021-6=2015
x=2015/4=503.75
x is not a integer
One-ninth of all sales at a local Subway are for cash. If cash sales for the week were $690, what were
Subway's total sales?
Select one:
O a. $22,600
O b. $2,611
O c. $6,210
O d. $2,610
e. None of these
Answer:
c. $6,210Step-by-step explanation:
Total sales = x
x*1/9 = 690x = 690*9x = 6210Correct choice is C
A storage box with a square base must have a volume of 80 cubic centimeters. The top and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Find the dimensions that will minimize cost. (Let x represent the length of the sides of the square base and let y represent the height. Round your answers to two decimal places.) x
Answer:
Box dimensions:
x = 3.42 cm
y = 6.84 cm
C(min) = 14.04 $
Step-by-step explanation:
We need the surface area of the cube:
S(c) = 2*S₁ ( surface area of top or base) + 4*S₂ ( surface lateral area)
S₁ = x² 2*S₁ = 2*x²
Surface lateral area is:
4*S₂ = 4*x*h V(c) = 80 cm³ = x²*h h = 80/x²
4*S₂ = 4*80/x
4*S₂ = 320 / x
Costs
C (x) = 0.2* 2*x² + 0.1 * 320/x
Taking derivatives on both sides of the equation we get:
C´(x) = 0.8*x - 32/x²
C´(x) = 0 0.8*x - 32/x² = 0
0.8*x³ - 32 = 0 x³ = 32/0.8
x³ = 40
x = 3.42 cm
h = 80/(3.42)² h = 6.84 cm
To find out if x = 3.42 brings a minimum value for C we go to the second derivative
C´´(x) = 64/x³ is always positive for x > 0
The C(min) = 0.4*(3.42)² + 32/(3.42)
C(min) = 4.68 + 9.36
C(min) = 14.04 $
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green
Answer:
The probability that exactly 12 buyers would prefer green
=0.00555
Step-by-step explanation:
We are given that
p=50%=50/100=0.50
n=14
We have to find the probability that exactly 12 buyers would prefer green.
q=1-p
q=1-0.50=0.50
Using binomial distribution formula
[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]
[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]
[tex]P(x=12)=0.00555[/tex]
Hence, the probability that exactly 12 buyers would prefer green
=0.00555
In the diagram below, POR is a diameter, <QPR is a°,<PRS is (4a+12)°. find the value of a
Answer:
22=4
Step-by-step explanation:
0977-=ytb
2.6.58
The lot in the figure shown, except for the house, shed, and driveway, is lawn. One bag of lawn fertilizer
costs $15.00 and covers 3,000 square feet.
Please help :)
Answer:
50 bags ;
£750
Step-by-step explanation:
The dimension of the rectangular lawn is 500ft by 300 ft
The area of the lawn an e obtained thus :
Area of rectangle = Length * width
Area of rectangle = 500 ft * 300 ft
Area of rectangle = 150000 feets
1 bag of fertilizer covers 3000 feets
The minimum bags of fertilizer required :
Area of rectangle / Area covered by 1 bag of fertilizer
Minimum bags of fertilizer required :
(150,000 / 3000) = 50 bags
50 bags of fertilizer
Cost per bag = 15
Total cost = 15 * 50 = £750
We have two circles A and X. The radius and perimeter of the circle A are b and c respectively.
The radius and perimeter of the circle X are y and z respectively. Consider the following ratios
K=c/b and L=Z/y.
Which of the following statements is true? *
K>L
K
K=L
K=2L
Answer:
[tex]K = L[/tex]
Step-by-step explanation:
Given
Circle A
[tex]r = b[/tex] --- radius
[tex]p = c[/tex] ---- perimeter
Circle B
[tex]r = y[/tex] --- radius
[tex]p =z[/tex] --- perimeter
[tex]K = \frac{c}{b}[/tex]
[tex]L = \frac{z}{y}[/tex]
Required
Select the true option
The perimeter of a circle is:
[tex]Perimeter = 2\pi r[/tex] ------ the circumference
So, we have:
[tex]c = 2\pi b[/tex] --- circle A
[tex]z = 2\pi y[/tex] --- circle B
Calculate K
[tex]K = \frac{c}{b}[/tex]
[tex]K = \frac{2\pi b}{b}[/tex]
[tex]K = 2\pi[/tex]
Calculate L
[tex]L = \frac{z}{y}[/tex]
[tex]L = \frac{2\pi y}{y}[/tex]
[tex]L = 2\pi[/tex]
So, we have:
[tex]K = L = 2\pi[/tex]
14. 14. If f(x)= sec^2x, thenf'(x)=
Answer:
1 (2) f(x) = 1 (3) 1< f(x) < 2 (4) f(x) greater than or equal to 2
Step-by-step explanation:
We know AM ≥ GM
(cos2x+sec2x )/2 ≥ √(cos2x sec2x)
(cos2x+sec2x ) ≥ 2√(cos2x (1/cos2x)
f(x) ≥ 2
Hence option (4) is the answer.
Expand 5(2x-1) please I need it for homework.
10x-5
Answer:
5(2x-1)
5*2x 5*-1
10x-5
Hey there!
5(2x - 1)
= 5(2x) + 5(-1)
= 10x - 5
Therefore, your answer should be: 5x - 5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A venture capital company feels that the rate of return (X) on a proposed investment is approximately normally distributed with mean 30% and standard deviation 10%.
(a) Find the probability that the return will exceed 55%.
(b) Find the probability that the return will be less than 25%
(c) What is the expected value of the return?
(d) Find the 75th percentile of returns.
Answer:
a) 0.0062 = 0.62% probability that the return will exceed 55%.
b) 0.3085 = 30.85% probability that the return will be less than 25%
c) 30%.
d) The 75th percentile of returns is 36.75%.
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.
Mean 30% and standard deviation 10%.
This means that [tex]\mu = 30, \sigma = 10[/tex]
(a) Find the probability that the return will exceed 55%.
This is 1 subtracted by the p-value of Z when X = 55. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 30}{10}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability that the return will exceed 55%.
(b) Find the probability that the return will be less than 25%
p-value of Z when X = 25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 30}{10}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085
0.3085 = 30.85% probability that the return will be less than 25%.
(c) What is the expected value of the return?
The mean, that is, 30%.
(d) Find the 75th percentile of returns.
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 30}{10}[/tex]
[tex]X - 30 = 0.675*10[/tex]
[tex]X = 36.75[/tex]
The 75th percentile of returns is 36.75%.
Lorena and Julio purchased a home for $205,950. Their loan amount was $164,760, and the assessed value is now $200,500. Their tax rate is 1.5%. How much will their monthly taxes be?
Answer:
Monthly taxes = $250.63 (Approx.)
Step-by-step explanation:
Given:
Amount of purchase = $205,950
Loan amount = $164,760
Assessed value = $200,500
Tax rate is 1.5%
Find:
Monthly taxes
Computation:
Tax always calculated on Assessed value
Annual tax amount = 200,500 x 1.5%
Annual tax amount = 3,007.5
Monthly taxes = Annual tax amount / 12
Monthly taxes = 3,007.5 / 12
Monthly taxes = 250.625
Monthly taxes = $250.63 (Approx.)
Consider the quadratic function y = 0.3 (x-4)2 - 2.5
Determine the axis of symmetry, x =
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
We have the quadratic function:
[tex]\displaystyle y=0.3(x-4)^2-2.5[/tex]
And we want to determine its axis of symmetry.
Notice that this is in vertex form:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola.
From our function, we can see that h = 4 and k = -2.5. Hence, our vertex is the point (4, -2.5).
The axis of symmetry is equivalent to the x-coordinate of the vertex.
The x-coordinate of the vertex is 4.
Therefore, the axis of symmetry is x = 4.
Solve. SHOW ALL YOUR WORK
2.51 * .2
77/ 1.2
Answer:
0.502
64.1666
Step-by-step explanation:
Detained explanation of the product operation and division operation is attached below.
2.51 * 0.2 = 0.502
(after multiplying) the number of decimal places of the town values is added and counted from the right in the product to place the data Comal point appropriately.
77/1.2 ; values were multiplied by 10 in other to obtain inter values for the denominator.
fill in the blink
Given ,Simplify ,BC=EF ,Multiplication Property of Equality ,Substitution Property of Equality AC=DF DE+EF=DF Reflexive Property of Equality Transitive Property of Equality ,Segment Addition Postulate, Division Property of Equality ,Addition Property of Equality, Distributive Property, Subtraction Property of Equality
Answer:
see below
Step-by-step explanation:
[tex] \displaystyle AB = DE[/tex]
[given]
[tex] \displaystyle \boxed{BC = EF}[/tex]
[given]
[tex] \displaystyle AB + BC = AC[/tex]
[segment addition Postulate]
[tex] \displaystyle \boxed{DE+ EF=DF}[/tex]
[segment addition Postulate]
[tex] \rm\displaystyle DE+ BC = AC \: \: \text{and} \: \: DE+ BC = DF[/tex]
[Substitution Property of Equality]
[tex] \displaystyle \boxed{AE= DE}[/tex]
[Proven]
FREE
Circle O has a circumference of approximately 250 ft.
What is the approximate length of the diameter, d?
O 40 ft
O 80 ft
O 125 ft
O 250 ft
Save and Exit
Next
Submit
Mark this and return
Answer:
Step-by-step explanation:
circumference = πd ≅ 250 ft
d ≅ 250/π ≅80 ft
rotation 180 degrees about the origin.
Answer:
Click the rotate 'button' twice.
Observe.
The rotate button is rotating the image about the orgin.
Answer:
Click the rotate 'button' twice.
Observe.
The rotate button is rotating the image about the orgin.
Step-by-step explanation:
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occur
Complete question is;
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occurs?
(a) A defective component will be detected only by the first inspector?
b) A defective component will be detected by exactly one of the two inspectors?
(c) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?
Answer:
A) 0.17
B) 0.34
C) 0
Step-by-step explanation:
a) We are told that the first inspector(A) detects 83% of all defectives that are present, and the second inspector(B) also does the same.
This means that;
P(A) = P(B) = 83% = 0.83
We are also told that at least one inspector does not detect a defect on 34% of all defective components.
Thus;
P(A' ⋃ B') = 0.34
Also, we now that;
P(A ⋂ B) = 1 - P(A' ⋃ B')
P(A ⋂ B) = 1 - 0.34
P(A ⋂ B) = 0.66
Probability that A defective component will be detected only by the first inspector is;
P(A ⋂ B') = P(A) - P(A ⋂ B)
P(A ⋂ B') = 0.83 - 0.66
P(A ⋂ B') = 0.17
B) probability that a defective component will be detected by exactly one of the two inspectors is given as;
P(A ⋂ B') + P(A' ⋂ B) = P(A) + P(B) - 2P(A ⋂ B)
P(A) + P(B) - 2P(A ⋂ B) ; 0.83 + 0.83 - 2(0.66) = 0.34
C) Probability that All three defective components in a batch escape detection by both inspectors is written as;
P(A' ⋃ B') - (P(A ⋂ B') + P(A' ⋂ B))
Plugging in the relevant values, we have;
0.34 - 0.34 = 0
Help me or ill fail plz
Answer:
1,108 in²
Step-by-step explanation:
SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)
+ (2×20×11)
= 240+320+108+440
= 1,108 in²
What is the domain of the function f(x) = (-5/6)(3/5)superscript x
Answer:
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]
Required
The domain
There are no undefined points such as denominator of x or square roots.
Hence, the domain is:
[tex]-\infty < x < \infty[/tex]
An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
Weight % of Total Underweight 2.5 Satisfactory 90.0 Overweight 7.5a) What is the probability of selecting and finding that all three bags are overweight?b) What is the probability of selecting and finding that all three bags are satisfactory?
Answer:
a) 0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) 0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
Step-by-step explanation:
The condition of the bags in the sample is independent of the other bags, which means that the binomial probability distribution is used 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.
a) What is the probability of selecting and finding that all three bags are overweight?
2.5% are overweight, which means that [tex]p = 0.025[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.025)^{3}.(0.975)^{0} = 0.000016[/tex]
0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) What is the probability of selecting and finding that all three bags are satisfactory?
90% are satisfactory, which means that [tex]p = 0.9[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.9)^{3}.(0.1)^{0} = 0.729[/tex]
0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
(3a+2b-4c)+(3a+2b-4c)
6
+
4
−
8
Step-by-step explanation:
Please mark me as brain list and please like my answer and rate also
Answer:
hope this will help you more
The formula for centripetal acceleration, a, is given by this formula, where v is the velocity of the object and r is the object’s distance from the center of the circular path:
A= V2/R
Solve the formula for r.
Answer:r=v^2/A
Step-by-step explanation: To solve for r means you have to isolate r on one side and put all the other terms on the other. To get r out from under the fraction, multiply both sides by r. This leaves:
A*r=v^2 so to isolate r, divide by A and get:
r=v^2/A.
Please help it’s a test and I can’t get logged out
Answer:
the anwer is B ( i mean second option)
And you can try it
you will find ;
[tex]y = \frac{x}{3} - 1[/tex]
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
For a popular Broadway music the theater box office sold 356 tickets at $80 a piece275 tickets at $60 a piece and 369 tickets at $ 45 a piece. How much money did the box office take in?
Answer:
Step-by-step explanation:
356 * 80 = 28 480
275 * 60 = 16 500
369 * 45 = 16 605
sum = $ 61 585
Drag the label to the correct location on the image
9514 1404 393
Answer:
-∞ < y ≤ 12
Step-by-step explanation:
The range is the vertical extent of the graph of the function. Here the function values range from -∞ to a maximum of about 12. An appropriate description is ...
-∞ < y ≤ 12
In the figure below. JLM is similar to JKN if JM=14 inches what is the length of JN
Answer:
Hello good evening friend
Let Y1 and Y2 denote the proportions of time (out of one workday) during which employees I and II, respectively, perform their assigned tasks. The joint relative frequency behavior of Y1 and Y2 is modeled by the density function.
f (y 1,y2)=y 1+y 2 o<=y 1<=1, 0<=y2<=1(0 elsewhere)
a. Find P (Y1< 1/2,y2>1/4)
b. Find P(Y 1+Y2<=1)
Are Y1 and Y2 independent?
(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,
{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}
Integrate the joint density over this region:
[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]
(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,
{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}
Integrate to get the probability:
[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]
Y₁ and Y₂ are not independent because
P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)
To see this, compute the marginal densities of Y₁ and Y₂.
[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]
[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]
[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]
but this clearly does not match the joint density.
