Answers
Let's see
\(\\ \rm\Rrightarrow {\displaystyle{\sum^{275}_{k=1}}}(-5k+12)\)
\(\\ \rm\Rrightarrow (-5(1)+12)+(-5(2)+12)\dots (-5(275)+12)\)
\(\\ \rm\Rrightarrow 7+5+3+2+1+\dots -1363\)
So
a=7l=-1363n=275Sum:-
\(\\ \rm\Rrightarrow S_n=\dfrac{n}{2}[a+l]\)
\(\\ \rm\Rrightarrow \dfrac{275}{2}(7-1363)\)
\(\\ \rm\Rrightarrow \dfrac{275}{2}(-1356)\)
\(\\ \rm\Rrightarrow 275(-678)\)
\(\\ \rm\Rrightarrow -186450\)
Answer:
-186,450
Step-by-step explanation:
Sum of arithmetic series formula
\(S_n=\dfrac{n}{2}[2a+(n-1)d]\)
where:
a is the first termd is the common difference between the termsn is the total number of terms in the sequence\(\displaystyle \sum\limits_{k=1}^{275} (-5k+12)\)
To find the first term, substitute \(k = 1\) into \((-5k+12)\)
\(a_1=-5(1)+12=7\)
To find the common difference, find \(a_2\) then subtract \(a_1\) from \(a_2\):
\(a_2=-5(2)+12=2\)
\(\begin{aligned}d & =a_2-a_1\\ & =2-7\\ & =-5\end{aligned}\)
Given:
\(a=7\)\(d=-5\)\(n=275\)\(\begin{aligned}S_{275} & = \dfrac{275}{2}[2(7)+(275-1)(-5)]\\& = \dfrac{275}{2}[14-1370]\\& = \dfrac{275}{2}[-1356]\\& = -186450\end{aligned}\)
Related Questions
What is the value of x? Please provide an explanation, thanks!
Answers
Answer:
28
Step-by-step explanation:
What you do is add up 42 and 76, then you subtract that from 180, because all triangles add up to 180. the subtracted amount is what z equals. Then since its a straight line you know it adds up to 180. You add z (62) and 90 because its a right angle. then you subtract 180 by 152 to get 28.
brianliest pls
Carl and tommy are on the cross countryteam on Wednesday carl ran 12. 5 Miles altogether carl and Tommy ran 26 Miles how many miles did tommy run
Answers
Tommy ran 13.5 miles. if we know the total distance run and the distance run by one person, we can subtract the known distance from the total to find the unknown distance.
The problem provides two pieces of information: the total distance run by Carl and Tommy combined, and the distance run by Carl individually. We can use these two pieces of information to determine the distance run by Tommy.
The total distance run by Carl and Tommy combined is 26 miles. This means that if we add up the distances run by both of them, it should equal 26 miles.
Carl ran 12.5 miles, so if we subtract his distance from the total distance, we can find Tommy's distance.
26 miles - 12.5 miles = 13.5 miles
Therefore, Tommy ran 13.5 miles.
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two complementary angles are in a ratio of $3:2$. what is the measure, in degrees, of the smaller angle?
Answers
The measure of the smaller angle of the complementary angles is: 36 degrees.
What are Complementary Angles?If the sum of two angles equals 90 degrees, then they are complementary angles.
Given that the ratio of two complementary angles is 3:2, therefor:
3x + 2x = 90
5x = 90
5x/5 = 90/5
x = 18
The smaller angle = 2x = 2(18) = 36 degrees.
The larger angle = 3x = 3(18) = 54 degrees.
Therefore, the measure of the smaller angle of the complementary angles is: 36 degrees.
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Find the other endpoint of the line segment with the given endpoint
and midpoint. Endpoint: (-9,-5) Midpoint: (-9,0)
PLEASE QUICK I CANT LEAVE THE ZOOM UNTIL I FINISH
Answers
Answer:
(-9,5)
Step-by-step explanation:
the midpoint occurs 5 units to the right of the endpoint. using this we can deduce that the other endpoint should also be 5 units right to the midpoint
Assume you have a balance of $1200 on a credit card with an APR of 18%. You start
making monthly payments of $300 but at the same time charge an additional $75 a
month. Assuming that interest for a given month is based on the balance for the previous
month, how long does it take you to pay off the credit card debt?
Answers
Assuming that interest for a given month is based on the balance for the previous month, it will take 6 months to pay off the credit card debt of $1,200 when making a net payment of $225.
How is the period determined?An online finance calculator can determine the period for a compound interest system.
The length of payment uses the beginning credit card balance of $1,200 and the net payment of $225 (since a monthly payment of $300 is made when an additional charge of $75 is withdrawn from the card).
I/Y (Interest per year) = 18%
PV (Present Value) = $1,200
PMT (Periodic Payment) = $-225 ($300 - $75)
FV (Future Value) = $0
Results:
Period (N #) = 5.6
Sum of all periodic payments = $-1,260.08
Total Interest = $60.08
Thus, within six months you can pay off the credit card debt.
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suppose that from previous evidence, anthropologists had believed that for each 1 mm increase in chord length, cranial capacity would be expected to increase by 20 cm3. do the data given here strongly contradict prior belief? use a 0.05 level of significance.
Answers
The data does contradict with the prior evidence
To determine whether the data presented here are significantly inconsistent with previous assumptions, a statistical test was performed to verify that the observed relationship between tendon length and cranial volume was significantly greater than the expected relationship. You have to decide if they are different.
To do this, fit a line to the data using linear regression analysis and test the hypothesis that the slope of the line is equal to 20 cm3/mm. If the p-value for this hypothesis test is less than 0.05, you can conclude that the data are inconsistent with previous assumptions at the 0.05 significance level.
It is crucial to realize that this analysis assumes that the relationship between tendon length and cranial volume is linear.
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A. y+2 = -4(X-8)
B. y- 8 = -4(x + 2)
C. y+ 8 = -4(x-2)
D. y-2 = -4(x+8)
PLEASE HELP AND ASAP THANKS!!!!!
Answers
\(y-y_1=m(x-x_1)\)
Given the x1 and y1 = given point.
Substitution x1 = 2 and y1 = -8 in the equation.
\( \begin{cases} x_1 = 2 \\ y_1 = - 8 \end{cases} \\ y - ( - 8) = - 4(x - 2) \\ y + 8 = - 4(x - 2)\)
Hence, the solution is C choice.
Answer\(y + 8 = - 4(x - 2)\)
Solve the equation given a domain of {-3}.
3x - 2y = 5
Answers
The solution to the equations is y = -7
How to solve the equations using the domain of the replacement sets?From the question, we have the equation to be given as
3x - 2y = 5
The above equation is a linear equation
The domain or the replacement set is given as
{-3}
Rewrite properly as
Domain = {-3}
or
x = -3
So, we replace the variables using the elements in the replacement set
When x = -3, we have
3 x -3 - 2y = 5
Evaluate the products
This gives
-9 - 2y = 5
Add 9 to both sides
-2y = 14
Divide both sides by -2
y = -7
So, we have
x = -3 and y = -7
Hence, the solution to the equation is y = -7
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how many times larger is 4.5 times 10^6 than 4.5 times 10^4
Answers
Answer:
100 Times larger.
Step-by-step explanation:
4500000/45000=100
which angle pair represents same-side interior angles?
Answers
Answer:
A
Step-by-step explanation:
3 and 5 are both inside the diagonal lines
we would associate the term inferential statistics with which task?
Answers
Inferential statistics involves using sample data to make inferences, predictions, or generalizations about a larger population, providing valuable insights and conclusions based on statistical analysis.
The term "inferential statistics" is associated with the task of making inferences or drawing conclusions about a population based on sample data.
In other words, it involves using sample data to make generalizations or predictions about a larger population.
Inferential statistics is concerned with analyzing and interpreting data in a way that allows us to make inferences about the population from which the data is collected.
It goes beyond simply describing the sample and aims to make broader statements or predictions about the population as a whole.
This branch of statistics utilizes various techniques and methodologies to draw conclusions from the sample data, such as hypothesis testing, confidence intervals, and regression analysis.
These techniques involve making assumptions about the underlying population and using statistical tools to estimate parameters, test hypotheses, or predict outcomes.
The goal of inferential statistics is to provide insights into the larger population based on a representative sample.
It allows researchers and analysts to generalize their findings beyond the specific sample and make informed decisions or predictions about the population as a whole.
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What is the value of x in the equation 5 x + 3 = 4 x? –3 Negative one-third One-third 3
Answers
Answer:
?
Step-by-step explanation:
Answer:
x=-3
Step-by-step explanation:
5 x + 3 = 4 x
5x+3-3=4x-3
5x=4x-3
subtract four from both sides=x=-3
x=-3 is your final answer!
Suppose you read on the back of a lottery ticket that the chances of winning a prize are 1 out of 10. Select the best interpretation. a. If many people buy a ticket, about 1 in 10 will win. b. If you buy 10 tickets, more likely than not you will win exactly once. c. You will win at least once out of the next 10 times you play. d. You will win exactly once out of the next 10 times you play. I
Answers
The best interpretation of the statement "the chances of winning a prize are 1 out of 10" is that if many people buy a ticket, about 1 in 10 will win.
This statement means that for every 10 tickets sold, on average, only one ticket will win a prize. It does not guarantee that you will win a prize if you buy a single ticket or even several tickets. The probability of winning a prize remains the same for every ticket purchased. It is important to note that winning a prize in a lottery is largely a matter of luck, and the odds are always against the player. While buying more tickets may increase your chances of winning, it does not guarantee a win.
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PLEDAE HELP ASAP
Pleseeee
Answers
Answer:
Step-by-step explanation:
The answer would be 34.56
Someone please help me on this.
Answers
Answer:
\(36n^2+12n+1\)
Step-by-step explanation:
Foil the equation!
1. You see that is to the second power so it means this \((6n+1)*(6n+1)\)
2. Then you use the Foil method. First, Outside, Inside, and Last.
3. Combined like terms
4. Answer!
A tip you can use to avoid Foil is this mental math trick: (Keep in mind this only works if the polynomial is being squared.)
1. Multiply the first number by itself = \(6n *6n = 36n^2\)
2. Add the first number by itself = \(6n+6n = 12n\)
3. Multiply the last number by itself = \(1*1 =1\)
4. Combined to form your answer = \(36n^2+12n+1\)
NOTE: This is the same thing as a foil but it uses mental math so it takes less time!
f(x)=3x2+2x−3
g(x)=2x+4
Answers
Answer:
A: 6
B: 16
C: 2
D: -12
Step-by-step explanation:
They are asking you to multiply the equations:
(3x^2 + 2x - 3)(2x + 4)
Distribute and you should get:
6x^3 + 16x^2 + 2x - 12
The Coefficients A,B,C, and D are 6, 16, 2, and -12.
Please answer asap! Giving brainly to correct answer!
Answers
the null hypothesis typically corresponds to a presumed default state of nature. t/f
Answers
False. The null hypothesis does not inherently represent a presumed default state of nature but rather serves as a reference point for hypothesis testing.
The null hypothesis does not necessarily correspond to a presumed default state of nature. In hypothesis testing, the null hypothesis represents the assumption of no effect, no difference, or no relationship between variables. It is often formulated to reflect the status quo or a commonly accepted belief.
The alternative hypothesis, on the other hand, represents the researcher's claim or the possibility of an effect, difference, or relationship between variables. The null hypothesis is tested against the alternative hypothesis to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
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Beniah sells hats and umbrellas. He charges 57.75 per hat and $9.50 per umbrella. Last week he sold 90 items for a total
of $757
Answers
explanation: 57.75 + 9.50 = 67.25
67.25/757
why are marcel’s and stephanie’s taxable incomes less than their annual salaries?
Answers
The taxable income of Marcel and Stephanie is less than their annual salary because they are allowed to make deductions from their income before calculating their taxable income.
These deductions include contributions to retirement plans, health insurance premiums, and other eligible expenses. The amount of deductions varies depending on factors such as the type of expense and the individual's tax filing status.
Thus, the taxable income is the amount of income that is subject to taxation, and it is generally lower than the individual's annual salary. In the case of Marcel and Stephanie, their taxable incomes are calculated by subtracting their deductions from their respective annual salaries.
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Complete Question:
Why are Marcel's and Stephanie's taxable incomes less than their annual salary? Marcel's annual salary is $30,000 and his income is $17,450. Stephanie's annual salary is $50,000 and her income is $37,600.
Type either > or < in the blank.
Answers
Using the law of sines, the relation between the lengths x and y is given as follows:
x < y.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is given by a.The length of the side opposite to angle B is given by b.The length of the side opposite to angle C is given by c.The lengths and the sine of the angles are related as follows:
\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)
On the given triangle, we have that:
The side opposite to the angle of 50º has length y.The side opposite to the angle of 48º has length x.Then:
sin(50º)/y = sin(48º)/x
x/y = sin(48º)/sin(50º)
The sine is increasing throughout the first quadrant, meaning that:
sin(50º) > sin(48º).
From the other side of the equality, this also means that:
y > x -> x < y.
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let a and b be two disjoint events. under what conditions are they independent?
Answers
Disjoint events are events that cannot happen at the same time. Two events A and B are independent if the occurrence of A does not affect the probability of B happening, and vice versa. Mathematically, this can be written as P(A and B) = P(A)P(B).
In the case of disjoint events, P(A and B) = 0 because they cannot occur at the same time. Therefore, the condition for A and B to be independent is that either P(A) = 0 or P(B) = 0, since any non-zero probability for either event would make the product P(A)P(B) also non-zero.
Two disjoint events are independent if and only if at least one of them has zero probability.
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PLEASE HELP ASAP I ONLY HAVE 15 MINUTES LEFT
THANKS IF YOU DO HELP
Find the distance between the complex numbers in the complex plane.
−5 + i, −3 + 5i
Answers
Answer:
-8+6i
Step-by-step explanation:
-5+-3=-8 since they are both negative its a a negative number
i is 1 but no on e puts 1 i so i plus 5i is 6i
-8+6i
correct me if im wrong please
have a good day :)
Several friends (Calvin, Dean, Kelli, and Lee) went to Cal's Late Night Diner for a bite to eat. Match each person to their drink (Iced tea, Lemonade, Root Beer, and Water) and determine how much each paid ($4.99, $5.99, $6.99, and $7.99) for their meal.
Clues:
1. The Diner who paid $4.99 was either Calvin or the one who got the Root Beer.
2. Kelli paid $6.99
3. The one who got the water paid 1 dollar less than Dean.
4. Calvin paid more than Lee.
5. The one who got the Root beer paid 1 dollar less than the one who got the Iced Tea.
Answers
Based on the given clues, we can determine the person, drink, and price paid for each individual:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
How to determine how much each friends paidFrom clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.
From clue 2, Kelli paid $6.99.
From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.
From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.
Therefore, the final assignments are:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
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A researcher is investigating the effect of sleep deprivation on learning. She recruits 30 participants and randomly assigns half to a "no sleep" group and half to a "regular sleep" group. The "no sleep" group are required to stay up all night and report to a testing room at 2PM the following day. The "regular sleep" group are instructed to have a normal night's sleep and report to the testing room at 9AM the following day. Unfortunately, a water pipe broke outside the testing room window and there was noisy construction crew working the whole day of testing. Which of the following statements is true?
a. The study may be affected by a situational variable.
b. The construction noise may contribute to variability in test scores.
C. The study has a confounding variable. The groups differ in the time they are to report to the testing room.
d. All of these are true.
Answers
The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
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Compare and Contrast Graph y = 2x + 5 and y=-13x+5. Describe how these lines are alike and how they are different. *
Answers
Here are a couple I found:
Similarities:
They have the same y-intercept of (0,5). They are both in slope-intercept form.Differences:
The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right. They have different x-intercepts. (y = 2x + 5 intersects (-\(\frac{5}{2}\), 0) while y = -13x + 5 intersects at (\(\frac{5}{13}\), 0)Explanation:
Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).
As for differences, we can see that the coefficient in place of that "m" is positive in y = 2x + 5 and negative in y = -13x + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.
I forgot how to solve this type of math equation
Answers
Step-by-step explanation:
= 3900 ( 1 + .86 )^x the .86 represents 86 % growth increase
Using a Table to Multiply Multivariable Polynomials What is the product of 6x – y and 2x – y + 2? 8x2 – 4xy + 12x + y2 – 2y 12x2 – 8xy + 12x + y2 – 2y 8x2 + 4xy + 4x + y2 – 2y 12x2 + 8xy + 4x + y2 + 2y
Answers
Answer: B.
\(12x^{2}\) \(-8xy + 12x + y^2 - 2y\)
Step-by-step explanation:
i just took the assignment
assume that there are 10 students in a class. the average grade on a test for the nine of the students is 85. the grade of the tenth student is 90. the average grade for the class will be
Answers
Answer:
85.5
Step-by-step explanation:
85 • 9 is 765
If you add 90 to 765 and then divide the sum by 10, you get 85.5.
41 One side of a triangular garden is x feet long. The other two sides of
the garden are both 5 feet less than twice the length of the first side
of the garden
Part A: Write a simplified expression for the perimeter, in feet, of
the garden
Answer:
A fence is placed along the entire perimeter of the triangular garden
The roll of fencing is 40 feet long.
Part B: Write a simplified expression to show the amount of fencing,
in feet, which is left from the roll of fencing.
Answer:
Answers
Given,One side of a triangular garden is x feet long. The other two sides of the garden are both 5 feet less than twice the length of the first side of the garden.
The perimeter of the garden can be written as; Perimeter = Side1 + Side2 + Side3 Length of side 1 = xLength of side 2 = 2x - 5Length of side 3 = 2x - 5Perimeter of the garden = x + 2x - 5 + 2x - 5= 5x - 10Thus, the simplified expression for the perimeter, in feet, of the garden is 5x - 10.A fence is placed along the entire perimeter of the triangular garden.The roll of fencing is 40 feet long. Amount of fencing used = Perimeter of the garden = 5x - 10Left from the roll of fencing = Length of roll of fencing - Amount of fencing used Length of roll of fencing = 40 feet Amount of fencing used = 5x - 10Left from the roll of fencing = 40 - (5x - 10)= 50 - 5xThus, the simplified expression to show the amount of fencing, in feet, which is left from the roll of fencing is 50 - 5x feet.
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