Complete Question
The mean height of women in a country (ages 20-29) is 64.4 inches. A random sample of 75 women in this age ground is selected. what is the probability that the mean height for the sample is greater than 65 inches? assume [tex]\sigma = 2.97[/tex]
Answer:
The value is [tex]P(X > 65) = 0.039715[/tex]
Step-by-step explanation:
From question we are told that
The mean is [tex]\mu = 64.4 \ inches[/tex]
The sample size is [tex]n = 75[/tex]
The probability that the mean height for the sample is greater than 65 inches is mathematically represented as
[tex]P(X > 65) = P[\frac{X - \mu }{ \sigma_{\= x} } > \frac{65 - 64.4 }{ \sigma_{\= x} } ][/tex]
Where [tex]\sigma _{\= x }[/tex] is the standard error of mean which is evaluated as
[tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x } = \frac{2.97}{\sqrt{75} }[/tex]
=> [tex]\sigma_{\= x } = 0.343[/tex]
Generally [tex]\frac{X - \mu }{ \sigma_{\= x } } = Z(The \ standardized \ value \ of \ X )[/tex]
[tex]P(X > 65) = P[Z> \frac{65 - 64.4 }{0.342 } ][/tex]
So
[tex]P(X > 65) = P[Z >1.754 ][/tex]
From the z-table the value of
[tex]P(X > 65) = P[Z >1.754 ] = 0.039715[/tex]
[tex]P(X > 65) = 0.039715[/tex]
The Brazilian free-tailed bat can travel 99 miles per hour. After sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. How long before these bats cover an area of 80,000 square miles? Use π = 3.14
Answer: 1.6 hours.
Step-by-step explanation:
Ok, the speed of the bats is 99mph.
Here we can think this situation as a circle where the radius is growing at a speed of 99mph.
We assume that the initial radius is r = 0, and we can write the equation of the radius as a linear equation that depends on the time t.
r(t) = 99mi/h*t
First, let's find the radius that we need:
The area of a circle is:
A = ´pi*r^2
If we want A = 80,000 mi^2 we have:
80,000 mi^2 = 3.14*r^2
r = √(80,000 mi^2/3.14) = 159.6 mi
So the radius must be 159.6 miles.
Now, we know that the speed at which the radius increases is 99miles per hour, and we also know that:
Distance = Speed*Time.
in this case:
Distance = 159.6 mi
Speed = 99mi/h
Time = is the thing we want to find.
159.6mi = 99mi/h*T
T = 159.6mi/99mi/h = 1.6 hours.
Fine the length of the side labeled x. Around intermediate values to the nearest tenth. use the rounded values to calculate the next value. round your answer to the nearest tenth.
Answer:
A. 23.6
Step-by-step explanation:
Let the dotted line be y
Then
y/x = sin(50°) ⇒ x = y/sin (50°)and
29/y = tan (58°) ⇒ y = 29/tan (58°)So
x = 29/tan (58°)/sin (50°) ≈ 23.6Correct answer is A. 23.6
Answer:
23.6
Step-by-step explanation:
what divides a two dimensional shape into two congruent shapes
Answer:
Rectangle is a 2dimensional shape so, let me explain using it
The diagonal of a rectangle divides the rectangle into two triangles that are congruent and they are the same size and shape.
Another example is parallelogram
The diagonal of a parallelogram also divides the figure into two triangles that are congruent.
Step-by-step explanation:
Use counting to determine the whole number that corresponds to the cardinality of these sets:______. (a) A= (xl x € Nand 20.< x<27)
(b) B=(xixeNandx+1=x)
(c) C={xl xe Nand(x- I)(x - 9) = 0)
(d) D={xlx E N, H X 5 100, and xis divisible by both 5 and 8)
Answer:
Step-by-step explanation:
Cardinality of a set is defined as number of element in a set. It is represented as n(X) where X is any set.
a) Given the set A =(x l x € N and 20.< x<27). According to the set, the set contains the values of natural numbers between 20 and 27. The values are 21, 22, 23, 24, 25 and 26
A = (21, 22, 23, 24, 25, 26)
According to the set A, it can be seen that there are 6 elements in the set, this means n(A) = 6.
b) Given B=(x | xeN and x+1=x)
Since natural numbers starts from 1, the first element in the set is 2 i.e 1+1
The elements of the set B = (2, 3, 4, 4...)
The number of whole number in the set is therefore infinite.
c) For the set C={x l xe N and (x- 1)(x - 9) = 0)
We need to get the root of the equation (x- 1)(x - 9) = 0
x-1 = 0 and x-9 = 0
x = 1 and x = 9
Hence the element C = (1,9)
The number of whole number in the set is n(C) = 2
d) D={xlx E N, H X 5 100, and x is divisible by both 5 and 8)
Given the value of x between 5 and 100, the values of x divisible by 5 = (10, 15, 20, 25, 30, 35, 40, 45, 50 , 55, 60 , 65, 70, 75, 80 85, 90, 95)
values of x divisible by 8 = (16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96)
The total number of elements in both set = 29 i.e n(D) = 29
7. Given the following information, calculate, in order, the amount credited and the outstanding balance.
Invoice: $1,000
Terms: 3/10, n/30
Invoice date: May 5
Payment amount: $800
Date paid: May 9
A. $265 26: $624 74
B. $176 00, $824 00
C. $824.74 $175.26
D. $724.74 $275 26
Answer:
C. $824.74, $175.26
Step-by-step explanation:
1) Amount Credited
The formula to calculate the amount credited =
Amount paid ÷ ( 100% - Discount)
Discount is given in the question as 3/10
Where 3 = Discount rate
Amount paid = $800
Amount credited = 800/( 100% - 3%)
= 800/ 97%
= 800/ 0.97
= $824.74
b) Outstanding balance = Invoice - Amount credited
Invoice = $1000
Amount credited = $824.74
Outstanding balance = $1000 - $824.74
= $175.26
A professor teaches an undergraduate course in statistics. He uses a lot of sports examples to explain key concepts. He is concerned that this may have biased his instruction to favor male students. To test this, he measures exam grades among women (n = 10) and men (n = 10). The mean score in the male group was 82 ± 4.0 (M ± SD); in the female group, it was 74 ± 8.0 (M ± SD) points. If the null hypothesis is that there is no difference in exam scores, then test the null hypothesis at a .05 level of significance for a two-tailed test. Use denominator of 2.98.
Answer:
The null hypothesis is rejected
Therefore there is sufficient evidence to conclude that the professors teaching method favored the male
Step-by-step explanation:
From the question we are told that
The sample size for each population is [tex]n_1 = n_2 = n = 10[/tex]
The first sample mean is [tex]\= x_1 = 82[/tex]
The second sample mean is [tex]\= x_2 = 74[/tex]
The first standard deviation is [tex]\sigma _1 = 4[/tex]
The second standard deviation is [tex]\sigma_2 = 8.0[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 \ne \mu_2[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{ \frac{ \sigma_1^2}{n_1} + \frac{ \sigma_2^2}{n_2} }[/tex]
=> [tex]SE = \sqrt{ \frac{ 4^2}{10} + \frac{ 8^2}{10} }[/tex]
=> [tex]SE = 2.83[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_1 - \= x_2 }{SE}[/tex]
=> [tex]t = \frac{82 - 74}{2.83}[/tex]
=> t = 2.83
Generally the p-value mathematically represented as
[tex]p-value = 2 P(Z > 2.83)[/tex]
From the z table
[tex]P(Z > 2.83) = 0.0023274[/tex]
So
[tex]p-value = 2 * 0.0023274[/tex]
[tex]p-value = 0.0047[/tex]
Since
[tex]p-value < \alpha[/tex]
Hence the null hypothesis is rejected
Therefore there is sufficient evidence to conclude that the professors teaching method favored the male
The ratio of a quarterback’s completed passes to attempted passes in 2:5. If he attempted 20 passes he completed. Round to the nearest whole number if necessary
Four more than one third x
Answer:
4 + x/3
4 + 1/3x
Step-by-step explanation:
Step 1: Convert "four" to number
4
Step 2: Covert "more than" to number
4 +
Step 3: Convert "one-third" to number
4 + 1/3
Step 4: Add variable x (multiplication)
4 + 1/3x
PLEASE HELPPPP Using the diagram below, which of the following angle pairs represent vertical angles?
Answer:
DCE and BCA
Step-by-step explanation:
Vertical angles are angles which lie directly opposite each other on intersecting lines. Because of this they are equal, and share the same vertex. Out of these pairs, only DCE and BCA are vertical angles because they lie opposite to each other on the lines FJ and IM, and share a vertex of point C.
Hope this helped!
Suppose that the value of a stock varies each day from $11.82 to $15.17 with a uniform distribution. Find the third quartile, i.e., 75% of all days the stock is below what value?
The third quartile, or the value at which 75% of all days the stock is below, is $14.3325.
Used the formula that states,
the range of the distribution by subtracting the minimum value from the maximum value:
Range = Max value - Min value = $15.17 - $11.82 = $3.35
Given that the stock value follows a uniform distribution from $11.82 to $15.17.
Hence,
Range = $15.17 - $11.82
= $3.35
Now, the uniform distribution is symmetric, and the median (50th percentile) is the midpoint of the range,
Median = (Min value + Max value) / 2
= ($11.82 + $15.17) / 2
= $13.495
Hence, the third quartile (75th percentile);
75th percentile = Median + (0.25 × Range)
= $13.495 + (0.25 × $3.35)
= $13.495 + $0.8375
= $14.3325
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Solve F(x) for the given domain.
F(x)= x2 + 3x-2
F(-1) =
Jutaານເພະາ
a. -4
b. -6
C. 2.
Answer:
A. -4
Step-by-step explanation:
F(-1) means we must plug the number "-1" in for each x.
F(x) = x^2 + 3x - 2
F(-1) = (-1)^2 + 3(-1) - 2
= 1 - 3 - 2
= -4
If f(x) = 5x, what is f^-1(x)
Answer:
f^-1(x) = 1/5 x
Step-by-step explanation:
y = 5x
Exchange x and y to find the inverse
x = 5y
Solve for y
1/5x = y
The inverse is 1/5x
Answer:
[tex]\Large \boxed{f^{-1}(x)=\frac{x}{5} }[/tex]
Step-by-step explanation:
f(x) = 5x
Replace f(x) with y.
y = 5x
Switch variables.
x = 5y
Divide both sides by 5.
[tex]\frac{x}{5} =y[/tex]
(x+3)/(x-5)=(19-3x)/(x-5)
Answer: 4
Step-by-step explanation:
(x+3)/(x-5)=(19-3x)/(x-5)
x+3=19-3x
4x=16
x=4
Evaluate Algebraic Expressions
The classroom is divided into four equal parts. The area of each part is 5.3 meters. What is the are of the classroom?
I think that the answer is 21.2 .I can't say it with confidence but still maybe it will help you
School a has graduated 1700 students and graduates 50 students each year school b has graduated 600 students but 150 each year how many years will it be before school b has as many graduates as school a
Answer:
11 years
Step-by-step explanation:
t=time
1700+50t=600+150t
The reason we have this equation is because they both have the same time and based on the initial numbers that they have equating the two will give you the exact year and number of students of both school.
If 2^x=5 what is 2^3^x - 4
Answer: 121
Step-by-step explanation:
If 2^x = 5, what is the value of 2³^×
This can also be re arranged in the form
(2^x)³ - 4
Since 2^x = 5, we now substitute for the value in the expression above.
5³ - 4
= 125 - 4
= 121.
how many kilometres are there in 1 metre
Answer: 0.001 kilometer in 1 meter
Step-by-step explanation:
1 kilometer = 1000 meter
so there are 0.001 kilometer in 1 meter
A spring with a mass of 5 Kg has natural length 0.5m. A force of 35.6 N is required to maintain it stretched to a length of 0.5m. If the spring is stretched to a length of 0.5m and released with initial velocity 0, find the position of the mass at any time t. Here damping constant is zero.
Answer:
Step-by-step explanation:
Need help on questions 3 and 4
Answer:
y=3x
2y=x
Step-by-step explanation:
N/A
big brain award pls
A number N is greater than 3. Which of the following best represents the location of 3N
on a number line?
Answer:
The second number line represent the location of 3N values.
Step-by-step explanation:
The first number line represent the inequality N > 3.
Now, the new number is 3N.
Consider the second number line values:
3N = {12, 15, 18, 21, ....}
The second number line represent the location of 3N values.
Answer:
d
Step-by-step explanation:
Name the image of A after a rotation of -90° about the origin.
minus 90 degree means that it will go anti clock-wise direction. So, this shape will touch on under the y-axis
Let un be the nth Fibonacci number. Prove that the Euclidean algorithm takes precisely n steps to prove that gcd(un+1, un) = 1.
Answer:
Following are the answer to this question:
Step-by-step explanation:
According to Eucharistic algorithm:
[tex]gcd(un+1,un) = gcd (un+1-un, un)[/tex]
[tex]= gcd (un , un-1)[/tex]
so many recursions following
It was the first two the Fibonacci 1,1 numbers
[tex]gcd(un+1, un) = gcd(1,1) = 1 \\\\ from 1 =1 \text{and euclidean principle} \\\\?gcd (un+1,un ) = 1[/tex]
what's is the area of circle of circle with a radius of 7 inches use =3.14.
Answer: To find the area of a circle you use pi x rsquared. So just 3.14x7^2= 153.86
Step-by-step explanation:
3. One morning, the elevator in Emilio's apartment building was out of order. When he walked down the stairs from
his apartment to the ground floor, he counted 252 steps. Emilio lives on the 14th floor. How many steps are
between each floor?
A 10
C 22
B 18
D 32
Answer:
Number of steps per floor= 18 steps
Step-by-step explanation:
he counted 252 steps. Emilio lives on the 14th floor.
The number of steps between the ground floor and the fourteenth floor.
Let's bear in mind that there 14 floors .
Number of steps per floor= total steps/floor
Number of steps per floor= 252/14
Number of steps per floor= 18 steps
Construct a simulation model to estimate the average profit per unit. What is a 95% confidence interval around this average
Answer:
The answer is not complete. But you can use a spreadsheet to construct a simulation model to estimate the average profit per unit of a set of data.
Step-by-step explanation:
To calculate the Expected value of profit, we use:
Selling price - Expected value of different costs
Selling price is Total Cost * Probability
Confidence Interval
A Confidence Interval is a range of values that someone can be sure the true value lies in.
To calculate the confidence interval, we use the formula x ± z * S/√n
Where S is the standard deviation
n is the number of observations
x is the mean
z is the chosen z value
Use the distributive property to simplify the expression 3(4x + 9).
Answer:
12x+27
Step-by-step explanation:
The solution is A = 12x + 27
The value of the equation is A = 12x + 27
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
A = 3 ( 4x + 9 )
Now , on simplifying the equation , we get
By using the distributive property in the equation
Multiplying by 3 on both the values in the brackets , we get
A = 3 ( 4x ) + 3 ( 9 )
On further simplification of the equation ,
The value of A = 12x + 27
Therefore , the value of A is 12x + 27
Hence , the value of the equation is A = 12x + 27
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an experiment consists of rolling two fair dice and adding the dots on the two sides facing up assuming each simple event is as likely as any other find the probability that the sum of the dots is greater than 2
Answer:
35/36
Step-by-step explanation:
Sample space = S
n(S) = 36
Event of obtaining sum greater than 2, = A
Event of obtaining sum less than 2, B =( 1, 1)
n(B) = 1
Probability of obtaining sum less than 2, P(B) = n(B)/n(S) = 1/36
n(A) = 36 - 1 = 35
∴ Probability of obtaining sum greater than 2, P(A) = n(A)/n(S) = 35/36
I will give you brainliest if you right down the answer and explain it
to find the mid point,
m=-2+1/2,-5+3/2
=-1/2,-1
Hunter is bisecting the angle shown. When drawing the arcs centered on points P and Q, why must he keep the compass the same width for both arcs?
If Hunter adjusts the width of the compass between drawing the first and second arc, it will be impossible for both arcs to be drawn in the interior of the angle. <-- MY ANSWER
If Hunter adjusts the width of the compass between drawing the first and second arc, it will be impossible for the arcs to intersect.
The compass width should not be adjusted at all when bisecting the angle. This means that Hunter should keep the compass at the same width as when he drew the arc through P and Q.
The arcs are drawn to find a point on the bisecting ray. If the arcs are the same width, it makes sure that they are equidistant from the points on the rays of the angle. This causes the point to be on the bisecting ray.
thanks!
Answer:
The arcs are drawn to find a point on the bisecting ray. If the arcs are the same width, it makes sure that they are equidistant from the points on the rays of the angle. This causes the point to be on the bisecting ray.
Step-by-step explanation:
Bisection of an angle implies dividing the angle into two equal parts. The ray that divides the angle is called a bisector.
The hunter should use the same radius or width to draw the two arcs, using points P and Q as the center interchangeably, so that they would intersect at an equidistant point to P and Q. The point of intersection lies on the bisecting ray of the angle.
13ab + 4a²b-9ab + 2ab? - a²b
Simplify this expression by combining like terms.
Answer:
6ab+3a^2b
Step-by-step explanation:
13ab+4a^2b-9ab+2ab-a^2b
13ab-9ab+2ab+4a^2b-a^2b
4ab+2ab+4a^2b-a^2b
6ab+3a^2b
Hope this helps ;) ❤❤❤
Answer:
6ab+3a^2b
Step-by-step explanation:
13ab + 4a^2b - 9ab + 2ab - a^2b
13ab - 9ab + 2ab + 4a^2b - a^2b
4ab + 2ab + 4a^2b - a^2b
6ab + 3a^2b