1200 ml of water needs to be added to lower it to a 2% solution.
Step-by-step explanation:
Given that,
A scientist has 400ml of a 8% solution.
you need to find how water is required to lower the 400 ml to 2% solution.
Let 'x' be the amount of water added to lower it 2% solution.
The formula is given by,
volume of the liquid × % of solution = volume of the new liquid × new %
This can be denoted in chemical relationship ⇒ c₁v₁=c₂v₂ where c is concentration and v is volume .
Now, to find the total volume of new liquid in ml :
400 ml = v₁
0.08= c₁
0.02=c₂
v₂=?
400 × 0.08 =v₂ × 0.02
v₂=1600 ml
To find the x value :
Amount to be added = volume of new liquid - volume of liquid before.
⇒ x =1600-400
⇒ x =1200 ml
∴ 1200 ml of water needs to be added to lower it to a 2% solution.
el Bowen borrowed $10,000 for 3 years
13.75% rate of interest. Find the simple
interest.
Answer:$4125
Step-by-step explanation:
Using the I = P x R x T formula, we can find the simple interest. Substitute all the values into this equation and you get : I = 10,000 x 13.75 x 3. Once you multiply all the values, $4125 is the answer you get. :)
Hello everyone! I have some sample work I'm working on and having trouble with, please help!
And please show your work ^^
|
|
|
v
Answer:
D: 286 [tex]in^{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] * 5.5 * 13 = 35.75 (area of one triangle)
35.75 * 8 = 286 (area of entire octagon)
In 24 games, Jaime has 48 scoring attempts. Which unit rate describes Jaime’s scoring attempts?
a. 1/2 a scoring attempt per game
b. 2 scoring attempts per game
c. 24 scoring attempts per game
d. 72 scoring attempts per game
Answer:
2 Scoring Attempts
Step-by-step explanation:
There are 48 attempts divided by 24 game which equals 2.
Answer:
it is b
Step-by-step explanation:
an
Diego and Lin are drinking milkshakes. Lin starts with 12 ounces and drinks
ounce per second. Diego starts with 20 ounces and drinks.How long will it take lin and Diego to finish their milkshakes?
It will take Lin 12 seconds to finish her milkshake. The time it takes Diego to finish his milkshake cannot be determined without the rate at which he drinks.
Explanation:The problem is about how long it will take for Diego and Lin to finish their milkshakes. Lin is drinking her milkshake at a rate of 1 ounce per second and began with a total of 12 ounces. Therefore, it will take her 12 seconds to finish. For Diego, it doesn't specify how quickly he is drinking his milkshake, which began with 20 ounces, it is impossible to calculate how long it would take him to finish his drink without this information. Hence, to fully solve this problem, you need additional rate information for Diego.
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6. A farmer needs to enclose a section of land in the shape of a parallelogram by using
one side of a barn for one side. The barn and the side adjacent to the barn form a 65°
angle. What is the measure of the angle opposite from this angle? (Circle the correct
answer.)
A. 35°
B. 65°
c. 115°
D. 25°
Answer:
C. 115 degrees
Step-by-step explanation:
Knowing one side of a circle is 180 degrees, we should subtract 180-65.
- 180-65=115 degrees
The 22 members of a baseball team are trying to raise at least $1968.00 to cover the traveling cost for a holiday tournament. If they have already raised $421.00, at least how much should each member still raise, on average, to meet the goal
About $70.31.
You would take $1968.00 and subtract $421.00 from it. Once you've subtracted, you would have gotten $1547.00. You would divide $1547.00 by the 22 people and get about $70.31 per person. :)
A farmer sells 9.1 kilograms of apples and pears at the farmer's market. 2 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer:
5.46 kilograms or 6.6 kilograms
Step-by-step explanation:
Assume that 2 5 in your question has two possible meaning:
2/5 of this weight is applesLet divide 9.1 kilograms into 5 equal part
=> 1 equal part = 9.1 / 5 = 1.82 kilograms
Because 2/5 of this weight is apples, so the weight of apples accounted for 2 equal parts
=> the weight of apples is: 2*1.82 kilograms = 3.64 kilograms
=> the weight of pears is: 9.1 kilograms - 3.64 kilograms = 5.46 kilograms
2.5 kg of this weight is applesGiven the total weight is 9.1 kilograms
=> the weight of pears is: 9.1 kilograms - 2.5 kilograms = 6.6 kilograms
Final answer:
To find the amount of pears sold, calculate two-fifths of the total weight for the apples and subtract this from the total weight. The farmer sold 5.46 kilograms of pears.
Explanation:
The student has asked a question that requires understanding of basic fractions and weight calculation in a real-life context, specifically within a farmer's market scenario. To solve the problem, we note that the total weight of apples and pears sold is 9.1 kilograms. If two-fifths (2/5) of this weight is apples, then to find the weight of pears, we first calculate the weight of apples and then subtract this from the total weight to get the weight of pears.
Step 1: Calculate the weight of apples by multiplying the total weight by the fraction that represents apples. This is 2/5 of 9.1 kg.
Step 2: Subtract the weight of the apples from the total weight to find the weight of pears.
Here are the calculations:
Weight of apples = (2/5) × 9.1 kg = 3.64 kg
Weight of pears = Total weight - Weight of apples = 9.1 kg - 3.64 kg = 5.46 kg
Therefore, the farmer sold 5.46 kilograms of pears at the farmer's market.
Eliminate the parameter to find the cartesian equation of the curve: x=7sinθ,y=cos2θ,−π2≤θ≤π2 x=7sinθ,y=cos2θ,−π2≤θ≤π2 the equation of the curve is: y = equation editorequation editor from x = equation editorequation editor to x =
To eliminate the parameter and find the Cartesian equation of the curve x = 7sinθ,y = cos2θ, we can express x in terms of θ, rearrange the equation, and substitute it into the other equation to eliminate the parameter θ. The resulting equation 2(x/7)² + y - 1 = 0 represents the Cartesian equation of the curve.
Explanation:To eliminate the parameter and find the Cartesian equation of the curve, we can express x in terms of θ using the given equation x = 7sinθ. Rearranging this equation, we get sinθ = x/7. Similarly, we can express y in terms of θ using the given equation y = cos2θ, which can be rewritten as cos(2θ) = y.
Now we can use the trigonometric identity cos(2θ) = 1 - 2sin²θ to eliminate θ from the equations. Substituting this identity into the second equation, we get 1 - 2(sinθ)² = y.
Simplifying this equation, we have 2(sinθ)² + y - 1 = 0. Finally, we can express sinθ in terms of x using the equation sinθ = x/7, and substitute it into the simplified equation to eliminate θ. This gives us 2(x/7)² + y - 1 = 0, which represents the Cartesian equation of the given curve.
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CONGRATS! Your parents bought you a car for graduation. They paid $9000 for it. The bad news is that it depreciates at 12% per year. Write a function to represent the value of the car versus time
Answer:
If the price before depretiation be P and price after depreciation be Pt..
The eqn would be,
Pt=P(1-12/100)^t
Hope it helps!!
Final answer:
The function to represent the value of a car over time, with an initial value of $9000 and depreciating at 12% per year, is V = 9000(1 - 0.12)^t. This exponential decay function calculates the car's value at any time t years after purchase.
Explanation:
The question asks for a function to represent the value of a car over time, given that the car was purchased for $9000 and depreciates at a rate of 12% per year. To model this, we can use an exponential decay function. The general form of an exponential decay function is V = P(1 - r)^t, where V represents the value of the car at time t, P is the initial purchase price, r is the rate of depreciation, and t is the time in years.
Substituting the given values into the formula, we get V = 9000(1 - 0.12)^t. This function can be used to calculate the value of the car at any given time t years after the purchase. The rate of depreciation (12%) and the initial purchase price ($9000) are the critical factors that determine the car's value over time.
Depth d (in feet) of a river can be modeled by the equation d=−0.25t2+1.7t+3.5, where 0≤t≤7 and t is the time (in hours) after a heavy rain begins. When is the river 6 feet deep?
Answer:
The river is 6 feet at two times, 2.15 hours after the rain and 4.65 hours after the rain.
Step-by-step explanation:
We are given the following in the question:
[tex]d=-0.25t^2+1.7t+3.5[/tex]
[tex]0\leq t\leq 7[/tex]
where, d is the depth of river in feet and t is time in hours after a heavy rain.
We have to find the number of hours for which the depth of river is 6 feet.
Putting d = 6 in the equation, we get,
[tex]6=-0.25t^2+1.7t+3.5\\\Rightarrow +0.25t^2-1.7t+2.5 = 0\\\text{Using quadratic formula}\\\\\Rightarrow t = \dfrac{1.7\pm \sqrt{(-1.7)^2-4(0.25)(2.5)}}{2(0.25)}\\\\t\approx 4.65, 2.15[/tex]
Thus, the river is 6 feet at two times, 2.115 hours after the rain and 4.65 hours after the rain.
The attached image shows the graph.
Barry needs to find the area of a rectangular room with a length that is 2 feet longer than the width. Write an expression for the area of the rectangle in terms of the width.
Final answer:
The area of the rectangular room with length 2 feet longer than the width can be expressed as w^2 + 2w square feet, where w represents the width of the room.
Explanation:
Barry needs to calculate the area of a rectangular room where the length is 2 feet longer than the width. If we denote the width as w, then the length will be w + 2 feet. The area of a rectangle is found by multiplying the length by the width.
Therefore, the expression for the area in terms of the width will be:
Area = width × length
Area = w × (w + 2 feet)
Area = w² + 2w square feet
This expression will give us the area of the rectangle in square feet.
If you punch a wall with a force of 30 N, what force will you feel in your fist??
Answer:
30N
Step-by-step explanation:
Normal reaction
The force feel by fist is 30N.
What is Force?
A Force is a push or pull upon an object resulting from the object's interaction with another object.
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.
Since you punch a wall with a force of 30N, the fist will feel the same force in the opposite direction as per the Newton's Third Law of Motion.
Hence The force feel by fist is 30N.
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A rectangular red sticker is 8 millimeters wide and 5 millimeters tall. What is it’s area
Answer:
40 milimeters
Step-by-step explanation:
8*5=40
Joshua is reading a book for history class. He has read 180 pages so far. This number represents 30% of the total
number of pages in the book.
What is the total number of pages in the book?
54 pages
126 pages
385 pages
600 pages
Oo oo
600 is the total number of pages in the book
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Joshua is reading a book for history class.
He has read 180 pages so far.
This number represents 30% of the total number of pages in the book.
We need to find total number of pages in the book.
Let x be the number of pages in the book.
30% of x=180
Convert 30% to decimal
30/100x=180
0.3x=180
Divide both sides by 0.3
x=600
Hence, 600 is the total number of pages in the book
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x + 8y = 2; (10, -1)
In order for you to answer the question correctly, please use the following image 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. (Note- If you are unable to explain your work then it's completely fine. The only thing that I'm asking for is for you to show all the work so I can understand how you got your answer)
Answer:
The value of x is 16°
Step-by-step explanation:
Using the formula, angle = 1/2(θ°-x°) :
Let θ = 96°, x = x°, angle = 40°,
1/2×(96°-x°) = 40°
96° - x° = 80°
-x° = 80° - 96°
-x° = -16°
x = 16°
Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that (28+45)^2=73^2.Which best describes Nadia’s solution?
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
She is incorrect because she should have used 45 as the length of the hypotenuse.
She is incorrect because she should have squared each leg length and then found the sum.
She is correct because the hypotenuse is the longest side of the triangle.
Answer: She is incorrect because she should have squared each leg length and then found the sum.
The Pythagorean Theorem is a² + b² = c² not (a+b)²=c² as written.
Answer:
Answer is c)))
Rico does not work for Street Bikes Company,but wrongfully obtains inside information concerning the firm.Based on the information,Rico buys and sells Street Bikes stock for personal gain.The Securities and Exchange Commission prosecutes Rico,arguing that he is liable because he stole information rightfully belonging to another.This argument is:_________.
A) the blue-sky theory.
B) the misappropriation theory.
C) the free-writing prospectus theory.
D) the tipper/tippee theory.
Answer:
B) The misappropriation theory
Step-by-step explanation:
The misappropriation theory states that a person who uses insider information in trading securities has committed securities fraud against the information source.
In this case, Street Bikes Company is the information source because the information rightfully belong to them, Rico trades Street Bikes Stocks because he stole the firm's information which does not belong to him, according to the misappropriation theory, Rico is liable to the offence of insider trading.
If a fair die is rolled 4 times, what is the probability, to the
nearest thousandth, of getting exactly o threes?
The probability of not getting a '3' when a fair die is rolled four times, rounded to the nearest thousandth, is approximately 0.482.
Explanation:In a fair die, the probability of getting any one number, such as a 3, is 1/6 because a die has 6 possible outcomes (1 through 6). So, the probability of not getting a 3 is 5/6. If the die is rolled four times, the probability of not getting a 3 on each roll is (5/6)^4. To find this, multiply 5/6 by itself 4 times. The result is approximately 0.482, or rounded to the nearest thousandth, 0.482. So, "the probability of not getting a 3 on four rolls of a die to the nearest thousandth is 0.482."
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Find the solutions/ show steps
Sin2x+sin(4x) =0
Answer:
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
Step-by-step explanation:
sin(2x) + sin(4x) = 0
Use double angle formula.
sin(2x) + 2 sin(2x) cos(2x) = 0
Factor.
sin(2x) (1 + 2 cos(2x)) = 0
Solve.
sin(2x) = 0, cos(2x) = -½
2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
find the area of the circle. round your answer to the nearest hundredths. the diameter is 2cm
Answer:
3.14 cm squared
Step-by-step explanation:
First, identify the formula necessary to calculate the area of the circle.
Area of a circle = pi x r^2
Remember, the radius is just half of the diameter! Then to square a number, is to multiply it by itself once.
pi x 1^2 =?
pi x 1
Pi
The circumference of your circle is approximately 3.14 cm squared.
Fill in the blanks to correctly complete the sentence below.
Suppose a simple random sample of size n is drawn from a large population with mean muμ and standard deviation sigma σ. The sampling distribution of [tex]\bar x[/tex] has mean [tex]\mu_{\bar x}[/tex] =______ and standard deviation [tex]\sigma_{\bar x}[/tex] =______.
Answer:
Mean of the sampling distribution, [tex]\mu_{\bar{x}}=\mu[/tex]
Standard deviation of the sampling distribution [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Step-by-step explanation:
Given a simple random sample of size n which is drawn from a large population
If the mean of the simple random sample of size n [tex]=\mu[/tex] The sampling distribution of [tex]\bar{x}[/tex] has the same mean [tex]\mu_{\bar{x}}=\mu[/tex]If the standard deviation of the simple random sample of size n is [tex]\sigma[/tex] The sampling distribution of will have a standard deviation of [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]Find the area of a circle with a diameter of \color{green}{16}16start color green, 16, end color green.
Answer:
if you can write a comment so that makes sense, i might be able to help you
Step-by-step explanation:
sorry
Answer:
The answer is 64pi
Step-by-step explanation:
Which of these pieces of data about a football team is considered numerical data?
Answer:
1. Points scored
Step-by-step explanation:
A numerical data is defined as a data that is made up of numbers representing the quantity of a measurement. It is a measurable data such as weight or height, at it can be arranged in ascending or descending order as well as being able to provide an average.
The two types of numeric data are discrete and continuous data
A categorical data is made up of item labels, names or description, that are qualitative in their nature.
Information about a football team that is considered as numeric includes
1. Points scored
Which represents a quantifiable measurement that can be different with different teams and matches
2. Attendance this year.
A company knows that unit cost C and unit revenue R from the production and sale of x units are related by Upper C equals StartFraction Upper R squared Over 220 comma 000 EndFraction plus 3221.C= R2 220,000+3221. Find the rate of change of revenue per unit when the cost per unit is changing by $ 9$9 and the revenue is $1 comma 0001,000.
Answer:
$990 per unit.
Step-by-step explanation:
The Unit Cost (C) and Unit Revenue R from the production and sale of x units are related by the function:
[tex]C=\dfrac{R^2}{220000} +3221[/tex]
We are required to find the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is $1,000.
Rate of Change of C,
[tex]\dfrac{dC}{dt}=\dfrac{R}{110000} \dfrac{dR}{dt} \\\dfrac{dC}{dt}=\$9, R=\$1000\\9=\dfrac{1000}{110000} \dfrac{dR}{dt}\\\dfrac{dR}{dt}=9 \div \dfrac{1000}{110000}\\=9 X \dfrac{110000}{1000}\\\dfrac{dR}{dt}=\$990 $ per unit$[/tex]
The Revenue is changing at a rate of $990 per unit.
The problem is solved by first finding the derivative of the given equation to determine the rate of change. Given that the cost per unit is changing by $9, we substitute this in the derivative equation to get the revenue. Real-world applications of such problems help understand the concepts of marginal revenue and marginal cost.
Explanation:As per the equation C = R2/220000 + 3221, we first need to find the derivative to determine the rate of change. So, C'(R) = 2R/220000 where C' represents the derivative of the cost with respect to revenue.
Given that the cost per unit is changing by $9, we can represent this as C' = 9 and solve for R using the derivative equation. Hence, R = sqrt(220000 * 9 / 2) = $1000. Therefore, the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is $1,000 is found by substituting the revenue value into derivative equation.
These types of problems demonstrate how rates of change can be evaluated using calculus concepts in real-world applications such as understanding marginal revenue and marginal cost in economics and business studies.
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A bag contains 5 red marbles, 3 green marbles, 2 purple marbles, 2 orange marbles, and 1 blue marble.
Which color marble is less likely to be picked than purple?
Answer:
blue marble is the right answer
Combine the like terms
Answer: -4
Step-by-step explanation:
[tex]3x-7x=x\\-4x=-4x[/tex]
Answer:
The answer is -4x.
Step-by-step explanation:
You can just substract easily by writing 7-3 but remember to add negative to the final value as 3 is smaller than 7 and lastly, you only have to add x to the final answer.
erin ran 7 1/2 miles around the track. Each lap is 1 1/2 miles. How many laps did Erin run
Answer:
She ran 5 laps
Step-by-step explanation:
Why? Because with each lap stating to be one and a half miles; you first and only step is to divide, seeing how each time you put 1 1/2 into the value of this 7 1/2 miles, you got a lap each time.
you divide 7 1/2 by 1 1/2,
this results in getting, 5
Answer: Erin ran 5 laps.
Step-by-step explanation
if he ran 7 1/2 miles and one lap is 1 1/2 miles then you need to add 1 1/2 miles up until you get the distance he ran which is 7 1/2 miles and when u keep adding 1 1/2 miles to get to 7 1/2 you get 5 laps. hope this helps :)
Jake has decided to give a bonus to the employee who has worked the greatest total number of hours over the past six months. Four candidates are currently up for consideration. The following graph shows how many hours each one has worked over the past six months.
A graph titled Hours Worked has name on the x-axis and Hours on the y-axis. For October: Vince, 130; Claire, 129; Joey, 134; Katharine, 122. For November: Vince, 135; Claire, 130; Joey, 121; Katherine, 131. For December: Vince, 131; Claire, 125; Joey, 119; Katherine, 134. For January: Vince, 133; Claire, 126; Joey, 127; Katharine, 133. For February: Vince, 134; Claire, 121; Joey, 132; Katharine, 115. For March: Vince, 118; Claire, 133; Joey, 134; Katharine, 140.
To which employee will Jake give the bonus?
a.
Vince
b.
Claire
c.
Joey
d.
Katharine
Please select the best answer from the choices provided
A
B
C
D
Answer:
The answer is A) Vince.
Step-by-step explanation:
Vince had 781 total hours. Claire had 764 total hours. Joey had 767 total hours. Katharine had 775 total hours. Therefore the person with the most hours, Vince, gets the bonus.
Jake will give the bonus to Vince, as she has worked the greatest total number of hours over the past six months.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To determine who will receive the bonus, we need to calculate the total number of hours worked by each employee over the past six months.
For Vince:
130 + 135 + 131 + 133 + 134 + 118 = 781
For Claire:
129 + 130 + 125 + 126 + 121 + 133 = 764
For Joey:
134 + 121 + 119 + 127 + 132 + 134 = 767
For Katharine:
122 + 131 + 134 + 133 + 115 + 140 = 775
Jake will give the bonus to Vince, as she has worked the greatest total number of hours over the past six months.
Hence, Jake will give the bonus to Vince, as she has worked the greatest total number of hours over the past six months.
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Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.) 5 sin2 θ − 9 cos 2θ = 03
Answer:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]
Step-by-step explanation:
The equation needs to be rearranged in terms of one trigonometric function:
[tex]5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0[/tex]
[tex]5\cdot \tan 2\theta - 9 = 0[/tex]
[tex]5\cdot \tan 2\theta = 9[/tex]
[tex]\tan 2\theta = \frac{9}{5}[/tex]
[tex]\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)[/tex]
The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]