Answers
The distributive property of multiplication can be used to calculate the sum of the difference between the multiples of the variables expression as follows;
\(\sum\limits_{i = 1}^{124} (29\cdot a_i - 13 \cdot b_i)\) = -30
What is the distributive property?The distributive property states that multiplying the difference between addend by a value produces a result which is equivalent to the multiplication of each addend individually and finding the difference from the resulting values.
The distributive property of multiplication indicates that we get;
Where; \(\sum\limits_{i=1}^{124} a_i = -10\), and \(\sum\limits_{i=1}^{124} b_i = -20\)
\(\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) = 29 \times \sum\limits_{i=1}^{124} a_i - 13 \times \sum\limits_{i=1}^{124} b_i = 29 \times (-20) - 13 \times (-10))\)
29 × (-10) - 13 × (-20) = -30
Therefore;
\(\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) =-30\)
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Related Questions
The floor of Aisha’s rectangular bedroom has an area of 144 feet squared. Which are possible dimensions of her bedroom? Select three options. 14.4 ft by 10 ft 6 ft by 12 ft 8 ft by 9 ft 8 ft by 18 ft 9 ft by 16 ft
Answers
Answer: The correct options are
14.4 ft. by 10 ft.
8 ft. by 18 ft.
and 9 ft. by 16 ft.
I think.
Answer:
A. 14.4 ft by 10 ft
D. 8 ft by 18 ft
E. 9 ft by 16 ft
Step-by-step explanation:
I hope this helped
Can somebody please help?? i’ll give Brainliest to whoever answers first.
There are 625 students in Leon's school. He takes a random sample of 75 students from the entire school population. In the sample, 33
students are planning to attend the end of year picnic.
Based on his data, how many students from the entire school are planning to attend the end of year picnic? Show ALL your work!
Answers
Answer:
The answer is 275 students.
Step-by-step explanation:
In 75 students, 33 students attend.
So the ratio is 33/75.
so multiply with 625.
625 x 33/75 = 275
The vertex form of a function is g(x) = (x-3)² + 9. How does the graph of g(x) compare to the graph of the function
f(x)=x²?
Og(x) is shifted 3 units left and 9 units up.
O g(x) is shifted 3 units right and 9 units up.
O g(x) is shifted 9 units left and 3 units down.
Og(x) is shifted 9 units right and 3 units down.
Answers
Answer:
(3,9)
Step-by-step explanation:
Solve for y. -3 = 7 (y - 9/7)
Answers
Answer:
y = 1
Step-by-step explanation:
y - 3 = 7 (y - 9/7)
y - 3 = 7*y + 7*-9/7
y - 3 = 7y - 9
y - 7y = 3 - 9
-6y = -6
y = -6/-6
y = 1
probe:
1 - 3 = 7(1 - 9/7)
-2 = 7*-2/7
Work out the value of (-8)2
Answers
Answer:
-16
Step-by-step explanation:
2x(-8)=16
Hey there!
Assuming you meant:
(-8)^2
= (-8)(-8)
= 64
Therefore, your answer should be:
64
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Adrianna has $20 in her savings account. Each week she will add $5 to it. Which equation represents this situation?
Answers
we would have
y = 5x + 20
Answer:
Let y = the amount in Adrianna's savings account
Let x = the number of weeks passed
y = 5x + 20
What is the variable type for the type of flooring in a room? O Qualitative Discrete O Qualitative Continuous O Quantitative O Quantitative Discrete O Qualitative O Quantitative Continuous
Answers
The variable type for the type of flooring in a room is Qualitative Discrete. This type of variable takes on unmistakable classes and can't be estimated on a mathematical scale.
Let us consider that the type of flooring in a room may be rug, tile, or hardwood, and there is no way to quantify the type of flooring on a mathematical scale.
The variable type for the type of cooking served in a café is likewise Qualitative Discrete. This variable takes on unmistakable classes like Italian, Chinese, and Mexican, and it is basically impossible to gauge the type of food on a mathematical scale.
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The function f(x) = 12,000(1 + 0. 05)x models the fish population in a lake. What will the population be in 4 years? what was the population 4 years ago?.
Answers
About 14,586 will the population be in 4 years.
About 9,872 was the population 4 years ago.
Assuming an exponential function
\(f(x) = 12,000(1 + 0. 05)^x\)
(Where x is the number of years and f(x) is the population of fish in a lake.)
Put x = 4 in the function to determine the population in 4 years:
\(If, x=4,\\f(4) = 12,000(1 + 0. 05)^4\\f(4) = 12,000(1 . 05)^4\\f(4) = 12,000(1.21550625)\\f(4) = 14586.075\\f(4) = 14586approx\)
Add x = -4 to the function to determine the population four years ago:
\(If, x=-4,\\f(-4) = 12,000(1 + 0. 05)^{-4}\\f(-4) = 12,000(1. 05)^{-4}\\f(-4) = 12,000(0.8227024748)\\f(4) = 9872.429698\\f(-4) = 9872approx\)
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For each sequence, state if it is arithmetic, geometric, or neither.
0, 3, 8, 15, 24
Answers
Answer:
Step-by-step explanation:
0, 3, 8, 15, 24, . . .
it is arithmetic
fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
Answers
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
A basketball roster is shown in the table.
A 4-column table with 7 rows titled Basketball Roster. Column 1 is labeled Player with entries Adams, Brock, Cup, Dennis, Early, Finn, Graham. Column 2 is labeled Grade with entries 11, 12, 11, 10, 12, 11, 12. Column 3 is labeled Position with entries G, F, F, G, C, F, G. Column 4 is labeled height with entries 5 foot 6, 5 foot 8, 5 foot 9, 5 foot 3, 5 foot 11, 5 foot 9, 5 foot 5.
Which variable would be classified as a continuous quantitative variable?
grade
height
player name
position
Answers
Using variable concepts, it is found that the player's height is a continuous quantitative variable.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, ...What are qualitative and quantitative variables?Qualitative variables: Assumes labels or ranks.Quantitative variables: Assume numerical values.In this problem:
The player name and position are qualitative variables.Grade assumes only integer values, hence it is discrete.The height is quantitative, assuming decimal values in inches, hence it is also continuous.You can learn more about continuous and discrete variables at https://brainly.com/question/16978770
Answer:
height
Step-by-step explanation:
noballz
-2(x+4)²= -200
can you guys please help
Answers
2x-1=y
3x-1=y
Consider the system of equations above. Which of the following statements about this system is true?
Answers
Answer:
B; There is only one (x,y) solution and y is negative
Step-by-step explanation:
First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.
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62. A chemist mixes 15 liters of 40 percent acid solution and 25 liters of 20 percent acid solution.
What percent of the mixture is acid?
Answers
40% of 15 L = 6 L of acid
20% of 25 L = 5 L of acid
This means the mixture contains a total of 11 L of acid, and with a total volume of 15 L + 25 L = 40 L, that means the mixture is at a concentration of
(11 L acid) / (40 L solution) = 0.275 = 27.5%
if f(x)=-3x-2 find f(3)
Answers
Answer:
-11
Step-by-step explanation:
Answer:
-11
Step-by-step explanation:
f(3) means that you plug in 3 for x in the entire equation of f(x)
This means when f(x) = -3x - 2
f(3) = -(3)(3) - 2
= -9 -2
= -11
Rewrite the equation in Ax+By=C form
y-6=5(x+2)
Answers
y-6=5(x+2), distribute the 5 into the parenthesis
=> y-6=5x+10, add the value of 6 to both sides
=> y=5x+16, subtract the value 5x from both sides
=> y-5x=16, thus we are in the form Ax+By=C
help to solve -7 - 3a = 1 - 4a
Answers
Answer:
-7 - 3a = 1 – 4a
Step one: Add 4a to -3a
-7 + a = 1
Step two: Add 7 to 1
A = 8
You're done! A=8 for this problem!
Hopefully this helps! Feel free to mark brainliest!
Answer:
\(a =8\)
Step-by-step explanation:
\(-7 - 3a = 1 - 4a\)
add \(3a\) to both sides
\(-7 - 3a + 3a = 1 -4a + 3a \\-7 = 1 -a\)
add \(-1\) to both sides
\(-7 - 1 = 1 - a -1\\-8 = -a\)
multiply both sides by \(-1\)
\(-8 * (-1) = -a * (-1) \\8 = a\)
a piece of rubber tubing maintains a cylindrical shape as it is stretched. at the instant that the inner radius of the tube is 2 millimeters and the height is 20 millimeters, the inner radius is decreasing at the rate of 0.1 millimeter per second and the height is increasing at the rate of 3 millimeters per second. which of the following statements about the volume of the tube is true at this instant? (the volume
Answers
The volume of the tube is increasing at the rate of 0.6 cubic millimeters per second.
The formula V = r2h, where r is the radius and h is the height, describes the volume of a cylinder.
The tube's volume is V = (2 mm)2 (20 mm), which equals 125.66 mm3.
Dr/dt = -0.1 mm/s and dh/dt = 3 mm/s are the formulas used to calculate the rate of change of the radius and height, respectively.
Using the chain rule, the rate of change of the volume is given by
dV/dt = π·2·[(2 mm)·(-0.1 mm/s) + (20 mm)·(3 mm/s)] = 0.6 mm3/s.
Therefore, the volume of the tube is increasing at the rate of 0.6 cubic millimeters per second.
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What is the range of the function in the table
X Y
1 2
2 4
3 3
4 2
A) (1,2,3,4)
B) (1,2) (2,4) (3,3) (4,2)
C) (1,2)
D) (2,3,4)
Answers
Answer:
D. (2, 3, 4)
Step-by-step explanation:
The range is the y values. The y values, in numerical order, range from 2 to 4. The 2s do not need to be repeated.
I think of a certain number. If I multiply it by 6, add -18 to the product and take away one-third of the sum, I will get -2. What is the number?
Answers
work:
-2(3)=-6
-6-(-18)=12
12/6=2
2
Which of the following are equivalent to x2 – 4x + 9? Select four answers.
A. (x – 3)2 – 4x
B. (3x2 – 3x + 1) – (2x2 + x – 8)
C. (x – 3)(x + 3) – 2x
D. (x – 3)2 +2x
E. (x – 5)(x + 1) +14
F. (8x2 + 2x) – (4x2 + 6x) + (9 – 3x2)
Answers
Answer:
a).2x-6-5x-12x. this is answer
Mr. Rogers is designing the layout for a new floor of his office. His new layout will have 8 workstations in one row, with the side length of each workstation being 2 feet longer than the side length (s) of the workstations in the existing layout. He writes this expression to help him design the layout.
8(s + 2)
Which algebraic expression is equivalent to this expression?
A.
8s + 16
B.
8s + 2
C.
8s + 10
D.
s + 16
Answers
Abram needs to build a window frame. He needs 2 pieces of lumber that are feet long and 2 more that are feet long. How much lumber does Abram need in all?
A.8 1/10 ft
B.8 1/4 ft
C.15 4/5 ft
D.16 1/6
pls answer quick
Answers
Answer:
D
Step-by-step explanation:
Answer:
I think 8 1/4 feet
Step-by-step explanation:
pls help me toooo
A Pizza restaurant offers the following deals:
Deal #1: $8.99 for a large pizza and $5 for each additional large pizza on the same order
Deal #2: $6.00 per large pizza
At what number of pizzas does Deal #1 become a better deal?
What is the cost of 10 pizzas for Deal #1$53.99 for Deal #2 $60
AT WHAT NUMBER OF PIZZAS DOES DEAL #1 BECOME A BETTER DEAL?
Answers
The number of pizzas does Deal #1 become a better deal will be 9 and the cost of 10 pizzas in each deal will be $58.99 and $60.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A Pizza café offers the accompanying arrangements:
Deal #1: $8.99 for an enormous pizza and $5 for each extra huge pizza on a similar request.
Deal #2: $6.00 per enormous pizza.
Let 'x' be the number of pizzas and 'y' be the total cost. Then we have
y = 5x + 8.99 ...1
y = 6x ...2
From equations 1 and 2, then we have
6x = 5x + 8.99
x = 8.99
x ≈ 9
The cost of 10 pizzas in each deal, then we have
y = 5(10) + 8.99
y = 50 + 8.99
y = $58.99
y = 6(10)
y = $60
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Help 9-11 thank you !
Answers
Answer:
9 - 11 = -2
Step-by-step explanation:
Because 9 is being subtracted by a number greater than itself, the answer has to be a negative and because:
9 + 2 = 11
9 - 11 = (-2)
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The original plan for assigning telephone numbers that you investigated in
Applications Task 4 was implemented in
1947. At that time, the supply of numbers was expected to last for 300 years. However, by the 1970s the numbers were already starting to run out. So, the numbering plan
had to be modified. In this task, you will count the number of different phone numbers that were available in 2012.
a. For three-digit area codes, the first digit cannot be a 0 or a 1. Assuming no additional restrictions, how many three-digit area codes are possible under
this plan?
b. Certain area codes are classified as "Easily Recognizable Codes" (BRCs).
ERCs designate special services, like 888 for toll-free calls. The requirement for an ERC is that the second and third digit of the area code must be the same. The first digit again cannot be a 0 or a 1. How many ERCs are there?
c. Consider the seven digits after the area code. As with the area code, the first digit of the three-digit local prefix cannot be a 0 or a 1. The remaining six digits for the local number have no restrictions. How many of these seven-digit phone numbers are possible?
d. Assuming only the 0 and 1 restrictions in Parts a and c, how many ten-digit phone numbers are possible?
Answers
a. Assuming no additional restrictions, there are 800 possible three-digit area codes.
b. Considering ERCs, there are 80 ERCs.
c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\) possible seven-digit phone numbers.
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.
a. For three-digit area codes, the first digit cannot be 0 or 1.
Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)
b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).
Since the second digit must be the same as the third digit, there is only 1 possibility.
Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)
c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.
There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).
Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.
For the area code (part a), there are 800 possibilities.
For the seven digits after the area code (part c), there are 8,000,000 possibilities.
Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.
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After the point B(2, 3) is translated along the vector <5, 7> the image will be located at ?
Answers
Answer:
(7, 10)
Step-by-step explanation:
The vector has an x component of 5 and a y component of 7, so we can add each of these components to the coordinates of B to get its image:
B(2,3)
B'(2 + 5, 3 + 7) = B'(7, 10)
The image will be located at (7, 10).
What is vector?Vectors, in Maths, exist as objects which have both, magnitude and direction. Magnitude determines the size of the vector. It exists described by a line with an arrow, where the length of the line exists the magnitude of the vector and the arrow displays the direction.
The vector has an x component of 5 and a y component of 7, so we can add each of these components to the coordinates of B to get its image:
B(2,3)
B'(2 + 5, 3 + 7) = B'(7, 10)
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If y varies inversely as x, and y=9 when x =10, find y when x=5
Answers
The value of the y is 18 when x = 5.
Given,
In the question:
If y varies inversely as x
and, y=9 when x =10
To find the value of y when x = 5
Now, According to the question:
Based on the given conditions:
Formulate:
y = k/x
Calculate and substitute y = 9 , x = 10 into y = k/x
9 = k/10
k = 90
To find the equation of the function:
y = 90/x
Calculate and substitution x = 5 into y = 90/x
y = 18
Hence, The value of the y is 18 when x = 5.
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A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answers
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
\(f(x) = \lambda e^{-\lambda x}\)
And the cumulative distribution function (CDF) is,
\(CDF = 1 - e^{-\lambda x}\)
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Two angles form a linear pair. The measure of one angle is 6 less then the measure of the other angle. Find the measure of each angle
Answers
Answer: one angle would be 50 degrees while the other would be 130 degrees.
Step-by-step explanation: