Answer:
S₁₃ = 455
Step-by-step explanation:
the sum to n terms of an arithmetic is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
We require to find both a₁ and d
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₄ = 20 and a₁₃ = 65 , then
a₁ + 3d = 20 → (1)
a₁ + 12d = 65 → (2)
subtract (1) from (2) term by term to eliminate a₁
9d = 45 ( divide both sides by 9 )
d = 5
substitute d = 5 into (1) and solve for a₁
a₁ + 3(5) = 20
a₁ + 15 = 20 ( subtract 15 from both sides )
a₁ = 5
Then
S₁₃ = [tex]\frac{13}{2}[/tex] [ (2 × 5 ) + (12 × 5 ) }
= 6.5 (10 + 60)
= 6.5 × 70
= 455
A city population which was initially 15,500 has been decreasing 3% a year. What will the population be after five years? Round your answer to the nearest whole number
Answer:
3% = .03 x 15,500 = 465 / yr
465/yr x 5yrs = 2325
15,500 - 2325 = 13,175
Step-by-step explanation:
Jahnay wants to estimate how many ducks there are in her local park.
One day she puts a non-harmful tag on 20 of the ducks in the park.
The next day she catches 27 ducks and notices that 3 of these have a tag on them.
Work out an estimate for the total number of ducks in her local park.
Answer:
44 aproximately
Step-by-step explanation:
She puts a tag on 20 of them, the next day she catches 27 and notices 3 of them have a tag so we substract 27-3=24 we add 24 to the initial number of ducks (20) and the result is 44
Step-by-step explanation:
27÷3×20=180
or
3/27=20/n =180
so the numbers of ducks in her local park is 180
Find the missing angle.
Answer:
? = 56
Step-by-step explanation:
I've attached my work
Hope it helps, let me know if you have questions !
Have a nice rest of your day :)
In a game, if you roll a 6 on a 6-sided number cube, you lose a turn. (a) What is the probability that you roll a 6? Explain your reasoning. (b) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning. (c) What is the probability that you don't roll a 6? Explain your reasoning
The total cost of 4 sodas and 6 patties is $840. If a customer buys 5 sodas and 5 patties, the total cost is $800. What is the cost of 1 soda and 1 patty?
Answer:
S = $76 and P = $236
Step-by-step explanation:
Let the sodas be S and the patties P. So
4S + 6P = 840 and 5S + 5P = 800
By substitution method we will have the solution
5S + 5P = 800
5S = 800 - 5P
S = 800 - 5P
5
We'll sustitute S with this equation
4S + 6P = 840
[tex]4(\frac{800 - 5P}{5})[/tex] + 6P = 80
4(800 - 5P) + 6P(5) = 840
3200 - 20P + 30P = 840
-20P + 30P = 840 - 3200
10P = -2360
P = -2360
10
P = -236
Since the cost of the patty can't be negative, P = $236
Now that we know the cost of the patty, we can calculate the cost of the soda
S = 800 - 5P
5
S = 800 - 5(236)
5
S = 800 - 1180
5
S = -380
5
S = -76
Here S can't be negative, so S = $76
What is an equation of the line that passes through the points (3,6) and (−3,4)?
Answer:
y = x/3 +5
Step-by-step explanation:
Step1 : finding the slope
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
(3,6) and (−3,4)
m = [tex]\frac{4-6}{-3-3}[/tex]
m = 1/3
Solving for the equation
y-y1 = m(x-x1) , (3,6)
y-6 = 1/3(x-3)
y = x/3 -1 +6
y = x/3 +5
In a school of 900 pupils, 30% are boys and 40% of the boys wear glasses.
How many boys wear glasses?
Answer:
180
Step-by-step explanation:
First, we have to find out how many boys are in the school:
900 * 0.30 = 270
Now, we know that there are 270 boys. Out of these boys we need to find out how many boys have glasses:
270 * 0.40 = 108
180 is our answer.
Lowest common multiple of 10 and 20
Answer:
The lowest common multiple of 10 and 20 is twenty, and the maximum common multiple is 10
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
What is the lowest common multiple of 10 and 20?
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
First let's list a few common multiples of 10 and 20:-
[tex]\Large\textsf{Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100...}}[/tex]
Now, let's list some multiples of 20:-
[tex]\Large\textit{Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160...}[/tex]
Now let's find the Least common multiple (L.C.M.) of 10 and 20:-
[tex]\Large\textsc{The LCM is 20}[/tex]
Good luck with your studies.[tex]\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
The table below represents what type of function?
A. Linear
B. Nonlinear
C. Linear and nonlinear
D. Neither linear nor nonlinear
PLEASEEE I NEED THE ANSWER RIGHT NOWW
Answer:
nonlinear because the second row isn't going up by the same number
One angle on a parallelogram measures 155 what are the measures of the other angle
Answer: 25, 90 ,90
Step-by-step explanation:
One angle on a paralel = 155
=> x+ y + z + 155 = 360
x + y + z = 205 ; x + y ; y + z ; x + z = 180
x + y = 180
=> Z = 205 - 180
Z = 25 Degree
x = y = 90 degree
Mark me as Brainliest pls ! Tysm !
Find the slope will give brainlest
Answer:
See below ~
Step-by-step explanation:
Problem 20
Slope (m) = -4 + 6 / 4 + 5m = 2/9Problem 17
m = rise / runm = 3/1m = 3Problem 19
m = 2 + 3 / 6 - 2m = 5/4Answer:
Problem 20: [tex]\frac{2}{9}[/tex]
Problem 17: 3
Problem 19: [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
The formula to find slope is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Plugging in the given values in each problem, we can solve.
-----------------------------------
Problem 20:
[tex]\frac{-4-(-6)}{4-(-5)}[/tex]
[tex]=\frac{2}{9}[/tex]
-----------------------------------
Problem 17:
[tex]\frac{5-2}{3-2}[/tex]
[tex]=\frac{3}{1} =3[/tex]
-----------------------------------
Problem 19:
[tex]\frac{2-(-3)}{6-2}[/tex]
[tex]=\frac{5}{4}[/tex]
hope this helps!
delete = bad moderator
A Honda fit drove 3,172 km
Find what the gas mileage was for the vehicle used on the trip. Give the details on how you found it by showing the numbers and calculations you performed. Hint: a Honda fit drives 13.5 km per liter.
Answer:
See below ~
Step-by-step explanation:
Let's take an example :
I'm driving a car Z for 1,750 km and it has consumed 70 L of fuel.
===============================================================
Formula for mileage :
Mileage = Distance / Fuel consumed
=============================================================
Solving :
⇒ Mileage = 1,750 km / 70 L
⇒ Mileage = 25 km/L
=============================================================
Understanding by this method :
We can solve for the mileage of a car if we know how much distance it has covered in unit time, and the amount of fuel it has consumed, we can calculate mileage.
What is the value of 5k2−6 when k = 9?
Answer:
84
Step-by-step explanation:
Plug in 9 for k.
5(9)(2) - 6
first: (9)(2) = 9 x 2 = 18
5(18) - 6
second: 5(18) = 5 x 18 = 90
last: 90 - 6 = ?
84
hope this helps
Solve for the value of t
Answer:
T = 12
Step-by-step explanation:
8t+1=97
We move all terms to the left:
8t+1-(97)=0
We add all the numbers together, and all the variables
8t-96=0
We move all terms containing t to the left, all other terms to the right
8t=96
t=96/8
t=12
How many papayas could Star Market buy at Farm B for the same amount of money it spent at Farm A? Enter the answer in the box.
Navya has 104 feet of craft wire that she uses to make earrings. If each pair of earring requires & foot of wire, how hiany pairs of earrings is Navya able to make?
Answer:
14 pairs of earrings
Step-by-step explanation:
Question
Navya has 10 ¹/₂ feet of craft wire that she uses to make earrings. If each pair of earring requires 3/4 foot of wire, how many pairs of earrings is Navya able to make.
Given:
Total wire = 10 ¹/₂ ftWire required to make 1 pair of earrings = 3/4 ftTo calculate the number of pairs of earrings Navya can make, divide the total amount of wire by the wire required to make 1 pair of earrings:
[tex]\begin{aligned}\implies \sf 10\frac{1}{2} \div \dfrac{3}{4} &= \sf \dfrac{21}{2} \div \dfrac{3}{4}\\ \\& = \sf \dfrac{21}{2} \times \dfrac{4}{3}\\ \\& = \sf \dfrac{21 \times 4}{2 \times 3}\\ \\& = \sf \dfrac{84}{6}\\ \\& = \sf 14 \end{aligned}[/tex]
Therefore, Navya can make 14 pairs of earrings.
A lender estimates that the closing costs on a $170,000 home loan will be $6,375.00. The actual closing costs were 4.0%of the loan amount. Determine if the closing costs were higher or
lower than the estimate and by what percent
higher by 0.25%
higher by 0.5%
lower by 0.25%
lower by 0.5%
Answer:
(a) higher by 0.25%
Step-by-step explanation:
The error in the estimate is found by comparing the estimated rate to the actual rate.
__
The rate of estimated closing costs is ...
(estimated cost)/(home cost) × 100% = 6375/170000×100% = 3.75%
The actual rate is 4.00%.
actual - estimate = 4.00% -3.75% = 0.25%
The actual closing costs were higher than the estimate by 0.25%.
Perform the indicated operation and simplify your answer.
7/17+(-6/17)
Answer:
1/17 or 0.059
Step-by-step explanation:
7/17 + (-6/17) = 7/17 - 6/17 = 7-6/17 = 1/17
Dana is attaching a shelf to a wall and needs the shelf to be parallel to the floor. How many degrees should the shelf be
relatve to the foor?
A) O degrees
B) 90 degrees
C) 45 degrees
D) 225 degrees
Explanation:
By definition, the floor is assumed to be level and that means the floor is at a 0 degree angle. The shelf must also have this same angle relative to the floor so we have the shelf and floor as parallel planes. For more info, check out the converse of the corresponding angles theorem.
At the mall, 6 shirts cost $57. Each shirt costs the same amount. At this rate, how much would it cost to buy 4 shirts?
PRETTY PLEASE HELP!!!!
57/6 = $9.50 per shirt
9.50 x 4 = $38
Answer: $38
Answer:
$38
Step-by-step explanation:
57 ÷ 6 = 9.5
9.5 x 4 = 38
hope this helps
have a good day
What’s the answer to this question
Step-by-step explanation:
[tex] = 2(x - 5) ^{2} + 4(x - 5) + 1[/tex]
Now for the first term use the formula :
[tex] {a}^{2} - 2ab + {b}^{2} [/tex]
[tex] = 2( {x}^{2} - 10x + 25) + 4(x - 5) + 1[/tex]
[tex] = 2 {x}^{2} - 20x + 50 + 4x - 20 + 1[/tex]
[tex] = 2 {x}^{2} - 20x + 4x + 50 - 20 + 1[/tex]
[tex] = 2 {x}^{2} - 16x + 31[/tex]
HELP!!
Find x. Round to the nearest tenth.
Answer:
31.9°
Step-by-step explanation:
Applying the Law of Sines,
A = 75°a = 22 cmB = x°b = 12 cm⇒ sin75° / 22 = sin x° / 12
⇒ sin (45 + 30)° / 22 = sin x° / 12
⇒ (1/√2)(√3/2) + (1/√2)(1/2) / 22 = sin x° / 12
⇒ (1/√2)(√3 + 1 / 2) / 22 = sin x° / 12
⇒ 12 × (2.73/2.82) / 22 = sin x°
⇒ x = sin⁻¹ (0.529)
⇒ x = 31.9° (nearest tenth)
What is 1 percent of 510
Answer: " 5.1 " .
____________
Step-by-step explanation:
____________
To find 1 percent (i.e. " 1% " ) of: 510 ;
Note: 1 % = (1 /100) = (1 ÷ 100) ;
Note the following about "dividing by "100" ;
We take the number: "510" in our case;
and move the decimal point "2 (two) places backward" .
We move it "backward" (instead of "forward") because we are "dividing" ;
and we are moving the decimal point "2 (two)" spaces backward; since we are dividing by "100" ; which has "2 (two) zeros" .
So: " (510.) ÷ 100 " ;
Take: " 510." ; and move the decimal point two (2) spaces backward:
5.10.
↩
To get: " 5.10 " ; which we can simplify as:
→ " 5.1 " ; which is our answer.
Hope this is helpful to you! Wishing you well!
____________
I’ll give Brainlylist to whoever gets this correct - Due today
Please and thank you
P.S there’s two boxes called Data set 1 and Data set 2
Answer:
Step-by-step explanation:
Mean: Add all the values and divide by the # of values
Median: The center of the values
Mode: The value that appears the most in the data set
Mean for data set 1: 86
Mean for data set 2: (85+89+71+85+86+91+92+96+87)/2= approximately 86.89
Median for data set 1: 72,75,78,80,88,90,95,98,98
We've sorted it from least to greatest, and the center is 88 because there is 4 values to the left of it, and 4 values to the right. It's at the very center.
Median for data set 2: 71,85,85,86,87,89,91,92,96
The center for this is 87 because it is again, at the absolute center/middle between the data.
Mode for data set 1: 98 because it appears 2 times, which is more often than other values
Mode for data set 2: 85 because it appears most often (2 times) in the data set
Hope this helps! :)
Find the value of the variable that results in congruent triangles
Answer:
y = 5
Step-by-step explanation:
The triangles will be congruent when corresponding sides are congruent. __
We already have ...
KL ≅ NP . . . = 15 mm
JL ≅ MP . . . = 22 mm
So, we need ...
JK ≅ MN
4y +12 = 32 . . . . substitute given values
This will be the case when ...
4y = 20 . . . . . subtract 12
y = 5 . . . . . . . divide by 4
The value of y that makes the triangles congruent is 5.
7. If c 1 b, what is <2?
A. 90
B. Not enough information
C. 82
D. 98
Answer:
A. 90°
Step-by-step explanation:
A perpendicular on a straight line creates 2 right angles.
We know the value of a right angle is 90°.
Hence :
∠2 = 90°
The mean of a math test took by 50 students is 85%. Teo students got 10%
Answer:
88%
Step-by-step explanation:
What is the slope of the line passing through the points
ear Equations
(-2, - 8) and (-3, — 9)₂
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-2)}}} \implies \cfrac{-9 +8}{-3 +2}\implies \cfrac{-1}{-1}\implies 1[/tex]
Answer:
Step-by-step explanation:
(-9 + 8)/(-3 + 2)= -1/-1= 1
Alex jogs 5,000 meters twice a day. How many kilometers does Alex jog each day?
A) 0.01 kilometer
B) 0.1 kilometer
C) 1 kilometer
D) 10 kilometers
1 kilometer = 1000 meters
5000 meters / 1000 = 5 kilometers
5 kilometers x 2 times per day = 10 kilometers per day.
answer: D) 10 kilometers
Solve for TV and SV. Select BOTH correct answers.
tv=8
sv=8√2
tv=8√2
sv-8
Answer:
TV = 8 , SV = 8[tex]\sqrt{2}[/tex]
Step-by-step explanation:
given ST = TV , then
TV = 8
using Pythagoras' identity in the right triangle
SV² = ST² + TV² = 8² + 8² = 64 + 64 = 128 ( take square root of both sides )
SV = [tex]\sqrt{128}[/tex] = [tex]\sqrt{64(2)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{2}[/tex] = 8[tex]\sqrt{2}[/tex]