Answer:
a) 0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.
b) 0.9463 = 94.63% probability that Jodi will score 77% or lower.
c) 400 questions.
d) Yes, because the formula is the same, independently of the value of p.
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 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]
In this question:
[tex]p = 0.81[/tex]
Question a:
100 questions means that [tex]n = 100[/tex]
For the approximation, we have that:
[tex]\mu = p = 0.81[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{100}} = 0.0392[/tex]
This probability is the pvalue of Z when X = 0.77. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.77 - 0.81}{0.0392}[/tex]
[tex]Z = 1.02[/tex]
[tex]Z = 1.02[/tex] has a pvalue of 0.8461
0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.
Question b:
Now [tex]n = 250[/tex], so:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{250}} = 0.0248[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.77 - 0.81}{0.0248}[/tex]
[tex]Z = 1.61[/tex]
[tex]Z = 1.61[/tex] has a pvalue of 0.9463
0.9463 = 94.63% probability that Jodi will score 77% or lower.
Question c:
The formula for the standard deviation is:
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Meaning that it is inversely proportional to the square root of the sample size.
So, to reduce the standard deviation by half, the number of question must be multiplied by (2)^2 = 4.
100*4 = 400
So 400 questions.
d. Laura is a weaker student for whom p = 0.76. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?
Yes, because the formula is the same, independently of the value of p.
Simplify: 0÷(x−1/3), where x≠1/3.
Answer:
0
Step-by-step explanation:
0 divided by any nonzero quantity is zero.
27 POINTS!! The price of 2 items in P and Q come to a ratio of 4:5. When the price of P is increased of $12 and the price of Q is reduced by $6,the items have the same price. Find the original price of P
The original price P will be $72
To find the ratiosIf we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.
4 × y =?
5 × y =?
We need to input a value in for y.
Let's put 9.
4 × 9 = 36 (P)
5 × 9 = 45 (Q)
Now adding 12 to P, and take away 6 from Q.
36 + 12 = 48
45 - 6 = 39
The numbers aren't the same yet.
Let's use a different value for y.
y = 18
The equations will now look like this:
4 × 18 = 72 (P)
5 × 18 = 90 (Q)
Let's add 12 and 6 to the numbers again.
72 + 12 = 84
90 - 6 = 84
The numbers are now equal
Therefore, the original price of P = $72
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what is 10+40-11+100=
Answer:139 is the answer
Step-by-step explanation:
Tom received a $75 gift certificate for the local sporting goods store. He
bought two baseballs for $1.79 each, a baseball glove for $49.99, and a
baseball bat for $12.19. About how much of his gift certificate will he have
left?
Answer:
He has $9.24 left of his gift certificate
Step-by-step explanation:
Given that,
He bought two baseballs for $1.79
Baseball= 1.79+1.79 or 1.79 × 2 (because there are two baseballs.
= $3.58
Baseball Glove = $49.99
Baseball Bat = $12.19
Altogether = $3.58 + $49.99 + $12.19
= $65.76
So you subtract $65.76 from the Original amount in the gift certificate,
=> $75 - $65.76
= $9.24
Write a fraction for which the sum of the numerator and denominator is 20, and the value of the
fraction is equal to 2/3
Answer:
[tex]\dfrac{8}{12}[/tex]
Step-by-step explanation:
Let the unknown fraction be:
[tex]\dfrac{a}{b}[/tex]If the sum of the numerator and denominator is 20 then:
[tex]\implies a+b=20[/tex]
Rewrite the equation to isolate b:
[tex]\implies b=20-a[/tex]
If the fraction is equal to 2/3 then:
[tex]\implies \dfrac{a}{b}=\dfrac{2}{3}[/tex]
Cross multiply:
[tex]\implies 3a=2b[/tex]
Substitute the expression for b into the cross-multiplied equation and solve for a:
[tex]\implies 3a=2(20-a)[/tex]
[tex]\implies 3a=40-2a[/tex]
[tex]\implies 5a=40[/tex]
[tex]\implies a=8[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\implies b=20-8[/tex]
[tex]\implies b=12[/tex]
Therefore, the fraction for which the sum of the numerator and denominator is 20, and the value of the fraction is equal to 2/3 is:
[tex]\dfrac{8}{12}[/tex]Find the missing side length
Answer:
8
Step-by-step explanation:
x+7=15 so x=15-7 which is x=8
Answer:
8 ft
Step-by-step explanation:
The length of the shape is 15 ft. The length on the bottom is equal to the length on the top.
We are given 2 "sides" or lines on the bottom. One of them is 7 ft. Find the other "side" length.
x + 7 =15
x = 15 - 7
x = 8
The length of a rectangle is 1 7/9 inches and its width is 3/4 of its length. Find the area of this rectangle.
Answer:
Area = 2 10/27 inch²
Step-by-step explanation:
Length: 1 7/9 inches
Width: (3/4)(1 7/9 inches)
Area = Length × Width
Area = (1 7/9 inches) × (3/4)(1 7/9 inches)
Area = 16/9 inches × 16/9 inches × 3/4
Area = 768/324 inch²
Area = 256/108 inch²
Area = 128/54 inch²
Area = 64/27 inch²
Area = 2 10/27 inch²
Here are summary statistics for the weights of Pepsi in randomly selected cans: n=36, x=0.82412 lb, s=0.00573 lb.
Use a confidence level of 90% to complete parts (a) through (d) below.
a. Identify the critical value ta/2 used for finding the margin of error.
¹a/2=
(Round to two decimal places as needed.)
The critical value is given as 1.69
The margin of error is 0.00161
How to solve for the critical valueWe are to find the critical value ta/2 used for finding the margin of error
T∝ / 2 = 1 - 0.10 / 2
1 - 0.05 = 0.95
The critical value at the level if we use the critical value table is 1.69
2. Next we would have to solve for the margin of error
When comparing your results to the actual population value, a margin of error indicates how many percentage points they will deviate.
ME= [tex]z * \frac{s}{\sqrt{n} }[/tex]
z is the critical value = 1.69
s = standard deviation = 0.00573
n = sample size
where z = 1.69
s = 0.00573
n = 36
We would have to put these values in the formula above to get the margin of error
[tex]1.69 * \frac{0.00573}{\sqrt{36} }[/tex]
Margin of error = 0.00161
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Assume you are buying a bond with a par value of $1,000 which is listed in the Wall Street Journal at a price of 100.50. Find the bond price.
Assume you are buying a bond with a par value of $1,000 which is listed in the Wall Street Journal at a price of 100.50. The bond price is: $1,005.
How to find the bond price?Using this formula to determine the bond price
Bond price = Bond par value × price/100
Where:
Bond par value = $1,000
Price = 100.50
Let plug in the formula
Bond price = $1,000 × 100.50 /100
Bond price = $100,500 /100
Bond price =$1,005
Therefore the bond price is $1,005.
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1. Anya is at camp and walks 2km due north and then turns and walks another 3km at a bearing angle of 35° . Find her distance back to camp and the bearing angle from her starting point.
Anya her distance back to camp and the bearing angle from her starting point is 4.78 km North 26.3° West.
Define direction ?
Direction gives the information about the way towards which an object moves or tends.
The angle formed by the 2 km and 3 km is the supplement of the 35 ° angle west of north;
180°- 35° = 145°
We know that the length of two sides and one angle.
The opposite side know angle is the direct distance between the starting and ending points.
Using the law of cosines.
[tex]a^{2} = b^{2} + c^{2} - 2bc (cosA)[/tex]
[tex]a^{2} = 2^{2} + 3^{2} - 2(2)(3)(cos 145)[/tex]
[tex]a^{2} = 4 + 9 - 12 (-0.8192)[/tex]
[tex]a^{2} = 22.83[/tex]
a = 4.78 km
To determine the bearing from the starting point , we must determine the angle between the first leg and the direct path.
Using the law of sines
[tex]\frac{4.78}{sin(145)} = \frac{3}{sin C}[/tex] sin(145°)
4.78 sin C = 3 sin 145°
sin C = [tex]\frac{3 sin (145^ 0)}{4.78}[/tex]
sin C = 0.4438
C = 26.3°
Therefore, the distance and bearing of the end point from the starting point is 4.78 km North 26.3 ° West.
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By first rounding Both number to 1 significant figure estimate the answer to 13 x 378
The solution is A = 4000
The equation after rounding up numbers is A = 10 x 400 = 4000
What is rounding up numbers?
There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Leading zeros are never significant
Trailing zeros are only significant if the number contains a decimal point
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be = p
The value of p = 13
Let the second number be = q
The value of q = 378
Rounding the number p to 1 significant figure , p = 10
Rounding the number q to 1 significant number q = 400
So , the equation is A = p x q
Substituting the values in the equation , we get
A = 10 x 400
The value of A = 4000
Hence , The equation after rounding up numbers is A = 10 x 400 = 4000
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what is 1 + 1 i dont know it
Answer:
2
Step-by-step explanation:
1+1=2
XD
Answer:
2
Step-by-step explanation:
I know this is a joke but I don't care
10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x+y=8
-x-3y=-12
O 3y + 12
O-3y + 12
O 3y - 12
-3y - 12
The expression that we can use to substitute into the first equation is
x = - 3y + 12.
Substitution Method:
The algebraic approach to solving linear equations is known as the substitution method. This procedure involves substituting a variable's value from one equation into the other. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
Here we have
2x + y = 8 ---- (1)
- x - 3y = -12 ----- (2)
We can isolate x in the second equation as given below
=> - x - 3y = -12
Add 3y on both sides
=> - x - 3y + 3y = - 12 + 3y
=> - x = - 12 + 3y
Multiply by -1 on both sides
=> -(- x) = - (- 12 + 3y)
=> x = + 12 - 3y
=> x = - 3y + 12
Therefore,
The expression that we can use to substitute into the first equation is
x = - 3y + 12.
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In a sale, normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20 Work out the normal price of the pen.
Answer:
The normal price of a pen is £8
Step-by-step explanation:
let p be the normal price.
The statement : “normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20”
Means
[tex]p \times \frac{15}{100} = 1.20[/tex]
Then
[tex]p = 1.20 \times \frac{100}{15} = \frac{120}{15} = 8[/tex]
Answer:
The normal price of the pen is £8
Step-by-step explanation:
Reduced by 15%
Reduced by £1.20
Meaning that 15% is £1.20
To find the 100% or the normal price of the pen we find the 1% first then the 100%
So, 1% = £1.20/15
100% =£1.20/15 x 100
= 8
Checking..
If normal price was 8 and reduction is 15%
8(1- R/100) {R = %}
8(1 -15/100) = 6.8 (Reduced price)
8 - 6.8 = £1.20 ( Reduction price aka the 15%)
Therefore, the normal price of the pen is £8.
7. (85D) Richards Park charges an admission fee of
$10 plus an hourly fee for each sport that you
choose to participate in. Which equation
represents the cost C, in terms of the number of
hours, h, you pay to sled?
HELP PLEAAASEEE 20 POINTS
Answer:
C. C = $10 +$5h
Step-by-step explanation:
The cost is a $10 admission fee plus $5 per hour for sledding. You want an equation representing the cost C in terms of hours h.
CostThe cost is ...
cost = admission fee + hourly charge
The hourly charge is the product of the cost per hour ($5) and the number of hours (h).
C = $10 +$5h
Find the least common denominator (LCD) of 1/30 and 9/20
Answer: LCD = 60
Step-by-step explanation:
Rewriting input as fractions if necessary:
1/30, 9/20
For the denominators (30, 20) the least common multiple (LCM) is 60.
Therefore, the least common denominator (LCD) is 60.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
1/30 = 1/30 × 2/2 = 2/60
9/20 = 9/20 × 3/3 = 27/60
(Scientific Notation in the Real World MC)
The length of a bacterial cell is about 3 x 10−6 m, and the length of an amoeba cell is about 4.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
2 x 102
2 x 103
0.7 x 101
6.67 x 102
By dividing the length of bacteria cell to length of amoeba cell we find option (D) i.e 6.67x102 is the correct answer.
what is division?Division is an arithmetic operation that involves dividing one number (the dividend) by another number (the divisor) to find the quotient.
What are different arithmetic operators?Arithmetic operators are symbols that represent mathematical operations that can be performed on one or more operands. The most common arithmetic operators are:
Addition (+): Adds two operands and produces the sum.
Subtraction (-): Subtracts one operand from another and produces the difference.
Multiplication (*): Multiplies two operands and produces the product.
Division (/): Divides one operand by another and produces the quotient.
Modulo (%) : Divides one operand by another and produces the remainder.
Exponentiation (**): Raises one operand to the power of the other and produces the result.
To compare the sizes of the two cells, we need to divide the length of the bacterial cell by the length of the amoeba cell. The result is 3 x 10^−6 m / 4.5 x 10^−4 m = 0.67 x 10^−2.
So, the bacterial cell is approximately 0.67 x 10^−2 times smaller than the amoeba cell.
The correct answer is therefore (D) 6.67 x 10
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Write a linear inequality to represent the information given. Shanley would like to give $5 gift cards and $8 teddy bears as party favors. Shanley has $144 to spend on party favors. Enter an inequality to find the number of gift cards x and teddy bears y Shanley could purchase. Give one solution to the inequality.
Is 1.765 an example of an integer?
Answer:
No.
Step-by-step explanation:
An integer is defined as a whole number.
The number given, "1.765", is not a whole number, as it includes the decimal .765. 1.765, as implied by decimal point, is a decimal number.
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Name
1. Consider the expression 7x² + 3x - 4.
Part A
Write the completely factored expression.
Answer:
After factorization the result is: (7x + 4)(x - 1).
Step-by-step explanation:
To factor 7x² + 3x - 4, we can use the following steps:
Look for two numbers that multiply to give the constant term (-4) and add to give the coefficient of the linear term (3). These two numbers are -4 and 1.
Use these numbers to create two binomials, one with a positive sign and one with a negative sign: (7x + 4) and (7x - 1).
Factor the quadratic expression by grouping:
(7x + 4)(x - 1)
We can check that this is the correct answer by multiplying the two binomials:
(7x + 4)(x - 1) = 7x² + 3x - 4
This is the original expression, so we have successfully factored it.
Note: Depending on the specific problem, there may be more than one way to factor the expression. This is just one possible solution.
HELPPPPPPPP PLEASESEEEEEEEE
Answer: 7/3 or 2.333
Step-by-step explanation:
the formula for slope is y2-y1 over x2-x1
so if you apply the formula here its going to be
4-(-3) over 5-2
which is 7 over 3 therefore your slope will be
7/3
Answer:
[tex]m=\frac{7}{3} =2.33333... = 2.\overline{3}[/tex]
Step-by-step explanation:
The length of the side of a quadrilateral are 6 cm, 5 cm, 8cm. and 11cm the perimeter of
the similar quadrilateral is 20 cm.
Find the length of the sides of the second, quadrilateral
Answer:
Step-by-step explanation:
Let's call the side lengths of the first quadrilateral a, b, c, and d, and the side lengths of the second quadrilateral A, B, C, and D. We are given that the perimeter of the second quadrilateral is 20 cm, and that the quadrilaterals are similar. This means that the ratio of the side lengths of the two quadrilaterals is the same for all four sides. Let's call this ratio r. Then we have:
A + B + C + D = 20 cm
and
A/a = B/b = C/c = D/d = r
We can find the value of r by taking the ratio of any two sides of the quadrilaterals. For example, we can take the ratio of A to a:
A/a = r
Substituting the expressions for A and a in terms of r, we get:
(ra)/a = r
Solving for r, we get:
r = a/a = 1
This means that the ratio of the side lengths of the two quadrilaterals is 1. Therefore, the side lengths of the second quadrilateral are equal to the side lengths of the first quadrilateral. Substituting the given values for the side lengths of the first quadrilateral, we get:
A = 6 cm
B = 5 cm
C = 8 cm
D = 11 cm
Therefore, the side lengths of the second quadrilateral are A = 6 cm, B = 5 cm, C = 8 cm, and D = 11 cm.
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus? Check all that apply. The sample needs to be random but we don’t know if it is. The actual count of drivers is too small. The actual count of those who do not drive to campus is too small. n ^ p is not greater than 10. n ( 1 − ^ p ) is not greater than 10.
The statements that apply to the given random sample situation are:
(A) Despite the idea that the sample must be random, we are unsure of this.
(C) It is underreported how many pupils don't drive to school.
(D) n(1p) is not greater than 10.
What is a Simple random sample?A simple random sample, also known as an SRS, is a smaller group of individuals (also known as a sample) chosen randomly and with equal probability from a larger population.
This technique involves picking a sample at random.
The probability of being chosen from any subset of k persons in SRS is the same as that of being chosen from any other subset of k people.
A simple random sample is an objective sampling approach.
A basic sampling method that can be used in conjunction with other, more advanced sampling techniques is simple random sampling.
So, statements that apply in the given situation are:
- We don't know if the sample is random, despite the fact that it must be.
- The number of students who don't drive to school is undercounted.
- n(1−^p) does not exceed 10.
Therefore, the statements that apply to the given random sample situation are:
(A) Despite the idea that the sample must be random, we are unsure of this.
(C) It is underreported how many pupils don't drive to school.
(D) n(1p) is not greater than 10.
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Correct question:
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of drivers is too small.
c. The actual count of those who does not drive to campus is too small.
d. n ^ p is not greater than 10. n ( 1 − ^ p ) is not greater than 10.
Please help this is percentages.
The percentage of boys in the class is 60% and the percentage of girls in the class is 40%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Total number of students in class = 45
Total number of boys in the class = 27
Then, the percentage of boys in the class will be,
Let the percentage of boys be x.
x% Of 45 = 27
x = (27 × 100)/45
x = 2700/45
x = 60%
Then, total number of girls in the class = 45 - 27 = 18
Assume the percentage of girls in the class be y.
y% Of 45 = 18
y = (18 × 100)/45
y = 1800/45
y = 40%
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solve the following inequality.4x-6<10
Answer:
x < 4
Step-by-step explanation:
4x - 6 < 10
4x < 16
x < 4
[tex]4x-6 < 10[/tex]
Add 6 to both sides:
[tex]4x-6+6 < 10+6[/tex]
[tex]4x < 16[/tex]
Divide both sides by 4:
[tex]\dfrac{4x}{4} < \dfrac{16}{4}[/tex]
[tex]\fbox{x} < \fbox{4}[/tex]
Can someone evaluate these
1 × ( –6 × – 18 – 8) ÷ 4
–4 – –20 + –5 ×( –11 – –18)
13 – –10 × 16 ÷(14 + –16)
1– –9 × 12 × (–19 + 20)
Answer:
1 × ( –6 × – 18 – 8) ÷ 4=[tex]\frac{1}{404}[/tex]
–4 – –20 + –5 ×( –11 – –18)=[tex]18[/tex]
13 – –10 × 16 ÷(14 + –16)=[tex]173[/tex]
1– –9 × 12 × (–19 + 20)=[tex]110[/tex]
the product of w and 10
Answer: 10w
Step-by-step explanation:
in a survey of 1,000 adults in a country, 722 said that they had eaten fast food at least once in the past month. create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month. use excel to create the confidence interval, rounding to four decimal places.
To create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month, we need to first calculate the sample proportion.
The sample proportion is calculated by dividing the number of adults who ate fast food at least once in the past month (722) by the total number of adults surveyed (1000). This gives us a sample proportion of 0.722.
To calculate the confidence interval, we can use the following formula:
Sample proportion +/- 1.96 * sqrt((Sample proportion * (1 - Sample proportion)) / Sample size)Plugging in the values, we get:
0.722 +/- 1.96 * sqrt((0.722 * (1 - 0.722)) / 1000)This gives us a 95% confidence interval of (0.6901, 0.7539). Rounded to four decimal places, the confidence interval is (0.6901, 0.7539).
Note: To calculate the confidence interval using Excel, you can use the following formula:
=CONFIDENCE.NORM(alpha, standard_dev, size)Where "alpha" is the desired confidence level (e.g., 0.95 for a 95% confidence interval), "standard_dev" is the standard deviation of the sample, and "size" is the sample size. To calculate the standard deviation, you can use the STDEV.P function.
For example, to calculate the lower and upper bounds of the 95% confidence interval, you could use the following formulas:
Lower bound: =CONFIDENCE.NORM(0.95, STDEV.P(A1:A1000), 1000) - (1.96 * STDEV.P(A1:A1000))Upper bound: =CONFIDENCE.NORM(0.95, STDEV.P(A1:A1000), 1000) + (1.96 * STDEV.P(A1:A1000))Where A1:A1000 is a range containing the values "1" for those adults who ate fast food at least once in the past month and "0" for those who did not. This will give you the same result as the manual calculation above.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The slant height of the cone c² = 5² + (1)² or c ≅ 5.1.
Option (A) is correct option.
What is cone?A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.
Given that,
The radius of the cone = 1 inch,
And the height of the cone = 5 inch.
Let the slant height of the cone is c,
To find the slant height of the cone, use Pythagorean theorem,
c² = 5² + (1)²
c² = 25 + 1
c² = 26
c= 5.09
c ≅ 5.1
The slant height of the cone is 5.1 inch.
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There are various mathematical equations that help us understand the structures of the ear and how they contribute to hearing. the decibel equation, expressed as db
The decibel equation is used in many different contexts, including acoustics, audiology, and engineering, to measure and compare the intensity of sounds.
The decibel equation is a measure of sound intensity, which is a way to describe the strength or magnitude of a sound. It is expressed as dB, and it is defined as the ratio of the intensity of a sound to a reference intensity. The reference intensity is usually set at a level that is the minimum intensity that a person can hear, which is approximately 0 dB.
The decibel equation is typically written as:
dB = 10 × log10(I / I0)
where I is the intensity of the sound being measured and I0 is the reference intensity. The log10 part of the equation is used to express the ratio of the two intensities on a logarithmic scale, which allows the decibel value to be more easily interpreted.
The decibel scale is logarithmic, which means that a small change in decibel value corresponds to a much larger change in sound intensity. For example, a sound with a decibel value of 60 dB is much louder than a sound with a decibel value of 50 dB, even though the difference between the two values is only 10 dB.
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