Answer:
The amount of thermal energy that is generated is 1000 joules.
Step-by-step explanation:
Let consider the person diving into a pool as a closed system, that is, a system with only energy interaction with the surroundings. According to the First Law of Thermodynamics, which is a generalization of the Principle of Energy Conservation, the total energy of the system is neither destroyed, nor created, only transformed. The initial gravitational potential energy is transformed into translational kinetic and thermal energy. That is to say:
[tex]U_{g} - K - Q = 0[/tex]
Where:
[tex]U_{g}[/tex] - Gravitational potential energy, measured in joules.
[tex]K_{tr}[/tex] - Translational kinetic energy, measured in joules.
[tex]Q[/tex] - Thermal energy, measured in joules.
The thermal energy is now cleared:
[tex]Q = U_{g}-K[/tex]
Given that [tex]U_{g} = 8000\,J[/tex] and [tex]K = 7000\,J[/tex], the amount of thermal energy that is generated is:
[tex]Q = 8000\,J - 7000\,J[/tex]
[tex]Q = 1000\,J[/tex]
The amount of thermal energy that is generated is 1000 joules.
Answer:
1000J
Step-by-step explanation:
EDGE2020
prove identity trigonometric equation
[tex]2 \tan(x) = \frac{ \cos(x) }{ \csc(x - 1) } + \frac{ \cos(x) }{ \csc(x + 1) } [/tex]
Explanation:
The given equation is False, so cannot be proven to be true.
__
Perhaps you want to prove ...
[tex]2\tan{x}=\dfrac{\cos{x}}{\csc{(x)}-1}+\dfrac{\cos{x}}{\csc{(x)}+1}[/tex]
This is one way to show it:
[tex]2\tan{x}=\cos{(x)}\dfrac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=\cos{(x)}\dfrac{2\csc{(x)}}{\csc{(x)}^2-1}=2\cos{(x)}\dfrac{\csc{x}}{\cot{(x)}^2}=2\dfrac{\cos{(x)}\sin{(x)}^2}{\cos{(x)}^2\sin{(x)}}\\\\=2\dfrac{\sin{x}}{\cos{x}}\\\\2\tan{x}=2\tan{x}\qquad\text{QED}[/tex]
__
We have used the identities ...
csc = 1/sin
cot = cos/sin
csc^2 -1 = cot^2
tan = sin/cos
Write the equation of the graph shown below in the factored form f(x) = (x + 2) (x - 1) (x - 3) f(x) = (x - 2) (x + 1) (x + 3) f(x) = (x + 2) (x + 1) (x + 3) f(x) = (x - 2) (x - 1) (x - 3)
Answer:
[tex]f(x)=(x-1)\,(x-3)\.(x+2)[/tex]
which agrees with the first answer shown in the list of possible options.
Step-by-step explanation:
Notice that there are three roots for this polynomial clearly shown on the graph's crossings of the x axis: x = 1, x = 3, and x = -2.
Therefore, based on such, we can write three binomial factors of the form [tex](x-root)[/tex] for the polynomial:
[tex]f(x)=(x-1)\,(x-3)\.(x-(-2))=(x-1)\,(x-3)\.(x+2)[/tex]
Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted at two stores where the two new systems have been installed result in the following summary of the data.
System System B
n1=120 n2=100
x1=4.1 minutes x2=3.4 minutes
σ1=2.2minutes σ2= 1.5 minutes
Test at the 0.05 level of significance to determinewhether the population mean checkout times of the two newsystems differ. Which system is preferred?
Answer:
We conclude that the population means checkout times of the two new systems differ.
Step-by-step explanation:
We are given the result in the following summary of the data;
System System B
n1=120 n2=100
x1=4.1 min x2=3.4 min
σ1=2.2 min σ2= 1.5 min
Let [tex]\mu_1[/tex] = population mean checkout time of the first new system
[tex]\mu_2[/tex] = population mean checkout time of the second new system
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that the population mean checkout times of the two new systems are equal}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that the population mean checkout times of the two new systems differ}
The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex] ~ N(0,1)
where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min
[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min
[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min
[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min
[tex]n_1[/tex] = sample of the first new systems = 120
[tex]n_2[/tex] = sample of the second new systems = 100
So, the test statistics = [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]
= 2.792
The value of z-test statistics is 2.792.
Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.
Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the population mean checkout times of the two new systems differ.
Use the graph to solve the given system of equations, then enter your solution below. {x−3y=−3x+y=5
Answer:
Step-by-step explanation:
Given the system of equation x−3y=−3 and x+y=5, we can solve for x and y by solving the equation simultaneously using the substitution method.
x−3y=−3_____________ 1
x+y=5 ______________2
From equation 2; x = 5- y ________ 3
Substitute equation 3 into equation 1
Since x - 3y = -3
(5-y)-3y = -3
5-y-3y = -3
5-4y = -3
Subtract 5 from both sides of the equation
5-4y-5 = -3-5
-4y = -8
Divide both sides by -4
-4y/-4 = -8/-4
y = 2
Substitute y = 2 into equation 2 to get the value of y;
From equation 2, x+y = 5
x+2 = 5
Subtract 2 from both sides of the equation
x+2-2 = 5-2
x = 3
Hence the value of x and y from the graph will be 3 and 2 respectively.
Searches related to Searches related to A motorboat travels 135 kilometers in 3 hours going upstream. It travels 183 kilometers going downstream in the same amount of time. What is the rate of the boat in still water? what is the rate of the current?
Answer:
[tex]\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }[/tex]
Step-by-step explanation:
Hello, let's note v the rate of the boat and r the rate of the current. We can write the following
[tex]\dfrac{135}{v-r}=3=\dfrac{183}{v+r}[/tex]
It means that
[tex]135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}[/tex]
But we can as well use the second equation:
[tex]3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}[/tex]
and then
[tex]\boxed{v=\dfrac{159*8}{24}=53}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the solution of log3(3x+2)= log3 (4x-6)?
Answer:
x=8 i got it right on my homework on khan academy
Step-by-step explanation:
Answer: Using logarithms to solve you will get x = 8
(25 points) PLEASE HELP! Gotta get this done before my mom comes home
1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 0.27 lb.; peanuts: 0.23 1b.
E. Cashews: 0.23 lb.; peanuts: 0.27 1b.
F. Cashews: 0.08 lb.; peanuts: 0.42 1b
2. A nursery owner has 288 rose bushes. There are 36 fewer red roses than pink roses. How many of each type of roses are there?
A. Red roses: 162; pink roses: 252.
B. Red roses: 162; pink roses: 126.
C. Red roses: 99; pink roses: 126.
D. Red roses: 126; pink roses: 162
E. Red roses: 126; pink roses: 99
F. Red roses: 252; pink roses: 162
3. The sum of the ages of Stephanie and Heather is 46. Heather is two years younger than Stephanie. Write a system of equations to determine the ages of Stephanie and Heather.
A) S + H = 46
H = S + 2
B) S - H = 46
H - 2 = S
C) S + H = 46
H = S - 2
D) S - H = 2
H = S - 46
E) S + H = 2
H = S - 46
F) 2S – H = 46
4. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
A. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 12 country CDs, and 3 soundtracks.
B. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and 3 soundtracks.
C. After borrowing 3 rock CDs, your friend will have 25 rock CDs, 10 country CDs, and 4 soundtracks.
D. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 9 country CDs, and 3 soundtracks.
E. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and no soundtracks.
F. After borrowing 3 rock CDs, your friend will have 18 rock CDs, 15 country CDs, and 3 soundtracks.
5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A) 3W = 2L + 2
2L = 2W + 12
B) 3W + 2 = 2L
4L = P – 12
C) 3W = 2L + 2
4L + 12 = P
D) 2W + 2 = 2L
4L = 12 + P
E) 3W + 2 = 2L
4L = 12 + P
F) 2L – 2 = 3W
P = 4L - 12
Thank you!!!!
I really need help on this
Answer:
Congruent
Step-by-step explanation:
I am not 100% sure because there are no measurements but it looks like the two shapes are the same size.
If this helped, please consider giving me brainliest, it will help me a lot :)
Have a good day.
There are 450 people and each pays 5 dollars how much do you get? Please show me the work
Answer:
The total amount is $2250.
Step-by-step explanation:
Given that each person pays $5 and there is 450 people so you have to multiply :
$5 × 450 = $2250
Solve of the following equations for x: 2 − x = −3
Answer:
x=5
Step-by-step explanation:
2 − x = −3
Subtract 2 from each side
2-2 − x = −3-2
-x = -5
Multiply by -1
x = 5
A local orchestra is holding a charity concert concert at the community center. Each adult ticket $12, and child ticket costs $8. The organizers of the event hope to raise no less than $2,500, and the community center can seat up to 280 people. This graph and system in inequalities represent this situation, where x represents the number of adult tickets and y represents the number of child tickets. 12x + 8y> 2,500. X + y < 280
The answer is (180,80)
To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.
InequalityThe given question is an inequality situation where we are asked to use graph to solve.
The data given are
adult ticket = $12child ticket = $8Total amount raised = $2500Total number of people = 280The inequality for this problem is given is as
[tex]12x + 8y > 2500\\x + y < 280[/tex]
Kindly find the attached image as the graph and solution to this problem.
Learn more on graphically solution for inequality here;
https://brainly.com/question/24372553
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The function y = sin^?1(3x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative. d dx [f(g(x))] = f '(g(x))g'(x) For the given function sin^?1(3x + 1), the "inside" function is 3x + 1 and the "outside" function is f(x) = arcsin(x).
Recall that the derivative of y = sin?1(x) is y' =__________?
Answer:
dy/dx = 3/√1-(3x+1)²
Step-by-step exxplanation:
Given the inverse function y = sin^-1(3x+1), to find the derivative of the expression, we will use the chain rule as shown;
Let u = 3x+1 ...1
y = sin⁻¹u ...2
From equation 1, du/dx = 3
from equation 2;
Taking the sin of both sides;
siny = sin(sin⁻¹u)
siny = u
u = siny
du/dy = cosy
dy/du = 1/cosy
from trig identity, cos y = √1-sin²y
dy/du = 1/√1-sin²y
Ssince u = siny
dy/du = 1/√1-u²
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/√1-u² * 3
dy/dx = 3/√1-u²
Substituting u = 3x+1 into the final equation, we will have;
dy/dx = 3/√1-(3x+1)²
72 students choose to attend one of three after school activities: football, tennis or running. There are 25 boys. 27 students choose football, of which 17 are girls. 18 students choose tennis. 24 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.
Answer:
3/8
Step-by-step explanation:
There are 72 students. 27 students choose football, and 18 choose tennis, which means 27 choose running.
So the probability that a student chooses running is 27/72, which reduces to 3/8.
One number is 26 more than another. Their product is -169.
Answer:
13 and -13
Step-by-step explanation:
The only factors of 169 are 1, 13, and 169.
Since the product is negative, you have to use 13 and -13. These numbers have a difference to 26. And when multiplied they equals -169
Consider the line y=2x-7 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
Answer:
The slope of the given line is 2
Answer -1/2 is the line perpendicular
Step-by-step explanation:
This can be rewritten in fraction form as 2/1 since x/1 = x.
Calculate: 1/(1×3) + 1/(3×5) + ... + 1/(47×49) . Please give explanation
Answer:
4611/11515
Step-by-step explanation:
1/(1×3)- 1 times 3 simply equals 3. so the answer would be 1/3.
1/(3×5)- 3 times 5 simply equals 15. so the answer would be 1/15.
1/(47×49)- 47 times 49 is 2303. so the answer would be 1/2303.
after all this you find the common deonomator. The common denominator is 34545. 34545 divided by 3 equals to 11515 so you muliplty that number by 1/3. 34545 divided by 15 equals to 2303 so you muliplty that number by 1/15.
34545 divided by 2303 equals to 15 so you multiply that number by 1/2303. After adding all that together you get 13833/34545. However after you simplify that number you get 4611/11515
A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled?
a. n=36, p=0.97, x=1
b. n=12, p=0.36, x=97
c. n=12, p=0.97, x=0
d. n=36, p=0.97, x=36
Answer:
Option d: n = 36, p = 0.97, x = 36.
Step-by-step explanation:
We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.
We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.
Let X = Number of cans that are properly filled
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]
where, n = number of trials (samples) taken = 36 cans
x = number of success = all cans are properly filled = 36
p = probabilitiy of success which in our question is probability that
can have the correct amount, i.e. p = 97%
So, X ~ Binom (n = 36, p = 0.97)
Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.
Which of the binomials below is a factor of this trinomial?
5x2-18x+9
O A. 5x-3
O B. X-1
O c. X+1
O D. 5x+3
Answer:
The answer is option A.
Step-by-step explanation:
here, 5x^2-18x+9
=5x^2-(15+3)x+9
=5x^2-15x-3x+9
=5x(x-3)-3(x-3)
=(5x-3)(x-3)
so, the answer from the above options is (5x-3).
hope it helps..
What is the range of the function f(x)=3/4|x|-3
Range is [tex]y\in[-3,+\infty)[/tex].
Hope this helps.
Which of the following can be calculated using the formula c=2r ?
A.
Area of a circle
B.
Circumference of a circle
C.
Arc length of a circle
D.
Diameter of a circle
Answer:
B. Circumference of a circle
Step-by-step explanation:
The circumference of a circle can be found using formula 2πr where r is the radius of circle.
What is the circumference of a circle?A circle's or an ellipse's circumference is its perimeter. The circumference would be the length of the circle's arc, if the circle were opened up and straightened out to a line segment, in other words.
Here, we have,
Suppose the radius of a circle is 5cm
So, we can find the circumference by using formula 2πr
Circumference = 2 × π × 5 = 10π cm.
Hence, The circumference of a circle can be found using formula 2πr where r is the radius of circle.
To learn more about Circumference and Perimeter,
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complete question;
The circumference of a circle can be found using the formula c 2r
Devaughn is 8 years older than Sydney. The sum of their ages is 64. What is Sydney's age?
Answer:
Sydney's age is 28
Step-by-step explanation:
Let Devaughn be D
And Sydney be S
D=S+8..... equation 1
D+S=64...... equation 2
Substitute equation 1 to equation 2
S+8+S=64
2S+8=64
2S=64-8
2S=56
S=56/2
S=28
Hope it helps
Good luck
Brenda is going from $(-4,5)$ to $(5,-4)$, but she needs to stop by the origin on the way. How far does she have to travel?
Answer:
[tex]\boxed{D = 6.4 units}[/tex]
Step-by-step explanation:
She stops by (0,0)
She further needs to travel to (5,-4)
Let's calculate the distance using the Distance Formula:
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
D = [tex]\sqrt{(5-0)^2+(-4-0)^2}[/tex]
D = [tex]\sqrt{(5)^2+(-4)^2}[/tex]
D = [tex]\sqrt{25+16}[/tex]
D = [tex]\sqrt{41}[/tex]
D = 6.4 units
She needs to travel 6.4 units more.
Answer:
2sqrt41
Step-by-step explanation:
Origin=(0,0)
Brenda wants to go from (-4,5) to (0,0) and then to (5,-4). So we need to calculate the distance from (-4,5) to (0,0), and the distance of (0,0) to (5,-4).
The distance formula is sqrt (x2-xs1)^2+(y2-y1`)^2.
So: sqrt (5-0)^2+(-4-0)^2
sqrt (5^2+-4^2)
sqrt 25+16
sqrt 41
Now we need to figure out the distance from (0,0) to (5,-4)
sqrt(0-5)^2+(0-(-4))^2
sqrt(-5^2+4^2)
sqrt 25+16
sqrt 41
sqrt 41+sqrt 41
2sqrt41
VW=40in. The radius of the circle is 25 inches. Find the length of CT.
Answer:
The answer is B. 40 inches.
Step-by-step explanation:
The question starts by telling you that line VW is equal to 40 in. If you look at the picture you can see it is divided into 2 equal parts of 20 in each. If you look at line CT, you can see that there are the same marks meaning that those segments are also 20 in. That means that line CT and line VW are equal and that line CT is equal to 40 in.
solve this for me plzzz
Answer: a- steve
Step-by-step explanation:
Answer:
B Emma is correct
Step-by-step explanation:
How do I do this? I need the correct option
option A is correct answer.
because angle JKL is half of of arc JL .
so, angle JK is equal to 64°.
hope it helps...
helpp me please will give brralinst
Answer:
0
Step-by-step explanation:
the answer is 0
Have a great day
I really need help on this question
Answer:
d. 38
Step-by-step explanation:
AB = AD - BD = 54 - 36 = 18
AC = AB + BC = 18 + 20 = 38
2
A student winds a strip of paper eight times
round a cylindrical pencil of diameter 7 mm.
Use the value 22/7 for pie to find the length of
the paper.
Answer:
176 mm
Step-by-step explanation:
The circumference of a circle is the perimeter of a circle (length of a circle). The circumference of a circle is given as:
Circumference (C) = 2πr = πd, where d is the diameter
The circumference of a circle with diameter 7 mm is:
C = πd = 22/7(7) = 22 mm
The length of the paper to round the cylindrical pencil is the same as the perimeter of the pencil which is 22 mm.
To round the pencil 8 times, the length of the paper needed = 8 × 22 mm = 176 mm
Factories A, B and C produce computers. Factory A produces 4 times as manycomputers as factory C, and factory B produces 7 times as many computers asfactory C. The probability that a computer produced by factory A is defective is0.04, the probability that a computer produced by factory B is defective is 0.02,and the probability that a computer produced by factory C is defective is 0.03. Acomputer is selected at random and found to be defective. What is the probabilityit came from factory A?
Answer:
The probability is [tex]P(A') = 0.485[/tex]
Step-by-step explanation:
Let assume that the number of computer produced by factory C is k = 1
So From the question we are told that
The number produced by factory A is 4k = 4
The number produced by factory B is 7k = 7
The probability of defective computers from A is [tex]P(A) = 0.04[/tex]
The probability of defective computers from B is [tex]P(B) = 0.02[/tex]
The probability of defective computers from C is [tex]P(C) = 0.03[/tex]
Now the probability of factory A producing a defective computer out of the 4 computers produced is
[tex]P(a) = 4 * P(A)[/tex]
substituting values
[tex]P(a) = 4 * 0.04[/tex]
[tex]P(a) = 0.16[/tex]
The probability of factory B producing a defective computer out of the 7 computers produced is
[tex]P(b) = 7 * P(B)[/tex]
substituting values
[tex]P(b) = 7 * 0.02[/tex]
[tex]P(b) = 0.14[/tex]
The probability of factory C producing a defective computer out of the 1 computer produced is
[tex]P(c) = 1 * P(C)[/tex]
substituting values
[tex]P(c) = 1 * 0.03[/tex]
[tex]P(b) = 0.03[/tex]
So the probability that the a computer produced from the three factory will be defective is
[tex]P(t) = P(a) + P(b) + P(c)[/tex]
substituting values
[tex]P(t) = 0.16 + 0.14 + 0.03[/tex]
[tex]P(t) = 0.33[/tex]
Now the probability that the defective computer is produced from factory A is
[tex]P(A') = \frac{P(a)}{P(t)}[/tex]
[tex]P(A') = \frac{ 0.16}{0.33}[/tex]
[tex]P(A') = 0.485[/tex]
Determine the domain of the function. f as a function of x is equal to the square root of two minus x.
x ≤ 2
All real numbers
x > 2
All real numbers except 2
Answer:
A. x <= 2
Step-by-step explanation:
The domain of a real function should be all real numbers. In
f(x) = sqrt(2-x)
we need 2-x to be non-negative, therefore
2-x >= 0
which implies
x <= 2
Answer:
[tex]\Huge \boxed{{x\leq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=\sqrt{2-x}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.
[tex]2-x\geq 0[/tex]
[tex]-x\geq -2[/tex]
[tex]x\leq 2[/tex]
The domain of the function is x ≤ 2.