For the sample size of 20, the 95% confidence interval is (-4.87, 27.16), which is narrower than the previous interval due to the larger sample size.
What is mean?In statistics, mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total number of values in the set. Mean is also commonly referred to as the arithmetic mean. It is a commonly used statistical measure in many fields including finance, economics, social sciences, and more.
Here,
To calculate the z-scores associated with each student, we first need to calculate the sample mean and standard deviation for the Distance to Work variable:
Sample mean: (0+0+5+10+15+30+32)/7 = 10.71
Sample standard deviation: √(((0-10.71)² + (0-10.71)² + (5-10.71)² + (10-10.71)² + (15-10.71)² + (30-10.71)² + (32-10.71)²)/6) = 10.72
Now we can calculate the z-scores for each student:
Student 1: (0 - 10.71) / 10.72 = -0.94
Student 2: (0 - 10.71) / 10.72 = -0.94
Student 3: (5 - 10.71) / 10.72 = -0.53
Student 4: (10 - 10.71) / 10.72 = -0.07
Student 5: (15 - 10.71) / 10.72 = 0.40
Student 6: (30 - 10.71) / 10.72 = 1.80
Student 7: (32 - 10.71) / 10.72 = 1.98
Student 8: (8 - 10.71) / 10.72 = -0.25
Student 9: (36 - 10.71) / 10.72 = 2.37
Student 10: (9 - 10.71) / 10.72 = -0.16
Student 11: (22 - 10.71) / 10.72 = 1.05
Student 12: (10 - 10.71) / 10.72 = -0.07
Student 13: (15 - 10.71) / 10.72 = 0.40
Student 14: (28 - 10.71) / 10.72 = 1.54
Student 15: (12 - 10.71) / 10.72 = 0.12
Student 16: (6 - 10.71) / 10.72 = -0.44
Student 17: (0 - 10.71) / 10.72 = -0.94
Student 18: (10 - 10.71) / 10.72 = -0.07
Student 19: (30 - 10.71) / 10.72 = 1.80
Student 20: (0 - 10.71) / 10.72 = -0.94
To identify potential outliers, we can look for z-scores that are more than 2 standard deviations away from the mean (i.e., greater than 2 or less than -2). From the list above, we can see that Students 6, 7, 9, and 19 have z-scores greater than 2, indicating that they may be potential outliers.
For the second sample of seven data points (0, 0, 5, 10, 15, 30, 32), the mean is 11.14 and the standard deviation is 12.05. Using a t-distribution with 6 degrees of freedom (n-1), the 95% confidence interval is (-7.54, 29.82).
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Let f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6. Identify the solution(s) of
f(x) = g(x).
The solutions of the function as required to be determined is; x = 8 or x = -4.
What is the solution of the equation?As evident in the task content; the given equation are;
f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6.
The solution of the equation can be determined as follows;
9x² - 5x - 58 = 7x² + 3x + 6.
2x² -8x - 64 = 0
x² - 4x - 32 = 0
(x - 8) (x + 4) = 0
x = 8 Or x = -4.
Ultimately, the solutions of the equation are; x = 8 or x = -4.
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Please help!
What is the principal square root? And why is it used when solving radical
polynomials?
Answer:
The principal square root of a non-negative real number is the positive square root. For example, the principal square root of 25 is 5, since 5^2 = 25.
When solving radical polynomials, the principal square root is used because it is the most commonly used square root. In many contexts, including mathematical and scientific calculations, the principal square root is the default choice unless otherwise specified. Additionally, when working with radical expressions, we often simplify expressions by taking the principal square root, as it can help us to simplify calculations and express answers more clearly.
PLEASE ANSWER BEFORE 11:59 TONIGHT
1. A factory needs two raw materials. The probability of not having an adequate supply of material A is 0.05, whereas the probability of not having an adequate supply of material B is 0.03. A study determines that the probability of a shortage in both A and B is 0.01. a. Let E be the event "shortage of A" and F be the event "shortage of B". Construct a Venn diagram representing events E and F.
The Venn diagram needed based on the question is given below:
The Venn Diagram__________
/ \
/ A \
/____________\
\ /
\ E ∩ F /
\_________/
B
In the diagram, the set A represents the event of having an adequate supply of material A, and the set B represents the event of having an adequate supply of material B.
The overlap of A and B represents the event of having an adequate supply of both materials.
The set E represents the event of a shortage in material A, and the set F represents the event of a shortage in material B.
The intersection of E and F, denoted by E ∩ F, represents the event of a shortage in both materials.
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Which answer shows shows the equation below written in different forms 9-3=6
The equatiοn 9 -3 = 6 can be written in different fοrms, but the correct one is 9 = 3 + 6.
Are expressiοns cοnsidered equatiοns?Every cοmbinatiοn οf a number, a variables, and οperatiοn symbοls is cοnsidered an expressiοn. An equatiοn is created by cοmbining twο expressiοns and jοining them with the equal sign.
Cοnditiοns οn the parameters are fοund in simple equatiοns. It is clear frοm an equatiοn that the answer οn the left and right are equivalent. The expressiοn tο the left οf the symbοl "=" is the LHS, while the expressiοn tο the right is the RHS. With the fοrm y = "sοme expressiοn invοlving x," a sοlutiοn invοlving x and y can be expressed, such as y = f. ( x). This final statement, which may be interpreted as "y equals f οf x," denοtes that y is a cοefficient οf x.
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Complete question:
Which answer shows the equation 9-3=6 below written in different forms?
6 + 3 = 9, 9 = 3 + 6, 9 - 6 = 3, 3 = 9 - 6If 25% of a number is 10, find 5% of that number.
Answer:
0.125
Step-by-step explanation:
Answer:
5% of 40 is 2
Step-by-step explanation:
number = x
25% of x is = 10
25% = 25/100, or 1/4
[tex]\frac{1}{4}x = 10[/tex]
multiply each side by 4
[tex]x = 40[/tex]
5% is 5/100, or 1/20
[tex]\frac{1}{20}x = ?[/tex]
plug-in the known value
[tex]\frac{1}{20}*40 = ?\\\frac{40}{20} = ?\\\frac{4}{2} = ?\\\\? = 2[/tex]
Solve For The Radius:
a. r = 9.7 m
b. r = 7 m
c. r = 123.5 m
d. r = 19.4 m
Answer:
a) r = 9.7 m
Step-by-step explanation:
CD = CE + ED
= 9 + r +r
= 9 + 2r
If a tangent and a secant are drawn from a common point outside the circle, then
CE * CD = CB *CB
9 * ( 9 + 2r) = 16 * 16 {Distributive property}
9*9 + 9*2r = 256
81 + 18r = 256
Subtract 81 from both sides,
18r = 256 - 81
18r = 175
Divide both sides by 18,
r = 175÷ 18
[tex]\boxed{\bf r = 9.7 \ m }[/tex]
Together, teammates Pedro and Ricky got 2686 base hits last season. Pedro had 280 more hits than Ricky. How many hits did each player have?
Answer:
1483 pedro 1203 ricky
Step-by-step explanation:
1203+1483 = 2686
I need help what is, 8y - 7 - 4y =
show work
Answer:
Step-by-step explanation:
8y-7-4y=
8y-4y= -7
4y=-7
DBS by 4
y=1.75
Juan is hiking a trail that is 2 miles long. He hikes 14 miles before resting.
How much farther does he have to hike?
Answer:
I think the answer is D.) 7/8 mile
Step-by-step explanation:
If you make the mixed numbers improper fractions. 2 and 1/8 is 17/8, 1 and 1/4 (2/8) is 10/8, then you subtract the numerators and keep the denomitators the same to get 7/8 mile (sorry if I spelt something wrong)
Please help asap! Need the answer quickly!
The time needed for the sample size to double is given as follows:
26.3 hours.
How to obtain the time needed for the sample size to double?The exponential function that models the sample size after t hours is given as follows:
y(t) = y(0)e^(0.0264t).
The parameter y(0) represents the initial population, hence when the population is doubled, we have that:
y(t) = 2y(0).
Then we must solve the exponential function for the variable t, applying the natural logarithm, which is the inverse of the exponential, as follows:
2y(0) = y(0)e^(0.0264t).
e^(0.0264t) = 2
0.0264t = ln(2)
t = ln(2)/0.0264
t = 26.3 hours.
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Determining Whether a Point Lies on a Circle
10
8
-10 8-6-4-2
6
4
2
-2
-6
8
-10
Y
2
6 8 10
A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8. √17).
O Yes, the distance from the origin to the point
(8,√17) is 9 units.
Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.
The correct statement regarding whether (8, √17) lies on the circle is given as follows:
Yes, the distance from the origin to the point (8,√17) is 9 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The parameters for this circle are given as follows:
Center (0,0).Radius 9.Hence the equation is given as follows:
x² + y² = 81.
For point (8, √17), we have that:
8² + (√17)² = 81
64 + 17 = 81
81 = 81.
Hence the point lies on the circle.
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Determine the value of y, if x is - 2.
y = x + 8
answer: 10
y = |2| + 8
y = 2 + 8
y = 10
In track and field, the 440-yd. race was replaced with the 400-m race when Canada changed from the imperial system to the SI system. Which race is longer and by how much? Use the exact conversion: 1 yd. = 0.9144 m
Answer:
The 440-yd race is longer than the 400-m race by 2.336 meters.
Step-by-step explanation:
We can convert the distance of the 440-yd race to meters using the conversion factor 1 yd = 0.9144 m:
440 yd = 440 x 0.9144 m/yd = 402.336 m
Therefore, the 440-yd race is 402.336 meters long.
On the other hand, the 400-m race is already in meters.
Comparing the two distances, we can see that the 440-yd race is longer than the 400-m race.
To find out by how much longer, we can subtract the length of the 400-m race from the length of the 440-yd race:
402.336 m - 400 m = 2.336 m
Therefore, the 440-yd race is longer than the 400-m race by 2.336 meters.
I will mark you brainiest!
In a proof to show two triangles are congruent if a given is PR ⟂ CK, which of the following statements most likely will be used within the proof?
A) PR and CK are congruent.
B) PR and CK are similar.
C) PR and CK form acute angles.
D) PR and CK form right angles.
Answer:
D) PR and CK form right angles
Step-by-step explanation:
⟂ is the symbol for a perpendicular, so it is a perpendicular bisector.
- Perpendicular bisectors divide an angle into 2 90° angles.
Please help me solve these questions that are attached.
The sums, differences, product, and quotient of the functions and their domains are;
f(x) = √(16 - x^2), g(x) = √(x + 3)
f + g = √(16 - x^2) + √(x + 3)
Domain; [-3, 4]
f - g = √(16 - x^2) - √(x + 3)
Domain: [-3, 4]
f × g = √(16 - x^2) × √(x + 3) = √(-x³ - 3·x² + 16·x + 48)
f × g = √(-x³ - 3·x² + 16·x + 48)
Domain; [-3, 4]
f/g = √(16 - x^2)/√(x + 3) = √(16 - x^2)/(x + 3))
f/g = √(16 - x^2)/(x + 3))
Domai; [-3, 4] ∪ [1, 4]
f(x) = √(81 - x^q2), g(x) = √(x² - 16)
f + g = √(81 - x^2) + √(x² - 16)
Domain [-9, -4] ∪ [4, 9]
f - g = √(81 - x^2) - √(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
f × g = √(81 - x^2) × √(x² - 16) = √(-x⁴ + 97·x² - 1296)
f × g = √(-x⁴ + 97·x² - 1296)
Domain: [-9, -4] ∪ [4, 9]
f/g = √(81 - x^2)/√(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
What is the sum of two functions?The sum of two functions is obtained by adding the values of the functions at each point.
The sum of two functions is obtained by adding the values of the functions at each point. The domain of the sum is the intersection of the domains of the two functions, In this case, the domain of f + g is [-3, 4]
The difference of two functions is obtained by subtracting the functions values at each point. The domain of the difference is the intersection of the domains of the two functions. In this case, the domain of f - g is [-3, 4]
The product of two functions is obtained by multiplying the values of the functions at each point. The domain of the product of the functions is the domain of the intersection of the domains of the two functions. The domain of f × g is [-3, 4]
The quotient of two functions is obtained by dividing the values of the functions at each point. The domain of the quotient is the same as the domain of the intersection of two functions, excluding any points where the denominators is zero. The domain of f/g is [-3, -1] ∪ [1, 4].
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Pls help simplify liner expressions
The answers to the questions are in the picture
The difference between two numbers is 2. When each number is rounded to nearest hundred, the difference between them is 100. What could the numbers be?
[tex]101 - 99 = 2[/tex]
each number is rounded to nearest hundred101 → 200
99 → 100
the difference between them is 100:[tex]200 - 100 = 100[/tex]
⇒ the numbers could be: 99 and 101
other pairs of numbers: (199,201), (299,301) ...
what is the area of the circle below?
The area of the circle shown above is equal to: A. 1,520.5 cm².
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using the following mathematical expression:
Area of a circle, A = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of a circle, A = πr²
Area of a circle, A = 3.14 × 22²
Area of a circle, A = 1,520.5 cm².
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if 85% of 'a' is 'b' then which of the following is true a, a=b b,ab
Answer:
Step-by-step explanation:
The statement "85% of 'a' is 'b'" can be represented mathematically as:
0.85a = b
This means that 'b' is 85% of 'a'.
To answer the question:
a = b/0.85
So, a is equal to 'b' divided by 0.85.
Therefore, the correct option is (a) a=b.
what has a sum of 147
Answer:
146 and 1
Step-by-step explanation:
146+1=147
Tara uses 6.6 pints of white paint and blue paint to paint her bedroom walls. 3 4 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:
1.65 pints
Step-by-step explanation:
If Tara used 6.6 pints of white and blue paint combined, and 3/4 of that amount is white paint, then we can find the amount of white paint she used by multiplying 6.6 by 3/4:
6.6 x 3/4 = 4.95
So Tara used 4.95 pints of white paint to paint her bedroom walls.
To find out how much blue paint she used, we can subtract the amount of white paint from the total amount of paint:
6.6 - 4.95 = 1.65
Therefore, Tara used 1.65 pints of blue paint to paint her bedroom walls.
A dice is tossed once,what is the probability that a prime number shows upwards
PLEASE HURRY!!! I WILL GIVE THE BRAINLIEST!!!
Which answer shows the correct steps to solve the equation
a
Subtract 4 from both sides,, multiply by 12 on both sides, subtract 10 from both sides, and divide both sides by 5 to get x=2/5
b
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
c
Subtract 10 from both sides, multiply by 15 on both sides, and divide by 5 to get x=(-18)
d
Subtract 5x from both sides, subtract 10/15 from both sides, and divide both sides by 5 to get x=10
Answer:
Answer is B
Step-by-step explanation:
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
What is the x and the y Intercept?
For the given function the intercepts are:
x-intercept: x = -4
y-intercept: y = 12.
How to find the intercepts for the given function?Here we have a table that defines a function, and we want to find the intercepts of said function.
We can assume it is linear, then the slope of the function will be given by:
a = (9 - 3)/(-1 + 3) = 6/2 = 3
The linear function is like:
y = 3x + b
To find the value of b we can replace the values of the last point on the table, x = 2 and y = 18.
18 = 3*2 + b
18 = 6 + b
18 - 6 = b = 12
The linear function is:
y = 3x + 12
The x-intercept is the value of x when y = 0
0 = 3*x + 12
-12 = 3x
-12/3 = x = -4
And the y-intercept is the value of y when x = 0.
y = 3*0 + 12
y = 12
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f(x) =
4 if x≤3
-4 if x>3
What is the functions range ?
Answer:
(−∞,∞)
Step-by-step explanation:
Pearl earns $34,000 per year, and she is considering buying a $130,000 house by
making a down payment of 10% of the purchase price and taking out a 30-year
fixed-rate mortgage with a 6.3% interest rate. She would pay $1280 annually in
property taxes, and for the first 2 years of the mortgage, she would pay $608.40
annually for PMI. Use this information to answer the following six questions.
1.
How much would Pearl's
mortgage be?
Pearl's mortgage payment would be $678.47 per month.
What is mortgage?A mortgage is a type of loan that is used to finance the purchase of real estate, such as a house or a piece of land. When a person takes out a mortgage, they borrow money from a lender (usually a bank or other financial institution) to buy the property, and they agree to pay back the loan over a set period of time, typically 15 to 30 years.
In the given question,
To calculate Pearl's mortgage, we need to first determine the amount of her down payment.
Down payment = 10% x $130,000
Down payment = $13,000
The amount that Pearl needs to finance with her mortgage is:
$130,000 - $13,000 = $117,000
To calculate the mortgage payment, we can use the formula for a fixed-rate mortgage:
Mortgage Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal (amount borrowed)
r = Monthly interest rate (annual rate divided by 12)
n = Number of monthly payments (30 years x 12 months per year)
Monthly interest rate = 6.3% / 12 = 0.00525
Number of monthly payments = 30 years x 12 months = 360
Using these values, we can calculate the monthly mortgage payment:
Mortgage Payment = $117,000 * 0.00525 * (1 + 0.00525)^360 / ((1 + 0.00525)^360 - 1)
Mortgage Payment = $678.47 (rounded to the nearest cent)
Therefore, Pearl's mortgage payment would be $678.47 per month.
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a block exerts a force of 7nm on the ground. what is the pressure on the ground in nm2 when its flat on the grounds the area of its base is 0.04m2
The pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is [tex]175 nm^{-2[/tex].
First, we need tο cοnvert the area οf the blοck's base frοm square meters tο square nanοmeters, since the fοrce is given in newtοn-meters (N m) and we want tο find the pressure in newtοn-meters-squared ([tex]N/m^2[/tex] οr[tex]Nm^{-2[/tex]):
[tex]0.04 m^2 = 0.04 \times 10^18 nm^2 (since 1 m = 10^9 nm)[/tex]
Next, we can use the fοrmula fοr pressure, which is:
pressure = fοrce/area
Substituting the given values, we get:
[tex]pressure = 7 N m / 0.04\times 10^{18} nm^2[/tex]
Simplifying this expressiοn, we get:
[tex]pressure = (7 / 0.04) \times 10^{(-9)} N/nm^2[/tex]
[tex]pressure = 175 \times 10^{(-9)} N/nm{^2[/tex]
[tex]pressure = 175 nm^{-2[/tex]
Therefοre, the pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is[tex]175 nm^{-2[/tex].
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What is a frequency distribution?
Answer:
Frequency distributions are visual displays that organize and present frequency counts so that the information can be interpreted more easily.
Step-by-step explanation:
The distribution of a variable is the pattern of frequencies, meaning the set of all possible values and the frequencies associated with these values.
Professor Yi, M.A. is an expert on mindfulness meditation, and completed a study on how this practice can reduce stress. In the untreated population of Ionia, stress levels as measured by the HRSI (higher values indicate higher levels of stress) the mean stress level is μ = 30 and σ = 12. Professor Yi obtained a sample of n = 16 students to teach mindfulness meditation to for two months. After the two months of lessons the students show average HRSI stress scores of M = 24. Yi decided in advance he was going to run a two-tailed hypothesis test at an α = .05.
What is the null hypothesis for this study?
The null hypothesis for this study is that there is no significant difference in stress levels between the untreated population and the sample of students who were taught mindfulness meditation.
How to find the null hypothesis ?The null hypothesis states that the mindfulness meditation has no effect on the stress levels of the students.
In terms of the mean stress level (μ), the null hypothesis can be expressed as:
H₀: μ = 30
This means that under the null hypothesis, the mean stress level of the students who were taught mindfulness meditation is equal to the mean stress level of the untreated population (μ = 30).
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How would you characterize the relationship between the hours spent on homework and the test
scores? Explain.
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h
of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation
Paul scοre 64 fοr the mοdel predict fοr 3 h οf hοmewοrk and test scοre tο be 40.
What is function?A functiοn is defined as a relatiοnship between a set οf inputs that each have οne οutput. A functiοn is a relatiοnship between inputs in which each input is related tο exactly οne οutput. Every functiοn has a dοmain and a cοdοmain, as well as a range. In general, a functiοn is denοted by f(x), where x is the input. A functiοn's general representatiοn is y = f. (x).
Scοre can be defined as tοtal number which any persοn achieve after dοing any wοrk οr target. Suppοse a Batsman make 100 run it means he scοre 100 fοr his team.
a. Fοr three hοurs οf study we have that the nοte wοuld be apprοximately:
y = 8x + 4
b. The number 40 means that if yοu dο nοt devοte any study time, then yοu expect the test scοre tο be 40.
y = 8(3) + 40
y = 64
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Which net represents this solid figure?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
_________________________________
The net that represents this solid figure is diagram D.
What is a solid figure?A solid figure is a three-dimensional geometric shape that has length, width, and height. It is also called a three-dimensional or 3D figure. Some examples of solid figures include cubes, spheres, cylinders, cones, and pyramids.
Solid figures are different from two-dimensional shapes, which only have length and width. In contrast, solid figures have depth or thickness, making them more complex and interesting.
Solid figures can be classified based on their properties, such as the number of faces, vertices, and edges they have. For example, a cube has six faces, eight vertices, and 12 edges, while a sphere has no faces, vertices, or edges.
In this case, it has 2 squares and 4 rectangles. The appropriate diagram is D
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