Answer:
x = -4
y = 1
Step-by-step explanation:
I added a photo of my solution
A random survey of enrollment at 35 community colleges across the United States yielded the following figures:
6,414; 1,550; 2,109; 9,350; 21,828; 4,300; 5,944; 5,722; 2,825; 2,044; 5,481; 5,200; 5,853; 2,750; 10,012; 6,357; 27,000; 9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080; 11,622.
Assume the underlying population is normal.
a.
i. = __________
ii. sx = __________
iii. n = __________
iv. n – 1 = __________
b. Define the random variables X and in words.
c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United States.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
e. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?
The larger sample size also reduces the impact of individual outliers, which could potentially skew the results. Therefore, increasing the sample size will result in more reliable results, and a smaller error bound and confidence interval.
The error bound (E) for the sample size of 35 community colleges is calculated using the formula: E =[tex]1.96 * √[p*(1-p)/n].[/tex]
With n = 35, p = 0.5 (assuming the mean of the enrollment figures is 0.5), the error bound is calculated to be E = 0.823.
If the sample size is increased to 500 community colleges, the error bound would be reduced to 0.338. This is because the larger the sample size, the smaller the error bound. The confidence interval would also be reduced, since it is directly proportional to the error bound.
In practical terms, a larger sample size means more reliable results. This is because when the sample size is increased, the results tend to be more representative of the entire population, leading to more accurate conclusions.
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Find the critical t-value that corresponds to 90% confidence. Assume 16 degrees of freedom. (Round to three decimal places as needed.)
1.746 is the critical t value that corresponds to 90% confidence.
To find the critical t-value that corresponds to 90% confidence with 16 degrees of freedom, follow these steps:
1. Determine the desired confidence level: 90%
2. Calculate the corresponding significance level (alpha) by subtracting the confidence level from 100%: 100% - 90% = 10%
3. Divide the significance level by 2 to get the value for a two-tailed test: 10% / 2 = 5%
4. Look up the critical t-value in a t-distribution table using the degrees of freedom (16) and the 5% value.
From the t-distribution table, the critical t-value for 16 degrees of freedom and 90% confidence is approximately 1.746.
So, the CRITICAL T VALUE that corresponds to a 90% CONFIDENCE level with 16 DEGREES FREEDOM is 1.746, rounded to three decimal places.
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Kim's hourly wage is $14. She works 37 hours per week. What is her monthly income?
Answer:
2072
Step-by-step explanation:
Multiply 14 x 37
518 x 4
2072
Answer: $2,072 a month
Step-by-step explanation:
multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply 518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072
1. Representar en GeoGebra las funciones dadas y determinar comprobando analíticamente: a. Tipo de función b. Dominio y rango c. Asíntotas, tanto vertical y horizontal, si las tiene: [tex]f(x)=\frac{2x^{2}-4}{x^{2}-4 }[/tex]
The given functions in GeoGebra and determine by analytically checking:
a. function type is [tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]
b. Domain and range Range (-2, +2).
c. Asymptotes is HA = 2 and VA = ±2
The function y = f( x) is classified into different types of functions, grounded on factors similar as the sphere and range of a function, and the function expression. The functions have a sphere x value that's appertained as input. The sphere value can be a number, angle, numeric, bit.
[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]
Functions in mathematics can be compared to the operations of a dealing (soda pop) machine. When you put in a certain quantum of plutocrat, you can elect different types of tonics. also, for functions, we input different figures and we get new figures as the result. sphere and range are the main aspects of functions.
[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]
x² = 4
x = ± 2
Range (-2, +2).
An asymptote is a line being approached by a wind but noway touching the wind. i.e., an asymptote is a line to which the graph of a function converges. We generally don't need to draw asymptotes while graphing functions. But graphing them using dotted lines( imaginary lines) makes us take care of the wind not touching the asymptote. Hence, the asymptotes are just imaginary lines.
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Complete question:
Represent the given functions in GeoGebra and determine by analytically checking: a. function type b. Domain and range c. Asymptotes, both vertical and horizontal, if it has them:
The graphs of line a and b are shown in this coordinate grid
Match each line with it's equation. Drag each equation to the corresponding box for each line
The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).
For option 1: intersection point (1,1)
substitute the values of x & y in the given equation.
1 = 3 (1) - 2
1 = 1
LHS = RHS
For option 2: point (1,1)
substitute the values of x & y in the given equation.
1 = 2 (1) + 3
1 = 5
LHS ≠ RHS
For option 3: point (1,1)
substitute the values of x & y in the given equation.
1 = -2 (1) + 3
1 = 1
LHS = RHS
For option 4: point (1,1)
substitute the values of x & y in the given equation.
1 = - [tex]\frac{1}{2}[/tex] (1) + 3
1 = [tex]\frac{5}{2}[/tex]
LHS ≠ RHS
For option 5: point (1,1)
substitute the values of x & y in the given equation.
1 = - [tex]\frac{1}{3}[/tex] (1) + 3
1 = [tex]\frac{8}{9}[/tex]
LHS ≠ RHS
Therefore, correct option for the given graph is option 1 and option 3.
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draw a quadratic function that only has one root at 3
The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2
What is quadratic equation?A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:
ax^2 + bx + c = 0
If a quadratic function has only one root at 3, then it must be of the form:
f(x) = a(x - 3)^2
where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.
To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:
4 = a(0 - 3)^2
4 = 9a
a = 4/9
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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]
Why is it called a quadratic equation?A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.
A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:
[tex]ax^2+bx+c=0[/tex]
If the quadratic function has only one root at 3, it must have the following form:
[tex]f(x)=a(x-3)^2[/tex]
This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.
We know that f(0) = 4, so we can plug these numbers into the equation to get:
[tex]4=a(0-3)^2[/tex]
simplify the above equation
4 = 9a
The value is,
a = 4/9
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1. Compare the two box plots.
Looking at the majority, which group is taller?
Circle.
●
Boys
●
Girls
Which group has a smaller center of data? By how much?
Circle: Boys Girls
by
inches.
Which group has a larger range? Circle.
2. Compare the two dot plots.
● Are the graphs symmetrical or skewed?
Which dot plot has a larger center of data?
Which dot plot has a larger range?
Boys
Girls
Boys
+ + +
60 61
Girls
Height (inches) of Girls and Boys
.
62 63
+
64 65 66 67
+
69
68
+
70
+
71
Number of Fruit Smoothies Sold
+
72
Smoothies
Galore
50 55 60 65 70 75 80 85 90 95 100
Sunshine
Smoothies
Boys are taller than girls on average, with a larger center of data and larger range in height;
the dot plots are not shown.
kevin and micah collect seashells on the beach. the table shows the number of broken and whole seashells each person collects. if kevin collects 200 shells and micah collects 100 shells, who would be expected to have more whole seashells?
Kevin is expected to have more whole seashells, with [tex]75[/tex]% of his collection being whole seashells, compared to Micah's [tex]60[/tex]%.
What is the ratio?To determine who is expected to have more whole seashells, we need to compare the ratio of whole seashells to the total number of seashells collected for each person.
Person Whole Seashells Broken Seashells Total Seashells
Kevin 150 50 200
Micah 60 40 100
To calculate the ratio of whole seashells to total seashells, we divide the number of whole seashells by the total number of seashells, and then multiply by 100 to get a percentage:
Kevin: 150/200 [tex]\times[/tex] 100 = [tex]75[/tex]%
Micah: 60/100 [tex]\times[/tex] 100 = [tex]60[/tex]%
Therefore, Kevin is expected to have more whole seashells, with [tex]75[/tex]% of his collection being whole seashells, compared to Micah's [tex]60[/tex]%.
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The complete question is: Kevin and Micah collected seashells on the beach. The table below shows the number of broken and whole seashells each person collected. If Kevin collected 200 shells and Micah collected 100 shells, who is expected to have collected more whole seashells?
Broken Seashells Whole Seashells
Kevin 70 130
Micah 40 60
Please help with 14!! 30 points please give a correct answer
Answer:
r=8
Step-by-step explanation:
a. -3(6-r)=6
-18+3r=6
3r=6+18
3r=24
r=[tex]\frac{24}{3}[/tex]
r=8
b. 3r instead of -3r
Help please Hurry
Brenda throws a dart at this square shaped target: Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)
The probability of hitting the black circle is closer to 0 and the probability of hitting the white portion of the target is closer to 1.
What is probability?
Probability refers to the numerical measure of the likelihood or possibility of a specific event taking place. It is a mathematical concept that involves calculating the ratio of the number of desired outcomes to the total number of possible outcomes. Probability ranges from 0 (representing an impossible event) to 1 (representing a certain event), with values in between indicating the degree of likelihood. Probability is widely used in various fields, including mathematics, statistics, science, engineering, finance, and social sciences, to make predictions, analyze data, and make decisions under uncertainty.
Explanation of the given questions :
Part A: The black circle has a radius of 1 unit and its center is the same as that of the square. Therefore, its diameter is 2 units, which is much smaller than the side length of the square, which is 11 units. This means that the area of the circle is much smaller than the area of the square.
Therefore, the probability of hitting the black circle is closer to 0.
Part B: The white portion of the target is the area of the square minus the area of the black circle. The area of the square is [tex]11 x 11 = 121[/tex] square units.
The area of the circle is [tex]\pi \times r^2 = \pi\times 1^2 = \pi[/tex] square units, which is approximately 3.14 square units. Therefore, the area of the white portion of the target is [tex]121 - 3.14 = 117.86[/tex] square units.
Since this is much larger than the area of the black circle, the probability of hitting the white portion of the target is closer to 1.
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noah sold 30 avocados that were small and large. he sold the small avocados for 35 cents and the large ones for 50 cents. if noah made $13.50, how many of each kind did he sell?
Noah sold 10 small avocados and 20 large avocados.
Let's assume that Noah sold "x" small avocados and "y" large avocados.
From the given information, we can write two equations:
x + y = 30 (since Noah sold a total of 30 avocados)
0.35x + 0.50y = 13.50 (since Noah made $13.50)
Now, we can use any method to solve these equations, such as substitution or elimination. Here, we will use the substitution method:
From the first equation, we can write:
x = 30 - y
Substituting this value of x in the second equation, we get:
0.35(30 - y) + 0.50y = 13.50
Simplifying this equation, we get:
10.50 - 0.35y + 0.50y = 13.50
0.15y = 3
y = 20
Substituting this value of y in the equation x = 30 - y, we get:
x = 30 - 20 = 10
Therefore, Noah sold 10 small avocados and 20 large avocados.
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1. use the quadratic equation to find the exact solutions to this equation, and simplify your answer: 2x^2 6x 12
As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].
To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.
Substituting these values in the quadratic formula, we get
[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]
Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]
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Suppose that the next day there were sales of $7,100. What measure of center would you use to summarize the typical daily revenue of the food truck now?
Answer:
To summarize the typical daily revenue of the food truck now, we would use the new mean of the daily revenue, which takes into account the new sale of $7,100. We can add this new value to the previous sum of daily revenues and divide the total by the number of days to find the new mean:
New mean = (total sum of daily revenues + $7,100) / (number of days + 1)
This would give us the updated measure of center that reflects the new data point.
The mean daily revenue of the food truck now is $6,550.
What is average?The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.
To summarize the typical daily revenue of the food truck now, we would use the mean as the measure of the center.
We can calculate the mean daily revenue by adding the daily revenues from the two days ($6,000 + $7,100 = $13,100) and dividing by the number of days (2).
Mean daily revenue = (Total revenue) / (Number of days) = $13,100 / 2 = $6,550
Therefore, the mean daily revenue of the food truck now is $6,550.
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hills vanessa is walking up a hill. after walking 40 feet, she has climbed a total of 8 feet vertically. if she walks an additional 25 feet up the hill, how many feet will she have climbed vertically in total?
Vanessa's vertical climb rate is 0.2 feet per foot of horizontal distance. When she walks 65 feet horizontally up the hill and climbs an additional 25 feet, her total vertical climb will be 21 feet.
For every 40 feet of horizontal distance Vanessa walks, she climbs 8 feet vertically. So her vertical climb rate is 8/40 = 0.2 feet per foot of horizontal distance.
If she walks an additional 25 feet up the hill, her total horizontal distance traveled will be 40 + 25 = 65 feet.
Therefore, her total vertical climb will be 0.2 times her total horizontal distance:
8 + (0.2 * 65) = 8 + 13 = 21 feet
So, Vanessa will have climbed a total of 21 feet vertically after walking 65 feet horizontally up the hill.
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g when is welch's t-test used to compare two population means, and what distributional assumptions are needed?
In the following question, Welch's t-test is used to compare the means of two populations with unequal variances. It is a variation of the standard Student's t-test, which is used when the variances are assumed to be equal.
Welch's t-test is generally used when the sample sizes are small and the variances are significantly different.
The distributional assumptions that are needed for Welch's t-test include:
Normality - The data from each population must be normally distributed, although this assumption is not always strictly required for the test to be valid.
Equal variances - The variances of the two populations must be equal. In practice, this assumption is often difficult to satisfy, particularly when the sample sizes are small. Welch's t-test does not require the assumption of equal variances.
Independence - The samples from each population must be independent of each other. This means that the observations in one sample should not be related to the observations in the other sample.
Welch's t-test is a parametric test, which means that it is based on assumptions about the underlying distribution of the data. If the distributional assumptions are not met, then the test may not be valid. In such cases, non-parametric tests may be used instead, such as the Wilcoxon rank-sum test.
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there are 3 soccer games in a month, and 8 are played at night. the season is 4 months. how many games are the season?
There are a total of 48 soccer games in the season.
Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:
Number of day games = Total number of games - Number of night games
= 12 games/month x 4 months - 8 night games/month x 4 months
= 48 games - 32 games
= 16 games
Therefore, the total number of games in the season is:
Total number of games = Number of day games + Number of night games
= 16 games + 32 games
= 48 games
So, there are 48 soccer games in the season.
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Algebraic Inequalities
Help pls need assistance
DUE today in
Answer:
8, 8.001, 8.01, 8.1, 9, 11, 13, 16
Step-by-step explanation:
From the instructions given, we know that variable u [tex]\geq[/tex] 8. the [tex]\geq[/tex] sign means that the number is greater than or is equal to the number, which is in this case, 8. In the numbers given, (0, 7, 7.999, 8.01, 11, 3, 7.9, 8, 8.1, 13, 5, 7.99, 8.001, 9, 16) we name the numbers greater than or equal to 8 that are stated in the list.
suppose the data on natural birth weights (collected by the world health organization (who)) is normally distributed with the mean equal to 7.25 pound for a full-term birth and standard deviation of 1.0 pounds. what is the probability that a randomly selected baby will weigh more than 9.75 pounds at birth? 0.0062
The probability that a randomly selected baby will weigh more than 9.75 pounds at birth is 0.0062, or about 0.62%. This means that the vast majority of babies will weigh less than 9.75 pounds at birth, as this value is more than two standard deviations above the mean.
We can use the standard normal distribution to solve this problem by first standardizing the value of 9.75 pounds using the formula:
z = (x - mu) / sigma
where x is the value of 9.75 pounds, mu is the mean of 7.25 pounds, and sigma is the standard deviation of 1.0 pound.
Substituting the values, we get:
z = (9.75 - 7.25) / 1.0 = 2.5
We can then use a standard normal distribution table or calculator to find the probability of a z-score greater than 2.5. From the table or calculator, we find that this probability is approximately 0.0062.
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Helen flips a coin and rolls a dice calculate the probability of getting 4 and tails
Answer:
1/12 or 0.0833
Step-by-step explanation:
P(Coin) = 1/2
P(Dice) = 1/6
1/2 × 1/6 = 1/12
Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content
The expression represents the constraint that the amount of fat in the cookie should not deviate from the target fat content by more than 1.8 grams per cookie is |f - 5| ≤ 1.8
To express the difference between the fat in a cookie from the new recipe and the target fat content, we can use an expression. Let's represent the amount of fat in a cookie from the new recipe as f. Then, the difference between the fat in the cookie and the target fat content of 5 grams per cookie can be expressed as:
|f - 5|
The vertical bars around the expression indicate the absolute value, which means that we want the difference to be positive, regardless of whether f is greater or less than 5.
Now, we also know that the company will accept a difference of up to 1.8 grams per cookie. This means that the expression above should be less than or equal to 1.8:
|f - 5| ≤ 1.8
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Complete Question:
The Billing sly Cookie Company is experimenting with a new low-fat cookie recipe. The management wants the bakers to come up with a cookie that is low in fat but still has good taste. The company decides on a target fat content of 5 grams per cookie. In order to be labeled low-fat, a difference of 1.8 grams per cookie is acceptable. This means the amount of fat should be no more than 1.8 grams above 5 or no more than 1.8 grams below 5.
Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content. Use f to represent the amount of fat in a cookie from the new recipe.
what is the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud?
There is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
To find the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud, we need to use the formula for the margin of error:
[tex]$$E = z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$[/tex]
where E is the margin of error, [tex]$z_{\alpha/2}$[/tex] is the critical value for the desired confidence level (let's assume 95%, so [tex]$z_{\alpha/2} = 1.96$[/tex]), p is the population proportion of websites experiencing click fraud, and n is the sample size.
We know that p=0.15, so we can plug in the values:
[tex]$$E = 1.96\sqrt{\frac{0.15(1-0.15)}{400}} = 0.05$$[/tex]
So the margin of error is 0.05. This means that there is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
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For what real numbers x is the value of x2
– 6x + 9 negative?
Answer:
Step-by-step explanation:
EZ
its 21
Geometry, and Slope. Worth 15 Points
Please Explain
The equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].
Given,
x+2y=2
y = 1 - [tex]\frac{x}{2}[/tex]
Slope = -1/2 = [tex]m_{1}[/tex]
Let Slope of line perpendicular to line x+2y=2 is [tex]m_{2}[/tex]
⇒ [tex]m_{1}[/tex] * [tex]m_{2}[/tex] = -1
Then [tex]m_{2}[/tex] = 1/2
Equation of line perpendicular is given by
[tex]y = \frac{1}{2}x + c[/tex]
Since it contains point (5,6)
6 = [tex]\frac{1}{2} (5) + c[/tex]
c= [tex]\frac{7}{2}[/tex]
Then the equation of line is:
[tex]y = \frac{1}{2}x+ \frac{7}{2}[/tex].
Therefore, the equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].
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I ask you, to solve the system.
y=x2+2x-2
y=x+10
Answer:
y = 22 - x2 or x = 12 - x2
Step-by-step explanation:
which formula would you use to calculate the total enclosed space of firms 2’s structure?
Answer:
Firm 2's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,
Volume = πr²h
where r = radius of the structure
h = height of the Firm
By substituting the values of 'r' and 'h' in the given formula,
V =
�
(
70
2
)
2
(
60
)
π(
2
70
)
2
(60)
=
�
(
35
)
×
60
π(35)×60
= 6597.345
≈ 6597.35 cubic feet
Total enclosed space of Firm 2 is 6597.35 cubic feet.
Find the value of x.
The value of x is 5
What is a chord?A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. All diameters are chord and but all chords are not diameter.
Since the value of the chords are thesame, the arc length RS and PQ are thesame.
Therefore ;
x+17 = 4x+2
collect like terms
4x -x = 17-2
3x = 15
divide both sides by 3
x = 15/3
x = 5
therefore the value of x is 5
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What 25% of 140? Question 8 options: 25 35 45 50
Answer:
35
Step-by-step explanation:
Change the percent to decimal form and of means multiply.
25% of 140
.25 * 140
35
Answer:
35
Step-by-step explanation:
g calculate the labor force participation rate if you know that the adult working-age population is 320 million, 114 million of which are not in the labor force. what is the labor force participation rate? (round your answer to the nearest tenth.)
The labor force participation rate is 64.4%.
To calculate the labor force participation rate, we need to know the number of people who are either employed or actively seeking employment. We can calculate this as follows:
Labor force = adult working-age population - not in labor force
Labor force = 320 million - 114 million
Subtract the numbers
Labor force = 206 million
So the labor force participation rate is
Labor force participation rate = (labor force / adult working-age population) x 100%
Substitute the values in the equation
Labor force participation rate = (206 million / 320 million) x 100%
Labor force participation rate = 64.4%
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5x+2y=10
Find the Y intercept and gradient
solve for a "7a = 14"
Answer: a=2
7a=14
a=14/7
a=2