Answer:
32 years old
Step-by-step explanation:
The husband is 32 years old as the wife is 3 years younger than the husband. The son is 3 years older than the daughter. Their family altogether total age today is 68 years while 4 years ago their age total was 54 years. The difference is 14 years. If we divide the difference into 4 then the age can not be whole number which means daughter is born after 2 years. She is now 2 years older. Son is 3 years older than the daughter which means he is 5 years old. The husband then must be 32 years old and wife is 3 years younger which means she is 29 years old now.
32 + 29 + 5 + 2 = 68 years.
The radius of a sphere is measured as 7 centimeters, with a possible error of 0.025 centimeter.
Required:
a. Use differentials to approximate the possible propagated error, in cm3, in computing the volume of the sphere.
b. Use differentials to approximate the possible propagated error in computing the surface area of the sphere.
c. Approximate the percent errors in parts (a) and (b).
Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
The higher the bowling score the better. The lower the golf score the better. Assume both are normally distributed. a. Suppose we have a sample of the Santa Ana Strikers' bowling scores. Q1 = 125 and Q3 = 156. Would it be usual or unusual to have a score of 200?b. Suppose the mean bowling score is 155 with a standard deviation of 16 points. What is the probability that in a sample of 40 bowling scores, the mean will be smaller than 150?c. Suppose the mean golf score is 77 with a standard deviation of 3 strokes We will give a trophy for the best 5% of scores. What score must you get to receive a trophy? d. Suppose the mean golf score is 77 with a standard deviation of 3 strokes. Would a golf score of 70 be ordinary, a mild outlier, or an extreme outlier?
Answer:
Explained below.
Step-by-step explanation:
(a)
The first and third quartiles of bowling scores are as follows:
Q₁ = 125 and Q₃ = 156
Then the inter quartile range will be:
IQR = Q₁ - Q₃
= 156 - 125
= 31
Any value lying outside the range (Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) are considered as unusual.
The range is:
(Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) = (125 - 1.5×31, 156 + 1.5×31)
= (78.5, 202.5)
The bowling score of 200 lies in this range.
Thus, the bowling score of 200 is usual.
(b)
Compute the probability that the mean bowling score will be smaller than 150 as follows:
[tex]P(\bar X<150)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{150-155}{16/\sqrt{40}})[/tex]
[tex]=P(Z<-1.98)\\=1-P(Z<1.98)\\=1-0.97615\\=0.02385\\\approx 0.024[/tex]
Thus, the probability that in a sample of 40 bowling scores, the mean will be smaller than 150 is 0.024.
(c)
It is provided that, the lower the golf score the better.
So, the best 5% of scores would be the bottom 5%.
That is, P (X > x) = 0.05.
⇒ P (Z > z) = 0.05
⇒ P (Z < z) = 0.95
⇒ z = 1.645
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\1.645=\frac{x-77}{3}\\\\x=77+(3\times 1.645)\\\\x=81.935\\\\x\approx 82[/tex]
Thus, the score is 82.
(d)
A z-scores outside the range (-2, +2) are considered as mild outlier and the z-scores outside the range (-3, +3) are considered as extreme outlier.
Compute the z-score for the golf score of 70 as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\farc{70-77}{3}\\\\=\frac{-7}{3}\\\\=-2.33[/tex]
As the z-score for the golf score of 70 is less than -2, it is considered as a mild outlier.
Find the value of 18÷9•3
Answer:
6
Step-by-step explanation:
18 : 9 · 3 = 2 · 3 = 6
How is multiplying 3 - 2i by ia represented on the complex plane?
Drag a term or measure into each box to correctly complete the statements
The complex number 3 - 2i lies in quadrant IV
of the complex plane. When any complex number is multiplied by the
imaginary unit, the complex number undergoes a
90°
rotation in a counterclockwise direction This means that
the complex product of 3 - 2i and 22 lies in
quadrant I
of the complex plane.
The equation is represented 3 units to the left of the complex plane and 2 units up.
What is complex equation?A complex equation is an equation that involves complex numbers when solving it. A complex number is a number that has both a real part and an imaginary part.
Well to see how this is represented, we first need to multiply it out so we can see how it looks when it is simplified!
[tex]=(3-2i)(i^2)\\\\\\i^2=-1\\\\\\=(3-2i)(-1)\\\\\\=(-3+2i)[/tex]
We know that on a complex plane, our imaginary numbers are represented on the vertical axis.
So the original expression, (3-2i) would have been 3 units to the right on a complex graph and 2 units downward!
The equation I input above should be pretty straightforward, but one thing I didn't mention was that i^2 should = -1 when dealing with complex numbers!
Therefore, the equation 3-2i * i^2 is equal to -3 + 2i, this is graphed 3 units to the left and to units upward!
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Help pleaseeeee!!!!!!
Answer:
0.05m^2
Step-by-step explanation:
5 divided by 100
Decide whether the pair of ratios form a proportion 15/12=4.5/3.6
Answer: Yes they form a proportion. The given equation is a true equation.
==========================================
Explanation:
The idea is that if we have
a/b = c/d
then that it is the same as
a*d = b*c
This is known as cross multiplication. We'll use this rule to get
15/12 = 4.5/3.6
15*3.6 = 12*4.5
54 = 54
We got the same value on both sides, meaning that the last equation is true. Consequently, it means the first equation is true as well (all three equations are true).
--------
You could also use your calculator to see that
15/12 = 1.25
4.5/3.6 = 1.25
showing that 15/12 = 4.5/3.6 is a true equation and the ratios form a proportion.
Answer:
15/12=4.5/3.6 = True
Step-by-step explanation:
Simplify the following: Left-hand
15/12
Hint: | Reduce 15/12 to lowest terms. Start by finding the GCD of 15 and 12.
The gcd of 15 and 12 is 3, so 15/12 = (3×5)/(3×4) = 3/3×5/4 = 5/4:
Answer: 5/4
______________________________
Approximate the following:
4.5/3.6
Hint: | Express 4.5/3.6 in decimal form.
4.5/3.6 = 1.25:
Answer: 1.25 = 5/4
The expression (x - 4)2 is equivalent to which expression
Answer:
8-2x
Step-by-step explanation:
2 distributed over the entire expression equals 8-2x
Answer:
the answer is b
Step-by-step explanation:
What are the Links of two sides of a special right triangle with a 306090° and a Hypotenuse of 10
Answer:
Step-by-step explanation:
60°=2×30°
one angle is double the angle of the same right angled triangle.
so hypotenuse is double the smallest side.
Hypotenuse=10
smallest side=10/2=5
third side =√(10²-5²)=5√(2²-1)=5√3
Tonya and Leo each bought a cell phone at the same time. The trade-in values, in dollars, of the cell phones are modeled by the given functions, where x is the number of months that each person has owned the phone.
Answer:
The answer is: Leo's phone had the greater initial trade-in value. Tonya's phone decreases at an average rate slower than the trade in value of Leo's phone.
Step-by-step explanation:
I got it right. Hope this helps.
The initial trade-in value of Tonia's phone is greater when compared with Leo's
There is a decrease in the trade-in value of Leo's phone at an average slower rate
[tex]f(x) = 490\times 0.88[/tex]
[tex](x)[/tex] ⇒ [tex]g(x)[/tex]
[tex]0[/tex] ⇒ [tex]480[/tex]
[tex]2[/tex] ⇒ [tex]360[/tex]
[tex]4[/tex] ⇒ [tex]470[/tex]
Now we will solve with the greater initial value
The initial value is when x = 0. So, we have
[tex]f(x) = 490 \times o.88^x\\\ f(o) = 490 \times 0.88 ^0\\f(0 =490 \times 1 \\f(o) = 490[/tex]
From leos table
[tex]g(0) = 480\\f(0) > g(o)\\i.e \\490 > 480[/tex]
So Tonia had a greater initial value
Solving (b): The phone with a lesser rate
y [tex]y = a b ^ x[/tex]
An exponential function is:
where [tex]b \rightarrow rate[/tex]
For Tonia
[tex]b = o.88[/tex]
For Leo we have
[tex](x_{1} , y_{1} )= (0,480)\\(x_{1}, y_{1} ) = (2, 360)[/tex]
So the equation becomes
[tex]y = ab ^x \\480 = ab ^0 \\and \\360 = ab ^2[/tex]
On solving
[tex]480 = a \times 1\\a = 480[/tex]
[tex]360 = ab ^ 2[/tex]
so it becomes
[tex]480 = 360 \times b ^2 \\[/tex]
On dividing both sides by [tex]480[/tex] we get
[tex]b ^ 2 = 0.87[/tex]
[tex]b ^ 2 = 0.75[/tex]
On taking square root we get
[tex]b = 0.87[/tex]
In comparison, we get Leo's rate is slower.
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ACDF,BE is a mid segment what is x?
Answer:
X= 15
Step-by-step explanation:
the above equation will be used to determine the value of x.
the above equation will be used to determine the value of x.
6x-12= 2x+20+18
6x-2x = 20+12+18
4x= 60.
X= 60/4
X= 15
x = 15
What is the error in this problem
Answer:
The error is the use of wrong trigonometric ratio formula.
Sine was used instead of tangent.
It should be: [tex] tan(A) = \frac{36}{84} [/tex]
Step-by-step explanation:
Side length, 36, is opposite to <A. Side length, 84, is the adjacent side. Therefore, the right trigonometric ratio formula to use is:
[tex] tan(A) = \frac{opposite}{adjacent} [/tex]
[tex] tan(A) = \frac{36}{84} [/tex]
[tex] A = tan^{-1}(\frac{36}{84}) [/tex]
m<A ≈ 23°
The error made was the use of wrong trigonometric ratio formula.
A?
B?
C?
D?
The box plots below represent the scores for games played by two high schools basketball teams over the last 5 seasons
Answer:
A. No conclusion can be drawn regarding the means because the box plots only show medians and quartiles.
Step-by-step explanation:
A box display tells represents a five-number summary that consists of the minimum value, lower quartile, median, upper quartile and maximum value. It could also tell you which data point is an outlier, if there are any.
Mean value for a data set that can hardly be ascertained or derived from a box plot display itself.
Therefore, the statements regarding the means of both data sets that is most likely true is: "A. No conclusion can be drawn regarding the means because the box plots only show medians and quartiles."
Need Help
Please Show Work
Answer:
-36
Step-by-step explanation:
3*12=36
she is going down (negative) so, it is -36
not sure if this is what you are asking for, if not try this
0-12-12-12=-36
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.
About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Complete Question
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.
About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Answer:
About 97.219% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Step-by-step explanation:
From the question given we can see that they both are the same so 1 will just solve one
Now the area under this given range can be represented mathematically as
[tex]P ( -2.2 < z < 2.2) = P(z < 2.2 ) - P(z < -2.2 )[/tex]
Now from the z-table
[tex]p(z < 2.2 ) = 0.9861[/tex]
and
[tex]p(z < - 2.2 ) = 0.013903[/tex]
So
[tex]P ( -2.2 < z < 2.2) = 0.9861 - 0.013903[/tex]
[tex]P ( -2.2 < z < 2.2) = 0.97219[/tex]
So converting to percentage
[tex]P ( -2.2 < z < 2.2) = 0.97219 * 100[/tex]
[tex]P ( -2.2 < z < 2.2) = 97.219 \%[/tex]
Which is the zero of the function f(x)=(x+3) (2x-1)(x+2) ?
Answer:
x= -3 x = 1/2 x=-2
Step-by-step explanation:
f(x)=(x+3) (2x-1)(x+2)
Set equal to zero
0 =(x+3) (2x-1)(x+2)
Using the zero product property
x+3 =0 2x-1 =0 x+2 =0
x= -3 2x =1 x = -2
x= -3 x = 1/2 x=-2
During the 2014 season, the Los Angeles Dodgers won 58% of their games. Assuming that the outcomes of the baseball games are independent and that the percentage of wins this season will be the same as in 2014: What is the probability that the Dodgers will win at least one of their next seven games
Answer: 0.98
Step-by-step explanation:
given data:
probability they won a game = 58% = 0.58
since outcome of games are independent, and percentage would remain same as 2014.
probablility that Dodgers wins atleast 1 of their next 7 games
= 1 - p
= 1 - ( 0.58 )^ 7
= 1 - 0.02208
= 0.98
probabikotun that Dodgers would win one of their next seven games is 0.98
NEED ASAP! Given: AB = 12 AC = 6 Prove: C is the midpoint of AB. A line has points A, C, B. Proof: We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments. Answer choices: Congruence Symmetric Reflexive Transitive
Answer:
It’s symmetric property
Answer:
Symmetry
Step-by-step explanation:
The guy above me
A tank contains 1080 L of pure water. Solution that contains 0.07 kg of sugar per liter enters the tank at the rate 7 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate.Required:a. How much sugar is in the tank at the begining?b. Find the amount of sugar after t minutes.c. As t becomes large, what value is y(t) approaching ?
(a) Let [tex]A(t)[/tex] denote the amount of sugar in the tank at time [tex]t[/tex]. The tank starts with only pure water, so [tex]\boxed{A(0)=0}[/tex].
(b) Sugar flows in at a rate of
(0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min
and flows out at a rate of
(A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min
so that the net rate of change of [tex]A(t)[/tex] is governed by the ODE,
[tex]\dfrac{\mathrm dA(t)}[\mathrm dt}=\dfrac{49}{100}-\dfrac{7A(t)}{1080}[/tex]
or
[tex]A'(t)+\dfrac7{1080}A(t)=\dfrac{49}{100}[/tex]
Multiply both sides by the integrating factor [tex]e^{7t/1080}[/tex] to condense the left side into the derivative of a product:
[tex]e^{\frac{7t}{1080}}A'(t)+\dfrac7{1080}e^{\frac{7t}{1080}}A(t)=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]
[tex]\left(e^{\frac{7t}{1080}}A(t)\right)'=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]
Integrate both sides:
[tex]e^{\frac{7t}{1080}}A(t)=\displaystyle\frac{49}{100}\int e^{\frac{7t}{1080}}\,\mathrm dt[/tex]
[tex]e^{\frac{7t}{1080}}A(t)=\dfrac{378}5e^{\frac{7t}{1080}}+C[/tex]
Solve for [tex]A(t)[/tex]:
[tex]A(t)=\dfrac{378}5+Ce^{-\frac{7t}{1080}}[/tex]
Given that [tex]A(0)=0[/tex], we find
[tex]0=\dfrac{378}5+C\implies C=-\dfrac{378}5[/tex]
so that the amount of sugar at any time [tex]t[/tex] is
[tex]\boxed{A(t)=\dfrac{378}5\left(1-e^{-\frac{7t}{1080}}\right)}[/tex]
(c) As [tex]t\to\infty[/tex], the exponential term converges to 0 and we're left with
[tex]\displaystyle\lim_{t\to\infty}A(t)=\frac{378}5[/tex]
or 75.6 kg of sugar.
in a class of 40 students, 30 students read chemistry, 40 students read physics, if all students read at least one of the subject, find the probability a students is selected at random will read only chemistry
Answer: 0%
Step-by-step explanation:
There's 40 students, and 40 students read physics. That means that every student reads physics. So, no student could read only chemistry.
Please please help :((((
Answer:
y = x-4
Step-by-step explanation:
The y intercept is -4
We have 2 points so we can find the slope
( 0,-4) and(4,0)
m = ( y2-y1)/(x2-x1)
= ( 0- -4)/ (4-0)
= 4/4
=1
The slope intercept form is
y = mx+b
y = 1x-4
y = x-4
What are the polar coordinates of the rectangular coordinates
(V3,-1)?
o (2,5)
O (2,11)
(4, 15)
Answer:
1)
[tex] \sqrt{( \sqrt{} 3 {}^{2} } + 1 {}^{2} )[/tex]
[tex] \sqrt{4} = 2[/tex]
then the angle,
[tex] \tan( \alpha ) = - 1 \div \sqrt{3} = 330[/tex]
in radians,
[tex]11\pi \div 6[/tex]
hope this helps for the next questions
An escalator moves at the rate of 2 feet per second. At what rate does the escalator move in miles per hour? 5280 feet=1 mile
Answer:
7200ft/per Hour divide it by mile ( 5280) makes 1.363 so maybe 1.4 Miles
Step-by-step explanation:
Work Shown:
1 mile = 5280 feet
1 hour = 3600 seconds (since 60*60 = 3600)
[tex]2 \text{ ft per sec} = \frac{2 \text{ ft}}{1 \text{ sec}}\\\\2 \text{ ft per sec} = \frac{2 \text{ ft}}{1 \text{ sec}}*\frac{1 \text{ mi}}{5280 \text{ ft}}*\frac{3600 \text{ sec}}{1 \text{ hr}}\\\\2 \text{ ft per sec} = \frac{2*1*3600}{1*5280*1} \text{ mph}\\\\2 \text{ ft per sec} = \frac{7200}{5280} \text{ mph}\\\\2 \text{ ft per sec} \approx 1.363636 \text{ mph}\\\\[/tex]
The result is approximate and the "36" portion repeats forever.
Please answer this correctly without making mistakes
Answer:
[tex]51\frac{4}{17}[/tex]
Step-by-step explanation:
If we add all of the fractions together, we 'd get 55/17 of an hour. The question is to find how many hours she spent exercising. Well, for that we'd just need to see how many seventeens fit inside 55. We could divide, but that'd lead us to a really long, weird number.
Since 17*3=51, we know that in total, three seventeens fit inside 55. Yet, there's still remainders.
55-51=4
So, our answer would be 51 (how many 17s go into 55) and 4/17 (the remainder.)
Hope this helps!! <3 :)
If a system of linear equations has no solution, what does this mean about the two lines?
Answer:
The two lines do not intersect, and are parallel to one another on a graph.
Step-by-step explanation:
A system of equations consists of two or more equations with two or more variables. The solution to these variables must satisfy all of the variables in the equations in the system at the same time. Usually, all the equations in the system are considered and solved simultaneously. A linear equation might have a unique solution, an infinite solution, or no solution at all.
A system with exactly one solution is called a consistent system, and it is said to be independent, and the graph of its lines intersects at the point that is the solution to the equations. A system with an infinite number of solution is said to be dependent and the lines are coincident on a graph.
If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, and the lines are parallel to one another on the graph.
For two lines of linear equations to have no solution, they must be parallel to each other i.e they must have the same slope.
The standard form of writing linear equation is expressed as y = mx + b
m is the slope of the line
b is the y-intercept
For two lines of linear equations to have no solution, they must be parallel to each other i.e they must have the same slope.
For instance, the system of equations y = 2x + 7 and y = 2x - 3 have no solutions because they have the same slope.
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Factor completely 6x - 18.
6(x + 3)
6(x-3)
6X (-18)
Prime
Answer:
6(x-3)
Step-by-step explanation:
the common number for 6 and 18 is 6 so if you extract that from the expression then it turns to 6(x-3) which cannot be factored further
Answer:
Option B: 6(x - 3)
Step-by-step explanation:
how do I write 1/2 in a from of a decimal?
Answer:
0.5
1 divide by 2 = 0.5
The sum of two numbers is twenty-four. The second number is equal to twice the first number. Call the first number m and the second number n.
Answer:
Step-by-step explanation:
Hello, please consider the following.
m and n are the two numbers.
m + n = 24, right?
n = 2 m
We replace n in the first equation, it comes
m + 2m =24
3m = 24 = 3*8
So, m = 8 and n = 16
Thank you
The first number is 8 and second number is 16.
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Given that the sum of two numbers is twenty-four
The second number is equal to twice the first number
Let x and y are the two numbers.
According to the question,
m + n = 24,
n = 2m
Substitute the value of n in the first equation,
m + 2m =24
3m = 24
m = 24/3
m = 8
Substitute the value of m in the n = 2m
So, n = 2(8)
n = 16
Hence, the first number is 8 and second number is 16.
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What is the midpoint of the segment below?
A.
(0, 0)
B.
(-1, 1)
C.
(0.5, 0.5)
D.
(0.5, -0.5)
Answer:
Step-by-step explanation:
(5+(-4))/2 = 1/2 or 0.5
(-7 + 6)/2 = -1/2 or -0.5
the solution is D
(0.5, -0.5)
nick used 1 3/4 kg of salt to melt the ice on his sidewalk. He then used another 3 4/5 kg on the driveway. How much salt did he use in all?
Answer:
5 11/20
Step-by-step explanation:
1 3/4 + 3 4/5
Get a common denominator of 20
1 3/4 * 5/5 + 3 4/5 *4/4
1 15/20 + 3 16/20
4 31/20
Rewriting
4 + 20/20 + 11/ 20
4+1 + 11/20
5 11/20
a=5,and 5+z=14,so a+z=14
Answer:
Z=9
Step-by-step explanation:
Insert A into A+Z=14
5+z=14
Subtract 5 on both sides, to find Z.
-5 -5
z=9
