Answer:
The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.
Step-by-step explanation:
We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.
A sample of 50 men and 40 women is selected.
The z-score probability distribution for the two-sample normal distribution is given by;
Z = [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex] ~ N(0,1)
where, [tex]\mu_M[/tex] = population mean height of men at UMBC = 69 inches
[tex]\mu_W[/tex] = population mean height of women at UMBC = 65 inches
[tex]\sigma_M[/tex] = standard deviation of men at UMBC = 4 inches
[tex]\sigma_M[/tex] = standard deviation of women at UMBC = 3 inches
[tex]n_M[/tex] = sample of men = 50
[tex]n_W[/tex] = sample of women = 40
Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P([tex]\bar X_M-\bar X_W[/tex] > 5 inches)
P([tex]\bar X_M-\bar X_W[/tex] > 5 inches) = P( [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex] > [tex]\frac{(5)-(69-65)}{\sqrt{\frac{4^{2} }{50}+\frac{3^{2} }{40} } }[/tex] ) = P(Z > 1.35)
= 1 - P(Z [tex]\leq[/tex] 1.35) = 1 - 0.9115 = 0.0885
The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.
The lower edge of a 5 foot tall painting is 5 feet above your eye level. At what distance should you stand from the wall so your viewing angle of the painting is maximized?
Answer:
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Step-by-step explanation:
referring to the diagram
theta (x) = atan(10/x) - atan(5/x)
differentiate with respect to x
theta'(x) = 5/(x^2+25) - 10/(x^2+100)
For x to have an extremum (max. or min)
theta'(x) = 0 ="
5/(x^2+25) - 10/(x^2+100) = 0
transpose and cross multiply
10(x^2+25) -5(x^2+100) = 0
expand and simplify
10x^2+250 - 5x^2-500 = 0
5x^2 = 250
x^2=50
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Since we know that if x becomes large, theta will decrease, so
x = 5sqrt(2) is a maximum.
Write the quadratic in a verbal sentence. PLEASE HELP I’m super stuck!! If you can explain how to do this as well that would help so much!!
Answer:
n = 8
Step-by-step explanation:
Follow the question when turning the word equation into an equation
Because we know this is a quadratic equation, the product is a result of n multiplied by itself
[tex]n^{2} -4=60[/tex]
Solve for n
[tex]n^{2} =64[/tex]
[tex]\sqrt{n^{2} } =\sqrt{64}[/tex]
n = 8
Rewrite the expression as the algebraic expression in x
Sin
(tan^-1(x))
9514 1404 393
Answer:
sin(tan^-1(x)) = x/√(x² +1)
Step-by-step explanation:
We know that for an angle in a right triangle...
Tan = Opposite/Adjacent
and
Sin = Opposite/Hypotenuse
so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...
Hypotenuse² = Opposite² + Adjacent² = x² +1
Then the sine of the angle is ...
sin(tan^-1(x)) = x/√(x² +1)
Nine less than the quotient of
twice a number and four.
Answer:
-1
Step-by-step explanation:
Twice a number of 4 equals 8
4×2=8
less than 9 of the quotient (answer) of twice a number of 4, is -1
8-9= -1
The required expression for Nine less than the quotient of twice a number and four gives the equation, y =2x/4 - 9.
An expression Nine less than the quotient of twice a number and four. is to be determined.
The process in mathematics to operate and interpret the function to make the function simple or more understandableis called simplify and the process is called simplification.
The quotient is the result when one value gets divided by some other value.
Using simple arithmetic,
Let the number be x,
A number y is equal to nine less than the quotient of twice of x and four. So,
y = quotient of 2x and four - 9
y = 2x/4 - 9
Thus, the required expression for Nine less than the quotient of twice a number and four gives the equation, y =2x/4 - 9.
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URGENT, PLEASE HELP! (3/5) -50 POINTS- !please no wrong answers for the points.! A) [tex]y = \frac{9}{2} x + \frac{1}{2}[/tex] B) [tex]y = - \frac{1}{2} x + \frac{7}{2}[/tex] C) [tex]y = -4x + 9[/tex] D) [tex]y = 4x + 15[/tex]
Answer:
B y = -1/2x + 7/2
Step-by-step explanation:
We know that it has a negative slope since the points go from the top left to the bottom right
We can eliminate A and D
The y intercept is where it crosses the y axis
It should cross somewhere between 2 and 4
C has a y intercept of 9 which is too big
Lets verify with a point
x = -4
y = -4(-4)+9 = 16+9 = 25 (-4,25) not even close to being near the points on the graph
checking B
y = -1/2 (-4) +7/2
= 2 + 7/2 = 11/2 = 5.5 it seems reasonable
Answer:
[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]
Step-by-step explanation:
Using a graph,
we can see that the line y = -1/2x + 7/2 best fits for the data.
The diagonals of a rhombus bisect each other of measures 8cm and 6cm .Find its perimeter. please help !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
20 cm
Step-by-step explanation:
20 cm
8/2 = 4
6/2 = 3
3 and 4 are the sides of the triangle (four triangles in rhombus)
a²+b²=c²
4³+3²=c²
c = 5
5 x 4 = 20
Hope this helped
Answer:
perimeter = 20 cm
Step-by-step explanation:
consider breaking the rhombus into four equal parts.
and that gives you a triangle.
(refer to image attached for more clarification)
let a = 3, b = 4
to get the side c, use Pythagorean theorem = c² = a² + b²
c = sqrt (3² + 4²)
side c = 5
therefore,
perimeter = 4 x sides (c)
perimeter = 4 x 5
perimeter = 20 cm
*please help* If multiple forces are acting on an object, which statement is always true?
The acceleration will be directed in the direction of the gravitational force.
The acceleration will be directed in the direction of the applied force.
The acceleration will be directed in the direction of the net force. <-- MY ANSWER
The acceleration will be directed in the direction of the normal force.
Answer: You are correct. The answer is choice C.
The sum of the vectors is the resultant vector, which is where the net force is directed.
An example would be if you had a ball rolling on a table and you bumped the ball perpendicular to its initial velocity, then the ball would move at a diagonal angle rather than move straight in the direction where you bumped it.
Acceleration is the change in velocity over time, so the acceleration vector tells us how the velocity's direction is changing.
The direction of the acceleration on a body upon which multiple forces are applied depends on the direction of the netforce acting on the body.
When multiple forces acts on a body, such that the different forces acts in different directions. The acceleration will be in the direction of the netforce. This is the direction where the Cummulative sum of the forces is greatest. Acceleration due to gravity is always acting downward, if the upward force is greater than the Gravitational force, then the acceleration won't be in that direction.Therefore, acceleration will be due in the direction of the netforce.
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first off thanks to the ppl who answered before 2nd off i need help again
Answer:
This number line show the inequality x > 2
I need help with these questions asap, I will post pictures if you know them all answer them in the order of the photos from 1-5 thank you.
Answer:
1. step 4
2.idk
3. step 2
4.-5n = 1 ---------> n= -1/5
n + 15 = -10 -------> -25
n/5 = -1/5 ------> n = -1
n - 13 = -12 ------> n = 1
5. cant see the drop down menu or possible answers
but if an answer is the addition one thing
then the second one is the subtraction thing
Step-by-step explanation:
Verizon charges a $40 sign-up fee and the $60 a month for their new hotspot. T-Mobile
charges $100 sign-up fee and then $45 per month for their new hotspot. After how many
months of service will the two company's fees be the same?
Step-by-step explanation:
Start Unlimited:
$70 for one line
$60 for two lines
$45 for three lines
$35 for four lines
Play More Unlimited:
$80 for one line
$70 for two lines
$55 for three lines
$45 for four lines
Do More Unlimited:
$80 for one line
$70 for two lines
$55 for three lines
$45 for four lines
Get More Unlimited:
$90 for one line
$80 for two lines
$65 for three lines
$55 for four lines
Answer:
4 months
As we show that ;
40 + (60x * 4) = 280
100 + (45x * 4) = 280
but in simultaneous equations Verizon must be set equal to 240 being 80 x 3
and T mobile must be equal to 45 x 4 = 180
so that 240+ 180 = 420 to find 4
This would be a method on distribution as "60 sign up is 1/3 more than 1st equation.
Step-by-step explanation:
This is a simultaneous equation but trial and error is below to prove all is true.
step 1 make all equations same
40s + (60x) * 3 = 180x LCM = 80 x 3 = 1 1/3 of 60
100s + (45x) * 4 = 180x LCM = 45 x 4 = 1 of 45 as verizon charges 1/3 more sign up.
100s- 40s + 180x = (180x) = 240 + 180
60s + 180x = 420
s = 60
so our equations must each end with 420
when we get 60s + 180x = 420 then
420 - 180 = 240
240/60 = 4
x = 4 months
Verizon = 1st and T mobile = 2nd
40 + (60x * 5) = 340
100 + 45x * 5 = 325
with $15 out after 5 months so we try 6 months
40 + (60x * 6) = 400
100 + 45x * 6 = 370
and see this is increasing in difference, so try a smaller value of months..
We try 4 months;
40 + (60x * 4) = 280
100 + (45x * 4) = 280
A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
its multiple choice
A. 26inches (1inch/25.4mm)
B. 26inches (25.4mm/1inch)
C. 25.4inches (1mm/26inch)
D. 26inches (1mm/25.4inch)
and its b
What is the correct alternate hypothesis if the pilots' average gain score due to alcohol is indicated in the hypothesis statement by
Answer:
Ha : Pilots average gain score not due to alcohol.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. Here the null hypothesis is that pilots average gain due to alcohol. Then if there is no alcohol what is pilots average gain. This thing will be tested as alternative hypothesis.
A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the:
Answer:
Student t-distribution.
Step-by-step explanation:
In this scenario, a test is being conducted to test the difference between two population "means" using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the student t-distribution.
In Statistics and probability, a student t-distribution can be defined as the probability distribution which can be used to estimate population parameters when the population variance is not known (unknown) and the sample population is relatively small. The student t-distribution is a statistical distribution which was published in 1908 by William Sealy Gosset.
A student t-distribution has a similar curve with the normal distribution curve, except that it is fatter and a little bit shorter.
a² +6²
a-b
if a = 3 and b = 4
Evaluate each expression using the variable replacements.
Answer:
-45Step-by-step explanation:
let a= 3 and b= 4a² + 6² / a - b= 3² + 6² / 3 - 4= 9 + 36 / -1= 45 / -1= -45[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Evaluate the line integral
Soydx + zdy + xdz,
[»= f (t)=dw= f'(t)dt
where C is the parametric curve
x=t, y=t, z=ť, Ost<1.
It looks like you're asked to compute
[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz[/tex]
where C is parameterized by ⟨t, t, t⟩ with 0 ≤ t ≤ 1.
In other words, x = y = z = t, so dx = dy = dz = dt, and the integral reduces to
[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz = \int_0^1 t\,\mathrm dt + t\,\mathrm dt + t\,\mathrm dt \\\\ = 3 \int_0^1 t\,\mathrm dt \\\\ =\frac32t^2\bigg|_{t=0}^{t=1} \\\\ =\boxed{\frac32}[/tex]
Sienna is solving the quadratic equation by completing the square. 3x2 + 9x – 4 = 0 3x2 + 9x = 4 A(x2 + 3x) = 4 What is the value of A? –4 –3 3 4
Answer:
I am going to show you the first steps to complete squares for the given equation: 1) Starting equation: 3x^2 + 9x -4 = 0 2) Add 4 to both sides => 3x^2 + 9x - 4 + 4 = 4 => 3x^2 + 9x = 4 3) Extract common factor 3 in the left side => 3 (x^2 + 3x). Now, compare with a(x^2 + 3x) and you get a = 3. Answer: a = 3.
Answer:
its c
Step-by-step explanation:
g A random sample of size 16 taken from a normally distributed population revealed a sample mean of 50 and a sample variance of 36. The upper limit of a 95% confidence interval for the population mean would equal:
Answer:
The upper limit is
[tex]k = 52.94[/tex]
Step-by-step explanation:
From the question we told that
The sample size is [tex]n = 16[/tex]
The sample mean is [tex]\= x = 50[/tex]
The sample variance is [tex]\sigma ^2 = 36[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference- math dot armstrong dot edu), the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
Here [tex]\sigma[/tex] is the standard deviation which is mathematically evaluated as
[tex]\sigma = \sqrt{\sigma^2}[/tex]
substituting values
[tex]\sigma = \sqrt{36}[/tex]
=> [tex]\sigma = 6[/tex]
So
[tex]E = 1.96 * \frac{6}{\sqrt{16} }[/tex]
[tex]E = 2.94[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]50 -2.94 < \mu <50 +2.94[/tex]
[tex]47.06 < \mu <52.94[/tex]
The upper limit is
[tex]k = 52.94[/tex]
PLEASE ANSWER ASAP!!!!
Divide. Equation and answer choices in picture
any unrelated answer will be reported
Answer:
B =
[tex]4x - 1 - \frac{4}{2x - 3} [/tex]
Step-by-step explanation:
In this type of questions the answers are required in the
[tex]quotient \: + \frac{remainder}{divisor} [/tex]
form.
First of all, the equations in question must be arranged properly
[tex](8 {x}^{2} - 14x - 1) \div 2x - 3[/tex]
Then you divide.
[tex]2x - 3 \sqrt{8 {x}^{2} - 14x - 1 } [/tex]
Answer
[tex]4x - 1 - \frac{4}{2x - 3} [/tex]
If 2y = 6 - 3x, find y when x = 0
Answer:
2y= 6-3x when x=0
2y= 6-3(0)
2y= 6-0
2y= 6
y= 6/2
y= 3
#i'm indonesian
#hope it helps.
Answer:
[tex] \boxed{y = 3}[/tex]
Step-by-step explanation:
Given, x = 0
[tex] \mathsf{2y = 6 - 3x}[/tex]
plug the value of x
⇒[tex] \mathsf{2y = 6 - 3 \times 0}[/tex]
Multiply the numbers
⇒[tex] \mathsf{2y = 6 - 0}[/tex]
Calculate the difference
⇒[tex] \mathsf{2y = 6}[/tex]
Divide both sides of the equation by 2
⇒[tex] \mathsf{ \frac{2y}{2} = \frac{6}{2} }[/tex]
Calculate
⇒[tex] \mathsf{y = 3}[/tex]
Hope I helped!
Best regards!
Is y = 8x -15 a function?
Answer:
Hey there!
A function only has one y value for every x value, so this is a function. Additionally, all linear equations (that are in the y=mx+b form) are functions.
Hope this helps :)
The value of y varies jointly with x and z. If y = 2 when z = 110 and x = 11, find the approximate value of y when x = 13 and z = 195.
Answer:
y = 4Step-by-step explanation:
To find the approximate value of y when
x = 13 and z = 195 we must first find the relationship between them
The statement
y varies jointly with x and z is written as
y = kxzwhere k is the constant of proportionality
From the question
y = 2
x = 11
z = 110
We have
2 = 11(110)k
2 = 1210k
Divide both sides by 1210
[tex]k = \frac{1}{605} [/tex]
So the formula for the variation is
[tex]y = \frac{1}{605} xz[/tex]
When
x = 13
z = 195
y is
[tex]y = \frac{1}{605} (13)(195)[/tex]
[tex]y = \frac{507}{121} [/tex]
y = 4.1900
We have the final answer as
y = 4Hope this helps you
You really want to buy a used car for $11,000, but can only afford $200 a month. What interest rate would you need to find to be able to afford the car, assuming the loan is for 60 months? is the answer 0.03% which formula would you use? I am doing too many to get the correct answer.
Answer:
3.48%
Step-by-step explanation:
Interest rate is the one variable in the amortization formula that cannot be solved for directly. An iterative or graphical approach is needed. There is no formula. Financial calculators, financial apps, and spreadsheets are all able to do this calculation.
__
In the attached, we have used a graphing calculator to find the value of interest rate (in %) that makes the loan payment be $200 for a loan of $11,000. It shows us the rate is 3.48%. (A financial calculator confirms this value.) The x-intercept in the graph is the interest rate that makes the difference between the payment and $200 be zero. In our formula for the payment, we have used t for years. 60 monthly payments is 5 years.
f(t)= 102,000/1+4400e^-t
Answer:
Beginning (t=0) population with flu is 23.
After 4 weeks, population with flu is 1250.
After an infinite amount of weeks, the population witf flu is 102000
Step-by-step explanation:
First question asks you to replace t with 0 because it says beginning.
102000/(1+4400e^-0)=102000/(1+4400)=102000/4401=23.17655 approximately. To nearest whole number this is 23.
After 4 weeks means we replace t with 4:
102000/(1+4400e^-4)
Calculator time:
1250.17142 which to nearest whole number is 1250
If t is super large, then e^-t is super close to 0.
So the limiting number is
102000/(1+4400×0)=102000/1=102000
General solution of equation sin x + sin 5x = sin 2x + sin 4x is
Answer:
x=nπ3, n∈I
Step-by-step explanation:
sin x + sin 5x = sin 2x + sin 4x
⇒⇒ 2 sin 3x cos 2x = 2 sin 3x cos x
⇒⇒ 2 sin 3x(cos 2x - cos x) = 0
⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I
or cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x
⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3 , n∈I, n∈I
But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I
Please answer spammers will be reported
Answer:
Answer is number 2 as twice of 2 is 4 and double of 4 is 8 and 8+2=10
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Find the probability that when a couple has four children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
Answer:
The probability that at least, one of the four children the couple has is a boy is 0.8.
Step-by-step explanation:
Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..
Note that it is possible to have the following for 4 children:
1. 4 boys, 0 girls
2. 3 boys, 1 girl
3. 2 boys, 2 girls
4. 1 boy, 3 girls
5. 0 boys, 4 girls.
To have at least, one boy, out of the 5 options, only 4 is possible.
1. 4 boys, 0 girls.........YES
2. 3 boys, 1 girl ...........YES
3. 2 boys, 2 girls.........YES
4. 1 boy, 3 girls.............YES
5. 0 boys, 4 girls..........NO
The probability is therefore,
(Probability of event = 4) ÷ (Total possible outcome = 5)
P = 4/5 = 0.8
The local resale store buys used designer jeans for $15. The
store increases their purchase price by 400%. What is the
sale price of the designer jeans?
the answer to your question is $75
The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have. A 2-column table has 4 rows. The first column is labeled Number of siblings with entries 0, 1, 2, 3. The second column is labeled number of students with entries 4, 18, 10, 8. What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings? Round to the nearest whole percent. 65% 70% 75% 80%
Answer:
70%
Step-by-step explanation:
Given
Number of Siblings: || 0 || 1 || 2 || 3
Number of Students: || 4 || 18 || 10 || 8
Required
Determine the probability of a student having at least one but not more than 2 siblings
First, we have to determine the total number of 10th grade students
[tex]Total = 4 + 18 + 10 + 8[/tex]
[tex]Total = 40[/tex]
The probability of a student having at least one but not more than 2 siblings = P(1) + P(2)
Solving for P(1)
P(1) = number of students with 1 sibling / total number of students
From the given parameters, we have that:
Number of students with 1 sibling = 18
So:
[tex]P(1) = \frac{18}{40}[/tex]
Solving for P(2)
P(2) = number of students with 2 siblings / total number of students
From the given parameters, we have that:
Number of students with 2 siblings = 10
So:
[tex]P(2) = \frac{10}{40}[/tex]
[tex]P(1) + P(2) = \frac{18}{40} + \frac{10}{40}[/tex]
Take LCM
[tex]P(1) + P(2) = \frac{18 + 10}{40}[/tex]
[tex]P(1) + P(2) = \frac{28}{40}[/tex]
Divide numerator and denominator by 4
[tex]P(1) + P(2) = \frac{7}{10}[/tex]
[tex]P(1) + P(2) = 0.7[/tex]
Convert to percentage
[tex]P(1) + P(2) = 70\%[/tex]
Hence, the required probability is 70%
Answer:
Step-by-step explanation:
bB
Which table represents a function?
GO
х
-3
0
-2
8
y
-1
0
-1
1
х
-5
0
-5
6
y
-5
0
5
-6
х
-4
-2
-2
0
у
8
2
4
2
х
-4
3
1
-4
у
2.
5
3
0
The table that represents a function in the options given is: Table A. (see image attached below).
Recall:
If a relation represents a function, the relation must have exactly one y-value assigned or related to each x-value.In the tables given, only the first table has exactly one y-value assigned or related to every x-value given.
Therefore, the table that represents a function in the options given is: Table A. (see image attached below).
Learn more about function table on:
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Answer:
Graph A
Step-by-step explanation:
Factor 4(20) + 84. 4(20 + 21) 4(21 + 20) 20(4 + 84) 20(4 + 4)
Answer:
[tex]\huge\boxed{4 ( 20 + 21)}[/tex]
Step-by-step explanation:
4(20) + 84
Resolve Parenthesis
80 + 84
Taking 4 common as both are the multiples of 4
4 ( 20 + 21)