ANSWER
[tex]S_{26}=1300[/tex]
EXPLANATION
The sum of an arithmetic sequence whose first term and last terms are known is calculated using
[tex]S_{n}= \frac{n}{2} (a + l)[/tex]
From the given information, the first term of the series is
[tex]a = 7[/tex]
and the last term of the series is
[tex]l = 93[/tex]
The sum of the first 26 terms is
[tex]S_{26}= \frac{26}{2} (7 + 93)[/tex]
[tex]S_{26}= 13 (100)[/tex]
[tex]S_{26}=1300[/tex]
The sum of the first 26 terms of the given arithmetic series is 1300, obtained using the sum formula S = n/2 * (a1 + an) for arithmetic series.
Explanation:To find the sum of the first 26 terms of an arithmetic series whose first term (a1) is 7 and the 26th term (a26) is 93, you can use the formula for the sum of an arithmetic series: S = n/2*(a1 + an). Here, n is the number of terms, a1 is the first term, and an is the nth term. In this case, we have n = 26, a1 = 7, and a26 = 93.
The sum, S, of the series is calculated as follows:
S = 26/2 * (7 + 93) = 13 * (100) = 1300.
Therefore, the sum of the first 26 terms of the arithmetic series is 1300.
The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii.
Answer:
6√2.
Step-by-step explanation:
The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90. Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.
Can someone help me out?
Answer:
see below
Step-by-step explanation:
If you haven't memorized it so you know it already, it takes about 10 seconds with your calculator to discover that ...
arccos((√3)/2) = β = 30°
This fact matches only one answer choice.
Someone, please help. Will Mark brainlist if the answer is correct.
Screenshot it below.
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-9)^2+y^2=4\implies (x-\stackrel{h}{9})^2+(y-\stackrel{k}{0})^2=2^2~\hfill \stackrel{center}{(9,0)} \\\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=4\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=2^2~\hfill \stackrel{center}{(3,2)}[/tex]
Check the picture below.
well, its radius didn't change, anyhow, you know what to check out.
Answer:
The circle moves left and up
Step-by-step explanation:
The circle's center changes from (9, 0) to (3,2) and the radius stayed the same.
In the figure, AB ||CD and m3=130. What is
m<6 = 180° - m<3
m<6 = 180° - 130°
m<6 = 50°
Answer: m6 equals 50 degrees
Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50
Mr. McGregor has discovered that a large dog can destroy his entire garden in 2 hours and that a small boy can do the same job in 1 hour. How long would it take the large dog and the small boy working together to destroy Mr McGregor's garden?
The large dog and small boy working together will take 2/3 hour to destroy Mr McGregor's garden.
Explanation:To solve this problem, we can add the rates at which the large dog and the small boy work together:
Large dog's rate = 1 garden / 2 hours = 1/2 garden per hour
Small boy's rate = 1 garden / 1 hour = 1 garden per hour
Combined rate = 1/2 garden per hour + 1 garden per hour = 3/2 gardens per hour
Now, we can use the combined rate to find the time it would take for the large dog and the small boy to destroy Mr. McGregor's garden:
Time = 1 garden / Combined rate = 1 garden / (3/2 gardens per hour) = 2/3 hour
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Which explanation best describes how to solve this problem? Marcia covered her kitchen floor with twice as much tile as her bathroom floor. She tiled 15 square feet of her bathroom floor. She also tiled a 9-square-foot area by her front door. How many square feet of her house did Marcia tile altogether?
Answer:
54 ft^2
Step-by-step explanation:
Bathroom area is 15 ft^2
The kitchen is twice the bathroom
2*15 = 30 ft^2
Kitchen: 30 ft^2
Front door: 9ft^2
The total is all the areas added together
Total = bathroom + kitchen + front door
= 15 ft^2 + 30 ft^2 + 9 ft^2
= 54 ft^2
Tammy mixes the letters s, c, h, o, o, and l thoroughly. without looking, allen draws one letter. expressed as a fraction, decimal, and percentage, what is the probability that allen will not select a consonant? (1 point)
There are 6 letters: (4 consonants, 2 vowels)
The probability that Allen will not select a consonant is: (2/6 which simplifies to 1/3) because there are only 2 letters out of the 6 that are not consonants
Fraction: 1/3
Decimal: 0.3333
Percentage: 33.33%
The probability that Allen does not select a consonant is 1/3 as a fraction, 0.3333 as a decimal, and 33.33% as a percentage.
You've asked what the probability is that Allen will not select a consonant when drawing one letter from the mix of letters 's, c, h, o, o, l'. First, let's determine how many vowels and consonants there are in the selection. We have two vowels ('o', 'o') and four consonants ('s', 'c', 'h', 'l'). This gives us a total of six letters.
To find the probability of not selecting a consonant, we look at the likelihood of selecting a vowel instead, since those are the only two types of letters available. There are 2 vowels out of a total of 6 letters. The probability as a fraction is thus 2/6, which simplifies to 1/3.
To express this probability as a decimal, divide the numerator by the denominator: 1 divided by 3 equals approximately 0.3333. Finally, to express this as a percentage, multiply the decimal by 100 to get 33.33%.
In summary:
Fraction: 1/3Decimal: 0.3333Percentage: 33.33%The fish population of Lake Collins is decreasing at a rate of 5% per year. In 2004 there were about 1,350 fish. Write an exponential decay function that models this situation. Then find the population in 2010.
Answer:
Part 1) The exponential function is equal to [tex]y=1,350(0.95)^{x}[/tex]
Part 2) The population in 2010 was [tex]992\ fish[/tex]
Step-by-step explanation:
Part 1) Write an exponential decay function that models this situation
we know that
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
y ----> the fish population of Lake Collins since 2004
x ----> the time in years
a is the initial value
b is the base
we have
[tex]a=1,350\ fish[/tex]
[tex]b=(100\%-5\%)=95\%=0.95[/tex]
substitute
[tex]y=1,350(0.95)^{x}[/tex] ----> exponential function that represent this scenario
Part 2) Find the population in 2010
we have
[tex]y=1,350(0.95)^{x}[/tex]
so
For [tex]x=(2010-2004)=6\ years[/tex]
substitute
[tex]y=1,350(0.95)^{6}=992\ fish[/tex]
Final answer:
The exponential decay function for the fish population in Lake Collins is P(t) = 1350 * e^(-0.05t). Using this, the estimated fish population in 2010 is about 1,000.
Explanation:
We need to write an exponential decay function to model the decreasing fish population in Lake Collins and then use it to find the population in 2010.
To create an exponential decay function, we can use the formula P(t) = P0 * e^(rt), where:
P(t) is the population at time t,
P0 is the initial population,
r is the rate of decay (as a negative value), and
t is the time in years since the initial count.
Given the initial population of 1,350 fish in 2004 and a decay rate of 5% per year, we can write the function as:
P(t) = 1350 * e^(-0.05t)
To find the population in 2010, we first calculate the time passed since 2004, which is 6 years. Thus, t = 6:
P(6) = 1350 * e^(-0.05*6)
Calculating this gives us:
P(6) ≈ 1350 * e^(-0.3) ≈ 1350 * 0.740818 ≈ 1000 (rounded to the nearest whole number)
Therefore, the fish population in 2010 was approximately 1,000 individuals.
Write an explicit rule and recursive rule for a geometric sequence with a second term of 6 and a third term of 12.
Step-by-step answer:
Given:
Geometric sequence with
second term, T2 = 6
third term, T3 = 12
Wants to have the explicit and recursive rules.
Solution:
common ratio, r = 12/6 = 2
Therefore the first term, T1
= second term /r
= 6/2
=3
Thus the absolute rule is
Tn = T1 *r^(n-1) where T1 = 3, r=2. Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good
The recursive rule (depending on the previous term)
Tn = Tn-1*r = 2*Tn-1
The explicit rule for the sequence is a_n = 3 * 2^(n-1), and the recursive rule is a_n = a_(n-1) * 2. These were determined by identifying the common ratio of the sequence as 2.
Explanation:In a geometric sequence, each term is generated by multiplying the previous term by a common ratio. Given the second term (6) and third term (12) in the sequence, we can identify the common ratio by dividing the third term by the second term. So, 12 divided by 6 equals 2. Therefore, the common ratio is 2.
So, the explicit rule (the nth term) of this sequence would be: a_n = a_1 * r^(n-1) = 6 / 2 * 2^(n-1) = 3 * 2^(n-1).
The recursive rule for the sequence would be: a_n = a_(n-1) * r = a_(n-1) * 2.
To summarize, we determined the common ratio to be 2 by dividing the third term by the second term. We then used this ratio to create the explicit and recursive rules for the geometric sequence.
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Use the domain and range of each of the following relations to determine which is a function.
Answer:
a) Function
b) Not a function
c) Function
d) Not a function
Step-by-step explanation:
a) Domain = { 7,-6,2}
Range = {5,0,3}
It is a function as every value in domain has some and unique value mapped to it in Range
b)
Domain = { 7,-6,2}
Range = {5,0,-2,3}
It is not a function as -6 value in domain has two values mapped to it in Range
c)
Domain = { 7,2}
Range = {-6,-7}
It is a function as every value in domain has some and unique value mapped to it in Range
d)
Domain = { 7,-6}
Range = {5,0,3}
It is not a function as 7 value in domain has two values 3 and 5 mapped to it in Range
Jackie contributed a batch of baklava to the school bazaar. There are 12 pieces in a batch, and each piece sells for $1.50. If all the baklava is sold, what will Jackie's total contribution to the school be?
Answer:
Jackie's total contribution the school would be $18.00
Step-by-step explanation:
Jackie's contribution to the school bazaar = a batch of baklava
No. of pieces in a batch = 12 pieces
Price of one piece = $1.50
CASE: All baklava is sold
No. of pieces of Baklava sold = 12 pieces
Price of 12 pieces of Baklava = no. of pieces * Price of one piece
= 12 * $1.50
= $18.00
If a right circular cone is intersected by a plane that goes through both napped of the cone but not through the vertex, as in the picture below, what shape is produced?
Answer:
F. Hyperbola
Step-by-step explanation:
In each napped, you'll have a parabola, combined they form an hyperbola.
It's one of the various shapes that can be produced by a plane intercepting a right circular cone, as you can see in the attached picture.
Each plane intersection is different, based on the angle and the position it passes through.
I hope that helps.
Answer:
hyperbola
Step-by-step explanation:
apeex
Three friends buy one pack of 80 stickers. T hey divide the stickers equally and give the remainder to their teacher. How many will each friend get?
Answer:
26
Step-by-step explanation:
80 divided by three = 26.666666
26 times 3 = 78
2 leftover
The number sticker each student get is 26 and the number stickers teacher got is 2.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, three friends buy one pack of 80 stickers.
Now, number of stickers each friend = 80/3
3|80|26
78
_____
2
Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.
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Simplify 3ab + 4ab + 5
12ab
7ab + 5
not possible
Answer:
7ab+5
Step-by-step explanation:
add like terms (3ab+4ab=7ab)
5 doesn't have a like term so it stays by itself
Hey there! :)
3ab + 4ab + 5
In order to simplify this, we must add like terms. In addition, when simplifying, you can ONLY add like terms.
Since both "3ab" & "4ab" contain "ab," you are able to combine them together!
When combining like terms, you only add the numerical value, not the letters.
This leaves us with : 7ab + 5
Therefore, your answer is 7ab + 5
~Hope I helped!~
PLEASE HELP ASAP 45 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
The answer is C. I have the work for it in the image bellow
Hope this helped!
~Just a girl in love with Shawn Mendes
A survey of patients at a hospital classified the patients by gender and blood type, as seen in the two-way table. Gender Blood Type Male Female TOTAL A 105 93 198 B 99 84 183 O 160 140 300 AB 15 18 33 TOTAL 379 335 714 What percent of all patients are blood type AB? Round your answer to the nearest tenth of a percent. Type a numerical answer in the space provided. Do not include % or spaces in your answer.
Answer:
4.6
Step-by-step explanation:
We are given the results of a survey of patients at a hospital of their blood type, categorized by their gender.
We are to find the percentage of patients with blood type AB among all patients.
Number of patients with blood type AB = 33
Total number of patients = 714
Percent of patients with blood type AB = [tex] \frac { 3 3 } { 7 1 4 } \times 100 [/tex] = 4.6
Which choice is equivalent to the fraction below when x is greater than or equal to 2?
Answer:
D. 2(√{x} + √{x - 2})
Step-by-step explanation:
As hinted in the question, we have to simplify the denominator.
To understand it easier, let's imagine we have x - y in the denominator. If we multiply it with x + y we'll get x² - y², right? Check the next line:
(x - y) (x + y) = x² + xy -xy - y² = x² - y²
If we have the square of those nasty square roots, it will be much simpler to deal with. So, let's multiply the initial fraction using x+y, but with the real values:
[tex]\frac{4}{\sqrt{x} - \sqrt{x - 2} } * \frac{\sqrt{x} + \sqrt{x - 2}}{\sqrt{x} - \sqrt{x - 2}} = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} }[/tex]
Then we simplify:
[tex]\frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(x) - (x - 2) } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{ 2 } = 2(\sqrt{x} + \sqrt{x - 2})[/tex]
Answer is D. 2(√{x} + √{x - 2})
The hypotenuse of a 45°-45°-90° triangle measures 128 cm. What is the length of one leg of the triangle?
Answer:
90.51 (rounded to the nearest hundredth)
Step-by-step explanation:
We can use trigonometry to figure this out
sin = opposite side / hypothenuse
The 45° angle's opposite side is a leg of the triangle
sin 45 = leg / 128
sin 45 * 128 = (leg / 128 ) * 128
0.7071 * 128 = leg
90.51 = leg
Answer:
b
Step-by-step explanation:
The diameter of the base of the cone measures 8 units.
The height measures 6 units.
What is the volume of the cone?
Answer: [tex]32\pi[/tex] cubic units.
Step-by-step explanation:
You can use this formula for calculate the volume of a cone:
[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:
[tex]r=\frac{8units}{2}\\\\r=4units[/tex]
Since you already know that height and the radius, you can substitute them into the formula. Then, the volume of this cone is:
[tex]V_{cone}=\frac{1}{3}\pi (4units)^2(6units)[/tex]
[tex]V_{cone}=32\pi \ units^3[/tex]
Answer: 48
Step-by-step explanation:
You flip a fair coin what is the probability that it show heads on the first flip and it shows how tails on the second flip
Answer:
25% = 1/4
Step-by-step explanation:
It is 25% because there are 4 outcomes that you can get which are
HT, TH, HH, TT
H = Head
T = Tail
and out of the four outcomes, there is one that will be Head first and Tails on the second flip. So 1 out of 4 = 25%
A student rolls a number cube Whose six faces are numbered 1 through 6 what is the sample space for this experiment.
Answer:
It depends on how you define an outcome.
Usually, the outcomes are considered to be the number showing on the top face of the die (number cube) when it comes to rest on a horizontal surface. If that is how you define outcomes, then the sample space is the set of numbers 1–6: {1, 2, 3, 4, 5, 6}.
Step-by-step explanation:
"This experiment" covers a lot of territory. The student could be checking to see if the die stays on the table or falls to the floor. The student could be experimenting to see if the die changes color or makes a certain kind of noise. The experiment could involve the number of times the die rolls over to a new face before it comes to rest. Until the experiment is properly defined, the sample space is unknown.
If the experiment is to see what number shows on the top face of the die at rest on a horizontal surface, then the sample space is presumably the set of numbers 1 through 6.
Please help me please
Answer:
b = 17
Step-by-step explanation:
Since PQ = RQ then ΔPQR is isosceles and QS is a perpendicular bisector
Hence PS = RS = 17 ⇒ b = 17
Which expression represents the area of the triangle drawn below (4x-3) (2x-1) (4x-2) (3x-3)?
Answer:
option C
Step-by-step explanation:
Area of the triangle=4x²+4x+1
What is the solution to the equation below?
Please show work.
Answer:
x = -9
Step-by-step explanation:
Multiply both sides by √(x - 6) to eliminate the fraction:
√(3x) = 3√(x - 6)
Now square both sides:
3x = 9(x - 6), or 3x = 9x - 54.
Combining the x terms results in -6x = -54, and thus x = 9.
Answer:
The correct answer is option D. x = 9
Step-by-step explanation:
From the attached question we get an expression,
√3x/√(x - 6) = 3
To find the solution of given expression
√3x/√(x - 6) = 3
Squaring both side we get,
3x/(x - 6) = 9
3x = 9 * (x - 6)
3x = 9x - 54
9x - 3x = 54
6x = 54
x = 54/6 = 9
Therefore the correct option is D. x = 9
please help me figure out the radius
Answer:
Step-by-step explanation:
<EAF is a central angle. Its measure is 12o
Arc EF has angular measure of 12 degrees as well.
The formula for the arc length in cm is
Arc length = (given arc angle/360) * 2 * pi * r
r = 30 cm which is given
Given arc angle = 12 degrees.
Arc length = (12/360) * 2* pi * r
Arc length = 1/30 * 2*pi * 30
Arc length = 6.28
A parking lot has sixty-one parking spaces numbered from 1 to 61. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 22?
A. 61/21
B. 40/61
C. 61/40
D. 21/61
Answer:
B. 40/61
Step-by-step explanation:
There are 40 spots out of the 61 in the lot with numbers greater than or equal to 22. The probability of choosing one of them at random is 40/61.
_____
About the answer choices
61/21 and 61/40 are both numbers that are greater than 1. A probability is always a number between 0 and 1 (inclusive), so these answers can be rejected immediately.
There are 21 spots with numbers less than 22, so 21/61 is the probability of choosing one of those. That is not what the question is asking for.
Heo started to solve the quadratic equation (x + 2)2 – 9 = –5. He added 9 to both sides and the resulting equation was (x + 2)2 = 4. Next, he took the square root of each side. Which was the resulting equation of that step?
Step-by-step explanation:
After taking the square root:
x + 2 = ±2
Notice that x + 2 can also equal -2, because (-2)² = 4.
Graph the system of equations on graph paper to answer the question.
{y=14x+3
{y=2x+10
What is the solution for this system of equations?
Answer:
(x, y) = (7/12, 11 1/6)
Step-by-step explanation:
A graph will show you the solution is near (x, y) ≈ (0.6, 11.2). For an exact answer, an algebraic solution is indicated.
Subtracting the second equation from the first gives ...
0 = 12x -7
7/12 = x
Substituting for x in the second equation gives ...
y = 2(7/12) +10 = 7/6 +10
y = 11 1/6
Phillip has a box of crayons. 45 are yellow, 12 are green, 25 are blue, and 7 are red. If Phillip selects a crayon at random, which color crayon would he be MOST likely to select? Why?
Answer:
yellow b/c there are the most
Step-by-step explanation:
Fred's dog groomer charges $25 to give his dog a haircut. The groomer is increasing the price for a haircut by 35%. What will Fred pay the groomer the next time his dog has a haircut?
Answer:
33.75
Step-by-step explanation:
Step 1- Find the decimal form of 35%
Step 2- When you find that multiply that by 25
Step 3- When you find the answer to step 2 add that to 25
That is your answer
Final answer:
The price that Fred will pay the groomer the next time when his dog has a haircut is $33.75.
Explanation:
The question asks us to calculate the new price Fred will pay for his dog's haircut after the groomer increases the price by 35%. To find the new price, we'll use the formula for calculating percentage increase, which is: New Price = Original Price + (Original Price * Percentage Increase).
First, convert the percentage increase to a decimal by dividing it by 100, so 35% becomes 0.35. Then, multiply the original price of $25 by 0.35 to find the amount of the increase, which is $8.75.Finally, add the increase to the original price to find the new price, which is $25 + $8.75 = $33.75. So, Fred will pay $33.75 the next time his dog has a haircut.