The solutions for all the given statements are,
1. True, 2. True, 3. False, 4. True, 5. True, 6. True, 7. False, 8. False
Given statements and their conclusions;
1. The best point estimate for the population mean is the sample mean.
→ True, since the central limit theorem states that the sample mean corresponds to the population mean.
2. The level of confidence that a confidence interval contains the population parameter being estimated increases as its length does (confidence level).
→ True, when the CI widens, our confidence grows as well since we are more certain that the true mean (or another statistic) will fall inside the range.
3. If a confidence interval is very long, it means that the corresponding prediction is highly significant.
→ False, as the length increases, the confidence interval's range similarly expands, giving the correct point estimate a wider range of possible values.
4. A 90% confidence interval for a population mean implies that there is a 0.90 probability that the true population means will be contained in the confidence interval.
→ True, a 90% CI means that we are 90% confident that the range of the confidence interval contains the true value of the mean.
5. A 90% confidence interval for a population parameter means that if a large number of confidence intervals were constructed from repeated samples, then on average, 90% of these intervals would contain the true parameter.
→ True, 90% of the values attains positive values.
6.A population parameter's point estimate is always in the middle of the parameter's confidence interval.
→ It is true that the sample statistic, such as a sample mean or sample proportion, is at the center of a confidence interval. The point estimate is what is used here. The margin of error determines the width of the confidence interval.
7. A population's point estimate for a particular parameter will always be the same when repeated samples are taken from it.
→ False.
8. The larger the level of confidence, the shorter the confidence interval.
→ False, an increase in the margin of error follows an increase in the level of confidence. A broader confidence interval is produced by a higher margin of error.
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Determine whether the following sequence is arithmetic, geometric, or neither. 12,17,22,27
Answer:
Arithmetic
Step-by-step explanation:
The difference between consecutive terms is 5. Thus, this is an arithmetic sequence with a common difference of 5.
-4(w + 5) + 2w simplify
Answer:
-2w-20
Step-by-step explanation:
Which of the following rules describes the function graphed below? On a coordinate plane, points are at (negative 1, 1), (1, 2), (3, 3), (5, 4). a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3
The rule that describes ( -1, 1), (1, 2), (3, 3), (5, 4) is c. Output = (0.5)(Input) + 1.5
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, On a coordinate plane, points are at ( -1, 1), (1, 2), (3, 3), (5, 4).
By observing the given options we conclude that it is Output = (0.5)(Input) + 1.5 to confirm let's put the values.
Given when input is - 1 output is 1.
∴ 1 = 0.5(-1) + 1.5.
1 = - 0.5 + 1.5.
1 = 1 ( satisfied).
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5a<−35 or a−14>1
Algebra 1, high school
Answer:156
Step-by-step explanation:
Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
3. x-int: (-4,0) , (7,0)
P (3,8)
Answer:
y = -2/7(x + 4)(x - 7)=============================
Givenx- intercepts (-4, 0) and (7, 0),Point P (3, 8).SolutionThe given translates as:
p = -4, q = 7, x = 3, y = 8Use given x - intercepts to get the equation:
y = a(x + 4)(x - 7)Use the coordinates of P to find the value of a:
8 = a(3 + 4)(3 - 7)8 = a*7*(-4)8 = - 28aa = 8 / - 28a = - 2/7The equation of this parabola is:
y = - 2/7(x + 4)(x - 7)Answer:
[tex]\textsf{Intercept form}: \quad y=-\dfrac{2}{7}(x+4)(x-7)[/tex]
[tex]\textsf{Standard form}: \quad y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-4, 0) and (7, 0) then:
p = -4q = 7Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-4))(x-7)[/tex]
[tex]\implies y=a(x+4)(x-7)[/tex]
To find a, substitute the given point on the curve P (3, 8) into the equation:
[tex]\implies 8=a(3+4)(3-7)[/tex]
[tex]\implies 8=a(7)(-4)[/tex]
[tex]\implies 8=-28x[/tex]
[tex]\implies a=\dfrac{8}{-28}[/tex]
[tex]\implies a=-\dfrac{2}{7}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=-\dfrac{2}{7}(x+4)(x-7)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=-\dfrac{2}{7}(x^2-3x-28)[/tex]
[tex]\implies y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]
Barbara drew a scale drawing of a game room. The scale she used was 2 inches : 1 foot. If the actual length of the pool table is 6 feet, how long is the pool table in the drawing?
If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches .
In the question,
it is given that ,
Barbara drew an scale drawing of the game room.
the scale that she used is 1 feet in the actual length is represented by 2 inches in the drawing ,
which means ,
1 feet = 2 inches
to find the length of 6 feet in the drawing ,
6 feet = 6 × 2 inches
= 12 inches
Therefore , If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches .
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Find the length of YZ when Y is the midpoint of XZ
X
20+2a
Y
8 +6a
Z
XZ=
The length of the line YZ is 26 units
The Y is the mid point of the line XZ
The length of the line XY = 20 + 2a
The length of the line YZ = 8 + 6a
When Y is the mid point of the line XZ, then the length of the line XY is equal to the length of the line YZ
The length of the line XY = The length of the line YZ
Substitute the values in the equation and find the value of a
20 + 2a = 8 +6a
Rearrange and group the like term
6a - 2a = 20 - 8
4a = 12
a = 12 / 4
a = 3
The length of the YZ = 8 +6a
= 8 + 6×3
= 8 + 18
= 26 units
Hence, the length of the line YZ is 26 units
The complete question is:
Find the length of YZ when Y is the midpoint of XZ, if XY = 20+2a and YZ = 8+6a.
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How many solutions does 5 + x/3 = x/3 + 6 + x/9
A. Infinitely many solutions
B. Two solutions
C. No solutions
D. One solution
========================================================
Explanation:
A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation
5 = 6 + (x/9)
Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1
Then plug in w = x/9 and solve for x.
w = -1
x/9 = -1
x = 9*(-1)
x = -9
We get exactly one solution and it is x = -9
--------------
Check:
5 + x/3 = x/3 + 6 + x/9
5 + (-9)/3 = (-9)/3 + 6 + (-9)/9
5 - 3 = -3 + 6 - 1
2 = 3 - 1
2 = 2
We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.
1. Simon drives 32 miles in 15 minutes. What is his speed in miles per hour?
2. Triangle BIG is similar to triangle CAT. If BG is 6 units and CT is 15 units, then what is the length of IG if At is 20 units?
3. Quadrilateral SMAK is similar to quadrilateral DOWN. Assuming the length of SM is 34u and the length of DO is 17u, what is the ratio of AK to WN in simplest form?
1) the speed of Simon per hour is 128 miles/Hr
2) The length of IG is 20 Units.
3) The ratio of SM is 2:1
What is the explanation of the above answer?1) For 1, to obtain the speed of Simon per hour, all you need to do is multiply 32 x 4.
This is because in every hour, 15 minutes occurs four times. That is:
1 hour = 60 minutes
Hence, if 32 miles is done in 15 minutes, then 60 minutes =
32 x 4
= 128 miles
Hence the speed of Simon per hour is 128 Miles/ Hour
2) Given that the two triangles are identical, it means that on the basis on RHS theorem we have been given all the sides. Note that BG is 6 Units (we are assuming that this is the base) , then AT from the other triangle (see attached) is 20.
We assume this is the Hypotenuse. CT is also given. We assume this is the height. If we have CT and AT, and both triangles are the same, then IG is 20 units.
3) For the quadrilateral, recall that in quadrilaterals opposite sides are equal. If one side is 34u on one, and the other side is 17u on the other quadrilateral, then we already have the measure of the sides for both quadrilaterals.
So the Ratio of AK to WN
34u: 17u - Simplified by dividing by 17u we have
Ratio 2:1
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The graph to the right is the uniform probability density function for a friend who is x minutes late
(a) Find the probability that the friend is between 25 and 30 minutes late.
(b) It is 10 A.M. There is a 10% probability the friend will arrive within how many minutes?
(a)The probability that the friend is between 25 and 30 minutes late is 1/2.
(b) It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.Uniform distribution
a = 0
b = 10
a) P(friend is between 25 and 30 minutes late) = (30 - 25)/(b - a)
= 5/(10-0)
= 1/2
b) Let the time for arrival be A minutes
(A - 0)/(b-a) = 0.10
A = 0.10 x (10 - 0)
A = 1 minute
Hence, The probability that the friend is between 25 and 30 minutes late is 1/2 and It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.
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HELP ASAP PLEASE
What is the equation of p(x) in vertex form? p(x) = 2(x − 1)2 − 2 p(x) = 2(x + 1)2 − 2 p(x) = 3(x − 1)2 − 2 p(x) = 3(x + 1)2 − 2
Answer:
p(x)=-2*p*x+4*x+-4=1*-2*p*x+4*x+4=1*-2*p*x+6*x+-6=6*x+4*1*1
Step-by-step explanation:
What expressions represents the multiplex version of the expression below ?
(6x^2 +5) (2x^3+3)
Answer:
12x^5+18x^2+10x^3+15
Step-by-step explanation:
first you apply the distribution property (FOIL) and you get
12x^5+18x^2+10x^3+15
the lifetime of a certain type of battery is normally dis- tributed with mean value 10 hours and standard deviation 1 hour. there are four batteries in a package. what life- time value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?
The total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that,
mean,μ=10 hr
standard deviation,σ=1hr
n=4
The lifespan of four batteries combined is,
=4μ
=4×10
=40 hr
z = (x-μ)/σ
1.645=(x-40)/2
x-40=3.29
x=43.29
Thus, the total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.
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What is the solution of the system?
10x + 3y = 50
- 5x - y = -20
(2, 4. 4)
(4. 4, 2)
(2,10)
(10, 2)
The linear equation two variables can be solved by various methods one of the methods to solve the linear equations is the substitution method. The solution of the given equation is x=2 and y=10.
What is linear equation in two variables ?
A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.
Main body:
The given equations are :
10x+3y=50 .... (1)
-5x-y=-20 ....(2)
Multiply equation (2) by 3 and then add the equation (1) to eliminate the variable y.
10x+3y+3(-5x-y)=50+3*-20
-5x=-10
x=2
Now putting the value of x in equation (1), and solve it further.
10*2+3y=50
3y=30
y=10
Hence, the value of x is 2 and the value of y is 10.
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at the lone butte ranch 6 goats and 5 sheep sell for 305 while 2 goats and 9 sheep sell for 285. Find the cost of a single goat and a single sheep.
By solving a system of equations we can see that each goat costs $30 and each sheep costs $25.
How to find the cost of each animal?Let's define the variables:
x = cost of a goat
y = cost of a sheep.
We can write the system of equations with the given info:
6*x + 5*y = 305
2*x + 9*y = 285
If we subtract 3 times the second equation from the first one, we get:
(6*x + 5*y) - 3*(2*x + 9*y) = 305 - 3*285
-22*y = -550
y = -550/-22 = 25
Now that we know the value of y we can try to find the value of x:
2*x +9*25 = 285
2*x = 285 - 9*25 = 60
x = 60/2 = 30
These are the costs of each animal.
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The average annual rainfall for a town is 43.2 inches. The average monthly rainfall for the previous 9 months was 4 inches. Did the town exceed its average annual rainfall? If so, by how much?
Answer:
Yes, the town exceeded the average annual rainfall by 0.4 inchesStep-by-step explanation:
The average annual rainfall for a town is 43.2 inches.
This is converted to average monthly as:
43.2 in / 12 = 3.6 inThe difference is:
4 in - 3.6 in = 0.4 inAnswer:
Yeah, they exceeded by 0.4 inches.
Step-by-step explanation:
It is given that,
→ the average monthly rainfall for the previous 9 months was 4 inches.
The monthly rainfall in 12 months,
→ 43.2 inches ÷ 12 months
→ 43.2/12
→ 3.6 inches
Then the difference will be,
→ 4 inches - 3.6 inches
→ 4 - 3.6
→ 0.4 inches
Hence, the difference is 0.4 inches.
Use the diagram to find the measure of angle 2
The measure of angle 2 is 75°
From the question, we have
∠1= 105°
∠2= 180°- 105° (Linear pair)
∠2=75°
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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A machine in a factory make 3 1/2 pound of nail in 1 1⁄4 hour. At what rate, in pound per hour, doe the machine make nail?
Answer:
2.8 pounds per hour
Step-by-step explanation:
[tex] \frac{3.5}{1.25} = \frac{350}{125} = \frac{14}{5} = 2.8[/tex]
In a farm houe, there are 80 cow and 30 buffaloe. What i the rate of the cow
and the buffaloe
If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3 .
In the question,
it is given that ,
the number of cows in the farm house = 80
the number of buffaloe in the farm house = 30
we need to find the ratio of cow and the buffaloe .
the ratio can be calculated using the formula .
ratio = (number of cows)/(number of buffaloe)
Substituting the vales , we get
= 80/30
cancelling out the common factor 10 , from both numerator and denominator , we get
= 8/3
So , the ratio is 8:3 .
Therefore , If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3 .
The given question is incomplete , the complete question is
In a farm house, there are 80 cows and 30 buffaloes . What is the ratio of the cow and the buffaloe ?
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for the function g(x)=-1/5 x^2 + 4x+1, find the range of g(x)
Plotting the graph of the quadratic function g(x)=-1/5x^2 + 4x + 1 the range is
y ≥ -19How to determine the range of the quadratic functionThe range of the quadratic function is seen at the vertex were the maximum or minimum y value is seen
The graph of the function g(x)=-1/5x^2 + 4x + 1 is plotted and attached
From the graph the vertex coordinates is v(-10, -16). The y coordinates of the vertex is -19 and this is the minimum values for y
Therefore the range is y ≥ -19
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Andrew has picked out some party favors. He calculates that they will cost $7 per guest.
Write an equation that shows how the total cost of the party favors, y, depends on the number of guests, x
Do not include dollar signs in the equation. what does y equal?
Answer:
Step-by-step explanation:
y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Andrew has picked out some party favors.
He calculates that they will cost $7 per guest.
We need to find the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
So y=7x where y is the total cost and x is the number of guests and 7 is the cost per guest.
If there are 2 guests then the total cost will be 14.
Hence y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
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which of the following ratios are connected to 5/20?
multiple choice
a 1/5
b1/4
c 20/100
d 25/100
Answer:
which of the following ratios are connected to 5/20?
multiple choice
a 1/5
c 20/100
d 25/100
d is the option 25/100 and
b 1/4
- Describe all transformations from the parent
function
given the function below.
f(x)=(x-3)² +7
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50. How many of each type of ticket were purchased?.
23 tickets are purchased for children and 9 tickets are purchased for adults.
Given,
In the question:
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50.
To find the how many of each type of ticket were purchased?
Now, According to the question:
It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x
Now cost of one ticket for adult = $7.50
Total amount spent on adult tickets = 7.50 × (32-x)
Similarly, cost of one ticket for child= $3.50
Total amount spent on children tickets = 3.50 × x =3.5x
Total amount spent by group on tickets = $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.
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can someone please help me with this
Answer:
B
Step-by-step explanation:
given 1 pound = 16 ounces , then
5 pounds = 5 × 16 = 80 ounces
Raman purchased books and stationery items and paid the total amount of rupees 963 if he paid 7% tax what was the net value of the item purchased.
The net value of the items purchased is ₹ 900.
Raman purchased books and stationery items and paid the total amount of rupees 963.
Paid tax = 7%
Let the net value of the items purchased be `x.
VAT = 7%
Selling price = ₹x + (7% of x)
= ₹x+ ₹ ( 7/100 * x)
=₹( x +7 x /100)
= ₹ 107 x /100
But Raman purchased books and stationery items for ₹963.
107x/100 = ₹963
x = 963 x 100/107
x = 900
Hence the answer is the net value of the items purchased is ₹ 900.
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I really need help! Can anyone please answer this!!
The function f has domain : [-4, 5], range : [0, 9], zero : (3, 0), the function is increasing in intervals at [-4, 0] U [3, 5], decreasing in intervals at (0, 3], the relative minimum values of f : (3, 0), and relative maximum values of f : (5, 9).
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The function f is given in the graph.
According to the given function, the required solution would be as:
The domain and range of f will be :
domain : [-4, 5]
range : [0, 9]
The zero of f will be :
(x, y) = (3, 0)
The function is increasing in intervals at [-4, 0] U [3, 5]
The function is decreasing in intervals at (0, 3]
The relative minimum values of f : (3, 0)
The relative maximum values of f : (5, 9)
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Two sevenths divided by 1 half
Answer:
4/7
Step-by-step explanation:
2/7 ÷ 1/2 = 2/7 × 2/1 = 4/7
Answer:
Step-by-step explanation:
1. Write Words into math
2/7/1/2
2. Solve
2/7/1/2=
2/7*2/1=
4/7
Answer: 4/7
When 6 less than 3 times a number is increased by 2 it's at least 5 times the same number decreased by 8
Answer: 2>=n
Step-by-step explanation:
3n-6 +2 >= 5n-8
3n-4 >= 5n-8
-4>= 2n -8
4>=2
2>=n
Hope this helped!!
Solve 2y + x + 3 = 0 and 3y - x + 1 = 0 graphically using -4 ≤x ≤ 2
help pls
Answer:
Step-by-step explanation:
We have to the graph from x = -4 to x = 2
2y + x + 3 = 0
Rearrange the equation to make y the subject
2y = -x - 3
y = (-1/2)x -3/2
-3/2 is the y intercept
the gradients is -1/2
since the value is negative, the graph will be sloping downwards
Point your pen at y = -3/2 on the y axis (-3/2 is -1.5)
go 1 point down and 2 points to the right, make a point and connect these 2 dots and make a line across the graph.
Do the same with the other equation:
3y - x + 1 = 0
3y = x - 1
y = (1/3)x -1/3
y intercept is -1/3
gradient is 1/3
point your pen at -1/3 on the y axis, go 1 point up and 3 points to the right
and mark this point and connect these 2 points and make a line across the graph.