By using the shell method to find the volume of the solid generated when R is revolved about the y-axis is V = 2π∫3⁹(11−x0)x0(11−x0−dx)dx
The volume of a solid that is generated by rotating a region about a given axis is called the volume of revolution. One of the methods to find the volume of revolution is the shell method.
Let's consider the region R bounded by the curves y = 11−x, y = 0, x = 3, x = 9 and find its volume when it is revolved about the y-axis.
The first step is to sketch the region R in the xy-plane. The curves y = 11−x and y = 0 intersect at x = 11, y = 0. The region R is a trapezoid with height 11 and bases 3 and 9.
Next, we need to find the expression for the volume of a thin shell of thickness dx, whose axis is along the y-axis.
Let us consider a thin shell at x = x0. The height of the shell at x = x0 is given by 11−x0. The inner and outer radii of the shell are given by y = 11−x0 and y = 11−x0−dx respectively.
The volume of the shell is given by the formula:
=> V = 2π(y2−y1)x0 = 2π(11−x0)x0(11−x0−dx)
We can now integrate this expression over x0 to find the total volume of the solid.
The limits of integration are x0 = 3 and x0 = 9. The volume of the solid is given by:
V = 2π∫3⁹(11−x0)x0(11−x0−dx)dx
Solving this definite integral will give us the volume of the solid.
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if you add 21 to my number, multiply the result by 3, you will get 84 more than two thirds of my number. what is my number?
Answer:
9
Step-by-step explanation:
Let's suppose "my number" is x
If you add 21 to my number: 21 + x
Multiply the result by 3: 3(21+x)
You will get 84 more than two thirds of my number
[tex]3(21 + x) = 84 + \frac{2}{3} x \\ 63 + 3x = 84 + \frac{2}{3} x \\ \frac{7}{3} x = 21 \\ 7x = 63 \\ x = 9[/tex]
Therefore my number is 9
If you need any help with the algebra part feel free to let me know!
Hector pent $38. 45 for 2DVD the ale tax wa $2. 85, and he didn't have a coupon. Each DVD cot the ame amount. How much would each DVD cot?
Each DVD cost is $17.80
This is a simple equation
From the question we have the following information :
1. Total spent for 2 dvd ( before tax ) = $17.80
2. Sales Tax for those spending = $2.85
Let's call the cost of each DVD "x".
The total cost of both DVDs would be 2x.
We know that the total cost of both DVDs and the sales tax was $38.45, so we can set up an equation:
2x + $2.85 = $38.45
Solving for x:
2x = $38.45 - $2.85 = $35.60
x = $35.60 / 2 = $17.80
Hence from explanation above, each DVD cost $17.80.
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779/84 as a mixed number
Answer:
9 23/84
Step-by-step explanation:
divide then mulitply
suppose that mean retail price per gallon of regular grade gasoline 3.43 is with a standard deviation of and that the retail price per gallon has a bell-shaped distribution. note: please use empirical rule approximations for this problem. a. what percentage of regular grade gasoline sells for between and per gallon (to decimal)? b. what percentage of regular grade gasoline sells for between and per gallon (to decimal)? c. what percentage of regular grade gasoline sells for less than per gallon (to decimal)?
The 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).
Suppose that mean retail price per gallon of regular grade gasoline 3.43.
empirical rule explains that approximately 68%,95% and 99.7% of data lies between (µ ± 1*σ) ,(µ ± 2*σ) and (µ ± 3*σ) respectively.
⇒If some data {x} are normally distributed, the corresponding {z} will be normal with mean 0 and standard deviation 1 where the correspondence between the {x} and {z} is given by
z = [tex]\frac{x-\mu}{\sigma}[/tex]Such z's are called z-scores.
(µ ± 1*σ)=68%
(µ ± 2*σ)=95%
(µ ± 3*σ)=99.7%
a)
P(3.23<x<3.63) =[tex]P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ][/tex]
=P[( [tex]\frac{3.23-3.43}{0.10}[/tex] < z < [tex]\frac{3.63-3.43}{0.10}[/tex] ]
=P[-2 < z < 2 ]
=0.95
=95.0 %
b)
P(3.23<x<3.53) =[tex]P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ][/tex]
=P[( [tex]\frac{3.23-3.43}{0.10}[/tex] < z < ([tex]\frac{3.53-3.43}{0.10}[/tex] ]
=P[-2 < z < 1 ]
=0.815
=81.5 %
c)
P(x>3.53) =[tex]P[ z > \frac{x-\mu}{\sigma} ][/tex]
=P[ z > [tex]\frac{3.53-3.43}{0.10}[/tex] ]
=P[ z > 1 ]
=0.16
=16.0 %.
Therefore, 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).
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Compute the number of permutations of given set a = x | x is an integer and x2 < 16 , r =4
There are 840 permutations of the set a, taken 4 at a time.
What is integer ?
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
A permutation of a set is an arrangement of its elements in a specific order. To find the number of permutations of a set with n elements, taken r at a time, the formula is given by n! / (n - r)!, where n! is the factorial of n.
Given the set a = {x | x is an integer and x^2 < 16}, we can find the elements of the set:
x^2 < 16
x = ±1, ±2, ±3, ±4
So the set a has 8 elements: {-4, -3, -2, -1, 1, 2, 3, 4}.
The number of permutations of a set with 8 elements, taken 4 at a time, is given by 8! / (8 - 4)! = 8! / 4! = 40320 / 24 = 840.
Therefore, there are 840 permutations of the set a, taken 4 at a time.
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FIND AREA PLS HELP ASAP!!!
Area of a rhombus is half the product of its diagonals:
A = d₁d₂/2A = (3+3)(9+9)/2 = 54 units²Question 6Area of a trapezoid is the product of the height and half the sum of its bases:
A = (b₁ + b₂)h/2A = (17 + 29)*5/2 = 115 units²which number is the smallest? a. 4.38 × 103 b. 4.38 × 10–3 c. 4.38 × 10–2 d. 438 e. 4.38 × 102
After simplifying the number, the number 4.38 × 10^{–3} = 0.00438 is the smallest number. So the number b is the smallest number.
We simplify the numbers to find the smallest number.
The numbers are
a. 4.38 × 10^3
We can write 10^3 as 1000
Now the number is
= 4.38 × 1000
Multiply
= 4380
b. 4.38 × 10^{–3}
The number of times to divide the base number is indicated by negative power. For each power of 10, the decimal points are moved to the left when multiplying the integer by the negative power of 10.
So we can write that number as
= 4.38 × 1/1000
Simplify
= 0.00438
c. 4.38 × 10^{–2}
We can write that number as
= 4.38 × 1/100
Simplify
= 0.0438
d. 438
e. 4.38 × 10^2
We can write that number as
= 4.38 × 100
Multiply
= 438
We can see that the number 4.38 × 10^{–3} = 0.00438 is the smallest number.
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The complete question is:
Which number is the smallest?
a. 4.38 × 10^3
b. 4.38 × 10^{–3}
c. 4.38 × 10^{–2}
d. 438
e. 4.38 × 10^2
Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers.
1. ∃x(x2=−1)∃x(x2=−1)
2. ∃x∀y≠0(xy=1)∃x∀y≠0(xy=1)
3. ∀x∃y(x2=y)∀x∃y(x2=y)
4. ∃x∃y(x+y≠y+x)∃x∃y(x+y≠y+x)
5. ∃x∀y(xy=0)∃x∀y(xy=0)
6. ∀x∃y(x=y2)∀x∃y(x=y2)
7. ∀x∀y∃z(z=x+y2)∀x∀y∃z(z=x+y2)
8. ∀x≠0∃y(xy=1)∀x≠0∃y(xy=1)
9. ∃x(x2=2)∃x(x2=2)
10. ∀x∃y(x+y=1)∀x∃y(x+y=1)
11. ∃x∃y((x+2y=2)∧(2x+4y=5))∃x∃y((x+2y=2)∧(2x+4y=5))
12. ∀x∃y((x+y=2)∧(2x−y=1))
The truth value of the given statements if the universe of discourse of each variable is the set of real numbers are 1. false, 2. false, 3. true, 4. false, 5. false, 6. false, 7. true, 8. true, 9. false, 10. true, 11. true, and 12. true.
1. False. There is no real number x such that x^2 = -1.
2. False. For any x in the real numbers, there exists a y such that xy ≠ 1. For example, if x ≠ 0, then y = 1/x will satisfy xy ≠ 1.
3. True. For any real number x, the real number y = x^2 satisfies the equation x^2 = y.
4. False. For any x and y in the real numbers, x + y = y + x.
5. False. For any x in the real numbers, there exists a y such that xy ≠ 0. For example, if x ≠ 0, then y = 1/x will satisfy xy ≠ 0.
6. False. There is no real number y such that y^2 = -1.
7. True. For any x and y in the real numbers, the real number z = x + y^2 satisfies the equation z = x + y^2.
8. True. For any x ≠ 0 in the real numbers, the real number y = 1/x satisfies the equation xy = 1.
9. False. There is no real number x such that x^2 = 2.
10. True. For any x in the real numbers, the real number y = 1 - x satisfies the equation x + y = 1.
11. True. The solution to the system of equations x + 2y = 2 and 2x + 4y = 5 is x = -1 and y = 3.
12. True. For any x in the real numbers, the real number y = (1 - x)/2 satisfies the equation (x + y = 2) and (2x - y = 1).
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PLEASE HELP ME WITH THIS
Answer: 48 cups
Step-by-step explanation: The way to scale a recipe by number of servings is to multiply the original amount by the desired serving size and then divide by the original serving size.
someone help please. i need to turn this in tomorrow. Question is in the picture!
Answer:
0.35 mL
Step-by-step explanation:
There are 1000 mL in 1 Liter. 350 of 1000 is 0.35
an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?
Answer:
Step-by-step explanation:
an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?
find the size of the angle marked Q
please could you help me thank you very much
Answer:
Q=70
Step-by-step explanation:
（180-40）/2=70
Answer:
is that 70°
if it is then Q=70
Step-by-step explanation:
because an equilateral angles are the same
Simplify the given expression. Show all steps. Submit your handwritten work or use the equation editor to receive credit.
Answer:
[tex]\frac{1}{x^2}[/tex]
Step-by-step explanation:
first, simplify [tex](x^{10})^\frac{1}{5}[/tex] [tex]\frac{10}{1} =\frac{1}{5}[/tex] , 5 and 10 cancel each other, so [tex]\frac{2}{1}[/tex] or 2. [tex]x^2[/tex]
secondly, [tex]\sqrt{x^8}[/tex], we need to only do [tex]\sqrt{8}[/tex] which is 4, so answer is [tex]x^4[/tex].
then divide [tex]\frac{x^2}{x^4}[/tex] , minus 2 - 4= -2, [tex]x^-2[/tex]
but if there was any negative exponent in math it needs to be down so answer is [tex]\frac{1}{x^2}[/tex].
Answer:
1/x² = x^(-2)
Step-by-step explanation:
((x¹⁰)^(1/5))/sqrt(x⁸)
4 things are important to remember here :
when we put an exponent on an exponent, we multiply both exponents.when we multiply terms with the same base, we add the exponents, and when we divide, we subtract the exponents.a negative sign in the exponent means 1/...and a fraction as exponent is defined as[tex] {x}^{a \div b} = \sqrt[b]{ {x}^{a} } [/tex]
so, for example, a square root is the same as 1/2 as exponent.
now we can simplify.
let's start with the numerator :
(x¹⁰)^(1/5) = x^(10×1/5) = x²
then the denominator :
sqrt(x⁸) = x^(8×1/2) = x⁴
the whole fraction looks like
x²/x⁴
remember about the subtraction of exponents when dividing :
x²/x⁴ = x^(2-4) = x^-2 = 1/x²
FYI
when you remember, what an exponent actually is : the number how often the base had to be multiplied by itself, ...
x×x / x×x×x×x
the top 2 x can be reduced to 1 by division by 2 of the bottom x.
what is left is 1/x²
6 people equally share 56 gummy worms. how many gummy worms does each person get? (4 points)nine and one sixth gummy wormsnine and two sixths gummy wormsten and one sixth gummy wormsten and two eighths gummy worms
Each person get nine and two sixths gummy worms
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
Information about the problem:
Number of person = 6Total gummy worms = 56Calculating how many gummy worms each person get:
Gummy worms per person = 56/6
Gummy worms per person = 9.33
Rounding down = 9 gummy worms per person
Total gummies gave = 9 * 6
Total gummies gave = 54
Gummies left = 56 - 54
Gummies left = 2
Gummy worms per person = 9 2/6
Nine and two sixths gummy worms
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(3) The table shows some values of the linear
function f(n). Find the linear equation of f(n)
n f(n)
6 -1
4 2
2 5
The linear equation of f(n) can be written as mn + b, where m is the slope of the line and b is the y-intercept.
What is a linear equation?A linear equation is one that has the formula Ax + B = 0, where A and B are constants and x is a variable. When graphed, these equations produce a straight line, which is why they are termed linear equations. Linear equations are used to describe the connection between two variables known as the independent variable (x) and the dependent variable (y) (y). When the value of the independent variable is known, the equation may be used to discover the value of the dependent variable.
The linear equation of f(n) can be written as: f(n) = mn + b, where m is the slope of the line and b is the y-intercept.
To find the equation, we need to calculate the slope m and the y-intercept b. We can do this by using the given values of n and f(n).
First, let's calculate the slope m. We can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, we can use the points (6, -1) and (4, 2):
m = (2 - (-1))/(4 - 6) = 3/-2 = -1.5
Next, let's calculate the y-intercept b. We can use the formula b = y - mx, where (x,y) is a point on the line and m is the slope. In this case, we can use the point (2, 5):
b = 5 - (-1.5)(2) = 5 + 3 = 8
Therefore, the linear equation of f(n) is f(n) = -1.5n + 8.
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Which of these groups of values plugged into the TVM Solver of a graphing
calculator will return the same value for PV as the expression
($415)((1+0.003) 24-1)
(0.003)(1+0.003) 24
A. N=2; 1%-3.6; PV = ; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
B. N=24; 1%-0.3; PV = ; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=24; 1%-3.6; PV =; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
D. N=2; 1%-0.3; PV =; PMT=-415; FV=0; P/Y=12; C/Y=12; PMT:END
D. N = 24, I% = 3.6, PV =, PMT = -415, FV = 0, P/Y = 12, C/Y = 12, and PMT:END are the values in the group that would provide the same result as the given equation.
What in math is PV?The present value of a sum of money is its current value. For instance, the present value is what $110 is currently worth if you are promised $110 in a year.
In the TVM solver, we have;
I = The annual percentage rate
N = n × t
t = The number of years
PV = Present value
PMT = Payment
P/Y = Payments made annually = n
C/Y equals the number of compounding periods in a year.
The following is how the monthly payment formula is stated.
M = P(r/n)(1+r/n)ⁿˣⁿ/(1+r/n)ⁿˣⁿ-1
which gives,
P = M [(1+r/n)ⁿˣⁿ-1] / (r/n)(1+r/n)ⁿˣⁿ
Therefore, we get:
where:
M = PMT = -415
P = PV
r = I
P/Y = n = 12
Therefore,
0.003 = I/12
I = 0.003 × 12 = 0.036 = 3.6%
N = n×t = 24
P = (415)[(1+I/12)²⁴- 1] /(I/12)(1+I/12)²⁴
= ( 415) [(1+0.003)²⁴ - 1] / (0.003)(1+0.003)²⁴ = ?
The present value, PV, is the equation's value.
We have FV = 0 when payments are paid based on the PV.
The set of values with the same value as ($415)(1+0.003)24 - 1 / (0.003)(1+0,003)
24 has the following values when entered into a calculator's TVM solver: D. N = 24, I% = 3.6, PV =, PMT = -415, FV = 0 and PMT:END.
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The following list of prices is for a used original radio for a 1955 Thunderbird. The prices vary depending on the condition of the radio.
$210, $210, $320, $200, $300, $10, $340,
$300, $245, $325, $700, $250, $240, $200
b. Find the median of the radio prices.
c. Find the mode of the radio prices. (Place in ascending order.)
d. Find the four quartiles.
Q1 -
Q2 -
Q3 -
Q4 -
e. Find the interquartile range for this data set.
f. Find the boundary for lower outliers.
What is the lower outlier?
g. Find the boundary for upper outliers.
What is the upper outlier?
The answers to each part is given below.
What is a quartile?In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size.
The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic
Given is the list of prices for a used original radio for a 1955 Thunderbird. The prices vary depending on the condition of the radio.
$210, $210, $320, $200, $300, $10, $340, $300, $245, $325, $700, $250, $240, $200
We can write the sorted data as -
10, 200, 200, 210, 210, 240, 245, 250, 300, 300, 320, 325, 340, 700
{ b } - Median calculation
{n} = 14
Median = (x{n/2} + x{n/2 + 1})/2 = (245 + 250)/2 = 247.5
{ c } - Mode calculation
The mode is the value or values that occur most frequently in the data set. Count the number of times each value in a data set occurs. The mode is the data value with the highest count. We can write the mode as follows -
210, 200, 300
{ d } - Quartiles calculation
Quartiles mark each 25% of a set of data -
The first quartile Q1 is the 25th percentile : 210
The second quartile Q2 is the 50th percentile : 247.5
The third quartile Q3 is the 75th percentile : 320
{ e } - Interquartile range calculation
The interquartile range IQR is the range in values from the first quartile Q1 to the third quartile Q3. Find the IQR by subtracting Q1 from Q3.
IQR = Q3 - Q1
IQR = 320 - 210
IQR = 110
{ f } -
Lower Outlier Boundary : 45
{ e } -
Upper Outlier Boundary : 485
Therefore, the answers to each part is given above.
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The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in². The slant height of the pyramid is 6 in. What is the surface area of the pyramid? Enter your answer in the box. in²
Answer:
249.6 in^2
Step-by-step explanation:
Since it's an equilateral triangle as the base, all of the other faces will be the same equilateral triangle, so 62.4 x 4 gives you the answer.
 Which 3-dimensional figure is associated with the volume formula?
The 3-dimensional figure is associated with the Volume formula is B)Sphere.
What is volume?
The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.
Here the given volume is V= [tex]\frac{4}{3} \pi r^3[/tex]
In given formula we only have r which is radius. Then cylinder , Cone and prism have both radius and height.
Sphere does not have height and volume of the sphere is
=> V= [tex]\frac{4}{3} \pi r^3[/tex]
Hence the correct option is B) sphere.
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If you were comparing human organisms to cities, what would the atom be?
We can compare atom to the peoples that live, work and control the city.
What is atom?The smallest part of a substance that cannot be broken down chemically is called atom.Each atom has a nucleus (center) made up of protons (positive particles) and neutrons (particles with no charge). Electrons (negative particles) move around the nucleus.Given is you were comparing human organisms to cities.
Atom is important for the existence of human body. If the atoms would not be there, the human body would not exist. Similarly, a city exist because of the people living in the city. So, we can compare atom to the peoples that live, work and control the city.
Therefore, we can compare atom to the peoples that live, work and control the city.
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find 30% of 60
give simple working out pls :)
Step-by-step explanation:
To find 30% of 60, you can multiply 60 by 0.30.
Here's the calculation:
60 x 0.30 = 18
So, 30% of 60 is 18.
I REALLY NEED THIS ANSWERED
Brenda invests $4,848 in a savings account with an interest rate compounded semiannually. If the account balance after 6 years is $6,520.02, what is the interest rate?
(Hint: SADMEP-Do not round calculations until the final answer.)
Round your answer to the nearest percent. ( Two decimal places or a whole number percentage)
The interest rate is -17.72%
What is the interest rate?
The proportion of a loan that is charged as interest to the borrower is typically expressed as an annual percentage of the loan outstanding.
The formula for finding the interest rate is:
A = P * (1 + r/n)^(nt)
Where A is the end balance, P is the starting principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
Since the interest rate is compounded semi-annually, n = 2. And the starting principal is $4,848, t = 6 years. So the equation becomes:
$6,520.02 = $4,848 * (1 + r/2)^(2 * 6)
Now we'll isolate r by taking the natural logarithm of both sides:
ln(6520.02 / 4848) = ln((1 + r/2)^(2 * 6))
ln(6520.02 / 4848) = 12 * ln(1 + r/2)
Now we'll solve for r by dividing both sides by 12 and taking the exponential of the result:
r/2 = (ln(6520.02 / 4848) / 12)^(1/12) - 1
r = 2 * ((ln(6520.02 / 4848) / 12)^(1/12) - 1)
Finally, we'll convert the interest rate to a percentage by multiplying by 100:
r = (2 * ((ln(6520.02 / 4848) / 12)^(1/12) - 1)) * 100%
= (2 * ((ln(1.34814) / 12)^(1/12) - 1)) * 100%
= (2 * (0.113774 - 1)) * 100%
= (2 * -0.886226) * 100%
= -17.72452%
hence, the interest rate is -17.72%
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i am 1 mile in the oceam and wish to get to a town 3 miles down the coast which is very rocky. i need to swim to the shore and then walk along the shore. what point should i swim to along the shoreline so that the time it takes to get to town is a minimum? i swim 2 mph and walk 4 mph.
To minimize the time it takes us to get to the town, we should swim to a point that is √(1/14) miles from the town.
We can use the Pythagorean theorem to solve this problem. Let's assume the point where we swim to shore is x miles from the town.
The distance we need to swim is √(1^2 + x^2) = √(x^2 + 1)
The distance we need to walk is 3-x
The total time it takes us to get to the town is the sum of the time it takes us to swim and walk.
So, Time = (distance to swim)/(swimming speed) + (distance to walk)/(walking speed)
Time = √([tex]x^2[/tex] + 1)/2 + (3-x)/4
To minimize the time, we need to find the value of x that minimizes the expression above. To do this, we can take the derivative of the expression with respect to x and set it equal to zero:
d/dx (√( [tex]x^2[/tex] + 1)/2 + (3-x)/4) = 0
Expanding the derivative:
(x/(2√( [tex]x^2[/tex] + 1))) - 1/4 = 0
Solving for x, we get,
x/(2√([tex]x^2[/tex] + 1)) = 1/4
x = √([tex]x^2[/tex] + 1)/4
Squaring both sides, we get,
[tex]x^2[/tex] = ([tex]x^2[/tex] + 1)/16
15[tex]x^2[/tex] = x^2 + 1
14[tex]x^2[/tex] = 1
[tex]x^2[/tex] = 1/14
Taking square root, we get,
x = ± √(1/14)
Since x must be positive, we have x = √(1/14)
So, to minimize the time it takes us to get to the town, we should swim to a point that is √(1/14) miles from the town.
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The complete question is -
I am 1 mile in the ocean and wish to get to a town 3 miles down the coast. I need to swim to the shore and then walk along the shore and I can swim at 2 mph and walk at 4 mph. To what point on the shore should I swim to minimize the time it takes me to get to the town?
f(x)=5x-7. Find f^-1(-2)
Answer:
The answer to the question is 1.75
b) The average age of Kishan and Dolma is 15 years and that of Dolma and Shashwat is 14 years. If Kishan is 17 years old, find the age of Dolma and Shashwat.
Step-by-step explanation:
average means the sum of all values divided by a number of values
Find the area of the composite figure.
A) 103.5
B) 39.5
C) 42.95
D) 64.25
Answer:
D) 64.25
Step-by-step explanation:
Break the figure up into 2 shapes: half-circle with radius of 5; triangle with base of 10 and height of 5
Area-half-circle = πr² = (π(5)²) / 2 = 25π /2 = 39.27
Area-triangle = 1/2bh = 1/2(10)(5) = 25
Atotal = 25 + 39.27 = 64.27
closest answer is D) 64.25. They used π=3.14 to get this answer.
certain standardized math exams have a mena of 120 and a standarad deviation of 20. of the students who take this exam. what percent could you expect to score betwen 60 amd 120
After finding the z score, total 49.865% you could expect to score between 60 and 120.
Math exams mean(μ) = 120
Math exams standard deviation(σ) = 20
We have to determine the percent you could expect to score between 60 and 120.
The area total included to the left of any score or value is indicated in the Z-score table (x). The top row and the first column of the Z-table represent the Z-values, while all of the numbers in the middle represent the areas.
P(60 < x < 120) = P((60 - 120)/20 < (x - μ)/σ < (120 - 120)/20)
Simplifying
P(60 < x < 120) = P((-60)/20 < (x - μ)/σ < 0/20)
P(60 < x < 120) = P(-3 < Z < 0)
We can write this as
P(60 < x < 120) = P(Z > -3) - P(Z < 0)
P(60 < x < 120) = 0.99865 - 0.5
P(60 < x < 120) = 0.49865
P(60 < x < 120) = 49.865%
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The number of songs enjoyed from Aesop Rock for all Learn4Life students is normally distributed with a mean of 5.0 songs and a standard deviation of 2.0 songs.
1. What is the probability an individual student likes more than 7 songs from Aesop Rock?
2. What is the probability an individual student likes less than 3 songs from Aesop Rock?
3. What is the probability an individual student likes between 3 and 7 songs from Aesop Rock?
4. What is the probability an individual student likes between 1 and 9 songs from Aesop Rock?
help please!
Answer:
1.The probability an individual student likes more than 7 songs from Aesop Rock is 0.1587.
2.The probability an individual student likes less than 3 songs from Aesop Rock is 0.3173.
3.The probability an individual student likes between 3 and 7 songs from Aesop Rock is 0.6826.
4.The probability an individual student likes between 1 and 9 songs from Aesop Rock is 0.9973.
given triangle abc, how many possible triangles can be formed for the following conditions: ab = 37cm, ac = 26cm, angle b = 32.5°
Given the lengths of the two sides and the angle between them, only one triangle can be created under the given circumstances.
1. Given that angle B is 32.5°, side AB is 37 cm, side AC is 26 cm, etc.
2. Calculate side BC using the Law of Cosines:
BC = (2(AB)(AC)cosB) + (AB)(AC)2
3. Input the values that are known: BC = (37 2 + 26 2 - 2(37)(26)cos32.5°)
4. Condense: BC = (1369 plus 676 minus 1848 cos 32.5 °)
5. Determine BC =. (2095 - 1539.07)
6. Condense: BC = 556.93
7. Determine BC as 23.701 cm.
8. Since the lengths of the two sides and the angle between them are specified, only one triangle can be formed under the current circumstances.
By applying the Law of Cosines, we can determine the length of the third side, BC, given that side AB is 37 cm, side AC is 26 cm, and angle B is 32.5°. In order to perform this, we must first determine the cosine of angle B, which comes out to be 32.5°. Then, we enter this value, together with the lengths of AB and AC, into the Law of Cosines equation to obtain BC.BC = (AB2 + AC2 - 2(AB)(AC)cosB) is the equation. BC is then calculated by plugging in the known variables to obtain (37 + 26 - 2(37)(26)cos32.5°). By condensing this formula, we arrive at BC = (1369 + 676 - 1848cos32.5°). Then, we calculate BC as BC = (2095 - 1539.07), and finally, we simplify to obtain BC = 556.93. Finally, we determine that BC is 23.701 cm. Given the lengths of the two sides and the angle between them.
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A and B are two similar solids.
15 cm
JA VA
10 cm
B
The volume of A is 400 cm³.
Work out the volume of B.
Optional working
+
The volume of B will be 1350 cm³.
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
If two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides.
we have given that,
Height of A = 10 cm.
Volume of A = 400cm³.
Height of B = 15 cm.
Both A and B solids are similar .
from above told concept we get,
→ V(A) / V(B) = (Height of A)³ / (Height of B)³
Putting all given values we get,
→ 400/ V(B) = (10)³/(15)³
→ 400/V(B) = (1000/3375)
→ V(B) = (400 * 3375) / 1000
→ V(B) = (4 * 3375) / 10
→ V(B) = 1350 cm³. (Ans.)
Hence, Volume of B will be 1350 cm³.
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