Solution :
68 % of the students owns iPod and a smart phone. So
p' = 0.68
q' = 1'
= 1 - 0.68
= 0.32
Since CL = 0.97, we know that [tex]$\alpha = 1 - 0.97 = 0.03 $[/tex]
The area to the left of [tex]$z_{0.015}$[/tex] is 0.015 and the area to the right of [tex]$z_{0.015}$[/tex] is [tex]$1 - 0.015 = 0.985 $[/tex]
Thus using [tex]$TI \ 83, 83+ \ or \ 84+$[/tex] calculator function [tex]$\text{InvNorm} (0.985, 0.1), z_{0.015} = 2.17$[/tex]
[tex]$\text{EBP} = z_{\alpha / 2} \times \left( \sqrt{\frac{p'q'}{n}}\right) $[/tex]
[tex]$\text{EBP} = 1.645 \times \sqrt{\frac{0.68 \times 0.32}{300}} $[/tex]
= 0.0269
Therefore, we are ninety seven percent confident that a true proportion of all the students who has iPod as well as a smart phone is between the 0.6531 and 0.7069
a). (0.7731, 0.8269); We estimated that with 90% confidence, the true percentage of all the students in district who are against a new legislation is between 77.31% and 82.69%.
b). Now,
Press the 'STAT' and then arrow over to perform TEST.
Now arrow down to the A:1 - PropZint and then place Enter.
Arrow a down x and then enter the 300 x 0.68
Similarly arrow a down to given n and then enter the 300
Now arrow down to the C-level and the enter the 0.97
Arrow a down for calculating and press the enter button.
The confidence interval is (0.6531, 0.7069)
a). (0.7731, 0.8269); We estimated that with 90% confidence, the true percentage of all the students in district who are against a new legislation is between 77.31% and 82.69%.
Please help I need an equation for this graph
What inequality symbol does "at least" correspond to?
A. less than
B. less than or equal to
C. greater than
D. greater than or equal to
Answer:
C, if someone else gets the same answer as me then its right
Step-by-step explanation:
A scuba diver descends 0.75 meters per second. What is her change in elevation after 25 seconds?
-25.75 meters
-50.00 meters
-18.75 meters
-100 meters
Answer:
-18.75 Meters
Step-by-step explanation:
0.75 x -25 = -18.75 Meters :D
i need help with these questions asap
Answer:
11. the first one 12. the last one
Step-by-step explanation:
Answer:
Step-by-step explanation:
11 - the first option
12-the second option
Type the correct answer in the box.
If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is
°.
Correct question is;
Type the correct answer in the box bellow: If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is ...........
Answer:
x = 35°
Step-by-step explanation:
We are told that;
cos x = sin(20 + x)°
and 0° < x < 90°
From trigonometric identities, we know that;
cos x = sin (90 - x)
Applying to our question gives;
sin (90 - x) = sin (20 + x)°
Comparing both sides, we have;
90 - x = 20 + x
Rearranging;
90 - 20 = x + x
70 = 2x
x = 70/2
x = 35°
which of these values could be the slope of the line? Select TWO options
Answer:
7/4 and 3
Step-by-step explanation:
It's a positive slope (sloping up and to the right).
If its sloping from quadrant 3 to 1, it's positive
Watch help video
In an all boys school, the heights of the student body are normally distributed with a
mean of 69 inches and a standard deviation of 2.5 inches. Using the empirical rule,
what percentage of the boys are between 61.5 and 76.5 inches tall?
Answer:
99.7%
Step-by-step explanation:
99.7% of boys fall between 61.5 and 76.5
The percentage of the boys that are between 61.5 and 76.5 inches tall is 99.73%
How to determine the percentage between the range?The given parameters are:
Mean = 69Standard deviation = 2.5Start by calculating the z score for x = 61.5 and 76.5 using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z_1 = \frac{61.5 - 69}{2.5} = -3[/tex]
[tex]z_2 = \frac{76.5 - 69}{2.5} = 3[/tex]
The percentage is then represented as:
Percentage = P(-3 < x < 3)
Using the z table of probabilities, we have:
Percentage = 0.9973
Express as percentage
Percentage = 99.73%
Hence, 99.73% of the boys are between 61.5 and 76.5 inches tall
Read more about normal distribution at:
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5) Express as a single logarithm. You do NOT need to expand the polynomials:
5 In(x - 2) + 8 In(x + 3) - 3 ln(x + 8)
5 ln(x - 2) + 8 ln(x + 3) - 3 ln(x + 8)
ln(x - 2)⁵ + ln(x + 3)⁸ - ln(x + 8)³
since [tex]a\log_cb=\log_cb^a[/tex] (for any base c)
ln((x - 2)⁵ (x + 3)⁸ / (x + 8)³)
since [tex]\log_c(a)+\log_c(b)=\log_c(ab)[/tex] and [tex]\log_c(a)-\log_c(b)=\log_c\frac ab[/tex] (also for any base c)
One box has 16 apples another box has 24 lemons.
Answer:
Like the other person said there's 40 apples.
Step-by-step explanation:
but is there more to the question or..?
Jemima receives £5 pocket money
she spends £1.75 on a magazine and 80p on a drink
a)what fraction of the pocket money is spent
b)what fraction of the pocket money does she have left
Answer:
51% of the money was spent, that is, 51/100. In conclusion, Jemina still has 49/100 of the money available.
Step-by-step explanation:
Since Jemima received $ 5 in pocket money, and spent $ 1.75 on a magazine and $ 0.80 on a drink, to determine the proportion of money he spent and the proportion he has left, the following calculation must be performed:
5 - (1.75 + 0.80) = X
5 - 2.55 = X
2.45 = X
5 = 100
2.55 = X
(2.55 x 100) / 5 = X
255/5 = X
51 = X
Therefore, 51% of the money was spent, that is, 51/100. In conclusion, Jemina still has 49/100 of the money available.
This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, please help
First,
tan(θ) = sin(θ) / cos(θ)
and given that 90° < θ < 180°, meaning θ lies in the second quadrant, we know that cos(θ) < 0. (We also then know the sign of sin(θ), but that won't be important.)
Dividing each part of the inequality by 2 tells us that 45° < θ/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(θ/2) > 0 and sin(θ/2) > 0.
Now recall the half-angle identities,
cos²(θ/2) = (1 + cos(θ)) / 2
sin²(θ/2) = (1 - cos(θ)) / 2
and taking the positive square roots, we have
cos(θ/2) = √[(1 + cos(θ)) / 2]
sin(θ/2) = √[(1 - cos(θ)) / 2]
Then
tan(θ/2) = sin(θ/2) / cos(θ/2) = √[(1 - cos(θ)) / (1 + cos(θ))]
Notice how we don't need sin(θ) ?
Now, recall the Pythagorean identity:
cos²(θ) + sin²(θ) = 1
Dividing both sides by cos²(θ) gives
1 + tan²(θ) = 1/cos²(θ)
We know cos(θ) is negative, so solve for cos²(θ) and take the negative square root.
cos²(θ) = 1/(1 + tan²(θ))
cos(θ) = - 1/√[1 + tan²(θ)]
Plug in tan(θ) = - 12/5 and solve for cos(θ) :
cos(θ) = - 1/√[1 + (-12/5)²] = - 5/13
Finally, solve for sin(θ/2) and tan(θ/2) :
sin(θ/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)
tan(θ/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2
Three students wrote equations on their dry erase boards.
Which of these students wrote an equation that is true?
Answer:
13/20 = 65%
Step-by-step explanation:
1/4 = 25%
7/10 = 70%
13/20 = 65%
Only the last one had the correct percentage.
After the first round of a trivia game, Ryleigh’s score is -259 points. During the second round of the game, she earns 348 points. What is her score after the second round? Record your answer on the grid. Then fill in the bubbles.
Answer: 89
Step-by-step explanation:
You add the points of the two rounds (-259) + 348= 89
If logx= -2, what is x?
3r + 6y - 2z = -6 2x + y + 4z = 19 -5x - 2y+8z = 62
solve each system of equations
The price of a 7 -minute phone call is $1.75. What is the price of a 14 -minute phone call?
Answer:
$3.50
Step-by-step explanation:
14 is double 7
So the price should be double
1.75 x 2 = 3.5
(Assuming there's no base fee and the charge is purely for minutes)
Which line diagram models the expression 2/3+1/6-1/2?
Answer:
1 /3
≈0.333
Step-by-step explanation:
The representation which the arrow point out 0.666...
What is number line?A number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
given:
2/3+1 1/6-1/2
Taking LCM
=2*2/3*2+1 1/6-1*3/2*3
=4/6+7/6-3/6
=8/6
=2/3
=0.666...
So, the number that represent 0.666... is not shown it should be a representation which the arrow point out 0.666...
Learn more about number line here:
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What is the result of 122÷8? Use the number line to find the answer
A: 7
B:14
C:16
D:28
Please help!
Answer: I would go towards B
Step-by-step explanation:
122/8 = 15.25
This is more towards 15, so put the dot in the middle of 14 and 16
Ford Motor Company decided against building a new plant in California because of the high cost of taxes. The state of California proposed an assessment rate of 52% of the estimated market value of the plant. The tax rate proposal was $233.00 per $1,000 of assessed value. What would Ford Motor pay in property taxes per year if it decided to build a $25 million plant?
Answer:
$5825000
Step-by-step explanation:
You just take 23.3% of the 25 million dollars silly.
Help, I’ll give brainliest if you tell me what like terms and terms are.
Answer:
Step-by-step explanation:
7x + 6 + 5
six and five both are regular numbers but the 7x is not like term
7x + 11
There were 400 people at a concert. Half of them wore yellow T-shirts, 2/10 wore gray T-shirts, and the rest wore orange T-shirts. How many people wore gray T-shirts?
Answer:
80 ppl have gray T-shirts
Step-by-step explanation:
Hope this helps! :3
Plz mark as brainliest!
Find the length of BC
Answer:
BC=26.05
Step-by-step explanation:
by tan(X) rule
tan(61)=47/BC
BC= 47 / tan(61)
BC=26.05
Answer:
BC = 26.05Step-by-step explanation:
Given Information :
Hypotenuse : Not given
Opposite : 47
Adjacent : BC
Angle ( θ) = 61°
Using SOHCAHTOA
[tex]Tan\: \theta = \frac{Opposite}{Adjacent} \\\\Tan \: 61 = \frac{47}{BC} \\\\1.804 = \frac{47}{BC}\\\\Cross\:Multiply\\1.804BC= 47\\\\Divide\:both\:sides\:by\:1.8 \\\\\frac{1.804BC}{1.804} = \frac{47}{1.804} \\\\BC= 26.05[/tex]
Again I need help, sorry but thank you!
Answer:
B)13 pints
Step-by-step explanation:
SO first we find the unit rate
We know that in 90 minutes (hour and a half), the water leaked 6 pints form 2;30 to 4
Now So we can divide to find unit rate
6/90=1/15
So 1 pint for every 15 minutes
And now we want to know the amount it takes from 2:30 to 6:30 which is 4 hours
40 hours is 240 minutes
SO we can divide now
240/15=16
SO 16 pints leaked but the question asked for remaining water in container
So 29-16 is 13
So B)13
HELP ASAP EASY MATH ***25 Points
What is the slope of the line passing through the points (-1, 3) and (4, – 7)?
A. -2
B. 3/4
C. -4/3 (1 1/3)
D. 2
A football team won 75% of 120 games in a season. How many games is that?
Answer:
90 games
Step-by-step explanation:
Of the 120 games the football team played, they won 75% of them.
Remember that in mathematics, "of" almost always means to multiply. Here, that means we must multiply 75% by 120:
75% * 120
Remember also that % just means divided by 100, so 75% = 75 / 100. So:
75% * 120 = (75/100) * 120 = 9000/100 = 90 games
Divide four people into three rooms, in which only one room could host two people. How many ways are there to arrange them so that A, B are not in the same room
Step-by-step explanation:
AC B D
AD B C
A BC D
A BD C
hope it's right
x + y = 152,
8.5x + 12y = 1,656
How many hats were sold?
Answer:
x = 48 and y = 104
Step-by-step explanation:
Given equations are:
[tex]x+y = 152\\8.5x+12y=1656[/tex]
From equation 1:
[tex]x = 152-y[/tex]
Putting the value of y in equation 2
[tex]8.5(152-y)+12y = 1656\\1292-8.5y+12y = 1656\\3.5y+1292 = 1656\\3.5y = 1656-1292\\3.5y = 364\\\frac{3.5y}{3.5} = \frac{364}{3.5}\\y = 104[/tex]
Now we have to put the value of y in one of the equation to find the value of x
Putting y = 104 in the first equation
[tex]x+y = 152\\x+ 104 = 152\\x = 152-104\\x = 48[/tex]
Hence,
The solution of the system of equations is x = 48 and y = 104
The value of variable which was assumed for number of hats, is the total number of hats.
Answer:
48 hats
Step-by-step explanation:
Need help, I’ll give brainliest if correct.
I HAVE A QUESTION.. so on 8 and 9, do I keep it addition or do I put it as subtraction? ALSO I NEED HELP ON 13 AND 14
Step-by-step explanation:
question 8 answer = -4
questions 9 answer = -18
pls mark my answer as brainlist plzzzz vote me also
Megan cut a string into 4 equal pieces. Each piece is 4 fifths of a foot long. How many feet long was the string before Megan cut it? Enter your answer as a mixed number in the solution box.
Answer:
3 1/5 feetStep-by-step explanation:
Let the length of the string be x:
x/4 = 4/5 x = 4*4/5x = 16/5x = 3 1/5 feet