Answers
X is the hypotenuse. Using the given angle and side dimension use the law of sins.
Sin( angle) = opposite leg/ hypotenuse
Sin(30) = 5/2 / x
X = 5/2 / sin(30)
X = 5
The answer is x = 5
Related Questions
Choose ALL of the following functions that represent exponential decay. f(x) = 5(2/3)^x
Answers
Answer:
exponential decay
Step-by-step explanation:
The function is in the form
y = ab^x where a is the initial value and b is the growth or decay rate
If b >1 then it is growth
b < 1 then it is decay
f(x) = 5(2/3)^x
a = 5
b = 2/3
2/3 <1 so it is decay
Male bluethroats have a complex song which is thought to be used to attract female birds. Let x denote the duration of a randomly selected song (in seconds) from a male bluethroat. The authors of research on bluethroat song report the mean song duration is 13.8 seconds and the standard deviation of song durations is 11.8 seconds. The authors also noted that the song length distribution is not normal.
Required:
a. Let = average song duration (in seconds) for a sample of 36 male bluethroat songs. Is this distribution of the sample mean song duration " normally distributed" ?
b. Find the probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. Draw, label, and shade a graph to illustrate your result.
Answers
Answer:
a) Sample size larger than 30, so by the Central Limit Theorem, yes.
b) 0.8199 = 81.99% probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. The sketch is given at the end.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean song duration is 13.8 seconds and the standard deviation of song durations is 11.8 seconds.
This means that [tex]\mu = 13.8, \sigma = 11.8[/tex]
Sample of 36
This means that [tex]n = 36, s = \frac{11.8}{\sqrt{36}} = 1.9667[/tex]
a. Let = average song duration (in seconds) for a sample of 36 male bluethroat songs. Is this distribution of the sample mean song duration " normally distributed" ?
Sample size larger than 30, so by the Central Limit Theorem, yes.
b. Find the probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. Draw, label, and shade a graph to illustrate your result.
This is 1 subtracted by the p-value of Z when X = 12. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{12 - 13.8}{1.9667}[/tex]
[tex]Z = -0.915[/tex]
[tex]Z = -0.915[/tex] has a p-value of 0.1801.
1 - 0.1801 = 0.8199
0.8199 = 81.99% probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds.
Sketch:
I’m new and i need help!!
Please help me of you know the answers.
Answers
Answer:
2, x, 2x
Step-by-step explanation:
A) 2
They are even numbers, so it is going to be 2.
B) x
It is going to only be x because the exponents are even and odd.
C) 2x
It is going to be 2x because the numbers are even but the exponents are even and odd.
Hope this helps.
Could someone help me solve this please.
Answers
Answer: maybe 20 % at least because it might me adding
Is the following shape a square? How do you know?
.8
C.
A
0
O A. No, the opposite sides are not parallel.
B. Yes, the opposite sides are parallel, and all sides are the same
length
O C. No, the sides are not congruent.
D. Yes, the adjacent sides are perpendicular, and all sides are the
same length
Answers
720 companies 8 companies win what is the probability
Answers
Step-by-step explanation:
total outcomes = 720
favourable outcomes =8
=8/720
=0.01111
PLEASEEEE HELPPPPPPP!!!!!
Answers
To find S or T add them together:
3/5 + 1/3
Rewrite the fractions to have a common denominator
9/15 + 5/15 = 14/15
Answer: 14/15
Step-by-step explanation:
Here is your answer . Hope it helps.
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. P(X > 3), n = 5, p = 0.2
Answers
Answer:
0.0064
0.00032
Step-by-step explanation:
Given the details:
P(X > 3), n = 5, p = 0.2
The binomial distribution is related using the formula:
P(x = x) = nCx * p^x * q^(n-x)
q = 1 - p = 1 - 0.2 = 0.8
P(X > 3) = p(x = 4) + p(x = 5)
P(x = 4) = 5C4 * 0.2^4 * 0.8^1 = 5 * 0.2^4 * 0.8^1 = 0.0064
P(x = 5) = 5C5 * 0.2^5 * 0.8^0 = 1 * 0.2^5 * 0.8^0 = 0.00032
A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box, $2.25 per pound. Which equation represents the shipping cost as a function of x, the weight in pounds?
f(x) = 2.25x + 5
f(x) = 5x + 2.25
f(x) = 2.25x − 5
f(x) = 5x − 2.25
Answers
Answer:
f(x) = 2.25x + 5
Step-by-step explanation:
The cost from the weight in pounds of the box can be represented by 2.25x, since the charge is $2.25 per pound.
The flat fee of $5 can be represented in the function by adding 5 to 2.25x.
Put these together in function notation:
f(x) = 2.25x + 5
So, the equation is f(x) = 2.25x + 5
What is the length of segment AC?
Answers
Answer:
10 units
Step-by-step explanation:
Point A (3,-1)
Point B (-5,5)
Distance between them,
√{(-5-3)²+(5-(-1))²}
= √{(-8)²+6²}
= √(64+36)
= √100
= 10 units
the expression -6x-7(4+3) is equivalent to?
Answers
Answer:
x(12y+4)
2 0 l e t t e r s
f(x)=-2x^2+x-5 find f(-6)
Answers
f(x) = 2x² + x - 5
f(-6) = 2(-6)² + (-6) -5
=> f(-6) = 2(36) -11
=> f(-6) = 72 - 11
=> f(-6) = 61
If the number of observations for each sample is 150 units, what is the 3-sigma upper control limit of the process
Answers
Complete Question
Complete Question is attached below
Answer:
[tex]UCL= 0.25[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size[tex]n=150[/tex]
Sample Variants [tex]s=7[/tex]
Sigma control limits [tex]Z = 3[/tex]
Therefore
Total number of observations is Given as
[tex]T_o=n*s[/tex]
[tex]T_o=150 *7[/tex]
[tex]T_0=1050[/tex]
Generally
Summation of defectivee
[tex]\sum np=23+34+15+30+25+22+18[/tex]
[tex]\sum np= 167[/tex]
Generally the equation for P-bar is mathematically given by
[tex]P-bar=\frac{\sum np}{T_o}[/tex]
[tex]P-bar=\frac{167}{1050}[/tex]
[tex]P-bar=0.16[/tex]
Therefore
[tex]Sp=\sqrt{\frac{P-bar(1-P-bar)]}{ n}}[/tex]
[tex]Sp=\sqrt{\frac{[0.159(1-0.159)]}{150}}[/tex]
[tex]Sp=0.03[/tex]
Generally the equation for 3-sigma upper control limit of the process is mathematically given by
[tex]UCL = P-bar + Z*Sp[/tex]
[tex]UCL= 0.16 + 3*0.03[/tex]
[tex]UCL= 0.25[/tex]
Kezang was 5 times as old as his son 10 years ago. After 8 years, Kezang will be twice as
old as his son. What are their present age
Answers
let father's age = x
son's age = y
Five years hence, age of father = x+5
age of son =y+5
So (x+5)= 3(y+5)
⇒x=3y+10
Five years ago, age of father = x-5
age of son = y-5
Sox-5=7(y-5)
⇒3y + 10-5=7y - 35
⇒ 4y = 40
⇒y=10 <<<<<<<
x = 3y +10= 40 <<<<<
38)
A man completes a job in 5 days working 8 hours a day. How many days will he take to complete the same job working 2 hours overtime per day in addition?
Answers
Answer:
dbcjchdiskcnbcksksnnckdkxnn
Revised Work Schedule: = 40 Hours Work
Answer: 10 hours per day x 4 days x 1 man.
The Balancing Ratio on Time, an 20% uplift in daily labour input with 10 hours worked instead of 8 hours per day.
= 20% reduction in Total Length of Time from 5 days to 4 days)
Omar keeps his sneaker collection carefully arranged on the floor of his closet. 8 pairs of
sneakers fit perfectly side-by-side from one end of the closet to the other. The closet is 60
inches wide.
How wide is each pair of sneakers?
Answers
Answer:
7.5 inches wide. I wasnt wrong. for a second i thought it was asking for the width of each individual sneaker.
Answer:
each pair of sneakers are 7.5 inches wide
Where did this part came from how did this value came from
Answers
Answer:
Sin (theta) has the same value for the both value of theta, so both applies.
Answered by GAUTHMATH
On a coordinate plane, rhombus W X Y Z has points (negative 3, 1), (1, 4), (5, 1), and (1, negative 2). Rhombus WXYZ is graphed on a coordinate plane. What is the area of the rhombus?
Answers
Answer:
B. 20 Units
Step-by-step explanation:
unit test review edge 2021
The area of rhombus WXYZ as shown in the diagram given with the given vertices is: 24 units².
What is the Area of a Rhombus?Area of a rhombus = pq/2, where p and q are the diagonals of the rhombus.
Find the lengths of diagonals XZ and WY:
XZ = |4 -(-2)| = 6 units
WY = |-3 - 5| = 8 units
Area of rhombus WXYZ = 1/2(XZ × WY) = 1/2(6 × 8)
Area of rhombus WXYZ = 24 units².
Learn more about the area of a rhombus on:
https://brainly.com/question/2456096
#SPJ2
It cost $52 to use 800 kWh of electricity. How much will 650 kWh cost?
Answers
Hello!
$52 ..... 800kWh
$x ..... 650kWh
_____________
52/x = 800/650 <=>
<=> 52 × 650 = 800x <=>
<=> 33800 = 800x <=>
<=> 800x = 33800 <=>
<=> x = 33800/800 <=>
<=> x = 338/8 <=>
<=> x = 169/4 <=>
<=> x = 42,25$
Good luck! :)
PLEASE ANSWER!!
What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39
Answers
A: 25.
Explanation: Check the attached image.
For synthetic division, you just need to multiply the 1st number of the polynomial by the divisior, and then, add it up to the next number; then, the coefficient will be multiplied by the divisor, and so on and so forth until you reach the last number... that last coefficient at the end is the reminder that you've been asked for
B
15x+7
6x+2y|
y +3
2y + 1
С
E
The triangles are congruent. Find the length of each hypotenuse.
A. 3
B. 5
C 17
Answers
Answer:
Hypothenus = 22
Step-by-step explanation:
From the question given above, we were told that the triangles are congruent (i.e same size). Thus,
AC = EF
BC = DE
To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:
For y:
AC = y + 3
EF = 2y + 1
AC = EF
y + 3 = 2y + 1
Collect like terms
3 – 1 = 2y – y
2 = y
y = 2
For x:
BC = 5x + 7
DE = 6x + 2y
y = 2
DE = 6x + 2(2)
DE = 6x + 4
BC = DE
5x + 7 = 6x + 4
Collect like terms
7 – 4 = 6x – 5x
3 = x
x = 3
Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:
Hypothenus = BC
Hypothenus = 5x + 7
x = 3
Hypothenus = 5x + 7
Hypothenus = 5(3) + 7
Hypothenus = 15 + 7
Hypothenus = 22
OR
Hypothenus = DE
DE = 6x + 2y
y = 2
x = 3
Hypothenus = 6(3) + 2(2)
Hypothenus = 18 + 4
Hypothenus = 22
Does the picture below indicate that:
ZJAC ZDBE?
С DA
J
939
A
B
→E
Yes
No
Pls help
Answers
Answer:
No
Step-by-step explanation:
The measure of <JAC is shown to be 93°.
The little square symbol inside <DBE shows that <DBE is a right angle.
The measure of a right angle is 90°.
m<DBE = 90°
Congruent angles are angles with equal measures.
Since the measures of angles JAC and DBE are different, they are not congruent.
Answer: No
A metal rod will be cut into pieces that are each 1/20 meters long. The rod is 4/5 meters long. How many pieces will be made from the rod?
Write your answer in simplest form.
Answers
4/5 ÷ 1/20
Reciprocate 1/20
4/5 ÷ 20/1
Multiply numerators and denominators of both fractions:
4 x 20 = 80
5 x 1 = 5
80/5 sinplified is 16.
Hope this helps!
Please helpppppp
ASAPpppppp
Answers
Two buses leave towns 576 kilometers apart at the same time and travel toward each other. One bus travels 12
h
slower than the other. If they meet in 3 hours, what is the rate of each bus?
km
Rate of the slower bus:
Rate of the faster bus:
Answers
Answer:
Rate of slower bus; 90 km/h
Rate of faster bus; 102 km/b
Step-by-step explanation:
We know that formula do distance is;
Distance = speed/time
We are told that One bus travels 12h slower than the other.
Let speed of slower bus be x.
Thus;
Speed of faster bus = x + 12
Speed of slower bus = x
After 3 hours, distance by faster bus = 3(x + 12)
Speed of slower bus = 3x
Since the towns are 576 km apart, then;
3(x + 12) + 3x = 576
Divide through by 3 to get;
x + 12 + x = 192
2x + 12 = 192
2x = 192 - 12
2x = 180
x = 180/2
x = 90 km/h
Faster bus speed = 90 + 12 = 102 km/h
1. Define the following: Odds ratio Relative risk 2. Describe how to calculate the Odds ratio and provde the formula. 3. Describe how to calculate the Relative Risk and provide the formula.
Answers
Answer and Explanation:
Odds ratio is the odds that an outcome would happen given a level of exposure in comparison to the occurrence of that outcome without exposure. Odds ratio is calculated by dividing odds of event occurring with exposure(the first group) by odds of event(usually disease) occurring without exposure. Odds is different from probability(denoted p/1-p). While probability is the number of favorable events divided by total number of events, odds is number of favorable events/number of unfavorable events.
Relative risk, also measuring relationship between exposure and outcome, is the ratio of the probability that an outcome would occur without exposure and probability that an outcome would occur with exposure.
Evaluate the following expressions using the chip method. SHOW ALL WORK!!!
Answers
Answer:
a. -7 b. -20c. 7Step-by-step explanation:
a. -9+2, in this case, it is -7 because you take the bigger number and subtract it by the lower number. If the bigger number is negative your answer will be negative, if the bigger number is positive it will be positive it is just really a basic subtraction problem just add the sign.b. In multiplication +++=+ ++-=- and a -+-=+ do your problem without thinking about the signs and then add the signs with the formula I showed you.c. ---=+Hope this helps :)!
I have completed everything except for the last box. Can someone please help me on the last box? Thank you for your help!
Answers
Answer:
[tex]2.5\%[/tex]
Step-by-step explanation:
From the Empirical Rule, 95% of the data shown falls between 63 and 95. The other 5% is evenly distributed to each side (since the distribution is bell-shaped), hence there being [tex]\boxed{2.5\%}[/tex] of scores less than 63.
The directions say to give the approximate percentage which is vague. You may have to input [tex]3\%[/tex] if it does not accept [tex]2.5\%[/tex].
!!! HELP ASAP !!! I almost got the problem but the problem was the rounding. I believe I rounded right but it is still incorrect. Can someone please help me on the rounding portion of the question? Thank you for your help!!!
Answers
The question is asking you to round to the nearest hundredth. That means that if it’s asking you to round 2.03, it would round down to 2.00.
Does this graph represent a function?
Answers
Answer:
I think it's a function
Step-by-step explanation:
as you can see in the picture curve drawn in a graph represents a function, if every vertical line intersects the curve in at most one point. So I think its a function.
Answer:
yes
Step-by-step explanation:
it's a cubic function having maximum and minimum turning points
it has a point of inflation, y - intercept and x-intercept
