Answer:
5 km/h
Step-by-step explanation:
In this problem, Lashonda swam 4 km against the current. So the distance covered in this case is
[tex]d_1=4 km[/tex]
Calling [tex]v[/tex] the velocity of Lahonda without the current, and [tex]c[/tex] the velocity of the current, in this situation Lahonda's velocity is
[tex]v-c[/tex]
So we can write:
[tex]t_1=\frac{d_1}{v-c}[/tex]
where [tex]t_1[/tex] is the time taken to cover the distance.
When Lashonda swims with the current, her velocity is
[tex]v+c[/tex]
So we can write
[tex]t_2=\frac{d_2}{v+c}[/tex]
where
[tex]d_2=16 km[/tex] is the distance covered in this case, and [tex]t_2[/tex] the time taken.
The velocity of the current is
[tex]c=3 km/h[/tex]
Since Lashonad takes the same time to cover the two distances,
[tex]t_1=t_2[/tex]
So we can write
[tex]\frac{d_1}{v-c}=\frac{d_2}{v+c}[/tex]
And solving for v, we find Lashonda's velocity without the current:
[tex]d_1(v+c)=d_2(v-c)\\d_1 v+d_1c = d_2v-d_2c\\v(d_2-d_1)=c(d_1+d_2)\\v=\frac{d_2+d_2}{d_2-d_1}c=\frac{16+4}{16-4}(3)=5 km/h[/tex]
Final answer:
To find Lashonda's swimming speed without the current given the rate of the current and the distances swam with and against it.
Explanation:
The rate of the current is 3 kilometers per hour. To find the speed of Lashonda without the current, we can set up equations using the formula: speed = distance/time.
Let's denote Lashonda's speed in still water as x kilometers per hour. When swimming against the current, her effective speed is x - 3 km/h, and when swimming with the current, her effective speed is x + 3 km/h.
By setting up and solving the equations, we find Lashonda's speed without the current is 9 kilometers per hour.
Regions $A, B, C, J$ and $K$ represent ponds. Logs leave pond $A$ and float down flumes (represented by arrows) to eventually end up in pond $B$ or pond $C$. On leaving a pond, the logs are equally likely to use any available exit flume. Logs can only float in the direction the arrow is pointing. What is the probability that a log in pond $A$ will end up in pond $B$?
Answer:
Step-by-step explanation:
1 1/5
Answer:
5/18
Step-by-step explanation:
There is a 1/3 chance of going to k. From K, there is a 1/2 chance of going to b, so that way has a prob of 1/6. By the same concept, there is a 1/9 chance of going to B via J. The prob you are asking for is 5/18
June ran 1/4 of a mile in 3 minutes. How long will it take her to run a full mile?
Answer:
12 minutes !
Step-by-step explanation:
Hope this helps!!
Answer:
12 minutes
Step-by-step explanation:
3 x 4 = 12
y= arctan(-4x) when dy/dx at x = 3
Answer:
200\cdot25-84\cdot\frac{91}{12-65}\cdot\frac{8412}{1.000}-2000000\cdot46512
Step-by-step explanation:=−9.30227818×1010
Determine which pair of points has a positive slope.
A. (5, -4), (-2, 1)
B. (-10, -2), (6,6)
C. (6, -10), (2, 10)
D. (5, -1), (-6, 6)
Here are the weights, in pounds, of a sample of 13 adult female golden retriever dogs: 59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4. what are the degrees of freedom, and what's the critical value of t needed to construct a 95% confidence interval for the population mean weight of adult female golden retrievers? answer:
Answer:
95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].
Step-by-step explanation:
We are given that the weights, in pounds, of a sample of 13 adult female golden retriever dogs :
59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean weight = [tex]\frac{\sum X }{n}[/tex] = 54.9 pounds
s = sample standard deviation = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 3.12 pounds
n = sample of female = 13
[tex]\mu[/tex] = population mean weight
Here for constructing 95% confidence interval we have used One-sample t test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.179 < [tex]t_1_2[/tex] < 2.179) = 0.95 {As the critical value of t at 12 degree
of freedom are -2.179 & 2.179 with P = 2.5%}
P(-2.179 < [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.179) = 0.95
P( [tex]-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X -\mu}[/tex] < [tex]2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X +2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [tex]\bar X \pm 2.179 \times {\frac{s}{\sqrt{n} } }[/tex]
= [ [tex]54.9 - 2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] , [tex]54.9 +2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] ]
= [53.01 pounds , 56.78 pounds]
Therefore, 95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].
When a number is increased by 2.8%, the result is 56. What is the original number to
the nearest tenth?
Answer:
The original number was 54.5.
Step-by-step explanation:
If a number is increased by 2.8%, then it is 102.8% of it's original number.
In mathematics, "of" in virtually all cases means "multiplied by".
Therefore, we do the opposite:
1. Convert to a decimal.
102.8% = 1.028
2. Divide by the decimal.
[tex]56 \div 1.028 = 54.47[/tex]
3. Round it to the nearest tenth.
54.47 rounds to 54.5.
To find the original number when increased by 2.8%, we set up and solve an equation. The original number to the nearest tenth is approximately 54.4.
Explanation:To find the original number, we can set up the equation:
x + 0.028x = 56
Simplifying gives:
1.028x = 56
Dividing both sides by 1.028 gives:
x = 56 / 1.028 ≈ 54.41
So, the original number to the nearest tenth is approximately 54.4.
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Can someone please help with this?
Answer:
8 square units
Step-by-step explanation:
Draw vertical and horizontal lines, dividing the triangle into 9 equally sized smaller triangles. 4 of the smaller triangles are shaded, so the area of the square is 4/9 the area of the triangle.
A = 4/9 (½ (6)(6))
A = 8
Which of these is a correct expansion of (4x-2)(2x + 3)?
O A. 4x: 2x + 4x:3+ (-2): 2x + (-2): 3
O B. 4x. 27+ 4x• 3 + 2 + 2+ + 2-3
O c. 4x• 2x + (-2): 2x + 27.3+(-2) - 3
Answer:
C
Step-by-step explanation
You have to do the rainbow move which is basically multiplying
4x*2x, 4x*3, -2*2x, -2*3
which then simplified would equal to 8x^2+8x-6
1. What is the shape of the distribution below?
(a) The distribution is symmetrical
(b) The distribution is not symmetrical
Answer: A
Step-by-step explanation: Because you have a dot in the middle and it is very equal
Answer: the distribution is symmetrical.
Step-by-step explanation:
Which expression is equivalent to 12x – 3x? *
8x
9
3(3x - x)
x(12-3)
Answer:
x(12-3)
Step-by-step explanation:
The expression given is equal to 9x. The only given answer equivalent to 9x is the last one, x(12-3).
Derek has a cylindrical water bottle with a diameter of 4 centimeters and a height of 15 centimeters. If he filled the water 3/4 full of water, how much water is in the water bottle?
Answer:
141 3/8
Step-by-step explanation:
First find the volume by multiplying pi, the radius squared, and the height. Pi is 3.14. The radius is half the diameter, so it would be 2. 2^2 is 4. The height is 15. 3.14*4*15=188.5 Then multiply 3/4 and 188.5 to get your answer. 141.375 or 141 3/8.
MAY SOMEBODY HELP ME THANKS!
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 706.50 square feet? Use 3.14 for pi.
IM MARKING BRAINLIEST!!
Answer:
15 feet of water spread
Step-by-step explanation:
Area of the circular pattern is 706.50 sq. feet
Area = A = π r^2 = (3.14)* r^2
706.50 = (3.14)* r^2
r^2 = 706.50 / 3.14
r^2 = 706.50 / 3.14
r = root (225)
r = 15 feet
Answer:
15 feet
Step-by-step explanation:
The area of a circle is pi*r^2, and we're using 3.14 as pi, so we get: area= 3.14 r^2
We plug 706.50 into the equation and get:
706.50 = 3.14 r^2
Divide both sides by 3.14:
225 = r^2
Square root both sides:
15 = r
y = 1/2x - 6
X = - 4
What is the solution to the system of equations?
titte
(-8, -4)
(-4,-8)
(-4,4)
(4,-4)
Step-by-step explanation:
Putting value of x
Y = 1/2 ( - 4) - 6
Y = - 2 - 6
Y = - 8
( - 4, - 8)
find the percent of change to nearest percent:56 to 80
Answer:
26 %
Step-by-step explanation:
you just go from 80 and count backwards all the way to 56 and count how many spaces or tally's that was and then you got your answer.
In order to answer the following question, please use the following image down below:
Find the value of x.
X=(Blank)
What is the value of X? Please show all the work on how you got your answer.
(If you can't explain your work, then it's fine. The only thing that I'm asking for is for you to show the work alongside your answer)
Answer:
12
Step-by-step explanation:
X^2 = (7+9)(9) -->
X^2 = 16(9) -->
X = 12
which is true regarding the system of equations 6x+2y=46 3x+y=23
Answer:
Step-by-step explanation:
hello :
the system is : 6x+2y=46
3x+y=23
if you multiply the second equation by : 2 you have 6x+2y =46(same first equation )
conclusion : the system have infinity solutions ( graphically same line)
conclusion :
Lester's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 80 espressos in all, 80% of which were single-shot. How many single-shot espressos did the cafe sell?
Answer:
64 single-shot espressos
Step-by-step explanation:
Let's say that the cafe sold x single-shot espressos. The total number of espressos sold was 80, and 80% of that total 80 were single-shot. So, we have the equation:
x = 80% * 80
Remember that % just means "out of 100". So, 80% = 80/100:
x = (80/100) * 80 = 6400/100 = 64 single-shot espressos
Hope this helps!
Answer:
64
Step-by-step explanation:
80% of 80 were single-shots
80/100 × 80
64
Which expression is equivalent to the following complex fraction?
StartFraction negative 2 Over x EndFraction + StartFraction 5 Over y EndFraction divided by StartFraction 3 Over y EndFraction minus StartFraction 2 Over x EndFraction
Answer:
(-2y+5x) / (3x - 2y)
Step-by-step explanation:
If we write this sentence, we have:
((-2/x) + (5/y)) / ((3/y) - (2/x))
If we do LCM in the denominators of each fraction, we have:
((-2y+5x)/xy) / ((3x - 2y)/xy)
We can cut the 'xy' in the numerator and denominator of the whole fraction:
(-2y+5x) / (3x - 2y)
The final expression we have is (-2y+5x) / (3x - 2y)
Answer:
a
Step-by-step explanation:
(-2y+5x) / (3x-2y)
3. An amusement park charges $6 to enter, and $3 per game. If you paid a
total of $18, how many games did you play?
Answer:
You played 4 games
Step-by-step explanation:
You start with $18 and subtract 6 from the entry fee. Then, you divide the 12 you got from that and divide it by 3
Final answer:
To determine the number of games played, subtract the access fee from the total cost and then divide by the per-game price. In this case, the student paid for an access fee of $6, and played 4 games at $3 each to reach a total cost of $18.
Explanation:
The question posed is a basic algebra problem involving a fixed entry fee and a variable cost per game. The given information states that the access fee is $6 and the per-unit price, which in this case is the cost per game, is $3. If the total amount paid was $18, the number of games played can be calculated.
To solve, let's denote the number of games played as x. The total cost is made up of a fixed access fee plus the cost of the games played. The expression for the total cost is thus $6 (access fee) + $3x (cost of games).
The equation based on the total amount paid would be:
6 + 3x = 18
To find the value of x, we subtract the access fee from the total amount paid:
18 - 6 = 3x
That simplifies to:
12 = 3x
Which can then be solved by dividing both sides by 3:
x = 12 / 3
x = 4
The student thus played 4 games.
which of the following statements about rotations are true? select all that apply
Circle A has a circumference of 8/3 m. Circle B has a diameter that is 3/2 times as long as Circle A’s diameter. What is the circumference of Circle B?
Answer:
the answer is 4
Step-by-step explanation:
if my calculations are right
Serena has attached a 10 inch ribbon to the corners of a frame to hang it on the wall. The frame 9 inches wide. How far above the top of the frame will the hook need to be? Round
Answer: The hook would be 2.2 inches (approximately) above the top of the frame
Step-by-step explanation: Please refer to the picture attached for further details.
The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (longest side) and AB and BC are the other two sides
5^2 = 4.5^2 + BC^2
25 = 20.25 + BC^2
Subtract 20.25 from both sides of the equation
4.75 = BC^2
Add the square root sign to both sides of the equation
2.1794 = BC
Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches
To find the distance above the frame for hanging, use the Pythagorean theorem by considering the diagonal created by the ribbon. The hook needs to be approximately 5.39 inches above the top of the frame.
To find how far above the top of the frame the hook needs to be, we need to consider the diagonal of the frame created by the ribbon. Using the Pythagorean theorem, we can calculate this distance.
Width of the frame = 9 inchesLength of the ribbon attached diagonally = 10 inchesUsing Pythagorean theorem: (9)² + x² = (10)²x = square root of (10² - 9²)x = 5.39 inchesTherefore, the hook needs to be approximately 5.39 inches above the top of the frame.
Eighty-five percent of what number is 42.5?
A.
180
B.
36.125
C.
50
D.
30
Answer:
50
Step-by-step explanation:
Hope this helped
:)
What is the ratio for relative frequency?
Relative frequency = StartFraction row total Over column total EndFraction
Relative frequency = StartFraction row total Over total count EndFraction
Relative frequency = StartFraction total count Over subtotal count EndFraction
Relative frequency = StartFraction subtotal count Over total count EndFraction
Answer:
Relative frequency= subtotal count - total count
Step-by-step explanation:
Answer:
D.Relative frequency= subtotal count / total count
HELLPPP Mariah is shopping at the mall for a sweatshirt. She finds a sweatshirt that is marked down 55% off the original price of the sweatshirt is $78.25. What is the sale price of the sweatshirt?
Answer:
Her Original PRICE WAS $117.375
Step-by-step explanation:
If the sale price is 55% of the original price of the sweatshirt, the sale price is $78.25.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Given that, Mariah is shopping at the mall for a sweatshirt. She finds a sweatshirt that is marked down 55% off the original price of the sweatshirt is $78.25.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
The sale price of the sweatshirt is,
sale price = 55% of the current price
sale price =(55/100)× $78.25
sale price = $43.03
Thus, if the sale price is 55% of the original price of the sweatshirt, the sale price is $78.25.
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What is 9.22 × 103 in standard form
Answer:
=>9.4966×10^2
Step-by-step explanation:
9.22×103
=>949.66
in standard form
=>9.4966×10^2
Factor out a GCF
[tex]3x^{2} +12x[/tex]
Answer:
3x(x+4)
Step-by-step explanation:
3x^2+12x
3x^2 = 3*x*x
12x = 2*2*3*x
We can factor out 3x
3x (x+2*2)
3x(x+4)
HELP PLEASE!
Jackson runs around a track in the evening for exercise. How far does Jackson run each evening if he runs 3 times around the track shown in the diagram below? Round your answer to the nearest whole yard.
1042 I just took the test I can't remember if that is the right number but it is the largest number
9. Bryce goes och for a walk. He walks 9/8 miles from home. He walks back 1/2
mile before meeting up with his friend Mya. Write and simplify an expression (a
sum) that describes this situation.
Answer:
Expression:
[tex]\frac{9}{8}+(-\frac{1}{2})=\frac{5}{8}[/tex]
Step-by-step explanation:
We are given that
Bryce traveled distance from his home=[tex]\frac{9}{8}miles[/tex]
Bryce traveled distance back=[tex]\frac{1}{2}miles[/tex]
We have to find the expression and then simplify.
According to question
Total distance traveled by Bryce
=[tex]\frac{9}{8}+(-\frac{1}{2})[/tex]
This is required expression.
Total distance traveled by Bryce=[tex]\frac{9-4}{8}=\frac{5}{8}miles[/tex]
Hence, the total distance traveled by Bryce from his home=[tex]\frac{5}{8}miles[/tex]
Final answer:
To find the total distance Bryce walked, we add 9/8 miles to 1/2 mile, which equals 13/8 miles or simplified to 1 5/8 miles.
Explanation:
Bryce initially walks 9/8 miles from home. On his way back, he walks 1/2 mile before meeting up with his friend Mya. To describe this situation with an expression and simplify it, we add these distances together:
Total distance walked = 9/8 miles + 1/2 mile
To simplify, find a common denominator (which in this case is 8), and then add the numerators:
Total distance walked = (9/8) + (4/8)
Total distance walked = (9 + 4) / 8
Total distance walked = 13/8
Total distance walked = 1 5/8 miles
This is the sum describing the distance Bryce walked before meeting Mya, which simplifies to 1 and 5/8 miles.
The middle schools baseball team the badgers won 20 games last year this year they won 22 games what is the percentage increase of games one from this year to last year
Answer:
The correct answer is 10%.
Step-by-step explanation:
The middle school's baseball team the badgers won 20 games last year.
This year they won 22 games.
Increase in the number of wins = 22 - 20 = 2.
We need to find the percentage increase of games as compared to the last year. That is given by dividing the increase in wins divided by the wins last year multiplied by 100.
Percentage increase as compared to the last years is given by [tex]\frac{2}{20}[/tex] × 100 = 10%
There is an increase of 10% in the number of wins in this year as compared to the last year.