The shaded area on the grid represents the part of kira's free throws that she made in the basketball practice today.
The percentage of Kira's free throws is 68%.
We have,
From the grid,
We can see that,
There are 25 boxes.
Now,
The number of shaded boxes = 17
Now,
The percentage of the shaded boxes.
= 17/25 x 100
= 17 x 4
= 68%
Thus,
The percentage of Kira's free throws is 68%.
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The complete question.
The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.
Find the percentage of Kira's free throws.
Type the correct answer in each box.
The probabilities of a positive response for two government programs from the citizens in eight cities are given in the table.
City Positive Response
for Program 1 (%) Positive Response
for Program 2 (%)
Atlanta 77.80 82.10
Boston 86.40 86.60
Chicago 65.90 87.50
Dallas 73.80 80.90
Houston 69.70 79.40
Los Angeles 78.40 88.10
Miami 82.50 82.60
Newark 81.40 83.30
Total 68.80 81.70
The chance that a positive response is obtained from Chicago for program 1 is
%. The chance that a positive response is obtained from Chicago for program 2 is
%.
Programme 2 in Los Angeles will be well received by 22 out of 25 people.
what is Probability?Given that the chances of a positive response from Los Angeles residents to two government programmes are 78.4% for Programme 1 and 88.1% for Programme 2, the likelihood of a positive response for Programme 2 given that the person is from Los Angeles must be calculated as follows:
88.1 / 100 = X 44.05 / 50 = X 22,025 / 25 = X
Therefore, Programme 2 will be well-received by 22 out of 25 people in Los Angeles.
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The equation x^2-8x-5=0 can be transformed into the equation (x-p)^2=q, where p and q are real numbers. What is the value of q?
Since p and q are real numbers, the value of q is 21.
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
x² - 8x - 5 = 0
x² - 8x = 5
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 8x + (-8/2)² = 5 + (-8/2)²
x² - 8x + 16 = 5 + 16
x² - 8x + 16 = 21
By simplifying, we have;
(x - 4)² = 21
p = 4 and q = 21
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find the mass of the lamina that is a portion of the cone z=sqrt(x^2+y^2) that lies between the planes z=1 and z=3 if the density function is fi(x,y,z)=x^2z
Answer: 6 units
Step-by-step explanation: To find the mass of the lamina, we need to integrate the density function fi(x,y,z) over the volume of the lamina. The lamina is a portion of the cone z=sqrt(x^2+y^2) between the planes z=1 and z=3. We can express this volume using cylindrical coordinates, where rho is the distance from the origin to the point (x,y,z), phi is the angle between the positive x-axis and the line connecting the origin to the point (x,y,z), and z is the height of the point (x,y,z) above the xy-plane.
We have:
1 <= z <= 3
0 <= rho <= 3sin(phi)
0 <= phi <= 2pi
The density function is given by fi(x,y,z) = x^2z. In cylindrical coordinates, we have x = rhocos(phi), y = rhosin(phi), and z = z. Therefore, we can express the density function as:
fi(rho, phi, z) = (rhocos(phi))^2 * z = rho^2cos^2(phi) * z
The mass of the lamina is given by the triple integral of the density function over the volume of the lamina:
M = ∭ fi(rho, phi, z) dV
= ∫∫∫ rho^2cos^2(phi) * z dz dA
= ∫∫[1,3] ∫[0,2pi] ∫[0,3sin(phi)] rho^2cos^2(phi) * z dz d(phi) drho
= ∫[0,2pi] ∫[0,3] ∫[0,rhosin(phi)] rho^2cos^2(phi) * z dz drho d(phi)
= ∫[0,2pi] ∫[0,3] (1/3)rho^3sin(phi)cos^2(phi) d(phi) drho
= ∫[0,2pi] (1/3)[9sin(phi)cos^2(phi)] d(phi)
= (1/3)[9(2/3)]
= 6
Therefore, the mass of the lamina is 6 units.
A division of a company produces income tax apps for smartphones. Each income tax app sells for $8. The monthly fixed costs incurred by the division are $20,000, and the variable cost of producing each income tax app is $3.
a) The break-even point for the division is: 4000 units
b) The level of sales for 10% profit is: 4681 units
How to find the break even point for the profit function?The break-even point is defined as the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. In other words, you've reached the level of production at which the costs of production equals the revenues for a product.
a) We are told that:
Selling price for income tax app = $8
Monthly fixed cost = $20000
Variable cost producing each app = $3
Thus:
8x = 3x + 20000
5x = 20000
x = 4000 units
b) 8x = 1.1(3x + 20000)
8x = 3.3x + 22000
4.7x = 22000
47x =220000
x = 4681 units
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Missing questions are:
(a) Find the break-even point for the division.
(x,y)=
(b) What should be the level of sales in order for the division to realize a 10% profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
Answer:
To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:
A = (-3, 3 + 3) = (-3, 6)
B = (0, 7 + 3) = (0, 10)
C = (-3, 0 + 3) = (-3, 3)
Therefore, the coordinates of the vertices for the image triangle A'B'C' are A(-3, 6), B'(0, 10), and C(-3, 3).
So the correct answer is: A(−3, 6), B(0, 10), C(−3, 3).
The circle graph shows the results of a survey about favorite farm animals. If 400 people were surveyed, how many more people prefer pigs than chickens?
From the circle graph of the survey, 52 more people prefer pigs than chickens.
What is a circle graph?A sort of data visualisation tool used to depict data as a circular chart is a circle graph, commonly referred to as a pie chart. Each slice of the circle graph, also known as a sector, represents a certain category or chunk of the entire. Each slice's size is proportional to how much data or what percentage it represents, and the sum of all slices is 100%.
Circle graphs are frequently used to depict percentages or categorical data, and they are especially helpful for comparing and illustrating relative proportions among several categories within a data collection.
From the circle graph we see that the percentage of people who prefer chickens are 29%.
Thus, 29/100 (400) = 116 people
Also, 16% people prefer pig:
Thus, 16/100 (400) = 64 people
Thus, the difference is:
116 - 64 = 52
Hence, from the circle graph of the survey, 52 more people prefer pigs than chickens.
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The complete question is:
Math calculator help me please
The third player hit 4 more home runs than the first player. The algebraic expression that shows the relationship between a and b is: a = 3b. So option A is correct
What is a linear equation and examples?A linear equation in one variable is an equation that has only one variable. It is of the form Ax B = 0, where A and B are two real numbers and x is an unknown variable with only one solution. For example, 9x + 78 = 18 is a linear equation in one variable.
2) Each player's home runs are labeled A, B, C, and D, where A is the first baseman, B is the second baseman, C is the third baseman, and D is the shortstop. We know this:
C = 2B (the third player hit twice as many home runs as the second player)
C/B = D/B = A/C (numbers for first baseman and shortstop are proportional to numbers for third baseman and second baseman)
B = D 4 (second baseman hit 4 more home runs than shortstop)
To solve for the values of A, B, C, and D, we can use the second equation to write:
C/B = D/B
C = D (multiply both sides by B)
C = B - 4 (using the fourth equation to substitute D)
2B = B - 4 (using the first equation to substitute C)
B = 4 (interface to both sides 4)
C = 8 (using the first equation to find C)
D = 4 (using the fourth equation to find D)
A = C/2 = 4 (use another equation to find A)
Therefore the third player (C) hit 8 home runs and the first player (A) hit 4 home runs, so the third player hit 4 more home runs than the first player.
3) The relative relationship between a and b can be expressed as follows:
a/b = 6/2 = 3/1
To write this relationship as an algebraic equation, we can cross multiply to get:
a = 3b
Therefore, the algebraic expression that shows the relationship between a and b is:
a = 3b. So option A is correct
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A diagram shows a garden bed. The area of the garden bed is 21ft to the power of 2. What is the Height of the garden bed. Need help ASAP
Answer: 1.75
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Since the garden bed looks like the shape of a trapezoid the equation to find the area of a trapezoid is A = 1/2h (base 1 + base 2)
The area is already given so you can just plug it in. Also you can plug in the bases.
21 = 1/2h (3 + 4)
21 = 1/2h (7) rewrite
21 = 1/2(7)h
21 = 3.5h Divide both sides by 3.5
6 = h
A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the
volume of the silo if it has a height of 31 m and a radius of 5 m. Round your answer to
the nearest tenth if necessary. (Note: diagram is not drawn to scale.)
I hope this helps you.
NO LINKS!!! URGENT HELP PLEASE!!!
Find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1).
(x, y) = __________
Answer:
(-8.89, -26.69)
Step-by-step explanation:
To find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1), we can use the following steps:
Since the point is in the third quadrant, both the x-coordinate and the y-coordinate must be negative. Therefore, we can write (a, 3a) as (-|a|, -3|a|).We know that the distance between P(2,1) and (-|a|, -3|a|) is 5. We can use the distance formula to set up an equation and solve for |a|:[tex]\sqrt{(2 - (-|a|))^2 + (1 - (-3|a|))^2} = 5\\\sqrt{(2 + |a|)^2 + (1 + 3|a|)^2} = 5[/tex]
Squaring both sides of the equation and simplifying, we get:[tex]a^2 + 8a - 8 = 0[/tex]
Solving for a using the quadratic formula, we get:[tex]a = \frac{-8 ±\sqrt{8^2 - 4(1)(-8)}} {(2(1))}\\a = \frac{-8 ± \sqrt{96}}{ 2}\\a = -4 ± 2\sqrt{6}[/tex]
Since the point is in the third quadrant, we want the negative root, so:[tex]a = -4 - 2\sqrt(6)[/tex]
Substituting this value of a into (-|a|, -3|a|), we get:(x, y) =[tex](-|-4 - 2\sqrt(6)|, -3|-4 - 2\sqrt(6)|)[/tex]
(x, y) ≈ (-8.89, -26.69)
Therefore, the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1) is approximately (-8.89, -26.69).
Freshman
Sophomores
Total
Blology
0.15
0.2
0.35
Which statement is false?
Chemistry
0.1
0.25
0.35
Physical
science
0.2
0.1
0.3
OA. 15% of her students are in biology.
OB. 30% of her students are in physical science.
OC. 35% of her students are in chemistry.
OD. 45% of her students are freshmen.
Total
0.45
0.55
1.0
The statement that is false, given the table of Ms Stewart's class would be A. 15 % of her students are in biology.
How is this statement false ?The table shows that out of all he students, Ms. Stewart has 35 % that are doing Biology and not 15 %. But, she does have 15 % of Freshmen doing Biology and not of all her students.
30 % of the students are indeed engaged in doing physical science, and 35 % of her students are in chemistry from the table. 45 % of the total cohort that Ms. Stewart teaches are freshmen.
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Which is the most precise description of quadrilateral ABCD?
The most precise description of quadrilateral ABCD is a square.
We have,
Quadrilateral ABCD.
We see that,
AB is parallel to CD
AB = CD _____(1)
AD is parallel to BC.
AD = BC _____(2)
Now,
AB = AD ______(30
From (1), (2), and (3).
AB = BC = CD = AD
This means,
The Quadrilateral ABCD is a square.
Thus,
The most precise description of quadrilateral ABCD is a square.
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Find the circumference of the circle. Round to the nearest tenth.
A. 251.3 in.
B. 125.7 in.
C. 164.8 in.
D. 225.4 in.
Answer: A. 251.3 in.
Step-by-step explanation:
We can use this formula to solve for the circumference of a circle. r is equal to the radius, or half of the circle's width.
C = 2πr
C = 2πr
C = 2π(40)
C ≈ 251.3
A. 251.3 in.
Solve the following system of equations:
2x + 3y − z = 1
3x + y + 2z = 12
x + 2y − 3z = −5
PLEASE HELP!! 25 POINTS!!
The solution to the system of equations is:
x = -19/5, y = 2, z = 1/10
How do we calculate?4x + 6y - 2z = 2 (multiply first equation by 2)
x + 2y - 3z = -5 (third equation)
Add the two equations, we get:
5x + 8y = -3 (eliminated z)
-7x + 7y - 6z = -33 (multiplying second equation by 3 and subtracting from the first)
3x + y + 2z = 12 (second equation)
Add these two equations, we have:
-4x + 8y = -21 (eliminated z)
5x + 8y = -3
5x = -8y - 3
x = (-8y - 3)/5
Substituting this expression for x into the second equation, we get:
3((-8y - 3)/5) + y + 2z = 12
z = (39/10) - (19/10)y
Finally, substituting these expressions for x and z into any of the original equations (let's use the first one), we can solve for y:
2((-8y - 3)/5) + 3y - ((39/10) - (19/10)y) = 1
Simplifying and solving for y, we get:
y = 2
x = (-8(2) - 3)/5 = -19/5
z = (39/10) - (19/10)(2) = 1/10
In conclusion, the solution to the system of equations is:
x = -19/5, y = 2, z = 1/10
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The solution to the given system of linear equations is
x = 3, y = -1 and z = 2
Solving System of Linear EquationsFrom the question, we are to solve the given system of linear equations.
The given system of linear equations is
2x + 3y − z = 1
3x + y + 2z = 12
x + 2y − 3z = −5
Multiply the third equation by 2
x + 2y − 3z = −5 ) ×2
2x + 4y - 6z = -10
Subtract the first equation from the resulting equation
2x + 4y - 6z = -10
- (2x + 3y − z = 1
----------------------------------------
y - 5z = -11 ---------- (1)
Now,
Multiply the third equation by 3
x + 2y − 3z = −5 ) ×3
3x + 6y -9z = -15
Subtract the second equation from the resulting equation
3x + 6y -9z = -15
- (3x + y + 2z = 12
-----------------------------------------
5y - 11z = -27 ----------- (2)
Solve equations (1) and (2) simultaneously
y - 5z = -11 ------------ (1)
5y - 11z = -27 ------------ (2)
Multiply equation (1) by 5
y - 5z = -11 ) ×5
5y - 25z = -55
Subtract the resulting equation from equation (2)
5y - 11z = -27
-( 5y - 25z = -55
-----------------------------
14z = 28
Divide both sides by 14
14z/14 = 28/14
z = 2
Substitute the value of z into equation (1)
y - 5z = -11
y - 5(2) = -11
y - 10 = -11
Add 10 to both sides of the equation
y - 10 + 10 = -11 + 10
y = -1
Substitute the value of y and z into the third equation
x + 2y − 3z = −5
x + 2(-1) − 3(2) = −5
x - 2 - 6 = -5
x - 8 = -5
Add 8 to both sides of the equation
x - 8 + 8 = -5 + 8
x = 3
Hence,
The solution is
x = 3, y = -1 and z = 2
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help I need the answer quick
Answer: 228[tex]cm^2[/tex]
Step-by-step explanation:
The lateral area is 2lh + 2wh
= (2 * 14 * 6) + (2 * 5 * 6)
= 228[tex]cm^2[/tex]
I really need help with this! :'(
The expressions that are equivalent to 6x²y + 2xy⁵; are 2(3x²y + xy⁵), 2xy(3x + y⁴), xy(6x + 2y⁴) and 4xy(3/2x + 1/2y⁴). So, the correct options are a, b, e and g.
Give a brief account on algebraic equations.Algebra is known to be a branch of mathematics in which problems are represented as mathematical expressions using letters or variables (x, y, z, etc.) to represent unknown values that may change. The purpose of algebra is to understand what the unknown values are in order to find solutions to problems. The degree of an algebraic equation is the largest power that exists for the variables in the equation. Algebraic equations can be classified by degree as follows:
Linear equationsQuadratic equationsCubic equationsEquation A: 2(3x²y + xy⁵) = 6x²y + 2xy⁵
Equation B: 2xy(3x + y⁴) = 6x²y + 2xy⁵
Equation C: 2x²y(6 + 5y) = 12x²y + 10x²y²
Equation D: 6x²y.2xy⁵
Equation E: xy(6x + 2y⁴) = 6x²y + 2xy⁵
Equation F: 2y(3x + xy⁴)⁰ = 2y
Equation G: 4xy(3/2x + 1/2y⁴) = 6xy + 2xy⁵
Hence, Equation A, B, E and G are the equations found equivalent to the given equation, 6x²y + 2xy⁵.
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according to the law of sines, which of the following is equal to sin(B)/b
Answer:
[tex]\frac{sin(A)}{a}[/tex]
A crayon factory monitored the number of broken crayons per box during the past day.
Broken crayons per box
Stem Leaf
0 0 4 4 9
1 4 6 8 9 9
2 3 8
3 3
4 0 9
5 1 9
6 1
7 1 3
8 2 4 6 8
9 4 9
How many boxes had at least 20 broken crayons but fewer than 60 broken crayons?
the total number of boxes with at least 20 but fewer than 60 broken crayons is 33.To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20
what is at least ?
"At least" is a phrase that is used to indicate a minimum quantity or degree of something. It means that the stated quantity or degree is the smallest amount that is acceptable or possible. For example, if someone says "I need at least 10 dollars,"
In the given question,
To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20 but fewer than 60 broken crayons.
From the stem-and-leaf plot, we can see that the stems 2, 3, 4, and 5 have leaves that add up to at least 20 but fewer than 60:
Stem 2 has leaves 3 and 8, which add up to 11.
Stem 3 has leaf 3, which adds up to 3.
Stem 4 has leaves 0 and 9, which add up to 9.
Stem 5 has leaves 1 and 9, which add up to 10.
Therefore, the total number of boxes with at least 20 but fewer than 60 broken crayons is 11 + 3 + 9 + 10 = 33.
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Need answers ASAP!!!
Also, I will give Brainliest to whoever includes an explanation on what 9 ⁻³ means.
The given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.
What is Exponentiation?A number's power or exponent, in other words, tells how many times it must be multiplied by itself.
Any integer, fraction, or decimal can serve as the basis in this situation.
Additionally, the exponent might have either a positive or negative value.
Subtract the exponents to divide exponents (or powers) with the same base.
Given that division is the inverse operation of multiplication, it stands to reason that, just as exponents are added when multiplying numbers with the same base, exponents are subtracted when dividing numbers with the same base.
So, we have the exponents as;
9⁻³/9¹²
Then, solve as follows:
9⁻³/9¹²
9⁻³⁻¹²
9⁻¹⁵
Therefore, the given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.
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Given a continuous-time system with the input-output relation:
[tex]y(t) = T\left\{x(t) \right\} = x^2(t)[/tex]
Determine whether this system is:
- Linear
- Time-invariant
The given input-output relation is a nonlinear function of the input signal x(t), since it involves squaring the signal at every point in time. A linear system must satisfy the property of superposition, which states that the output to a linear combination of inputs must be the same as the linear combination of the outputs to each individual input.
To determine whether the system is time-invariant, we need to check if a time shift in the input signal produces the same time shift in the output signal. That is, if: [tex]y(t) = T{x(t)}[/tex] for all values of t. Then we want to check [tex]y(t - τ) = T{x(t - τ)}[/tex] for all values of [tex]τ[/tex] and [tex]t[/tex].
We shall the consider the case where [tex]τ > 0[/tex], then we have:
[tex]y(t - τ) = (x(t - τ))^2[/tex]
[tex]T{x(t - τ)} = (x(t - τ))^2[/tex]
Since [tex]y(t - τ) = T{x(t - τ)}[/tex], we can conclude that the given system is time-invariant.
Therefore, the given system is nonlinear but time-invariant.
A right triangle has sides 14 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse.
Answer:
According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Substituting the given values, we get:
c^2 = 14^2 + 48^2
c^2 = 196 + 2304
c^2 = 2500
Taking the square root of both sides, we get:
c = 50
Therefore, the length of the hypotenuse is 50 units.
Is (2, 6) a solution to this system of equations?
y = 3/2x + 3
y = -9x + 1
yes
no
To determine if (2, 6) is a solution to the system of equations:
y = 3/2x + 3 ... (equation 1)
y = -9x + 1 ... (equation 2)
We need to substitute x = 2 and y = 6 into both equations and check if they are true.
Substituting x = 2 and y = 6 into equation 1, we get:
6 = 3/2(2) + 3
6 = 3 + 3
6 = 6
This equation is true.
Substituting x = 2 and y = 6 into equation 2, we get:
6 = -9(2) + 1
6 = -18 + 1
6 = -17
This equation is false.
Since (2, 6) does not satisfy equation 2, it is not a solution to the system of equations. Therefore, the answer is: no.
Find the error. A student was finding the measure angle 5 in the figure below. She concluded that m angle 5=86
The answer is Option 2: The measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
What is a supplementary angle?An angle that, when combined with another angle, creates a straight angle (measuring 180 degrees), is known as a supplementary angle. In other words, if the sum of the measurements of two angles is 180 degrees, they are supplementary. Contrarily, a complimentary angle is one that, when combined with another angle, creates a right angle (which has a 90-degree angle). In other words, if the sum of the measurements of two angles is 90 degrees, they are complimentary. A straight angle and a right angle are not the same thing, hence it is crucial to understand that one angle cannot be both supplementary and complimentary at the same time.
From the given figure we see that the measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
Hence, option 2 is correct.
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The complete question is:
Help me please 14 points.
The best percentage bar graph that represents Camryn's data is:
C Winter | Spring | Summer | Fall
0% 20% 40% 60% 80% 100%
What is the use of a bar graph?A bar graph's purpose is to visually convey relational information quickly. The bars show the value for a specific type of data.
This is because the graph correctly shows the percentage of students who prefer each season, with the bar for each season extending to the appropriate percentage mark on the graph. It also clearly labels each season under the corresponding bar.
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100 Points! Find the third term of (11x+3y)^6. Photo attached. Please show as much work as possible. Thank you!
the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.we can use the binomial theorem to solve this .
what is binomial theorem ?
The binomial theorem is a theorem in algebra that describes the algebraic expansion of powers of a binomial. A binomial is a polynomial with two terms, such as (a + b) or (x - y).
In the given question,
To find the third term of the expansion of (11x+3y)⁶, we can use the binomial theorem, which states that:
(a + b)ⁿ = C(n,0)aⁿb⁰ + C(n,1)*aⁿ⁻¹*b¹+ C(n,2)*aⁿ⁻¹*b² + ... + C(n,n)a⁰bⁿ
where C(n,k) denotes the binomial coefficient, which is the number of ways to choose k items from a set of n items.
In this case, we have a = 11x and b = 3y, and n = 6. We want to find the third term, which corresponds to k = 3 in the expansion. Therefore, we need to compute the binomial coefficient C(6,3), as well as the powers of 11x and 3y that appear in the third term.
The binomial coefficient C(6,3) can be computed as follows:
C(6,3) = 6! / (3! * (6-3)!) = 20
To find the powers of 11x and 3y that appear in the third term, we need to look at the general pattern in the expansion. Each term in the expansion consists of a product of powers of a and b, with the powers of a decreasing by 1 from n to 0, and the powers of b increasing by 1 from 0 to n. Therefore, the kth term in the expansion will have powers of a and b given by aⁿ⁻ᵇand bᵃ, respectively.
In the third term, we have k = 3, so we need to find the coefficient of a³ = a³ = (11x)³ and b³ = (3y)³. The third term is given by:
C(6,3)(11x)³(3y)³
Plugging in the values for C(6,3), (11x)³, and (3y)³, we get:
20*(11x)³*(3y)³ = 2011³x³3³y³ = 798,720x³y³
Therefore, the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.
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Helpppppppp pleaseeeeee
The result of adding -3 (row 1) to row 2 is determined as (0 10) |-14.
What is the result of the row multiplication?The result of the row multiplication in the matrix is calculated by applying the following method;
row 1 in the given matrix = [1 -4] | 8
To multiply row1 by -3, we will multiply each entity by -3 as shown below;
= -3(1 -4) | 8
= (-3 12) | -24
To add the result to 3;
(-3 12) | -24 + (3 -2)|10
= (0 10) |-14
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.
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Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
[1 mark]
(b) How much does Jack receive the following Christmas?
[1 mark]
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
a) Jill receives £45
b) Jack receives £20 the following Christmas
c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.
Explain the term years
Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.
According to the given information
(a) Let's first find the total ratio of their ages:
1 + 3 = 4
So Jack's share will be:
1/4 x £60 = £15
And Jill's share will be:
3/4 x £60 = £45
Therefore, Jill receives £45.
(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:
2/6 x £60 = £20
So Jack receives £20.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:
1/4 x £60 = £25
Multiplying both sides by 4/60, we get:x = 5/4
So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.
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please helppppp this is past due will give brainliest
The mean of the data set is 25, the median is 25, the range is 20, the variance is 20, and the standard deviation is 4.47.
Solution to the Data AnalysisGiven the dataset:
x = 30, 20, 35, 25, 15
N = 5
Mean of the data set is the average of the dataset. To find the average, we add up all the numbers and divide by the total number of values:
Mean (Xbar) = (30 + 20 + 35 + 25 + 15) / 5 = 25
Median is the number that fall at the middle of the dataset. To find the median of the data set, we need to arrange the numbers in order from smallest to largest:
15, 20, 25, 30, 35
The median is the middle number, which is 25 in this case.
Range of the data set can be calculated by subtract the smallest value from the largest value:
Range = 35 - 15 = 20
Standard Deviation and Variance
First find the deviations of each value from the mean:
(x - Xbar) = d
30 - 25 = 5
20 - 25 = -5
35 - 25 = 10
25 - 25 = 0
15 - 25 = -10
To find the variance, we square each deviation, add them up, and divide by the number of values:
Variance = d²/N
= (5² + (-5)² + 10² + 0² + (-10)²) / 5
= 100/5 = 20
To find the standard deviation, we take the square root of the variance:
Standard Deviation = sqrt(variance)
= sqrt(20)
= 4.47 (rounded to two decimal places)
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in buying ground beef for hamburgers, there are several packages from which to choose, as shown in the table below. If johannes needs 5 pounds of beef for his barbeque, what will he pay?
Johannes will need to pay $8.61 for 5 pounds of ground beef
What is the cost of the beef?Since Johannes needs 5 pounds of ground beef, and the available pounds are 1.5, 2, 3, and 3.75 pounds.
To reduce the cost, he need to select the package with the lowest cost per pound.
The cost per pound for each package is:
Package 1: $5.58 / 1.5
= $3.72 per pound
Package 2: $7.44 / 2
= $3.72 per pound
Package 3: $1.16 / 3
= $0.39 per pound
Package 4: $13.95 / 3.75
= $3.72 per pound
Therefore, the package with the lowest cost per pound is Package 3 and package 2 which will give us 5 pounds
So he can do it as:
$1.16 + $7.44
= $8.6
Or
(1 package of 3 pounds x $0.39 per pound) + (1 package of 2 pounds x $3.72 per pound)
= $1.17 + $7.44
= $8.61
Therefore, Johannes will need to pay $8.61 for 5 pounds of ground beef.
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