Answer:
Following are the responses to the given question:
Step-by-step explanation:
Level of Significance,[tex]\alpha = 0.05[/tex]
Sample Size, [tex]n = 120[/tex]
Sample Proportion, [tex]\hat{P} = 0.600[/tex]
[tex]z -value = Z_{\frac{\alpha}{2}} = 1.960 \ \ [excel formula =NORMSINV(\frac{\alpha}{2})][/tex]
Standard Error[tex]SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = 0.0447[/tex]
margin of error [tex]E = Z\times SE = 1.960 \times 0.0447 = 0.0877[/tex]
When [tex]95\%[/tex] Confidence Interval
Interval Lower Limit[tex]= \hat{p} - E = 0.600 - 0.0877 = 0.5123[/tex]
Interval Upper Limit [tex]=\hat{p}+ E = 0.600 + 0.0877 = 0.6877[/tex]
The lengths of adult males' hands are normally distributed with mean 187 mm and standard deviation is 7.1 mm. Suppose that 12 individuals are randomly chosen. Round all answers to 4 where possible. What is the distribution of ¯ x
Answer:
By the Central Limit Theorem, the distribution of ¯ x is approximately normal with mean 187 and standard deviation 2.05.
Step-by-step explanation:
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.
The lengths of adult males' hands are normally distributed with mean 187 mm and standard deviation is 7.1 mm.
This means that [tex]\mu = 187, \sigma = 7.1[/tex]
Suppose that 12 individuals are randomly chosen.
This means that [tex]n = 12, s = \frac{7.1}{\sqrt{12}} = 2.05[/tex]
What is the distribution of ¯ x?
By the Central Limit Theorem, the distribution of ¯ x is approximately normal with mean 187 and standard deviation 2.05.
The Unit Circle
What is cos(-30*)? Sketch a graph to help determine the answer
a. 0.50
b. 0.87
c. -1
d. 0
Please select the best answer from the choices provided
Answer:
C. -1
Step-by-step explanation:
I calculated it logically
Robin has a rectangular picture frame that is 8 1/2 by 11 inches. What is the
approximate perimeter of the picture frame in centimeters?
Answer: 99.06cm
Step-by-step explanation:
Note that 1 inch = 2.54cm
Therefore, we'll convert the sides of the frame in inches to cm. This will be:
8 1/2 inch = 8.5 × 2.54cm = 21.59cm
11inches = 11 × 2.54cm = 27.94cm
Therefore, the perimeter of a rectangle will be:
= 2(length + width)
= 2(27.94 + 21.59)
= 2(49.53)
= 99.06cm
PlS help lots of points
In ΔQRS, q = 890 cm, s = 810 cm and ∠S=120°. Find all possible values of ∠Q, to the nearest degree.
Answer: no possible triangles
Step-by-step explanation:
What’s the inequality of N<-1
Answer:
ℎℎ ℎ
Step-by-step explanation:
ℎℎℎℎ ℎ ℎ
sin 0 =(8)/(9), tan 0 >0
find sec 0
Answer:
[tex]\displaystyle \sec(\theta)=\frac{9\sqrt{17}}{17}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \sin(\theta)=\frac{8}{9}\text{ and } \tan(\theta)>0[/tex]
And we want to find sec(θ).
First, note that both sine and tangent are positive. The only quadrant in which this can occur is QI. Hence, all trig ratios will be positive.
Also, recall that sine is the ratio of the opposite side to the hypotenuse. Using this information and the Pythagorean Theorem, we can determine the adjacent side:
[tex]a=\sqrt{9^2-8^2}=\sqrt{17}[/tex]
So, with respect to θ, the adjacent side is √(17), the opposite side is 8, and the hypotenuse is 9.
Secant is the ratio of the hypotenuse to the adjacent. Hence:
[tex]\displaystyle \sec(\theta)=\frac{9}{\sqrt{17}}=\frac{9\sqrt{17}}{17}[/tex]
Again, since θ is in QI, all trig ratios are positive.
2. Find the sum of the 7th term of the
geometric series. 3+1+1/3+ ...
How do I find it, must show work
Answer:
sum
In the given G.S., we have,
a
=
the
1
s
t
term
=
3
,
& the common ratio
r
=
−
6
3
=
−
2
Hence, the sum
S
n
of its first
n
terms is given by,
S
n
=
a
(
1
−
r
n
)
1
−
r
∴
The Reqd. Sum S_7
=
3
(
1
−
(
−
2
)
7
)
1
−
(
−
2
)
=
3
(
1
+
128
)
3
=
129
It’s either C or D? Please help
Answer:
c
Step-by-step explanation:
The Unit Circle
In the unit circle, the value of sine is the y-coordinate of the unit radius. What is the value of cosine?
a. x-coordinate
b. quadrant IV
c. a function
d. tangent
Please select the best answer from the choices provided
Answer:
A. X-coordinate
Step-by-step explanation:
I calculated it logically
Answer:
I think it's x -coordinate
LUVP is an example of:
PLEASE HELP ASAP! THE CORRECT ANSWER WILL RECEIVE BRAINLIEST!
How does the variable of Data Set A compare to the variability of Data Set B?
Data Set A: 14, 15, 19, 29, 44
Data Set B: 9, 20, 25, 30, 38
Select from the drop-down menus to correctly complete the statements.
Data Set A has {Choose...} Data Set B because the range of Data Set A is {Choose...}
the range of Data Set B.
{Choose...} 1: A. Less variability than | B. The same variability as | C. Greater variability than
{Choose...} 2: A: Less than | B: Equal to | C: Greater than
Please answer for branliest
Answer:
50%
Step-by-step explanation:
There are 2 cards greater than 5 , that is 6 and 7 , then
P( greater than 5 ) = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] = 50%
The circumference of a circle is 15π ft. What is the area, in square feet? Express your answer in terms of π.
Answer: Circle
Solve for area
A≈17.9
C Circumference
15
d
r
r
r
d
d
C
A
Using the formulas
A=πr2
C=2πr
Solving forA
A=C2
4π=152
4·π≈17.90493
Step-by-step explanation:
Find the volume of the cylinder.
Either enter an exact answer in terms of π or use 3.14 for π
Answer:
[tex]144\pi[/tex]
Step-by-step explanation:
Formula for the volume of a cylinder is the Base Area x Height
or
[tex]V= \pi r^{2} * h[/tex]
Plug in the values:
[tex]V = \pi(6)^2 * 4[/tex]
[tex]V = 36\pi *4 = 144\pi[/tex]
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 163 people in the first group and this group will be administered the new drug. There are 160 people in the second group and this group wil be administered a placebo. After one year, 13% of the first group has a second episode and 14% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups.
a) [0.00590, 0.0251].
b) [0.00690, 0.0551].
c) [0.0890, 0.0551].
d) [0.00690, 0.0351].
e) [0.00890, 0.0651].
Answer:
90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
First group: Sample of 163, 13% has a second episode.
This means that:
[tex]p_1 = 0.13, s_1 = \sqrt{\frac{0.13*0.87}{163}} = 0.026[/tex]
Second group: Sample of 160, 14% has a second episode
This means that:
[tex]p_2 = 0.14, s_2 = \sqrt{\frac{0.14*0.86}{160}} = 0.027[/tex]
Distribution of the difference:
[tex]p = p_1 - p_2 = 0.13 - 0.14 = -0.01[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.026^2+0.027^2} = 0.0375[/tex]
Confidence interval:
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Lower bound:
[tex]p - 1.645s = -0.01 - 1.645*0.0375 = -0.0717[/tex]
Upper bound:
[tex]p + 1.645s = -0.01 + 1.645*0.0375 = 0.0517[/tex]
90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).
Which two expressions are equivalent? B. A 4(2 + x) 4.2 +2.x 4 + 2 + x (4 + 2) + X D. C. 4. X + 2 4. (x + 2) 4 = (2-x) 4- 2 = X
Help plz ill give v bucks
Answer:
a = 4
Step-by-step explanation:
Lets call a² the side a
Let's call b² the side with 3
The hypotenuse, the longest side and the opposite side from the 90° angle is c²
a² + b² = c²
a² + 3² = 5²
a² + 9 = 25
subtract 9 from both sides
a² = 16
sq root 16 = 4
a = 4
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Please Help ASAP
Find the expected value of the
random variable with the
following probability distribution:
0
1
2
3
4
5
6
7
8
P
.03
.15
.27
.20
.13
.10
.07
.03
.02
Answer:
3.1
Step-by-step explanation:
In order to solve for this expected value, you need to do:
(0*0.3)+(1*0.15)+(2*.27)+(3*20)+(4*.13)+(5*.10)+(6*.07)+(7*0.3)+(8*0.2)
Meaning that it is:
0+.15+.54+.6+.52+.5+.42+.21+.16
Which equals to: 3.1
Also: Feel free to correct my answer by any means, I feel like I got some parts wrong.
Answer:
The answer is, 3.1
Step-by-step explanation:
Definition of probability distribution:A probability distribution is a statistical function that describes all of the potential values and probabilities for a random variable within a particular range.
To find this predicted value, you must do the following:[tex](0*0.3)+(1*0.15)+(2*.27)+(3*20)+(4*.13)+(5*.10)+(6*.07)+(7*0.3)+(8*0.2)[/tex]
That is to say, it is:
[tex]0+.15+.54+.6+.52+.5+.42+.21+.16[/tex]
3.1 is the value of the random variable.
To know more about probability distribution here, https://brainly.com/question/9385303
#SPJ2
Find the volume of a pyramid with a square base, where the area of the base is
12.2 m² and the height of the pyramid is 12.3 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:
50.0 cm²
Step-by-step explanation:
Applying
Volume of a pyramid (V) = 1/3×Area of the base(A')×Heigth(H)
A= 1/3A'h.................... Equation 1
A' = Area of the base, h = height of the pyramid
From the question,
Given: A' = 12.2 m², h = 12.3 m
Substitute these values into equation 1
A = 1/3(12.2×12.3)
A = 50.02
A = 50.02 cm²
A = 50.0 cm²
What is the length of the hypotenuse if a= 5 and b= 7
Answer:
[tex]\sqrt{74}\\[/tex]
Step-by-step explanation:
Use hypotenus formula
A^2+b^2=C^2
5^2+7^2=C^2
25+49=c^2
74=C^2
[tex]\sqrt{74}\\[/tex]
Which of the following is the best estimate for -21/4 •7.89 + 13/3 ÷ (-4.17)
-17
-4
3
5
what is the measure of m
9514 1404 393
Answer:
m = 8
n = 4√3
Step-by-step explanation:
The right triangles in this figure are all similar, so the ratios of hypotenuse to short side are the same.
(12+4)/m = m/4
64 = m² . . . . multiply by 4m
8 = m . . . . . . square root
__
Likewise, the ratio of long side to short side is the same.
12/n = n/4
48 = n² . . . . . . multiply by 4n
4√3 = n . . . . . take the square root
_____
Additional comment
You may have noticed that the ratios of side lengths are ...
4 : n : m = 4 : 4√3 : 8 = 1 : √3 : 2 . . . . . side lengths of a 30°-60°-90° triangle
This means the unmarked side is 8√3.
__
We supplied all of the missing lengths because we know this problem is likely to be presented in different forms, asking for values other than m.
Michiko bought pens for $3.85 and pencils for $1.25. How much did she spend all together
Answer:
$5.10
Step-by-step explanation:
$3.85+$1.25=$5.10
Answer:
If she only bought one pen and one pencil, $5.10
Step-by-step explanation:
−
7
<
−
1
2 i really need help plz
Answer:
I'm guessing you mean -7 < -12 and if it's true and false, if so the answer would be false because -7 is larger than -12.
Step-by-step explanation:
I'm guessing you mean -7 < -12 and if it's true and false, if so the answer would be false because -7 is larger than -12.
(Tell me the question if this is incorrect. Thanks!!!)
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
line passes through points (-1,-2) and (1,4). What is the equation of the line?
Write the linear equation
Answer: y=3x+1
Step-by-step explanation:
First find slope using formula
m= y2–y1/x2–x1
m= 4– (—2)/ 1— (—1)
m= 3
So,
y= mx+b
y=3x+b. Using (1,4) plug into equation of a line
4= 3(1)+b
4 – 3= b
1= b. So,
y=3x+1
Answer:
y= 3x+1.
Step-by-step explanation:
(-1,-2) and (1,4)
x1 = -1
x2= 1
y1= -2
y2=4
y - y1= (y2 - y1)
______ ( x - x1)
(x2 - x1)
y- (-2)=(4-(-2))
_____ (x- (-1))
(1-(-1))
y+2= 4+2
___ (x+1)
1+1
y+2= 6
_ (x + 1)
2
y+2=3(x+1)
y+2=3x+3
y=3x+1.
Anna mixed together 3 gallons of brand a orange juice in 2 gallons of brand b orange juice. Brand b orange juice contains 64% fruit juice. What is the percent of fruit juice in brand if the mixture contains 49% fruit juice? Above are the options
Solve for the missing side ?
Answer:
BC = x = 8.12
AB = 15.33
Step-by-step explanation:
The missing sides of the right triangle is AB and BC;
Step 1: solve for BC using the following formula;
[tex]tan(\theta) = \frac{Opposite \ side}{Adjacent \ side} \\\\tan (32)= \frac{BC}{AC} \\\\tan(32) = \frac{x}{13} \\\\x = 13 \times tan(32) \\\\x = 8.12 \[/tex]
Step 2; solve for AB using a trig ratio or Pythagoras theorem;
[tex]cos (\theta) = \frac{Adjacent \ side }{Hypotenuse \ side} \\\\cos (32) = \frac{AC}{AB} \\\\cos (32) = \frac{13}{AB} \\\\AB = \frac{13}{cos (32)} \\\\AB = 15.33[/tex]
Two wires
tether a balloon to the ground, as shown. How
high is the balloon above the ground? (Must Use Right
Triangle Trigonometry)
Answer:
am i suppoesd to do number 7 as well?
Step-by-step explanation:
Two wires
tether a balloon to the ground, as shown. How
high is the balloon above the ground? (Must Use Right
Triangle Trigonometry)
look at picture
The height of the balloon above the ground is 554 ft.
I have attached a diagram where i have divided the triangle shown into 2.From the attached image, the third angle in triangle 1 would be;
180 - (90 + 85) = 5°
The supplementary angle in triangle 2 to 85° in triangle 1 is;
180 - 85 = 95°(because supplementary angles add up to 180)
The third angle of triangle 2 is; 180 - (95 + 75) = 10°
If we label the shared slant side between the two triangles as z, the we can use sine rule to find z from triangle 2;100/sin10 = z/sin 75
z = 100(sin 75)/(sin 10)
Applying trigonometric ratio to triangle 1, we can find h as;h/z = sin 85
h = z sin 85
h = [100(sin 75)/(sin 10)] × sin 85
h ≈ 554 ft
Read more at; https://brainly.com/question/6241673
HELPP ME PLSS the work is below
Answer:
peregrine falcon
Step-by-step explanation:
you convert the 61.6 feet to miles which is 0.01166667 miles. you multiply that by the seconds in an hour(3600)
so 0.01166667*3600 = 42 miles an hour 75>42