The sums of series using Polya's four-step problem-solving strategy in (a), (b) and (c) are 79800, 150975, and 1560 respectively.
(a) Let S = 1 + 2 + 3 + … + 398 + 399Write the series in reverse order and then add both series.S = 1 + 2 + 3 + … + 398 + 399S = 399 + 398 + … + 2 + 12S = 400 + 400 + … + 400 + 4002S = 400 x 399S = (400 X 399 ) / 2 = 200x399 = 79800(b) Let S = 1 + 2 + 3 + … + 548 + 549Write the series in reverse order and then add both series.S = 549 + 548 + … + 2 + 12S = 550 + 550 + … + 550 + 5502S = 550 x 549S = (550x549 ) / 2 = 275x549 = 150975(c) Let S = 2 + 4 + 6 + 8 + … + 72 + 74 + 76 + 78Write the series in reverse order and then add both series.S = 2 + 4 + 6 + … + 72 + 74 + 76 + 78S = 78 + 76 + 74 + … + 6 + 4 + 22S = 80 + 80 + … + 80 + 802S = 80 x 39S = (80 X 39 ) / 2 = 40 x 39 = 1560a sequence is, more or less speaking, a description of the operation of adding infinitely many quantities, one after the opposite, to a given starting quantity. The examine of series is a chief part of calculus and its generalization, mathematical evaluation. series are utilized in maximum areas of mathematics, even for reading finite structures (which includes in combinatorics) thru producing features.
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Simplify
√5 x √12 x √50
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3 } \times \sqrt{2 \times {5}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \times 5 \sqrt{5 \times 3 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 10 \sqrt{30} [/tex]
all the numbers from 1 to a 99 are multiplied together.Use a pattern to determine the last digit of the product
The last digit of the product of numbers from 0 to 99 is 0.
What is multiplication?Multiplication is a method of finding the product of two or more numbers.
We have,
1, 2, 3, .............till 99.
We know that any number multiplied by 10 will give us 0 as the last digit.
And there are 10, 20, 30, 40, 50, 60, 70, 80, and 90.
We also know that 5, 15, 25, 35, 45, 65, 75, 85, 95 if multiplied with an even number the last digit is zero.
So if all the numbers from 1 to 99 are multiplied together, the last digit of the product will be a zero.
Thus the last digit of the product of numbers from 0 to 99 is 0.
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What is the solution set for -3x ? 3 > -21?
The solution set for the inequality expression is (-∞, -6)
Solving inequalitiesInequality are expressions that does not involve an equality sign.
Given the following parameters
-3x + 3 > -21
Subtract 3 from both sides
-3x + 3 - 3 > 21 - 3
-3x > 18
Divide both sides by -3
-3x/-3 < 18/-3
x < -6
Hence the solution set for the inequality expression is (-∞, -6)
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Solve the following equation for q
7p-5q=-35
Answer:
q = [tex]\frac{7}{5}[/tex]p + 7
Step-by-step explanation:
7p -5q = -35 Subtract 7p from both sides of the equation
-5q = -7p - 35 /Dive all the way through by -5
q = [tex]\frac{7}{5}[/tex]p + 7
At a farm market, watermelons are selling 5 for $20. Each watermelon weighs about 8 pounds. What does the unit rate tell you? Responses The number of pounds each watermelon weighs. The number of pounds each watermelon weighs. The number of pounds all of the watermelons weigh. The number of pounds all of the watermelons weigh. The cost of all the watermelons. The cost of all the watermelons. The cost of one watermelon. The cost of one watermelon.
The unit rate of the watermelons would tell us the cost of 1 of the watermelon. The last option is correct.
How to solve for the costThe question tells us that the melons are sold for 5 for $20.
Hence the price of 1 would be at: 20/5
= 4 dollars per watermelon.
The weight of one of the melons is 8 pounds and the unit rate for 1 is 4 dollars. The unit rate is the price per one of the fruits or the cost of the fruit.
Hence we can say that The unit rate of the watermelons would tell us the cost of 1 of the watermelon.
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WILL GIVE BRAINLIEST
To pay for a home improvement project that totals $11,000, Genesis is choosing between taking out a simple interest bank loan at 6% for 3 years or paying with a credit card that compounds monthly at an annual rate of 16% for 6 years. Which plan would give Genesis the lowest monthly payment?%0D%0A%0D%0A The monthly credit card payment would be $396.49, which is lower than the monthly payment on the bank loan.%0D%0A The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.%0D%0A The monthly credit card payment would be $354.44, which is lower than the monthly payment on the bank loan.%0D%0A The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.
Using the monthly payment formula, it is found that the best plan is given by:
The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For the simple interest payment method, the parameters are given as follows:
r = 0.06, n = 3 x 12 = 36, P = 11000, r/12 = 0.06/12 = 0.005.
Hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 11000(0.005)\frac{(1.005)^{36}}{(1.005)^{36} - 1}[/tex]
A = 334.64.
For the credit card payment method, the parameters are given as follows:
r = 0.16, n = 6 x 12 = 72, P = 11000, r/12 = 0.16/12 = 0.0133.
Hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 11000(0.0133)\frac{(1.0133)^{72}}{(1.0133)^{72} - 1}[/tex]
A = 238.37.
The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.
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In 4 games, Larry averaged 23 PPG (points per game). How many points does he need to score in the last game to have an average of 25 PPG? Explain how to use the mean and data given to find the answer.
The points does he need to score in the last game to have an average of 25 PPG is 33 points
Larry will need 33 points in his 5th game to average 25 PPG.Given that
Larry averaged 23 PPG (points per game) in 4 games.To find
How many points are required to have an average of 25 PPG?So, according to the question
We have,
Larry's average in 4 games = 23 PPG.∵ [tex]average = \frac{sum\;of\;terms}{number\;of\;terms}[/tex]
∴ Total points gained by Larry in 4 games
= (average points in 4 games) × 4
= 23 × 4
= 92 points.
Let's assume Larry scored x points in the 5th match to have an average of 25 PPG.
So, we can say that
Larry's average in 5 games = [tex]\frac{total\;points\; in\; 5\;games}{5}[/tex]
25 = [tex]\frac{92+x}{5}[/tex]
25 × 5 = 92 + x
125 = 92 + x
x = 125 - 92
x = 33.
He will need 33 points in his 5th game.
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Multiply 5 by 25 to find the total points Larry needs to score in 5 games, 5 × 25 = 125. Then find the total points Larry scored in the frist 4 games, 4 × 23 = 92. Subtract to find the number of points Larry needs to score
took the quiz
Please help due tonight
Answer:
Step-by-step explanation.
answer please due at 12
Answer:
11: Area as sum: 7d + 28
Area as product 7(d+4)
12: Area as sum: 2y + 3y (could also be y^2 + 3y)
Area as product: y(y+3)
Step-by-step explanation:
For area as sum it's just distributing to each box, and then adding.
For area as product you just undistribute it and put it into parenthesis.
What is the solution set to the inequality m - 7 > -2(m + 0.5)
The solution set to the inequality is m>2.The correct ray to represent the solution is o---> placed at 2.
Inequality is a statement of order,greater than, less than, greater than or equal to or less than or equal to between two algebraic expression. Inorder to solve an inequality we change the sides of the unknown variable and the constants. We always have to keep in mind the change of sign, if we change sign then we have to change the relation between the two expressions too. Here we have been given an inequality which is
m-7>-2(m+0.5)
In this inequality m is the unknown variable and we have to solve for m,
m-7>-2(m+0.5)
⇒m-7>-2m-1
⇒2m+m>7-1
⇒3m>6
⇒m>2
The solution set to the given inequality is m>2, so the correct ray to represent the solution is o---> placed at 2 on the number line.
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someone pls help me w this. I rlly need this!! thank uu! "what is the midpoint of a line segment with endpoints (3,8) and (-2,6)"
Answer:(1/2, 7) as decimal = (0.5, 7)
Step-by-step explanation:
===================================================
Explanation:
The x coordinates are 3 and -2
Add them up: 3 + (-2) = 1Divide the result in half: 1/2 = 0.5The x coordinate of the midpoint is 0.5
--------------
The steps are the same idea for the y coordinates
Add: 8+6 = 14Divide in half: 14/2 = 7The y coordinate of the midpoint is 7
--------------
Overall, the midpoint is located at (0.5, 7)
You can confirm this by letting
A = (3,8)
B = (0.5, 7)
C = (-2,6)
Then use the distance formula to see that AB = BC
DVE
Note: Please make sure to property format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to Include a percentage sign (%%). For all items without specific rounding instructions, round your answers to two decimal piaces,
o show both decimal places (5.05).
4 recent survey by the American Automobile Association showed that a family of two adults and two children on vacation in the United States will pay an average of $247 per
day
10.
for food and lodging with a standard deviation of $60 per day. You can compute the mean food and lodging cost of a 10-day vacation by multiplying the per-day mean by
The standard deviation for the 10-day vacation can be found by multiplying by 10 also.
a. What is the mean for food and lodging for a 10-day vacation?
b. What is the standard deviation of the distribution for the 10-day vacation?
What is the variance of the distribution for the 10-day vacation?
The statistical measures for the 10-day vacation are given as follows:
a) Mean: $2470.
b) Standard deviation: $189.74.
c) Variance: $²36,001.
What is the mean for the 10-day distribution?To find the mean for n days, we take the mean amount for the distribution in a single day and multiply by n.
Hence, considering that the mean for a single day is of $247:
247 x 10 = $2470.
What is the standard deviation for the 10-day distribution?To find the standard deviation for n days, we take the standard deviation for a single day and multiply by the square root n.
Hence, considering that the standard deviation for a single day is of $60, we have that:
60 x sqrt(10) = $189.74.
What is the variance for the 10-day distribution?For any distribution, the variance is the square of the standard deviation, hence:
($189.74)² = $²36,001.
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solve for x
3(2x+18)=36
Answer:
x = -3
Hope this helps
Step-by-step explanation:
( (2x*3) + (18*3) ) = 36
(6x + 54) = 36
6x + 54 = 36
6x + 54 - 54 = 36 - 54
6x = -18
6x / 6 = -18 / 6
x = -3
Overview
Question Progress
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Express 56 as the product of its prime factors.
Write the prime factors in ascending order.
7
8
The prime factors in ascending order are 2,7.
Given that, 56 is a number that is needed to be expressed as the product of prime numbers that is prime factors.
prime number is defined as , if a number is divided by only one and itself then it is named as a prime number.
prime factor is defined as , if a number can be represented in terms of multiplication of the prime numbers is known as the prime factor.
prime numbers are 2,3,5,7,11,13,17,1923,29,31,37..etc.
expressing 56 in terms of prime factors.
As 56 is an even number, you can just express this in smallest prime number that is 2 .
firstly you can express 56 in product of 23 and 2.
you can not divide again 23 as it was prime number.
so , you can express 56 as 23*2 or you may access this as 2*2*2*7
Prime factors in ascending order are , 2,7 or 2,23.
As we choose least prime factors we prefer 56 = 2*2*2*7.
Therefore ascending order of prime factors will be 2,7.
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A manufacturer makes widgets and gadgets. At least 500 widgets and 700 gadgets are
needed to meet minimum daily demands. The machinery can produce no more than 1200
widgets and 1400 gadgets per day. The combined number of widgets and gadgets that the
packaging department can handle is 2300 per day
The combined number of widgets and gadgets that the packaging department can handle is 2300 per day that is x + y =2300
A manufacturer makes widgets and gadgets. At least 500 widgets(x) and 700 gadgets (y) are
[tex]x\geq 500\\\\y\geq 700[/tex]
The machinery can produce no more than 1200 widgets(x) and 1400 gadgets(y) per day
[tex]x\leq 1200\\\\y\leq 1400[/tex]
The combined number of widgets and gadgets that the packaging department can handle is 2300 per day
x+ y =2300
then the possible values of x and y are
( 1000, 1300)
(1100, 1200)
( 1200,1100) etc.
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Rafael wants to find the average time it takes Central High School students to run a lap around the track. So he will consider 55 students to find the average
time.
Answer the questions below.
(a) Which unit(s) could be used for the unit of measurement? Check all that apply.
seconds Omilligrams 0 minutes
kilograms
grams
(b) Which of the procedures below would be the best way to find the average time?
O Randomly pick 55 students to run a lap around the track and measure their times.
O Randomly pick 55 students to run a lap around the track and have them state their own times.
O Ask for 55 volunteers to run a lap around the track and have them state their own times.
O Measure the times of 55 volunteers who run a lap around the track.
Answer:
Seconds and Minutes
Step-by-step explanation:
Randomly pick 55 students to run a lap around the track and measure their time.
This is the only option that avoids any type of bias.
when constructing a congruent line segment to cd the ray needed for the construction must be shorter
This statement is false. when constructing a congruent line segment to cd the ray needed for the construction it must be not shorter.
Why configured line segment to CD the ray never can be shorter?Because when constituting a configured line segment to CD the ray never can be shorter. The reason is when we constitute a configured it's Ray line is always increase that mean it's go up Hight and it's must be longer . That's why this statement is false.
What is a congruent line segment?Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments. The congruent segments continue to be congruent even after being turned, flipped, or rotated.
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b. Name three points coplanar with point B.
FO
OE
G
D
A
B
l
m
P
Keisha has $585.43 in her checking account. She must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today. Write an inequality, using x for the variable, that would be used for the least amount of money she needs to deposit to avoid a fee.
The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.
How to calculate the value?From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.
The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:
585.43 + x - 302.05 ≥ 300
Collect like terms
x ≥ 300 - 585.43 + 302.05
x ≥ $16.62
She's needs to deposit at least $16.62.
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3. What is the perimeter of a square
that is 3 inches on one side?
A 15 inches
(B) 12 inches
C
D
9 inches
3 inches
Step-by-step explanation:
(B) 12 Inches is the answer because perimeter (P) =4l =4×3=12
A tram moved upward for 12 seconds what was the total change in the trams elevation
Answer:
It depends on the steepness of the climb
Step-by-step explanation:
The graph shown corresponds to someone who makes ___
help quick pls
Answer:B $20 an hour
Step-by-step explanation:
if you look at the graph, in one hour he made $20
whitney makes $60000 in salary eight percent commission in may whitney had $13000 in sales how much did whitney make in may including her salary and commission
The total earning of Whitney in may including her salary and commission is $70,400.
What is sales commission?A sales commission is money given to an employee for completing a task, typically selling a specific amount of products or services.
Sales commissions are sometimes used as incentives by employers to increase work efficiency. A commission can be paid in regards to or in place of a salary.Now, as per the given question;
The monthly salary of Whitney is $60000.
The sales he did in the month of the may is $13000.
He got 8% commission on his total sales.
8% of $13000 = 10,400.
Thus, the total earning of the may will be-
Total earning = Salary + commission
Total earning = $60000 + 10,400
Total earning = $70,400
Therefore, the total earning done by Whitney in the May is $70,400.
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Probability Question, please help me im stuck!
Answer:
27%
Step-by-step explanation:
3000 + 3500 + 4000 + 4200 = 14700
4000 / 14700 ≈ 0.27
0.27 = 27%
in science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. if x represents a student's score, write an equation that represents the minimum and maximum scores. |x − 87|
The equation representing the minimum and maximum scores |x-87| = 1.8
Given that the average score on a lab report is 87 points. All students score within 1.8 points of the average.
Let 'x' be the score of student. The maximum and minimum score of a student lies within 1.8 points of the average.
Then, maximum score of a student, x = 87+1.8
and minimum score of a student, x = 87-1.8
Combining these two equations, we get, x = 87 ±1.8
Or, more conveniently, |x-87| = 1.8 represents the minimum and maximum scores obtained by a student.
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what is the value of the expression 2[I(y-5z)] when I=5/2 y=7 and z=1/5
Answer:
Plug in the numbers to the variables
Step-by-step explanation:
Im not giving ya'll the straight answer because I use it all the time in almost all of my math.
Because you have the value of the variables, all you need to do is plug those variables in and the solve like you usually would (PEMDAS)
Hope this helps and ya'll got this! ;)
A.10x-5 )=1000 B.10x+5)=1000 C.10x+5=1000 D.10x-5=1000
I need help getting my answer
A boat is currently 63 miles from its destination and is traveling against a river current. The boat travels 10 miles per hour (mph) in still water. The boat's distance from its destination is given by the following formula. D=63-h(10 - c) Given: D = distance in miles, h = number of hours, c = speed of the river's current in mph What is a correct formula for the boat's distance from its destination after 3 hours
The distance of the boat from its destination depends on
Speed of the boatSpeed of the river currentDirection of the river current.So with these factors, the distance of the boat from its distance can be calculated.
The distance of the boat from the destination currently is 63 miles
Speed of the boat is 10 miles / hr
Let c be the speed of the river current and
h be the number of hours to reach a particular destination
So, the formula to find the distance of the boat from destination is given by
D = 63 - h(10 - c)
We need to find the formula for boat's distance from its destination after 3 hours
Thus h = 3 hrs
Let us substitute h in above equation, Then
D = 63 - 3(10 - c)
D = 63 - 30 - 3c
D = 33 - 3c
which is the formula for the boat's distance from its destination after 3 hours.
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how can we reduce the rate of refusals in telephone surveys? most people who answer at all listen to the interviewer’s introductory remarks and then decide whether to continue. one study made telephone calls to randomly selected households to ask opinions about the next election. in some calls, the interviewer gave her name; in others, she identified the university she was representing; and in still others, she identified both herself and the university. for each type of call, the interviewer either did or did not offer to send a copy of the final survey results to the person interviewed. what are the factors in this experiment and how many levels does each factor have?
We can reduce the rate of refusals in telephone surveys by doing face to face surveys.
What are telephone surveys?A phone study can keep going extremely lengthy, which brings about getting legitimate reactions and knowledge of the respondent's perspective which helps
social event a lot of information. Time limits are a disadvantage of telephone interview studies. Frequently, when you contact individuals at home, they are engaged with different exercises, like having supper or sitting in front of the TV. A few potential interviewees may be hesitant to partake in a meeting because of how much time they dread it will take. Examination can be assembled rapidly in light of the fact that telephone interviews are prompt and gifted questioners can finish a great deal of overviews in a day of work. A great many people have phones, so you have an adequate crowd for get-together a delegate test to finish the study.
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