The 95% confidence interval for the population proportion of members who vote yes is (0.782, 0.818).
What is Random Sample?A choice that is made at random (purely by chance, with no predictability). They tapes of samples are:
Convenient: Sample taken from a pool that is easily accessible.
Random: Put all the possibilities into a hat, then pull some of them at random. Every kth element is taken in a systematic manner. If you wanted to survey anything on the street, for instance, you may interview every fifth person.
Cluster: The population is divided into groupings, or clusters, and every component of each cluster is surveyed.
Stratified: Additionally stratifies the people into several groupings. But only a small portion of the group is questioned after that.
Now, finding the sample proportion,
[tex]p=\frac{x}{n} \\\\=\frac{1600}{2000}\\\\ =0.8[/tex]
The confidence level is given as,
[tex]C=p\pm[z(\frac{\alpha}{2})\times\sqrt{\frac{p(1-p)}{n} } ][/tex]
The value of [tex]z(\frac{\alpha}{2})[/tex] is 1.96
Putting the values, we get
[tex]C=0.8\pm[1.96\times\sqrt{\frac{0.8(1-0.8)}{2000} } ]\\\\C=0.8\pm[1.96\times\sqrt{\frac{0.8(0.2)}{2000} } ]\\\\C=0.8\pm0.018\\\\C=(0.782,0.818)[/tex]
Therefore, the 95% confidence interval is (0.782,0.818).
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The given question is incomplete. Here is the complete question.
a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?
a) 0.782 to 0.818
b) 0.754 to 0.799
c) 0.690 to 0.713
d) 0.799 to 0.951
X
-3
-2
0
2
g(x)=x³+6x² + 12x+8
3
g(x)
-1
0
8
64
125
Determine the function's value when x=-1.
Og(-1)=-3
O g(-1)=0
O g(-1)=1
O g(-1)=27
The function g(-1) has its value to be (c) g(-1) = 1
How to evaluate the function at the input value?The definition of the function is given as
g(x)=x³+6x² + 12x+8
Rewrite the above function properly
So, we have the following representation
g(x) = x³ + 6x² + 12x + 8
To find the function g(-1), we set the value of x in the equation g(x) = x³ + 6x² + 12x + 8 to -1
This is represented by
Calculate g(x), when x = -1
Substitute -1 for x in the equation g(x) = x³ + 6x² + 12x + 8
So, we have the following equation
g(-1) = (-1)³ + 6(-1)² + 12(-1) + 8
Evaluate the exponents
This gives
g(-1) = -1 + 6(1) + 12(-1) + 8
Evaluate the products
This gives
g(-1) = -1 + 6 - 12 + 8
Evaluate the sum
g(-1) = 1
Hence, the value of the function is g(-1) = 1
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70 points need help asap
The angle ∠C is 130° by the alternative angles.
Given that,
In the figure we have a diagram.
We have to find the angle c.
The angles created on the opposing side of the transversal with regard to both straight lines when two straight lines are cut by it are referred to as alternative angles. Therefore, the angles that are on the opposing sides of the transversal and have distinct vertices are those.
We know that,
By alternative angles
∠M=∠C
So,
130°=∠C
Therefore, The angle ∠C is 130° by the alternative angles.
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Find the geometric mean between ab³ and a³b?
[tex]{ \green{ \sf{G = \sqrt{ ab}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ (ab³)(a³b)}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ a⁴b⁴}}}}[/tex]
[tex]{ \red{ \boxed{ \pink{ \sf{G = \sqrt{ a².b²}}}}}}[/tex]
Lines AB and CD are straight lines. Find x and y .
⇒ ∠AOC+∠AOE+∠EOD=180°(angles on a straight line are supplementary)
16°+90°+2y=180°
[tex]106+2y=180\\2y=180-106\\2y=74\\\frac{2y}{2} =\frac{74}{2} \\y=37[/tex]
∴y=37°
∠AOC+∠COF∠BOF=180°(angles on a straight line are supplementary)
16°+90°+4x=180
[tex]106+4x=180\\4x=180-106\\4x=74\\\frac{4x}{4} =\frac{74}{4} \\x=18.5[/tex]
∴x=18.5°
what is 382 3/10 minus 191 87/100
Answer:
190 43/100
Step-by-step explanation:
First, you turn the mixed fractions into improper fractions. 382 3/10 is 3823/10, and 191 87/100 is 19187/100. Then, you need to have a common denominator in order to subtract. This turns 3823/10 into 38230/100. 38230/100 - 9187/100 is 19043/100 since you only subtract the numerators. Finally, you turn it back into a mixed fraction by dividing 19043/100. This equals 190 with a remainder of 43. In conclusion, the answer is 190 43/100. I attached the image where I worked it out to show my thought process a bit more as well. I hope this helped! :D
Solve the equation for w.
4w + 2 + 0.6w = −3.4w − 6
No solution
w = 0
w = 1
w = −1
Please help
Answer:
The answer is w= -1
Step-by-step explanation:
4w + 2 + 0.6w = -3.4w - 6
4.6w + 2 = -3.4w - 6
8w + 2 = -6
8w = -8
w = -1
A container with 3½ liters of weed killer can spray of a lawn. How many liters would it
take to spray 1 entire lawn?
The amount a container would take to spray 1 entire lawn is 7 litres.
Given that a container with 3½ liters of weed killer can spray 1/2 of a lawn.
We want to find the amount of liters to take a spray 1 entire lawn.
3½ liters of weed killer can spray 1/2,
liters take to spray 1 lawn is 3½/1/2=7 liters
Hence, the amount of liters it would take to spray 1 entire lawn when a container with 3½ liters of weed killer can spray of a lawn is 7 liters.
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3x + 4y = 7
2x - y = 12
please help?
Answer:
x=5
y=-2
Step-by-step explanation:
even though this looks like they want you to do it elimination ima do substation cause I like that better
2x-y=12
+y. +y
2x=12+y
-12 -12
2x-12=y
Now we can fill in y
3x+4(2x-12)=7
3x+8x-48=7
11x-48=7
+48. +48
11x=55
/11. /11
x=5
fill in X to find y
2(5)-y=12
10-y=12
-10. -10
-y=2
y=-2
hopes this helps please mark brainliest
1: 20% of 50 2: 50% of 80
Answer:
1. 10
Step-by-step explanation:
1. 20% of 50
[tex] \frac{20}{100} \: \: \: \times \: \: \: 50 \\[/tex]
=
[tex] \frac{1000}{100} [/tex]
= 10
If p is portional to q and p =4.5 when q= 12 .
Find the relationship between p and q
P when q =16
Q when p= 2.4
The relationship between variables p and q is given by p = kq. Also, the value of the variable p when q = 16 is 6 and when p = 2.4, the variable q is 6.4.
How to determine the proportional relationship?Mathematically, a proportional relationship can be represented with the following mathematical expression:
p = kq
Where:
p and q are the variables.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = p/q
Constant of proportionality (k) = 4.5/12
Constant of proportionality (k) = 0.375.
When q = 16, the variable p is given by:
p = kq
p = 0.375 × 16
p = 6.
When p = 2.4, the variable q is given by:
q = p/k
q = 2.4/0.375
q = 6.4
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On the interstate there is a ratio of 2 trucks to 4 cars to 3 SUVs, if there are a total of 1800 vehicles on the road, how many of each type of vehicle is on the road?
Answer:
Step-by-step explanation:
yes Saab do
The temperature dropped to 24 degrees in 8 days. what was the average daily change in temperature? a) 3 degrees b) -8 degrees c) -3 degrees d) 16 degrees
The average daily change in temperature will be 3 degrees The temperature dropped to 24 degrees in 8 days
Since we know an average could be a single number taken as an agent of a list of numbers, as a rule, the whole of the numbers divided by how numerous numbers are within the list. We are said the temperature dropped to 24 degrees in the 8 days
So the average of it will be =24 /8 = 3, which means the temperature needed to drop for at least 3 degrees in order to get the sum of 28 in 8 days.
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question 4: a school group went to a carnival on a field trip. the function c(x) represents the amount of money spent in dollars, where x is the number of students. does a possible solution of (29.5, $212.50) make sense for this function? explain your answer.
Step-by-step explanation:
only limited sense.
first of all, directly it does not make any sense. we can only send integer number of students on a field trip. not half-persons.
therefore, 29.5 students for a single field trip calculation does not make sense.
but : we could want to use the same function to calculate or analyze the costs of multiple field trips by using things like mean values of students participating. there fractions as student numbers make sense.
Base of an isosceles triangle can be right angles
We can actually deduce here that the statement, "base of an isosceles triangle can be right angles" is false.
What is an isosceles triangle?An isosceles triangle is actually known to be a triangle which has two sides equal and opposite angles of the sides also equal. In other words, an isosceles triangle must have at least two equal triangles.
Some of the properties of an isosceles triangle are:
It is a triangle whose two sides are congruent to each otherIt has a third side known as the base of the isosceles triangle.It has angles that are opposite to the equal sides which are congruent to each other.We see here that the base of an isosceles triangle cannot be a right angles. It is still to have one side as a right angle but not the two sides as right angles.
The complete question is:
True or false: Base angles of an isosceles triangle can be right angles.
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Diana works at a clothing store. She sold 1/5 of the total number of green shirts on Monday and 3/12 of the total number of green shirts on Tuesday. What fraction of green shirts did Diana sell on Monday and Tuesday? 27/60 is the answer. Diana sold 2/15 of the total number of green shirts on Wednesday. What is the difference in the fraction of the total number of green shirts that were sold on Tuesday and Wednesday?
Answer:
your answer is [tex]27/60[/tex] and [tex]7/60[/tex]
in a particular chi-square goodness-of-fit test, there are eight categories and 825 observations. use the 0.10 significance level. a. how many degrees of freedom are there?
By probability , 7 is degrees of freedom are there .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.It is predicated on the likelihood that something will occur. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of getting a head is 1 in 2.825 Observations and 8 categories .
Degree of freedom = k - 1
df = 8 - 1
df = 7
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Find the equation of the straight line passing through the point (3, 5)
which is perpendicular to the line
y = 3x + 2
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through (3, 5) perpendicular to the line y = 3x +2.
Perpendicular lineThe given equation is in slope-intercept form. This lets us identify its slope as 3.
y = mx + b . . . . . . line with slope m and y-intercept b
y = 3x +2 . . . . . . . line with slope 3 and y-intercept 2
The perpendicular line will have a slope that is the opposite reciprocal of this:
m = -1/3 . . . . slope of the perpendicular line
Point-slope formThe equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The equation for a line with slope -1/3 through point (3, 5) is ...
y -5 = -1/3(x -3)
Slope-intercept formSolving for y gives us ...
y = -1/3x +1 +5 . . . . . eliminate parentheses, add 5
y = -1/3x +6 . . . . . equation of the desired line
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Please Help! What is the ratio of a:b?
a+3b/5 = a-2b/2
The ratio of a : b in the given expression is 16:3 .
In the question ,
it is given that
the algebraic expression is (a+3b)/5 = (a-2b)/2
we have to find the ratio of a:b ,
in order to find the ratio,
we cross multiplying ,
On cross multiplying , we get
2 * (a+3b) = 5 * (a-2b)
2a + 6b = 5a - 10b
5a - 2a = 10b + 6b
3a = 16b
dividing both sides by b ,
a/b = 16/3
a:b = 16:3
Therefore , The ratio of a : b in the given expression is 16:3 .
The given question is incomplete , the complete question is
What is the ratio of a:b in the expression (a+3b)/5 = (a-2b)/2 ?
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a marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce. how many kilometers did he run? (note: 1 mi
He ran 42.1 kilometers.
Define conversion.A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet. The act or process of transforming something into a different condition or form is known as conversion. to convert a value or expression between two different forms. • Measurement: converting between different units, for as from inches to millimeters or liters to gallons. For instance, change 12 inches to millimeters. 304.8 millimeters are equal to 12 inches multiplied by the inch-to-millimeter ratio of 25.4.
Given,
A marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce.
1 mile = 1.609
Converting miles into kilometer:
26.2 miles
= 26.2 × 1.609
= 42.1
He ran 42.1 kilometers.
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Graph this system of equations on the coordinate plane:
y=4/3x+4
3y=-2x-6
The graph the system of linear equations on a coordinate plane is added as an attachment
How to graph the system of linear equations on a coordinate plane?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y=4/3x+4
3y=-2x-6
Rewrite the equations in the system of equations as follows:
So, we have the following representation
y = 4/3x + 4
3y = -2x - 6
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, 0)
This means that the solution to the system of equations is (-3, 0)
See attachment for the graph of the system of equations
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Question:
simplify 5√18
Answer template:
___ √ ___
The simplification of the number by solving square root 5√18 is 15√2.
What is meant by the term square root?A number's square root is a value that, if multiplied by itself, yields the original number. The other procedure to square an integer is to find its square root. Squares as well as square roots are hence related ideas.Providing that x is just the square root of y, the equation would be written as x=y or as x² = y. The radical symbol for the number's root is "√" in this instance. The square of the positive number is shown by multiplying it by itself. The original number is obtained by taking the square root of a square of such a positive number.For the given number
= 5√18
Find the factors of 18 by prime factorization.
18 = 2 ×3 ×3
Put in the number.
= 5√2 ×3 ×3
Taking 3 out of root.
= 5×3√2
Further solving.
= 15√2
Thus, the simplification of the number by solving square root 5√18 is 15√2.
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The temperature over the course of a day was being monitored. In the morning, the temperature was −3°F. In the middle of the day, the temperature rose to 12°F. After dark, the temperature dropped again to −6°F. What was the average temperature for the day?
A. −3°F
B. −1°F
C .1°F
D. 3°F
Latisha wants to buy pumpkins and autumn squash for a fall display. She has a budget of $117 but wants to buy more than 10 vegetables. The pumpkins are $5. 59 each. The squash are $3. 50 each. List THREE possible combinations of pumpkins and squash that latisha can purchase to represent the situation
(x,y) = (8,20), (6,24), and (10,17).are three alternative combinations of pumpkins and squash that Latisha may buy to depict the circumstance.
Latisha's total wealth is $17.
More than 10 veggies are the number of vegetables that Latisha wants to purchase.
A pumpkin costs $5.50.
An autumn squash costs $3.50.
Let n pumpkins purchased equal x.
Purchased number of autumn squash = y
There are three alternative squash and pumpkin combination that Latisha might buy to symbolize the circumstance.
With x acting as the independent variable, we may identify many y's.
x ( Pumpkin) y(Autumn squash) (integral value)
8 20
6 24
10 17
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A rectangular book measures 3*5. What is the length of its diagonal to the nearest tenth?
The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
Area of rectangle = length × width.
The angle between any two consecutive sides will be 90 degrees.
As per the given rectangle with dimensions 3 × 5.
The rectangle has been attached below,
The length of the diagonal using Pythagoras' theorem is,
x = √(3² + 5²)
x = √34 = 5.8
Hence "The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8".
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6 x 7/8
(six x seven eighth's) This is a review for last year but I forgot how to do it also can you show how you got it please?
Answer:
5 1/4 // 5.25
Step-by-step explanation:
convert 6 into a fraction:6/1 x 7/8multiply numerators by numerators, and denominators by denominators42/8 (6 x 7 = 42, 8 x 1 = 8)Simplify the fraction using the Lowest Common Multiples42/8 --> 21/4 convert the improper fraction into a mixed number:5 1/4OR
5.25Answer:
5 1/4
Step-by-step explanation:
You want the product of 6 and 7/8.
Product with a fractionYour written-out version of the question gives you a clue how to solve it:
six times seven eighths
The associative property of multiplication lets you rearrange this to ...
(six times seven) eighths = forty-two eighths
That is, the product is formed by multiplying the integer by the numerator, and expressing the whole thing over the denominator:
[tex]6\times\dfrac{7}{8}= \dfrac{6\times7}{8}=\dfrac{42}{8}\\\\=\dfrac{40+2}{8}=\dfrac{40}{8}+\dfrac{2}{8}=5+\dfrac{1}{4}\\\\=\boxed{5\dfrac{1}{4}}[/tex]
Improper fractionThe improper fraction is converted to a mixed number by looking at the quotient and remainder from the division: 42/8 = 5 r 2 = 5 2/8 = 5 1/4.
__
Alternate solution
Sometimes, it can be helpful to look at the problem another way.
6 × 7/8 = 6 × (1 -1/8) = 6 -6/8
= 6 -3/4 = 5 1/4
In the diagram below, \angle C\cong\angle F∠C≅∠F, \angle D\cong\angle G∠D≅∠G. Enter segments in the blanks provided that would result in a true equation.
The sides of similar triangles are proportional, therefore, the true equation would be: FG/CD = EG/BD.
What are Proportional Lengths of Similar Triangles?Two similar triangles have corresponding angle measures that are congruent to each other, but have corresponding side lengths that are proportional to each other.
Similar triangles have the same shape but their sizes are different.
Given that angles C and F are congruent, and angles D and G are congruent, therefore triangle BCD is similar to triangle EFG based on the AA similarity theorem.
Therefore, the corresponding side lengths of both triangles will be proportional, which means that the following equation would be true:
FG/CD = EG/BD
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a(n) is a scatter chart with time on the horizontal axis and measurement scale on the vertical axis, displays the mean and control limits, and may mark two standard deviations from the mean. histogram control chart pareto chart gantt chart affinity diagram
A(n) Control Chart is a scatter chart with time on the horizontal axis, measurement scale on the vertical axis, displays mean and control limits, and may mark two standard deviations from the mean.
A control chart is one of the process improvement techniques or simply it is a graph to study how a process changes over time. In layman's terms the control chart shows if a process is under control or out of control. For calculating the average, there is always a central line in the control chart, an upper line and a lower line for upper control limit and lower control limit respectively.
The control charts are used to serve many purposes including monitoring a process for special variations and their causes and to remove them, estimating the process average and the variation, predicting the impacts of the process , etc.
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Camilla borrows a book from the library for dd days. The library charges a late fee of 0. 10 dollars per day that the book is late. If Camilla returns the book more than 21 days after she borrowed it, the expression 0. 10(d-21) represents the total late fee Camilla owes
The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.
What is Algebra?
Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
Camilla borrows a book from the library for d days.
The library charges a late fee 0.10 dollars per day that the book is late.
If Camilla returns the book more than 21 days after she borrowed it.
Then the expression will be 0.10d.
The total amount is given as
Total amount = 0.10 d
Total amount = 0.10 x 21
Total amount = $2.1
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Anna received a gift of $5,000 from her grandmother and decided to invest it. The expression 5000(1.0005)^12t represents the amount of money Anna is earning on her investment. Select all of the following that are equivalent expressions so that Anna can better understand how her money is invested.
a) 5000(1.0005^12)^t
b) 5025^12t
c) 5000(1+0.0005)^12t
d) 5000(1.0005^t)^12
e) (5000+2.5)^12t
f) 5000(1+0.06/12)^12t
The equivalent expression that represents the amount Anna can better understand how her money is invested is 5000(1+0.0005)^12t.
The correct answer option is option c.
What is the equivalent expression of Anna's investment?Based on the expression given, Anna's investment is compounded monthly.
The formula for calculating future value:
FV = P (1 + r)^(nm)
Where,
FV = Future valueP = Present valueR = interest ratem = number of compoundingn = number of years5000(1.0005)^12t
Given options:
a) 5000(1.0005^12)^t
False
b) 5025^12t
False
c) 5000(1+0.0005)^12t
= 5,000(1.0005)^12t
True
d) 5000(1.0005^t)^12
False
e) (5000+2.5)^12t
False
f) 5000(1+0.06/12)^12t
= 5000(1 + 0.005)^12t
= 5000(1.005)^12t
False
In conclusion, the expression equivalent to Anna's investment is 5000(1+0.0005)^12t
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assume that blood pressure readings are normally distributed with and a blood pressure reading of 145 or more may require medical attention. what percent of people have a blood pressure reading greater than 145?
0.08891% percent of people have a blood pressure reading greater than 145.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
145) = (145-120)/8 = 25/8.P(x > 145) = P(z > 27/8) = 0.0008891.. = 0.08891%Hence, 0.08891% percent of people have a blood pressure reading greater than 145.
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