Answer:
A. x<-5
Step-by-step explanation:
-0.4x - 1.2 > 0.8
-0.4x > 2
x < -5
So, the answer is A. x<-5
the following correlation matrix shows the pearson correlations between various baseball pitching related statistics, of which the number of wins (w) is considered to be a criterion measure of pitching performance by a team. which statistic has an inverse relationship with the number of wins?
To decide which measurement has a reverse relationship with the number of wins, we ought to seek for a relationship coefficient with negative esteem. A negative correlation coefficient shows that as one variable increments, the other variable tends to diminish.
Without seeing the real relationship framework, we cannot point out the precise statistic that has a reverse relationship with the number of wins. In any case, ready to search for the relationship coefficient that features negative esteem.
For illustration, in the event that we have a relationship network like this:
markdown
| W | Period | WHIP | SO/9 | BB/9 |
----------------------------------------------
W | 1 | -0.7 | -0.6 | 0.5 | -0.3 |
----------------------------------------------
Period | -0.7| 1 | 0.9 | -0.8 | 0.5 |
----------------------------------------------
WHIP | -0.6| 0.9 | 1 | -0.7 | 0.4 |
----------------------------------------------
SO/9 | 0.5| -0.8 | -0.7 | 1 | -0.4 |
----------------------------------------------
BB/9 | -0.3| 0.5 | 0.4 | -0.4 | 1 |
----------------------------------------------
We are able to see that the relationship coefficient between the number of wins (W) and the earned run normal (Time) is -0.7, which indicates a strong negative relationship. This implies that as the Time increments (showing poorer pitching execution), the number of wins tends to diminish. Subsequently, Time has a reverse relationship with the number of wins.
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On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. What is the probability that the appliance will work at least six years without requiring repairs?
The probability that the appliance will work at least six years without requiring repairs is 0.2231 or 22.31%.
To find the probability that the appliance will work at least six years without requiring repairs, we need to consider the exponential distribution and the given average repair time. Given that the appliance requires repairs once every four years on average, the rate parameter (λ) for the exponential distribution is 1/4, or 0.25.
Here we want to find the probability that the appliance will work at least six years without requiring repairs, which can be represented as [tex]P(X ≥ 6)[/tex], where X is the time between repairs. Using the complementary probability, we can rewrite this as [tex]P(X ≥ 6) = 1 - P(X < 6)[/tex]
The cumulative distribution function (CDF) of the exponential distribution is given by
[tex]F(x) = 1 - e^{(-λx)}[/tex]
Now, we can plug in the values:
[tex]P(X ≥ 6) = 1 - F(6) \\ P(X ≥ 6) = 1 - (1 - e^{(-0.25 \times 6)}) \\ P(X ≥ 6) = 1 - (1 - e^{(-1.5)}) \\ P(X ≥ 6) = e^{(-1.5)}[/tex]
Therefore, the probability that the appliance will work at least six years without requiring repairs is approximately 0.2231 or 22.31%.
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You start driving west for 3 miles, turn right, and drive north for another 11 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
FIND Z OF THIS CIRCLE
Answer:
Step-by-step explanation:
riends' scores on a science
er of minutes they spent
s weekend. How can Paul
f his data?
raph is most appropriate for displa
itter
lations
in the table as ordered pairs.
ered pairs. Include a title and
's Chores
1
Time
2 3 4
5 27
Minute
Test S
"aph is most appropriate for dis
table? Explain.
5
4
bet
Answer:
Step-by-step explanation:
One way for Paul to display his data is by using a scatter plot. A scatter plot is a graph that uses ordered pairs to represent data points. In this case, each data point would represent a friend's score and the number of minutes they spent studying science over the weekend.
To create a scatter plot, Paul would plot each data point as an ordered pair on a coordinate plane. The x-coordinate would represent the number of minutes spent studying, and the y-coordinate would represent the friend's score on the science test. Paul could then use a title and labels for the x and y axes to make the graph clear and informative.
A scatter plot is a good choice for this data because it allows Paul to easily see any relationship between the amount of time spent studying and the scores on the science test. He can also use the graph to identify any outliers or patterns in the data.
Question 1 (1 point)
Given parallelogram WXYZ, where WX = 2x + 15, XY = x + 27 and YZ = 4x - 21,
determine the length of ZW, in inches.
The length of ZW=
The length of ZW is 45 inches.
What is a parallelogram?A parallelogram is a member of quadrilateral which has a pair of opposite sides to be equal, and a pair of slant opposite sides.
In the given information, we have;
WX = YZ (a pair of opposite side of a parallelogram are equal)
2x + 15 = 4x - 21
collect like terms,
21 + 15 = 4x - 2x
36 = 2x
x = 36/2
x = 18
So that;
WX = 2x + 15
= 2(18) + 15
WX = 36 + 15
= 51
XY = x + 27
= 18 + 27
= 45
Therefore,
ZW = XY (a pair of opposite sides are equal)
ZW = 45
The length of ZW is 45 inches.
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a student has 12 toys. her friend has 2 times as many toys. how many toys do they have together
Answer:
Together, they have 12 + 2(12) = 12 + 24 = 36 toys.
Answer:
so in total they have 36 toys
Step-by-step explanation:
What is an equation of the line that passes through the point ( − 2 , − 2 ) and is parallel to the line 5x − y = 4 ?
Answer:
(-2,-2)
Step-by-step explanation:
To find the equation of the line that passes through the point (-2,-2) and is parallel to the line 5x - y = 4, we need to first find the slope of the given line. We can rearrange the given equation into slope-intercept form y=5x-4, where the slope is 5.
Since parallel lines have the same slope, the slope of the line we want to find is also 5. We can use the point-slope formula y-y1 = m(x-x1), where m is the slope and (x1,y1) is the given point.
Substituting m=5, x1=-2, and y1=-2, we get:
y-(-2) = 5(x-(-2))
y+2 = 5x+10
y = 5x+8
Therefore, the equation of the line that passes through the point (-2,-2) and is parallel to the
Jodi has $4,862.33 in a savings account that will earn 2.99% interest on the principal for
5 years. What is the amount of simple interest that she will earn?
Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at negative 5 comma 3, negative 5 comma 6, negative 9 comma 6, negative 9 comma 3, negative 7 comma 1.
Determine the line of reflection.
Reflection across x = −4
Reflection across y = 1
Reflection across the x-axis
Reflection across the y-axis
The line of reflection is reflection across x = −4
Explain the term line
A line is an infinitely long and infinitely thin one-dimensional object that extends in opposite directions. It has no endpoints and is often represented by a straight line with two arrowheads. Lines are a fundamental concept in mathematics and are used to define other objects such as planes, angles, and shapes.
According to the given information
Let's use points A(-3, 3) and A'(-5, 3). The midpoint of the line segment connecting A and A' is ((-3 + (-5))/2, (3 + 3)/2) = (-4, 3). The slope of the line segment connecting A and A' is (3 - 3)/(-5 - (-3)) = 0. Since the line of reflection is perpendicular to this line segment, its slope is the negative reciprocal of 0, which is undefined. This means that the line of reflection is a vertical line.
Since the midpoint of the line segment connecting A and A' lies on the line of reflection and has an x-coordinate of -4, we can conclude that the line of reflection is x = -4.
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Julio is planting a tree. He needs to dig a hole that is 2 feet deep. He has already dug a hole that is 1 ¼ feet deep. How many more inches does Julio need to dig to make sure the hole is deep enough?
Answer:
9 inches
Step-by-step explanation:
A foot is 12 inches long. To find a fourth of a foot, divide 12 by four to get 3. This means that Julio has already dug a hole one foot and three inches deep. To make his hole two feet deep, he will need to dig the other 3/4 of the foot. To find 3/4 of a foot, take 1/4 of a foot (3 inches) and multiply by 3 (9 inches).
Julio will have to dig 9 more inches.
Can someone please help me ASAP? It’s due tomorrow!! I will give brainliest if it’s all correct
Please do part a, b, and c
The mean and range of the same population can differ if there is a significant difference between the sampled respondents.
Between Jayden and Carter, Carter's calculation will provide a better understanding of the population.
The reason is that he sampled more people with a wider time range.
Why the mean and range differThe mean is the average number of minutes it took for the respondents to dress up. The goal of any survey work is to capture a significant size of the population whose opinions can give a true picture of the situation being examined.
In the case of Carter, we see that he took a more sizable amount of the population having randomly selected 7 samples of 10 students. A greater number of respondents will give a truer picture of the factor being surveyed.
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Identify the area of the figure. PLEASE RESPOND ASAP TYSM!!!
Answer:
184 cm to the 3
Step-by-step explanation:
13x7 91+90+181 and add 3
how to find the slope of a normal line based on the equation of a tangent line
By following these steps, we can easily find the slope of a normal line based on the equation of a tangent line.
To find the slope of a normal line based on the equation of a tangent line.
Identify the slope of the tangent line:
Look at the equation of the tangent line, which will usually be in the form y = mx + b, where m is the slope of the tangent line and b is the y-intercept.
Extract the value of m from the equation.
Calculate the negative reciprocal:
To find the slope of the normal line, we'll need to calculate the negative reciprocal of the tangent line's slope.
The negative reciprocal of a number is found by flipping the fraction and changing the sign (from positive to negative, or from negative to positive).
For example, if the slope of the tangent line (m) is 3, the negative reciprocal will be -1/3.
If the slope of the tangent line is -2/3, the negative reciprocal will be 3/2.
The slope of the normal line:
The negative reciprocal calculated in step 2 is the slope of the normal line.
This slope will be perpendicular to the tangent line, meaning that the angle between the normal and tangent lines is 90 degrees.
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Which statement is true?
From Lesson 9.06 Probability & Two-Way Tables
The two-way table shows the ages of the players on different soccer teams.
A 6-column table has 4 rows. The first column has entries 8 years old, 9 years old, 10 years old, Total. The second column is labeled Team A with entries 4, 9, 2, 15. The third column is labeled Team B with entries 6, 4, 3, 13. The fourth column is labeled Team C with entries 8, 3, 5, 16. The fifth column is labeled Team D with entries 3, 7, 4, 14. The sixth column is labeled Total with entries 21, 23, 14, 58.
Which statement is true?
The probability that a randomly selected player on Team C is 10 years old is StartFraction 5 Over 16 EndFraction.
The probability that a randomly selected player on Team A is 8 years old is StartFraction 4 Over 21 EndFraction.
The probability that a randomly selected 8-year-old player is on Team C is StartFraction 16 Over 21 EndFraction.
The probability that a randomly selected 10-year-old player is on Team B is StartFraction 13 Over 58 EndFraction.
The statement that is true is:
The probability that a randomly selected player on Team C is 10 years old is 5/16.
Option A is the correct answer.
We have,
The probability that a randomly selected player on Team C is 10 years old.
= Number of 10 years old players in Team C / Total players in Team C
= 5./16
The probability that a randomly selected player on Team A is 8 years old.
= Number of 8 years old players in Team A / Total players in Team A
= 4/15
The probability that a randomly selected 8-year-old player is on Team C.
= Number of 8 years old players in Team C / Total 8 years old players
= 8/21
The probability that a randomly selected 10-year-old player is on Team B.
= Number of 10 years old players in Team C / Total 10 years old players
= 5/14
Thus,
The probability that a randomly selected player on Team C is 10 years old is 5/16.
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Can someone help with this question????
Answer:
besides this pic nothing else can be done
In 2011, the total number of cars produced in the world was 59.9 million.
In 2016, the total number of cars produced in the world was 21% greater than the total
number produced in 2011
In 2016, the total number of cars produced in the world was N million.
(b) Work out the value of N.
Give your answer correct to the nearest whole number.
In 2016, the total number of cars produced in the world was 72 million (rounded to the nearest whole number) by forming linear equation.
In 2011, the total number of cars produced in the world was 59.9 million.
In 2016, the total number of cars produced in the world was 21% greater than the total number produced in 2011.
Let us say in 2016 the total number of cars produced in the world was N million.
Therefore, by expressing the given problem in a linear equation we get,
Total number produced in 2016, N = 59.9 + (21% of 59.9 ) in millions
⇒ N = 59.9 + [tex][ \frac{21}{100} ] 59.9[/tex] ( in millions )
= 59.9 + 12.579 ( in millions )
= 72.479 ( in millions )
= 72 millions ( rounded to the nearest whole number)
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Question 19
By age 65 the number of Americans who experience hearing loss sufficient to affect communication is:
a. 1 in 2
b. 1 in 3
c. 1 in 4
d. 1 in 5
The number of Americans experience hearing loss sufficient to affect communication is: 1 in 4.
According to the National Institute on Deafness and Other Communication Disorders (NIDCD).
Approximately 1 in 4 adults in the United States aged 65 and older have hearing loss that is sufficient to affect communication.
This is based on data from a survey conducted by the NIDCD and the National Health Interview Survey.
NIDCD (National Institute on Deafness and Other Communication Disorders).
In the United States, 1 in 4 persons 65 and older suffer hearing loss severe enough to impair conversation.
This is based on information from surveys done by the National Health Interview Survey and the NIDCD.
The number of Americans who experience hearing loss sufficient to affect communication is: 1 in 4.
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Which model is appropriate for the set {(-2,4. 5),(0,8),(1,10. 67),(3,18. 96)}
We can conclude that a quadratic model is appropriate for the given set of points {(-2,4. 5),(0,8),(1,10. 67),(3,18. 96)}.
To determine which model is appropriate for the given set of points {(-2,4.5),(0,8),(1,10.67),(3,18.96)}, we need to examine the pattern in the data and choose a model that fits the pattern well.
One common approach to fitting a model to data is to use regression analysis. In this case, we can start by plotting the points on a graph and visually examining the pattern.
When we plot the points, we see that they form a curved shape that resembles a quadratic function. To confirm this, we can use regression analysis to fit a quadratic model to the data.
Using a quadratic regression model, we obtain an equation of the form y = ax^2 + bx + c, where a, b, and c are constants to be determined. The regression analysis yields the following coefficients: a = 2.138, b = 1.959, and c = 5.48.
We can now use this quadratic equation to predict y for any given value of x within the range of the data.
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it takes about 700,000 cubic feet of helium to fill a giant parade balloon. Each year, a total of 6.2 billion cubic feet of helium is used by industries around the globe. How many giant parade balloons would that fill?
Answer:
To find out how many giant parade balloons could be filled with 6.2 billion cubic feet of helium, we can divide the total volume of helium by the volume of one balloon:
Number of balloons = Total volume of helium / Volume of one balloon
First, we need to convert 6.2 billion cubic feet to cubic feet:
6.2 billion = 6,200,000,000
Now we can calculate the number of balloons:
Number of balloons = 6,200,000,000 / 700,000
Number of balloons = 8,857.14
So, approximately 8,857 giant parade balloons could be filled with 6.2 billion cubic feet of helium.
How many milliliters is 0.005 L?A) 0.5 mL B) 5 mL C) 0.50 mL D) 0.000005 mL E) 200 mLAns: B Category: Medium Section: 1.9
After conversion, B) 5 mL is 0.005 L milliliters
The quantity given = 0.005 L
Using a unit conversion, the same property is stated in a different unit of measurement. Minutes can be used to measure time instead of hours, and feet, kilometres, or any other measurement method can be used to measure distance in place of miles.
To convert from litres to millilitres, it is required to multiply the quantity by 1000. This is because there are 1000 millilitres in one litre.
Therefore, converting the given value-
= 0.005 L x 1000 mL/L
= 5
Thus, the resultant value after conversion is 5mL
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with a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because
With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
With a simple random sample, each participant is selected at random from the population, ensuring that everyone has an equal chance of being selected.
This eliminates any potential bias or manipulation, as no one can control or influence the selection process. Additionally, the sample size can be increased to amplify the accuracy and representativeness of the data collected. Therefore, a simple random sample is a reliable method for gathering unbiased data.
With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
This means that each individual or element in the population has an equal chance of being chosen, ensuring unbiased and representative sample results.
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With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
With a simple random sample, each participant is selected at random from the population, ensuring that everyone has an equal chance of being selected.
This eliminates any potential bias or manipulation, as no one can control or influence the selection process. Additionally, the sample size can be increased to amplify the accuracy and representativeness of the data collected. Therefore, a simple random sample is a reliable method for gathering unbiased data.
With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
This means that each individual or element in the population has an equal chance of being chosen, ensuring unbiased and representative sample results.
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Divide.
389.5÷1000
pls answer correctly
0.3895 Answer
Step-by-step explanation:
I thought you meant it on paper.
Answer:
0.3895
Step-by-step explanation:
Write out the division problem: 389.5 ÷ 1000.
Since we're dividing a decimal number by 1000, we can simply move the decimal point three places to the left to convert 1000 to 1.000: 389.5 ÷ 1.000.
Moving the decimal point three places to the left also means we need to add three trailing zeroes to the dividend: 389.5 becomes 389.500.
Now we can perform the long division: divide 3 by 1, write the quotient 3 above the 8, and subtract 3 from 8 to get 5 as the new remainder. Bring down the next digit 8 to get 58.
Divide 58 by 1, write the quotient 58 above the 9, and subtract 58 from 89 to get 31 as the new remainder. Bring down the next digit 5 to get 315.
Divide 315 by 1, write the quotient 315 above the decimal point, and subtract 315 from 389 to get 74 as the new remainder.
Since there are no more digits to bring down, we've reached the end of the long division. The final quotient is 0.3895.
Don't forget to include the decimal point in the answer, since we moved it three places to the left in step 2. The final answer is 0.3895.
So, 389.5 ÷ 1000 = 0.3895.
NEED HELP WITH THESE TWO PLEASE
The values of x and y using trigonometric ratios are: 12) x = 8, y = 4√3 and 14) y = 11√2, x = 11√2
How to use Trigonometric Ratios?Some of the common trigonometric ratios are:
sin x = opposite/hypotenusecos x = adjacent/hypotenusetan x = adjacent/hypotenuseUsing the above as a guide, we have the following:
12) Let us solve for x and y using trigonometric ratios to get:
4/x = sin 30
4/0.5 = x
x = 8
Similarly:
4/y = tan 30
y = 4/tan 30
y = 4√3
Using the above as a guide, we have the following:
14) Let us solve for x and y using trigonometric ratios to get:
y/22 = sin 45
y = 11√2
Similarly:
x/22 = cos 45
x = 11√2
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The values of x and y using trigonometric ratios are:
12) x = 8, y = 4√3
14) x = 11√2, y = 11√2
How to use Trigonometric Ratios?The three most common trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = adjacent/hypotenuse
12) We can find x and y using trigonometric ratios as follows:
4/x = sin 30
x = 4/sin 30
x =4/0.5
x = 8
We can solve for y as:
4/y = tan 30
y = 4/tan 30
y = 4(1/√3)
y = 4√3
14) We can find x and y using trigonometric ratios as follows:
y/22 = sin 45
y = 22 * 1/√2
Rationalizing the denominator gives:
y = 11√2
We can find x as:
x/22 = cos 45
x = 22 * 1/√2
Rationalizing the denominator gives:
x = 11√2
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GEOMETRY HELP SHOW STEPS PLEASE. HOW TO FIND AREA OF A REGULAR PENTAGON WITH SIDES OF 2
The area of the regular pentagon is 6.88 unit².
How to find the area of a regular pentagon?The area of a regular pentagon can be found if one side is known. The formula used for finding the area of a regular pentagon is:
A = 1/4 * [√5(5+ 2√5)] * s²
where s is the length of one side of the regular pentagon.
In this case, s = 2:
A = 1/4 * [√5(5+ 2√5)] * s²
A = 1/4 * [√5(5+ 2√5)] * 2²
A = 1/4 * [√5(5+ 2√5)] * 4
A = 6.88 unit²
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imagine that you are offered two jobs. there is a 50% chance that you will take the first job and a 40% chance that you will take the second job. assume that you cannot take both jobs. what is the probability that you will take either one job or the other job?
Answer:
The probability of taking either one job or the other job can be calculated by adding the probabilities of taking the first job and taking the second job, and then subtracting the probability of taking both jobs (since we cannot take both).
Let A be the event of taking the first job, and B be the event of taking the second job. Then, the probability of taking the first job is P(A) = 0.5, and the probability of taking the second job is P(B) = 0.4. The probability of taking both jobs is zero, since we cannot take both.
Therefore, the probability of taking either one job or the other job is:
P(A or B) = P(A) + P(B) - P(A and B)
= 0.5 + 0.4 - 0
= 0.9
So the probability of taking either one job or the other job is 0.9 or 90%
i need help will give brainliest am failing class its due tomorrow
The length of the second shelf is 98 centimeters.
Let's denote the length of the first shelf as x centimeters. According to the problem, we have the following equations for the lengths of the other shelves:
Second shelf: 2x + 18 cm
Third shelf: x - 12 cm
Fourth shelf: x + 4 cm
Robert must use the entire 2.5-meter board for the shelves, so the sum of the lengths of the four shelves should be equal to 2.5 meters, or 250 centimeters. Thus, we can write an equation:
x + (2x + 18) + (x - 12) + (x + 4) = 250
Simplify the equation:
x + 2x + 18 + x - 12 + x + 4 = 250
Combine like terms:
6x + 10 = 250
Subtract 10 from both sides:
6x = 240
Now, divide by 6:
x = 40
Now that we have the length of the first shelf (x = 40 cm), we can find the length of the second shelf:
Second shelf = 2x + 18 = 2(40) + 18 = 80 + 18 = 98 cm
So, the length of the second shelf is 98 centimeters.
Answer:
114 cm
Step-by-step explanation:
Let's start by finding the shortest shelf.
The second shelf is 18 centimeters longer than twice the length of the first shelf. The first shelf is smaller than the second shelf.
The third shelf is 12 centimeters shorter than the first shelf. The third shelf is shorter than the first shelf, so, the third shelf is the shortest shelf.
Let's call the length of the third shelf s.
We know that the third shelf is 12 centimeters shorter than the first shelf. In other words, s is 12 centimeters shorter than the first shelf. So, we can write the length of the first shelf as:
[tex]s+12[/tex]
We also know that the second shelf is 18 cm longer than twice the length of the first shelf.
Start by multiplying the length of the first shelf by 2.
[tex]2(s+12)=2s+24[/tex]
Now, let's add 18.
[tex]2s+24+18=2s+42[/tex]
So, the length of the second shelf is 2s+42.
The remaining shelf is 4 centimeters longer than the first shelf. Remember that the first shelf is s+12. Let's add 4.
[tex]s+12+4=s+16[/tex]
So, the first shelf is s+12, the second shelf is 2s+42, the third shelf is s, and the remaining shelf is s+16.
When you add them all together, you will get the 2.5 meter board.
2.5 meters is equal to 250 cm.
So, the first shelf plus the second shelf plus the third shelf plus the remaining shelf is equal to the entire board, or 250 cm.
Let's rewrite that in terms of s:
[tex](s+12)+(2s+42)+s+(s+16)=250=\\5s+70=250=\\5s=180=\\s=36[/tex]
We now know that s=36 cm.
The problem asks how long the second shelf is. Recall that the second shelf is 2s+42.
Let's plug in 36 to this expression:
[tex]2s+42=\\2(36)+42=\\72+42=\\114[/tex]
So, the second shelf is equal to 114 cm.
A cylinder has a height of 20 millimeters and a radius of 6 millimeters. What is its volume?
Use 3.14 and round your answer to the nearest hundredth.
Answer:
V = hpi(r)^2
= 20(3.14)(17)^2 = 18,149.20 cubic mm
More accurately,
V = 20(3.14159)(17)^2 = 18158.39 mm^3
Step-by-step explanation:
The ratio of red counters to green counters in a bag is 3:17. What percentage of the counters are red
Answer:
0.15%
Step-by-step explanation:
red is 3
the total is 20
percentage of red counters = 3 ÷ 20 = 0.15%
a study is to be made to estimate the percent- age of citizens in a town who favor having their water fluoridated. how large a sample is needed if one wishes to be at least 95% confident that the estimate is within 1% of the true percentage?
A sample size of approximately 9604 citizens is needed to achieve at least 95% confidence that the estimate is within 1% of the true percentage.
To determine the sample size needed for a study to estimate the percentage of citizens in a town who favor water fluoridation with 95% confidence and a margin of error within 1%, you can use the following formula:
Sample Size (n) = ([tex]z^{2}[/tex] * P * (1-P)) / [tex]E^{2}[/tex]
where:
Z = 1.96 (the Z-score corresponding to a 95% confidence level)
P = estimated proportion of the population (use 0.5 if no prior knowledge)
E = margin of error (0.01 for 1%)
Plugging the values into the formula:
n = ([tex]1.96^{2}[/tex] * 0.5 * (1-0.5)) / [tex]0.01^{2}[/tex]
n = (3.8416 * 0.5 * 0.5) / 0.0001
n = 0.9604 / 0.0001
n ≈ 9604
Therefore, a sample size of approximately 9604 citizens is needed to achieve at least 95% confidence that the estimate is within 1% of the true percentage.
Know more about sample size here:
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