Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
What is proportionality ?In mathematics, proportionality is the connection between two factors that maintains a fixed ratio called scale factor. Or, to put it another way, if one variable is increased or divided by a specific number, the second variable will also be doubled or divided by that identical number, maintaining their proportionality. Calculus, algebra, and geometry are three areas of mathematics where this idea is frequently applied.
given
(a) If 20% of adult Americans favour the suggested reforms, the sample size needed at the very least is:
n = [(zα/2)² * p * (1-p)] / E²
where z/2 is the standard normal distribution's critical value for the chosen degree of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.2 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.2 * (1-0.2)] / 0.05²
n = 1536.64
Thus, the study would require at least 1537 more adult Americans to be sampled.
(b) The minimal sample size needed if the proposed modifications are
supported by 25% of all adult Americans is:
n = [(zα/2)² * p * (1-p)] / E²
where:
The standard normal distribution's critical value, z/2, depends on the desired level of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.25 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.25 * (1-0.25)] / 0.05² \sn = 384.16
Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
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Area of a semicircle is 308cm. Find the perimeter
Answer:
72 cm
Step-by-step explanation:
Find the radius using the given information
308=1/2(πr^2)
r^2=616/π
r=14
The perimeter is πr + 2r so plug in 14
π(14) + 2(14)
43.96+28=71.96
I need help plz WILL GIVE BRAINLIEST
Answer: 7 miles
Step-by-step explanation:
The points for Tom's house (4, 2) and the store (-3, 2) are on the same level; they are on the same horizontal line 2 units above the x-axis.
The distance between the points is therefor the difference between the x coordinates.
4 - (-3) = 7
You can also just count the spaces between the points!
giving brainliest!!!!
Answer:
1209 square meters
Step-by-step explanation:
2(1/2*16*15)+3(17*19)=1209
A quality control expert wants to estimate the proportion of defective components that are being manufactured by his company. A sample of 300 components showed that 20 were defective. How large a sample is needed to estimate the true proportion of defective components to within 2.5 percentage points with 99% confidence?
A sample size of approximately 9909 components is needed to estimate the true proportion of defective components within 2.5 percentage points with 99% confidence.
To estimate the true proportion of defective components with a desired level of confidence and precision, we can use the formula for sample size determination in a proportion estimation problem.
The formula is given by:
n = (Z² p (1-p)) / E²
Where:
- n is the required sample size,
- Z is the Z-value corresponding to the desired confidence level (in this case, 99% confidence),
- p is the estimated proportion of defective components from the initial sample (20/300 = 0.0667),
- (1-p) is the estimated proportion of non-defective components,
- E is the desired margin of error (2.5 percentage points = 0.025).
Determine the Z-value corresponding to a 99% confidence level. The Z-value can be obtained from a standard normal distribution table or using statistical software. For a 99% confidence level, the Z-value is approximately 2.576.
Substitute the values into the formula:
n = (2.576² * 0.0667 * (1-0.0667)) / (0.025²)
n = (6.641 * 0.9333) / 0.000625
n = 6.194 / 0.000625
n ≈ 9908.8
Therefore, a sample size of approximately 9909 components is needed to estimate the true proportion of defective components within 2.5 percentage points with 99% confidence.
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Write in slope form : -5x+15y=-30
Answer:
hope this helps
Step-by-step explanation:
y=1/3x-2 is the slope form of -5x+15y=-30.
What is straight line?a line is an infinitely long object with no width, depth, or curvature.
The given equation is -5x+15y=-30
minus five x plus fifteen y equal to minus thirty.
The standard form or slope form of a line is
y=mx+c
Where m is the slope and c is y intercept.
We need to convert -5x+15y=-30 to standard form or slope intercept form of a line.
-5x+15y=-30
15y=-30+5x
15y=5x-30
Divide both sides by 15
y=5/15 x-30/15
y=1/3x-2
Hence y=1/3x-2 is the slope form of -5x+15y=-30.
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A contractor is required by a county planning department to submit 1, 2, 3, 4, or 5 forms (depending on the nature of the project) when applying for a building permit. Let y denote the number of forms required for an application, and suppose the mass function is given by p(y) 5 cy for y 5 1, 2, 3, 4, or 5. Determine the value of c, as well as the long-run proportion of applications that require at most three forms and the long-run proportion that require between two and four forms, inclusive.
Answer:
[tex](a)\ c = \frac{1}{15}[/tex]
[tex](b)\ 40\%[/tex]
[tex](c)\ 60\%[/tex]
Step-by-step explanation:
The given parameters can be represented as:
[tex]P_Y(y) \ge 0, y =1,2,3,4,5[/tex]
[tex]P_y(y) = cy, y=1,2,3,4,5[/tex]
Solving (a): The value of c
To do this, we make use of the following rule;
[tex]\sum\limit^5_{y=1}P_Y(y_i) = 1[/tex]
Given that:
[tex]P_y(y) = cy, y=1,2,3,4,5[/tex]
This is translated to:
[tex]c*1 + c * 2 + c * 3 + c * 4 + c * 5 = 1[/tex]
[tex]c + 2c + 3c + 4c + 5c = 1[/tex]
[tex]15c = 1[/tex]
Solve for c
[tex]c = \frac{1}{15}[/tex]
(b) The proportions of applications that requires at most 3 forms
This implies that: y = 1,2,3
So, we make use of:
[tex]P(Y \le 3) = P(Y=1) + P(y=2) + P(Y=3)[/tex]
Recall that:
[tex]P_y(y) = cy, y=1,2,3,4,5[/tex]
Substitute [tex]c = \frac{1}{15}[/tex]
[tex]P_y(y) =\frac{1}{15}y[/tex]
So:
[tex]P(Y \le 3) = P(Y=1) + P(y=2) + P(Y=3)[/tex]
[tex]P(Y\le 3) = \frac{1}{15} * 1 +\frac{1}{15} * 2 +\frac{1}{15} * 3[/tex]
[tex]P(Y\le 3) = \frac{1}{15} +\frac{2}{15} +\frac{3}{15}[/tex]
Take LCM
[tex]P(Y\le 3) = \frac{1+2+3}{15}[/tex]
[tex]P(Y\le 3) = \frac{6}{15}[/tex]
[tex]P(Y\le 3) = 0.4[/tex]
Express as percentage
[tex]P(Y\le 3) = 0.4*100\%[/tex]
[tex]P(Y\le 3) = 40\%[/tex]
(c) The proportions of applications that requires between 2 and 4 forms (inclusive)
This implies that: y = 2,3,4
So, we make use of:
[tex]P(2 \le Y \le 4) = P(Y=2) + P(Y=3) + P(Y=4)[/tex]
[tex]P(2 \le Y \le 4) = 2 * \frac{1}{15} + 3 * \frac{1}{15} + 4 * \frac{1}{15}[/tex]
[tex]P(2 \le Y \le 4) = \frac{2}{15} + \frac{3}{15} + \frac{4}{15}[/tex]
Take LCM
[tex]P(2 \le Y \le 4) = \frac{2+3+4}{15}[/tex]
[tex]P(2 \le Y \le 4) = \frac{9}{15}[/tex]
[tex]P(2 \le Y \le 4) = 0.6[/tex]
Express as percentage
[tex]P(2 \le Y \le 4) = 0.6 * 100\%[/tex]
[tex]P(2 \le Y \le 4) = 60\%[/tex]
A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling a number greater than .
If there is more than one element in the set, separate them with commas.
Question:
A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number greater than 2.
If there is more than one element in the set, separate them with commas.
Answer:
[tex]S = \{1,2,3,4,5,6\}[/tex]
[tex]Greater2 = \{3,4,5,6\}[/tex]
Step-by-step explanation:
Given
A roll of a 6 sided number cube
Solving (a): The sample space
This implies that we list out all number on the number cube.
So:
[tex]S = \{1,2,3,4,5,6\}[/tex]
Solving (b): Outcomes greater than 2
This implies that we list out all number on the number cube greater than 2 i.e. 3 to 6.
So:
[tex]Greater2 = \{3,4,5,6\}[/tex]
PLEASE HELP NOW!!!
fill in "always", "sometimes", or "never" to make a correct statement.
if you add a multiple of 4 and a multiple of 7, the sum is ____ a multiple of 7
9514 1404 393
Answer:
sometimes
Step-by-step explanation:
4 + 7 = 11 . . . not a multiple of 7
28 + 7 = 35 . . . a multiple of 7
If you add a multiple of 4 and a multiple of 7, the sum is sometimes a multiple of 7.
__
It will be a multiple of 7 when the multiple of 4 used is a multiple of 7, such as 4×7 or 4×14 or 4×21, for example.
Make a scatter plot of the data below.
Speed (mph)
Stopping distance (ft)
10
12.5
20
36.0
30
69.5
40
114.0
50
169.5
60
249.0
70
325.5
Use the quadratic regression feature of a graphing calculator to find a quadratic model. Round to the nearest hundredths place.
a.
y = 0.06 x squared + 0.31 x + 4
b.
y = negative 4.03 x squared + 0.32 x + 8.19
c.
y = 0.06 x squared minus 0.31 x minus 4
d.
y = 4.03 x squared minus 0.32 x minus 8.19
Answer:
c
Step-by-step explanation:
By using the quadratic regression feature of a graphing calculator a quadratic model would be [tex]y = 0.06 x^2 + 0.31 x + 4[/tex]
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Speed (mph) Stopping distance (ft)
10 12.5
20 36.0
30 69.5
40 114.0
50 169.5
60 249.0
70 325.5
Use the quadratic regression feature of a graphing calculator to find a quadratic model.
From the above data, we get
[tex]y = 0.06 x^2 + 0.31 x + 4[/tex]
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PLEASE HELP!!!!
use Euler's formula to find the missing number
faces: 25
verticies: 17
edges: ?
answer choice-
a. 43
b. 41
c. 39
d. 40
Answer:
d. 40
Step-by-step explanation:
The number of faces, edges and vertices is related by the following formula:
[tex]V - E + F = 2[/tex]
In which V is the number of vertices, E is the number of edges and F is the number of faces.
In this question:
[tex]F = 25, V = 17[/tex]
We want to find E. So
[tex]V - E + F = 2[/tex]
[tex]17 - E + 25 = 2[/tex]
[tex]E = 42 - 2 = 40[/tex]
The correct answer is given by option D.
Evaluate 4x3 + 4x when x = 3.
Answer:
24
Step-by-step explanation:
12 + 4(3)
24
Answer:
[tex]4 \times {3}^{3} + 4 \times 3 \\ 108 + 12 \\ = 120[/tex]
help i need answers quickly about this
Answer:
938 millibars
Step-by-step explanation:
please mark me as brainlist..
Help pls I need it someone
Answer:
search up demos graphing calculator and plug in the numbers there.
Step-by-step explanation:
its super easy to use try it :)
Mary was looking at a map with the following scale indicator:
inch 5 miles
Mary measured 2 inches between two towns on the map. What is the distance between the two townsply
You deposited $10.00 in your bank at 8% for a period of 6 years. What will be your total amount at the bank according to: a) simple interest, b) compound interest?
Answer:
Simple=$14.80 Compound=$16.14
Step-by-step explanation:
Simple=A=P(1+rt)
10.00(1+0.08×6)
Compound-A=P(1+r/n)^nt
10.00(1+0.08/6)^12*6
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08
Answer:
a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.
b) Capacity of 252.6 cubic feet per second
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).
This means that [tex]m = 100, \mu = \frac{1}{100} = 0.01[/tex]
(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)
We have that:
[tex]P(X > x) = e^{-\mu x}[/tex]
This is P(X > 190). So
[tex]P(X > 190) = e^{-0.01*190} = 0.1496[/tex]
0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.
(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?
This is x for which:
[tex]P(X > x) = 0.08[/tex]
So
[tex]e^{-0.01x} = 0.08[/tex]
[tex]\ln{e^{-0.01x}} = \ln{0.08}[/tex]
[tex]-0.01x = \ln{0.08}[/tex]
[tex]x = -\frac{\ln{0.08}}{0.01}[/tex]
[tex]x = 252.6[/tex]
Capacity of 252.6 cubic feet per second
I NEED A REAL ANSWER PLEASE!
Find a polynomial that had a leading coefficient of 4 and has the given degree and zeros.
Degree 3 with 2, 1/2, and 3/2 as zeros
[tex] ?x^{3} + {?}x^{2} + ?x + ?[/tex]
Answer:
4x^3-6x^2-6x+9
Step-by-step explanation:
I would write out the solutions as expressions and expand them:
(x-2)(x-1/2)(x-3/2)
(x^2-1/2x-2x+1)(x-3/2)
(x^2-5/2x+1)(x-3/2)
x^3-(3/2)x^2-(5/2)x+15/4+x-3/2
x^3-(3/2)x^2-(3/2)x+9/4
Next, since the leading coefficient has to be 4x^3, I could just multiply the entire expression by 4:
4x^3-(12/2)x^2-(12/2)x+36/4
4x^3-6x^2-6x+9
Hopefully, this was helpful! Comment below if you would like me to explain further!
The area of a rectangular picture frame is 93.5 square inches. The area formula for a rectangle is A=l⋅w. Write and solve an equation to find the width, w, of the picture frame.
Answer:
W=A/L
Step-by-step explanation:
If the area of the rectangle is L*W, you can just rearrange the equation A=L*W to get W=A/L, an equivalent equation.
Ryan bought a sofa on sale for $342. This price was 28% less than the original price.
What was the original price?
A CD cost a music store $5.75 to make. If the markup is 125%, what is going to be the cost of the CD in the store?
Answer:
12.94
Step-by-step explanation:
5.75x125%=7.19
7.19+5.75=12.94
You need 3/4 cup of yogurt for one smoothie. Which picture shows how many cups of yogurt you nor 3 smoothies?
Answer:
9/4 = 2 1/4
Step-by-step explanation:
According to the information shown in this word problem, you need 3/4 of a cup of yogurt for one smoothie. In order to find out how many cups of yogurt you would need for three smoothies, you would need to multiply 3/4 by three.
Like this,
3/4 x 3 = 9/4
9/4 = 2 1/4 (simplified)
What is m∠XYQ? A line segment QY intersects another line segment XZ at the point Y to form the angles XYQ and QYZ measuring (10a+2) degrees and (5a-2) degrees respectively. m∠XYQ =
Answer:
Determine the measure, in degrees, ... Score 2: The student had a complete and correct response. ... a conceptual error and did not find the measure of the smallest angle. ... y x is ΔA B C . State and label the coordinates of ΔA B C . [The use of ... Score 1: The student stated and labeled two points correctly.
Step-by-step explanation:
The data below represents the ages of the first 10 people in line at the movie theater 24 28 26 24 28 30 26 24 27 23 which line plot represents the data
Answer:
obj
Step-by-step explanation:
Helppppp
The sides of a triangle measure 7, 4, and 9. If the longest side of a similar triangle measures 36, determine and state the length of the shortest side of this triangle.
The aspect ratio (the ratio of screen width to height) of a rectangular flat-screen television is 16 : 9. The length of the diagonal of the screen is the television's screen size. Determine and state, the width of the flat-screen television if the height is 20.6 inches. Round your answer to the nearest hundredth.
Answer:
1. 16
2. 36.62 in
Step-by-step explanation:
For the first one:
If you don't want to read the explanation go to the next section in bold
We are told that the triangles are similar.
We are told that the side lengths of the smaller triangle measure 7,4 and 9
And we are told that the longest side of the similar triangle measures 36
Given this information we need to find the other side lengths.
Because the triangles are similar each side length will share similar ratios. Note that the ratios must be between the two longest side, the two medium length sides and the two shorter sides
Because we are given the longest side length of the similar triangle and the longest side length of the smaller triangle we can set up a proportion to find the other side lengths.
The proportion can be found by dividing the longest side length of the larger triangle (36) by the longest side length of the smaller triangle (9)
proportion = [tex]\frac{36}{9} or4[/tex]
So the ratio to the side lengths of the triangle is 4 to 1
Now that we have created a proportion we can find the other side lengths.
Once again this information is not needed. If you don't want to read it go to the next section in bold.
For the medium length side: [tex]\frac{4}{1} =\frac{x}{7}[/tex] ( remember x = missing side length)
multiply each side by 7
4 * 7 = 28
x/7 * 7 = x
x = 28
For the shorter side: [tex]\frac{4}{1} =\frac{x}{4}[/tex] ( once again x = missing side length )
multiply each side by 4
4 * 4 = 16
x/4 * 4 = x
x = 16
So we can conclude that the side length of the shortest side is 16
For the second one
This problem is like the other one.
The only difference is we are already given the ratio
( note that the ratio is width to height )
16 : 9
Given the proportion and the height (20.6) of the other flat screen tv we need to find the width
To do so we set up an equation using the ratio:
let x = width
[tex]\frac{16}{9} =\frac{x}{20.6}[/tex]
using cross multiplication
16 * 20.6 = 329.6
9 * x = 9x now we have 9x = 329.6
step 2 divide each side by 9
9x / 9 = x
329.6/9 = 36.62
we're left with x = 36.62
Meaning that the width of the other flat screen tv is 36.62 in
What is the area of the triangle below?
4
18
A. 72 sq. units
B. 16 sq. units
C. 36 sq. units
D. 32 sq. units
Answer:
it is a
Step-by-step explanation:
its 72 sq. units igdoug
The area of the triangle is 36 square units, option C is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We have to find the area of triangle whose base is 4 units and height is 18 units
Area of triangle = 1/2 base ×height
Plug in the values of base and height in the above formula
=1/2×4×18
Divide numerator and denominator by 2
=36 square units
Hence, the area of the triangle is 36 square units, option C is correct.
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Find the value of x and AB if ST is a segment bisector of AB.
HELO PLEASE ILL DO ANYTHING ITS DUE
Answer:
send money and i gotchu
Step-by-step explanation:
IT IS TIMED!!!!!
please help!!!!!!!
Answer:
b
Step-by-step explanation:
5/6 x 3/20 as a fraction
Answer:
1/8
Step-by-step explanation:
(5/6) × (3/20)
= (5*3) / (6*20)
= 15/120
= 3/24
= 1/8
The function p(x) = 8x – 10 shows the profit, in dollars, for selling x books.
Answer:
Every book is 8 dollars but you have to subtract 10, so like this:
Step-by-step explanation:
p(x) = 8x - 10 Lets say you sell 2 books
p(2) = 8(2) - 10
p(2) = 16 - 10
p(2) = 6 You would make 6 dollars.