Answer:
The 98% confidence interval of the proportion = (0.312, 0.374)
Step-by-step explanation:
(Give answers accurate to 3 decimal places.)
The formula for Confidence Interval of Proportion is given as:
p ± z × √p(1 - p)/n
Where p = Proportion = x/n
x = 440
n = 1282
p = 440/1282 = 0.34321372854
Approximately = 0.343
z = z-score of 98 % confidence interval
= 2.326
Confidence Interval =
= 0.343 ± 2.326 × √0.343(1 - 0.343)/1282
= 0.343 ± 2.326 × √0.225351/1282
= 0.343 ± 2.326 × √0.00017578081
= 0.343 ± 2.326 × 0.01325823555
= 0.343 ± 0.03083865589
0.343 - 0.03083865589
= 0.31216134411
Approximately = 0.312
0.343 + 0.03083865589
= 0.37383865589
Approximately to = 0.374
Therefore, the 98% confidence interval of the proportion = (0.312, 0.374)
How can you use the order of operation to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x+5)-x=42
Answer:
Step-by-step explanation:
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways
We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
Here the expression given is :
7(x+5)-x=42
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.
Read more about property of multiplication here :
https://brainly.com/question/14391436
#SPJ2
The centers of two small metal spheres with a charge of 7.4 × 10−8 C are 10 cm from each other. a) What is the electric force between them? b) One of the spheres touches another identical neutral one, what is now the electric force if they are kept at the same distance? The constant in the Coulomb's law expression is k = 9.0 × 109 Nm2C2.
Answer:
answer is 9 in th by form of the good answer is the to k=9.0 10á gd gd
Which of the following equations has exactly one solution?
O A. 4x - 4 + 2x = 6x - 4
O B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
O D. 3x + 5 = 2x - 6
Please help me with this problem please ;(
9514 1404 393
Answer:
-2
Step-by-step explanation:
The average rate of change on the interval [3, 9] is ...
(f(9) -f(3))/(9 -3) = (41 -53)/(9 -3) = -12/6 = -2
f(x) = (2x² – 3)^(-2a? – 9)11
Answer:
-44ax^2-198x^2+66a+297
Step-by-step explanation:
there
how do I write an equation in standard form with the points (3,3) (0,-3) (2,-3)
Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 6 days. Let a random variable X denote the time (in days) until the next change. What is the probability that the time until the next change is greater than 9.5 days
Answer:
The probability will be "0.205".
Step-by-step explanation:
The probability that perhaps the time remains greater than 9.5 days before the next shift will indeed be:
⇒ [tex]P(X>9.5)[/tex]
⇒ [tex]1-P(X<9.5)[/tex]
⇒ [tex]1-(1-exp(\frac{-9.5}{6} ))[/tex]
⇒ [tex]0.205[/tex]
if a number contains decimal places then it is an irrational number
Answer:
sometimes true
Step-by-step explanation:
Toni is shopping for clothes at the store she buys 8 shirts for $8.00 what is the unit rate for the shirts?
Answer:
$1.00
Step-by-step explanation:
The unit rate in this scenario would be $1.00 , meaning that Toni is paying $1.00 for every shirt. This can be calculated by dividing the total price that she is paying for the shirts by the total number of shirts that Toni is purchasing like so...
$8.00 / 8 = $1.00 per shirt
The unit rate is basically the value over the denominator of 1 which would be the case as seen above since $1 buys 1 shirt ([tex]\frac{1 dollar}{1 shirt}[/tex]) as opposed to $8 dollars 8 shirts ([tex]\frac{8 dollars}{8 shirts}[/tex]) as mentioned in the question.
Solve the following equation
4(3-2x)=15
Answer:x= -3/8
Step-by-step explanation:
Answer:
-3/8
Step-by-step explanation:
4(3-2x)=15
-3/8
I need to do this assignment but I need help on how to draw it and answer the questions because I am confused on how to do these things. Thank you
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1)
The domain of a function is the set of values of x (the input) for which the function itself is defined.
Instead, the range of a function is the set of values of y (the output) that the function can take.
To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between
x = 0 and x = 300
So, the domain is [0,300].
To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between
y = 0 and x = 250
So, the range is [0,250].
2)
The slope of a function in a certain range is given by
where
is the change in the y-coordinate
is the change in the x-coordinate
For the initial climb (pink line), we have:
Therefore, the slope in this part is
We can now write the equation of the line in the form
y = mx + b
where b is the y-intercept: since it is zero, the line has simply the form
3)
Again, to calculate the slope of the hill, we use:
where
is the change in the y-coordinate
is the change in the x-coordinate
For the green hill, we have:
So the rate of change is
4)
As before, the rate of change of the hill is
For the blue hill, we have:
So the rate of change is
5)
To know which hill is steeper, we need to compare the magnitude of their rate of change.
In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.
For the green hill:
For the blue hill:
We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.
6)
A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).
This means that a function cannot have multiple values of y for the same x (the input).
By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.
THIS IS DUE TODAY! PLEASE ANSWER!: Find the value of 'X' in the triangle below
Answer:
Step-by-step explanation:
First find the angle in the lower left.
180 - 100 = 80
3x + 2x + 80 = 360
solve for x
5x = 280
5x/5 = 280/ 5
x = 56
Plug this in to make sure the equation is true
3(56) + 2(56) + 80 = 360
168 + 112 + 80 = 360
360 =360
Therefore x = 56
the first 5 multiples of 18 after 0 are?
Answer:
18,36,54,72,90 are first five multiples of 18
Step-by-step explanation:
Answer:
18,36,54,72,90
Step-by-step explanation:
PLEASE HELPPPPPP
the side length of the base of a rectangular prism with a height of 18 inches can be found with the equation b=(v/18)^1/2 v is the volume of the prism find the side length of the base of the volume of the prism is 4050 cubic meters
Answer:
15 if b is supposed to the side length, √15 if b is the base which is a square.
Step-by-step explanation:
The sum of three times a number and seven is 22
Answer:
3x+7=22
Step-by-step explanation:
three times a number is
[tex]3\times x=3x[/tex]
so the sum of 3x and 7 is 22
[tex]3x+7=22\\\\3x=15\\\\x=5[/tex]
you can leave it here
[tex]3x+7=22[/tex]
if you need the value of x
then
[tex]x=5[/tex]
Evaluate the following expression,
5x [7+ (10-2) + 4)
Answer: 95x
Step-by-step explanation: Remove parentheses. 5x(7+10-2+4)
Add 7 and 10.
5x(17-2+4)
Add 15 and 4.
5x multiped by 19
Multiply 19 by 5
95x
On average, Carson saves about 53% of his allowance each month. When creating a circle graph of what Carson does
with his money, which of the following fractions would be the best to represent how much he saves?
1/2 1/4 3/10. 3/4
Answer:
1/2
Step-by-step explanation:
1/2 would be the best fraction to represent how much he saves.
Which expression is equivalent to -4(w-1)
4w-4
4w
-4w+4
-5w
None of the above
Answer:
-4w+4
Step-by-step explanation:
Answer:
-4w+4 Is te correct answer
Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock
30%. What was the list price of the clock?
holour
Answer:
942.50
Step-by-step explanation:
725×30% or 0.3 = 217.5
217.5+725=942.5
Kiran says “If I walk 3 miles per hour toward you, and you walk 3.4 miles per hour toward me, it’s the same as if you stay put and I jog 6.4 miles per hour.” What do you think Kiran means by this? Is he correct?
Answer:
Yes it is the same. Since the total distance left behind per time unit would be the same. Just that He would Do that by himself.
Answer:
yes
Step-by-step explanation:
Y = 3x + 4 Y = 3x + 7
Answer:
y-7/ 12y+3
Step-by-step explanation:
Write an equation in slope-intercept form for the line with slope 2/5 and y-intercept -6 .
Answer:
[tex] y = \frac{2}{3}x - 6 [/tex]
Step-by-step explanation:
Recall that the the equation of a line in slope-intercept form is given as [tex] y = mx + b [/tex].
m = the slope of the line
b = the y-intercept. This is the point at which the line intercepts the y-axis.
We are given:
slope (m) = ⅖
y-intercept (b) = -6
All you need to do to get an equation of the line is to simply substitute m = ⅔ and b = -6 into [tex] y = mx + b [/tex].
[tex] y = \frac{2}{3}x + (-6) [/tex]
[tex] y = \frac{2}{3}x - 6 [/tex]
The equation for the line is .[tex] y = \frac{2}{3}x - 6 [/tex]
Molly’s hair was 20 inches long . Three years later it was 35 inches long
Answer:
Step-by-step explanation:
75
A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of LaTeX: 50cm^3/hr. At what rate is it's diameter decreasing
Complete question is;
A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm/hr. At what rate is its diameter decreasing?
Answer:
Diameter is decreasing at the rate of 5/(2πr) cm/hr
Step-by-step explanation:
We are told the stone is wearing away at a rate of 50 cm/hr. This means the volume is decreasing. Thus;
dV/dt = -50 cm/hr
Now, a grindstone is in the shape of a cylinder. Thus, volume of grindstone is;
V = πr²h
dV/dr = 2πrh
Now,to find the rate at which the diameter is decreasing, we'll write;
dr/dt = (dV/dt)/(dV/dr)
dr/dt = -50/(2πrh)
We are given;
Diameter = 200 cm
Radius; r = 200/2 = 100 cm
Thickness; h = 10 cm
Thus;
dr/dt = -50/(2π × r × 10)
dr/dt = -5/(2πr) cm/hr
The rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex] and this can be determined by using the given data.
Given :
A 10 cm thick grindstone is initially 200 cm in diameter and it is wearing away at a rate of 50 [tex]\rm cm^3/hr[/tex].
The following steps can be used in order to determine the rate at which grindstone diameter decreases:
Step 1 - According to the given data, the rate at which grindstone volume decreases is:
[tex]\dfrac{dV}{dt} = 50\;{\rm cm^3/hr}[/tex] --- (1)
Step 2 - The formula of the volume of the cylinder (grindstone) is given below:
[tex]V = \pi r^2 h[/tex]
Step 3 - Differentiate the above expression with respect to 'r'.
[tex]\dfrac{dV}{dr} = 2\pi r h[/tex] --- (2)
Step 4 - So, using the expression (1) and (2) the rate at which grindstone diameter decreases is:
[tex]\dfrac{dr}{dt}=\dfrac{\frac{dV}{dt}}{\frac{dV}{dr}}[/tex]
[tex]\dfrac{dr}{dt}=\dfrac{-50}{2\pi r \times 10}\\[/tex]
[tex]\dfrac{dr}{dt} = -\dfrac{5}{2\pi r }\; {\rm cm/hr}[/tex]
So, the rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex].
For more information, refer to the link given below:
https://brainly.com/question/12748872
Find the solution set for this inequality -2 x + 4 > -4x + 8.
Answer:
x > 2
Step-by-step explanation:
"The intersection of two planes is a line" is a statement that is generally accepted as true, but
cannot be proven to be true. What type of statement is this?
1. defined
2. undefined
3. postulate
4. proof
A postulate is something that is assumed to be true and there isn't a proof for it as its something foundational to help set up further proofs later down the road. Another example of a postulate is that a line is defined by two distinct points.
Point V is on line segment UW. Given VW = 5x - 4, UV = 2x, and
UW = 52, determine the numerical length of VW.
Answer:
VW = 36
Step-by-step explanation:
From the question, we are given:
VW = 5x - 4, UV = 2x,
UW = 52
Hence,
UV + VW= UW
2x + 5x - 4 = 52
7x = 52 + 4
7x = 56
x = 56/7
x = 8
VW = 5x - 4,
VW = 5(8) - 4
VW = 40 - 4
VW = 36
Determine whether the given relations are functions.
Answer:
Yes, this relation is a function.
Step-by-step explanation:
It is a function because every input (left side) only has one output (right side). It doesn't matter if an output has multiple inputs. As long as an input has only one output, it is a function
Ex: 3 = 8 & 7 NOT an input
4 & 3 = 8 AN input
Find the value of x so that the function has given value
M(x)=4x+15; m(x)=7
The price of a technology stock was $9.71 yesterday today the price rose to $9.84 find the percentage increase round your answer to the nearest 10th of a percent
Answer:
1.34%
Step-by-step explanation:
In order to find the percentage increase between these two prices, we must first find the difference in price. We calculate this by subtracting the final price by the initial price like so...
$9.84 - 9.71 = 0.13
Now we divide the difference by the initial price to find what percentage of the initial price this difference is, since this percentage difference was added to the initial price to get the new and final price point.
0.13 / 9.71 = 0.013388 ... multiply by 100 to get percent value
0.013388 * 100 = 1.3388% or 1.34% rounded.