A middle school took all of its 6th grade students on a field trip to see a ballet at a theater that has 4500 seats. The students left 3105 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
[tex]\bull[/tex]Total number of seats in theatre = 4500
[tex]\bull[/tex]Total number of seats left vacant = 3105
Solution:-[tex]\longrightarrow[/tex]Number of seats occupied = Total number of seats in theatre - Total number of seats left vacant
[tex]\longrightarrow[/tex]Number of seats occupied
[tex]\quad[/tex]= 4500 - 3105
[tex]\longrightarrow[/tex] 1395
[tex]\\[/tex]
Now,
[tex]\begin{gathered}\bull \sf Percentage \:of \:seats \:filled = \frac{Seats \: filled \: by \:6th \:grader }{Total \:number \:of \:seats} \times 100 \% \\\end{gathered} [/tex]
[tex]\begin{gathered}\bull \sf Percentage \: of \:seats \: filled = \frac{1395}{45\cancel{00}} \times \cancel{100} \% \\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf \frac{1395}{45} \% \\\end{gathered} [/tex]
[tex]\begin{gathered}\implies\quad \sf 31 \% \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Thus , 31 % of seats in the theater were filled by the 6th graders on the trip
What is the solution to the equation startfraction m over m 4 endfraction startfraction 4 over 4 minus m endfraction = startfraction m squared over m squared minus 16 endfraction? m = –4 m = –2 m = 2 m = 4
The value of them after solving the equation will be m=-2
What will be the value of m?The given equation will be
[tex]\dfrac{m}{m+4} + \dfrac{4}{4-m} =\dfrac{m^2}{m^2-16}[/tex]
multiply both sides by [tex](m+4)(m-4)[/tex]
[tex](m+4)(m-4) (\dfrac{m}{m+4} + \dfrac{4}{4-m} )=(m+4)(m-4) \dfrac{m^2}{m^2-16}[/tex]
[tex]m(m-4)-4(m+4)=m^2[/tex]
[tex]m^2-4m-4m-16=m^2[/tex]
[tex]8m=-16[/tex]
[tex]m=-2[/tex]
Thus the value of them after solving the equation will be m=-2
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Answer:
b
Step-by-step explanation:
edge
HELP HELP HELP*. Hei has $1,700 in a retirement account earning 4% interest compounded annually. Each year after the first, she makes additional deposits of $1,700. After 5 years, what was her account balance if she did not make any withdrawals? Round each year's interest to the nearest cent if necessary.
what was account balance after 5 years
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}\\ ~~~~~~~~~~~~ \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill &1700\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=1700\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1\cdot 5}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=1700\left( \cfrac{1.04^5~~ - ~~1}{0.04} \right)(1.04)\implies A\approx 9576.06[/tex]
help me please, im struggling
Answer:
8.57
Step-by-step explanation:
Hope it helps.......
Answer:
x = 8.57
Step-by-step explanation:
Hi! So first of all, I attached an image that has my best visual explanation of how the 2 triangles overlap but are indeed two separate triangles!
Since the question states that the triangles are similar, that basically means in simple terms that their sides are proportional or, are all based on the same fraction (proportion)! (An example of this is the triangles with the sides that correlate [in this problem, 11 to 7] would be 1 to 2, 3 to 6, and 4 to 8)
Now, we have to figure out which of our sides correspond, the first one being 11 to 7, and the second one being x + 15 (which I got by adding the small portion I have from the big triangle, and the portion I have from the smaller triangle together because the small triangle is inside of the big one!) to 15.
Next, I have to find out what x is based on the fraction (proportion) I already have which is 11 to 7 or [tex]\frac{11}{7}[/tex]. Then, I compare this by setting this proportion equal to are other proportion with x in it!
[tex]\frac{11}{7} = \frac{x+15}{15}[/tex]
Finally, I have to get x by itself to find what it is equal to, which you can see in the image! (If you have a number in the denominator and a variable in the numerator, and a regular number or fraction without a variable on the other side, you can just multiply both sides by the number in the denominator to cancel out the bottom of said variable fraction!)
So! X is equal to 8.57!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
PLEASE HELP ASAP
Zeke has spent $3.75 on gel pens in the past, and now he plans to buy some new ones. The
new gel pens cost $1.25 each. If Zeke buys 6 new gel pens, how much will he have spent on
gel pens in total?
Answer:
11.25
Step-by-step explanation:
Base on the given we can conclude that:
3.75 + 6 × 1.25
Now solve the following:
3.75 + 6 × 1.25
3.75 + 7.50
=11.25
~lenvy~
Answer:11.25
Step-by-step explanation:
Given that
3x : 10 = 5: 2
Calculate the value of x.
Give your answer in its simplest form.
X =
Answer:
25/3
Step-by-step explanation:
3x:10=5:2
proportions are basically ratios, and ratios are basically fractions, so we can cross multiply
3x*2=10*5
6x=50
x=50/6
x=25/3
Step-by-step explanation:
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Which equation describes how the parent function, y = x cubed, is vertically stretched by a factor of 4? y = x cubed 4 y = (x 4) cubed y = 4 x cubed y = x superscript 4
The required function when the parent function is stretched comes to be [tex]f(x)=x^{3} +4[/tex].
The parent function is:
[tex]f(x)=x^3[/tex]
How vertical translation of the graph of a function takes place?If a function f(x) is vertically translated by k units f(x) becomes f(x)+k where k is positive.
Given function [tex]f(x)=x^3[/tex] is vertically shifted by 4 units
So, f(x) will become f(x)+4
[tex]f(x)+4 = x^{3} +4[/tex]
So, the required function is [tex]f(x)=x^{3} +4[/tex]
Therefore, the required function when the parent function is stretched comes to be [tex]f(x)=x^{3} +4[/tex].
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Answer:
A
Step-by-step explanation:
edge, 2022
Determine if S could lie on the perpendicular bisector of QR with the given coordinates
Q(-5 , 4), R(8 ,3) , S(-2,-5)
Step-by-step explanation:
The distance between two points, and is given by:
The endpoints are: Q(-5, -1), R(3, 7)
Point S is (4,-2).
The distance of S to Q is:
The distance of S to R is:
HELPP ME ITS BEEN SO LONG HELP PLEASEEE HELP PLEASEE HELPP Stevie needed twine for the gifts she was wrapping for a family party. The lengths of Stevie’s twine are shown on the line plot below. How many feet of twine does Stevie have total?
Answer:
Your answer would be:
57.75 or 57 3/4
(I will show how many of each length of twine that is on the graph)
Point 2 1/4:
2
Point 2 3/4:
4
Point 3:
1
Point 3 1/2:
2
Point 3 3/4:
3
Point 4:
1
Point 4 1/4:
4
We can show how much length in total Stevie used with the following equation:
(2 1/4 x 2) + (2 3/4 x 4) + ( 3 x 1 ) + ( 3 1/2 x 2 ) + (3 3/4 x 3 ) + (4 x 1 ) + (4 1/4 x 4)
Each smaller equation in paraphrases shows how much of each length of twine at each point with x's on the number line. Altogether it would equal 57.75 or 57 3/4.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Please Help Am Confused!
Answer:
Count the sides;
(look at image below)
= 17 - gon
A mother shared $600 amongst her three daughters Ana, Betty and Carol in the ratio of 2:3:5 respectively. How much money did Betty receive?
Ana, Betty and Carol in the ratio of 2:3:5 respectively
mom cut the $600 in (2+3+5) 10 parts
and gave 3 parts to betty
so B got 600 : 10 x 3 = $180
Is -4,6 a solution to y=-9
Answer:
No, (-4, 6) is not a solution to y = -9.
Step-by-step explanation:
y= -9 has a horizontal line graph. Every point on this line has -9 as its y-coordinate. (-4, 6) does not lie on that line and is therefore not a solution to y = -9.
Can someone explain to me how to use square root? How do I solve it? How do I use it? I'm not sure the right way to use square root and I have testing soon, so I wanted to know how to use it beforehand.
Answer: a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16
The square of any number is always a positive number, so every number has two square roots, one of a positive value, and one of a negative value. For example, both 2 and -2 are square roots of 4.
Ethan ran 11 miles in 2 hours What is the constent of proporttional of miles to a hour
Answer:
5.5 miles
Step-by-step explanation:
If he ran 11 miles in 2 hours then divide both of them by 2, so 1 hour is equal to 11 / 2 which is 5.5 miles
PLEASE HELP ME WITH THIS!!!!!
For the given experiment of spinning a spinner and drawing a card, we will see that:
A) Yes, the events are independent.B) P(3 and A) = 1/16C) P(5 and C) = 0D) P(4) = 1/4 P(B or C) = 1/2E) P(3 and not D) = 3/16What are independent events?
We say that two events are independent if the outcome of one does not affect the outcome of the other.
In this case, the outcome of the spinner clearly does not affect the outcome of the card draw, so the events are independent.
How to get the probabilities?
B) First we want to get the probability of getting 3 and A.
The probability of getting a 3 when drawing a card is given by the quotient between the numbers of card with the number 3 (only one) and the total number of cards, so we have:
p = 1/4
Similar for the case of the spinner, the letter A appears twice, and there are a total of 8 letters, then the probability is:
q = 2/8 = 1/4
The joint probability is the product of the two individual probabilities, we have:
P(3 and A) = p*q = 1/4*1/4 = 1/16
C) The probability of getting a 5 and the letter C is 0, because there is no card with the number 5.
D) P(4) is the probability of drawing the card with the number 4, this is:
p = 1/4
P(B or C) is the probability of spinning the letter B or C. There are 2 B's and 2 C's, and a total of 8 letters, so the probability is:
q = (2 + 2)/8 = 1/2
E) P(1 and not D) is equal to: P(1 and A or B or C).
P(1) is 1/4.
P(A or B or C) is 6 over 8 (because there are 6 cards that are either an A, a B, or a C)
Then the joint probability is:
P(1 and not D) = (1/4)*(6/8) = 3/16
If you want to learn more about probability, you can read:
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PLEASE HELP AS SOON AS EVER I NOYL HAVE 5 MINS WILL GIVE BRAINLY!
Answer: E
Step-by-step explanation:
Side triangles; 6.
(3x4/2=6)
There are 2 triangles.
Back of triangle thing is 24.
Top area is 40.
Bottom area is 32.
12+24+40+32
Answer is 108.
I THINK that is the correct answer. I am so so sorry if it isn't.
Answer:
E- 108 in squared. Hope this helps!
Step-by-step explanation:
HELP ASAPPPP
In two sample surveys, 125 people were asked about their favorite fruit. In the first survey, 40 people chose apples, 64 chose oranges, and 21 chose bananas. In the second, 43 chose apples, 63 chose oranges, and 19 chose bananas. Marianne inferred that most people prefer oranges. Is this inference true based on the data? Explain.
Answer:
More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.
I hope this helps you
Step-by-step explanation:
Simplify the expression 7+(9+x)
Answer: = 16 + x
Please mark brainliest, it helps alot
Step-by-step explanation:
==============================================================
Combine Like Terms:-
[tex]\bigstar{\boxed{\pmb{7+9x+x}}[/tex]
[tex]\bigstar{\boxed{\pmb{16+x}}[/tex]
Are there any more like terms? No, because 16 & x aren't like terms.
========================================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly comment, and I will comment and/or edit my answer :)
what is 122 / 600?
[tex]122 \div 600[/tex]
Answer:122/600= 0.20333333333
Step-by-step explanation:
find x , y , sin alpha, tg beta and area of triangle
Answer:
Step-by-step explanation:
which European country colonized Brazil?
Answer:
Portugal in 1815 colonize Brazil.
Find the surface area
Answer = 221.52cm²
Step-by-step explanation:
Surface area of a hexagonal pyramid = B × H ÷ 2
Where,
b = 6
h = 5.2
⇒ 6 × 5.2 ÷ 2 = 15.6
⇒ 15.6 × 5.2 = 81.12
⇒ 6 × 9 ÷ 2 ⇒ 54 ÷ 2 = 27
⇒ 27 × 5.2 = 140.4
140.4 + 81.12
= 221.52
Answer:
Step-by-step explanation:
a -> apotham of the hexagon ⇒ a = 3√3 cm
b -> base ⇒ b = 6 cm
s ->slant height ⇒ s= 9 cm
[tex]\text{Area of hexagonal pyramid=3*ab +3*b*s}[/tex]
= 3*3√3*6 + 3*6*9
= 54*1.732 + 162 [√3 = 1.732]
= 93.6 + 162
= 255.6 cm²
If triangle DEF is classified as equilateral, which statement must be true?
At least two sides are congruent.
Two sides are perpendicular.
All three sides are congruent.
Two sides are parallel.
Also could you put the answer in the question comment box? I'm out of free answers.
Answer:
Step-by-step explanation:
Answer: All three sides are congruent
The problem is with A. It's true as well. At least 2 of the sides are congruent. The way to eliminate it is to say that does not mean specifically that all three sides are congruent.
I would argue that this is a faulty question, and watch someone squirm as they try to explain to you why a is not the answer. I don't know how to comply with your request. How are the choices designated
A
B
C
or
1
2
3
Answer:
C. All three sides are congruent.
Step-by-step explanation:
Carmen received a gift of $5,000 from her grandmother and decided to invest it. the expression 5000(1.0005)^12t represents the amount of the money carmen is earning on her investment. carmen wants to write an equivalent expression so that she can better understand how her money is being invested. choose an equivalent expression in each drop down.
The equivalent expression for the expression that represents the amount Carmen would earn is 5000(1.0005^12)^t.
What is the equivalent expression?Based on the expression given, Carmen's investment is compounded monthly.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years5000(1.0005)^12t
= 5000(1.0005^12)^t
50002.5^12t
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svp c'est pour un dm de math
Answer:
d
Step-by-step explanation:
the answer is d because we learned about this everyday
A group of students is riding in a bike tour. They have biked 15 miles, which is 25% of the tour. How long is the tour?
Answer:
60 miles
Step-by-step explanation:
25% of 60 = 15
Hoped this helped<33
Help me on this question please!
[tex]\huge\fcolorbox{blue}{red}{Answer}[/tex]
════════════════════
[tex]\frac{ x }{ 3 } +6-2x=-6[/tex]
[tex]x+18-6x=-18 [/tex]
[tex]-5x+18=-18 [/tex]
[tex]-5x=-18-18 [/tex]
[tex]-5x=-36 [/tex]
[tex]x=\frac{-36}{-5} [/tex]
[tex]x=\frac{36}{5} [/tex]
[tex]= 7 \frac{1}{5}[/tex]
[tex]= 7.2[/tex]
So the answer is [tex]x = 7.2[/tex] or [tex]= 7.2[/tex]
══════════════════════
Step-by-step explanation:
#Carry on learning
Fisher Auto Parts is running a 45% clearance sale on batteries. One battery cost $149.99. If the consumer purchases 2 batteries. What would be the final cost?
Sales tax is 5%.
Answer:
$204.74
Step-by-step explanation:
At 45% off each battery, the price for 1 battery would be (149.99)*(0.65) = $94.50. Two batteries would be a total of $194.99.
Add 5% tax:
($194.99)(1.05) = $204.74
James has 16 balloons. 1/4 of his balloons are red. How many red balloons does he have? Half of his red ballons pop after 10 minutes of playing with them. How many of his red ballons pop?
. Using the pattern above, what is the
sales tax and total cost of a shirt that is
$9.10? Round to the nearest cent
Answer:
$10.10
Step-by-step explanation:
Answer:
$10.10
Step-by-step explanation:
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