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Related Questions
a tank contains 500 gal of a salt-water solution containing 0.05 lb of salt per gallon of water. pure water is poured into the tank and a drain at the bottom of the tank is adjusted so as to keep the volume of solution in the tank constant. at what rate (gal/min) should the water be poured into the tank to lower the salt concentration to 0.01 lb/gal of water in under one hour?
Answers
To lower the salt concentration to 0.01 lb/gal of water in under one hour, water should be poured into the tank at a rate of 500 gallons per minute.
To find the rate at which pure water should be poured into the tank, we can use the concept of salt balance. Let's denote the rate at which water is poured into the tank as 'R' (in gal/min).
The initial volume of the tank is 500 gallons, and the salt concentration is 0.05 lb/gal. The amount of salt initially in the tank is given by 500 gal * 0.05 lb/gal = 25 lb.
We want to lower the salt concentration to 0.01 lb/gal in under one hour, which is 60 minutes.
To do this, we need to remove 25 lb - (0.01 lb/gal * 500 gal) = 20 lb of salt.
Since the volume of the solution in the tank is kept constant, the rate at which salt is removed is equal to the rate at which water is poured in, multiplied by the difference in salt concentration. Therefore, we have:
R * (0.05 lb/gal - 0.01 lb/gal) = 20 lb
Simplifying, we get:
R * 0.04 lb/gal = 20 lb
Dividing both sides by 0.04 lb/gal, we find:
R = 20 lb / 0.04 lb/gal
R = 500 gal/min
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if 200 group rooms are reserved and only 160 are ultimately occupied, the pick-up rate is group of answer choices 60% 70% 80% 90%
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The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.
It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.
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explain how you can use absolute value to tell whether the fisherman or the end of his fishing line is farther from the surface of the water.
Answers
Answer:
So the answer is in your thoughts and also in your mind so therefor the answer is the fisherman is more farther away just by looking at him
Step-by-step explanation:
Answer:
The fisherman is farther away from the surface of water.
Step-by-step explanation:
So first of all, we know by looking at it that fisherman is farther away, but we need to use absolute value.
What is the absolute value of -12? 12.
That way, you can easily compare 16 and |-12|!
I hope this helped!
The number of bacteria in a refrigerated food product is given by N(T) = 307² - 112T+75,
3
When the food is removed from the refrigerator, the temperature is given by T(t) = 3t+1.7, where t is
the time in hours.
Find the composite function N(T(t)):
N(T(t)) =
Find the time when the bacteria count reaches 20082.
Time Needed ==
hours
Answers
The composite function N(T(t)) = 20082.The time when the bacteria count reaches 20082 is approximately 30.28 hours.
To find the composite function N(T(t)), we need to substitute the expression for T(t) into the function N(T).
Given:
N(T) = 307² - 112T + 75
T(t) = 3t + 1.7
Substituting T(t) into N(T), we get:
N(T(t)) = 307² - 112(3t + 1.7) + 75
Simplifying:
N(T(t)) = 307² - 336t - 190.4 + 75
N(T(t)) = 307² - 336t - 115.4
Now let's find the time when the bacteria count reaches 20082.
N(T(t)) = 20082
307² - 336t - 115.4 = 20082
Taking 115.4 to the other side:
\(307^2\) - 336t = 20082 + 115.4
307² - 336t = 20197.4
336t = 307² - 20197.4
Dividing by 336:
t = (307² - 20197.4) / 336
Calculating the value of t:
t ≈ 30.28
Therefore, the time when the bacteria count reaches 20082 is approximately 30.28 hours.
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geometry question! i need help!
Answers
Answer:
nl
Step-by-step explanation:
wider the angle, the side opposite to it will be big
let's take ∆lnm angle nlm = 180-(62+55)=180-117=63
take ∆lnp, angle pln = 180-(66+58)=56
angle l = 56+63 = 119
angle p iz the greatest, so side ln must be longest
(-5)-(-2)=
Please answer and explain
Answers
Answer:
-3
Step-by-step explanation:
(-5)-(-2)=
-5+2
=-3
Answer:
-3
Step-by-step explanation:
Get rid of the parenthesis
-5 - -2 = x
2 negatives = positive
We can rewrite this using a positive sign instead of two negative signs.
-5 + 2 = x
Solve the equation
The answer would be -3
Hope this helps :)
Have a nice day!
Use a calculator to evaluate the trigonometric functions of the given anglers. Round your answers to four decimal places. Please help
Answers
Answer: figure it out.
Step-by-step explanation: it's not hard, just put it in a calculator, knowledge...
In AABC shown below, L is the midpoint of BC, M is the midpoint of AB, and N is the midpoint of
AC. If MN = 8, ML = 5, and NL = 6, find the perimeter of trapezoid BMNC.
Need help ASAP pls
Answers
Answer:
35Step-by-step explanation:
see attached image.
perimeter of trapezoid = sides (6 + 8 + 5 + 8 + 8)
= 35
the perimeter of trapezoid BMNC is 35
Given :
In triangle ABC shown below, L is the midpoint of BC, M is the midpoint of AB, and N is the midpoint of AC. If MN = 8, ML = 5, and NL = 6
By midpoint theorem ,
\(BC= 2 \cdot MN\\BC=2 \cdot 8\\BC=16\)
M is the midpoint of AB, AB= 2 times NL
BM=NL
BM=6
N is the midpoint of AC
AC is 2 times of ML
NC=ML
NC=5
Perimeter of trapezoid is sum of all the sides
Perimeter of BMNC = BM+MN+NC+CB
Perimeter =\(6+8+5+16=35\)
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In the triangle below what is the length of AC?
A. 60
B. 14
C.90
D.28
Answers
Answer:
B 14
Step-by-step explanation:
All the angles of the triangle ABC are 60°.
Therefore it is an equilateral triangle.
All sides of an equilateral triangle are equal.
Hence, \( \overline{AC} = 14\)
I have a go to the store and she’s his clothes and shoes for a new job the purchases total of $200 even has a choice pay with cash or pay with credit card that gives a discount how much will ava save immediately if she uses the credit card and paid the balance during the billing cycle?
Answers
Answer:
$10, $30.40
Step-by-step explanation:
The volume of statue B is 20% less than the volume of statue A
The surface area of statue B is k% less than the surface area of statue A
Work out the value of k
Give your answer correct to 3 significant figures.
Answers
The value of k is approximately 10.32%.
Value of K calculation.
Let's assume that the volume of statue A is equal to V.
According to the problem statement, the volume of statue B is 20% less than the volume of statue A. Therefore, the volume of statue B can be expressed as:
Vb = 0.8V
Next, we are given that the surface area of statue B is k% less than the surface area of statue A. Let's calculate the surface area ratio of B to A:
(Sb / Sa) = 1 - (k/100)
We know that the surface area of a sphere is proportional to the square of its radius, while the volume of a sphere is proportional to the cube of its radius. Therefore, we can use the following formula to relate the volume and surface area of a sphere:
(V / S^1.5) = constant
Substituting the values for statues A and B, we get:
(Va / Sa^1.5) = (Vb / Sb^1.5)
Simplifying this equation using the values we already have, we get:
(0.8V / Sb^1.5) = (V / Sa^1.5)
Cross-multiplying and rearranging, we get:
(Sb / Sa) = (0.8)^(2/3) = 0.8968
Substituting this value in the earlier expression for the surface area ratio, we get:
0.8968 = 1 - (k/100)
Solving for k, we get:
k = (1 - 0.8968) * 100 = 10.32
Therefore, the value of k is approximately 10.32%.
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gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 25 feet high?
Answers
Below is the answer
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1Joe gets a job picking fruit. Joe is paid $5 for every bushel of apples he
picks. If B represents the number of bushels that Joe picks and P
represents the amount that joe is paid at the end of the day, which of the
following equations represent how much money Joe will make?
A P = B + $5
B) P = B($5)
C) B = $5+ P
OD) B = P (Joe)
Answers
Answer:
B
Step-by-step explanation:
The number of bushels of apples he picks (B) would be times by 5 as he would earn that much per bushel to get his pay (P)
which statement best describes this regression (y = highway miles per gallon in 91 cars)?
A) Statistically significant but large error in the MPG predictions
B) Statistically significant and quite small MPG prediction errors
C) Not quite significant, but predictions should be very good
Answers
Your answer: B) Statistically significant and quite small MPG prediction errors
This statement best describes the regression, as it indicates that the relationship between the variables is statistically significant.
Without specific data or statistical analysis, it is impossible to accurately determine which statement best describes the regression for y = highway miles per gallon in 91 cars. However, in general, a statistically significant regression means that there is a relationship between the variables being analyzed. The error in predictions refers to the difference between the predicted value and the actual value.
Therefore, A) statistically significant but large error in the MPG predictions and B) statistically significant and quite small MPG prediction errors could both be possible outcomes depending on the specific data and analysis. C) Not quite significant, but predictions should be very good is unlikely to be a valid statement if the regression is not statistically significant.
Additionally, the small MPG prediction errors suggest that the regression model is reliable and accurate in making predictions for highway miles per gallon in the 91 cars.
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graph:f(x)=2(2)^x. ……………………………….
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The function is an exponential function that increases exponentially as x increases; for every increase in x by 1, the output of the function is multiplied by 2.
First, let's define the function, \(f(x) = 2(2)^x.\) This is an exponential function where the base is 2 and the exponent is x.
Next, we need to calculate the output for a given input. For example, let's calculate f(3). This is equal to \(2(2)^3\). We can calculate this by multiplying 2 by 2 three times, giving us a result of 16.
Now let's calculate f(4). This is equal to \(2(2)^4\), which can be calculated by multiplying 2 by 2 four times. This gives us a result of 32.
We can continue this process by multiplying 2 by 2 x times, where x is the input value, to calculate the output of f(x).
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28 miles 56 yards divided by 28
= ? miles ? yards
Answers
As a result, the solution is 8 miles 56 yards times 28 is 0.2863636 miles, or around 0 miles 504 yards.
Why does a house have a yard?The majority of a yard will likely be a grassland or play area. The area behind a home is alluded to as the backyard, and the yard in front is referred to as the front yard. Since backyards tend to be more private, they are more frequently used as recreational spaces. The size of the yard varies with density of population.
Starting with 8 miles 56 yards, we can change it to just yards, which is:
8 × 1760 + 56 = 14136 yards.
Then, we may convert 14136 yards to yards by multiplying 28.
14136 yards ÷ 28 = 504 yards.
504 yards must now be converted back to kilometers and yards. Since 1 mile is equal to 1760 meters, we can calculate the distance by multiplying 504 by 1760:
504 yards ÷ 1760 yards/mile = 0.2863636 miles (rounded to 7 decimal places).
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Simplify: 14 - 2+ 8 = 2 *3
helppp meeee
Answers
Answer:
20=6?
Step-by-step explanation:
14-2+8=2*3
14-2+8=6
12+8=6
20=6?
Answer:
These to equations aren't equivalent.
Step-by-step explanation:
14-2+8=2*3
12+8=6
20=6
Hope this helps ;) ❤❤❤
12.6^2 - 0^2 / 2 x 16 =
Answers
12.6^2 - 0^2 / 2 x 16
= 4.96125
Hope this helped uyou-Have a good day bro cya)
Lauri is planning a bridal shower for her best friend. At the party , she wants to serve 3 beverages, 2 appetizers, and 2 desserts, but she does not have time to cook. She can choose from 18 bottled drinks,8 frozen appetizers, and 5 prepared dessertsat the supermarket. How many different ways can Lauri pick the food and drinks to serve at the bridal shower?
Answers
In order to calculate the probability of each item, we need to use a combination formula.
The combination of n choose p elements can be calculated with the formula below:
\(C(n,p)=\frac{n!}{p!(n-p)!}\)For the beverages, she will choose 3 items among 18 options, so the number of ways she can choose is:
\(C(18,3)=\frac{18!}{3!15!}=\frac{18\cdot17\operatorname{\cdot}16}{3\operatorname{\cdot}2}=816\)For the appetizers, she wants 2 items among 8 options, so:
\(C(8,2)=\frac{8!}{2!6!}=\frac{8\operatorname{\cdot}7}{2}=28\)For the desserts, she will choose 2 items from 5 options, so:
\(C(5,2)=\frac{5!}{2!3!}=\frac{5\operatorname{\cdot}4}{2}=10\)Now, calculating the total number of possibilities, we have:
\(\begin{gathered} N=C(18,3)\operatorname{\cdot}C(8,2)\operatorname{\cdot}C(5,2)\\ \\ N=816\operatorname{\cdot}28\operatorname{\cdot}10\\ \\ N=228480 \end{gathered}\)Solve for k. 4k – 10 = 8 . = Stuck? Watch a video or use a hint.
Answers
We are given the following equation
\(\frac{4k-10}{k}=8\)Let us solve this equation for k
Step 1:
Multiply both sides of the equation by k
\(\begin{gathered} k\cdot\frac{(4k-10)}{k}=8\cdot k \\ 4k-10=8k \end{gathered}\)Step 2:
Subtract 8k from both sides of the equation
\(\begin{gathered} 4k-8k-10=8k-8k \\ -4k-10=0 \end{gathered}\)Step 3:
Add 10 to both sides of the equation
\(\begin{gathered} -4k-10+10=10 \\ -4k=10 \end{gathered}\)Step 4:
Finally, divide both sides of the equation by -4
\(\begin{gathered} \frac{-4k}{-4}=\frac{10}{-4} \\ k=-\frac{10}{4} \\ k=-\frac{5}{2} \end{gathered}\)Therefore, the value of k is equal to -5/2
Refer attachment for working!
Given triangle MTW is congruent to triangle BGK,find y.
Answers
Answer:
y = 8
Step-by-step explanation:
As MTW and BGK are congruent
angle T = angle G
4x - 3 = 45
in triangle MTW
angle M = 180 - (T + W)
= 180 - (45 + 41)
= 180 - 86
= 94
and angle M = B
11y + 6 = 94
11y = 94 - 6
11y = 88
y = 8
Solve for x. −6≥10−4x
x≤4
x≥−4
x≤−4
x≥4
Answers
Answer:
x≥4
Step-by-step explanation:
_6≥10+4x
group like terms
4x≥10+6
4x≥16
divide both side by 4
4x\4≥16\4
x≥4
The solution to the inequality is given as x ≥ 4. Then the correct option is D.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
−6 ≥ 10 − 4x
The solution to the inequality is given below.
−6 ≥ 10 − 4x
4x ≥ 10 + 6
4x ≥ 16
x ≥ 16 / 4
x ≥ 4
The solution to the inequality is given as x ≥ 4. Then the correct option is D.
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One sheet of A4 paper has an area of 1/16 m^2. A4 paper has a mass of 80g per m^2. Work out the total mass of 320 sheets of A4 paper.
Answers
Answer: 1600g or 1.6kg
Step-by-step explanation:
80 x 1/16 = 5
5 x 320 = 1600g or 1.6kg
The total mass of 320 sheets of A4 paper is 1600 g.
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Given that,
Area of a sheet of paper = 1/16 m².
Mass of A4 paper = 80 g per m².
We have to find the total mass of 320 papers.
In order for that, first we have to find the total area of 320 papers.
Area of a sheet = 1/16
Area of 320 sheets = 1/16 × 320 = 20 m²
Mass of paper per m² = 80 g
Mass of paper for 20 m² = 80 × 20 = 1600 g
Hence the total mass is 1600 g.
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You are purchasing supplies for an art project. you need 3 containers of paint, 2 brushes, and 1 case of canvas. each container of paint is $3.99, each brush is $3.80, and each case of canvas is $15.99. write and evaluate an expression for the total cost of the art supplies.
Answers
The computation shows we that the total cost is $31.57.
How to compute the value?From the information, the person is purchasing supplies for an art project. you need 3 containers of paint, 2 brushes, and 1 case of canvas. each container of paint is $3.99, each brush is $3.80, and each case of canvas is $15.99.
This will be:
= 3($3.99) + 2($3.80) + 1($15.99)
= $7.98 + $7.60 + $15.99
= $31.57
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Find an equation for the hyperbola with foci (0,±5) and with asymptotes y=± 3/4 x.
Answers
The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:
y^2 / 25 - x^2 / a^2 = 1
where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.
Thus, the equation for the hyperbola is:
y^2 / 25 - x^2 / (400/9) = 1
or
9y^2 - 400x^2 = 900
The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.
To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.
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Please help and show all workings
If \(ac^3+bx^2+c\) is divided by (x-3) then the remainder is:
Silly answers will not be tolerated
Answers
Answer:
27a + 9b + c is reminder
Step-by-step explanation:
Remainder theorem says that when p(x) is divided by (x – a) the remainder is given
by p(a)
Let p(x) = ax³ + bx²+ c
P(x) when divided by (x – 3)
Using Remainder theorem, we have
Remainder = p(3) = a(3³) + b(3²) +c
= 27a + 9b + c
Find lcm of 861,1353 using methods
Answers
Answer:
Step-by-step explanation:
3 ∣ 861,1353
______________
41 ∣ 287,451
______________
7 ∣ 7,11
______________
11 ∣ 1,11
______________
1,1
LCM = 3 × 41 × 7 × 11
= 9471.
Hope this helps
plz mark as brainliest!!!!!!
Answer:
861 = 3×7×41
1353 = 3×11×41
LCM = 3×7×11×41
= 9471
Step-by-step explanation:
Write a word problem that must be solved with division and includes 2/7 as the dividend and 4 as the divisor.
Answers
The problem can be formed as, Joy has (2/7) ounces of honey and he divides this honey among four of his guests, How many ounces of honey will each of his friends get?
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Suppose, Joy has (2/7) ounces of honey and he divides this honey among four of his guests, How many ounces of honey will each of his friends get?
The amount of ounces of honey each of his friends gets is,
= (2/7)/4 ounces.
= (2/7)×(1/4) ounces.
= 2/28 ounces.
= 1/14 ounces.
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Find each unit price and decide which is the better buy. Assume that we are comparing different sizes of the same brand.Crackers:$1.19 for 12 ounces$1.59 for 16 ouncesAfter finding this information out decide which is a better buy
Answers
To find the unit price, we need to divide the price by the amount of ounces:
$1.19 for 12 ounces:
\(\frac{1.19}{12}=\frac{119}{1200}\approx0.099166\)$1.59 for 16 ounces:
\(\frac{1.59}{16}=\frac{159}{1600}=0.099375\)We can see that in the 4º decimal place, the first option has a 1 and the second option has a 3. Thus, is better to buy the second option
To 3 decimal places:
First option: $0.099 per ounce
Second option: $0.099 per ounce
Question 14 1pts A store manager studied the relationship between the number of umbrellas sold each month (y) and the monthly rainfall (x,mm) obtained the least square regression line based on the data of the past two years: 9-11.5+0.36x. If he also obtains the standard deviations for X andy as X-30.5, _Y-24.4,find the linear correlation r betweenx andy: r-0450 r-0.288 r-0.715 r-0.680
Answers
The formula for the linear correlation coefficient (r) between two variables x and y is given by: r = cov(x,y) / (std(x) * std(y)). Answer : we don't know the value of cov(x,y), we can't calculate r.
r = cov(x,y) / (std(x) * std(y))
where cov(x,y) is the covariance between x and y, and std(x) and std(y) are the standard deviations of x and y, respectively.
From the given information, we have:
Regression line: y = 9 - 11.5x + 0.36x
Standard deviations: std(x) = 30.5, std(y) = 24.4
To find the covariance between x and y, we need to know the values of x and y for the past two years. Assuming we don't have that information, we can use the regression line to estimate the values of y based on the given values of x.
Using the regression line, we have:
y = 9 - 11.5x + 0.36x
Substituting x with x - mean(x) and y with y - mean(y), we get:
y - mean(y) = 9 - 11.5(x - mean(x)) + 0.36(x - mean(x))
Expanding and simplifying, we get:
y - mean(y) = -11.14x + 344.7
Now we can use this equation to estimate the values of y for the given values of x, and then calculate the covariance and correlation coefficient.
Using the given values of x, we have:
x = [unknown values for the past two years]
Using the regression line to estimate the corresponding values of y, we get:
y = [9 - 11.5x + 0.36x for the unknown values of x]
Calculating the covariance between x and y, we get:
cov(x,y) = sum((x - mean(x)) * (y - mean(y))) / (n - 1)
where n is the number of observations. Since we don't have the actual values of x and y, we can't calculate the covariance directly.
Finally, using the formula for r, we get:
r = cov(x,y) / (std(x) * std(y))
Since we don't know the value of cov(x,y), we can't calculate r. Therefore, the answer is indeterminate.
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