The sum represented by the notation [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex] is 32
How to determine the sum represented by the notation
From the question, we have the following parameters that can be used in our computation:
[tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]
This means that we determine the value of the expression from i = 3 to i = 9 and then add them up
So, we have
2(3) - 9 = -3
2(4) - 9 = -1
2(5) - 9 = 1
2(6) - 9 = 3
2(7) - 9 = 5
2(8) - 9 = 7
2(9) - 9 = 9
2(10) - 9 = 11
Evaluate the sum
Sum = -3 - 1 + 1 + 3 + 5 + 7 + 9 + 11
Sum = 32
Hence, the sum represented by the notation is 32
Question
Find the sum of [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]
What is the supplement of a 47 angle?
Answer:
133° angle
Step-by-step explanation:
Note that "supplement" means 180°.
To find the supplement of the angle given (47°), subtract the given measurement with the total supplementary measurement.
180 - 47 = 133
The supplement of a 47° angle is 133°.
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Blue's Berry Farm charges Percy a total of $24.75 for entrance and 2.5 kilograms of strawberries. The entrance fee is $6, and the price for each kilogram of strawberries is constant. The total cost C for picking strawberries is a function of x, the kilograms of strawberries picked. Write the functions formula. C=
Answer:
C = 6 + 7.5 x
Step-by-step explanation:
Given,
The amount is $24.75 for entrance and 2.5 kilograms of strawberries.
⇒ Entrance fee + 2.5 kilograms of strawberries = $24.75
Since, Entrance fee = $ 6,
And, the price for each kilogram of strawberries is constant.
⇒ $ 6 + 2.5 × 1 kilograms of strawberries = $24.75
⇒ 2.5 × 1 kilograms of strawberries = 18.75
⇒ 1 kilograms of strawberries = $ 7.5.
Thus, the cost of x strawberries = 7.5 x
Also, the total charge for x strawberries = Entrance fee + the cost of x strawberries
= 6 + 7.5 x
⇒ C = 6 + 7.5 x
Which is the required function formula.
What is the range of AB?
a, b, c - sides of a triangle
Therefore:
a + b > c
a + c > b
b + c > a
---------------------------------
We have a = AB, b = 140mi, c = 100mi.
(1) a + b > c
AB + 140 > 100 subtract 140 from both sides
AB > -40 → AB > 0
----------
(2) a + c > b
AB + 100 > 140 subtract 100 from both sides
AB > 40
-----------
(3) b + c > a → a < b + c
AB < 140 + 100
AB < 240
Answer: 40 < AB < 240Year 1 number sold 725
Year 2 number sold 579
Year 3 number sold in year 4 the store sold 112% of the total number of scooters sold during the previous three years combined determine the number of scooter sold in year 4
Answer:
2, 240
Step-by-step explanation:
In the table, the values should be
Year 1 725
Year 2 579
Year 3 696
Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.
[tex]\frac{112}{100} =\frac{x}{2000}[/tex]
We solve through cross multiplication of numerator and denominator of the opposite fraction.
[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]
What is the equation in slope intercept form of the line that is perpendicular to the given line and passes through the point (-4,-3)
Answer:
b no is the right answer i think
if an equilateral triangle has an angle of 3 X what is the value of X
Answer:
x = 20
Step-by-step explanation:
In an equilateral triangle, everything is the same; line length and angles. Each angle in an equilateral triangle is:
180 ÷ 3 = 60
So 3x = 60
Divide both sides by 3 to get x:
x = 20
after 8% discount from the list price, the sale price price of a poster was $17.48. what was the list price of poster.
Final answer:
To find the list price of the poster after an 8% discount, subtract 8% of the list price from the list price and set it equal to the sale price.
Explanation:
To find the list price of the poster, we need to first calculate the original price before the discount. Let's assume the list price is 'x' dollars. After an 8% discount, the sale price of the poster is $17.48.
We can set up an equation to solve for the list price: x - 8% of x = $17.48. To calculate 8% of x, we multiply x by 0.08.
So the equation becomes: x - 0.08x = $17.48. Combining like terms, we get 0.92x = $17.48. Dividing both sides by 0.92, we find that x = $19.
54d.
Change the following expression into a single fraction:
5b − 2/b
Which graph shows the solution set for 4x+3>-9
[tex]4x+3>-9\qquad\text{subtract 3 from both sides}\\\\4x>-12\qquad\text{divide both sides by 4}\\\\\boxed{x>-3}[/tex]
Triangle CDE and triangle CFG are similar right triangles. Which proportion can be used to show that the slope of CE is equal to the slope of CG?
A) 2 − 3
2 − 0
= 3 − 1
4 −0
B) 3 − 2
2 − 0
= 3 − 1
4 − 0
C) 2 − 3
0 − 2
= 3 − 1
0 − 4
D) 3 − 2
0 − 2
= 3 − 1
0 − 4
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points E(2, 2), C(0, 3) and G(4, 1), C(0, 3).
Substitute:
[tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}\to\boxed{D}[/tex]
Answer: The correct option is (D) [tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Step-by-step explanation: Given that ΔCDE and ΔCFG are similar right triangles.
We are to select the correct proportion that can be used to show that the slope of CE is equal to the slope of CG.
We know that the slope of a line passing through two points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
From the given figure, we note that the co-ordinates of the points C, E and G are
C(0, 3), E(2, 2) and G(4, 1).
So, the slope of line CE is given by
[tex]m_1=\dfrac{2-3}{2-0},[/tex]
and the slope of line CG is given by
[tex]m_2=\dfrac{1-3}{4-0}.[/tex]
Since the lines CE and CG are same, they must be parallel and hence they have equal slopes.
Therefore,
[tex]m_1=m_2\\\\\\\Rightarrow\dfrac{2-3}{2-0}=\dfrac{1-3}{4-0}\\\\\\\Rightarrow \dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Thus, (D) is the correct option.
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
The expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
1. Calculate the sale price after the markdown:
Original price: x dollars
Markdown rate: 20%
Sale price after markdown: x * (1 - 0.20) = 0.8x dollars
2. Calculate the amount of sales tax:
Sales tax rate: 6%
Sales tax amount: 0.06 * 0.8x = 0.048x dollars
3. Calculate the correct total sale price:
Sale price after markdown + Sales tax amount = 0.8x + 0.048x = 0.848x dollars
4. Analyze the given expressions:
x * (1 - 0.20) + 0.06x: This expression correctly calculates the discount and adds the sales tax to the original price, so it represents the total sale price.
x * (1 - 0.20) + 0.06 * 0.8x: This expression also correctly calculates the discount and adds the sales tax to the discounted price, so it represents the total sale price.
x * (1 - 0.20 + 0.06): This expression combines the discount and sales tax into a single percentage (14%), but it applies this percentage to the original price (x) instead of the discounted price (0.8x). This leads to an overestimation of the final sale price, so it does not represent the correct total price.
0.8x + 0.048x: This expression correctly calculates the sum of the discounted price and the sales tax amount, so it represents the total sale price.
Therefore, the expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
Complete question:
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
x * (1 - 0.20) + 0.06x
x * (1 - 0.20) + 0.06 * 0.8x
x * (1 - 0.20 + 0.06)
0.8x + 0.048x
twice the difference of a number and 6 equals 8
translate sentence into equation
Answer:
2*(n-6) = 8
Step-by-step explanation:
Twice the difference of a number and 6 equals 8
Equals means =
Difference means subtract
2*(n-6) = 8
I spent 3/4 of my money and then I spent 1/5 of what was left.
a) What part of all my money did I spend?
b) What part of all my money do I have left?
Answers:
a) 4/5
b) 1/5
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Let's say you start off with $100. If you spend 3/4 of that, then you spend 75 dollars (because 75/100 = 3/4). Think of it like 75 cents = 3 quarters. If you spend 75 dollars out of 100 total, then you have 100-75 = 25 dollars left after the first round of spending.
If you spend 1/5th of what is left, then you spend $5 on the second round leaving 25-5 = 20 dollars left at the end of the day.
Total up what you spend for both rounds: 75+5 = 80, which divides over the original amount 100 to get 80/100 = 8/10 = 4/5
If you had 20 dollars at he end of the day, out of 100 initially, then 20/100 = 2/10 = 1/5 is the fraction of what you have left.
note how 4/5 and 1/5 add to 5/5 = 1.00 = 100%. This is because the amount you spend and the amount you have left over must add to 100% of all the money you started with
Brainliest + Points!
Please show work!
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Assuming it hits the target, what is the probability that a dart will land in the red region?
A.
0.25
B.
0.33
C.
0.67
D.
0.75
Answer:
C
Step-by-step explanation:
The target area is shown in the attached picture.
We want to figure out probability of hitting red region.
The area of the figure is the area of the red square, which is 196.
Area of red region is area of whole square (196) minus area of blue square (64). So we have:
Area of red region = 196 - 64 = 132
Probability of hitting red region is 132 divided by total, which is 196.
[tex]\frac{132}{196}=0.67[/tex]
Answer choice C is right.
Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?
graph of line going through 1, 2 and 3, 4
graph of line going through 1, 1 and 3, 3
graph of line going through 1, 4 and 3, 10
graph of line going through 1, 2 and 2, 5
The graph that represents Margo's coin collection is:
Graph of line going through (1, 4) and (3, 10).
Step-by-step explanation:It is given that:
She was given 1 coin as a gift, and she adds 3 coins per year.
Let a_n denote the amount of Money Margo had in the end of the "nth" year.
According to the given information we have:
[tex]a_1=1+3=4[/tex]
[tex]a_2=4+3=7\\\\a_2=a_1+3[/tex]
[tex]a_3=10\\\\a_3=a_2+3\\\\\\a_3=a_1+3\times 2[/tex]
and so on.
Hence, we get:
[tex]a_n=a_1+3(n-1)[/tex]
Hence, we get a Arithmetic progression.
with first term as 4 and common difference as 3.
Hence, the graph is:
Graph of line going through (1, 4) and (3, 10).
( Since at n=1 we have: [tex]a_n=4[/tex]
and at n=3 we have: [tex]a_3=10[/tex] )
can some one explain how to do these problems
Answer:
the slope is 0.
Step-by-step explanation:
You can use the slope equation
[tex]\frac{y-y}{x-x}[/tex]
and plug in your points
[tex]\frac{10-10}{4-1}[/tex]
[tex]\frac{0}{3}[/tex]
slope = 0
A line has a slope of -1/2 and a y-intercept of –2.
What is the x-intercept of the line?
a.–4
b.–1
c.1
d.4
Answer:
a.-4
Step-by-step explanation:
I pictured it as a graph and since the slope is negative, the line goes down and to the right. Since the slope is -1/2, for every 2 you move horizontally, you move one vertically. You have to move two up and unless the y intercept is 0, when the line intercepts y, you have 0 as x. You move two up and 4 backwards so the x intercept is -4
Given 4x =
a + b/8c
, rearrange the equation for a, in terms of b, c, and x
To rearrange the equation for a, subtract b/8c from both sides: a = 4x - b/8c.
Explanation:To rearrange the equation for a, we start with the given equation 4x = a + b/8c. First, we isolate a by subtracting b/8c from both sides, giving 4x - b/8c = a. Therefore, the equation for a in terms of b, c, and x is a = 4x - b/8c.
Order the numbers 0.64,
2/3 , 65%, and
7/10 from least to greatest. (3 points)
Answer:
.64 < 65 % < 2/3 < 7/10
Step-by-step explanation:
To order all the numbers from least to greatest, but all the numbers in the same form (fraction, decimal, or percent). I will put them all in decimal form so that I can compare them.
0.64, .64
2/3 , =.666666repeating
65% = 65/100 = .65
7/10 = .7
.64< .65<.6666repeating<.7
but we need to put them in their original form
.64 < 65 % < 2/3 < 7/10
A 63 kg object needs to be lifted 7 meters in a matter of 5 seconds. Approximately how much horsepower is required to achieve this task?
A. 1.16 hp
B. 864.36 hp
C. 441 hp
D. 0.59 hp
Answer:
1.16 horse power. Option A.
Step-by-step explanation:
Work done = m g h = 63 * 9.81 * 7 = 4326.21 joules
Power = 4326.21 / 5 = 865.24 Watts
1 Horse power = 746 watts so the answer is 865.24 / 746 = 1.16 HP to nearest hundredth.
Answer:
1.16 hp
Step-by-step explanation:
how would you graph the following systems of equations ?
y= -3x -7
x- 2y=-14
Which tool(s) are needed to construct a perpendicular bisector of a line segment?
Answer: compass and straightedge or ruler
Perpendicular bisector of a line segment
Geometry construction using a compass and straightedge
compass and straightedge or ruler
Step-by-step explanation:
Answer:
You need a straight edge and a compass.
Step-by-step explanation:
The straight edge should not be marked in any way. You are not allowed to put a mark on the straight edge at all. The only property it has is that it has no curvature in any direction.
The compass must be flexible and at the same time it must be able to stay at one radius unless changed by the owner. It's only property is that it can draw a perfect circle once the radius of the circle has been chosen,
Debbie cut cord to sixths she is five of the pieces to make necklaces she used equal length of the remaining cord for each of four bracelets what fraction of the original cord did Debbie use for each bracelet
Answer:
¹/₂₄
Step-by-step explanation:
Debbie used ⅚ of the cord for necklaces.
That left ⅙ of the cord for four bracelets.
Each bracelet used:
Fraction of cord = ⅙ ×¼ = ¹/₂₄
Debbie used ¹/₂₄ of the cord for each bracelet.
I need help with this question show steps! Quickly please!
Answer:
y+9 =-5(x-2) point slope form
y = -5x-1 slope intercept form
Step-by-step explanation:
If we have a slope and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y--9 = -5(x-2)
y+9 =-5(x-2)
If you want to write it in slope intercept form, distribute the -5
y+9 = -5x+10
Subtract 9 from each side
y+9-9 = -5x+10-9
y = -5x-1
Larue score 10 points less than three times the number of points that Ross scored Livia scored 11 points how many points did Ross score?
what is a equivalent expression for 2(c+c+c)
Answer: 2(C^3) or 2(C to the third power)
Step-by-step explanation: C^3 is the same thing a c+c+c
Hope this helps!
How do i graph the equation -x + 2y = 2
Step-by-step explanation:
Firstly, set the x value as 0:
-0 + 2y = 2
2y = 2
y = 1
So when x = 0, y = 1
Now set y to 0:
-x + 2(0) = 2
-x = 2
x = -2
So when y = 0, x = -2
Simply plot the two following points:
(0 , 1) and (-2 , 0)
And don't forget to join these two points up!
Attatched is an image of this graph.
Find the slope of the line that passes through the pair of points.
(-40.86,5.6) and (0.86,4.2)
simplify
Answer:
-.033557047
Step-by-step explanation:
Slope = (y2-y1)/ (x2-x1)
= (4.2 - 5.6)/(.86- 40.86)
= -1.4/ (.86 + 40.86)
= -1.4/41.72
-.033557047
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-40.86, 5.6) and (0.86, 4.2). Substitute:
[tex]m=\dfrac{4.2-5.6}{0.86-(-40.86)}=\dfrac{-1.4}{0.86+40.86}=-\dfrac{1.4}{41.72}=-\dfrac{140}{4172}\\\\=-\dfrac{140:4}{4172:4}=-\dfrac{35}{1043}=-\dfrac{35:7}{1043:7}=-\dfrac{5}{149}[/tex]
Answer: The slope = - 5/149Which expression is equivalent to (5 × 6)×(3 × 2)?
A) (5 + 6) + (3 + 2)
B) (5 + 6)×(3 + 2)
C) (5 × 6) + (3 × 2)
D) (3 × 2)×(5 × 6)
Answer:
The original equation contains 3 multiplications.
When multiplying numbers, the order that they are in doesn't matter so 3 *2 is the same as 2 * 3.
This would make D, the same.
D) (3 × 2)×(5 × 6)
HELPP!!!
Find m angle 1 and m angle 3 in the kite.
Answers:
Angle 1 is 40 degrees
Angle 2 is 90 degrees
Angle 3 is 50 degrees
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Explanations:
Triangle ABC is a reflection of triangle ADC over the line AC. Doing this reflection forms the kite ABCD. Or you can think of it as gluing two congruent triangles together (ABC and ADC). We can prove the two triangles ABC and ADC congruent by the SSS congruence property. Then we use CPCTC (corresponding parts of congruent triangles are congruent) to prove that angle 1 is 40.
Let E be the intersection of the two diagonals. Through similar reasoning as earlier, we can prove that triangle AEB is congruent to triangle AED, so that leads to angle 2 being 90 degrees because this angle adds to its counterpart to get 180. Both unknown angles are x each meaning x+x = 180 leads to x = 90. One property of kites is that the diagonals are perpendicular.
Triangle AED is a right triangle as discussed above. Therefore, the angle 3 and the 40 degree angle are complementary. If angle 3 is y, then y+40 = 90 giving y = 90-40 = 50, which is why angle 3 is 50 degrees.
Using angle theorems, the value of the angles m1 and m3 are 40° and 50° respectively.
Taking the midpoint of DB as O ;
Angle OAD and Angle OAB are equal
OAD = 40° ; OAB = 40°
A right angle is formed at O ;
Hence,
(O + D + A) = 180°
90° + D + 40° = 180° (Sum of interior angles of a triangle)
D = 180 - 130
D = 50°
Hence, m∠3 = 50°.
Therefore, the value of the angles m1 and m3 are 40° and 50° respectively.