The sum of the fifth and sixth term of an AP is 30.If the third term is 5.Find the first term.
Answer:
The first term is -3.
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between two consecutive terms is always the same, and it is called common difference d.
The nth term is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term.
If we have the mth term instead of the first, we have:
[tex]a_n = a_m + (n-m)d[/tex]
We have the third term, and need the fifth and the sixth:
So we write both the fifth and the sixth in function of the third, then:
[tex]a_5 = a_3 + 2d = 5 + 2d[/tex]
[tex]a_6 = a_3 + 3d = 5 + 3d[/tex]
The sum of the fifth and sixth term of an AP is 30
We use this to find [tex]d[/tex]. So
[tex]a_5 + a_6 = 30[/tex]
[tex]5 + 2d + 5 + 3d = 30[/tex]
[tex]5d + 10 = 30[/tex]
[tex]5d = 20[/tex]
[tex]d = \frac{20}{5} = 4[/tex]
First term:
The third term is:
[tex]a_3 = a_1 + 2d[/tex]
Since [tex]a_3 = 5, d = 4[/tex]
[tex]a_1 = a_3 - 2d = 5 - 8 = -3[/tex]
The first term is -3.
are these two triangles congruent? if so state, how you know.
Answer:
by SSS axiom
hope it helps.
Answer:
Step-by-step explanation:
Yes
the two sides that are marked make 2/3 of the sides needed for SSS
The line shared by both triangles make the third side.
Answer: SSS
HELP me pls pls I beg you
Answer:B 25%
Step-by-step explanation:
6 people had 6-8 and there are 24 total people so the fraction is 6/24 which is equivalant to 1/4 which equals 25%
Answer:
25%
Step-by-step explanation:
add up all you get 24
add absences between 6 and 8 you get 6
6/24= 25
You want to know if the students in your school have been to your town’s skate park. You randomly survey 50 of the 1100 students at your school. Of those surveyed, 15 have been to the skate park and 35 have not. You conclude that 30% of the students in your school have been to the skate park. Which statement below best describes your conclusion
Answer:
Step-by-step explanation:
The conclusion is invalid
The number of fish in a pond triples every 7 years. By what percent does the population change each year? 0 17% decay O 117% growth O 17% growth O 85.5% growth
Answer: O 17% growth it was a little bit confusing but this is the answer I came up with
Step-by-step explanation: hope it helps
Find the value of the trigonometric ratio.
Answer:
D
Step-by-step explanation:
sin=opposite/hypotenuse
Sinx=40/41
The Ratio of 5 cows for every 2 dogs is equivalent to what ratio?
A. 20:8
B. 6/12
C. 4 to 10
( If it is right I will mark it as brainiest ong)
20:8
Step-by-step explanation:
5:2
20:8
5×4= 20 and 2×4= 8
Answer:
A is the right answer. If you multiply the ratio 5: 2 by 4 it will give you 20:8
Find the sum of the angle measures in a regular polygon.
A) 720*
B) 900*
C) 1080*
D) 1260*
Please help!! Thanks
Answer:
D) 1260°
Step-by-step explanation:
In an n-sided polygon, the sum of all angles is equal to (n-2)*180°.
Look at it this way - let's add a point in the middle and connect it to each vertex. Then we've got n triangles for a total of n*180°, but all of the angles at the middle point aren't "part" of the polygon, so a full 360° angle should be subtracted, giving us n*180°-360° = (n-2)*180°
You can easily confirm that it works for triangles and quadrangles ;)
The figure in the picture has 9 sides, so the sum of angles is (9-2)*180° = 7*180° = 1260°
1260°
hope this helps ^-^
A bakery sells 12 cupcakes for $10. A Super Market sells 10 cupcakes for $8. Which store is cheaper per cupcake? *
Answer:
Step-by-step explanation:
hope this help
Answer: the super market is cheaper
Which two tables represent data sets that could be fit to a normal distribution curve? A. value 1 2 3 4 5 6 7 8 9 10 11 percentage 1.5% 2.1% 2.2% 3.3% 3.9% 10.5% 14.1% 14.7% 15.3% 15.9% 16.5%
B. value 1 2 3 4 5 6 7 8 9 10 11 percentage 2.3% 4.4% 6.8% 11.4% 20.2% 27.8% 14.1% 7.6% 3.2% 1.5% 0.7%
C. value 2 3 4 5 6 7 8 9 11 10 C. percentage 19.2% 17.3% 6.9% 5.4% 2.9% 0.8% 2.8% 4.6% 7.3% 15.7% 17.1%
D. value 1 2 3 4. 5 6 7 8 9 10 11 percentage 21.3% 15.1% 14.8% 12.3% 8.1% 7.9% 6.3% 5.5% 4.8% 2.3% 1.6% 1 3 2 4 E.value 5 6 9 8 7 10 11 E. percentage 1.2% 2.9% 3.3% 7.9% 17.1% 35.2% 16.7% 8.4% 4.1% 2.3% 0.9%
Answer: i put b and e
Step-by-step explanation:
i got it from the person above me lol
Option C is the only table that represents a data set that could be fit to a normal distribution curve.
In a normal distribution, the data is symmetrically distributed around the mean, and the percentages decrease as you move away from the mean.
Option C exhibits this characteristic, where the percentages are highest at the mean values (5, 6, 9, 10) and decrease as you move away from the mean.
Where as the tables in options A, B, and D do not exhibit the characteristics of a normal distribution as the percentages do not decrease symmetrically away from the mean values.
To learn more on Statistics click:
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Please may I have some help thank you x
Answer:
I think x=2 because
3x4=12
12×2=24
×=2
Answer:
Th answer is 2cm
Step-by-step explanation:
3 x 4 = 12
24 / 12 = 2
find the measure indicated. Assume that the lines which appear to be tangent are tangent. Part 4
NO LINKS OF ANY KIND
The angle between the two tangents drawn from an external point to a circle and the angle subtended by the line segment joining the points of the contact at the Centre are supplymentary,
So,
15.) let the unknown angle be x
=》x + 55° = 180°
=》x = 180° - 55°
=》
[tex] \boxed{x = 125°}[/tex]
16. let the unknown angle be n
=》n + 80° = 180°
=》n = 180° - 80°
=》
[tex] \boxed{n = 100°}[/tex]
9514 1404 393
Answer:
15) 125°
16 100°
Step-by-step explanation:
The short arc where two tangents intersect a circle, and the angle where the tangents meet are supplementary.
__
15) ? = 180° -55° = 125°
16) ? = 180° - 80° = 100°
_____
Additional comment
The quadrilateral formed by the tangents and the radii to the points of tangency has a total interior angle measure of 360°. The angles where the radii meet the tangents are 90°, so the sum of the external angle and the central angle is 360° -90° -90° = 180°. That is, the external angle and the central angle are supplementary.
2. 2 1 1 3
5' 4210
I
Arrange the fractions in ascending order.
D a) 1 1 2 3
2' 4' 5' 10
O c 1 3 2 2 1
4' 10' 5' 2
b) 3 2 1 1
10' 54'2
I
d) 1 2 1 3
2' 5' 4' 10
Answer:
a.1 1 2 3
2'4'5'10 that is ig
please help ill mark brainlist!!!
On a test a student got 15 problems correct out of a total of 20 problem.
What percent did the student get incorrect?
Answer:
1/4 or 25%
Step-by-step explanation:
Answer: 25%
Step-by-step explanation:
15/20=0.75
0.75x100=75
100-75=25
Hope this helped
At the U.S. Open Ternis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 97 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player's serves was between 110 mph and 136 mph
Step-by-step explanation:
At the U.S. Open Tennis Championship, a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 102 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph.
Answer please will make first answer brainliest
Answer:
The last one: 70/100 = x/80
And 56 free throws.
Explanation:
70% is 70 out of 100. And if the player is free throwing a total of 80 times, then 80 is 100% of the free throws. Both of the values that represent 100% are the denominators in the fractions.
[tex]\frac{70}{100} = \frac{x}{80}[/tex]
The equations are equal, and whatever you do to the bottom, you have to do to the top. 100 was multiplied by 4/5 to get 80. So 70 is multiplied by 4/5 to get x.
4/5 * 70 is 56
Help me pls I don't know what to do
A bag contains 20 slips of paper Individually numbered. If a slip of paper and a letter in the word PENNSYLVANIA is chosen at randomfind each probability.
Answer:
[tex]P(M4\ n\ V) = 2.083\%[/tex]
Step-by-step explanation:
Given
Paper = 20 slips
Word: PENNSYLVANIA
Required
Determine P(Multiple of 4 and V)
The sample size of the 20 slips is:
[tex]n(S) = 20[/tex]
The outcomes of multiples of 4 is:
[tex]M4= \{4,8,12,16,20\}[/tex]
[tex]n(M4) = 5[/tex]
So, the probability of multiples of 4 is:
[tex]Pr(M4) = \frac{5}{20}[/tex]
[tex]Pr(M4) = \frac{1}{4}[/tex]
The sample size of PENNSYLVANIA is:
[tex]n(S) = 12[/tex]
The outcome of V is:
[tex]n(V) = 1[/tex]
So, the probability of V is:
[tex]P(V) = \frac{1}{12}[/tex]
So, the required probability is: P(Multiple of 4 and V)
[tex]P(M4\ n\ V) = P(M4) * P(V)[/tex]
[tex]P(M4\ n\ V) = \frac{1}{4} * \frac{1}{12}[/tex]
[tex]P(M4\ n\ V) = \frac{1}{48}[/tex]
[tex]P(M4\ n\ V) = 0.02083[/tex]
Express as percentage
[tex]P(M4\ n\ V) = 0.02083 * 100\%[/tex]
[tex]P(M4\ n\ V) = 2.083\%[/tex]
please help me :(
.....
Answer:
128 i think
Step-by-step explanation:
5x7=32
x=4
32x4=128
2 3/6 boxes and 1 2/3 boxes were recycled what is the total
questions and answer choices attached to photo, please help ASAP :)
Answer:
D
Step-by-step explanation:
10 x 10 x 29 x .5 = 1,450
Find the measure of the indicated angle.
Answer:
fs :)
Step-by-step explanation:
You start at (7,9) in a coordinate plane you move left 7 units. Where do you end
Answer:
You end up at 0,9
Step-by-step explanation:
6.8 + [(0.5 times 7) + (3.1 times 3)] answer
Answer:
19.6
Step-by-step explanation:
find the diameter of a circle with the given dimensions r=13 cm
Answer:
the diameters of circle with radius 13cm
13×226cmhope it helps.
Answer:
your answer is
26 cm
hope it is helpful to you
Working alone, it would take Shandra 40 minutes to sand a table. To sand the same table, also working alone, it would take Kelly 1 hour. If they work together, the situation can be modeled by the following equation, where t is the time it would take to sand the table working together.
StartFraction 1 Over 0.75 EndFraction + StartFraction 1 Over 1.25 EndFraction = StartFraction 1 Over time to complete together EndFraction
Shandra claims it will take them about 50 minutes working together, because 50 is the mean of 40 and 60. Which best describes Shandra’s claim?
Answer: CCCCCC
Step-by-step explanation:
It would take 24 minutes to sand the table working together.
What is an Equation?An equation is used to show the relationship between two or more variables and numbers.
It would take Shandra 40 minutes (2/3 hours) to sand a table while it would take kelly 1 hour.
Let t be the time it would take to sand the table working together. Hence:
(1/(2/3) + 1/1)t = 1
(3/2 + 1)t = 1
2.5t = 1
t = 0.4 hours = 24 minutes
It would take 24 minutes to sand the table working together.
Find out more on Equation at: https://brainly.com/question/2972832
anyone wanna help me with this??
Answer:
1.c
2.b
3. c
4.d
Step-by-step explanation:
leave an brainlest!
Please helppppppppppp
Answer: what are you supposed to find out?
Step-by-step explanation:
Triangles ABC and ADE are similar, as shown. Which must be true? Check all that apply.
AC=AB
AC/AE=BC/DE
AC/AD=AB/AE
DE=2BC
BC=2DE
AC=2AE
AE=2AC
Answer:
AC/AE=BC/DE
AC/AD=AB/AE
DE=2BC
AE=2AC
Step-by-step explanation:
This is what I think.
help ..........................................
Answer:
c. 45d+.25m
Step-by-step explanation: