Using the z-distribution, it is found that the 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
31 out of 133 challenges were successful, hence:
[tex]n = 133, \pi = \frac{31}{133} = 0.2331[/tex]
90% confidence level, hence [tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 - 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.1728[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 + 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.2934[/tex]
As percentages:
0.1728 x 100% = 17.28%
0.2934 x 100% = 29.34%
The 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
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A rectangular garden is 5 ft longer than it is wide. Its area is 4550 ft. What are its dimensions?
Step-by-step explanation:
Area= lxb
L = 5+d
area= d(5+d)
4550=d²+5d
d²+5d-4550=0
d2+5d−4550=0
(d−65)(d+70)=0
d−65=0 or d+70=0
d=65 or d=−70
dimensions= 65, 70
Write the equation of the line in fully simplified slope-intercept form.
[tex]y = -\frac{1}{2}x - 1[/tex]
Step-by-step explanation:
Let's pick two points on the line: [tex]P_1(-4, 1)[/tex] and [tex]P_2(2, -2).[/tex] Let's calculate the slope of this line using these points:
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-2 - 1}{2 - (-4)} = -\dfrac{1}{2}[/tex]
With this value of the slope, we can write the general slope-intercept form of the equation as
[tex]y = -\frac{1}{2}x + b[/tex]
To solve for the y-intercept b, let's use either P1 or P2. I'm going to use P2:
[tex]-2 = -\frac{1}{2}(2) + b \Rightarrow b = -1[/tex]
Therefore, the slope-intercept form of the equation is
[tex]y = -\frac{1}{2}x - 1[/tex]
Which shows the expanded form of the number 54.98?
O a. 5x10+4x1+9x1+8 x 10
B. 5 x 10+ 4x1 +9 x 10+ 8 x 100
C 5x 10+4x1+9x to +8 100
10
D. 5 x 1000 + 4 x 100 + 9 x 10 + 8
(A) use the Pythagorean theorean to determine the length of the unknown side of the triangle
Answer:
a. = 36km
b. Perimeter = 108km
c. Area = 486km^2
Step-by-step explanation:
Pythagoras theorem
a^2 + b^2 = c^2
27^2 + b^2 = 45^2
b^2 = 45^2 - 27^2
b^2 = 1296
b = [tex]\sqrt{1296}[/tex]
b = 36km
Perimeter
a + b + c
27 + 36 + 45 = 108
Perimeter = 108km
Area = [tex]\frac{ab}{2}[/tex]
Area = [tex]\frac{27 * 36}{2}[/tex]
Area = [tex]\frac{972}{2}[/tex]
Area = 486km^2
What is the final cost of a $40 item after a 8% tax is applied
The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.
___feet, ___feet, ___feet
then then then
okokokokokokok
in which system are the lines parallel ?
Dеtеrmіnе tһе domain օf tһе fսnсtіօn f(х) = 2х + 1 ԝһеn tһе range іѕ {-3, 9, 15}.
x = -3 ==> 2(-3) + 1 = (-6) + 1 = -5
x = 9 ==> 2(9) + 1 = 18 + 1 = 19
x = 15 ==> 2(15) + 1 = 30 + 1 = 31
Domain = (-5, 19, 31)What is the probability of randomly selecting a month of the year and not getting a month that has fewer than 30 days
Answer
11 out of 12
11/12
Step-by-step explanation:
Solve
-12 + 23
A. -35
B. -11
C. 11
D. 35
Answer:
C. 11
Step-by-step explanation:
This can be rewritten as
23 - 12
This is equal to 11.
Answer:
11
Step-by-step explanation:
-12 + 23 = 11
since the 12 is negative subtract it from 23 and you get 11 as your answer
hooke’s law states that the extension or elastic string beyond its natural length as the force applied. if a weight of 9 9 pounds attached to s spring causes it to a length of 20 inches?
Answer:
https://brainly.com/question/25709302
Please find the correct answer will give high points, mark brainliest, give 4 stars, and hearts. PLS
if 1 dollar equals 0.72p what is the exchange rate from pounds to dollars
Answer:
1 pound = 1.389 dollars ( to nearest thousandth)
Step-by-step explanation:
1 pound = 1/0.72 = 1.388888...
The weight of an adult standard poodle was found to follow a normal distribution with a mean of 50 pounds and a standard deviation of 15 pounds. If represents the mean weight of a random sample of 7 adult standard poodles, what is (round off to second decimal place)
Using the Central Limit Theorem, it is found that the distribution of the sample means of the weights of the 7 adult standard poodles is normal, with mean of 50 pounds and standard deviation of 5.67 pounds.
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].
In this problem, for the population, [tex]\mu = 50, \sigma = 15[/tex].
Sample of 7, hence [tex]n = 7, s = \frac{15}{\sqrt{7}} = 5.67[/tex]The distribution of the sample means of the weights of the 7 adult standard poodles is normal, with mean of 50 pounds and standard deviation of 5.67 pounds.
A similar problem is given at https://brainly.com/question/25606713
Suppose that Y and Z are points on the number line.
If YZ=8 and Z lies at 5, where could Y be located?
If there is more than one location, separate them with commas.
Location(s) of Y :
9514 1404 393
Answer:
-3, 13
Step-by-step explanation:
8 units to the left of 5 on the number line is 5-8 = -3.
8 units to the right of 5 on the number line is 5+8 = 13.
The possible locations of Y are -3 or 13.
Moneysaver's Bank offers a savings account that earns 5% interest compounded continuously. If Ravi deposits $3200, how much will he have in the account
after six years, assuming he makes no withdrawals?
Do not round any intermediate computations, and round your answer to the nearest cent
x
5
?
the answer is 4160$
After 6 years of investment of $3200 compounded continuously, final amount in the account will be $4319.55.
Moneysaver's Bank offers a saving account with the features as,
Rate of interest = 5% annualTime of investment = 6 yearsPrincipal amount = $3200Expression to calculate the final amount when compounded continuously,
Final amount = [tex]P.e^{rt}[/tex]
Here, P = Principal amount
r = Rate of interest
t = Duration of investment
By substituting the values in the expression,
Final amount = [tex]3200.e^{0.05\times 6}[/tex]
= 3200(1.3498588)
= 4319.548
≈ $4319.55
Therefore, after 6 years of investment of $3200, final amount in the account will be $4319.55.
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HELP ASAP PLZ!!!!!!!!
Step-by-step explanation:
Triangle KLN has 3 equal angles so all sides of it must be equal ( equilateral triangle)
y+3=10
y=7
Triangle LNM has 2 equal angles as in an isosceles triangle so LN= ML
So sides opposite to equal angles must be equal too
x-6=y+3
x-6= 10
x= 16
Need the answer to this pls
Answer:
0
Step-by-step explanation:
1. First, we should know the slope-intercept form of any equation: y = mx + b.
y = y-coordinatem = slopex = x-coordinateb = y-intercept2. In the equation y = -2/3(x), it appears that the variables we can see are y, m, and x. However, the y-intercept, b, is still there with the value of 0.
Additionally, this is a proportional relationship because it follows the format y = kx. Proportional relationships always have a y-intercept of 0.Therefore, the y-intercept is 0.
Evaluate
[2- |-2/3 -2(-1/5)|] (-13)
What is the value of the expression?
Enter your answer as a simplified fraction in the box.
Answer: the answer - 2/15
Step-by-step explanation: i took the test
The value of the expression [2- |-2/3 -2(-1/5)|] ÷ (-13) is -2/15
What is an expression?Numbers, symbols and operators grouped together that show the value of something.
Given that an expression [2- |-2/3 -2(-1/5)|] ÷ (-13)
[2- |-2/3 -2(-1/5)|] ÷ (-13)
= [2 - 4/15]/ (-13)
= 26/15*1/(-13)
= -2/15
Hence, The value of the expression [2- |-2/3 -2(-1/5)|] ÷ (-13) is -2/15
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plz help!!!!!!!!!!!!!!!!
Answer:
C = 50°
Step-by-step explanation:
In the given figure, it tells us which angles are the same. ( You can look at the red marks. )
So, 68 + 62 = 130.
As we all know, the sum of all angles in any triangle is 180.
So, 180 - 130 = 50.
That is Angle C.
I hope it helps.
Your team wins 24 medals . The medals are Gold, silver and
bronze in a ratio of 1:1:6. How many of each did your team win ?
10.
Use the quadratic function to predict y if x equals 6.
y = 2x2 − 2x − 2
A. y = 60
B. y = 58
C. y = −60
D. y = −58
Answer:
B. y = 58
Step-by-step explanation:
b) y=58 you follow the instructions
...............................................................................................................................................
The given quadratic function is
y= 2x^2 - 2x - 2
We have to find the value of the function y at x=6.
Substitute x=6 in the given function.
y= 2(6)^2 - 2(6) - 2
y= 2(36) - 12 - 2
y= 72 - 14
y= 58
The value of the function is 58 at x=6 is 58.
Therefore the correct option is B.
1. Two linear functions are shown below. Which function has the greater rate of change? Function A Function B 10 у y 4 32 8 8 6 44 12 4 56 2 16 68 Х 0 20 80 0 2 4 6
Answer:
I don't understand clear ur question
A photograph measures 15 cm by 20 cm. It is made smaller in the ratio 4:5 What are the dimensions of the new photograph?
HELP PLSS !!!!!
Answer:
12cm by 15cm
8cm by 10cm
4cm by 5cm
Step-by-step explanation:
it is made smaller so any values smaller than 15cm but in ratio of 4:5 can be answer
Answer:
15 cm is the new dimensions of new photograph
Step-by-step explanation:
initial dimension of shorter side = 8 cm
initial dimension of longer side = 10 cm
final dimension ofshorter side = 12 cm
finial dimension of longer side = x cm
The enlargement always ensure the aspect ratio
aspect ratio = lonter side/shorter side
equating, [tex]\frac{10}{8}[/tex] = [tex]\frac{x}{12}[/tex]
Solving for x,
10 × 12 = 8 × x
[tex]x = \frac{10 x 12 }{8} = \frac{120}{8 } = 15[/tex]
/\
that says 10 x 12
longer side is 15cm
(Hope this helps can I pls have brainlist (crown)☺️)
What is the quotient of -9 Divided by 3 ?
[tex]\huge\text{\bf Hey there!}[/tex]
[tex]\large\text{\bf Guide to remember}\downarrow\\\large\textsf{2 negatives = positive}\\\large\textsf{1 negative \& 1 positive = negative}\\\large\textsf{2 positives = positve}\\\large\textsf{1 positive \& 1 negative = negative}[/tex]
[tex]\large\text{This means your answer will most likely be a \boxed{\text{negative}} because}\\\large\text{you have a negative number (-9) \& a positive number (3).}[/tex]
[tex]\large\boxed{\mathsf{-9 \div 3}}\\\large\boxed{\mathsf{= \dfrac{-9}{3}}}\\\large\boxed{\mathsf{= \dfrac{-9\div3}{3\div3}}}\\\large\boxed{\mathsf{= \dfrac{-3}{1}}}\\\large\boxed{\mathsf{= -3\div 1}}\\\large\boxed{\mathsf{= -3}}\\\\\\\\\\\huge\boxed{\text{Therefore. your answer is: \boxed{\textsf 3}}}\huge\checkmark[/tex]
[tex]\huge\text{\bf Good luck on your assignment \&}\\\huge\text{\bf enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Which value of x would make the following matrix singular?
5 x
3 6
Answer: 10
Explanation:
(30)-(30)= 0
Singular matrices must equal 0
(Correct on my quiz)
The value of x would make the following matrix singular is 10
Matrices of a functionFor a matrix to be singular, the determinant of the matrix must be zero.
For the given 2 by 2 matrix, for the matrix to be a singular matrix then, its determinant must be zero as shown;
(5* 6) - (3 * x) = 0
30 - 3x = 0
3x = 30
x = 10
Hence the value of x would make the following matrix singular is 10
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Find the value of a when b = 7 and c = 6 in the formula a=(b+c) - 2.
Answer:
a = 11
Step-by-step explanation:
a = (7+6) - 2
a = 13 - 2
a = 11
1. Find the coordinates of all points where the lines
x + y = 8, y = 5, and x = 1 intersect.
Answer:
(3)1. Find the coordinates of all points where the lines
x + y = 8, y = 5, and x = 1 intersect.
Step-by-step explanation:
this answer
The coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect are (0, 5), (1, 0), (3, 5) and (1, 7).
Given that;
The equation of lines is,
x + y = 8
y = 5
x = 1
Now all the coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect are find as,
x + y = 8
Put y = 5;
x + 5 = 8
x = 8 - 5
x = 3
Put x = 1;
1 + y = 8
y = 8 - 1
y = 7
Therefore, the points are (0, 5), (1, 0), (3, 5) and (1, 7).
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Last month, Irma’s deliveries consisted of $33,600 in groceries, and she made 140 deliveries of pet supplies. How much does Irma earn in total for the month?
Answer:
If in you little HMH thing it is 4044.8
Write x^2+3x-8 in the form of (x+p) ^2+q
Answer:
(x+1.5)^2 -10.25
Step-by-step explanation:
1)first, we half 3 to give us 1.5
(x+1.5)^2
2)square 1.5=2.25
so far we have (x+1.5)^2 - 2.25 --- the negative sign from 2.25 is part of the formula
3)we subtract 8 from -2.25. the 8 comes from here shown in bold ----- x^2+3x-8
4) (x+1.5)^2 -2.25 - 8
5)simplify the last part by doing -2.25 - 8= -10.25
6)answer is (x+1.5)^2 - 10.25