Zachary measures the area of a glacier at
the start of every year.
2
At the start of this year, the glacier had an
area of exactly 56.20 km². This is 0.2%
less than it was at the start of last year.
Work out what the area of the glacier was
at the start of last year.
2
Give your answer in km² to 2 d.p.
Answers
The area of the glacier at the start of last year was 56.31 km², based on a percentage reduction of 0.2%.
What is a percentage decrease?A percentage decrease represents the difference between the starting and ending values, expressed as a percentage of the starting value.
In working out the percentage reduction, we determine the difference between the ending and starting values. This difference is divided by the starting value and multiplied by 100.
The current area of the glacier = 56.20 km²
The percentage reduction = 0.2%
Proportionately, the current area, in percentage terms = 99.8% (1 - 0.2%)
99.8% = 56.20 km²
100% = 56.31 km²
Thus, to 2 decimal points, the area of the glacier at the start of last year was 56.31 km².
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Related Questions
Calculate the percent by mass of a solution where 13.687 grams is dissolved in 46.833 grams of water. answer without the percent sign
Answers
The percent by mass of a solution is 29.21.
To calculate the percent by mass of a solution, divide the mass of the solute (13.687 grams) by the total mass of the solution (46.833 grams). Then, multiply this value by 100 to get the percent.
% by mass = (mass of solute/total mass of solution) x 100
% by mass = (13.687/46.833) x 100 = 29.21.This calculation can be used to determine the amount of a solute in a given solution. It is important to know the percent by mass of a solution in order to make sure the solution is composed of the desired amount of solute. Knowing the percent by mass can also be used to compare the solutions of different concentrations.
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someone please answer and explain how to do this in steps i will give you a cookie
Answers
17. The equation can be rewritten as 2x²-8x+1=0.
18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.
How many solutions does the graph have?17.
The equation can be rewritten as 2x²-8x+1=0.
Vertex:
The vertex is (4, -1). A minimum.
Axis of symmetry:
The axis of symmetry is x = 4.
The parabola opens up.
The graph has 1 solution.
18. How many solutions does the quadratic
have?
Answer: The axis of symmetry is x = 5, which is calculated by taking the coefficient of x (which is -10) and dividing it by 2. This is because the axis of symmetry is always in the middle of the two x-intercepts. The parabola opens up, which means it has a maximum at the vertex. The vertex is (5, 6), which is calculated by substituting x = 5 into the equation and solving for y.The quadratic equation has two solutions, x = 4 and x = 6. To find the solutions, one must set the equation equal to 0 and solve for x. This can be done by either factoring or using the quadratic formula. After finding the x-intercepts, the solutions can be determined by plugging in the x-intercepts into the equation and solving for y.To learn more about Solutions in the graph refer :
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17. The equation can be rewritten as 2x²-8x+1=0. 18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.
17. The equation can be rewritten as 2x²-8x+1=0.
Vertex:
The vertex is (4, -1). A minimum.
Axis of symmetry:
The axis of symmetry is x = 4.
The parabola opens up.
The graph has 1 solution.
18. The coefficient of x, which is -10, is multiplied by two to determine the axis of symmetry, which is x = 5.
This is due to the fact that the axis of symmetry is always located halfway between the two x-intercepts.
The parabola widens, indicating that the vertex is where its maximum is located. The vertex is (5, 6), which is determined by solving for y while changing x = 5 in the equation.
There are two answers to the quadratic equation: x = 4 and x = 6. The equation must be made equal to 0 in order to get the solutions.
Either factoring or applying the quadratic formula can be used to accomplish this.
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(1 point) A company received a shipment of 42 laser printers, including 8 that are defective. 2 of these printers are selected to be used in the copy room. (a) How many selections can be made? (b) How many of these selections will contain no defective printers?
Answers
The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.
(a) There are 6,632 selections that can be made.
(b) There are 5,832 selections that will contain no defective printers.
(a)The number of selections can be found using the nCr formula: nCr = n!/(r!(n-r)!), where n is the total number of items (42) and r is the number of items selected (2). So nCr = 42!/(2!(42-2)!) = 42!/(2!40!) = 6,632.
(b) The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.
There are 6,632 selections that can be made when two printers are chosen from a shipment of 42, including 8 that are defective. Out of these selections, 5,832 will contain no defective printers.
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g the space complexities of bfs and dfs are o(b^d) and o(bd) respectivaly, why is one exponential with respect to d and the other not
Answers
BFS has an exponential space complexity with respect to d because it stores all the nodes at the same depth level before moving on to the next level
DFS doesn't have an exponential space complexity with respect to d because it only stores the nodes that need to be visited next.
The space complexity of breadth-first search (BFS) is O([tex]b^d[/tex]) and the space complexity of depth-first search (DFS) is O(bd), where b is the maximum branching factor of the search tree and d is the maximum depth of the tree.
The reason for the difference in the space complexities is that BFS uses a queue to store the nodes to be visited, while DFS uses a stack.
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question approximately 38 percent of people living in region w have the blood type o positive. a random sample of 100 people from region x revealed that 35 people in the sample had the blood type o positive. consider a hypothesis test to investigate whether the percent of people in region x with o positive blood is different from that of in region w. which of the following is the appropriate null hypothesis for the investigation? Ha: proportion 0.38 Ha: proportion >0.38 Ha: proportion =0.38 O Ha: proportion <0.38
Answers
Null hypothesis for the investigation Ha=0.38
The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.
This hypothesis is either rejected or not rejected based on the viability of the given population or sample.
In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance.
It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H0.
Here, the hypothesis test formulas are given below for reference.
The formula for the null hypothesis is:
H0: p = p0
The formula for the alternative hypothesis is:
Ha = p >p0, < p0≠ p0
The formula for the test static is:
[tex]z=\frac{p-p0}{\sqrt{\frac{p0(1-p0)}{n} } }[/tex]
Remember that, p0 is the null hypothesis and p – hat is the sample proportion.
38 percent of people living in region w have the blood type o positive.
w region
38% - o positive
x region
100 random sample
35 o positive
means 35/ 100*100
35% 0 positive
a hypothesis test to investigate whether the percent of people in region x with o positive blood is different from that of in region w
The formula for the null hypothesis is:
H0: p = p0 =0.38
Ha = p >p0, < p0≠ p0
Ha=0.38
Null hypothesis for the investigation Ha=0.38
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Rework problem 27 from section 1.2 of your textbook, about the three subsets X1, X2, and X3 that partition a set X, except assume that the number of elements in X, is 4 times the number of elements in X2, the number of elements in X3 is 6 times the number of elements in X2, and n(X) = 99. (1) n(X1) = (2) n(X2) = (3) n(X3) =
Answers
The value of three subsets is [tex]n(x_{1})=36, n(x_{2})=9, & n\left(x_3\right)=54[/tex].
A set is a collection of objects or elements, grouped in the curly braces, such as {a, b, c, d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.
The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.
If set A has {X, Y} and set B has {X, Y, Z}, then A is the subset of B because elements of A are also present in set B.
Let the number of elements in [tex]$x_2$[/tex] be [tex]$x$[/tex], then
[tex]$$\begin{aligned}& n\left(x_1\right)=4 x \\& n\left(x_2\right)=x \\& n\left(x_3\right)=6 x\end{aligned}$$[/tex]
Given that number of elements in [tex]$x=99$[/tex]
[tex]$$\begin{aligned}\Rightarrow & n\left(x_1\right)+n\left(x_2\right)+n\left(x_3\right)=99 \\\Rightarrow & 4 x+x+6 x=99 \\\Rightarrow & 11 x=99 \\\Rightarrow & x=9 \\\therefore & n\left(x_1\right)=4 x=4 \times 9=36 \\& n\left(x_2\right)=x=9 \\& n\left(x_3\right)=6 x=6 \times 9=54\end{aligned}$$[/tex]
Therefore, the value of [tex]& n\left(x_3\right)[/tex][tex]=54[/tex].
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There exist two complex numbers c, say c1 and c2, so that 2+2i, 5+i, and c form the vertices of an equilateral triangle. Find the product c1c2 .enter image description here
So far, I have used the distance formula to get (a−2)2+(b−2)2=(a−5)2+(b−1)2 for c1(a,b). I expanded and simolified this to get b=3a−9. What do I do next?
Answers
The product of the two complex number c₁c₂ is thus 10 + 9i.
Let c₁ = a + ib and c₂ = c + id. Also z₁ represent 2 + 2i and z₂ represent 5 + i. The length of side of the equilateral triangle formed can be obtained by
|z₁ - z₂| = r = √((5 - 2)² + (1 - 2)² = √10
a² + b² - 4a - 4b + 8 = 10
a² + b² - 10a - 2b + 26 = 10
So 6a - 2b = 18 that is 3a - b = 9
Thus b = 3a - 9
Similarly c² + d² - 4c - 4d + 8 = 10
c² + d² - 10c - 2d + 26 = 10
So 3c - d = 9, that is d = 3c - 9
Midpoint of line joining c₁ and c₂ is same as that of z₁ and z₂, so
(c + a)/2 = ( 5 + 2)/ 2 and (d + b)/2 = (1 + 2)/2
So midpoint is 3.5 + 1.5i
Altitude of equilateral triangle of side a is √3a/2
That is √(a - 3.5)² + (b - 1.5)² = √3×√10/2
√(a - 3.5)² + (3a - 9 - 1.5)² = √30 /2
a² - 7a + 12.25 + 9a² - 63a + 110.25 = 30/4
On solving a = (7 ± √3)/ 2
So a = (7 - √3)/ 2, c = (7 + √3)/ 2
b = 3a - 9 = (3 - 3√3)/ 2, d = (3 + 3√3)/2
So c
c₁ = (7 - √3)/2 + i (3 - 3√3)/ 2
c₂ = (7 + √3)/2 + i (3 + 3√3)/ 2
So the product c₁c₂ is
= ((7 - √3)/ 2) * ((7 + √3)/ 2) - ((3 - √3)/ 2) * ((3 + √3)/ 2) + i (((7 - √3)/ 2) * ((3 + √3)/ 2) + ((7 + √3)/ 2) * ((3 - √3)/ 2))
= 10 + 9i
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43)A tree13feet high grows at the rate of3feet each year. How many years will it take for the tree to grow to a height of 28 feet?
the answer is 5 please show me how to get that answer?
Answers
O $132.50
7) Kiron is buying $84 worth of groceries at the store. The sales tax rate is 8.75%. What is the total
cost of his groceries in dollars and cents?
Answers
The total cost of his groceries in dollars and cents is 91.35 on 8.75% sales tax.
A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.
Sales tax is an indirect fee that is always applied at the point of exchange or purchase and is calculated as a percentage of the item's worth. Retail, manufacturing, wholesale, use, and value-added taxes are the various types of sales taxes (VAT). Note: As of July 1, 2017, the Goods and Services Tax (GST) has taken the place of the Sales Tax.
Sales tax = 8.75%
⇒ 8.75/100 × 84
⇒ 7.35
Total price = 7.35 + 84
⇒ $ 91.35
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College Algebra! Worth 20 points. Can anyone help?
Answers
The solution set to inequality - 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14 is equal to - 6 ≤ m ≤ 13. (Correct choice: A)
How to solve a simultaneous inequality
Herein we find a simultaneous inequality, that is, the combination of two inequalities. We find the following case below by algebra properties:
- 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14
(1 / 2) · (2 · m + 2) ≥ - 5 and (1 / 2) · (2 · m + 2) ≤ 14
Now we proceed to determine the solution set to this inequality by algebra properties:
2 · m + 2 ≥ - 10 and 2 · m + 2 ≤ 28
2 · m ≥ - 12 and 2 · m ≤ 26
m ≥ - 6 and m ≤ 13
- 6 ≤ m ≤ 13
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Summarize what these bond funds have in common.
Vanguard and Fidelity
Answers
There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing.
What are bond funds?Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.
There are more than 8,300 domestic investment-grade bonds held by the Vanguard Total Bond Market ETF.
Therefore, You'll need to study two (or more) sets of statements, keep track of several phone numbers, access a number of websites, and comprehend and keep track of hundreds of different funds.
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There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing. Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.
What do you mean by Bond?Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.
By purchasing a bond, you are effectively lending the issuer money. In exchange, they commit to repay you the face amount of the loan on a particular date and to make periodic interest payments—typically twice a year—along the way. Unlike stocks, which grant you ownership rights, bonds issued by corporations do not.
Therefore, Vanguard's primary investment strategy is long-term buy-and-hold investing. On the other hand, Fidelity caters to investors who favor a more active strategy.
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Which equation has a solution of x= 3/4
Answers
The equation has a solution of x= 3/4 will be B. 8x = 6
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, the value of x in 3x = 6 will be:
x = 6 / 3
x = 2
The value of x in 8x = 6 will be:
x = 6 / 8
x = 3 / 4
The value of x in 4x = 2 will be:
x = 2/4
x = 1/2
The value of x in 3x = 15 will be:
x = 15 / 3
x = 5
The correct option is B.
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Complete question
Which equation has a solution of x= 3/4?
A. 3x = 6
B. 8x = 6
C. 4x = 2
D. 3x = 15
Can someone please help me
Answers
The cost of each shirt is $6 and the cost of each pant for the given condition is $9.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.
Let us suppose the cost of shirt = x.
Let us suppose the cost of pant = y.
Given that 3 shirts and 3 pants cost $45, this is represented as:
3x + 3y = 45 (equation 1)
1 shirt and 2 pants cost $24, this is represented as:
x + 2y = 24 (equation 2)
Using the elimination method to solve:
Multiply the second equation with 3 and change the signs of all the variables.
(x + 2y = 24) (3)
-3x - 6y = -72 (equation 3)
3x + 3y = 45
Comparing equation 1 and equation 3, the x term is cancelled, and the remaining equation after subtracting both equations is:
- 3y = -27
y = 9
Substitute the value of y in equation 2.
x + 2y = 24
x + 2(9) = 24
x + 18 = 24
x = 24 -18
x = 6
Hence, the cost of each shirt is $6 and the cost of each pant is $9.
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THIS IS URGENT, What is the GCF of 36x^2 and 18xy^2
Answers
The greatest common factor (GCF) of two or more expressions is the largest monomial that divides each expression exactly.
To find the GCF of 36x^2 and 18xy^2, we can factor out the greatest common factor from each expression.
The prime factorization of 36 is 2^2 * 3^2 and of 18 is 2*3^2
The GCF of 36x^2 and 18xy^2 is 18x^2y^2 = 2*3^2 * x^2 * y^2
So, the GCF of 36x^2 and 18xy^2 is 18x^2y^2
Answer:
18xy
Step-by-step explanation:
Si el costo de 1 Kg de azucar es $8?cual es el precio de 3 3/4 kg?
Answers
Answer:
$30
Step-by-step explanation:
1kg= $8
3kg *$8= $24
3/4= 0.75
$8 *0.75= $6
$24+$6= $30
3.75 kg * $8= 30
* = multiply
sam buys a computer for $590.00 plus $32.45 in sales tax find the sales tax rate?
Answers
Answer:
Is this what youre asking?
Step-by-step explanation:
Price before tax: $ 590.00
+ Sales tax (32.45%): $ 191.46
Total price including tax: $ 781.46
find the domain and range of the function. Use a graphing utility to verify your results. (Enter your answer using interval notation.)
f(x) = ?x2 ? 6x + 7
Answers
The domain is [0,100].[0,100]. The range is [0,1500] [0,1500]
(a) To find the cost of making 25 items substitute
x=25 in the equation
=10+500(25)
=10(25)+500(25)=750
c(x)=10x+500
c(25)=10(25)+500
c(25)=750
the cost of making 25 items is
$750
(b)
Since the maximum cost allowed is
$1500
10+500≤1500
10x+500≤1500
To solve this inequality
First, subtract 500 from both sides
10≤1000
10x≤1000
Divide both sides by 10
≤100x≤100
This means you can make at most 100 items.
The domain is
[0,100].[0,100].
The range is
[0,1500] [0,1500].
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Housing prices in a small town are normally distributed with a mean of
$157,000 and a standard deviation of $8,000. Use the empirical rule to
complete the following statement.
Approximately 99.7% of housing prices are between a low price of
$ and a high price of $
Answers
Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
So, using the empirical rule, we can say that approximately 99.7% of housing prices in this small town fall within 3 standard deviations of the mean.
To find the range of prices that this corresponds to, we can use the following formula:
(mean - (3 x standard deviation), mean + (3 x standard deviation))
Plugging in the given values:
(157,000 - (3 x 8,000), 157,000 + (3 x 8,000))
(141,000, 173,000)
So, approximately 99.7% of housing prices in this small town are between $141,000 and $173,000.
Step-by-step explanation:
Need help with question 12.
Answers
The length of the rectangle be 12 and Width be 6.
What is meant by rectangle?With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width.
A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.
4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other.
Let the equation be L = 2W and
P = 36 = 2 × ( L + W )
simplifying the equation, we get
⇒ 18 = L + W
⇒ 18 = 2W + W
⇒ 6 = W and L = 2 × W = 2 × 6 = 12
Therefore, the length of the rectangle be 12 and Width be 6.
The complete question is:
The length of a rectangle is twice the width. The perimeter of the rectangle is 36. What is the length and width of the rectangles?
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In the figure the boundary of the shaded region consists of four semicircular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find1 . The length of the boundary2 . The area of the shaded region
Answers
The area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.
A semicircle is a shape that is half of a circle. It is defined by a center point and a radius, and it is made up of an arc that is 180 degrees of the full circle.
The circumference of a semicircle is given by the formula: C = π * d, where C is the circumference and d is the diameter of the semicircle.
Diameter of the biggest semi-circle = 14cm.
Diameter to two small semi-circles = 3.5cm.
Diameter of other semi-circle = 14 - 2(Diameter to two small semi-circles)
=14 - 7 cm
= 7cm
Length of boundary = Circumference of bigger semi-circle + Circumference of small semi-circle + 2 ×circumference of the smaller semi-circles
∴Length of boundary= [tex]\pi R+\pi r_{1}+2\pi r_{2}[/tex]
=> Length of boundary=[tex]\pi (R+r_{1})+2\pi r_{2}[/tex]
=> [tex]\frac{22}{7}(7+3.5)+2X\frac{22}{7}X1.75[/tex]
=> 44cm
Area of the biggest semi-circle = [tex]\frac{1}{2}\pi (7)^{2} cm^{2}[/tex]
Area of two small semi-circles = [tex]\pi (1.75)^{2}cm^{2}[/tex]
Area of other semi-circle= [tex]\frac{1}{2}\pi (3.5)^{2}cm^{2}[/tex]
Area of shaded region= π×(24.5−3.0625+12.25)
=π×27.5625 cm^2 =86.59 cm^2
Therefore, the area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.
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Find Y if the slope between (8, y) and (14, -13) is -2/3
Answers
Answer: The slope between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
We are given that the slope between (8, y) and (14, -13) is -2/3. So we can use this information to set up the equation:
-2/3 = (-13 - y) / (14 - 8)
To find y, we can solve for y:
-2/3 = (-13 - y) / 6
-2 = -13 - y
y = 11
So the value of y is 11.
Step-by-step explanation:
SOLVE FOR Y 32=16Y+64X
Answers
Answer: y = 2-4x
Step-by-step explanation:
A 5 foot wide painting should be centered on a 13 foot wall type the left side of an equation that can be used to determine how many feet should be on each side of the painting
Answers
The number of feet that should be on each side of the painting is 4 feet.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Let x be the number of feet on each side of the painting.
The equation to determine the number of feet on each side of the painting would be:
x + 5 + x = 13
So x = (13-5)/2
x = 4
So there should be 4 feet on each side of the painting.
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i could really use some help please
Answers
The coordinate of the circumcentre of ΔABC is (-1, 0.15).
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle ABC.
A = (-5, -4)
B = (3, -4)
C = (-1, 6)
The circumcentre of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.
Now,
Let the circumcentre be M = (x, y).
The length from each side of the triangle to the circumcentre is equal.
So,
AO² = BO² = CO²
Now,
AO² = BO²
(x + 5)² + (y + 4)² = (x - 3)² + (y + 4)²
x² + 10x + 25 + y² + 8y + 16 = x² - 6x + 9 + y² + 8y + 16
10x + 25 = -6x + 9
16x + 16 = 0
x + 1 = 0
x = -1
BO² = CO²
(x - 3)² + (y + 4)² = (x + 1)² + (y - 6)²
x² - 6x + 9 + y² + 8y + 16 = x² + 2x + 1 + y² - 12y + 36
-6x + 9 + 8y + 16 = 2x + 1 - 12y + 36
20y - 8x + 25 - 36 = 0
20y - 8x - 11 = 0
20y = 11 + 8x
y = (11 + 8x)/20
y = (11 - 8)/20
y = 3/20
y = 0.15
Thus,
Circumcentre M = (-1, 0.15)
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Use the distributive property to write each expression as an equivalent
algebraic expression.
6(4+x)
Answers
Answer:
= -6x + 24
Step-by-step explanation:
6(4-x) = 6*4 + 6*-x
= 24 - 6x
= -6x + 24
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the different shade of green but has a smaller amount.
Answers
Use 1.75 cups of blue and 1 cup of yellow
What is a mixture?
Mixture can be defined as a substance made by combining two or more different materials in such a way that no chemical reaction occurs. A mixture can usually be separated back into its original components.
The given problem can be placed in the category of ratios and proportions.
There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too.
Therefore adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.
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Read the following prompt and type your response in the space provided.
Give an example of a problem involving multiplication of fractions that can be made easier using the associative property. Explain how it makes the problem easier.
Answers
An example of a question that can be solved using the associative method is : (2/5) * (3/4) * (5/6)
How to use the associative propertyOne example of a problem involving multiplication of fractions that can be made easier using the associative property is:
(2/5) * (3/4) * (5/6)
Using the associative property of multiplication, we can change the grouping of the fractions to make the problem easier. The associative property states that the way we group the numbers being multiplied does not change the product. For example,
(2/5) * (3/4) * (5/6) = (2/5 * 3/4) * (5/6) = (6/20) * (5/6) = 30/120
This simplification makes it easier to see that the final answer is 1/4.
By using the associative property, we can first multiply (2/5) * (3/4) = (6/20) which is easier to cancel out the common factor and then multiply it with (5/6) = (5/6) * (6/20) = (30/120) = 1/4 which is the final answer
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athletes in a particular sport are classified as either offense or defense. the distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. the distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. there are 1,000 athletes in each classification. which of the following is the best description of a histogram of the weights of all 2,000 athletes?
Answers
A histogram of the weights of all 2,000 athletes would be a graph with two normal distributions, one for offense and one for defense.
The offense distribution would have a bell shaped curve centered at 200 pounds, with a range of 150-250 pounds. The defense distribution would have a bell shaped curve centered at 300 pounds, with a range of 250-350 pounds. Each of the distributions would have the same area, representing 1,000 athletes in each group. The total area of the histogram would represent the combined 2,000 athletes with weights ranging from 150-350 pounds. It is important to note that the histogram would not represent the exact weights of the athletes, but rather the relative frequency of each weight.
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Show that the two-variable function f given by f(x, y) = 2x^2 − xy is
differentiable at any point (a, b). What is the derivative of f at (a, b)?
Answers
Step-by-step explanation:
To show that the function f(x,y) = 2x^2 − xy is differentiable at any point (a,b), we need to show that the partial derivatives of f with respect to x and y exist and are continuous at that point.
The partial derivative of f with respect to x is:
∂f/∂x = 4x - y
The partial derivative of f with respect to y is:
∂f/∂y = -x
We can see that both of these partial derivatives are continuous functions of x and y and are defined for all (x,y) in the domain of f. Therefore, f is differentiable at any point (a,b).
The derivative of f at (a,b) is the gradient vector of f evaluated at (a,b), which is given by:
Gradient vector of f(a,b) = ∇f(a,b) = ( ∂f/∂x, ∂f/∂y ) = (4a-b, -a)
So the derivative of f at (a, b) is (4a-b, -a).
For each of the following, count the number of four-digit numberssatisfying the condition and with digits in {1, 2,3, 4,5, 6}:(a) The digits are distinct(b) The number is even(c) The number is even and the digits are distinct.
Answers
(a) The number of four-digit numbers with distinct digits in {1, 2, 3, 4, 5, 6} is 6543 = 360.
(b) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even is (3543)/2 = 270.
(c) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even and have distinct digits is (321*1)/2 = 3.
Four-Digit Numbers CountingFor (a) the total number of four-digit numbers with digits in {1, 2, 3, 4, 5, 6} is 6 options for the first digit, 5 for the second, 4 for the third and 3 for the last one. So, 654*3 = 360.
For (b) since digits in {1, 2, 3, 4, 5, 6} the even digits are 2,4,6. for each of the even digits we have 5 options for the second digit, 4 for the third and 3 for the last one. In total, we have 354*3= 270 even numbers.
For (c) The total number of four-digit numbers with distinct digits that are even is 211 = 2, since there are 2 even digits in {1,2,3,4,5,6} and only one of each can be used. However, this count is double-counting the numbers, so we divide by 2 to get 3.
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