Answer:
11.33%
Step-by-step explanation:
Amount of salt which Larry has to mix= 15 grams
In 210 gm of salt solution, content of salt= 5%
Amount of salt in salt solution= 5 % of 210 grams
Amount of salt in salt solution= [tex]\frac{5}{100}[/tex] of 210 grams
Amount of salt in salt solution= [tex]\frac{21}{2}[/tex]
Amount of salt in salt solution= 10.5 grams
Now the 15 grams of salt have to mix with 5% of salt solution
Total amount of salt= 15+ 10.5
Total amount of salt = 25.5 gram
Total amount of salt solution=15+ 210= 225 grams
Percentage of salt in new solution=[tex]\frac{amount of new salt}{ amount of new solution}[/tex] ×100
Percentage of salt in new solution=[tex]\frac{25.5}{ 225}[/tex] ×100
Percentage of salt in new solution= 0.13333×100
Percentage of salt in new solution= 11.33% (approx)
Hence, the correct answer is 11.33%
G use lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane.x + 9y + 8z = 27
Suppose that f(x+h)−f(x)= −6hx2−7hx−6h2x−7h2+2h3.
Find f′(x).
f′(x)=
Final answer:
To find f'(x), simplify the given expression by canceling the common factor of h, then take the limit as h approaches zero. The resulting derivative is f'(x) = -6x² -7x.
Explanation:
To find the derivative of function f(x), denoted as f'(x), we use the definition of the derivative and the given equation f(x+h) - f(x) = -6hx2 - 7hx - 6h2x - 7h2 + 2h3. The definition of the derivative is the limit of the average rate of change as the interval approaches zero, formally:
f'(x) = lim (h -> 0) [f(x+h) - f(x)] / h
In the given difference quotient, every term includes an h, allowing us to simplify by cancelling an h from each term before taking the limit as h approaches zero. This gives us:
f'(x) = lim (h -> 0) [-6x² - 7x - 6h2 - 7h + 2h2]
When h approaches zero, the terms containing h also approach zero. Thus, we are left with:
f'(x) = -6x² - 7x
T Shirt sore keeps 7 white T-Shirts on the shelves for every 3 purple T- Shirts on the shelve how many white T-Shirts on the shelve if 15 purple T-Shirts on the shelve. Show how you get the answer in long form
What is 0.10221 in scientific notation
Find the instantaneous rate of change of w with respect to z if w=7/3z^2
The instantaneous rate of change of 'w' with respect to 'z', for the function w = 7/3z², is 14/3*z.
Explanation:The question is asking for the instantaneous rate of change of 'w' with respect to 'z'. To compute this, we need to take the derivative of w with respect to z, for the given function w = 7/3z². Using the power rule, which says that the derivative of z^n is n*z^(n-1), our derivative would be: (7/3)*2*z^(2-1) simplifying this gives 14/3*z. Hence, the instantaneous rate of change of 'w' with respect to 'z' for given function is 14/3*z.
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3x+y=5
y=2x
Substitution method
Find dy/dx by implicit differentiation. 3x + y = 8 + x2y2
To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x, apply the chain rule and product rule, isolate the terms involving dy, and simplify the equation to find dy/dx.
Explanation:To find dy/dx by implicit differentiation, we need to differentiate both sides of the equation with respect to x. Using the chain rule and product rule, we can simplify the equation and solve for dy/dx. Starting with 3x + y = 8 + x^2y^2:
Step 1: Differentiate each term with respect to x.
Step 2: Apply the chain rule and product rule to simplify the equation.
Step 3: Solve for dy/dx by isolating the terms involving dy.
Step 4: Simplify the equation and rearrange to get dy/dx.
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A restaurant requires customers to pay a 15% tip for the server. your family spends $45 on the meal.
a.how much money do you need to pay the server?
b.how much money will you spend total?
A) 45 * 0.15 = $6.75 paid to server
B 45 + 6.75 = $51.75 total
Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the rate of change of money in his savings account per week?
Finley makes 1 batch of her favorite shade of orange paint by mixing 5 liters of yellow paint with 3 liters of red paint. How many batches of orange paint can Finley make if she has 15 liters of red paint?
Suppose x follows a continuous uniform distribution from 1 to 5. determine the conditional probability p(x >2.5 | x ≤ 4).
Final answer:
The conditional probability P(x > 2.5 | x ≤ 4) for a variable x following a uniform distribution from 1 to 5 is calculated using the conditional probability formula, resulting in a probability of 0.5.
Explanation:
The question asks to determine the conditional probability P(x > 2.5 | x ≤ 4) when x follows a continuous uniform distribution from 1 to 5. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of A and B both happening, and P(B) is the probability of B happening.
Here, event A is 'x > 2.5' and event B is 'x ≤ 4'. The probability of x being greater than 2.5 and less than or equal to 4, P(A ∩ B), is the length of the interval from 2.5 to 4, which is 1.5 units. Since x is uniformly distributed, this translates to a probability of 1.5/(5-1), because the total length of the distribution is 4 units. Event B 'x ≤ 4' has a probability of 3/(5-1) since the interval from 1 to 4 is 3 units long.
Hence, the conditional probability is P(A|B) = (1.5/4) / (3/4) = 1.5/3 = 0.5.
Which are properties of rotations? Check all that apply.
1 Rotations are always counterclockwise.
2 Rotations preserve size.
3 Rotations of 360° map a figure to itself.
4 Lines connecting corresponding points on the pre-image and image are parallel.
5 Lines connecting corresponding points on the pre-image and image have equal length.
6 Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Answer:- The correct properties of rotation are as follows:-
2.Rotations preserve size.
3. Rotations of 360° map a figure to itself.
6. Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Explanation:-
Rotation transformation is a rigid transformation which create the image of a figure with same shape and size by rotating it by some degrees about the the center of rotation.1. False ; Rotations are always counterclockwise.→ it is not a property of rotation, ∵rotation can be clockwise or counterclockwise both.
2.True; Rotations preserve size. [by definition of rotation]
3.True; Rotations of 360° map a figure to itself. [It completes one turn and get back to the original position ]
4.False; Lines connecting corresponding points on the pre-image and image are parallel. [They can be intersect]
5.False ; Lines connecting corresponding points on the pre-image and image have equal length.[The point which is the center of rotation in a figure is nearest to its image rather than the other points. ]
6. True ; Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length. [∵ all the points of the figure is rotated about the center of the point ,so the distance of the center of rotation to the pre-image and the corresponding point on the image have equal length]
Rotations have several properties, including preserving size, mapping a figure to itself when rotated by 360°, and having lines connecting the centre of rotation to the pre-image and image equal in length.
Properties of rotations:
Rotations are not always counterclockwise.Rotations preserve size.Rotations of 360° map a figure to itself.Lines connecting corresponding points on the pre-image and image are parallel.Lines connecting corresponding points on the preimage and image have equal lengths.Lines connecting the centre of rotation to the pre-image and the corresponding point on the image have equal lengths.write 4.51 in expanded form
The expanded form of 4.52 is 4 + 0.5 + 0.01
Given.
4.51
We need to find the expanded form.
What is expanded form?It is a form of writing a given number by splitting it based on the place value.
Example:
56743
We can write it as:
50000 + 6000 + 700 + 40 + 3
Find the expanded form of 4.51
4 is in ones place
So,
4 - 4
5 is in tenths place
So,
0.5 - 0.5
1 is in hundredths place
So,
.01 - .01
The expanded form is:
4 + 0.5 + 0.01
Thus the expanded form of 4.52 is 4 + 0.5 + 0.01
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An aluminum recycling center pays $0.08 per pound for cans. How much will Mark receive for 21.5 pounds of cans?
How much force is required to push a 54-pound sofa across a carpeted floor?
Find each percentage decrease. round to the nearest percentage from 16 bagels to 0 bagels
To solve this problem:
The formula would be: New Value – Old Value)/Old Value] x 100 or in the form of variable it would be: [(B-A)/A] x 100 = Answer.
So plugging in the information given in our problem it would be:
0 – 16 / 16 x 100 = percent of change
0/16 x 100 = 0%
The answer is 0%
What is the relationship between 0.04 and 0.004?
What is the logarithmic form of 144=12^2
The logarithmic form of 144=12^2 is log12(144) = 2.
Explanation:The logarithmic form of 144=12^2 is log12(144) = 2.
The logarithm is the power to which a base number must be raised to equal a given number. In this case, the base is 12, and we are trying to find the power that results in 144.
Since 12^2 = 144, the logarithmic form is log12(144) = 2.
the logarithmic form of 144=12^2 is b: [tex]\( \log_{12}(144) = 2 \)[/tex].
The correct option is (b).
The logarithmic form of the expression [tex]\( 12^2 = 144 \)[/tex] translates an exponential equation into a logarithmic equation. The general form of converting from exponential to logarithmic form is:
[tex]\[ b^y = x \] is equivalent to[/tex]
[tex]\\ \[ \log_b(x) = y \][/tex]
where:
- [tex]\( b \)[/tex] is the base of the exponential expression,
-[tex]\( y \)[/tex] is the exponent,
-[tex]\( x \)[/tex] is the result of the exponential expression.
Applying this to the given equation[tex]\( 12^2 = 144 \)[/tex], we have:
-[tex]\( b = 12 \)[/tex],
- [tex]\( y = 2 \)[/tex],
- [tex]\( x = 144 \)[/tex].
So, the logarithmic form is:
[tex]\[ \log_{12}(144) = 2 \][/tex]
complete question given below:
What is the logarithmic form of 12² = 144?
a.log212=144
b.log12144=2
c.log1442=12
d.log2144=12
What is the equation of the line that passes through
(10, 4)
and is perpendicular to
5x−y=3
after 75% reduction, you purchase a new clothes dryer on sale for $200. What was the original price?
Original price was $800 for purchasing a new clothe dryer on sale for $200 after 75% reduction.
Original price is the price offered initially without applying any offer.
Discount offered is the amount of relaxation that is the difference between the marked price and selling price.
Given the following information:
Discount provided= 75%
Purchasing price after discount=200
Let the original price be x
x-75%x=200
[tex]x-\dfrac{75}{100}x=200\\\\100x-75x=200\times 100\\[/tex]
Solving the equation as follows to calculate the value of x:
[tex]25x=20000\\x=20000/25\\x=800[/tex]
Thus, original price was $800.
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A bathtub is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Three minutes later, it holds 12 gallons of water. Write an equation that represents the number y of gallons of water in the tub after x minutes.
3 minutes - 2 minutes = 1 minute
30 gallons - 12 gallons = 18 gallons
it is draining at 18 gallons per minute
equation would be: y = -18x
Evaluate. 4⋅(4+(2^6⋅2^−3))
Is this equation correct? 18/48=27/72?
How much will you pay the cashier for a candy bar that originally costs 79 cents and is now marked 15% off? Sales tax is 5.5%
You have 900-grams of an an unknown radioactive substance that has been determined to decay according to D ( t ) = 900 e − 0.002415 ⋅ t D ( t ) = 900 e - 0.002415 ⋅ t where t t is in years. How long before half of the initial amount has decayed?
It will take __ years for half of the initial amount to decay. (Round to 1 decimal place)
clark wants to figure out how many pens to order for the office. there are 36 workers, and he need to order one pen for each worker. he know that for every eight people who prefer red , there are four who prefer blue. How many blue pens should he order?
8 like red 4 like blue
8+4 = 12
36/12=3
4*3 = 12 blue pens
Manuel and Sonja are shopping for school supplies. Manuel is buying 5 notebooks and 3 pens at a cost of $21. Sonja is buying 6 notebooks and 5 pens at a cost of $28. The first equation, representing Manuel’s purchase, is mc015-1.jpg. What is the second equation needed to solve the system?
Answer:
Second equation is 6x + 5y = 28
Step-by-step explanation:
Let x is the cost of notebooks and y is the cost of pens.
Now we know Manuel is buying 5 notebooks and 3 pens at a cost of $21.
To represent this statement equation is 5x + 3y = 21
Similarly we will form the second equation to solve the system of equations.
Cost of 6 notebooks = 6x
Cost of 5 pens = 5y
Total cost of 6 notebooks and 5 pens = $28
So 6x + 5y = 28 will be the second equation.
By solving this system of equations we can find the cost of notebook as well as cost of pen purchased by Manuel.
a plumber charges a base fee of $55 for a service call plus $35 per hour for each hour worked during the service call the relationship between the total price of the service called and the number of hours worked
The relationship between the total price and the number of hours worked can be represented by a linear equation. The equation is y = 35x + 55, where y represents the total price and x represents the number of hours worked.
Explanation:The relationship between the total price of the service call and the number of hours worked can be represented by a linear equation. We can use the formula y = mx + b, where y represents the total price, x represents the number of hours worked, m represents the hourly fee, and b represents the base fee.
In this case, the plumber charges a base fee of $55 and $35 per hour. So the equation that expresses the total price is y = 35x + 55.
The independent variable in this situation is the number of hours worked, which is x. The dependent variable is the total price, which is y. The y-intercept of the equation is 55, which represents the base fee. The slope of the equation is 35, which represents the hourly fee. The y-intercept (b) is the point where the line intersects the y-axis, and the slope (m) determines how steep the line is.
Jessica purchased an $84 suit. The sales tax is 6.5%. What is the total price of the suit including tax?
Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.