(4a*2c)+(8a*2c)-(10a*2c)
Answer: 4ac
Step-by-step explanation: Combine like terms and follow PEMDAS
(pre calc) HELP ASAP
The solution is Option D.
The limit of the infinite series diverges and the limit goes off to infinity
What is convergent and divergent series?If a series is convergent then it has bounded partial sums. Equivalently, if a series fails to have bounded partial sums then it is divergent.
When the series' limits reach its finite range of values, the series is said to be convergent. It is important that, partial sum of series, there should be a limit existed and that is finite in nature then only series converges
An infinite series is one that doesn't converge at any point , had a series of incomplete sums that went on forever and had no end. A series diverges when each sum does not approach zero.
Given data ,
Let the infinite series be represented as A
Now , the value of A is
A = ∑n=1 to ∝ ( 3n⁴ / ( 15n⁴ + 5 )
On simplifying the equation , we get
A = 3 ∑n=1 to ∝ ( n⁴ / ( 15n⁴ + 5 )
In the equation , where the limit goes to infinity, there will finally be no exact solution because the sum of the series will be infinity and the infinite series diverges
Hence , the limit of the equation is infinity
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Nilsa borrows $2,000 for 90 days at 18% exact interest.
On solving the provided question, we can say that so, the Interest Rate to be paid will be as = 5.08%
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
Interest Rate =($ Paid in Interest / $ Amount borrowed) X (360 / borrowed period)
= ($33 / $2600) X (360 /90)
=0.050769231
=5.08%
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a number has the same digits in its hundreds place and it’s hundrthes place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place
In a case whereby a number has the same digits in its hundreds place and it’s hundredths place the number of times that the value is greater in the hundreds place than the value of the digit in the hundreds place is 10,000 times.
How can the value of the digit can be calculated?The question can be interpreted that the particular number has the same digit which is seen in hundreds place hence hundredths place.
we can then represent the digit as '1'.
The value of number's hundreds place can be represented as 100
we can as well represent the number's hundredths place as 0.01
the number of times the value of the hundreds place digit exceeds the value of the hundredths place digit can be expressed as 100/0.01 =(100*100)/1 = 10, 000
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missing options:
A. 100,00
B. 100
C. 1,000
D. 10,000
Mitchell travels from the US to Canada, where he exchanges 150 US dollars for Canadian dollars. He then spends 20 Canadian dollars, returns to the US, and exchanges the remaining money back to US dollars. How many US dollars does Mitchell have remaining? O 129.46 O 130.00 O 130.66 O 134.59
Going by current exchange rates, Mitchell has $134.13 dollars remaining.
What is unit conversion?Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.
The current exchange rate of Canadian dollars to US dollars is:
CAD $ 1.26 : 1 USD
When Mitchell first exchanged the USD to CAD$, it became:
= 150 x 1.26
= CAD$ 189
He then spends CAD$ 20 which leaves him with:
= 189 - 20
= CAD$ 169
He then exchanges this back to US$:
= 169 / 1.26
= US$ 134.13
Mitchell has US$ 134.13 remaining.
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A backyard pond has 12 sunfish and 30 rainbow shiners. Write the
ratio of sunfish to shiners in simplest form.
Answer: 2:5
Step-by-step explanation:
Given,
Number of sunfish = 12
Number of rainbow shiner = 30
To find,
The ratio of sunfish to rainbow shiner.
Solution,
We can simply solve this mathematical problem by using the following mathematical process.
Ratio of sunfish to rainbow shiner :
= Number of sunfish : Number of rainbow shiner
= 12 : 30
= 6 : 15
= 2 : 5
(This ratio cannot be for the simplified so we will have to assume this as the final answer of this question.)
Hence, the ratio is 2:5
Answer:
2:5
Find the number both sides can be divided by in this case, it is 6. Diving both sides by a common number gives us 2 from 12 and 5 from 30.
two-fifths of the students in central middle school are boys. One third of the girls have blonde hair and one quarter of the boys have blonde hair.
(A) what fraction of the students in central middlev school have blonde hair.
(B) if 36 of the students of central middle school have blond hair, then how many total does central middle school have.
PLEASE HELP
I did number one but i think its wrong
Answer: A: 3/10 of the school has blonde hair. B: there are 120 students
Step-by-step explanation: I might have done this wrong but anyway, I multiplied 2/5 by 1/4 and got 1/10, meaning 1/10 of the boys have blonde hair. I multiplied 3/5 (because 5/5 - 2/5 = 3/5) by 1/3 and got that 2/10 of the girls are blonde. I added these, and got that 3/10 of the school are blondes. That's A. Then, I set up the equation 3/10 = 36/x (x equals the total number of students in the school). When I solved it I got x = 120, meaning there are 120 students in the school.
If a cubic millimeter of blood contains 6, 200, 000 red blood
cells, how many red blood cells are contained in 60 cubic
millimeters of blood?in scientific notation
The scientific notation is [tex]3.7 \times10 ^8[/tex] in a blood volume of 60 ml. Take note that the power of 10 is evaluated using the product of power property.
What exactly are scientific figures?The reliability of a value, which is frequently an estimation affected by the item's decimal bit count. Beginning with the first non-zero digit, count the decimal places.
Up to the quel decimal place, all zeros are allowed. For example, the number 0.0079800 has five three-digit digits. When present, any digits to the right of the measurement's final non-zero number are required. equivalently increases an integer by three significant digits and three places.
After three, move upward, and start measuring at the first non-zero digit. The final digit must then be removed. The last two numbers are multiplied by zeros to the right of the decimal point.
given
If there are 6,200,000 red blood cells per cubic millimeter of blood,
then there are
[tex]60 \times 6,200,000=60 \times 6.2 \times 10^ 6=372 \times 10^6[/tex]
= [tex]3.7 \times10 ^8[/tex]
= [tex]3.7 \times10 ^8[/tex] in a blood volume of 60 ml. Take note that the power of 10 is evaluated using the product of power property.
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If anyone know how to do this comment
Answer:
[tex]\displaystyle y=-\frac{3}{8}x+2[/tex]
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes. So, we must first determine our slope of the original equation by converting to slope-intercept form:
[tex]-8x+3y=-6\\3y=8x-6\\y=\frac{8}{3}x-2[/tex]
Hence, because the slope of the original line is 8/3, then the slope of the perpendicular line is -3/8. We are not done, however, as we need to account for the point that the perpendicular line passes through by solving for the new y-intercept:
[tex]y=-\frac{3}{8}x+b\\ \\8=-\frac{3}{8}(-16)+b\\\\8=6+b\\\\2=b[/tex]
Thus, the perpendicular line equation is [tex]y=-\frac{3}{8}x+2[/tex]. See below for a graph.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]-8x+3y=-6\implies 3y=8x-6\implies y=\cfrac{8x-6}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{8}{3}}x-2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{8}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{8}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{8} }}[/tex]
so we're really looking for the equation of a line whose slope is -3/8 and it passes through (-16 , 8)
[tex](\stackrel{x_1}{-16}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{8} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- \cfrac{3}{8}}(x-\stackrel{x_1}{(-16)}) \implies y -8= -\cfrac{3}{8} (x +16) \\\\\\ y-8=-\cfrac{3}{8}x-6\implies {\Large \begin{array}{llll} y=-\cfrac{3}{8}x+2 \end{array}}[/tex]
Evaluate the expression $-8x+5-2x-4+5x$ when $x=2$ before and after simplifying.
Answer:
-9
Step-by-step explanation:
First combine like terms.
-8x+5-2x-4+5x -8x-2x+5x=-5x
-8x+5-2x-4+5x 5-4=1
Now plug in 2 for x
-5x+1
↓
-5(2)+1= -10+1=-9
If this is wrong, I'm sorry for the misguidance.
Explain why the statement "It will always rain on my birthday" uses inductive reasoning.
what is 18x+26.6 need asap
18x+26.6
18x+133/5
1/5(90x+133)
Jacob has 17 yards of fabric. He uses 1 third of it to make a cape. How many yards of fabric does Jacob use for the cape.
Answer:
49/3 or 16 1/3
Step-by-step explanation:
Answer:
Jacob uses 5.67 yards of fabric for the cape.
Step-by-step explanation:
Drag the tiles in the correct box. Consider the graph of the function f (x) =2x. Match each transformation of function f to a feature of the transformed function.
Answer:drag 1st 2 3rd box 2nd to 1st box 3rd to 1st box 4th to 4th
Step-by-step explanation:
so easy
State the definition of the limit f(x,y)
Therefore , the solution of the given problem of limit comes out to be it is the definition of the limit f(x,y).
Definition limit.A function's limit is a value that the function takes on as its input approaches or approaches a certain number. Continuity, integrals, & derivative are defined by limits. A function's limit is always interested in how the function behaves at a specific location.
Here,
Given :
If f(x,y) is a function that depends on x and y, then we have this function. Then, assuming that ϵ>0,∃ δ > 0 positive definite
|f (x,y)C| whenever, this given function does have the limit of C as (x,y) (a,b). 0 < ( x − a ) 2 + ( y − b ) 2 < δ
It's described as. lim (a, b) f (x, y) => ( x , y )
Thus , it is the definition of the limit f(x,y).
Therefore , the solution of the given problem of limit comes out to be it is the definition of the limit f(x,y).
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HELP ME PLEASE QUICK
What is the range of the equation shown in the graph
Answer:
the answer is y≤1
Step-by-step explanation:
i hope it is right sorry if wrong
A standard die is rolled. Find the probability that the number rolled is even
The probability of rolling an even number is P = 0.5
How to find the probability?We know that the possible outcomes of a standard die are {1, 2, 3, 4, 5, 6}
The outcomes that are even are {2, 4, 6}
If all the outcomes have the same probability, then the probability of rolling an even number is equal to the quotient between the nmber of even outcomes (3) and the total number of outcomes (6).
Then the probability is:
P = 3/6 = 1/2
That is the probability of rolling an even number,
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One number is four times as large as another and their sum is 5285 what are the two numbers
Answer:
One number is equal to 4228 and the other is equal to 1057
Step-by-step explanation:
1. Let's consider the number that four times the other X, and the other as N
2. We can write X as 4N to make it easier
3. Next, we can form a simple equation X + N = 5285 and substitute the value of X to get 4n + n = 5285
4. We get 5n = 5285
5. To get N we divide 5285 by 5 to get 1057
6. 5285 - 1057 = 4228
Therefore, one number is equal to 4228 and the other is 1057
-2x + 9y=-41 and -2x -5y =1
What is m∠LKH? - View the image attached.
Answer:
∠ LKH = 25°
Step-by-step explanation:
LK is the midsegment of Δ FGH
LK joins the midpoints of the sides FH and GH and is parallel to the third side FG.
Then
∠ LKH = ∠ FGH = 25° ( corresponding angles )
Points X and Y lie in both plane P and plane Q. What object defines the intersection of the two planes
A straight line defines the intersection of the two planes.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Points {X} and {Y} lie in both plane P and plane Q.
Two common points can only lie on a straight line. So, a straight line defines the intersection of the two planes.
Therefore, a straight line defines the intersection of the two planes.
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What is the Hcf for 18 and 36
Answer:
18
Step-by-step explanation:
GCF - The highest number that divides into two or more numbers, we are given the number 18 and 36.
Out of all the numbers divisible by 18 and 36, 18 is the greatest number out of all, making it the GCF.
Answer:
6
Step-by-step explanation:
The HCF (highest common factor) is the product of all the primes of both numbers!
1) List the prime factors of 18...
18 = 2 × 3 × 3
2) List the prime factors of 36...
2 × 2 × 3 × 3
3) Now see what numbers are in both!
We can see that the numbers 2 & 3 are in both prime factors so all we need to do is multiply them...
2 × 3 = 6Have a lovely day :)
THEORY
1a. In a class of 58 students, 35 offer Biology, 28 offer Economics and 15 offer Physics. Each
students offers at least one of the three subjects. If 12 students offer both Biology and
Economics, 7 students offer both Biology and Physics and 5 students offer both Economics and
Physics, how many students offer all three subjects?
b. A regular polygon with (2m+1) sides has each interior angle equal to 1440. Find the value of
m.
A. 9 students offer all three subjects.
B. The only possible value of m is 8.
Solution
A. We can use the Principle of Inclusion-Exclusion (PIE) to find the number of students who offer all three subjects.
Let's call the number of students who offer all three subjects "x".
The total number of students who offer Biology is 35, but we have to subtract the number of students who offer only Biology and Economics (12) and only Biology and Physics (7) to avoid counting them twice.
So, the number of students who offer Biology only is 35 - 12 - 7 + x = 16 + x.
Similarly, the number of students who offer Economics only is 28 - 12 - 5 + x = 11 + x.
And the number of students who offer Physics only is 15 - 7 - 5 + x = 3 + x.
The total number of students who offer at least one of the three subjects is 58, so:
16 + x + 11 + x + 3 + x = 58
30 + 3x = 58
3x = 28
x = 9
So, 9 students offer all three subjects.
B. In a regular polygon with (2m + 1) sides, each interior angle is equal to (2m + 1 - 2) * 180 / (2m + 1) = (2m - 1) * 180 / (2m + 1).
We know that this value is equal to 1440, so:
(2m - 1) * 180 / (2m + 1) = 1440
Expanding the right side:
2m - 1 = 1440 * (2m + 1) / 180
Dividing both sides by (2m + 1) and rearranging:
2m = 1440 * 2 / 180 + 1
2m = 16 + 1
m = 8.5
Since m must be a positive integer, the only possible value of m is 8.
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Write an equation of the line in point-slope form that passes through the given points (-2,3) and (-4,-4)
Answer:
tu x ella = ERROR
Step-by-step explanation:
A line has a slope of –9 and includes the points (–7,u) and (9,9). What is the value of u?
A line has a slope of –9 and includes the points (–7,u) and (9,9).
The value of u is 153.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
A line has a slope of –9 and includes the points (–7,u) and (9,9).
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
-9 = (9 - u)/(9 + 7)
-9 = (9- u)/16
9 - u = -144
u = 153.
Therefore, the value of u is 153.
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32 players show up to practice one day, and the coach realizes she can't
make equal teams of 6. With 32 players, how many players can the coach
put on each team so that each player is on a team and every team has the
same number of players?
Answer:
8 teams of 4 players or 4 teams of 8 players
Step-by-step explanation:
8 x 4 = 32
Create your own quadratic function ,f(x), and then evaluate the function at f(x-3). Find the domain of your function.
Domain of the function is all real numbers
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider a function f(x)= x² + 2x - 3
Now let us find the value of f(x-3)
Plug in the value x as x-3
f(x-3)= (x-3)² + 2(x-3) - 3
= x² +9-6x+ 2x-6 - 3
= x² -4x
The domain of this function is all real numbers. This means that any real value can be plugged into the function and produce a real output.
Hence, domain of this function is all real numbers
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A total of 312 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
Answer:
78
Step-by-step explanation:
312 divided by 4 equals 78
Solve for x. 8x-8+3(2x+2) = -4(x+3)
Answer:
x = - 5/9
Step-by-step explanatiion:
8x-8+3(2x+2) = -4(x+3) is the original equation
Consider each term and simplify
3(2x+2) = 6x + 6
-4(x + 3) = -4x - 12
Therefore the original expression becomes:
8x - 8 + 6x + 6 = -4x - 12
Move -4x to the left side; becomes + 4x
4x + 8x - 8 + 6x = -12
Group like terms on left side and simplify
(4x + 8x + 6x) (-8 +6) = -12
18x - 2 = - 12
Move -2 to right side -> becomes +2
18x = 2 - 12 = - 10
x = -10/18 = - 5/9
Kaya babysits to add money to her savings. She draws a graph to show how much she can earn by babysitting. What is the equation of Kaya’s line in slope-intercept form? What do the slope and y-intercept represent in the situation? Show your work.
The equation of the line of Kaya’s line in slope-intercept form is y = 15x + 25.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given this, Kaya babysits to add money to her savings. She draws a graph to show how much she can earn by babysitting.
To calculate the equation of the line we at least need Two points on the line.
Two points on the graph (0, 25) and (5, 100) and also the y-intercept of the given line is 25(where x is 0)
From the general formula of the slope-intercept form of an equation:
y=mx+b,
where m is the slope
b is the y-intercept,
Since. m = (y - y')/ (x -x')
In our case m = (100 - 25)/5-0)
m = 75 /5
m = 15
and b = 25
Thus, the equation of a line:
y = 15x + 25
Therefore, The equation of the line of Kaya’s line in slope-intercept form is y = 15x + 25.
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