Answer:
x equals 10, angle measure is 30°
Step-by-step explanation:
By using the Vertical Angles Theorem which states that opposite angles formed by 2 intersecting lines are congruent we can find that the measure of the angle with 3x is equal to the measure of it's opposite angle or 30°. Using this we can make an equation that can find us our answer.
3x = 30
Divide both sides by 3
3x/3 = 30/3
x = 10
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 210.00 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Answer:
a) 0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b) 0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c) The distribution of the population is normal, which means that the sample size does not need to exceed 30.
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm.
This means that [tex]\mu = 200, \sigma = 8.3[/tex]
a. Find the probability that an individual distance is greater than 210.00 cm.
This is 1 subtracted by the pvalue of Z when X = 210. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{210 - 200}{8.3}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849
1 - 0.8849 = 0.1151
0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm
Now [tex]n = 20, s = \frac{8.3}{\sqrt{20}} = 1.8559[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 197.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{197.8 - 200}{1.8559}[/tex]
[tex]Z = -1.19[/tex]
[tex]Z = -1.19[/tex] has a pvalue of 0.117
1 - 0.117 = 0.883
0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The distribution of the population is normal, which means that the sample size does not need to exceed 30.
Notice that the rule for each animal involves counting the number of chirps in different time intervals. For the Brookdale cricket you count the number of chirps in 15 seconds and for the katydid you count the number of chirps in 20 seconds. If c is the number of chirps per minute, what is the expression for the number of chirps for i) The Brookdale cricket in 15 seconds
The probability that a seed will germinate is 0.65. Find the probability that a seed selected at a random will not germinate. *
Answer:
0.35 or 35%
Step-by-step explanation:
The probability that any seed will germinate is said to be 0.65 (or 65%) in the question. This means that the remaining percentage is the probability that the randomly selected seed will not germinate. This is because there is only two possible outcomes to that given scenario, which is it will germinate or not. Meaning that the remaining percentage/probability is that it will not germinate
1 - 0.65 = 0.35 or 35%
ill mark brainlist plss help
to find the area of the rectangle it is is length x width so we do 3x4=12. then area of triangle is base x height divide by 2, so 2x4=8. 8 divide by 2 is 4, then we need to add them all up, so 12 + 4 + 4 is 20. Your answer is 20 cm2.
(Ps please mark brainliest i need for next rank)
Plsss help if u know the answer (application of systems)
Answer:
Step-by-step explanation:
C
there are 60 minutes in a hour.how many minutes are there in 24 hours
There are 1440 minutes in 1 hour
Step-by-step explanation:
Since there are 60 minutes in 1 hour multiply 60 by 24, you get 1440.
Solve thee equation shown
2 × 1/3 =
Answer:
0.66? (0.67 if you rounded it)
Step-by-step explanation:
2*1/3
2/3 = 0.6666666666
hey guys I need help on maths.
Answer:
x=122°
Step-by-step explanation:
sum of all interior angles in a quadrilateral = 360°
then ,
119+105+78+m = 360
m = 58
....
m+ x = 180 ( linear pair)
58+x = 180
x = 122
Evaluate the following expression when x = 3 and y = 5: x^2 + y^3 2+x
Answer:
139
Step-by-step explanation:
x^2 + y^3 2+x = 3^2 + 5^3 + 2 + 3
= 9 + 125 + 5
= 139!
Find the slope of the line that passes through the two points. (0, 0), (3, 2)
Answer:
the slope is 2/3 bcoz u do 2-0/3-0
In a choir, the ratio of men to women is 4:3
The ratio of women to children is 5:9
What is the ratio of men to children?
Answer:
4:9
Step-by-step explanation:
There's 4 of men and 9 to children and 5 of women
17 × 5/8 mixed solution
Answer:
10 5/8
Step-by-step explanation:
17/1 x 5/8. Multiply numerators together and denominators you will get 85/8. Then you convert the improper fraction.
Answer:
10 5/8
Step-by-step explanation:
17 × 5/8 = 85/8
Simplify, sub-step b: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
85 ÷ 8 = 10 remainder 5
85/8 = 10 5/8
AE←→ is a straight line in the diagram.
What is the sum of the measures that represent the measures of each angle if m∠ABC=2x°, m∠CBD=3x°, and m∠EBD=4x°?
What is the measure of each angle?
Explain how an equation can be written to find m∠CBD.
Answer:
hwqvh bjvs bhs ebf
Step-by-step explanation:
•) Zeeshaan bought 12 kilograms of wheat seeds and 18 kilograms of rice seeds. How many kilograms of seeds did he buy ?
Pls help extra points and mark
Answer:
x-6=6
Step-by-step explanation:
6+6=12
Answer:
c
Step-by-step explanation:
because 6+6=12 and the missing number would be 12 because 12-6=6
Solve for x leave your answers as a simplified radical
Answer:
D) 3√13
Step-by-step explanation:
6²+9²=x²
36+81=x²
117=x²
x=√117
x=√9√13
x=3√13
HELP PLS I NEED HELP
Answer:
133
Step-by-step explanation:
180 - 47 = 133
Answer:
133°
Step-by-step explanation:
If we assume the the given to adjacent lines to be parallel then ,
The x and supplement of 47° will be equal since they will be corresponding angles .Therefore :-
=> x = 180° - 47°
=> x = 133° .
Hence the size of angle X is 133°If 2/3z = 6, then z=
Answer:
z=9
Step-by-step explanation:
we are given: 2/3z=6
we need to find what z is by itself
6 is 2/3rds of what the value of z is.
to find z, we need to multiply both sides by 3/2 (the reciprocal of 2/3z, to make the coefficient of 1)
3/2*2/3z=6*3/2
z=9
hope this helps :)
z = 9
Step-by-step explanation:
2/3 . z = 6
2z/3 = 6
Multiple all terms by the same value to eliminate fraction denominator,
3 x 2z/3 = 3 x 6
2z = 18 ( 3,3 got cancelled)
Divide both sides of the equation by the same term,
2z/2 = 18/2
On Simplify,
z = 9.
*(2,2 gets cancelled and 18/2 = 9)
of 10 (0 complete)
This Question: 1 pt
A 2-ft vertical post casts a 16-in shadow at the same time a nearby cell phone tower casts a 122-ft shadow. How tall is the cell phone tower?
Answer: 180ft
Step-by-step explanation:
The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter.
Two cells are measured using this method:
Cell G: 4.21 x 10-3 centimeters
Cell H: 9.2 x 10-4 centimeters
How many times larger is the diameter of cell G than the diameter of cell H?
Write your answer in standard notation, rounding to the nearest tenth.
Answer:
Step-by-step explanation:
The answer is 6.868 10
The number of times that diameter of cell G is larger than diameter of Cell H is; 46 × 10¯¹ times
We are given;
Diameter of Cell G = 4.21 × 10^(-3) cmDiameter of Cell H = 9.2 × 10^(-4) cmNow, to find how much more larger the diameter of cell G is than diameter of cell H, we will divide the diameter of cell G by the diameter of cell H to get;
(4.21 × 10^(-3))/(9.2 × 10^(-4)) = 4.6
Thus,diameter of cell G is 4.6 times larger than diameter of Cell H
Read more about ratios at; https://brainly.com/question/2784798
When 6 is added to four times a number, the result is 50
Answer:
50-6= 54
54÷4= 13.5
editing for clarity.
first you subtract the 6 from the 50 to find out what the "4 times a number" came to.
in this case, 50-6, which equals 54.
then, you divide the 54 by 4 to get 13.5.
so, the whole math problem would be
4 times 13.5 plus 6 equals 50.
The shorter leg of a right triangle is 10 meters. the hypotenuse is 2 meters longer than the longer leg. Find all three sides
Answer:
the shorter leg is 10 meters, longer leg is 24 meters and the hypotenuse is 26 meters
Help!! Pythagorean theorem
Answer:
The Pythagorean theorem only works for right triangles. This is not a right triangle.
x = 23
All interior angles of a triangle = 180 degrees.
A + B + C + 180
(3x) + (2x+12) + (2x+7) = 180
7x + 19 = 180
7x = 161
x = 23
A = 3(23) = 69 degrees
B = 2(23) + 12 =58 degrees
C = 2(23) + 7 = 53 degrees
Answer:
x=23
Step-by-step explanation:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
The slope of a linear function is 1/5. For every rise of 5 units, what is the run?
Answer:
for every rise of 1 the run would be 25
What is the explicit rule for the arithmetic sequence? 20.5, 16, 11.5, 7, 2.5, ...
Answer:
To determine the explicit rule for the arithmetic sequence of 20.5, 16, 11.5, 7, 2.5, ..., the following logical reasoning must be performed:
20.5 - 16 = 4.5
16 - 11.5 = 4.5
11.5 - 7 = 4.5
7 - 2.5 = 4.5
Thus, the explicit rule of the arithmetic sequence is that the numbers are gradually subtracted by 4.5, with which the next number of said sequence would be -2.
pls help have a nice day
Answer:
I THINK the first and second choice, because it said the last two digits are between the numbers 0-9, them two are the only ones that end with them.
Step-by-step explanation:
You have a nice day to!!
Please help me out quick..
Answer:
A
Step-by-step explanation:
When you remove the top layer, you lose 9 squares. So now there are only 18 squares left. The length is 3 beacuse, now it is only 3 sqaures long. And it is still 3 wide. The only change is in height as it is now 2 squares high.
I hope this helps!!
The 3rd term of an arithinetic progression is-9
and the 7th term is -29. Find the 10th term of the
progression.
Answer:
-64
Step-by-step explanation:
The computation of the 10th term of the progression is shown below:
The 3rd term is -9
A_n = a + (n - 1)d
-9 = a + (3 - 1)d
-9 = a + 2d
-9 - 2d = a
Now the 7th term is -29
A_n = a + (n - 1)d
-29 = a + (7 - 1)d
-29 = a + 6d
Put the a value to the above equation
-29 = -9 - 2d + 6d
-29 + 9 = 4d
-20 = 4d
d = -5
Now
-9 - 2d = a
-9 - 2(-5) = a
-9 - 10 = a
a = -19
Now finally the 10th term of the progression is
= a + (n - 1)d
= -19 + (10- 1)-5
= -19 -45
= -64
200 students attend Ridgewood Junior High School. 25% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
sorry est un site Web Internet spécialement conçue 4
What is the measure of y?
3
27
Y у
N
y = [?]
Answer:
[tex]9\sqrt{3}[/tex]
Step-by-step explanation:
The right triangle on the right is a special right triangle: a 30-60-90 triangle
30-60-90 corresponds with the angle measures on the triangle
the sides on a 30-60-90 relate to the angle opposite of it
30 ⇒x 60 ⇒ x[tex]\sqrt{3}[/tex] 90 ⇒ 2x
27 is opposite to the 60° angle
[tex]\frac{x\sqrt{3}} {\sqrt{3}} =x[/tex] [tex]\frac{27}{\sqrt{3}}[/tex] simplify [tex]\frac{27}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] [tex]\frac{27\sqrt{3} }{3}[/tex] = [tex]9\sqrt{3}[/tex]
The required value of altitude y is 9 units which is determined by the geometric theorem.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
As we know that the geometric theorem states that h = √(ab),
where h is the altitude of a right triangle, a and b are the segments formed when the altitude divides the hypotenuse of a right triangle.
We have to determine the value of altitude y
As per the given figure, a = 3, and b = 27
Substitute the values in the formula, and we get
y = √(3 × 27)
y = √81
y = 9
Therefore, the measure of y = 9.
Learn more about the right triangle here:
brainly.com/question/6322314
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