Answers
Answer:
[tex]\sum_{i=1}^{12}(3i-1) = 222[/tex]
Step-by-step explanation:
The given series is
[tex]\sum_{i=1}^{12}(3i-1)[/tex]
The first term is
[tex]f(1) = 3 \times 1 - 1 = 2[/tex]
The last term is
[tex]f(12) = 3 \times 12 - 1 = 35[/tex]
To find the number of terms in the sequence, solve,
[tex]3i - 1 = 35[/tex]
[tex]3i = 36 \\ i = 12[/tex]
The sum of the first i-terms of an arithmetic sequence is:
[tex]S_i = \frac{i}{2} (f(1) + f(2))[/tex]
We substitute the values to get;
[tex]S_ {12}= \frac{12}{2} (2+ 35)[/tex]
[tex]S_ {12}=6(37)[/tex]
[tex]S_ {12}= 222[/tex]
Related Questions
INCOME; you earn a weekly salary of $200 plus a 3% commission on the total value of the sales made in the week. This week, your sales total $2000. What are your total earnings for the week?
#1 identify the percent, bass, and part of the base in the question
Answers
Answer:
Your total earning for the week is $260
Step-by-step explanation:
You earn a salary of $200 weekly, which is constant. Then there is 3% commission on sales you make weekly too.
So it you make $2000, your commission is
3/100 × 2000 = $60
So your total earning for the week is constant income (salary) + commission, which is
$200 +$60 = $260
Explanation of identifying the percentage, base, and part of the base in an income scenario.
The total earning is $ 200 + 3% of $2000
= $ 200 + 60 = $260
The question: Identify the percentage, base, and part of the base in the given scenario.
Percentage: 3%
Base: Total sales made in the week, which is $2000
Part of the base: The commission earned, which is 3% of $2000
15. Your friend paid $17 for a shirt. This amount was 85% of the total amount
your friend spent at the clothing store. How much money did your friend
spend?
Answers
To find out how much money your friend spent at the clothing store, set up a proportion using the information given. Your friend spent $20 at the clothing store.
Explanation:To find out how much money your friend spent at the clothing store, we can set up a proportion using the information given. Let's let x represent the total amount your friend spent.
Since your friend paid $17 for a shirt, and that amount was 85% of the total amount spent, we can set up the equation:
17/x = 85/100
Cross multiplying, we get:
100 * 17 = 85 * x
1700 = 85x
To solve for x, we divide both sides of the equation by 85:
x = 1700 / 85 = 20
Therefore, your friend spent $20 at the clothing store.
Wat does f(x)=x^2+x-30 solve to?
Answers
Answer:
F(X) = 5 or -6
Step-by-step explanation:
F(X) = [tex]x^{2} +x-30[/tex]
Using the Formula
[tex]-b[/tex]±[tex]\frac{\sqrt{b^{2} -4ac } }{2a}[/tex]
Where a = coefficient of [tex]x^{2}[/tex] i. e 1
b = coefficient of [tex]x[/tex] i. e 1
And c = 30
imputing the values, we have
[tex]-1[/tex] ± [tex]\frac{\sqrt{1^{2} - 4 X 1 X 30} }{2 X 1}[/tex]
[tex]-1[/tex] ± [tex]\frac{\sqrt{121} }{2}[/tex]
[tex]-1+\frac{11}{2}[/tex] OR [tex]-1-\frac{11}{2}[/tex]
Therefore, F(X) is either 5 or -6
Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
A) y= -8/5 x - 3
B) y= -8/5x+3
C) 3x - 5y =0
D) 5x-3y=0
Answers
Answer:
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=\frac{-8}{5}x-3[/tex]
Step-by-step explanation:
Given the point (-5, 5)
slope = m = -8/5
Using the slope intercept form:
[tex]y=mx+b[/tex]
Plugging point (-5, 5) and slope = m = -8/5 in the slope intercept form to find the y-intercept 'b'.
[tex]5=\frac{-8}{5}\left(-5\right)+b[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]\frac{-8}{5}\left(-5\right)+b=5[/tex]
[tex]8+b=5[/tex]
[tex]8+b-8=5-8[/tex]
[tex]b=-3[/tex]
so the equation of the line will be:
[tex]y=mx+b[/tex]
plugging m = -8/5 and b = -3 in slope intercept form
[tex]y=\frac{-8}{5}x-3[/tex]
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=\frac{-8}{5}x-3[/tex]
in a triangle ABC, mA=45, mB 40, and a=7. which equation sould you solve to find B?
Answers
Answer:
[tex]\frac{sin(45^o)}{7}=\frac{sin(40^o)}{b}[/tex]
Step-by-step explanation:
The correct question is
In a triangle ABC, m∠A=45°, m∠B 40°, and a=7. which equation should you solve to find b?
we know that
Applying the law of sines
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}[/tex]
substitute the given values
[tex]\frac{sin(45^o)}{7}=\frac{sin(40^o)}{b}[/tex]
solve for b
[tex]b=(7)sin(40^o)/sin(45^o)[/tex]
[tex]b=6.4\ units[/tex]
Answer:
Sin45/7 = sin40/b
Step-by-step explanation:
:D
on monday,the price of one share of webb company stock was 24.85. by friday,the price was 25.004. by how much did the price changre from monday to friday
Answers
The price of one share of Webb Company stock increased by $0.154 from Monday to Friday.
Explanation:To calculate the change in the price of a share of stock from Monday to Friday, we subtract the price of the stock on Monday from the price of the stock on Friday. In this case, the price on Monday was $24.85 and the price on Friday was $25.004.
Change in stock price = Price on Friday - Price on Monday
Change in stock price = $25.004 - $24.85
Change in stock price = $0.154
Therefore, the price of one share of Webb Company stock changed by $0.154 from Monday to Friday.
francine makes a diagram of her bedroom 10feet 14feet how many square feet of carpeting does she need to cover the floor
Answers
Answer:
140 feet²
Step-by-step explanation:
10 × 14 = 140
Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago. If Jenna’s age is x, which equation represents the situation? How many solutions does the equation have?
Answers
Answer: equations 1,3,4 and 5 stated has solutions.
Step-by-step explanation:
From the question, (x + 5) + 5 = (x + 5) + 5
The equations that represent the situation are:
1. x + 5 = (5 − x) − 5 :which has one solution
2. x + 5 = (x + 5) − 5 : many solutions
3. x + 5 = (x + 5) − 5: no solution
4. x + 5 = (5 − x) − 5 : many solutions
5. (x + 5) + 5 = (x + 5) + 5: many solutions
Equation 2 has no solution. While the other equations have one and more than one solutions.
find the equivalent expression for:
3+2(2p+4t)
Answers
Answer:
Step-by-step explanation:
Given that
3+2(2p+4t)
Let open the bracket first
3+ 2×2p + 2×4t
3+4p+8t
This is the equivalent of the expression.
The equivalent expression for 3+2(2p+4t) is given by performing the operations according to the mathematical rules of order of operations. First, apply the distributive property to get 4p + 8t. Then, the expression become 3 + 4p + 8t.
Explanation:The student is looking to simplify and find the equivalent mathematical expression for: 3 + 2(2p + 4t).
First, you should apply the distributive property of operations, which means you multiply the number outside the parenthesis with each term inside the parenthesis. So, 2(2p + 4t) becomes 4p + 8t.
Next, add the 3 to the simplified expression 4p + 8t. The final equivalent expression will be 3 + 4p + 8t.
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I need help answering all of these. My teacher thinks that we should know this even though he hasn´t taught us any of this. please help?! thank you!
Answers
Answer:
Step-by-step explanation:
x/2=3.5
x=3.5*2
x=7
Evaluate the expression when y=5 and x=48. (X-6y)
Answers
Answer:
18
Step-by-step explanation:
x-6y
Let x = 48 and y=5
48 -6(5)
48 - 30
18
Here is a FDT for a small da
data freq
33
| 34 | 3
35 3
I 36 3
I 37 | 10
Find the following measures of central tendency.
mean =
median =
mode =
Answers
Answer:
(a) Mean = 36.05; (b) median = 37; (c) mode = 37
Step-by-step explanation:
I am assuming your DFT is like this:
[tex]\begin{array}{c|c}\textbf{n} & \textbf{Frequency} \\33 & 0 \\34 & 3 \\35 & 3 \\36 & 3 \\37 & 10 \\\end{array}[/tex]
(a) Mean
The mean is the sum of all the data points divided by the number of points. I have done some of the calculations for you in the table below
[tex]\begin{array}{cccc}\textbf{n} & \textbf{f} & \mathbf{n\cdot f} & \mathbf{cf}\\33 & 0 & 0 &0 \\34 & 3&102 &3 \\35 & 3& 105 & 6\\36 & 3 &108 & 9\\37& 10& 370 & 19\\\textbf{SUM} & \mathbf{19}&\mathbf{685} \\\end{array}[/tex]
[tex]\begin{array}{rcl}\text{Mean} & = & \dfrac{\sum n}{n}\\\\& = & \dfrac{685}{19}\\\\& = & \mathbf{36.05}\\\end{array}[/tex]
(b) Median
The median is the middle value in your list of observations.
Your data set contains 19 terms, so the middle is (19/2)th term.
Count down the column of cumulative frequency (cf) until cf = 9½.
The 9½th term is 37.
Median = 37
(c) Mode
The mode is the value that appears most often in your list of observations.
It is obvious from your table that the number that occurs most frequently is 37.
Mode = 37
The diagram below shows that the score of 37 is predominant.
The mean, median and mode are measures of central tendency in mathematics. They are found using a Frequency Distribution Table; calculate the mean by summing up the product of each data point and its frequency, then dividing by total frequency. The median is the middle number when data is in ascending order, and the mode is the number appearing most often.
Explanation:In mathematics, the measures of central tendency referenced in your question; mean, median, and mode, are used to describe a set of data. Given your Frequency Distribution Table (FDT), here's how you would calculate each:
Mean: The mean is the average. Sum up the product of each data point and its frequency and then divide by the total frequency. In this case, (33*3) + (34*3) + (35*3) + (36*3) + (37*10), and divide that sum by the total frequency, which is 22. Median: The median is the middle number when your data is listed in ascending order. If there is an even amount of numbers, the median will be the mean of the two middle numbers. In this case, the median is between the 11th and 12th data points, which falls in the '37' range. Mode: The mode is the most frequently occurring number in a data set. Here, the value '37' appears most frequently with 10 occurrences. Learn more about Measures of Central Tendency here:
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Charles opened a door hinged at O by an angle of 45 degrees. The width of the door was 80 centimeters. Find the area swept by the door. Leave your answer in terms of pie
Answers
Answer:
A=800πcm²
Step-by-step explanation:
Knowing that the area of a circular sector is:
[tex]A_{cs}=\frac{\pi\alpha r^{2}}{360}[/tex]
where α is the sweep angle and r in the radio (according to the graph),
then
A=(45° π 80²)/360° = 800πcm²
Final answer:
The area swept by the door is 10π cm and the area of the sector is 200π cm².
Explanation:
To find the area swept by the door, we can first find the length of the arc created by the door when it opens. The arc length formula is given by:
Arc length = r × θ
Where r is the radius (half the width of the door) and θ is the angle through which the door opens. In this case, the radius is 40 centimeters (half of 80 centimeters) and the angle is 45 degrees.
So, the arc length = 40 cm × (45 degrees) = 40π/4 cm = 10π cm
The swept area can be approximated by treating it as a sector of a circle with radius 40 cm and central angle 45 degrees. The area of the sector is given by:
Area = (θ/360) × π × r²
Where θ is the central angle and r is the radius. Substituting the values, we get:
Area = (45/360) × π × (40 cm)² = 1/8 × π × 1600 cm² = 200π cm²
which best describes the triangle or triangles, if any that can be formed with two sides that each measure 5 inches and an angle that measures 60 degrees?
Answers
Answer: D. one equilateral triangle
explanation: Means, triangle is equilateral. If angle between , two sides having measure 5 cm , is not 60 degree, then the triangle will be always Isosceles. we will sine rule to find remaining measurements. In this case,also ,triangle is equilateral
Answer: one equilateral triangle
Step-by-step explanation:
The sum of a number x and 5 equals 14
Answers
Answer:
x = 9
Step-by-step explanation:
you subtract 5 from 14 to get x alone with 9
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of the number x is 9.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The sum of a number x and 5 equals 14.
This can be written as,
x + 5 = 14
Subtract 5 on both sides.
x = 14 - 5
x = 9
Thus,
The value of the number x is 9.
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how far will i travel if i am driving @75kmh for 18 mins. can the distance over speed applies?
thanks!
Answers
Answer:
22.5 km
Step-by-step explanation:
Speed = distance/time
Given speed = 75km/h
time = 18 mins
Distance = ?
Given the speed is in km/h , convert the time from minutes to hour .
18/60 = 0.3 hours
Therefore,
75 = distance/0.3
Cross multiply
75 x 0.3 = distance
22.5 = distance
Distance = 22.5 km
Plzzz help me I don’t understand aTT ALL if I don’t do it I’ll get a 0 in my report card plz help
Answers
Answer:
hi there! i can help you out! i don't want you to get a zero on your report card!!
Step-by-step explanation:
so, on the x-axis, which is all the numbers through 1-10 and there are the patient's number. so for ex, the first question says patient 1 : 3 hours right??
so the hours are the y-axis and you can label them 2,4,6,8 because skip counting by twos are probably the easiest! so for the first question, you would line a dot up on top of 1 and go up and you see 2 and 4 right, cuz you just labeled it... do go between 2 and 4 which is 3 and place the dot there...
and keep doing the same things with other ones too...
another ex! so on the second question, it says patient 2 : 7 hours so place the dot on top of the 2 and go up untill you see 6 and 8 and place the dot beween them!
Sorry but I forgot about Mean Median And Mode! Sorry I would hate to see you get a zero!
A football team scores 6 points for each touchdown scored. Which graph represents this situation?
24ty
Points
Points
Points
Touchdowns
Touchdowns
Touchdowns
Answers
Answer:
Step-by-step explanation:
how many touch downs did the team get?
A bar graph represents the points scored by a football team for each touchdown scored.
Explanation:The graph that represents this situation is a bar graph. The x-axis represents the number of touchdowns scored and the y-axis represents the number of points scored. Each bar on the graph represents a different number of touchdowns scored, and the height of the bar represents the number of points scored for that number of touchdowns. For example, if the team scores 2 touchdowns, the corresponding bar on the graph would have a height of 12 (2 touchdowns * 6 points per touchdown).
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What is the measure of arc EG?
Answers
The measure of arc EG = 16°.
Solution:
Given data:
m∠X = 47° and m(ar FH = 110°)
To find the measure of arc EG:
We know that,
Angle formed by two intersecting secants outside the circle is equal to half of the difference between the intercepted arcs.
[tex]$m \angle X=\frac{1}{2}({arc} \ FH-{arc} \ EG)[/tex]
[tex]$47^{\circ}=\frac{1}{2}\left(110^\circ- {arc} \ EG}\right)[/tex]
Multiply by 2 on both sides.
94° = 110° - arc EG
Subtract 110° from both sides.
-16° = -arc EG
Multiply -1 on both sides, we get
16° = arc EG
Switch the sides.
arc EG = 16°
The measure of arc EG = 16°.
Graph this line using the slope and y-intercept Y=1/2x+9
Answers
Answer:
Step-by-step explanation:
I don't have a picture so I'll visually describe it. You start at the point (0,9) because 9 is the y intercept. Now that you have your first point, to get the next point, move up one and 2 to the right. Now, you're at the point (2,10). Continue going up one and 2 to the right until you get to the end of the graph. Then, go back to the point (0,9). This time, go the opposite way. Go one down, and two to the left. Now, you should be at the point (-2,8). Continue going down one, two left until once again, you run out of room on the graph. Then, use a ruler or freehand draw a line connecting your points. Add arrows on the ends on the line. Hope this helped!
What is P (beaver)?
If necessary, round your answer to 2 decimal places
Answers
Answer:
Step-by-step explanation:
14/8
In the diagram below, lines l and p intersect. If the measure of is , what is the measure of
A. 109
B100
C.71
D.19
Answers
Answer: its c
Step-by-step explanation:
Identify the like terms.
-4a, -3b, 4b, 3
A -4a and 4b
B -3b and 3
C -3b and 4b
D -4a and -3b
Answers
Answer:
C
Step-by-step explanation:
Answer:c
Step-by-step explanation:
what’s the fifth square root of 256
Answers
Answer:
3.03143313302
Step-by-step explanation:
Answer:
3.03143313
Step-by-step explanation:
Joanne made 16 fruit bars in a square pan. The fruit bars are 2 inches by 2 inches. What are the dimensions of the pan she used to bake the fruit bars?
Answers
We then multiply 16*4 to get the area of the pan that she was using:
16*4=64
The dimensions of the pan have to be equal because the fruit bars’ dimensions are equal as well. So the sq root of 64 is 8.
So, the pan’s dimensions are 8*8. 8 inches for the height and 8 inches for the width.
I hope this helps!
7x +39 > 53
AND
16x + 15 > 31
Answers
Answer:
x > 2
Step-by-step explanation:
7x +39 > 53
AND
16x + 15 > 31
7x > 14
AND
16x > 16
x > 2
AND
x > 1
And is intersection, which is x > 2
Which number from the set {0, 2, 3, 5} is the solution to this equation?
5x − 4 = 3x + 6
A) 0
B) 2
C) 3
D) 5
Answers
Answer:
The answer is D: 5
Step-by-step explanation:
5 x 5 = 25 - 4 = 21 and 3 x 5 = 15 + 6 = 21
Answer: 5
Step-by-step explanation: Here, we want to determine which number can be replaced for the variable in this problem so the statement holds true.
5 would be the only number in this set that can work. Let's test it out.
We can do this by simply plugging in 5 for x. If the statement holds true when 5 is plugged in for x, then 5 is a solution.
Plugging in 5 for x, we have 5(5) - 4 = 3(5) + 6.
Simplifying, we have 25 - 4 = 15 + 6 or 21 = 21 which is a true statement.
So 5 is a solution.
a die is rolled. What is the probability that the result is less than 3?
Answers
Answer:
⅓
Step-by-step explanation:
Less than 3: 1 or 2
2/6 = 1/3
Select the correct answer.
For Bracken to break even (suffer no loss and earn no profit) over the passage of 3 years, about how many claims for surgical procedures can the 1,000 insured people file?
A. 1,000
B. 900.
C.90
D. 18
E. 180
Answers
Answer: 900
Step-by-step explanation:
Answer:
900
Step-by-step explanation:
−x+4y=−9
y=−2x+6
Is (2,3)(2,3)left parenthesis, 2, comma, 3, right parenthesis a solution of the system?
Answers
The solution of the equation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) is not the solution of the system.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equations are given below.
−x + 4y = −9 ...1
y = −2x + 6 ...2
From equations 1 and 2, then we have
−x + 4(−2x + 6) = −9
−x − 8x + 24 = −9
−9x + 24 = −9
9x = 24 + 9
9x = 33
x = 11 / 3
Then the value of the variable 'y' is calculated as,
y = −2(11/3) + 6
y = −22/3 + 6
y = −4/3
The arrangement of the situation 4y − x + 9 = 0 and y = 6 − 2x will be (11/3, −4/3). Point (2, 3) isn't the arrangement of the framework.
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The point (2, 3) does not satisfy either of the given equations, −x + 4y = −9 and y = −2x + 6. Therefore, it is not a solution to the system of equations.
Explanation:To determine if the point (2, 3) is a solution to the system of equations consisting of −x + 4y = −9 and y = −2x + 6, we need to check whether the point satisfies both equations.
For the first equation, substitute x with 2 and y with 3: −(2) + 4(3) = −9 to see if it results in a true statement.For the second equation, substitute x with 2: −2(2) + 6 = 3 to see if it equates to the y-value of 3.
Let's substitute the values into the first equation:
−(2) + 4(3) = −8 + 12 = 4, which does not equal −9. Therefore, the point does not satisfy the first equation.
For the second equation:
−2(2) + 6 = −4 + 6 = 2, which does not equal 3. Hence, the point does not satisfy the second equation either.
Since the point (2, 3) does not satisfy either equation, it is not a solution to the system of equations.