Answer:
Step-by-step explanation:
Base area =[tex]x^2[/tex]
side area=[tex]h*x[/tex]
Volume=[tex]x^2*h[/tex]=14
Surface area =[tex]4hx+2x^2[/tex]
upon substituting [tex]h=14/x^2[/tex]
surface area = [tex]4*\frac{14}{x^2}*x+2x^2[/tex]
upon differentiating and solving we get f"([tex]\sqrt[3]{14\\}[/tex]) >0 proves that this point is of minima
hence, dimensions are
[tex]x=\sqrt[3]{14}[/tex] ,h=[tex]\sqrt[3]{14}[/tex]
After the first essay examination in a class, a random sample of five papers was selected. The grades were 60, 75, 80, 70, and 90. What would be the 90% confidence interval for the mean grade of all the students?
Answer:
68.6433≤x≤82.3568
Explanation
confidence interval formula is expressed as
CI = xbar ± z × S/√n
xbar is the mean
z is the z score at 90% = 1.645
s is the Standard deviation
N is the sample size = 5
xbar = 60+75+80+70+ 90/5
xbar = 375/5
xbar = 75
Get standard deviation
SD =√\sum(x-xbar)²/N
SD = √(60-75)²+(75-75)²+(80-75)²+(70-75)²+(90-75)²/5
SD = √15²+0²+5²+5²+15²/5
SD = √225+50+225/5
SD = √500/5
SD =√100
SD = 10
Substitute the derived values into the formula
CI = 75±1.645 × 10/√5
CI = 75 ± (1.645×4.4721)
CI = 75±7.3568
CI = (75-7.3568, 75+7.3568)
CI = (67.6433, 82.3568)
Hence the 90% confidence interval of the student is:
68.6433≤x≤82.3568
Solve for x, y, and z in the figure below.
47° 58°
x
y° / 81°
zº
N
оа
Ob
Ос
x = 34, y = 99, z = 41
x = 41, y = 92, z = 41
x = 72, y = 61, z = 41
X = 63, y = 70, z = 41
Od
Answer:
Option (A)
Step-by-step explanation:
From the given triangle in the picture,
∠y and the angle measuring 81° is a pair of supplementary angles (linear pair angles).
m∠y + 81° = 180°
m∠y = 180° - 81°
= 99°
By the property of a triangle,
x° + y° + 47° = 180°
x° + y° = 180° - 47°
x° + y° = 133°
For y = 99°
x° + 99° = 133°
x° = 133° - 99°
= 34°
Similarly, z° + 58° + 81° = 180°
z° + 139° = 180°
z° = 180° - 139°
z° = 41°
Therefore, Option (A) will be the correct option.
Applying the definition of the straight line angle and sum of triangle, the values of the variables in the figure are:
x = 34, y = 99, z = 41Recall:
Angles on straight line = 180°Sum of triangle = 180°Thus:
y° + 81° = 180° (angles on a straight line)
Subtract 81 from each sidey° = 180° - 81°
y° = 99°
x° + y° + 47° = 180° (sum of triangle)
Substitutex° + 99° + 47° = 180°
x° + 146° = 180°
Subtract 146° from each sidex° = 180° - 146°
x° = 34°
z° + 81° + 58° = 180° (sum of triangle)
z° + 139° = 180°
Subtract 139° from each sidez° = 180° - 139°
z° = 41°
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Sue sees 30 adult elephants and 18 baby elephants at the zoo. What is the ratio of adult elephants to baby elephants
Answer: 30:18 or 30 to 18
Step-by-step explanation:
At a certain intersection, the traffic light is red for 15 seconds, yellow for 5 seconds and green for 30 seconds. Find the probability that, of the next eight cars that arrive randomly at the light, exactly three will be stopped by a red light.
Answer: 0.254
Step-by-step explanation:
Given that:
Number of cars = number of trials (n) = 8
Number that will be stopped by a red light = Numbe rof successes (r) = 3
Probability of success :
Red light = 15 seconds ; yellow = 5 seconds ; green = 30 seconds
P(red) = p(success) = p = 15 / (15 + 5 + 30) = 15/50 = 3 /10 = 0.3
1 - p = 1 - 3/10 = 7/10 = 0.7
Using the binomial probability relation:
p(exactly 3):
P(8, 3) = 8C3 * p^3 * (1-p)^(8-3)
P(8, 3) = 8C3 * p^3 * (1-p)^5
P(8, 3) = 56 * 0.3^3 * 0.7^5
= 0.25412
= 0.254
A goose is flying horizontally at an altitude of 300 ft and a speed of 50 ft/sec passes directly over a pond. Find the rate at which the distance from the goose to the pond is increasing when it is 500 ft away from the pond.
Answer:
The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.
Step-by-step explanation:
We assume that goose is flying at constant velocity. After reading carefully the statement of the problem, we create the following geometrical diagram, which is included at the end of this explanation and represents the following Pythagorean identity:
[tex]x^{2}+y^{2} = r^{2}[/tex] (Eq. 1)
Where:
[tex]x[/tex] - Horizontal distance of the goose from pond, measured in feet.
[tex]y[/tex] - Vertical distance of the goose from pond, measured in feet.
[tex]r[/tex] - Resultant distance of the goose from pond, measured in feet.
We find the rate of change in time at which resultant distance is increasing by differentiating on (Eq. 1):
[tex]2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y = 2\cdot r \cdot \dot r[/tex]
[tex]x\cdot \dot x + y\cdot \dot y = r\cdot \dot r[/tex]
[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex] (Eq. 2)
Where:
[tex]\dot x[/tex] - Rate of change of horizontal distance, measured in feet per second.
[tex]\dot y[/tex] - Rate of change of vertical distance, measured in feet per second.
[tex]\dot r[/tex] - Rate of change of resulting distance, measured in feet per second.
If we know that [tex]x = 500\,ft[/tex], [tex]y = 300\,ft[/tex], [tex]\dot x = 50\,\frac{ft}{s}[/tex] and [tex]\dot y = 0\,\frac{ft}{s}[/tex], the rate at which the distance from the goose to the pond is increasing is:
[tex]\dot r = \frac{(500\,ft)\cdot \left(50\,\frac{ft}{s}\right)+(300\,ft)\cdot \left(0\,\frac{ft}{s} \right) }{\sqrt{(500\,ft)^{2}+(300\,ft)^{2}}}[/tex]
[tex]\dot r \approx 42.875\,\frac{ft}{s}[/tex]
The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.
Suppose the scores on a chemistry test were normally distributed with a mean of 78 and a standard deviation of 10. If a student who completed the test is chosen at random,a.Find the probability that the student earned between 80 and 90 points.b.Find the probability that the student earned either less than 80 points or more than 90 points.
Answer:
a) 0.30567
b) 0.69433
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
,a.Find the probability that the student earned between 80 and 90 points.
For 80 students
z = 80 - 78/10
= 0.2
P-value from Z-Table:
P(x = 80) = 0.57926
For 90 students
z = 90 - 78/10
= 1.2
P-value from Z-Table:
P(x = 90) = 0.88493
The probability that the student earned between 80 and 90 points.
P(x = 90) - P(x = 80)
= 0.88493 - 0.57926
= 0.30567
b.Find the probability that the student earned either less than 80 points or more than 90 points.
For less than80 students
z = 80 - 78/10
= 0.2
P-value from Z-Table:
P(x < 80) = 0.57926
For 90 students
z = 90 - 78/10
= 1.2
P-value from Z-Table:
P(x<90) = 0.88493
P(x>90) = 1 - P(x<90) = 0.11507
The probability that the student earned either less than 80 points or more than 90 points.
= 0.57926 + 0.11507
= 0.69433
the graph shows favorite sports among third graders in a school how many third graders pick basketball or baseball than football as their favorite sport
Answer:
do you have the graph?
Step-by-step explanation:
In Fairbanks, Alaska, the average temperature in January is -9.7°F. The
average temperature in July is 62.4°F. On average, how many degrees
colder is Fairbanks in January than in July?
Answer:
72.1 degrees... 72 point 1 degress in case you cant see the ( . )
Step-by-step explanation:
62.4 minus -9.7= is 72.1
rounding to the nearest tenth, which of the following give an overestimate?
45.07 × 3.45
19.74 × 5.53
8.16 × 60.29
2.92 × 77.81
32.86 × 10.4
1. 157.5108.35
2. 108.35
3. 494.46
4. 233.7
5. 342.16
Step-by-step explanation:
solve for x explain pls
6+2x+31=x+26
SHNERPY GERPBY
Put the steps of the Electoral College Process in order.
Question 5 options:
First candidate to 270 electoral votes wins the presidency.
Electors cast the official vote.
Popular vote.
Whoever wins the state, gets all of that state's electoral votes.
Answer: (number 1 is the popular vote) (number 2 is whoever wins the state gets all the electoral votes) (number 3 is electors cast the official vote) (and finally at number 4 the first candidate to 270 wins the election)
The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
Answer: 1 student scored above an 85%.
Step-by-step explanation:
Let X = percentage score in test (normally distributed).
Given: Sample size = 15 , mean score : [tex]\mu[/tex]= 74.8% = 0.748 ,standard deviation : [tex]\sigma=7.57[/tex]
Now, The probability that student scores above 85%:
[tex]P(X>85)=P(\dfrac{X-\mu}{\sigma}>\dfrac{85-74.8}{7.57})\\\\=P(Z>1.347)\\\\=1-P(Z<1.347)\\\\=1-0.9110= 0.089[/tex]
Probability that student scores above 85% = 0.089
Number of students scored above an 85% = 0.089 x 15 = 1.335 ≈ 1
hence, 1 student scored above an 85%.
what is the bed what is it
Answer:
A bed is a type of object a person uses to sleep on. It usually contains blankets and pillows
Step-by-step explanation:
Can i have brainliest?
1/9 , Find the quotient in its simplest form .
Answer:
the simplest form of 1/9 is: 1/9
Step-by-step explanation:
1. A number that will divide evenly into both the numerator and denominator so it can be reduced. No such number exists for 1 and 9.
2. The numerator must be greater than the denominator, an improper fraction, so it can be converted to a mixed number. 1 is not greater than 9.
HELP ME PLEASE!! This is due today!! Use kcf and show ur work plzz!
Answer:
[tex]\frac{3}{2} \textrm{ cups of flour}[/tex]
Step-by-step explanation:
the ratio of cups of flour per 1 cup of water:
[tex]\frac{2\frac{1}{2}}{1\frac{2}{3}}=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{3}{2}[/tex]
2x-1/15=7.2/3 Find x
Answer:
x = 18.5
Step-by-step explanation:
If you do the butterfly method, you should get 2x-1 = 36
2x = 37
x = 18.5
1. Rosalie bought 0.2503 kg of garlic, 0.17 kg tomatoes, 2.05 kg of onions and 1.12 kg of
ginger. What was the total weight of this item?
answer is 3.5903 or 3 kg 5903 gram
Does the set of ordered pairs {(0,4),(2,6),(4,2), (6,2), (8,6)} represent a function?
Answer:
yes it does
Step-by-step explanation:
the x numbers do not repeat
Yes, the given relation is function.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
set of ordered pairs= {(0,4),(2,6),(4,2), (6,2), (8,6)}
As, we know that the function has one input with corresponding one output.
So, we can see from the ordered pair that no input value have repeated and have respective output.
Hence, the relation is function.
Learn more about function here:
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#SPJ2
Personal Finances Practice Active 1 2 You are starting a new job in sales for the company Buy 'n Large. Your hourly wage is $10.00 per hour and you get time and a half for anything over 40 hours. Based on a 5-day work week, 8-hour day, and 52 week year, determine your annual gross base salary a $21,650 C. $20,800 b. $18,798 d. $19,980
Answer:
C.20,800
Step-by-step explanation:
10.00 per hour so 10x8=80
then 80x5=400
400x52=20,800
If twice the number, added to 3 is divided by the number plus 9, the result is three halves. Find the number
Answer:
x=21
Step-by-step explanation:
(3+2x)/(x+9)=3/2
(x+9)(3+2x)=(3/2)(x+9)
3+2x=(3x+27)/2
2(3+2x)=3x+27
6+4x=3x+27
x=21
Which expression is equivalent to 1/3 p + 15
1/3 (p+45)
1/3 (p+5)
3 (p+45)
3(p+5)
Answer:
[tex]1/3 (p+5) [/tex]
Step-by-step explanation:
[tex]1/3 p + 15 = \frac{1}{3} p + 15 = \\ \frac{p + 5}{3} = \frac{1}{3} ( p+ 5)[/tex]
♨Rage♨
Answer all of these questions correctly. Will give brainliest.
Answer:
1-5
3-7
8-4
2-6
6-3
3-7
Step-by-step explanation:
Someone please help
Me with this
Answer:
y= 1/3x + 1.
Step-by-step explanation:
please help
simplify this
2³+4×8
Answer:
40
Step-by-step explanation:
2³ + 4×8
8 + 32 = 40
PEMDAS:
Handle the exponents, multiply, then add.
2) Which of the following equations has a slope (m) of -3 and a y-intercept 1 point
(b) of 8? *
O y = -3x - 8
O y=-3x + 8
Oy= 8x - 3
Math help! DUE IN 30 MINUTES (50 points)
Answer: i won't tell you the answer but i will break it up for you so i can make easier for you
Step-by-step explanation: (-5x^2) (y^c) x (x^5) (2y^3)(5x^7)(y^6)(2) Or for the ones for numerator and denominator you can do this
(x^5)
____ = ( -5x^7)
______
(2)
(2y^3)
So for the one with numerator and denominator i got a stuck on a little but i tried doing this way if you like this way i can keep it like this if you dont i can change it
A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the length of the guy wire (round to 2 decimal places)
Answer:
350.62 feet
Step-by-step explanation:
order the number from least to greatest: 10^5 10^-99 10^-17 10^14 10^-5 10^30
Answer:
I think it goes like this: 10^-99, 10^-17, 10^-5, 10^5, 10^14, 10^30
Step-by-step explanation:
Solve for x. What is the root? If there is no root, choose none.
Answer:
4
Step-by-step explanation:
What is the image point of
(1,4)(1,4)
(1,4) after a translation left 5 units and down 5 units?
Answer:
(-4,-1)
Step-by-step explanation:
