Answers
The sum of the arithmentic series is -127
Step - by - Step Explanation
What to find? The sum of the arithmetic series.
Parameter Given:
a₁ = -26/5 , d=-5/3 , n=10
To find the sum of the arithmetic series we will use the formula below:
[tex]S=\frac{n}{2}\mleft\lbrace2a+(n-1)d\mright\rbrace[/tex]Substitute the values and evaluate.
[tex]S=\frac{10}{2}\mleft\lbrace2(\frac{-26}{5}_{})+(10-1)(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace2(\frac{-26}{5})+9(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace-\frac{52}{5}-15\mright\rbrace[/tex][tex]=-52-75[/tex]=-127
Related Questions
n(n+1)(n+5) is multiple of?
Answers
n(n+1)(n+5) can be a multiple of 3.
Utilizing the mathematical induction formula for any n > N, we are going to demonstrate it.
P(n) = n(n+1) n(n+5) = 3d, where d N
P(1)=1(2)(6)=12, that is cleavable by three, for n=1.
Suppose P(k) is true.
Where m N k three +6k a pair of +5k=3m k, P(k)=k(k+1)(k+5)=3m.
3\s =−6k \s2\s −5k+3m
We will currently demonstrate that P(k+1) is true.
P(k+1)=K+1, K+2, K+6, K 3 +9 K 2, K twenty K + twelve
When we plug the worth of k three into the equation on top of, we tend to get 3m6k a pair of 5k)+9k a pair of +20k+12 =3.
m+3k \s2\s +15k+12\s=3
(m+k \s2\s +5k+4)
in which r=m+k a pair of + 5k + four
P(k+1) is often true since P(k) is often true.
Therefore, in step with the induction principle, P(n) is cleavable by three for all n N.
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You buy five equally priced gifts for a total of $75 what was the price of each candle
Answers
Answer:
$15
Explanation:
To find the price of each candle, we need to divide $75 by 5, so the price of each candle is:
$75 ÷ 5 = $15
So, the answer is $15
1. In a factory, a machine takes 5 minutes to stitch a book. How many machines are needed to stitch
50 books in 10 minutes?
Answers
Answer: just multiply 5 by 2
Step-by-step explanation:
6 to the negative 3rd power times 6 to the 2nd power times 6 to the 5th power times 6
Answers
The value of 6 to the negative 3rd power times 6 to the 2nd power times 6 to the 5th power times 6 is 6^5.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Based on the information given, the numbers will be expressed as:
6^-3 × 6^2 × 6^5 × 6
= 6^5
It's important to note that they've the same base. Therefore, the powers will be added thus:
= -3 + 2 + 5 + 1
= 5
This gives 6^5. This illustrates the concept of exponents.
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Tina couldn't wait to share the 36 cookies she made with her friends. If she shares with 8 friends, how many cookies (c) will each of them get?
Answers
Given:
Total number of cookies is, N = 36.
Number of friends is, n(f) = 8.
The objective is to find the number of cookies (c) will each of them get while sharing.
Consider the required number of cookies to each person as (c).
The value of c can be calculated as,
[tex]\begin{gathered} c=\frac{\text{Number of cookies (N)}}{Number\text{ of friends n(f)}} \\ =\frac{36}{8} \\ =4.5 \end{gathered}[/tex]Hence, each of them will get 4 and a half cookies.
Two numbers are called relatively prime if their greatest common divisor is $1$.
Grogg's favorite number is $10!$, the product of the integers from $1$ to $10$. (He pronounces it TEN!)
What is the smallest integer greater than $800$ that is relatively prime to Grogg's favorite number?
Answers
Answer:
Two numbers are called relatively prime if their greatest common divisor is $1$. Grogg's favorite number is the product of the integers from $1$ to $10$
Answer: The answer is 803. :) lol
Step-by-step explanation:
You gotta keep trying numbers. But the numbers cant be even because if it's even, it can be divided by 2! Try the odd numbers starting at 800. If the number is not divisible by any of the numbers from 1-10 then it's the correct number. Got it on my second try. LOL! I'm from AOPS like you. :) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Two fields of equal soil types and slope both had corn planted last year. It was the first year that the newly installed center pivot irrigation systems were used - one system per field. However, these systems were made by two different manufacturers.
Suspecting that one of the systems in particular is oversupplying water to the corn, the farmer set up sensors on the edge of the field adjacent to a drainage ditch to measure the total runoff in the two fields. The data from these two sensors is displayed below:
Water runoff (gallons)
Irrigation System #1
11.4 12.4 12.1 11.8 11.8 11.7 12.3 12.0 11.8
Irrigation System #2
13.0 12.4 12.4 12.1 12.3 12.1 12.5 12.0 12.1
The question of interest is whether these two systems produce significantly different runoff. Find the value of the test statistic for the this test (hint: this is a kind of t-test - read the problem carefully to infer exactly which kind).
Answers
More surprising was a recent report of severe erosion brought on by rain in a well-kept, drip-irrigated subtropical fruit orchard in Limpopo
It is widely known and has been extensively researched for many years how soil erosion occurs in rangelands and locations where crops are watered by rain. However, it appears that knowledge of and research on the severe soil erosion that occurs in irrigated regions is lacking. When center pivot irrigation was used on highly crusting, extremely unstable soils, such as those from the Eastern Cape and the Lowveld of Mpumalanga, major gully (donga) erosion ensued, according to information the author has previously and more recently received. After the irrigation was put in place, they grew quite fast. More surprising was a recent report of severe erosion brought on by rain in a well-kept, drip-irrigated subtropical fruit orchard in Limpopo.
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A 2070 kg space station orbits Earth at an altitude of 457 km. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98×1024 kg and 6370 km, respectively.
Answers
The magnitude of the force with which the space station attracts Earth.
17714.8532 N
This is further explained below.
The magnitude of the force :An influence that has the potential to alter the motion of an item is referred to as a force.
An object having mass may experience a change in its velocity, often known as acceleration, when subjected to a force.
Generally, the equation for the magnitude of the force is
F = G.M.m/r2
Where
G=gravitational constant
M and m mass
r=radius
F=force of attraction
Therefore
6.67*10^{-11} * 5.98*10^{24} * 2070/((6370+457)2*10^6)
= 17714.8532 N
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Which analytical model best represents the data in the table below?
Answers
When x = 0, y = 2, then the constant term of the polynomial must be 2. This discards the last 2 options.
When x = 1, y = 11. Substituting x = 1 into the first two options, we get:
[tex]\begin{gathered} y=9\cdot1^2+2=9+2=11 \\ y=9\cdot1^2+11\cdot1+2=9+11+2=22 \end{gathered}[/tex]Then, y = 9x² + 2 is correct.
Help?
(ii) Not sure what scale factor is
(ii) And I’ve never learnt this
Answers
This video from khan academy should clear up your confusion on scale factors.
https://www.khanacademy.org/math/7th-engage-ny/engage-7th-module-1/7th-module-1-topic-d/v/identifying-scale-factors
Carry your intermediate competations at least four decimal places were on your answer to 2 decimal places
Answers
Given that Z follows the standard normal distribution, and that the left-tailed probability for a z-score c is:
[tex]P(Z\leqslant c)=0.8531[/tex]Then, we can see that the value of c, round to two decimal places, is:
[tex]c=1.05[/tex]4) Say there are 500,000 people in a county, of which approximately 300,000 are registered voters. According to the pir chart below, what is an estimate to the nearest person of how many people in the county are registered independents? (10 points) Approximately people in this county are registered independents. Registered County Voters Other 64 Independent 40% - Democrat u Republican independent Other
Answers
Since the chart has the name "Registered Country Voters", it only includes the registered voters, that is the approximately 300,000 people. Since 16% are independet, we can take 16% of 300,000 to get the registered independets. that is, multiply 0.16 (16%) by 300,000:
[tex]0.16\cdot300,000=48,000[/tex]So, the answer is 48,000.
Malcolm's Bakery Shop sells gourment cupcakes. The shop's cost for making 3 cupcakes is $6.75, and the cost of making 5 cupcakes is $9.75 . What is the shop's cost per minute?
A. $1.50
B. $1.95
C. $2.25
D. $3.00
Answers
Solve for x usingcross multiplication.3x + 6 = 4x - 364=35x = [?]Enter
Answers
Solving for x,
[tex]\begin{gathered} \frac{3x+6}{4}=\frac{4x-3}{5} \\ \\ \rightarrow5(3x+6)=4(4x-3) \\ \rightarrow15x+30=16x-12 \\ \rightarrow30+12=16x-15x \\ \rightarrow42=x \\ \\ \Rightarrow x=42 \end{gathered}[/tex]Below, the two-way table is given for a classof students.FreshmenSophomore Juniors Seniors TotalMale4622Female 3463TotalIf a male student is selected at random, what is theprobability the student is a freshman.
Answers
29%
Explanations:Probability is the likelihood or chance that ab event will occur. Mathematically;
Probability = Expected/Total
From the given table, the total number of male student is the total outcome as shown:
Total outcome = 4 +6+ 2 + 2
Total outcome = 14
If a male freshmen is selected at random, the expected outcome will be 4.
Determine the probability
[tex]\begin{gathered} Pr(Freshman\text{ \mid Male})=\frac{Male\text{ freshmen}}{Total\text{ male studnt}} \\ Pr(Freshman\text{ \mid Male})=\frac{4}{14} \\ Pr(Freshman\text{ \mid Male})=0.2857\times100 \\ Pr(Freshman\text{ \mid Male})\approx29\% \\ \end{gathered}[/tex]Hence the probability that the male student is freshman is approximately 29%
Which number line represents the solution set for the inequality 2x - 6 2 6(x - 2) + 8?-1.5-1-0.500.51.5-1.5-1-0.500.51.55-0.500.51.5-1-0.500.51.5
Answers
Solve the inequality:
2x - 6 ≥ 6(x - 2) + 8
Operating the parentheses:
2x - 6 ≥ 6x - 12 + 8
Subtracting 6x:
2x - 6x - 6 ≥ - 12 + 8
Adding 6:
2x - 6x ≥ - 12 + 8 + 6
Simplifying:
- 4x ≥ 2
Dividing by -4 and changing the symbol:
x ≤ 2/(-4)
x ≤ -0.5
The solution in the number line starts at -0.5 and goes to the left with an arrow:
Xiao Mei covers a table with 8 rows of square unit tiles. There are 7 tiles in each row. What is the area that Xiao Mei covers in square units?
Answers
The area that Xiao Mei covers in square tiles is 56 sq. units.
Given,
In the question:
Xiao Mei covers a table with 8 rows of square unit tiles.
and, There are 7 tiles in each row.
To find the area that Xiao Mei covers in square tiles.
Now, According to the question:
Tables covers = 8 rows of sq. unit
In each row = 7 tiles
All you would have to do is multiply 8 times 7
it means, 8 x 7 = 56
Hence, The area that Xiao Mei covers in square tiles is 56 sq. units.
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Towson Corporation issued $150,000 of 7% ten year bonds at 103 on the semi-annual interest date. Towson uses the straight line method to amortize any bond premium or discount. What is the amount of bond amortization for each six month period? Answer in whole dollars (no cents).
Answers
The amount of bond amortization for each six month period is [tex]\$225[/tex].
In the given question,
Towson Corporation issued [tex]\$150,000[/tex] of [tex]7\%[/tex] ten year bonds at [tex]103[/tex] on the semi-annual interest date.
Towson uses the straight line method to amortize any bond premium or discount.
We have to find the amount of bond amortization for each six month period.
Cash issued [tex]=\$150,000[/tex]
Rate [tex]=7\%[/tex] ten year bond at [tex]103[/tex] n the semi-annual interest date.
So the cash proceed on issue of bond = Cash issued [tex]\times103[/tex] [tex]/100[/tex]
Cash proceed on issue of bond [tex]=\$150,000\times\frac{103}{100}[/tex]
Firstly simplifying ratio
After simplification of ratio
Cash proceed on issue of bond [tex]=\$150,000\times1.03[/tex]
Now simplifying after multiplication
Cash proceed on issue of bond [tex]=\$154,500[/tex]
Hence, the cash proceed on issue of bond is [tex]\$154,500[/tex].
Now we find the premium that issued in the bond.
Premium on issue of bond [tex]=\$154,500-\$150,000[/tex]
Simplifying
Premium on issue of bond [tex]=\$4,500[/tex]
Hence, the premium on issue of bond is [tex]\$4,500[/tex]
Now finding the amount of bond amortization for each six month period.
Bond Amortization = (Premium on issue of bond/10 years) * 1/2
Bond Amortization [tex]=(\frac{\$4500}{10})\times\frac{1}{2}[/tex]
Simplifying the ratio
Bond Amortization [tex]=\$450\times0.5[/tex]
Bond Amortization [tex]=\$225[/tex]
Hence, the amount of bond amortization for each six month period is [tex]\$225[/tex].
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there are 13 porters carrying total weight of 195 kg on an expeditioin. extra porters joined the group so, they carry average weight of 13kg of baggage. find the number of portes added
Answers
Answer: 2 porters joined the group
Step-by-step explanation:
First, you are told that "13 porters are carrying a total weight of 195kg". You can use this information to create an equation to find the average weight carried by each porter.
[tex]\frac{195 kg}{13}=15kg[/tex]
^195kg (total weight) divided by 13 (the number of porters) is equal to 15kg (the average weight carried by each of the 13 porters).
You are then told that "extra porters join the group, so they carry an average weight of 13 kg of baggage". because some porters joined the group, you'll have to add p (p = number of porters) to the original equation and change the average weight from 15kg to 13kg.
[tex]\frac{195kg}{13 +p} = 13kg[/tex]
^195kg (total weight) divided by 13+p (total number of porters after some joined group) is equal to 13kg (new average weight)
You can then use your new equation to solve for "p" and find the number of porters added.
p = 2
Question 1] Find the mean for each set of data6,9,2,4,3,6,5
Answers
Given:
The given set of data is
[tex]6,9,2,4,3,6,5[/tex]To find: The mean for the given set of data?
Explanation:
We can calculate the mean of a given set of data by using the formula
[tex]Mean=\frac{Sum\text{ of the terms}}{Number\text{ of terms}}[/tex]Here,
We can calculate the sum of terms as
The sum of terms = 6+9+2+4+3+6+5
The sum of terms =35.
and
The number of terms = 7.
Now, by substituting the value in the above formula
Therefore,
[tex]\begin{gathered} Mean=\frac{35}{7} \\ \\ Mean=5 \end{gathered}[/tex]Hence, the mean = 5.
Answer: The mean for a given set of data is 5.
One card is drawn from a standard deck of 52 playing cards. Find the probability of each of the following events:
Answers
1) Probability of drawing a spade is 14
2) Probability of drawing a seven is 1/13
3) Probability that a heart or spade is drawn = 1/2
4) Probability that blackjack is drawn = 1/26
Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
1) There are 13 spades in total.
hence, the likelihood of drawing a spade is 13/52, or 14.
2) The sum of the seven is four. (4 suits are in the room)
Probability = 4/52 = 1/13
(3) A heart or spade is drawn.
Total hearts and spades: 13 + 13 = 26
Probability = 26/52 = 1/2
4) A blackjack is drawn, with a total of two blackjacks.
Probability = 2/52 = 1/26.
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please help me with this calculate the volume of the cone and round it to the nearest hundredth
Answers
ANSWER:
The volumen of the cone is 667.07 cubic meters
The volume has the following formula
[tex]V=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]replacing:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.1416\cdot7^2\cdot13 \\ V=667.07 \end{gathered}[/tex]Given m∥n, find the value of x
Answers
Answer:
x=55
Step-by-step explanation:
2x+6+x+9=180
3x=165
x=55
:]
Simplify the expression 5(-7 + 3k)
Answers
The given expression is,
[tex]5(-7+3k)[/tex]Opening the brackets and multiplying each term inside the bracket with 5, we get,
[tex]\begin{gathered} \lbrack5\times(-7)\rbrack+(5\times3k)=-35+15\text{ k} \\ 15k=35 \\ k=\frac{35}{15}=2.33 \end{gathered}[/tex]The simplified expression is 15k = 35 and the value of k is 2.33.
Mrs. Jenkins is catering a school dance and wants to know how manystudents prefer tacos and how many prefer hot wings.296 students preferred tacos63% of students preferred hot wings.How many students in total were attending the dance?
Answers
Let x represent the total number of students that attended the dance. This means that
number of students that prefer tacos + number of students that prefer hot wings = x
Percentage is expressed in terms of 100. If 63% of the students preferred hot wings, then the number of students that preferred hotwings is
63/100 * x = 0.63x
If 296 students preferred tacos, it means that
293 + 0.63x = x
x - 0.63x = 296
0.37x = 296
x = 296/0.37
x = 800
Thus, a total of 800 students attended the dance
In triangle DEF, m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°. Determine the degree measure of the exterior angle to ∠D.
54°
39°
141°
126°
Answers
The value of x is equal to 10 and the exterior angle to angle d is equal to 141 degrees.
Exterior AnglesTo solve this problem, we have to recall that the sum of angles in a triangle is equal to 180 degrees.
Applying that formula here;
[tex]m < d + m < e + m < f = 180^0\\(2x + 19) + (3x + 24) + 87 = 180\\x = 10[/tex]
But the exterior angle to angle D can be found assuming the angle lies on a straight line, then the sum of angle D and it's exterior angle would be equal to 180 degrees.
Let y = exterior angle
[tex]m < d + y = 180\\2x + 19 + y = 180\\x = 10\\2(10) + 19 + y = 180\\20 + 19 + y = 180\\39 + y = 180\\y = 141^0[/tex]
The value of the exterior angle to d is equal to 141 degrees.
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Answer: its C
Step-by-step explanation: i got it right
Answer the question right and i will give u brainiest
Answers
Answer:
21 is -2 away, 22 is- 1 away 28 is 5 away, and 29 is 6 away
Step-by-step explanation:
Answer:
-2
-2
-2
-1
-1
-1
-1
-1
5
6
I need help with this question but no one is helping me! Can someone please help me.
Answers
Hope someone else answer it
a. Draw the figure and its reflection in the x-axis.
A(2,0), B(1,5), C(4,3)
Answers
Answer:
A: 2,0 B: 1,-5 C: 4,-3
Step-by-step explanation:
w
The table shows how much money Tearra has after buying some games and represents a linear function.
Number of games 0 1 2 3
Amount of money $106.50 $71 $35.50 $0
What is the yintercept of the function shown in the table, and what does it represent?
A. The y-intercept is (0,106,50). Tearra has $106.50 before buying any games.
B. The y-intercept is (0,106.50). Tearra spends $106.50 per game.
C. The y-intercept is (3,0), and the 3 represents the number of games Tearra buys.
D. The y intercept is (3,0), and the 3 represents the amount of money Tearra spends per game.
Answers
Answer:
C. The y-intercept is (0, 150). Diego has $150 before buying any
Step-by-step explanation:
Brainlylist?
Step-by-step explanation:
Answer: The answer would be A.
Step-by-step explanation: