Answer:
The speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
Step-by-step explanation:
Given that a riverboat travels 52 km downstream in 2 hours, and it travels 66 km upstream in 3 hours, the following calculations must be performed to find the speed of the boat and the speed of the stream:
Downstream = 52/2 = 26
Upstream = 66/3 = 22
Stream = 4/2 = 2
Therefore, the speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
Please help Ladder question!!
A 6 ft ladder, resting against a wall, begins to slip down the wall. When the angle of the ladder is 45 degrees, the bottom of the ladder is moving away from the wall at 0.5 m/s. At that moment, how fast is the top of ladder moving down the wall?
Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is
[tex]x^2+y^2=c^2[/tex] where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is
[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and dividing everything by 2 to simplify a bit:
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Upon analyzing that equation, it looks like we need values for x, y, [tex]\frac{dx}{dt}[/tex], and [tex]\frac{dy}{dt}[/tex]. And here's what we were given:
[tex]\theta=45[/tex] and [tex]\frac{dx}{dt}=.5[/tex] In the greater realm of things, that's nothing at all.
BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to
Find [tex]\frac{dy}{dt}[/tex] at the instant that [tex]\frac{dx}{dt}[/tex] = .5.
Solving for x and y:
[tex]tan45=\frac{x}{6}[/tex] and
6tan45 = x ( and since this is a 45-45-90 triangle, y = x):
[tex]6(\frac{\sqrt{2} }{2})=x=y[/tex] so
[tex]x=y=3\sqrt{2}[/tex] and now we can fill in our derivative. Remember the derivative was found to be
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so
[tex]3\sqrt{2}(\frac{1}{2})+3\sqrt{2}\frac{dy}{dt}=0[/tex] and
[tex]\frac{3\sqrt{2} }{2}+3\sqrt{2} \frac{dy}{dt}=0[/tex] and
[tex]3\sqrt{2}\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}[/tex] and multiplying by the reciprocal of the left gives us:
[tex]\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}(\frac{1}{3\sqrt{2} })[/tex] so
[tex]\frac{dy}{dt}=-\frac{1}{2}\frac{m}{s}[/tex]
Test scores for a Statistics class have a mean of 78 with a standard deviation of 6. Suppose a student gets an 81 on that test. What is the z-score for that grade?
Answer:
0.3209
in case you dont know A z-score tells you if the distribution it comes from is normal.
Step-by-step explanation:
Triangle A'B'C' is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between AABC
and A'B'C'?
Answer:
[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]k = 2[/tex] --- scale factor
Required
Relationship between ABC and A"B"C"
[tex]k = 2[/tex] implies that the sides of A"B"C" are bigger than ABC
i.e.
[tex]A"B" = 2AB[/tex]
[tex]A"C" = 2AC[/tex]
[tex]B"C" = 2BC[/tex]
In [tex]A"B" = 2AB[/tex]
Divide both sides by A"B"
[tex]1 = \frac{2AB}{A"B"}[/tex]
Divide both sides by 2
[tex]\frac{1}{2} = \frac{AB}{A"B"}[/tex]
Rewrite as:
[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]
(a) is correct
find the angle between following linesroot 3x-y=2,x-root 3y=7
Answer:
where I find? where is the directions
Celia was a contestant on Jeopardy. At the
beginning of the round her score was -40.
Celia's score at the end of the round was -
35. How many points did Celia score (or
lose) during the round?
Answer:
75
Step-by-step explanation:
She is in the negatives right now so add 40 to get Celicia points equal to 0. Then add an extra 35 points (which is what she ended with). Overall, she gained 75 points to end with 35.
Find the measure of the arc
The answer is kindly 21 (100% correct)
Why does it help to rearrange
addends in Example B to show that
2.5n +9.9+(-3n) is equal to
2.5n + (-3n) + 9.9?
Answer:
You don't really need to do it, but it helps you keep things more organized and easier to follow. Imagine if you're doing some multi-variable equation,
2a + 5b + 4d + 3c + b + a + 2d
that looks like a mess, it'll be easier to look at if you put all the similar variables next to each others like this:
a + 2a + b + 5b + 3c + 2d + 4d
(a + 2a) + (b + 5b) + 3c + (2d + 4d)
now you can add them up much easier.
You work at Happy Joe's family restaurant and want to see if customer meal satisfaction and gender are related to one another. You take a sample of customers and ask them if they were satisfied with their meal and note their gender. To determine if Satisfaction and Gender are dependent, what are the appropriate hypotheses
Answer:
[tex]H_o :[/tex] Satisfaction and Gender are independent of one another
[tex]H_a :[/tex] Satisfaction and Gender are dependent of one another
Step-by-step explanation:
Given
Parameters: Meal satisfaction and Gender
Test: If both parameters are dependent
Required
The appropriate hypotheses
To do this, we set the null hypothesis to independence of both parameters
i.e.
[tex]H_o :[/tex] Satisfaction and Gender are independent of one another
The alternate hypothesis will be the opposite, i.e. dependence of both parameters
i.e.
[tex]H_a :[/tex] Satisfaction and Gender are dependent of one another
Convert the following 11110011.001 to decimal
Answer:
243.125
Step-by-step explanation:
First do the integral part
11110011
1. From left to right, starting with a zero,
2. add the digit, double, move on to the next digit and repeat step 2 until digits are exhausted.
The successive results are
1
3
7
15
30
60
121
243
For the decimal part, we proceed similarly but
1. From the right-most digit proceed to the left, start with a zero.
2. Add the digit, halve, move on to the next digit and repeat step 2 until the decimal is reached.
Successive results are:
0.5
.25
.125
So the final result is 11110011.001 binary is 243.125 decimal
Jerome is cooking dinner. He needs 8 ounces of broccoli for each person. Part A: Jerome is not sure how many people will come to dinner. Write an expression with a variable that represents the amount of broccoli Jerome needs for dinner. Identify what the variable represents. Part B: If Jerome has 32 ounces of broccoli, how many people can he feed? Create an equation and show all work to solve it.
Answer:
A. 8x = amount of broccoli needed
B. 4 people; 32÷8=4
Step-by-step explanation:
A. the variable (x) represents the amount of people.
B. 32 ounces divided by 8 ounces is enough for four people.
How does the sample size affect the validity of an empirical argument? A. The larger the sample size the better. B. The smaller the sample size the better. C. The sample size is not relevant if it is greater than 30. D. The sample size is not relevant if it is greater than 50.
Answer:
A. The larger the sample size the better.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have to look at the standard error, which is:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
This means that an increase in the sample size reduces the standard error, and thus, the larger the sample size the better, and the correct answer is given by option a.
Round 620 to the nearest ten! Hurry please and please don't answer if you know you wrong !
Answer:
620 to the nearest ten is already rounded correctly.
Step-by-step explanation:
620 to the nearest ten is 620.
Find the domain and range of the relation: {(–20, 11), (6, –8), (1, –20), (–13, 13)}
Answer:
D: {-20, -13, 1, 6}
R: {-20, -8, 11, 13}
Step-by-step explanation:
Given the relation, {(–20, 11), (6, –8), (1, –20), (–13, 13)}, all x-values (inputs) make up the domain of the relation while all y-values make up the range of the relation.
Therefore:
Domain: {-20, -13, 1, 6}
Range: {-20, -8, 11, 13}
Jane has earned a 91, 85, and 84 on her first three quizzes of the semester. If she hopes to have an A quiz average (90 or above), what is the lowest score Jane can make on her fourth and final quiz?
She cannot earn an A quiz average*****
100
97
95
Answer:
100
Step-by-step explanation:
CalculationLet mark to be scored in fourth =x
but since the total will be more or above we will have the sign
[tex] \geqslant [/tex]
[tex]91 + 85 + 84 + x \div 4 \geqslant 90[/tex]
[tex]260 + x \div 4 \geqslant 90[/tex]
L.c.m =4 ( cross multiplying)
260+xtex 90*4
260+xtex 360
x tex 360-260
x tex 100
The value of the lowest score Jane can make on her fourth and final quiz is, 100
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
Jane has earned a 91, 85, and 84 on her first three quizzes of the semester.
And, she hopes to have an A quiz average (90 or above).
Let us assume that;
her fourth and final quiz = x
Hence, We get;
(91 + 85 + 84 + x) / 4 = 90
260 + x = 360
x = 360 - 260
x = 100
Thus, the lowest score Jane can make on her fourth and final quiz is,
x = 100
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ2
Identify the sampling technique used for the following study.
A statistics student interviews the last fifteen attendees to arrive.
A) Census
B) Stratified Sample
C) Systematic Sampling
D) Simple Random Sampling
E) Cluster Sampling
F) Convenience Sampling
Answer:
F) Convenience Sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
A statistics student interviews the last fifteen attendees to arrive.
Conveniently available, so convenience, and the correct answer is given by option F.
Help help help !!!!
the third choice
Step-by-step explanation:
check the exchange between logarithms and exponential functions srry but cannot write it here with my phone
Find the mean of 2,2,2,2 and 2
Answer:
2
Step-by-step explanation:
mean = sum of data / no of data
=2+2+2+2+2/5
=10/5
=2
[tex]5.5=2\pi \sqrt{\frac{L}{9.8}[/tex]
9514 1404 393
Answer:
7.51 m
Step-by-step explanation:
The equation matches that required for finding the length of a pendulum that has a period of 5.5 seconds. We can solve for L to find the length.
[tex]5.5=2\pi\sqrt{\dfrac{L}{9.8}}\\\\\dfrac{5.5}{2\pi}=\sqrt{\dfrac{L}{9.8}}\\\\\left(\dfrac{5.5}{2\pi}\right)^2=\dfrac{L}{9.8}\\\\L=74.1125/\pi^2\approx7.509[/tex]
The length of a pendulum with period 5.5 seconds is about 7.51 meters.
Answer:
The length, L = 7.52 m.
Step-by-step explanation:
The given expression is
[tex]5.5= 2 \pi \sqrt\frac{L}{9.8}\\\\Sqauring on both the sides\\\\5.5 \times 5.5 = 4\pi^2 \times \frac{L}{9.8}\\\\L = 7.52 m[/tex]
The value of length is 7.52 m.
help on part 3? not sure what i’m supposed to do
The x-intercepts are the points on the plot of a function f(x) where the graph crosses the x-axis. In other words, they're the values of x that make f(x) = 0.
In this case, the x-intercepts are the two roots of the parabola,
(x - 4) (x - 5) = 0 … … … (this is what the hint is referring to)
==> x - 4 = 0 or x - 5 = 0
==> x = 4 or x = 5
The intercepts themselves are points (x, f(x)), so you can report them as (4, 0) and (5, 0).
A survey of 249 people asks about their favorite flavor of ice cream. The results of this survey, broken down by the age group of the respondent and their favorite flavor, are as follows:
Chocolate Vanilla Strawberry
Children 40 10 44
Teens 34 10 38
Adults 17 43 13
If one person is chosen at random, find the probability that the person:______.
a) is an adult.
b) likes chocolate the best.
c) is an adult OR likes vanilla the best.
d) is a child AND likes vanilla the best.
e) likes strawberry the best, GIVEN that the person is a child.
f) is a child, GIVEN that the person likes strawberry the best.
Answer:
a) [tex]P(Adult)=\frac{73}{249}=0.2932=29.32%[/tex]
b) [tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]
c) [tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]
d) [tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]
e) [tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]
f) [tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]
Step-by-step explanation:
a)
In order to solve part a of the problem, we need to find the number of adults in the survey and divide them into the number of people in the survey by using the following formula>
[tex]P=\frac{desired}{possible}[/tex]
In this case we have a total of 17+43+13 adults which gives us 73 adults and a total of 249 people surveyed so we get:
[tex]P(Adults)=\frac{73}{249}=0.2932=29.32%[/tex]
b)
The same principle works for part b
there are: 40+34+17=91 people who likes chocolate ice cream the best so the probability is:
[tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]
c)
when it comes to the or statement, we can use the following formula:
P(A or B) = P(A) + P(B) - P( A and B)
In this case:
[tex]P(Adult)=\frac{73}{249}[/tex]
[tex]P(Vanilla)=\frac{10+10+43}{249}=\frac{63}{249}[/tex]
[tex]P(AdultandVanilla)=\frac{43}{249}[/tex]
so:
[tex]P(AdultorVanilla)=\frac{73}{249}+\frac{63}{249}-\frac{43}{249}[/tex]
[tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]
d)
Is a child and likes vanilla the best.
In the table we can see that 10 children like vanilla so the probability is:
[tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]
e)
Likes strawberry the best, GIVEN that the person is a child.
In this case we can make use of the following formula:
[tex]P(B/A)=\frac{P(AandB)}{P(A)}[/tex]
so we can get the desired probabilities. First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:
[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]
Then, we know there are 40+10+44=94 children, so the probability for the person being a child is:
[tex]P(Child)=\frac{94}{249}[/tex]
Therefore:
[tex]P(Strawberry/Child)=\frac{\frac{44}{249}}{\frac{94}{249}}[/tex]
[tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]
f)
The same works for the probability of the person being a child given that the person likes strawberry the best.
First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:
[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]
Then, we know there are 44+38+13 persons like strawberry, so the probability for the person liking strawberry is:
[tex]P(Child)=\frac{95}{249}[/tex]
Therefore:
[tex]P(Child/Strawberry)=\frac{\frac{44}{249}}{\frac{95}{249}}[/tex]
[tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]
I forgot how to solve these and it won't let me go to the tutor
9514 1404 393
Answer:
see attached
Step-by-step explanation:
I find a graphing calculator to be the quickest way to create a graph of a system of equations. That result is attached.
__
If you want to graph the equations by hand, you need to know a couple of points on each line. When the equations are in slope-intercept form, the y-intercept is often a good place to start. Another point is usually easy to find based on the slope of the line, starting at the y-intercept.
__
Here, the equations are not in that form, but are in the form ax+by=c. In this form, it is often easy to find both the x- and y-intercepts and use those points to plot the line. Each intercept is found by setting the other variable to zero.
x-intercept: c/a
y-intercept: c/b
__
For the given lines, the first equation has intercepts (2, 0) and (0, 2). The line has a slope of -1 and makes an isosceles triangle with the axes in the first quadrant.
The second equation has intercepts (-1, 0) and (0, 2). This line has a slope of +2 and makes a triangle with the axes in the second quadrant.
Which method correctly solves the equation using the distributive property?
Negative 0.2 (x minus 4) = negative 1.7
Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 4 = negative 1.7. Negative 0.2 x = 2.3. x = negative 11.5.
Negative 0.2 (x minus 4) = negative 1.7. x minus 4 = 0.34. x = 4.34.
Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x + 0.8 = negative 1.7. Negative 0.2 x = negative 2.5. x = 12.5.
Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 0.8 = negative 1.7. Negative 0.2 x = negative 0.9. x = 4.5.
9514 1404 393
Answer:
(c) x = 12.5
Step-by-step explanation:
-0.2(x -4) = -1.7
-0.2x +0.8 = -1.7 . . . eliminate parentheses using the distributive property
-0.2x = -2.5 . . . . . . subtract 0.8
x = 12.5 . . . . . . . . divide by -0.2
find the measure of angle c of a triangle ABC, if m
What is the GCF of 1683t, 4085, and 68t??
O 4
O 483t
O 8
O 8837
Answer:I’m pretty sure ( not 100% thou ) the awnser would be A) 4
Rewrite the expression by factoring out (u-8).3u^2(u-8)-2(u-8)
Answer:
The rewritten expression is [tex](u - 8)(3u^2 - 2)[/tex]
Step-by-step explanation:
We are given the following expression:
[tex]3u^2(u - 8) - 2(u - 8)[/tex]
Factoring out (u-8)
Place (u-8) to the front, and then divide each term by (u-8). So
[tex]3u^2(u - 8) - 2(u - 8) = (u - 8)\left[\frac{3u^2(u - 8)}{u - 8} - \frac{2(u-8)}{u - 8}\right] = (u - 8)(3u^2 - 2)[/tex]
The rewritten expression is [tex](u - 8)(3u^2 - 2)[/tex]
A flight leaves the airport at 22:00 hours. It is an 11 hours and 45 minutes flight. There is a 2-hour time difference. What time will they arrive at their destination, assuming the time difference is 2 hours ahead
Answer:
It's on the next day at 11.45am
Step-by-step explanation:
I hope it helps
Based on the time the plane left, the length of the flight, and the time difference, the plane will arrive at 11 : 45 am the next day.
Because the time is 2 hours ahead, adjust the departure time by 2 hours:
= 22:00 + 2
= 00:00
With the plane leaving by 12 am, the time of arrival is:
= 00:00 + 11 hours 45 mins
= 11 : 45 am
In conclusion, the plane will arrive at 11:45 am.
Find out more at https://brainly.com/question/25150454.
IM BEING TIMED PLEASE ANSWER ASAPPPPPP
solve this please:
1y2 + 3y − 6 + 4y − 7 + 2y2 + 3y2 − 8 + 5y
Answer:
just combine like terms, its that simple.
Step-by-step explanation:
A bricklayer needs to order 6 300 kg of building sand.
a) Write 6 300 kg in grams, giving your answer in standard form.
One grain of this sand approximately weighs 7 x 10°g.
b) How many grains of sand are there in 6 300 kg of sand? Give your answer in standard from.
Answer:
It would be 6300000. I can't write this in standard form.
Step-by-step explanation:
Answer:
6.3 x 10^6
Step-by-step explanation:
Find a power series representation for the function. (Give your power series representation centered at x = 0.)
f(x) = x2 x 4 + 81
f(x) = [infinity] n = 0.
Answer:
attached below
Step-by-step explanation:
The Function; F(x) = x^2 / (x^4 + 81 )
power series representation
F(x) = x^2 / ( 81 + x^4 )
= ( x^2/81 ) / 1 - ( -x^4/81 )
attached below is the remaining part of solution
Find the imagine of (x-1 ,y -8 )
Answer:
triangle KLM
Step-by-step explanation:
x-1 meaning subtractikn so u subtract l from its original x cord making it move left 1
y-8 same thing but for the y making it move down 8 spaces
