An atrium is being designed to house an exhibit of tropical birds. The atrium must enclose 250,000 cubic feet of space, and the designer wants it to have the shape of a hemisphere. Is such a design possible given that the plot of land on which it will be built is a rectangle 90 feet wide and 100 feet long?
Answers
The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium.
Can this atrium be built in the rectangular plot of land?
The atrium with the maximum allowable radius (R), in feet, is represented in the image attached. The real atrium is possible if and only if the real radius (r) is less than the maximum allowable radius and therefore, the real volume (V), in cubic feet, must be less than than maximum possible volume (V'), in cubic feet.
First, we calculate the volume occupied by the maximum allowable radius:
V' = (8 · π / 3) · (45 ft)³
V' ≈ 763407.015 ft³
The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium. [tex]\blacksquare[/tex]
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Related Questions
The median number of visitors to a local zoo each day is 893. A sample median of 1,005 visitors would be most likely to occur for which sample size? n = 20 n=75 n = 300 n 500 n=1,000
Answers
A sample median of 1,005 visitors would be most likely to occur for the sample size given by: Option A: 20
What does median behave like for large sample?As the value of n (the sample size) grows larger, the sampling distribution tends to being normal. For an approximate normal distribution, its mean, median, and mode all are approx coincident. And as the sample size increases, the sample mean tends to being the population mean as per the weak law of large numbers. For n > 30, we can approximate it using normal distribution usually.
We're given that:
Population median (the real median of the number of visitors to the zoo) = 893We want to choose value of n from 20, 75,, 300, 500, 1000 for which the sample median would be 1005.So, as we know, as the sample size increases, the sample mean and sample median and sample mode, all will tend to the population mean, median and mode (assuming population is large enough that they're all same).
Thus, the smaller the sample size, the more likely it is for holding 1005 as sample median instead of approx 893.
So, size 20 is most likely to have that median as it is the smallest sample size given.
Thus, a sample median of 1,005 visitors would be most likely to occur for the sample size given by: Option A: 20
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Which is equivalent to 7/10?
Answers
14/20 , 21/30 ,28/40 & 35/50 all are equivalent ratio to 7 /10
Which integer has the least value (-17,-7,-12,2)
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Why are the triangles congruent?
Answers
You can prove triangles’ congruence with things called axioms (or postulates). For triangles, there are four:
(S means Side, A means Angle)
SAS
SSS
ASA
AAS
If you go round a triangle, in order (so aside, then the next angle, next side, etc.), and find that everything from one of these postulates is equal, you have two congruent triangles.
(These triangles’ sides and angles, which are marked on the image, are equal to the other’s)
This diagram shows the SAS axiom, as the equal parts of the triangle go in order of a side (Y to Z), an angle (Y to Z to X), and another side (Z to X).
Hope this helps!
I NEED HELP FAST PLEASE HELP ME
Answers
Answer:
16, 0, 64
Step-by-step explanation:
Check out the attached photo
Hoping to be named Salesperson of the Month, Kylie called the names from 9 1/12 pages of the phone book last week. This week, she called the people listed on another 5 7/12 pages of the same phone book. How many pages worth of people did Kylie call in all?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
14 2/3
filler filler filler
A bank requires a four-digit access code for each account. the access code is generated using the digits 0–9, and the digits can be repeated. what is the probability of an access code "1234"? startfraction 1 over 10,000 endfraction startfraction 1 over 6,561 endfraction startfraction 1 over 10 endfraction two-fifths
Answers
Using it's concept, it is found that there is a [tex]\frac{1}{10000}[/tex] probability of an access code "1234".
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering that each digit has 10 possible outcomes, and there are 4 digits, the total number of outcomes is given by:
[tex]T = 10^4 = 10000[/tex].
1234 is only one access code, hence the probability is given by:
[tex]p = \frac{1}{10000}[/tex]
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Answer:
d
Step-by-step explanation:
A group of friends went to Starbucks and
ordered 2 muffins and 3 cups of coffee for $22.35.
In the same coffee shop, another group of friends
ordered 4 muffins and 3 cups of coffee for $32.85.
Algebraically determine the price of one muffin and
one cup of coffee.
Answers
Answer:
1 muffin is 5.25 and 1 cup of coffee is 3.95
Step-by-step explanation:
32.85 - 22.35 is 10.5. 10.5 divided by 2 is 5.25 that is the cost of 1 muffin. 22.35 - 10.5 is 11.85. 11.85 divided by 3 is 3.95.
After trick-or-treating, Juan counted his candy. He collected 25 pieces of candy and noticed that 2/5 of the candy was chocolate. How many pieces of Juan’s candy were chocolate?
Answers
Answer:
10 pieces of Juan's candy was chocolate
Step-by-step explanation:
to find 2/5 of something, you have to multiply.
of means to multiply.
So then you multiply 2/5 by 25.
[tex]\frac{2}{5}*\frac{25}{1} =\frac{10}{1} =10[/tex]
please help me solve this
Answers
Answer:
∠ F ≈ 24.2°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan F = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{GH}{FG}[/tex] = [tex]\frac{9}{20}[/tex] , then
F = [tex]tan^{-1}[/tex] ( [tex]\frac{9}{20}[/tex] ) ≈ 24.2° ( to the nearest tenth )
Step-by-step explanation:
using the tangent ratio in the right triangle
A car company claimed that it improved the gas mileage of a particular model of car between 2011 and 2012. A consumer advocacy group obtains a random sample of 16 cars from 2011 and finds the average number of miles driven on exactly 25 gallons of gas in laboratory conditions is 574. 4 miles, with a standard deviation of 43. 1 miles. The consumer advocacy group also obtains a random sample of 24 cars from 2012 and finds the average number of miles driven on exactly 25 gallons of gas in laboratory
conditions is 604. 6 miles, with a standard deviation of 27. 8 miles. The 99% confidence interval for the difference in mean miles driven on 25 gallons of gas (2012 model – 2011 model) is (–3. 95, 64. 35).
Does this confidence interval support the company’s assertion that their gas mileage has increased?
a)Yes, we are 99% confident that the true mean difference in miles driven per 25 gallons is 30. 2 miles.
b)Yes, the fact that most of the values in the confidence interval are positive means that the true mean number of miles driven on 25 gallons is higher in 2012.
c)Yes, the 2012 sample mean of 604. 4 miles per 25 gallons is 30. 2 more miles than the 2011 sample mean of 574. 4, which is an increase of 1. 208 miles per gallon.
d)No, the confidence interval contains 0, so we are 99% confident that the true mean increase in number of miles driven on 25 gallons is 0.
e)No, the confidence interval contains 0, so 0 is a plausible value for the true mean increase in number of miles driven on 25 gallons. An increase of 0 would indicate the gas mileage has not increased
Answers
Using the interpretation of the confidence interval, it is found that the correct option is:
e) No, the confidence interval contains 0, so 0 is a plausible value for the true mean increase in number of miles driven on 25 gallons. An increase of 0 would indicate the gas mileage has not increased.
What is the interpretation of a x% confidence interval?It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.
In this question, the 99% confidence interval for the increase is of (-3.95, 64.35). It contains 0 and negative values, hence those are plausible values, and this is not enough evidence that the mean has increased, hence option e is correct.
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The _____________________________________ Postulate says that If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Answers
Answer: Angle sum
Step-by-step explanation:
Sharina simplified the expression 3(2x – 6 – x 1)2 – 2 4x. in step 1 she simplified within the parentheses. in step 2 she expanded the exponent. a table titled sharina's work with 1 column and 4 rows. the column is labeled 3(2 x minus 6 minus x 1) squared minus 2 4 x. the first row has entry 3(x minus 5) squared minus 2 4 x. the second row has entry 3(x squared minus 10 x 25) minus 2 4x. rows 3 and 4 are blank. which is a possible next step? simplify the expression by adding and subtracting from left to right. combine like terms within the parentheses. combine all x-terms. distribute the 3 to each term in the parentheses by multiplying.
Answers
The work for the possible next step which Sharina need to do is to distribute the 3 to each term in the parentheses by multiplying.
How to simplify an equation?Simplified form of a term is the simplest way of expression the term, by applying the required operations of mathematics. To simplify the equation, the BODMOS method is used.
Sharina simplified the expression 3(2x – 6 – x 1)2 – 2 4x.
Step 1- She simplified within the parentheses. Step 2-She expanded the exponent.The table of Sharina's work
[tex]3(2x -6-x +1)^2 -2+ 4x[/tex] [tex]3(x -5)^2 -2 +4x.[/tex][tex]3(x^2 - 10x +25) -2 +4x.[/tex]In this table, rows 3 and 4 are blank. The next term to be filled in the 3rd row. The equation solved by her in the second row is,
[tex]3(x^2 - 10x +25) -2 +4x.[/tex]
According to the rule of BODMAS, she first has to open the bracket by distribute the 3 to each term in the parentheses by multiplying.
Hence, the work for the possible next step which Sharina need to do is to distribute the 3 to each term in the parentheses by multiplying.
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PLEASE ANSWER ASAP!! 57 POINTS!!! BRAINLY!) there were 80 teenagers in line for tickets to a concert. Forty percent were boys. Twenty-six girls wanted $10 tickets. The rest wanted $15 tickets. The results are shown below. $10 $15 Total Вoys ? 18 Girls 26 22 ? Total 40 40 80 How many of the teenagers in line are boys?
Answers
The other boxes are easy to fill in after that.
Total Girls is 48
and
$10 boys is 14
Good luck with your studies!!
An automobile tire at 30.0°c has a pressure of 3.00 atm. the temperature decreases to -5.00°c. assume that there is no volume change in the tire. formula to use: p1 t1 = p2 t2 how does the tire pressure change in response to the temperature change?
Answers
The process is an isochoric process. Then the tire pressure change in response to the change in temperature is 2.65 atm.
What is thermodynamics?It is a branch of science that deals with heat and work transfer.
An automobile tire at 30.0°C has a pressure of 3.00 atm.
The temperature decreases to -5.00°C.
Assume that there is no volume change in the tire.
Then for the constant volume process, we have
[tex]\dfrac{P_1}{P_2} = \dfrac{T_1}{T_2}\\\\\dfrac{3}{P_2} = \dfrac{303}{268}\\\\P_2 \ = 3\times \dfrac{268}{303}\\\\P_2 \ = 2.65[/tex]
The tire pressure change in response to the change in temperature is 2.65 atm.
More about the thermodynamics link is given below.
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Answer:
How does the tire pressure change in response to the temperature change?
✔ decreases
What is the new pressure of the tire after the temperature change?
2.65 ✔ atm
Step-by-step explanation:
Got it right on edge
The Courtwheys just sold their house I which was 2,400 square feet. The three equal-sized bedrooms in the house made up 1,200 square feet in the house. If each room is a square, how long and wide is each bedroom?
Answers
Answer:
20 feet
sorry!! I don't know how to explain
Every few years, Edgar's entire family gets together for a family reunion. This year, Edgar's parents are hosting, and they have to cook a lot of food to feed the crowd. Edgar has volunteered to do the most tedious job: shelling peas. There is a proportional relationship between the amount of time (in minutes) Edgar spends shelling peas, x, and the weight (in pounds) of the peas he has shelled, y.
The equation that models this relationship is y=0.5x.
How many pounds of peas does Edgar shell in 16 minutes? Write your answer as a whole number or decimal.
Answers
Henry owns a small business selling clothing. He knows that in the last week 70 customers paid cash, 20 customers used a debit card, and 22 customers used a credit card.
Based on these results, express the probability that the next customer will pay with something other than a debit card as a percent to the nearest whole number
Answers
Answer:
80%
Step-by-step explanation:
it’s 82% but rounded its 80
What do 32x4x3x2÷5 equal 20 points and brainliest if right.
Answers
Answer:
153.6
Step-by-step explanation:
Answer:
153.6
Step-by-step explanation:
32x4=128
128x3=384
384x2=768
768/5=153.6
Ramon received a $100 bill as a graduation gift. He bought a game online for $24. 95. Then he bought a backpack for $39. 75 at a variety store. How much money did he have left after making the purchases?
Answers
Answer:
$35.30
Step-by-step explanation:
24.95+39.75 because this is the money he has spent.
This, in total, will be 64.7
Lastly, the problem states that Ramon has $100 in total, so you subtract.
$100-64.7=35.3
He has $35 and 30 cents left.
reflect (7,4) across the x-axis then reflect the result across the y-axis what are the coordinates of the final point
Answers
The coordinates of the final point after the two reflections is (-7, -4)
How to reflect a point across an axis?
For a point (x, y), a reflection across the x-axis gives the point (x, -y), while for a point (x, y) a reflection across the y-axis gives (-x, y).
In this case, we have the point (7, 4), first we reflect across the x-axis, so we get the point (-7, 4).
Now we reflect across the y-axis, so the sign of the y-component changes, and we get (-7, -4)
So the coordinates of the final point after the two reflections is (-7, -4).
If you want to learn more about reflections, you can read:
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please help asap tysm <3
Answers
Step-by-step explanation:
internet check ?
that's the fastest, and the same I had to do :
there are 2 pints in 1 quart.
in other words
1 pint = 0.5 quarts
therefore,
13 pints = 13×1 = 13×0.5 quarts = 6.5 quarts
so,
13 pt = 6 qt + 1 pt
Answer:
13 pt = 6 qt 1 pt
Step-by-step explanation:
1 qt = 2 pt
12 pt = 6 qt + 1 remaining pt.
If x=2,y=-1 then (2x^2 times y^3)^2
Answers
Answer:
64
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
All you have to do is plug in the numbers, it will look like this
(2(2)^2 * -1^3)^2
It looks weird but trust me
Ok so first you have to mutiply 2*2 whitch is 4
(4^2 * -1^3)^2
now what is the 1 with the exponet of 3? It will stay at -1
(4^2 * -1) ^2
what is 4^2? it is the same a 4*4
whitch is 16
(16-1)^2
16-1?
(15)^2, same thing as 15*15
whitch is 225
makingn 255 your answer
PLEASE I NEED THIS escape room 4
Answers
The greatest possible probability in any experiment is 1 as the least possible probability in any experiment is 0.
What is probability?Probability simply means the likelihood of the occurence of an event.
In this case, the greatest possible probability in any experiment is 1 as the least possible probability in any experiment is 0.
Also, a probability around 0.5 means that the event is neither likely nor unlikely.
Learn more about probability on:
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Please answer the following questions correctly.
Answers
Answer:
(x_4)^2+(y+1)^2=81
Step-by-step explanation:
you change the signs of the x and y co efficient. The general formula is (a,-b) (x_a)^2+(y+b)^2=r^2
Patrick added 1/4 teaspoons of cayenne pepper and 1/3 teaspoons of black pepper to his enchilada sauce. What is the total amount of the two spices that Patrick added to his sauce?
Answers
Answer:
7/12
Step-by-step explanation:
You first make a common denominator. You make both the denominators 12, then make one numerator 3 and another numerator 4. Now you have an easy equation; 3/12 + 4/12, which equals to 7/12
What is the mode of the data set?
Math Test Scores
5 0 4
6 5 7 8
7 5 8
8 2 4 5 5 5 6 7 8 9
9 0 0 0 0 4 6 7 9
5 0 = 50
Answers
Reason:
We have this stem-and-leaf plot
[tex]\begin{array}{r|l}\text{stem} & \text{leaf}\\\cline{1-2}5 \ & \ 0 \ 4\\6 \ & \ 5 \ 7 \ 8\\7 \ & \ 5 \ 8\\8 \ & \ 2 \ 4 \ 5 \ 5 \ 5 \ 6 \ 7 \ 8 \ 9\\9 \ & \ 0 \ 0 \ 0 \ 0 \ 4 \ 6 \ 7 \ 9\\\end{array}[/tex]
where something like [tex]5 \big| 0[/tex] represents the number 50.
The most frequent leaf is "0" in the very bottom row. It shows up four times, which is the most of any of the other leaf.
This leaf ties to the stem of 9.
stem = 9 & leaf = 0 leads to the data value 90.
Therefore, the mode is 90
Find the value of x.
x = [ ? ]
Answers
Answer:
x = 7Step-by-step explanation:
The altitude is parallel to the hypotenuseThe sides are in proportionSolving
8/(8 + 10) = 12/(12 + 3x - 6)8/18 = 12/(3x + 6)4/9 = 12/3(x + 2)4/9 = 4/(x + 2)x + 2 = 9x = 7What do you know about a quadratic equation that has the following points (2, 0) and (10, 0)?
A. The parabola must open up.
B. The parabola will have a negative y-intercept.
C. The x-coordinate of the vertex must be 6.
D. The graph must be wider than the parent function.
Answers
Answer:
C. The x-coordinate of the vertex must be 6
Step-by-step explanation:
The parabola intercepts the x-axis when y = 0.
Therefore, if the quadratic equation has the points (2, 0) and (10, 0) then the x-intercepts or "zeros" are x = 2 and x = 10.
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\sf \implies midpoint=\dfrac{2+10}{2}=6[/tex]
Therefore, the solution is option C.
Additional Information
The leading coefficient of a quadratic tells us if the parabola opens upwards or downwards:
Positive leading coefficient = parabola opens upwardsNegative leading coefficient = parabola opens downwardsWe have not been given this information and so therefore cannot determine the way in which it opens.
As we do not know the way in which way the parabola opens, we cannot determine if the parabola will have a negative or positive y-intercept.
We have not been given the full quadratic equation, and so we cannot determine if the parabola is wider (or narrower) than the parent function.
Find the quadratic equation
[tex]\\ \rm\Rrightarrow (x-2)(x-10)=y[/tex]
[tex]\\ \rm\Rrightarrow y=x(x-10)-2(x-10)[/tex]
[tex]\\ \rm\Rrightarrow y=x^2-10x-2x+20[/tex]
[tex]\\ \rm\Rrightarrow y=x^2-12x+20[/tex]
Convert to vertex form of parabola
y=a(x-h)²+k[tex]\\ \rm\Rrightarrow y=x^2-2(6x)+20+16-16[/tex]
[tex]\\ \rm\Rrightarrow y=x^2-2(6x)+36-16[/tex]
[tex]\\ \rm\Rrightarrow y=(x-6)^2-16[/tex]
Vertex(h,k)=(6,-16)Option A and C is correct
Lindsay is very exited to be getting a great deal on an iPad. It was originally $500, but she will only be paying $325. What percent did she save?
heeeeeeeeeelp I'm dying.
Answers
30% of 500= 150
5% of 500= 25
30%+5%= 35%
35%=175
therefore she saves 35%
well, the original price was 500 bucks, but went down to 325, namely 500 - 325 = 175, so she'll be saving 175 bucks.
if we take 500 to be the 100%, what is 175 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 500 & 100\\ 175& x \end{array} \implies \cfrac{500}{175}=\cfrac{100}{x}\implies \cfrac{20}{7}=\cfrac{100}{x} \\\\\\ 20x=700\implies x=\cfrac{700}{20}\implies x=35[/tex]