Answer:
Step-by-step explan
Engineers are designing a large elevator that will accommodate 58 people. The maximum weight the elevator can hold safely is pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean pounds and standard deviation pounds, and the weights of adult U.S. women have mean pounds and standard deviation pounds. Use the TI-84 Plus calculator.
Required:
a. If 58 people are on the elevator, and their total weight is 11,716 pounds, what is their average weight?
b. If a random sample of 58 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
Complete question is;
Engineers are designing a large elevator that will accommodate 58 people. The maximum weight the elevator can hold safely is 11,716 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 190 pounds and standard deviation 62 pounds, and the weights of adult U.S. women have mean 184 pounds and standard deviation 71 pounds. Use the TI-84 Plus calculator.
Required:
a. If 58 people are on the elevator, and their total weight is 11,716 pounds, what is their average weight?
b. If a random sample of 58 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
Answer:
A) average weight = 202 pounds
B) the probability that the maximum safe weight will be exceeded = 42.47%
Step-by-step explanation:
A) We are told that 58 people are on the elevator and that their total weight is 11,716 pounds. Thus;
Average weight = total weight/number of people = 11716/58 = 202 pounds
B) We will use z-score formula in this;
z = (x¯ - μ)/σ
Now, in part a above, we saw that the average weight is 202 pounds. Thus; x¯ = 202 pounds
We are told that standard deviation for men is;
σ = 62 pounds
We are told that the weights of adult U.S. men have mean 190 pounds . Thus; μ = 190
Thus;
z = (202 - 190)/62
z = 0.19
From z-distribution table, p-value = 0.57535
Thus;
P(z > 0.19) = 1 - 0.57535 = 0.42465
Thus, the probability that the maximum safe weight will be exceeded = 0.42465 ≈ 42.47%
I need help I will give brainlest
I showed a screenshot of the question
X = (18/5)/(3/2)
= 18/5 x 2/3
=(18 x 2) / (5x3)
= 90/15
If you don’t want it as a fraction it’s 6!
Hope this helps!
PLEASE HELP FAST!! I MIGHT GIVE BRAINLIEST TO FASTEST AND ACCURATE
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time t, in seconds, and the number of bacteria, B(t) in the petri dish is modeled by the following function:
B(t) = 9300 x (1/64)^t
Complete the following sentence about the rate of change of the bacterial culture
The bacterial culture loses 1/2 of its size every_______ seconds
Answer:
1/6
Step-by-step explanation:
We want to find how long it takes for the bacteria to lose half its size. We can do this by taking one point of the bacteria and finding how long it takes to go to half its size. When t=0, 9300 * (1/64)^t = 9300 * 1 = 9300 as anything to the power of 0 is 1. Therefore, we can solve for t when the end result of the bacteria is 9300/2= 4650, making our equation
4650 = 9300 * (1/64)^t
divide both sides by 9300
1/2 = (1/64)^t
First, we can tell that 2^6 = 64*. Because of this, we can say that (1/2)^6 = 1^6/2^6 = 1/64, so (1/64)^(1/6) = 1/2. We know this because
(1/2)^6 = 64
take the 6th root of both sides
(1/2) = (64)^(1/6)
. This means that t=1/6, so the bacterial culture loses 1/2 of its size every 1/6 seconds
* if this is harder to figure out, e.g. 3 and 729, we can plug (log₃729) into a calculator
Answer:
0.17 seconds
Step-by-step explanation:
i got this correct on Khan :)
i hope it helps
Line segment AB is congruent to line segment CD.
Which of the following is an equivalent statement?
AB overbar similar to CD overbar
AB overbar congruent to CD overbar
AB overbar equal to CD overbar
AB overbar element to CD overbar
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Answer:
(b) AB overbar congruent to CD overbar
Step-by-step explanation:
AB with an overbar is the way that line segment AB is designated, where appropriate typesetting is possible. Thus the statement the line segments are congruent is fully equivalent to ...
AB overbar congruent to CD overbar
Which statement can be proved true using the given theorem?
Answer:
BF = 16
Step-by-step explanation:
18/12 = 1.5 * 6 = 9
Since DE and BF are parallel and DB and EF are parallel, they comprise a parallelogram. This means that DB = EF
DB = EF = 9
24/1.5 = 16
DE = 16
BF = 16
The statement which can be proven true using the given theorem (congruence) is Segment BF = 16.
Congruence theoremBy the congruence theorem;
We can conclude that triangles ABC and EFC are congruent triangles and as such have the ratio of corresponding sides to be equal.Hence, AE/EC = BF/FC.
Therefore; 12/18 = BF/24
Hence, BF = 24× 12/18
BF = 16Read more on congruent triangles;
https://brainly.com/question/1675117
Plz help me find side x on the triangle
Answer:
x=71
Step-by-step explanation:
Since this is an isosceles triangle as indicated by the lines on the sides, the sides lengths are equal.
When the sides are equal, the base angles are equal
x=71
The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas
(integer or a simplified fraction)
Thank you!
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Answer:
perimeter: 3 : 4area: 9 : 16Step-by-step explanation:
The perimeter ratio smaller : larger is the same as the side length ratio.
18 : 24 = 3 : 4 . . . smaller : larger perimeter ratio
The area ratio is the square of this.
3^2 : 4^2 = 9 : 16 . . . smaller : larger area ratio
If an orange seller bought 5 dozen oranges at the rate of tk.60 per four and sold them at the rate of tk50 per four,how much did he lose
Answer:
tk 30
Step-by-step explanation:
5 dozen = 5 * 12 = 60 oranges
12/4 = 3
total cost = 60 * 3 = tk.180
total sell = 50 * 3 = tk 150
total lose = 180 - 150 = tk 30
Suppose f(x) = loga(x) and f(7) = 2. Find f(343)
Answer:
6
Step-by-step explanation:
The given function to us is ,
[tex]\rm\implies f(x)= log_a(x) [/tex]
And its value at 7 is 2 , that is ,
[tex]\rm\implies f(x)= log_a(7) =2[/tex]
Taking this ,
[tex]\rm\implies 2= log_a(7) [/tex]
In general we know that ,
[tex]\bf\to log_a b = c ,\ then \ a^c = b [/tex]
Using this , we have ,
[tex]\rm\implies a^2 = 7 [/tex]
Squarerooting both sides ,
[tex]\rm\implies a =\sqrt{ 7 }[/tex]
Therefore , when x is 343 ,
[tex]\rm\implies f(343)= log_{\sqrt7} ( 343) [/tex]
We can write , 343 as 7³ ,
[tex]\rm\implies f(343)= log_{\sqrt7}7^3 [/tex]
[tex]\rm\implies f(343)= log_{7^{\frac{1}{2}}} 7^3 [/tex]
This can be written as ,
[tex]\rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}} [/tex]
[tex]\rm\implies \boxed{\blue{\rm f(343)= 6 }}[/tex]
Hence the required answer is 6.
what is the answer to this question
Answer:
18
Step-by-step explanation:
Shape = Isosceles Trapezoid
Area = 1/2 (a+b) h
= 1/2 (9+3) x 3
= 18
Answered by Gauthmath
Fine the area and circumference of each circle and round to the nearest tenth.
Answer: A=πr²
A=3.14(1.6inch)² r=d/2⇒3.2/2⇒1.6
A=3.14×2.56in²
A=8.0384in²
A≈8.04
now circumference,
C=2πr
C=2×3.14×1.6in
C=10.048in
C≈10.05
The planet Mercury travels in an elliptical orbit with eccentricity 0.203. Its minimum distance from the Sun is 4.5 x 10^7 km. If the perihelion distance from a planet to the Sun is a(1 - e) and the aphelion distance is a(1 + e), find the maximum distance (in km) from Mercury to the Sun.Pick from the following:1. 7.7 x 10^7 km.2. 6.6 x 10^7 km.3. 6.8 x 10^7 km.
Answer:
Option C
Step-by-step explanation:
From the question we are told that:
Eccentricity [tex]e=0.203[/tex]
Minimum distance from the Sun [tex]d_s= 4.5 x 10^7 km[/tex]
Perihelion distance from a planet to the Sun is [tex]r= a(1 - e)[/tex]
Aphelion distance [tex]r'=a(1 + e)[/tex]
Generally the equation for Perihelion distance is mathematically given by
[tex]4.5 * 10^7= a(1 - 0.203)[/tex]
[tex]4.5 * 10^7 = 0.797a[/tex]
[tex]a = 56.46 * 10^6 km[/tex]
Generally the equation for Aperihelion distance is mathematically given by
[tex]r' = a(1 + e)[/tex]
[tex]r' = 56.4617 * 10^6 (1 + 0.203)[/tex]
[tex]r'=6.8 * 10^7 km[/tex]
Option C
Find the domain and range of the function graphed below.
Answer:
Domain -1 ≤x<2
Range 0 < y ≤4
Step-by-step explanation:
Domain is the input values
X goes from -1 to 2 ( 2 not included)
Domain -1 ≤x<2
Range is the output values
y goes from 0 ( not included) to 4
Range 0 < y ≤4
I need to increase my sales by 35% in order to meet my goal for the month you currently have 45 sales and you will need to get blank in order to meet your goal
Answer:
61 sales
Step-by-step explanation:
First find the increase
45 * 35%
45*.35
15.75
Add this to your sales
45+15.75
60.75
Since you cannot have part of a sale, round up
61 sales
Can someone please help me .?
Answer:
5
Step-by-step explanation:
5+7
Order these in the correct order fanks
Answer:
0.05, 8%, 15/100, 3/10, 0.7
Step-by-step explanation:
so they are 5%, 8%, 15%, 30%, 70%
Add O used 6 cups of whole wheat flour and eggs we flower and ax cups of white flour in the recipe what is the equation that can be used to find the value of Y the total amount of flour that adult used in the recipe and what are the constraints and the values of X and Y
Answer:
6x+y
Step-by-step explanation:
Find the square root of 529/1080
Answer:
Square Root of 529:√529 = 23
Square Root of 1080: 32.863353450309965
My flvs teacher said that she was asked to hold off on grading my assignment. She will give me a call back when when gets more information. Anyone have the same problem?
Answer:
yeah, teachers kinda suck
In a study, 44% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 14 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 14 adults are randomly selected, 3 or fewer are in excellent health. Group of answer choices
Answer:
Step-by-step explanation:
Probability(P) (k events out of n trials) = nCk * p^k * (1-p)^(n-k), where p=0.40, n=10 and nCk is the number of combinations of n things taken k at a time
:
P ( k < or = 3 ) = P ( k = 3 ) + P ( k = 2 ) + P ( k = 1 ) + P ( k = 0 )
:
P ( k = 3 ) = 10C3 * (0.40)^3 * (0.60)^(10-3) = 0.2149
:
P ( k = 2 ) = 10C2 * (0.40)^2 * (0.60)^(10-2) = 0.1209
:
P ( k = 1 ) = 10C1 * (0.40)^1 * (0.60)^(10-1) = 0.0403
:
P ( k = 0 ) = 10C0 * (0.40)^0 * (0.60)^(10-0) = 0.0060
:
******************************************************************************
P ( k < or = 3 ) = 0.2149 + 0.1209 + 0.0403 + 0.0060 = 0.3821 is approximately 0.38
The probability that when 14 adults are randomly selected and 3 or fewer are in excellent health is 0.072
What is probability ?Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.
Given that,
The percentage of adults who reported their health was excellent = 44 %
The probability of excellent health P = 0.44
The probability of not excellent health = Q - 1 - 0.44 - 0.56
Since, 14 adults are randomly selected.
To find the probability that 3 or fewer are in excellent health,
Use formula
Probability = [tex]^nC_rP^n Q^{n-r}[/tex]
Where P = probability to happen an event, and Q= probability to not happen an event.
The probability that 3 or fewer are in excellent health
= [tex]^{14}C_3 (0.44)^3(0.56)^{14-3} +^{14}C_2(0.44)^2(0.56)^{14-2}+^{14}C_1 (0.44)^1(0.56)^{14-1} + ^{14}C_0 (0.44)^0(0.56)^{14}[/tex]
= 0.0526 + 0.0167 + 0.00328 + 0.000298
= 0.072282
The required probability is 0.072282.
To know more about Probability on:
https://brainly.com/question/12478394
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Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=t−t−1, y=1+t2, t=1
Answer:
Step-by-step explanation:
First, I would find the point on the curve. By substituting t=1, I get (x, y). Next, I will try to eliminate the t and make a xy equation. In this case, the t's will cancel out in 'x=t-t-1" which wouldnt make this a curve. To find the equation of the tangent line, find the deretitave of the xy equation, and subsitute x in to find the slope at that point. Next, use point slope form to find the equation at the point.
write your answer in simplest radical form
Answer:
3 =f
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = f/ sqrt(3)
sqrt(3) tan 60 = f
sqrt(3) * sqrt(3) = f
3 =f
What is the value of 3?
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Answer:
3 ⇒ 12
Step-by-step explanation:
Apparently "a = b" in this case is used to mean f(a) = b. It appears as though the function is ...
f(x) = x(x+1)
Then f(3) = 3(3+1) = 3·4 = 12
_____
Additional comment
IMO this is a poor use of the equal sign, which should be reserved for situations where the left side expression has the same value as the right side expression.
PLEASE HELP ME ON 6-11 AND SHOW WORK PLEASE!!
Answer:
6) 6[tex]\sqrt{2}[/tex]
9) 40
10) [tex]\frac{5\sqrt{2} }{2}[/tex]
11) 13
Step-by-step explanation:
6)A right triangle rule: if 2 legs are equal, the hypotenuse is the length of that leg*[tex]\sqrt{2}[/tex]
9) Pythagorean Theorem
[tex]a^{2} +b^{2} =c^{2}[/tex]
We know the hypotenuse (41) so we substitute that for c and 9 for b now we need to find a
[tex]\sqrt{41^{2}-9^{2} }[/tex] which gives us 40
10) same with #6 but we do the opposite. SInce we have the hypotenuse, we can divide that by [tex]\sqrt{2}[/tex] because we know that if 2 legs are equal, the hypotenuse is multiplied by [tex]\sqrt{2}[/tex]. Multiply the numerator and denominator by [tex]\sqrt{2}[/tex] because we can't have a square root in the denominator.
11) like #9 we have the a and b but we need to find c
a=5 b=12 c=r
so [tex]\sqrt{5^{2}+12^{2} }[/tex] which gives us 13
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {c}^{2} = {6}^{2} + {6}^{2} \\ {c}^{2} = 36 + 36 \\ c = \sqrt{2( {6}^{2} )} \\ c = \sqrt{2}{\sqrt{ {6}^{{2}} } } \\ c = 6 \sqrt{2} \: \: \: ans[/tex]
9TH PART:- GIVENRIGHT ANGLE SO ITS A RIGHT ANGLED TRIANGLE SO WE CAN USE PYTHAGOUS THEOREMBASE = 9HYPOTENUSE= 41SOLUTION->
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {41}^{2} = {x}^{2} + {9}^{2} \\ 1681 = {x}^{2} + 81 \\ 1681 - 81 = {x}^{2} \\ 1600 = {x}^{2} \\ x = \sqrt{40 \times 40} \\ x = 40 \: \: \: ans[/tex]
10 TH PART:-GIVEN
RIGHT ANGLE SO ITS A RIGHT ANGLED TRIANGLE SO WE CAN USE PYTHAGOUS THEOREMTWO SIDES ( BASE AND PERPENDICULAR) R EQUAL TO SHYPOTENUSE= 5SOLUTION->[tex]{h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {5}^{2} = {s}^{2} + {s}^{2} \\ 25 = 2 {s}^{2} \\ 12.5 = {s}^{2} \\ \sqrt{12.5} = s \\ 3.5 = s \: \: \: ans[/tex]
11TH PART:- GIVEN RIGHT ANGLE SO ITS A RIGHT ANGLED TRIANGLE SO WE CAN USE PYTHAGOUS THEOREMBASE = 5 PERPENDICULAR= 12 SOLUTION ->[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {r}^{2} = {12}^{2} + {5}^{2} \\ {r}^{2} \\ 144 + 25 \\ {r}^{2} = 169 \\ r = \sqrt{13 \times 13} \\ r = 13 \: \: \: \: ans[/tex]
HOPE IT HELPED
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: DEVIL005 \: \star[/tex]
A map that was created
using a scale of 1 inch : 3 miles
shows a lake with an area of
18 square inches. What is the
actual area of the lake?
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Answer:
162 mi²
Step-by-step explanation:
The area on the map is ...
18(1 in)²
Then the area on the ground will be ...
18(3 mi)² = 18·9 mi² = 162 mi²
WILL MARK BRAINIEST, QUESTION IS HARD, Ann works for a city’s parks and recreation department. She is looking for some commercial land to rezone for recreational use and has found two possible options. Ann’s first option is a plot of land adjacent to a current park. The current park is a square, and the addition will increase the width by 200 meters to give the expanded park a total area of 166,400 square meters. This equation represents the area of the first option, where x is the side length of the current square park: x2 + 200x = 166,400. Use the most direct method to solve this equation and find the side length of the current square park. Explain your reasoning for both the solving process and the solution.
Answer:
[tex]x =320[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 200x = 166400[/tex]
Required
Find x
We have:
[tex]x^2 + 200x = 166400[/tex]
Rewrite as:
[tex]x^2 + 200x - 166400 = 0[/tex]
Expand
[tex]x^2 + 520x - 320x - 166400 = 0[/tex]
Factorize
[tex]x(x + 520) - 320(x + 520)= 0[/tex]
Factor out x + 520
[tex](x - 320) (x + 520)= 0[/tex]
Split
[tex]x - 320 = 0\ or\ x + 520= 0[/tex]
Solve
[tex]x = 320\ or\ x =- 520[/tex]
Side length must be positive;
So:
[tex]x = 320[/tex]
Write an equivalent expression to 1/2 (2n+6).
Answer:
n+3
Step-by-step explanation:
1/2 × 2(n+3)=n +3
I hope this helps
Evaluate the given integral by changing to polar coordinates.
Integar sin(x2 + y2) dA R
where R is the region in the first quadrant between the circles with center the origin and radii 1 and 5.
In polar coordinate, R is the set of points
{(r, θ) | 1 < r < 5 and 0 < θ < π/2}
So the integral is
[tex]\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA = \int_0^{\frac\pi2}\int_1^5 r\sin(r^2)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac\pi2\int_1^5 r\sin(r^2)\,\mathrm dr[/tex]
[tex]=\displaystyle\frac\pi4\int_1^5 2r\sin(r^2)\,\mathrm dr[/tex]
[tex]=\displaystyle\frac\pi4\int_1^{25} \sin(s)\,\mathrm ds[/tex]
(where s = r ²)
[tex]=\displaystyle-\frac\pi4\cos(s)\bigg|_1^{25}= \boxed{\dfrac\pi4 (\cos(1) - \cos(25))}[/tex]
Find the equations of the tangents to the curve x=9t2+3, y=6t3+3 that pass through the point (12,9).
Answer:
The equation will be "[tex]y=x-3[/tex]".
Step-by-step explanation:
Given:
Points (12, 9) = (x, y)
⇒ [tex]x=9t^2+3[/tex]
then,
[tex]\frac{dy}{dt}=18t[/tex]
or,
⇒ [tex]y=6t^3+3[/tex]
then,
[tex]\frac{dy}{dt}=18t^2[/tex]
⇒ [tex]\frac{dy}{dx}=\frac{18t^2}{18t}[/tex]
[tex]=t[/tex]
By using the point slope form.
The equation of tangent will be:
⇒ [tex]y-9=1(x-12)[/tex]
[tex]y-9=x-12[/tex]
[tex]y=x-12+9[/tex]
[tex]y=x-3[/tex]
I need help with the question below
Answer:
a: 1/12
b: 1/6
c: 1/2
d: 1/2
e: 1/12
f: 1/3
Step-by-step explanation: