Arithmetic Sequence
rows ---------32-n
first term ------------26-----------a
d---------------------------4
Sn = n/2( 2a+(n-1)d)
=32/2 (2*26+(31)4)
=16(52+124)
=16(176)
=2816 seats
If theater has 30 rows of seats, then the number of people that the theater will hold is 2400 people.
To find out how many people the theater will hold, we need to calculate the total number of seats across all 30 rows. Since the number of seats increases by 4 for each successive row, we can treat this as an arithmetic sequence.
The formula to find the sum of an arithmetic sequence is = (n/2) × (first term + last term),
where n = number of terms and the first and last terms are given,
In this case : First term = 22,
Last term = 22 + (30 - 1) × 4 = 22 + 116 = 138,
Number of terms (rows) = 30,
Sum = (30/2) × (22 + 138) = 15 × 160 = 2400;
Therefore, The theater will hold 2400 people.
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Given below is an equation of a parabola. What are the coordinates of the vertex?
y = (x + 2)^2
a (–2, 0)
b (2, –2)
c (–2, 2)
d (2, 0)
BEST ANSWER WILL GET BRAINLIEST. Consider the table below. For what value of x does f(x)=-1f(x)=−1 ?
The correct answer would be 3. f(x) = -1, so you got to find the -1 in the y row of the table and just say that x =3 if y =-1.
Answer:
x = 3
Step-by-step explanation:
The question is asking for which value of x gives -1
You don't have an equation, however you do have a table of values
Y is similar to f(x) in the sense that it is the output, while x is the input.
All you must do is see where y = -1, this is the same for when f(x) = -1
So, there is only one moment where y = -1, which is when x = 3
With this, we can conclude that for the value of x = 3, f(x) = -1
Brad's science class is heading to Skylight Observatory on a field trip. The observatory offers
a group rate for students that is $4 less per person than the normal cost. There are 27
students in Brad's science class. His teacher called ahead and found that the total cost for the
class will be $378. What is the normal cost per person?
Answer:
$18
Step-by-step explanation:
378 ÷ 27 = 14
14 + 4 = 18
The normal cost per person = $18
The normal cost per person is $18.
Given,
Brad's science class is heading to Skylight Observatory on a field trip.
The observatory offers a group rate for students that is $4 less per person than the normal cost.
There are 27 students in Brad's science class.
The total cost for the class is $378.
We need to find the normal cost per person.
How do we equally find the cost of each item from the total cost?We divide the total cost by the number of items.
Example:
7 bags cost $49
1 bag cost = $49 / 7 = $7
We have,
The number of students = 27
The total cost of the class trip with the offer = $378
Offer = $4 less than the normal cost per student
Now,
The offer cost for each person:
= $378 / 27
= $14
The normal cost for each person:
= $14 + $4
= $18
Thus the normal cost per person is $18.
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Please help me I need help
Answer:
10
Step-by-step explanation:
Use Pythagorean theorem,
Base² + altitude²= hypotenuse²
8² + altitude² = (2√41)²
64 + altitude² = 2²*(√41)² {(√41)² = √41*√41 = 41}
64 +altitude² = 4 * 41
64 +altitude² = 164
altitude² = 164 - 64
altitude² = 100
altitude = √100 = 10
Please help !!! Aspen scored no fewer than 18 points in her
last basketball game. She scored 6 points on free
throws that are worth 1 point each. The rest of
the points she scored on 3-point field goals.
Which inequality can be used to
determine, p, the number of 3-point field
goals that Aspen made?
Inequalities are used to represent unequal expressions.
The inequality is: (c) [tex]\mathbf{3p + 6 \ge 18}[/tex]
The given parameter is:
[tex]\mathbf{Free = 6}[/tex]
Represent the number of 3-point field goals with p.
So, the total number of points is:
[tex]\mathbf{Total = 3 \times p + Free}[/tex]
[tex]\mathbf{Total = 3 p + Free}[/tex]
Substitute 6 for Free
[tex]\mathbf{Total = 3 p + 6}[/tex]
He scored no fewer than 18 points, means that:
He scored 18 or more points
So, the inequality is:
[tex]\mathbf{Total = 3 p + 6 \ge 18}[/tex]
Rewrite as:
[tex]\mathbf{3p + 6 \ge 18}[/tex]
Hence, the correct option is (c)
Read more about inequalities at:
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Solve the equation by factoring.
x2 – 64 = 0
Answer:
x=32
Step-by-step explanation:
x2 -64 = 0
+64 = +64
x2=64
x2/2 = 64/2
x = 32
hope this helps.
evaluate
8w - 2v if w = 5 and v = 3
Answer:
34
Here's Why:
8w - 2v = ?
8(5) - 2(3) = ?
40 - 6 = 34
Hope this helps!
Tori, Brielle, and Abby, go shopping together. Together they spend $215. Brielle spends twice as much as Tori, and Abby spends one dollar less than three times what Tori spends. How much did each girl spend?
Step-by-step explanation:
Tori + Brielle + Abby = 215
Give Tori spends x.
Brielle ; 2x and Abby ; 3x - 1
so
x + 2x + 3x - 1 = 215
6x - 1 = 215
6x = 216
x = 36
Tori spends $36 Brielle spends $72 and Abby spends $107.
please give me a brainliest answer
Determine which is the better buy.
4 gallons of oil for 9.16$ or 11 gallons of oil for 25.30$
HELP ME PLS
Answer:
4 gallons of oil for $9.16
Step-by-step explanation:
[tex] \frac{4}{9.16} = \frac{1}{x} [/tex]
[tex]4x = 9.16[/tex]
x = $2.29
[tex] \frac{11}{25.30} = \frac{1}{x} [/tex]
11x = 25.30
x = $2.30
4x - 1 < 7 i don’t know what to do
what is 4x+2=-12+6x?????????
Answer:
x=7
Step-by-step explanation:
If you deposit $400 into an account that offers a 5% interest rate. How much interest will you earn after 1 year?
20.00
...............
Problem:
Report Error
On Tuesday, a radio store reduces all of its prices by 20% from what they were on Monday.
On Wednesday, the store again reduces all of its prices by some percentage from what they were on Tuesday. If the resulting price of a radio is half of the original Monday price,
then by what percentage did the store reduce its prices from Tuesday to Wednesday?
Answer/Step-by-step explanation:
Call Monday's price, P
Tuesday's price must just be .80P [ 20% reduction]
Call Wednesday's price reduction ( 1 - R)
So...we have that
Tuesday's price * Wednesday's reduction = (1/2)P
(.80)P *( 1 - R) = (1/2)P divide through by P and note that 1/2 = .50
.80 (1 - R) = .50 divide both sides by .80
1 - R = .50/.80
1 - R = 5/8
1 - 5/8 = R
3/8 = R = .375 = 37.5% = the reduction from Tues. to Wed.
Proof of this...let Monday's price = 100
Tuesdays price = .80 * 100 = 80
Wed price = 80 (1 - R) = 80 (1 - .375) = 50 = half of Mon. price
Evaluate:
[tex] log_{\sqrt{3} }(729) \\ [/tex]
Give answer please..
[tex] \large\underline{\sf{Solution-}}[/tex]
Given Logarithmic expression is
[tex]\rm \longmapsto\: log_{ \sqrt{3} }(729) [/tex]
Let first factorize 729
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:729 \:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:243 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:81\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:27 \:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:9\:\:}}\\\underline{\sf{}}&{\sf{\:\:3 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
So,
[tex] \purple{\rm \longmapsto\:729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3}[/tex]
[tex] \purple{\rm \longmapsto\:729 = {3}^{6} }[/tex]
[tex] \purple{\rm \longmapsto\:729 = {( [{ \sqrt{3} ]}^{2}) }^{6} }[/tex]
[tex] \purple{\rm \longmapsto\:729 = {( \sqrt{3} )}^{12}}[/tex]
So,
[tex]\rm \longmapsto\: log_{ \sqrt{3} }(729) [/tex]
can be rewritten as
[tex]\rm \: = \: log_{ \sqrt{3} }( {( \sqrt{3}) }^{12} ) [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ log_{a}( {a}^{x} ) \: = \: x \: }}}[/tex]
So, using this identity, we get
[tex]\rm \: = \: 12[/tex]
Hence,
[tex] \green{\rm\implies \:\boxed{\tt{ \: \: log_{ \sqrt{3} }(729) \: = \: 12 \: \: }}}[/tex]
What is the value of h?
h = 20
h = 35
h = 55
h = 70
Answer:55
Step-by-step explanation:
Which fraction is equal to
2/8
A. 1/4
B. 2/4
C. 3/4
D. 6/4
E. 4/8
Answer:
a
Step-by-step explanation:
because if you divide 8 by 2 the number 2 goes into 8 4 times so 4 divided by 1 is 4 because 1 goes into 4 4 times
Answer:
a
Step-by-step explanation:
half the fraction
8%2=4
2%2=1
1/4
Dylan invested some money in his bank.
He agreed a simple interest rate of 3% per annum for a period of 2 years.
At the end of the 2-year period the value of his investment increased by £72.
Work out the value of Dylan's initial investment.
two years at 3% = .03*2 = .06
so
.06 times original deposit = 72
so 72/.06
which is
1200
Help me!
A 180
B 115
C 65
Answer:
ik this
Step-by-step explanation:
i believe its 180
Answer: B) 115
Step-by-step explanation: i hop this help if not sorry :(
It is roughly 5,900 miles to fly from Denver to Rio de Janeiro. If it takes the airplane roughly 12 hours to reach its destination of Rio de Janeiro, what was the average speed of the airplane in feet per hour?
Answer:
I think I know !
Step-by-step explanation:
Surface of a rectangular prism15 cm depth6 cm width7.5 cm height
Answer:
675 is the surface rectangle
Step-by-step explanation:
multiple the depth width and height together
The prices (in dollars) for a particular model of digital camera with 6.0
megapixels and an optical 3X zoom lens are shown here for 10 randomly selected online
retailers. Find 95% confidence interval of the true mean price for this particular
model.
225 240 215 206 211 210 193 250
225 202
Using the data given, the 95% confidence interval of the true mean is (205.20 ; 230.20)
Given the data :
225 240 215 206 211 210 193 250 225 202The confidence interval is defined as :
Since, sample size ls less than 30 we use a t-distribution table :
[tex] C.I = \bar{x} ± t_{α/2, n-1} \frac{s}{\sqrt{n}}[/tex]
Zcritical = [tex]t_{0.05/2, 9} = 2.26 [/tex] n = sample size = 10Using a calculator :
Mean, [tex]\bar{x} = 217.7 [/tex] Standard deviation, σ = 17.49Lower boundary = [tex] 217.7 - 2.26(\frac{17.49}{\sqrt{10}}) = 205.20[/tex]
Lower boundary = [tex] 217.7 + 2.26(\frac{17.49}{\sqrt{10}}) = 230.20[/tex]
Therefore, the confidence interval is (205.20 ; 230.20)
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The confidence interval is simply a range that contains the true mean of the population
The 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]
The given parameter is:
[tex]\mathbf{n = 10}[/tex]
Start by calculating the degree of freedom
[tex]\mathbf{df = n - 1}[/tex]
[tex]\mathbf{df = 10 - 1}[/tex]
[tex]\mathbf{df = 9}[/tex]
Next, calculate the mean
[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]
[tex]\mathbf{\bar x = \frac{225 + 240 + 215 + 206 + 211 + 210 + 193 +250 + 225 + 202}{10}}[/tex]
[tex]\mathbf{\bar x = \frac{2177}{10}}[/tex]
[tex]\mathbf{\bar x = 217.7}[/tex]
Calculate the standard deviation
[tex]\mathbf{\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n-1}}}[/tex]
[tex]\mathbf{\sigma = \sqrt{\frac{(225 -217.7)^2+ (240 -217.7)^2+..........+ (202 -217.7)^2}{10-1}}}[/tex]
[tex]\mathbf{\sigma = \sqrt{\frac{2752.1}{9}}}[/tex]
[tex]\mathbf{\sigma = 17.49}[/tex]
Calculate the standard error
[tex]\mathbf{SE = \frac{\sigma}{\sqrt n}}[/tex]
[tex]\mathbf{SE = \frac{17.49}{\sqrt {10}}}[/tex]
[tex]\mathbf{SE = 5.53}[/tex]
At 95%, df = 9. the t-value is:
[tex]\mathbf{t= 2.262}[/tex]
So, the confidence interval is:
[tex]\mathbf{CI = \bar x \pm t \times SE}[/tex]
So, we have:
[tex]\mathbf{CI = 217.7 \pm 2.262 \times 5.53}[/tex]
Split
[tex]\mathbf{CI = (217.7 - 2.262 \times 5.53, 217.7+ 2.262 \times 5.53)}[/tex]
[tex]\mathbf{CI = (205,19, 230.20)}[/tex]
Hence, the 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]
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A
32°
B
D
=
С
m2C = [?]
Enter the number that belongs in
the green box
Enter
Answer:
58°
Step-by-step explanation:
in ΔABD
∠ADB = 32°
∠DBA = 90°
∠BAD = 180° - (32 + 90)
∠BAD = 58°
As ΔBAD ≅ ΔBCD
∠BAD = ∠BCD
So ∠BCD = 58°
The table shows the number of miles 3 runners ran last week. Order the numbers from least to greatest. Which runner ran the farthest? How do you know
If you edit the question or repost I can answer if you provide an image! :D
Answer:
Step-by-step explanation:
The order of the decimals are 15.03, 15.2, then 15.25. Casey ran the farthest. (Casey is 15.25) I hope this helps you even though this was 2 weeks ago. :>
Determine how many centimeters are in 1 yard if there are 2.54 centimeter per inch and 3 feet in a yard.
Answer:
91.44 cm
Step-by-step explanation:
2.54 x 12 = 30.48 cm per foot
30.48 x 3 = 91.44cm
An ant moves at 14 cm a min. How many minutes will it take him to travel 10 points
364 cm? What is the time ? (Write your answer in "t=" form)
Answer:
26 minutes/ t=26
Step-by-step explanation:
F) c=14t
S) 364=14t
E) t=26
Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression that can be used to determine
the final cost of the DVD.
Answer:
0.88%y + 0.03%
K12 is how i know the answer
A stray dog ate 4 of your muffins. That was 2/9 of all of them! How many are left?
Answer:
14muffins are left. please give brainliest
Step-by-step explanation:
so first we need to figure out how many there are in total so if 4 muffins is 2/9 so every 2 muffins is 1/9 so we need 9x2 wich is 18 so there are 18 muffins in total but the stray dog ate 4 of them so 18-4 is 14 so the answer is 14muffins are left.
what is 3.26% of 1298
Answer:
42.3148
Step-by-step explanation:
3.26% of 1298
3.26/100*1298
42.3148
can someone please explain this
Answer:
11) is a
12) all answers are incorrect just put b
Step-by-step explanation:
Answer:
あなたをあきらめるつもりはありません
リック・アストリーの歌
Step-by-step explanation:私たちは愛する見知らぬ人ではありません
あなたはルールを知っています、そして私もそうです
完全なコミットメントは私が考えていることです
あなたは他の人からこれを取得しないでしょう
気分を伝えたいだけです
お奨めはあなたに理解させる
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
私たちは長い間お互いを知っていました
あなたの心は痛んでいますが、あなたはそれを言うには恥ずかしがり屋です
内部では、私たち二人は何が起こっているのかを知っています
私たちはゲームを知っていて、それをプレイするつもりです
そして、あなたが私にどのように感じているか尋ねれば
あなたが盲目すぎて見ることができないと私に言わないでください
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
決して与えるつもりはない、決して与えるつもりはない
（あきらめて）
私たちは長い間お互いを知っていました
あなたの心は痛んでいますが、あなたはそれを言うには恥ずかしがり屋です
内部では、私たち二人は何が起こっているのかを知っています
私たちはゲームを知っていて、それをプレイするつもりです
気分を伝えたいだけです
お奨めはあなたに理解させる
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
Which graph does not represent a function?
Answer:
the full circle one
Step-by-step explanation:
use the vertical line test. Hold up a pen on any given spot in the graph (the pen has to be vertical) and if it goes through the line in 2 or more different places its not a function