Answer:
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
Step-by-step explanation:
From the summary of the given statistical dataset
The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:
[tex]\mu_{\overline x} = \mu _x[/tex] = 64.5
[tex]\sigma_{\overline x }= \dfrac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{\sqrt {25}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{5}[/tex]
[tex]\sigma_{\overline x }[/tex] = 0.5
Thus X [tex]\sim[/tex] N (64.5,0.5)
Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:
[tex]P(\overline X > 66) = P ( \dfrac{\overline X - \mu_\overline x}{\sigma \overline x }>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{1.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>3 })[/tex]
[tex]P(\overline X > 66) = 1- P ( Z<3 })[/tex]
[tex]P(\overline X > 66) = 1- 0.9987[/tex]
[tex]P(\overline X > 66) =0.0013[/tex]
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
Solving exponential functions
Answer:
approximately 30Step-by-step explanation:
[tex]f(x) = 4 {e}^{x} [/tex]
[tex]f(2) = 4 {e}^{2} [/tex]
[tex]f(2) = 4 \times 7.389[/tex]
[tex]f(2) = 29.6[/tex]
( Approximately 30)
Hope this helps..
Good luck on your assignment..
Answer:
approximately 30
Step-by-step explanation:
[tex]f(x)=4e^x[/tex]
Put x as 2 and evaluate.
[tex]f(2)=4e^2[/tex]
[tex]f(2)=4(2.718282)^2[/tex]
[tex]f(2)= 29.556224 \approx 30[/tex]
PLEASE HELP Which ordered pair is a solution to the system of inequalities?
y< 3x
y< 5
Answer:
I am pretty sure that it is C
Step-by-step explanation:
A 1,3 so 3 < 3 no not true
x,y
B -12,50 50< -36 Also not true
x , y
C 9 , 4 4<27 Yes 4< 5 YEPPP
D 4,10 10<12 Yes 10<5 NOOPPPPPEEEE
A rectangular waterbed is 7 ft long 5 ft wide and 1 ft tall
How many gallons of water are needed to fill the waterbed?
Assume i gallon is 013 cu ft. Round to the nearest whole galon
Hey there! I'm happy to help!
We want to find the volume of this rectangular waterbed. This means the amount of space it takes up. To find the volume of a rectangular prism, you just multiply together the three side lengths.
7×5×1=35 cubic feet
Now, we need to see how many gallons fit into 35 cubic feet. We see that one gallon is equal to 0.13 cubic feet. So, we can set up a proportion to find how many gallons are needed. We will use g to represent our missing number of gallons.
[tex]\frac{gallons}{cubic feet} = \frac{1}{0.13} =\frac{g}{35}[/tex]
In a proportion, the products of the diagonal numbers are equal. This means that 35, which is 1 multiplied by 35, is equal to 0.13g, which is from multiplying 0.13 by the g.
0.13g=35
We divide both sides by 0.13/
g≈269.23
When rounded to the nearest whole gallon, we will need 269 gallons of water to fill the waterbed.
I hope that this helps! Have a wonderful day! :D
Answer:
Step-by-step explanation:
Since the waterbed is rectangular, its volume would be determined by applying the formula for determining the volume of a cuboid which is expressed as
Volume = length × width × height
Therefore,
Volume of waterbed = 7 × 5 × 1 = 35 cubic feet
1 US gallon = 0.133680556 cubic feet
Therefore, converting 35cubic feet to gallons, it becomes
35/0.133680556 = 261.81818094772 gallons
Rounding up to whole gallon, it becomes 262 gallons
Daniels freezer is set to 0degrees Fahrenheit he places a load of bread that was at a temperature of 78 degrees Fahrenheit in the freezer the bread cooled at a rate of 11 degrees Fahrenheit per hour write and graph an equation that models the temperature t of the bread
Answer:
it took 7 hours for the bread to drop at a constent rate
Step-by-step explanation:
how do you find the x- and y-intersepts of an equation
Answer:
To find the x-intercept, simply plug in the value y = 0 into your equation and then solve for x. To find the y-intercept, plug in x = 0 and solve for y.
Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid passwords are there with the given restriction(s)? Length is 13. No character repeats.
Answer:
2310789600
Step-by-step explanation:
10 digits + 26 letters = 36
₃₆C₁₃ = 2310789600
Hope this helps, although i am not 100 percent sure its right.
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 205 yards due west from your position and takes a bearing on the cabin of N 23.9°E. How far are you from the cabin? asap would be great also running out of points srry
Answer:
462.61 yards.
Step-by-step explanation:
To solve, you need to find the measurement of the angle that forms a 90 degree angle with the 23.9 degree angle.
90 - 23.9 = 66.1 degrees.
Now that you have the angle, you can use TOA to solve for x (TOA = Tangent; Opposite over Adjacent).
tan(66.1) = x / 205
x / 205 = tan(66.1)
x = tan(66.1) * 205
x = 2.256628263 * 205
x = 462.6087939
So, you are about 462.61 yards from the cabin.
Hope this helps!
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown. Step 1: –c = ax2 + bx Which best explains or justifies Step 1?
Answer:
Subtract c from each side, using the subtraction property of equality
Step-by-step explanation:
0 = ax^2 + bx + c
Subtract c from each side, using the subtraction property of equality
-c = ax^2 + bx + c-c
-c = ax^2 + bx
Answer:
subtract c from each side, so the answer would be D
I need to know if the following questions are true or false
Answer:
False
Step-by-step explanation:
To find <A, we can do 5x - 80 = 3x + 20.
As we simplify, we will get 2x = 100, which is x = 50
Therefore, <A will be 50 degrees and not 45 degrees.
Also, if you need y, you can do:
3y - 7 = y + 7
2y = 14
y = 7
odd function definition
how to simplify this expression ?
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{2x+1}{x^2(x+1)} \ \ }[/tex]
Step-by-step explanation:
Hello,
This is the same method as computing for instance:
[tex]\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}[/tex]
We need to find the same denominator.
Let's do it !
For any x real different from 0, we can write:
[tex]\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Solve for x in the equation X^2-16^x=0
Answer:
-1/2
Step-by-step explanation:
x^2- 16^x = 0x^2 = 16^xx^2 = 4^2xx = 4^xlogx = xlog41/x×logx = log4log(x^1/x) = log4x^(1/x) = 4At this point you can guess and try. And it seems that x = -1/2, lets check:
(-1/2)^(1 /-1/2)= (-1/2)^-2= 2^2= 4So, this is correct: x= -1/2
The graph of y=−x+2 is shown below.
Answer:
What is the question?
Step-by-step explanation:
At the city museum, child admission is $ 5.30 and adult admission is $ 9.40 . On Sunday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1206.00 . How many child tickets were sold that day?
Answer:
36 tickets
Step-by-step explanation:
At a city museum, child tickets are sold for $5.30, and adult tickets are sold for $9.40
The total sales that were made are $1206
Let x represent the number of child tickets that were sold
Let y represent the number of adult tickets that was sold
5.30x +9.40y= 1206
The number of adult tickets sold was three times greater than the child tickets
y= 3x
Substitute 3x for y in the equation
5.30x + 9.40y= 1206
5.30x + 9.40(3x)= 1206
5.30x + 28.2x= 1206
33.5x= 1206
Divide both sides by the coefficient of x which is 33.5
33.5x/33.5= 1206/33.5
x = 36
Hence the number of child tickets that were sold that day is 36 tickets
What are some key words used to note addition operations?
Answer:
The correct answer is
For addition, Caulleen used the words total, sum, altogether, and increase. But we could also have used the words combine, plus, more than, or even just the word "and". For subtraction, Caulleen used the words, fewer than, decrease, take away, and subtract. We also could have used less than, minus, and difference.
Step-by-step explanation:
hope this helps u!!!
A pile of 55 coins consisting of nickels and dimes is worth $3.90 . Find the number of each. PLZ ANSWER IN 1 MIN
Answer:
23 dimes; 32 nickel
Step-by-step explanation:
Let n = number of nickels.
Let d = number of dimes.
A nickel is worth $0.05; n nickels are worth 0.05n.
A dime is worth $0.10; d dimes are worth 0.1d.
Number of coins:
d + n = 55
Value of the coins:
0.1d + 0.05n = 3.9
Solve d + n = 55 for d:
d = 55 - n
Substitute 55 - n for d in second equation.
0.1(55 - n) + 0.05n = 3.9
5.5 - 0.1n + 0.05n = 3.9
-0.05n = -1.6
n = 32
Substitute 32 for n in d + n = 55 and solve for d.
d + 32 = 55
d = 23
Answer: 23 dimes; 32 nickel
Pretty much Self explanatory :) I don't understand this...
Answer:
Step-by-step explanation:
you have to keep going cause if you count the fives there's a 25 but right next to the 25 there's 24 all you have to do is watch what your doing just watch your steps
An important proportion that the ancient Greeks used was the
the ancient Greek used the golden ratio
Answer:
An important proportion that the Ancient Greeks used was the Golden Mean, the a0
Step-by-step explanation:
Also known as Golden Ratio, Divine Proportion, or Golden Section
A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses. How many courses worth 3 credits did the student complete?
Answer:
They completed 13, 3 credit classes
Step-by-step explanation:
1. Make 2 formulas. In this case: x+y=18
and 3x+4y=59
2. Then multiply x+y=18 by 3 and subtract the two equations.
Find y which is 5 and input into the equations. Then find your answer.
For each of the following determine a unit rate using the information given. Show the division that leads to your answer. Use appropriate units. All rates will be whole numbers. At a theatre, Mia paid $35 for five tickets
Answer:
Step-by-step explanation:
cool
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 109 in. and the height is 198 in.
Answer:
[tex]79591.8872 in^3/s[/tex]
Step-by-step explanation:
we know that the volume of a right circular cone is give as
[tex]V(r,h)= \frac{1}{3} \pi r^2h\\\\[/tex]
Therefore differentiating partially with respect to r and h we have
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]
[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]
[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]
The tee for the sixth hole on a golf course is 400 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard. Answer any time! :D
Answer:
181.8 yd
Step-by-step explanation:
The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...
c^2 = a^2 +b^2 -2ab·cos(C)
For the given geometry, this is ...
c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75
c ≈ √33037.75 ≈ 181.8 . . . yards
Marsha's ball is about 181.8 yards from the hole.
Answer:
181.8 yds
Step-by-step explanation:
I got it correct on founders edtell
Someone please help! Thxx
Answer:
E, needs more info to be determined
Step-by-step explanation:
We know that Kai takes 30 minutes round-trip to get to his school.
One way is uphill and the other is downhill.
He travels twice as fast downhill than uphill.
This means that uphill accounts for 20 minutes of the round-trip and downhill accounts for 10 minutes of his trip.
However, even with this information, we do not know how far his school is.
In order to figure out how far away his school is, we would need more information about the speed at which Kai is traveling.
Simply knowing that he travels twice as fast downhill is not enough.
This question could only be solved by knowing how many miles Kai travels uphill or downhill in a given time.
Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2
The graph which shows the solution to the system of inequalities is attached in the picture below :
Given the inequalities :
y ≥ 2x + 1
y ≤ 2x - 2
From y ≥ 2x + 1 ;
Since the inequality sign is ≥, a solid line is used to draw the straight line graph of y ≥ 2x + 1
From :
y = mx + c
Where, m = slope ; c = intercept
Hence, a straight line graph with ;
Intercept, c = 1 (where the line crosses the y-intercept)
Slope, m = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality :
0 ≥ 2(0) + 1
0 ≥ 0 + 1
0 ≥ 1
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
From : y ≤ 2x - 2
Since the inequality sign is ≤, a solid line is used to draw the straight line graph of y ≤ 2x - 2
Graph the line y ≤ 2x - 2, with ;
Intercept, c = - 2
Slope = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality y ≤ 2x - 2:
0 ≤ 2(0) - 2
0 ≤ 0 - 2
0 ≤ - 2
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
Learn more : https://brainly.com/question/19670553
Answer:
Its graph B on edge 2022
Step-by-step explanation:
A ball is thrown straight down from the top of a 435-foot building with an initial velocity of -27 feet per second. Use the position function below for free-falling objects. s(t) = -16t^2 + v_0t + s_0 What is its velocity after 2 seconds? v(2) = -91 ft/s What is its velocity after falling 364 feet? v = 1.61 ft/s Find an equation of the parabola y = ax^2 + bx + c that passes through (0, 1) and is tangent to the line y = 5x - 5 at (1, 0). Y = 5x + 10
Answer:
a) The velocity of the ball after 2 seconds is -91 feet per second, b) The velocity of the ball after falling 364 feet is 155 feet per second, c) The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].
Step-by-step explanation:
a) The velocity function is obtained after deriving the position function in time:
[tex]v (t) = -32\cdot t -27[/tex]
The velocity of the ball after 2 seconds is:
[tex]v(2\,s) = -32\cdot (2\,s) -27[/tex]
[tex]v(2\,s) = -91\,\frac{ft}{s}[/tex]
The velocity of the ball after 2 seconds is -91 feet per second.
b) The time of the ball after falling 364 feet is found after solving the position function as follows:
[tex]435\,ft - 364\,ft = -16\cdot t^{2}-27\cdot t + 435\,ft[/tex]
[tex]-16\cdot t^{2} - 27\cdot t + 364 = 0[/tex]
The solution of this second-grade polynomial is represented by two roots:
[tex]t_{1} = 4\,s[/tex] and [tex]t_{2} = -5.688\,s[/tex].
Only the first root is physically reasonable since time is a positive variable. Now, the velocity of the ball after falling 364 feet is:
[tex]v(4\,s) = -32\cdot (4\,s) - 27[/tex]
[tex]v(4\,s) = -155\,\frac{ft}{s}[/tex]
The velocity of the ball after falling 364 feet is 155 feet per second.
c) Let consider the equation for a second order polynomial that passes through (0, 1) and its first derivative that passes through (1, 0) and represents the give equation of the tangent line. That is to say:
Second-order polynomial evaluated at (0, 1)
[tex]c = 1[/tex]
Slope of the tangent line evaluated at (1, 0)
[tex]5 = 2\cdot a \cdot (1) + b[/tex]
[tex]2\cdot a + b = 5[/tex]
[tex]b = 5 - 2\cdot a[/tex]
Now, let evaluate the second order polynomial at (1, 0):
[tex]0 = a\cdot (1)^{2}+b\cdot (1) + c[/tex]
[tex]a + b + c = 0[/tex]
If [tex]c = 1[/tex] and [tex]b = 5 - 2\cdot a[/tex], then:
[tex]a + (5-2\cdot a) +1 = 0[/tex]
[tex]-a +6 = 0[/tex]
[tex]a = 6[/tex]
And the value of b is: ([tex]a = 6[/tex])
[tex]b = 5 - 2\cdot (6)[/tex]
[tex]b = -7[/tex]
The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].
Use the Pythagorean theorem to find the length of the hypotenuse in the triangle shown below 15 and 39
Answer:
36
Step-by-step explanation:
You did not attach a picture, so I just assumed where the lengths of 15 and 39 were.
Proving the sum of the Interior Angle Measures of a Triangle is 180
Answer:
theres the screenshot of it
The solution to prove the sum of the interior angles of a triangle is 180° is
∠1 + ∠2 + ∠3 = 180° ( angles in a straight line )
∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle )
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Now , the angles inside the triangle are ∠2 , ∠5 and ∠6
Now , the lines l₁ and l₂ are two parallel lines
From the figure ,
The measure of ∠1 = The measure of ∠5 ( alternate interior angles )
The measure of ∠3 = The measure of ∠6 ( alternate interior angles )
Now , for a straight line , the measure of angle = 180°
So , ∠1 + ∠2 + ∠3 = 180° ( angles in a straight line ) ( angle addition )
And , the sum interior angles of a triangle is 180°
So , ∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle ) ( substitution )
Hence , the sum of the angles inside a triangle is 180°
To learn more about triangles click :
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In parallelogram ABCD, the coordinates of A are (4,3) and the coordinates of the midpoint of diagonal AC
are (2,5). What are the coordinates of C?
Answer:
D. (0, 7).
Step-by-step explanation:
Moving from (4,3) to (2, 5) we move 2 to the left; 2 - 4 = 2 then 2 up 3 + 5 = +2.
So the point C is 2-2, 5+2 = (0, 7).
An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 2% of the true proportion with 99% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy?
Answer: n = 2401
Step-by-step explanation:
Given;
Confidence level = 2% - 99%
n = ? ( which is the sample size is unknown ).
Solution:
Where;
n = [z/E]^2*pq
Since no known value for ( p ) estimate is given, the "least biased" estimate is p = 1/2
Substituting the given data into the formula.
n = [1.96/0.02]^2(1/2)(1/2)
n = 2401
The minimum number of truck drivers the statistician needs to sample for an accurate result is 2401
You are dealt two card successively without replacement from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second is a queen. Round to nearest thousandth
Answer:
0.078
Step-by-step explanation:
The probability P(A) of an event A happening is given by;
P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]
From the question;
There are two events;
(i) Drawing a first card which is a king: Let the event be X. The probability is given by;
P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]
Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.
Also, the total number of sample space = 52, since there are 52 cards in total.
P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;
P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]
Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4
But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.
P(Y) = [tex]\frac{4}{51}[/tex]
Therefore, the probability of selecting a first card as king and a second card as queen is;
P(X and Y) = P(X) x P(Y)
= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078
Therefore the probability is 0.078