The most appropriate choice for unitary method will be given by-
a) Mass of 100 [tex]cm^3[/tex] of the material = 1000 g
b) Mass of 500 [tex]cm^3[/tex] of the material = 5000 g
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit.
Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here,
a)Mass of [tex]9 cm^3[/tex] of samples = 90 g
Mass of 1 [tex]cm^3[/tex] of sample = [tex]\frac{90}{9}[/tex] g
Mass of 1 [tex]cm^3[/tex] of sample = 10 g
Mass of 100 [tex]cm^3[/tex] of sample = [tex]10 \times 100 g[/tex] = 1000 g
b) Mass of 500 [tex]cm^3[/tex] of sample = [tex]10 \times 500[/tex] g = 5000 g
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How does this graph change between point D and point G?
5-G
554
32
3-
2
1
-5-4-3-2-1
-2-
3
-4
-5
1 2 3 4 5 x
The graph increases.
O The graph decreases.
The graph incro
Answer:
a
Step-by-step explanation:
hope that helps
1 pointIf A=(-1-7,0) and B(-8,8-10), find ||AB||. Round to 3 decimal places.Type your answer.
Basically we need to find the distance between A and B, so:
[tex]\begin{gathered} \mleft\Vert AB\mright||=d=\sqrt[]{(x2-x1)^2+(y2-y1)^2+(z2-z1)^2} \\ where \\ A=(x1,y1,z1)=(-1,-7,0) \\ B=(x2,y2,z2)=(-8,8,-10) \\ \Vert AB||=\sqrt[]{(-8-(-1))^2+(8-(-7))^2+(-10-0)^2} \\ \Vert AB||=\sqrt[]{49+225+100} \\ \Vert AB||=\sqrt[]{374} \\ \Vert AB||\approx19.339 \end{gathered}[/tex]so my equation is y=1/3 times 2 to the power of x we have to make a table and graph it.
Solution
We are given
[tex]y=\frac{1}{3}\times2^x[/tex]We want to find make table and graph
(a). To make table, We take
[tex]-3\leq x\leq3[/tex][tex]\begin{gathered} \text{when x = -3} \\ y=\frac{1}{3}(2^{-3})=\frac{1}{24}=0.042 \\ \text{when x = -2} \\ y=\frac{1}{3}(2^{-2})=\frac{1}{12}=0.083 \end{gathered}[/tex]Similarly, we find the values for the remaining values of x
[tex]\begin{gathered} \text{when x = }-1,\text{ y = 0.167} \\ \text{when x = 0, y =}\frac{1}{3} \\ \text{when x= 1, y = }\frac{2}{3} \\ \text{when x = 2, y =}\frac{4}{3} \\ \text{when x = 3, y=}\frac{8}{3} \end{gathered}[/tex]To draw the graph, we have
Rakesha claims that y = 5x - 7 is the linear function for the sequence that is represented by the explicit formula an = -2 + 5(n - 1). James doesn't understand how this can be the case.
a) Help James by rewriting the explicit formula of the given sequence in the form y = mx+ b. Provide a rationale for each step.
Rakesha claims y =5x -7 is linear function for the sequence and represented by explicit formula is represented by aₙ = -2 +5(n-1).
As given in the question,
Linear function for the sequence represented by ;
y = 5x -7
Compare it with y = mx + b
m = 5
b= -7
For x = 1
First term (a₁)
y = 5(1) -7
= -2
For x =2
second term (a₂)
y = 5(2) -7
=3
Common difference = second term - first term
= 3 - (-2)
= 5
nth term of the sequence :
aₙ = a₁ + (n-1)d
= -2 + (n-1)5
= -2 +5(n-1) represent the explicit formula.
Therefore, Rakesha claims y =5x -7 is linear function for the sequence and represented by explicit formula is represented by
aₙ = -2 +5(n-1).
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Determine the leading coefficient c of the polynomial given that the graph goes through the point (5,100)
f(x) = c(x - 1)(x + 1)(x-2)
The polynomial that passes through the point (5,100) has the leading coefficient or c equal to 1.38.
What do a polynomial's leading term and leading coefficient mean?The term with the highest power of x is the leading term in a polynomial. As an illustration, the leading term in 7+x3x2 is 3x2. A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.We need to determine the leading coefficient c of the polynomial which passes through the point (5,100).
Given polynomial: f(x) = c(x - 1)(x + 1)(x-2)
Substituting f(x) = 100 and x = 5,
100 = c(4)(6)(3)
100 = c72
c= 1.38
Therefore, the leading coefficient c of the polynomial given that the graph goes through the point (5,100) is 1.38.
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m/2=6x+6
54
Qu
2
X=?
How to solve(pls show steps)
Answer:
dancing
Step-by-step explanation:
d
a
n
c
I
n
g
don't
cry
ok
use the level curves to predict the location of the critical points of f and determine whether f has a saddle point, local maximum, or local minimum at each point. then use the second derivatives test to confirm your predictions. (if an answer does not exist, enter dne.)
(0,0) is a saddle point and (1,1) is a local minimum.
The point as in domain of something like the functions with the lowest value is known as the local minimum. You can calculate the local minimum by determining the function's derivative.A saddle point of minimax point is a location on the graph's surface where the slopes of all orthogonal derivatives are zero (a crucial point), but which isn't the function's local extremum.From the contour map, the level curves intersect at (0,0) . Hence (0,0) is a saddle point.
and the center of level curve 3.2 (1,1) is a local minimum.
Hence (0,0) is a saddle point and (1,1) is a local minimum.
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When solving an equation, the goal is to ____________________ the variable.
The answer for the missing piece is to 'find' the variable.
Shawn bought a 10-pound turkey to serve for Thanksgiving. He plans to serve eachadult 2/5 of a pound.Write an equation to represent the number of adult servings, x, Shawn canget from the 10-pound turkey. Use your equation to determine the number of adultservings.
Since each serving contains 2/5 of a pound, then, the total weight of x servings would be:
[tex]\frac{2}{5}x[/tex]If the total weight of x servings should be equal to the weight of the turkey, then:
[tex]\frac{2}{5}x=10[/tex]Multiply both sides of the equation by 5/2:
[tex]\frac{5}{2}\cdot\frac{2}{5}x=\frac{5}{2}\cdot10[/tex]Simplify the expressions on both sides of the equation:
[tex]x=25[/tex]Therefore, the number of adult servings from a 10 pound turkey, will be 25.
Zachary purchased a computer for $1.900 on a payment plan. Three months after he purchased the computer, his balance was $1.525. Eight months after he purchased the computer, his balance was
$900. What is an equation that models the balance y after x months?
The equation models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer)
The equation that models the balance of the payment plan loan, y, after x months is y = -125x + 1900.
What is an equation?An equation is a mathematical statement claiming that two mathematical expressions are equal or equivalent.
Equations are depicted using the equation sign (=) to show the equality of values.
Slope-Intercept Formula:y = mx+b
y = y-coordinate
m = slope
x = x coordinate
b = y-intercept
Purchase PlanPayment Period Balance
12 months $1,900
9 months (3 months after) $1,525
4 months (8 months after) $900
Let 12m = 1900 ... Equation 1
9m = 1525 ... Equation 2
4m = 900 ... Equation 3
Subtract Equation 3 from Equation 1:
12m = 1900
- 4m = 900
= 8m = 1000
m = 125 (1000/8)
Equation modeling the balance y after x months:
y = -125x + 1900
Thus, a model equation for the balance of the payment plan loan after x months is y = -125x + 1900.
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Nora s a race car driver. during a race the first pit stop took 8.352 seconds and the second pit stop took 8.025 seconds. how much faster was the second pit stop
The second pit stop was 0.327 seconds faster than the first pit stop which is the difference between both time
What is the Subtraction operation?
Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have been given that during a race the first pit stop took 8.352 seconds and the second pit stop took 8.025 seconds.
To determine how much faster the second pit stop.
We need to calculate the difference between the first pit stop and the second pit stop of time.
the difference = Time of first pit stop - Time of second pit stop
the difference = 8.352 - 8.025
the difference = 0.327 second
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Simon's bank account has a balance of -$28.16. He goes to the bank and deposits $40.25. How much money is in his account after the deposit?
What operation is needed to solve this problem? Explain how you know and then solve.
The money in his bank account after the deposit is $12.09.
The balance amount in Simon's bank account is -$28.16.We can clearly see that the balance amount is a negative number.Simon goes to the bank and deposits $40.25.He deposits the money in the bank. It means we need to add the amount deposited by him to the existing balance amount in his bank account.We need to perform an addition operation to solve the problem.Let the amount of money in his account after the deposit be "x".x is equal to the sum of the amount before the deposit and the money deposited.x = -$28.16 + $40.25x = $12.09To learn more about addition, visit :
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-30 = 3 (w + 6) + 5w solve for w and simplify your answer as much as possible
Answer: w = -6
Step-by-step explanation:
-30 = 3(w + 6) + 5w
-30 = 3w + 18 + 5w
-30 = 8w + 18
-48 = 8w
w = -6
Hope this helps
elba constructs a cube made of glass panels. Each panel has a side length of 3··4foot. What is the total surface area, in square feet, of the cube? Show your work.
The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions.
Surface area=6(3.4)^2=69.36 square feet
What is surface area?
A solid object's surface area is a measurement of the overall space that the object's surface takes up.
The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
A 3D object's surface area is the entire area that all of its faces cover. For instance, if we need to calculate how much paint is required to paint a cube, we can use the cube's surface area. determine how much paint is needed to paint it. It is consistently expressed in square units.
As a refresher, the surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions.
Surface area=6(3.4)^2=69.36 square feet
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The width of rectangle garden is 7cm shorter than its length. If the perimeter of the garden is 210. Find the length of the side
The length of the rectangle is 49 cm.
What is perimeter?
Perimeter is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
P = sum of all its four sides
P = a + b + a + b (Opposite sides of rectangle are equal)
P = 2(a + b)
where a is the length and b is the breadth.
According to question, the breadth is 7 cm shorter than length.
Let x be the length and x - 7 be the breadth.
perimeter = 210 cm
2(x+x-7) = 210
2x - 7 = 210/2
2x - 7 = 105
2x = 105 - 7
2x = 98
x = 49
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The sum of the three angles of
any triangle is [ ? ]0.
At its highest point, the elevation of a county is 5,776 feet above sea level. At its lowest point, the elevation of the county is 8 feet below sea level. Answer parts a through c. (Don’t simply
The difference or distance between the two points is 5768ft
The Difference in ElevationTo solve this problem, we have to find the difference between the highest point and lowest point of the county.
highest point = 5776ftlowest point = 8ftWhen the height of a point is its vertical distance above or below the surface of a reference plane* you have selected, it is called the elevation* of that point.
When the height of a point is its vertical distance above or below mean sea level (as the reference plane), it is called the altitude* of the point.
The difference between the points of elevation in this question is
[tex]5776 - 8 = 5768ft[/tex]
The difference in elevation is given as 5768ft
The complete question is-
At the highest point, the elevation of a county is 5,667 feet above sea level. At its lowest the elevation of the county is 7 feet below sea level. Answer parts a through c. Write an expression using integers to represent the difference between the elevations.
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Which situation best represents the equation 10.25h+6.50=11h+4
The situation that best represents the given equation is that there are two limo companies that charge based on the number of people, "h", that they carry. Limo A charges $6.5 plus $10.25 per person. Limo B charges $4 plus $11 per person. The equation equates the charges for the two companies to carry a "h" number of people.
An equation is given to us.The equation is linear in one variable.The equation is given below :10.25h + 6.50 = 11h + 4We need to find a situation that best fits the above equation.We can see that on the left hand side of the equation, 6.5 is the fixed cost of something and 10.25 is the cost per unit quantity of "h". Similarly, on the right hand side of the equation, 4 is the fixed cost of something and 11 is the cost per unit quantity of "h".The equation represents a situation where the two costs are equal in magnitude and we are able to find a suitable value for the quantity "h".For example, we can see the situation given below.There are two limo companies that charge based on the number of people, "h", that they carry. Limo A charges $6.5 plus $10.25 per person. Limo B charges $4 plus $11 per person. How many people can ride to make the two companies charge the same amount?To learn more about equations, visit :
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Which function is an extended function for f(x) = StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction that is continuous for all values of x?
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row negative 2, x = negative 1, 1.
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row negative 2, x = 1.
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row 4, x = negative 1, 1.
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row 4, x = 1.
The function is f(x)=(x³+3x²-x-3)/(x²-1). The continuous function option A is correct.
Given that,
The function is f(x)=(x³+3x²-x-3)/(x²-1)
We have find the continuous function.
If the function's curve DOES NOT break at the point x = a, it is said to be a continuous function at that point in calculus. The mathematical definition of a function's continuity is given below. If x = a, then f(x) is continuous at that moment.
f(a) exists;
limₓ → ₐ f(x) exists;
limₓ → ₐ₋ f(x) = limₓ → ₐ₊ f(x) and
Both of the above values are equal.
Now, limₓ → ₐ f(x) = f(a).
The function g(x)=[tex]\left \{ {{\frac{x^{3}+3x^{2}-x-3 }{x^{2} -1} }, x\neq -1,1 \atop {-2, x=-1,1}} \right.[/tex]
Therefore, the continuous function option A is correct.
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Hector got 42 out of 50 questions
correct on a math test. What percent of
the questions did Hector get correct?
Answer:
84%
Step-by-step explanation:
To solve this, the equation to find percent is AMOUNT divided by the TOTAL * 100. So 42 questions were right, divided by the total, 50. Therefore it would be 0.84 * 100, 84%
HELPPPPPPPPPPPPPPP
Determine if the table shows a proportional relationship.
Time (hours) 0 7 14 21 28
Pay (dollars) 0 91 182 273 364
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 12 dollars per hour.
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.
No, it is not proportional because 91 over 7 does not equal 273 over 21.
No, it is not proportional because 273 over 21 does not equal 364 over 28.
Answer: Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.
Step-by-step explanation:
By multiplying all of the hours by 13 they equal the pay in dollars therefore we can conclude that the ratio is proportional because all of the ratios are equal and the dollars per hour are equivalent to 13 dollars per hour.
If $a$ is 4 percent of $b$ and $b$ is 25 percent of $c$, what percent of $a$ is $c$?
c is 10,000 percent of a.
Here we are given that a is 4 percent of b and b is 25 percent of c.
Let us assume the value of c to be x
Then the value of b will be-
25 percent of x
= (25/100)x
= (1/4)x
= x/4
Now, the value of a will be-
4 percent of b
= 4 percent of x/4
= ( 4/100 )( x/4 )
= x/100
Thus, we have a = x/100 and c = x
Hence, the value of c as a percent of a can be calculated as follows-
x/( x/100 )*100
= ( 100x/x )*100
= 100*100
= 10,000
Thus, c is 10,000 percent of a.
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Random sampling complicates the analysis of cross-sectional data.
a. True
b. False
Random sampling do not complicates the analysis of cross-sectional data
Sampling is just an action of taking samples or subsets of a given data set for analysis. This means that when sampling is done, the next stage for the samples, are for them to be analyzed.
There different methods of sampling including random sampling. In this type, each member of the samples have equally probability of being chosen.
A cross-sectional data analysis is the analysis of samples or subsets at a fixed point in time. A systematic random sampling method is used in the analysis of cross-sectional data. And when this used, then each combinations of individuals samples in a data set has an equal chance of being selected.
Hence, the statements that says random sampling complicates the analysis of cross-sectional data is False.
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Help me please i don't know this
The rates for this problem are given as follows:
1) Between 0 and 2 seconds: 1 meter per second.
2) Between 2 and 4 seconds: 0.5 meters per second.
3) Between 4 and 7 seconds: -1 meter per second.
4) Between 7 and 9 seconds: 0 meters per second.
The rates are not constant.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given according to the following rule:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For the first rate, between 0 and 2 seconds, we have that:
f(0) = 5.f(2) = 7.Hence:
r = (7 - 5)/(2 - 0) = 2/2 = 1 meter per second.
For the second rate, between 2 and 4 seconds, we have that:
f(2) = 7.f(4) = 8.Hence:
r = (8 - 7)/(4 - 2) = 1/2 = 0.5 meters per second.
This rate is already different than the first rate, hence the rates are not constant.
For the third rate, between 4 and 7 seconds, we have that:
f(4) = 8.f(7) = 5.Hence:
r = (5 - 8)/(7 - 4) = -3/3 = -1 meter per second.
For the fourth rate, between 7 and 9 seconds, we have that:
f(7) = 5.f(9) = 5.Hence:
r = (5 - 5)/(9 - 7) = 0/2 = 0 meters per second.
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Simplify
Rewrite the expression in the form 5".
510
512
Answer:
510 by 2 is 255
255 by 2 is 127.5
127.5=63.75.63.75 by 2=31.875
31.875. by 2=15.9375
15.9375 by 2=7.96875
512 by 2=256
256 by 2=128
128 by 2=64
64 by 2=32
32 by 2=16
Enter the polnomial function f(x) in standard form given that f has leading coefficient 3 and roots 4, sqrt(2), and -sqrt(2)
Here is a picture of what I mean
Using the Factor Theorem, the polynomial function that has leading coefficient of 3 and the given roots is given as follows:
f(x) = 3x³ - 12x² - 6x + 24.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
a is the leading coefficient of the function f(x), determining if it is positive(a positive) or negative(a negative).
In the context of this problem, the leading coefficient and the roots are given as follows:
f(x) = 3(x - 4)(x - sqrt(2))(x + sqrt(2))
Applying the subtraction of perfect squares, the square root is simplified as follows:
(x - sqrt(2))(x + sqrt(2)) = x² - 2.
Hence the function is defined as follows:
f(x) = 3(x - 4)(x² - 2)
f(x) = 3(x³ - 4x² - 2x + 8)
f(x) = 3x³ - 12x² - 6x + 24.
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Please help me ,…………..
Answer:
answer 2 is correct as we have to put 6 in front of 3 , and x infront of 28. doesn't matter if we change its position.
HELPPPPP
the question is attached
The value of the equation illustrated by E = 50q + 80000 is 5248000.
What is an equation?Simply put, an equation shows the relationship that exist between the variables that are given.
The equation given is illustrated as:
E = 50q + 80000
where q = (80p + 100000)
Substitute q into the equation
E = 50q + 80000
E = 50(80q + 100000) + 80000
E = 4000p + 5000000 + 8000
E = 4000p + 5080000
Substitute 42 for p
E = 4000(42) + 5080000
E = 168000 + 5080000
E = 5248000
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Suppose sin(A) = 1/4. Use the trig identity sin^2(A) + cos^2(A) = 1 to find cos(A) in quadrant 2. Round to ten-thousandth.
Using the given trigonometric identity, the cosine of the angle in the second quadrant is given by:
cos(A) = 0.9682.
What is the cosine of angle A?The cosine and the sine of the angle are related according to the following relation:
sin²(A) + cos²(A) = 1.
Hence, knowing the sine of the angle, as we do in this problem, we can find the cosine of the same angle solving the above equality.
The value of the sine of angle A is given by:
sin(A) = 1/4.
Hence the equation can be solved for the cosine as follows:
cos²(A) = 1 - sin²(A)
cos²(A) = 1 - (1/4)²
cos²(A) = 1 - (1/16)
cos²(A) = (16/16) - (1/16)
cos²(A) = 15/16
The inverse of the square is the square root, hence:
cos(A) = ± sqrt(15/16)
In the second quadrant, the cosine is negative, hence:
cos(A) = -sqrt(15/16)
cos(A) = -0.9682.
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help if your smartest person in the world
Answer:
First one, the answer could be 1, 2, or 3, because the fraction you made is less than one. Second one, the answer could be any number above 4 (5, 6, 7, and so forth), because the fraction you made is greater than one.
