Drag the values to the correct locations to write this series using sigma notation and find the sum of the terms. Not all values will be used.
45 + [45 − 2.5] + ⋯ + [45 − 4(2.5)]
Answers
Answer:
[tex]\displaystyle \\\sum_{k=0}^4 45-2.5k=200[/tex]
Step-by-step explanation:
We start off with the term 45 and decrease by 2.5 each term, ending with four 2.5's subtracted from 45.
Therefore, our index starts at k=0 and ends at 4. The general term can be defined then as [tex]\displaystyle \\\sum_{k=0}^4 45-2.5k[/tex] and evaluating yields 200.
Related Questions
solve this two questions with explaining method also....
Answers
Answer:
6) Selling price = ₹ 1608
Labelled price = ₹ 2010
7) Profit percentage = 10.5%
Step-by-step explanation:
Finding the selling price:
6) Cost Price = ₹ 1200
[tex]\sf Profit = 33\dfrac{1}{3} \% * Cost\ price\\\\[/tex]
[tex]\sf = \dfrac{102}{300}*1200\\\\ = 102 * 4\\\\[/tex]
= ₹ 408
Selling price = Cost price + Profit
= 1200 + 408
= ₹ 1608
Let the labelled price = x
Discount % = 20%
(100-20)% of x = 1200 + 408
80% of x = 1608
[tex]\sf x = 1608*\dfrac{100}{80}\\\\[/tex]
x = ₹ 2010
Answer: Selling price = ₹ 1608
Labelled price = ₹ 2010
7) Let the Cost price = ₹ X
Marked price = (100 + 30)% of Cost price
[tex]\sf = \dfrac{130}{100}X\\\\ = 1.3 X[/tex]
Discount% = 15%
Selling price = (100 - 15)% of 1.3X
= 85% * 1.3X
= 0.85 * 1.3X
= 1.105X
[tex]\sf \boxed{\bf Profit \% =\dfrac{Selling \ price - Cost \ Price}{Cost \ price }*100}[/tex]
[tex]\sf = \dfrac{1.105X - X}{X}*100\\\\ = \dfrac{0.105X}{X}*100\\\\ = 0.105*100\\\\ = 10.5 \%[/tex]
make k the subject!
Answers
Leticia was driving 45 miles per hour. after traveling for four hours she found that she was to 250 miles east of albertville
Answers
Answer:
can you give the question?
Step-by-step explanation:
didnt ask a question
Using the order of operations, what should be done first to evaluate 12 divided by (negative 6) (3) + (negative 2)?
Answers
According to the order of operations, brackets are solved first which contains the division operation. Hence, 12 is divided by -6 first.
Order of Operations
Given expression is,
(12 ÷ (-6))(3) + (-2)
According to the BODMAS rule of operations, the precedence order of operations is as follows,
Brackets > Of > Division > Multiplication > Addition > Subtraction
Hence, we will start by solving the brackets first, then solve the division and then the addition.
Evaluation
Solving the given expression as per the order of operations,
Brackets are solved first, then division followed by multiplication and then addition. Division is always of the highest precedence among all operations after brackets and of.
12 ÷ (-6)(3) + (-2)
= 12 ÷ (-6)(3) - 2 [∵ +(-n) = -n]
= (-2)(3) -2
= -6 - 2
= -8
Thus, solving the +(-2) and then division of 12 by (-6) are the first operations to be performed in order to evaluate the given expression.
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What are the two numbers on the upper left and the three on the bottom?
Answers
The computation of the equation shows.that x is -4 and y is 0.6.
How to calculate the value?4x + 5y = -1
-5x - 8y = 10
The value of x and y will be calculated thus:
-5 × (4x + 5y = -1)
4 × -(5x - 8y = 10)
-20x - 25y = 5
-20x -32y = 40
Add the equation
57y = 45
y = 45/75 = 0.6
Since 4x + 5y = -1
4x + 5(0.6) = -1
4x + 3 = -1
x = -1 - 3
x = -4
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Consider the graph of rational function f
f(x)
-4
I
T
1
-2
6-
4-
2+
-2-
-4-
-6.
0
4+12
O
N.
2
Which equation represents function ?
OA f(2)= =+
OB. f(2)=426
Oc f(2)==
OD. f(2)=342-6
TY
6
X
Answers
Answer: B
Step-by-step explanation:
There is a hole at x=2, so the numerator and denominator should both have a factor of x-2.
This eliminates everything except for B.
Please help asap!!!!!!!!!!!!
Answers
Answer:
95
Step-by-step explanation:
We know the measure of angle 4 is 85, therefore the measure of angle 2 is also 85.
Measure 2 is equal to measure 6, therefore measure 6 also equals 85, measure 8 equals measure 6 giving it the measure of 85.
Now the sum of angles 5 and 7 must equal 190, given we have two 85 degree angles, and the other two are equal, they must sum to 190, since they are equal we will divide 190 into 2, making angles 5 and 7 have a measure of 95.
Answer: 95°
Step-by-step explanation: With 2 parallel lines cut by a transversal, the following conditions are true.
Alternate interior angles are congruent. <4 and <6 are alternate interior angles, and so are <3 and <5.
Corresponding angles are congruent. Corresponding angles are angles that are in the same position in one line as the other. <1 and <5 are corresponding angles, and <4 and <6 are congruent. <2 and <6 are congruent, and <3 and <7 are congruent.
Vertical angles are congruent. Angles that are directly diagonal on the same line are congruent. <5 and <7, and <6 and <8 are examples of this.
Supplementary angles are, well, supplementary. By definition, two angles that are supplementary add up to 180°. Supplementary angles are angles that are on the same line and transversal, but not vertical angles. Rather, the angles are right next to teach other.
Alternate exterior angles are congruent. Alternate exterior angles are angles that are like alternate interior angles, but both share a position on the outside (and are diagonal.) The alternate exterior angles are <2 and <8, and <1 and <7.
Now that we have all definitions and conditions at hand, this will be easy.
If m<4 is 85°, and we want m<5, then we can see that <4 and <3 are supplementary angles. So by definition, <4 + <3 = 180°. We can substitute in <4 since we know it. We get 85° + <3 = 180°. Subtracting 85° from both sides, we get <3 = 95°.
Now we see <3 and <5 are alternate interior angles. By definition they are congruent. Thus, m<5 is 95° too.
Hope this helped!
(If my post was helpful, please mark it as Brainliest.)
A rectangle is 2 feet long and
x+10) feet wide. What is the area?
A. (2x + 10) ft²
C. (22x) ft²
B. (2x + 20) ft²
D. (20x) ft²
Answers
Answer:
(2x + 20) ft^2.
Step-by-step explanation:
Area = length * width
= 2 * (x + 10)
= (2x + 20) ft^2.
At a charity fundraiser, each female attendant donated $1,200 and each male attendant donated $800. If the average donation at the fundraiser was $900, what was the ratio of the number of female attendants to the number of male attendants.
Answers
Using the mean concept, the ratio of the number of female attendants to the number of male attendants was of 3.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem:
There were f + m donations.The sum was of 1200f + 800m.The average was of 900.Hence:
[tex]\frac{1200f + 800m}{f + m} = 900[/tex]
1200f + 800m = 900f + 900m
100m = 300f
[tex]\frac{f}{m} = 3[/tex]
Hence the ratio was of 3.
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Construct the indicated confidence interval for the population mean mu.
Answers
Using the z-distribution, the confidence interval is given by: (11.95, 12.65).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The other parameters are given as follows:
[tex]\overline{x} = 12.3, \sigma = 1.5, n = 50[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95[/tex]
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65[/tex]
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what is the
area of
Rectangle with the length 3 XY
and width
14X2y
Answers
Answer: [tex]42x^3 y^2[/tex]
Step-by-step explanation:
[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]
Can someone do this please?
Answers
Answer:
<1 =73
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
72+ 35 + <1 = 180
Add like terms
107 + <1 = 180
Subtract 107 from each side
<1 = 180-107
<1 =73
To prove ABC is isosceles, which of the following
statements can be used in the proof?
Answers
Answer:
Angle CAB and angle CBA are congruent.
Step-by-step explanation:
Isosceles triangles have two sides of equal length as well as two congruent base angles.
Answer:
b
Step-by-step explanation:
Find the cube of (x-1/3x)
Answers
Answer:
2/3x
Step-by-step explanation
Answer:
(x³-3x²-3x-1) / (27x³)
Step-by-step explanation:
((x-1) / (3x))³
= (x-1)³ / /3x)³
(x-1)³ = (x-1)(x-1)(x-1) = x³ - 3x² - 3x - 1
then:
(x-1)³ / (3x³) = (x³-3x²-3x-1) / (27x³)
The number of bacteria in a certain population increases according to a continuous exponential growth model with a growth rate parameter of 4.9% per hour how many hours does it take for the size of the sample to double
Answers
Answer:
14.5 hours to the nearest tenth.
Step-by-step explanation:
4.9% = 0.049.
If the original number is 50 it will double to 100 so
100 = 50(1.049)^t
1.049^t = 2
t * log 1.049 = log 2
t = log 2 / log 1.049
= 14.49 hours,
verify commutative property of multiplication and addition 5 4
- -
2 5
then what will the answer of this with prof and detaling
Answers
The commutative property of multiplication addition is illustrated below.
How to illustrate the information?The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.
In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.
Likewise 2 + 5 as 5 + 2 gives 7.
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A sample of bacteria is growing at an hourly rate of 15% according to the continuous exponential growth function. The sample began with 11 bacteria. How many bacteria will be in the sample after 21 hours
Answers
If the sample of bacteria is growing at an hourly rate of 15% continuously and the bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.
Given growth of bacteria 15% ,bacteria at beginning 11.
We have to find the number of sample of bacteria after 21 hours.
We have to first form exponential function which shows the growth of bacteria in variable t.
Exponential function which shows the sum is y=P[tex]e^{rt}[/tex]
where P is initial amount ,
r is rate and
y is the sum
So in our problem P=11 and r=0.15
y=11*[tex]e^{0.15t}[/tex]
To find the samples after 21 hours we have to put t=21.
y=11[tex]e^{0.15*21}[/tex]
y=11*[tex]e^{3.1}[/tex]
y=11*22.198 ([tex]e^{3.1}[/tex]=22.198 from e table)
y=244.178
Hence the samples after 21 hours will be 244 approximately.
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x = 8, y = 11
The variables x and y vary inversely. Use the given values to write an equation relating x and y . Then find y when x=2.
Answers
[tex]y = \frac{1}{mx} [/tex]
[tex]11 = \frac{1}{8m} [/tex]
[tex]m = \frac{1}{88} [/tex]
[tex]y = \frac{1}{ \frac{1}{88}x } = \frac{88}{x} [/tex]
[tex]when \: x = 2 \\ y = \frac{88}{2} = 44[/tex]
If p= the motorcycle's original price in dollars, which algebraic expression
represents the reduced price?
A. 275-p
B. 275p
C. 275+ p
D. p - 275
Answers
Answer: D
Step-by-step explanation:
If the original price was p, a price reduction would be p- the amount. Per the given answers, $275 is used for the reduction amount.
The graph of y = f(x) is graphed below. Wat is the end behavior of f(x)?
PLEASE ASAP
Answers
Answer:
B.) as x --> -∞, f(x) --> ∞ and x --> ∞, f(x) --> ∞
Step-by-step explanation:
F(x) is another way of representing "y". That being said, the question is asking you the behavior of the graph in terms of the y-axis. On both sides of the function, there is an arrow pointing upwards, towards infinite, positive y-values. Therefore, as "x" approaches -∞ and ∞, f(x) is approaching ∞ (positive infinity).
Geometric Series
It has 6 terms, increases by a factor of 4, and has a sum of 1365. Find the value of the first term.
Answers
Since the geometric series has 6 terms, increases by a factor of 4, and has a sum of 1365, the value of the first term is 1.
What is the sum of a geometric series?The sum of a geometric series is given by
Sₙ = a(rⁿ - 1)/(r - 1) with r > 1 where
n = number of terms, a = first term and r = common ratioNow, since our Geometric Series has 6 terms, n = 6. Also, it increases by a factor of 4, so, r = 4 and has a sum of 1365, so Sₙ = 1356. So,we have that
n = 6, Sₙ = S₆ = 1365 andr = 4The value of the first termSince we require the first term, a , making a subject of the formula, we have
a = Sₙ(r - 1)/(rⁿ - 1)
Substituting the values of the variables into the equation, we have
a = Sₙ(r - 1)/(rⁿ - 1)
a = S₆(r - 1)/(r⁶ - 1)
a = 1365(4 - 1)/(4⁶ - 1)
a = 1365(3)/(4096 - 1)
a = 4095/4095
a = 1
So, the value of the first term is 1.
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Cody Ray's credit card company uses the unpaid-balance method and charges a monthly periodic rate of
1.8%. His finance charge was $17.54, he made $376.90 in new charges and a $250 payment.
Answers
Based on Cody Ray's credit card details and the unpaid-balance method, Cody Ray's unpaid balance is $144.44 and his previous balance is $144.44. His new balance is $147.04
What are Cody Ray's balances?His unpaid balance is:
= Purchases + Finance charge - (Payments + Credit)
= 376.90 + 17.54 - 250
= $144.44
Previous balance is the $17.54 finance charges.
New balance:
= Unpaid balance + Finance charge + New Purchases
= 144.44 + (144.44 x 1.8%)
= $147.04
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Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
The square root of the quantity 3 x plus 12 end quantity equals 9.
Answers
The value of x from the given expression is 23
Radical equationsGiven the following equation
√3x+12 = 9
Square both sides
√3x+12)² = 9²
3x + 12. = 81
Subtract 12 from both sides
3x + 12 - 12 = 81- 12
3x = 69
x = 23
Hence the value of x from the given expression is 23
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pls look at pic!!!!!!!!!!!!
Answers
Answer:
I don't think the answer is in the options.
Some bacteria double in every hour. if there were 2 bacteria in the beginning, how many bacteria will be there after 6 hours? how many bacteria will be there after 24 hours?\
Answers
Answer:
64
Step-by-step explanation:
if there 2 to begin with and the bacteria dobles every hour and there were 6 hours it would be 2⁶ and when you time 2 to the power of 6 you get 64
Write Your recurrring decimal 0.255555...... as a fraction
Answers
Answer:
[tex]\frac{23}{90}[/tex]
Step-by-step explanation:
we require 2 equations with the recurring digit placed after the decimal point.
let x = 0.2555.. ( multiply both sides by 10 and 100 )
10x = 2.555... (1)
100x = 25.555.... (2)
subtract (1) from (2) thus eliminating the recurring digits
90x = 23 ( divide both sides by 90 )
x = [tex]\frac{23}{90}[/tex]
Answer:
[tex]\sf \dfrac{23}{90}[/tex]
Step-by-step explanation:
x = 0.25555..... --------------(I)
Number of non-recurring digits is 1. So, multiply equation (I) by 10.
10x = 2.5555.... --------------(II)
Number of recurring digits is 1. So, multiply equation (II) by 10.
100x = 25.5555...... (III)
Subtract equation (II) from (III)
100x = 25.5555........
10x = 2.5555.......
- -
90x = 23
x = 23/90
WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answers
Answer:
B
Step-by-step explanation:
Let t and d be their ages now.
2 years ago, their ages were t - 2 and d 2.
Now, Tyler is 3 years older than David: t = d + 3
2 years ago, Tyler was 4 times as old as David: t - 2 = 4(d - 2)
The system of equations is:
t = d + 3
t - 2 = 4(d - 2)
Answer: B
Answer:
D
Step-by-step explanation:
4/5 = ? x 1/5 i need this for khanacademy pls
Answers
Answer:
? = 4
Step-by-step explanation:
4/5 = 4/1 x 1/5
4/5 = 4/5
Can someone help me with these two problems and show work please !!
Answers
I give u the answers of first and second one.
thank you
brainlist please
Answer:
First answer is 9 or 1 . Second answer is 7 or -7.
Step-by-step explanation:
[tex](x-5)^{2} =16[/tex]
[tex]x-5 = 4[/tex] or [tex]x - 5 =-4[/tex]
so [tex]x = 9[/tex] or [tex]x = 1[/tex]
[tex]2x^{2} = 98[/tex]
[tex]x^{2} =49[/tex]
[tex]x=7[/tex] or [tex]x = -7[/tex]
Which of the following is the graph of f(x) = x2 − 5x + 4? WILL MARK BRAINLIEST
A graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5
B graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
Answers
C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4
Step-by-step explanation:Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0
Given function: x² - 5x + 4
⇒ a = 1, b = -5, c = 4
The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.
The vertex or minimum.
Step 1: Find the x-value of the vertex.
[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]
Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.
[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]
Vertex: (2.5, -2.25)
The x-intercepts (roots).
We can use the Quadratic Formula to find the roots of this function.
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]
Equation: x² - 5x + 4 = 0
⇒ a = 1, b = -5, c = 4
Step 1: Substitute the values of a, b, and c into the formula.
[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]
Step 2: Separate into two possible cases.
[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]
The x-intercepts of the given function are 1 and 4.
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