The number of randomly selected Americans that must be surveyed is equal to 38 if the confidence interval is 97.5% with a 0.16 margin of error.
First, we calculate the critical value as follows;
a = (1 - 0.975) = 0.025 = 0.025 / 2 = 0.0125 = (1 - 0.0125) = 0.9875
Z - Critical value = NORM.S.INV (0.9875) = 1.96
As margin of error(ME) = 0.16
Therefore;
n = pq(Z²) / ME²
n = 0.5 × 0.5 (1.96)² / (0.16)²
n = 0.25 × 3.8416 / 0.0256
n = 0.9604 / 0.0256
n = 37.515
Rounding it to the nearest whole number;
n = 37.515 = 38
Hence 38 randomly selected Americans must be surveyed if the estimated confidence interval is 97.5% and the margin of error is 0.16.
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Solve 2x^2+3x-1=0 by completing the square
Answer:
x=(-3-√17)/4
x=(-3+√17)/4
Step-by-step explanation:
2x^2+3x-1=0
it can rewrite as,
x^2+3x/2-1/2=0
now adding and subtracting (3/4)^2 , in R.H.S,
x^2+3x/2+9/16-9/16-1/2=0
(x+3/4)^2-17/16=0
(x+3/4)^2-((√17)/4)^2=0
(x+3/4+√17/4)(x+3/4-√17/4)=0
x=(-3-√17)/4
x=(-3+√17)/4
Number 9 and 10 I’m stuck.
9:
By taking the quotient between the total debt and what they earn in a sold-out show, we conclude that they need to sell a total of 7 sold-out shows.
10:
A discount of 30%. Correct option is B.
How many sold-out shows they need to cover the loan?Answering part 9:
We know that they asked for a loan of $8,000, such that an interest of the 6% is applied to this, so the total amount that they need to return is:
$8,000*(1 + 6%/100%) = $8,000*(1.06) = $8,480
Now we know that the theater has 150 seats, and each ticket costs $8.50, so for every sold-out show they earn a total of:
T = 150*$8.50 = $1,275
Then the number of sold-out shows that they need is given by the quotient:
$8,480/$1,275 = 6.65
Rounding to the next whole number we get to 7. To cover the debt, they need to sell a total of 7 sold-out shows.
10. The original price is $180 and she pays $126, then the discount k is:
$180*k = $126
k = $126/$180 = 0.7
and 1 - 0.7 = 0.3
So the discount is of the 30%.
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I took a quiz about a week ago as of posting this and I found that this question was hard for me to answer I was wondering how I could find an easier way to solve this besides doing a long equation for scale factors. I am only here to learn so any answers to this are great.
Answer:
d(-6,-9),e(3,-9),f(3,-3),g(-6,-3
Step-by-step explanation:
first you look at the location of the point and follow in the direction of which number it is on the X line, then in the direction of which number it is on the Y line and in the parentheses of the coordinates, first write the number from the X line, then from the Y line
ps: I hope I helped you a bit :)
helpe3 meeeeeeeeeeeeeee please
Lines through the given points are as follow:
a. Line1 is perpendicular to line2.
b. Line1 is neither perpendicular nor parallel to line2.
c. Line1 is parallel to line2.
As given in the question,
Slopes of the lines through the given points are as follow:
Let m₁ and m₂ be the slope of line1 and line2 respectively.
a. Line1 ( 2,-3) , (-4, -6) and Line2 (-3,2) , (2,-8)
m₁=(-6+3)/ (-4-2)
=1/2
m₂=(-8-2)/ (2+3)
=-2
m₁ × m₂ = -1
Line1 and line2 are perpendicular.
b. Line1(-4, -5) , (4,1) and line2 (6,10) , (-3,-2)
m₁=(1+5)/ (4+4)
=3/4
m₂=(-2-10)/ (-3-6)
=4/3
m₁ × m₂=1
Line1 and line2 are neither perpendicular nor parallel .
c. Line1 (0,-4) , (-2,-8) and line2 (-1,5), (1,9)
m₁=(-8+4)/ (-2-0)
=2
m₂=(9-5)/ (1+1)
=2
m₁=m₂
Line1 and line2 are parallel
Therefore, lines through the given points are as follow:
a. Line1 is perpendicular to line2.
b. Line1 is neither perpendicular nor parallel to line2.
c. Line1 is parallel to line2.
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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
The solution –0.2 s can be eliminated because time cannot be a negative value.
The solution –0.2 s can be eliminated because the pass was not thrown backward.
The solution 2.7 s can be eliminated because the pass was thrown backward.
The solution 2.7 s can be eliminated because a ball cannot be in the air for that long due to gravity.
The solution that will be eliminated when a quarterback throws an incomplete pass is –0.2 s can be eliminated because time cannot be a negative value
What is parabolic equation?This is the equation used to trace the path made by a parabola. It is another name for quadratic equation.
We can say that the football traced a parabolic path represented by the equation h(t) = –16t2 + 40t + 7.
Parabolic equation will always produce two solutions then depending on the applicability of the solution the best option will be picked.
In this case time, which cannot be a negative value hence option A is the correct answer
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there is a line that includes the point (–2, 6) and has a slope of 2 What is its equation in slope-intercept form?
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -6= 2 (x +2) \\\\\\ y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}[/tex]
73.261-2.852 =______
Answer:70.409
Step-by-step explanation:73.261-2.852
7x^4 +1
The expression represents a___
polynomial with __ terms .
The constant term is __, the leading terms is __, and the leading coefficient is __.
the answer is 29 hope this helps
when you are finding the perimeter of a shape do you cancel out the negatives
Answer:
Yes, you would cancel them out.
Step-by-step explanation:
You cannot have negatives on the sides of a shape for perimeter.
Write 3 functions. In the first function, y should vary directly with x. In the second function, y should vary inversely with x. In the third function, the relationship between x and y should be neither inverse variation nor direct variation. Describe the graph of each function and give a real-world example for each.
first function: y = ([tex]\frac{3}{4}[/tex])x
Second function: y=[tex]\frac{12}{x}[/tex]
Third function y = 30 + 2x.
A) In the first function, y directly depends on x.
first formula: y = ([tex]\frac{3}{4}[/tex])x
2) Graph: It has a slope of ([tex]\frac{3}{4}[/tex]) and is a straight line that goes through the origin. According to the slope, the function changes at a rate of 3 units for every 4 units of x-value growth, or 0.75 units for every additional unit of x-value growth.
3) Use a real-world example
According to a cake recipe, 3 cups of sugar should be combined with every 4 cups of flour. Therefore, if you have 12 cups of sugar, how much flour do you need?
Y = ([tex]\frac{3}{4}[/tex])x, so if x = 3, y =([tex]\frac{3}{4}[/tex])×12= 9.
Given that : the variation is direct, you must multiply the number of cups of sugar by the constant rate, which is ([tex]\frac{3}{4}[/tex])x, to determine how many cups of flour correspond to the specified amount of sugar.
B) The second equation has an inverse relationship between y and x.
Inverse variation causes either y = constant / x or y*x = constant.
In other words, if x increases, y will decrease by the same amount as x increases.
1) formula: y=[tex]\frac{12}{x}[/tex]
2) Graph: The hyperbola, a diminishing line extending from left to right, is the shape of this graph. Both the x-axis and the y-axis asymptote to zero. This implies that neither x nor y can be zero.
As the x-value gets closer to 0, the y-value gets closer to positive or negative infinity; conversely, as the y-value gets closer to 0, the x-value gets closer to positive or negative infinity.
The graph is a declining curve in the first quadrant if you pick the positive numbers (x and y are positive).
The graph has a declining slope in the third quadrant if you pick the negative values (x and y are negative)
3) An actual world instance.
a uniform motion's relationship between time and velocity.
If an object runs a constant distance, time slows down proportionately as velocity rises.
Give the distance between cities A and B as 100 kilometers.
How long will it take to get from point A to point B traveling at 50 km/h or 25 km/h?
100 kilometers = speed * time
at 50 km/h: t = [100 km] / [50 km/h] = 2 hours 100 km = 50 km/h * t
at 25 km/h: t = [100 km] / [25 km/h] = 4 hours; 100 kg = 25 km/h * t.
C) In the third scenario, x and y should not have an inverse variation or a direct variation.
There are infinite types of functions that are neither inverse variations nor direct variations, including trigonometric sine, exponential, logarithmic, exponential, linear (that do not pass through the origin), and exponential, quadratic, and exponential.
1) A function illustration is y = 30 + 2x.
2) Graph: The line has a slope of 2 and a y-intercept of 30.
3) A case in point
In order to create chairs, it costs 30 dollars to rent the facility plus 2 dollars for each chair, for a total cost of 30 + 2x.
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on a multiple choice test with six possible answers for each question, what is the probability of answering a question correctly if you make a random guess?
Answer:
17%
Step-by-step explanation:
Hello!
Out of the 6 options, only 1 option will be correct. This can be represented as a ratio of 1:6.
If you randomly guess, there is an equal chance of choosing any of the 6 options.
To find the percentage of guessing the correct option, simply divide 1 by 6 (1 option is correct out of 6), and multiply the outcome by 100 (for percentage).
1:6 = 1/61/6 = 0.16666..... ≈ 0.170.17 * 100 = 17%The probability of getting an answer correct would be 17%.
The probability of getting an answer wrong would be 83%, which can be found by subtracting 17% from 100%.
What are some things that lincoln and Monica have in common in taking sides
The Roman Empire began in 31 B.C. and fell to the Goths in A.D. 476 How long did the Roman civilization last?
In case whereby the the Roman Empire began in 31 B.C. and fell to the Goths in A.D. 476,the Roman civilization lasted for 445 years.
What was Roman Empire?The Roman Empire can be described as the post-Republican period that can be associated with the ancient Rome , it can be described as the empire that came into the lime light around the 8th century BC , and actually came to an end around 5th century AD and the period it laste can be calculated below as :
In this case as regards to the question, we can calculate how long the Roman civilization lasted as [476+(-31)]
=445 years.
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the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 35 and 56 minutes. one student is selected at random. find the probability of the following events.
The amounts of time it takes for a student to complete a statistics quiz uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events.
a) the student requires more than 55 minutes to complete quiz
b) the student completes the quiz in a time between 30 and 40 minutes
c) the student completes the quiz in exactly 37.23 minutes
A student to complete a statistics quiz uniformly distributed between 30 and 60 minutes The probability of the events are a) 1/6, b )1/3 c) 0
Given, X similar U( a = 30, b = 60)
f(x) =1/60-30, 30 ≤ X ≤60
f(x) = 1/30, 30 ≤ X ≤60
a) the student requires more than 55 minutes to complete quiz
P(X > 55) = ∫_55^60▒f(x)dx = ∫_55^60▒〖1/30dx〗 = 1/30[x]6055 = 1/6
b) the student completes the quiz in a time between 30 and 40 minutes P (30 < X < 40) = ∫_30^40▒f(x)dx == ∫_30^40▒〖1/30dx〗 = 1/30[x]4030 = 1/3
C) the student completes the quiz in exactly 37.23 minutes P(X = 37.23) = ∫_37.23^37.23▒f(x)dx=∫_37.23^37.23▒〖1/30dx〗 = 0
A student to complete a statistics quiz uniformly distributed between 30 and 60 minutes The probability of the events are a) 1/6, b )1/3 c) 0
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358 |-14| how do I do this
Complete the statement to describe the expression 4.4.4.
You can write the expression as a power, using
as the exponent.
?
16. If 45/n, what other whole numbers divide n? Why?
Answer:
1,3,5,9,15,45
Step-by-step explanation:
All factors of 45 to get a whole number
Answer:
90, 135, 180, 225, 270... ∞
Step-by-step explanation:
All multiples of 45 are divisible by n
Hope this helps and feel free to mark this as brainliest :)
what is the answer to
32z-48 using factoring
The answer to 32z - 48 using factoring is 3/2.
Given,
32z - 48
We have to find the answer using factoring:
Factoring:
Finding things to multiply together to produce an expression is known as factoring. It is comparable to splitting an expression into numerous smaller expressions.
Here,
32z - 48 = 0
Add 48 to both sides
32z - 48 + 48 = 0 + 48
32z = 48
Divide 32 on both sides
32z/32 = 48/32
z = 48/32
Now, we can factorize 48/32
Take 2 as common factor
(48/2) / (32/2) = 24/16
Again, take 2 as common factor
(24/2) / (16/2) = 12/8
Now, take 4 as common factor
(12/4) / (8/4) = 3/2
Here, z = 3/2
That is, the answer for 32z - 48 using factoring is 3/2.
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If f(x)=1-x, which value is equivalent to f1?
0
√√√2
Answer: f(1)=0
Step-by-step explanation:
f(x)=1-x
f(1)=1-1
f(1)=0
How do you write 0.133333... as a fraction
The expression of the number 0.133333 as a fraction would give us 133333/1000000.
What is a fraction?Let us recall that the term fraction is used to show that there is a top and a bottom part in the expression. The top part of the fraction is called the numerator while the bottom part of the fraction is called the denominator.
If we want to convert the fraction as we have it back to the decimal then we just have to divide the numerator by the denominator and we are back to the decimal. The decimal is marked by the presence of a decimal point.
To convert 0.133333 to fraction, we would take the decimal point as 1 and all other digits after it as zero thus we have;
133333/1000000.
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Jose fue a una papeleria y saco 10 fotocopias a color tamaño carta a 2.75 cada una y 100 fotocopias blanco y negro tamaño carta a 0.75 cada una ¿cuanto pago en total por todas las fotocopias?
The total cost that Jose will pay for the photocopies is $102.50.
How to calculate the amount?From the information, the following can be deduced:
Number of letter size photocopies = 10
Amount for each color photocopies = 2.75
Number of black and white photocopies = 100
Amount for each = 0.75
Therefore, the total cost will be:
= Cost of colored + Cost of black and white
= (10 × 2.75) + (100 × 0.75)
= 27.5 + 75
= $102.50
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Jose went to a stationery store and took out 10 letter size color photocopies at 2.75 each and 100 letter size black and white photocopies at 0.75 each. How much did he pay in total for all the photocopies?
PLEASE HELP!! thank you!
Answer:
Step-by-step explanation:
36=p*60
36/60=(p*60)/60
p=0.6 or 60%
60%
Pls brainliest
What is the least integer? explain.
Answer:
The function whose value at any number x is the smallest integer greater than of equal to x is called the least integer function.
Step-by-step explanation:
It is denoted by ⌈x⌉ It is also known as ceiling of x. For example ⌈3.578⌉ = 4 , ⌈0.78⌉ = 1 , ⌈-4.64⌉ = - 4.
-5/9 multiplied by (-4)
Answer:
Step-by-step explanation:
-5/9* -4 = 20/9
Answer=20/9
When you multiply them, there is nothing to simplify in any of them. So when you multiply, the negatives become a positive because -*- is + so the answer is 20/9.
Find two consecutive whole numbers that √72 lies between.
The two consecutive whole numbers that √72 lies between are 8 and 9.
As per the question statement, we are supposed to find two consecutive whole numbers that √72 lies between.
We know,
8 squared is 64 and 9 squared is 81
since 72 lies in between 64 and 81, then the square root must lie between 8 and 9 which are also whole numbers and consecutive too.
Hence we accept out answer to be 8 and 9.
Hence the two consecutive whole numbers that √72 lies between are 8 and 9.
Whole numbers: Whole Numbers are all numbers, including zero and the natural numbers but not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}To learn more about whole numbers, click on the link given below:
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Compute the probability that a five-card poker hand is dealt to you that contains all hearts.
The probability of getting all 5 cards hearts 13C₅/ 52C₅.
What is probability?The probability of an event occurring is defined by probability.
There are many instances in real life where we may need to make predictions about how something will turn out.
The outcome of an event may be known to us or unknown to us.
When this happens, we say that there is a chance that the event will happen or not.
Given : A five card poker card
To find : the probability of all hearts
Let E be the events of getting all 5 cards of hearts
therefore n(E)= [tex]13C[/tex]₅
As we know that probability is defined as total number of favourable outcomes divided by total number of possible outcomes.
Thus the required probability is 13C₅/ 52C₅
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help!
Q. in a supermarket , five chicken cost 18.25 . what is the cost of one chicken ?
Answer:
each chicken cost 3.65
Step-by-step explanation:
divide 18.25 by 5 and you'll get 3.65
What calculation is showed on the number line
The calculation shown in the number line is -4/10 + ( -7/10) = - 1 1/10
What is a number line?
This is a sequential arrangement of numbers in a straight line. The scale of number line is shown to suit the problem at hand.
The number line in the question here has a scale of 1. This means that every number represent a unit. However in between the numbers are 10 strokes.
The value of each stroke is gotten from division of one by ten which is
1 ÷ 10 = 1/10
So every line in the number line represent 1/10. The positive side is 1/10 while the negative side is -1/10
The calculation done here is counting from 0 in the negative direction to get -4/10. Then adding -7/10 units to arrive at the point which is -1 1/10
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Doughnuts are sold in bags and bags and doughnuts. a bag holds 10 doughnuts and a carton holds 10 doughnuts. tom buys b bags of doughnuts and c cartons of doughnuts he buys a total of t doughnuts write down a formula for t in terms of b and c
Answer:
t = 10b + 10c
Step-by-step explanation:
As stated in the problem, 1 bag holds 10 doughnuts so that give us 10b since we don't know how many bags were bought/sold but we do know how many comes in each. Same goes for cartons.
Were asked to write a formula for t, and since we don't know how many bags(b) or cartons(c) were sold, our t remains t.
A grocery store clerk can scan 1 product every
1
2
of a second. At what rate can she scan products?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The rate at which the grocery store clerk can scan products is 2 products per second.
What is the rate?Rate is the speed at which an activity can be carried out. Rate can be determined by dividing the total products that are bagged by the time it takes to bag the product.
Division is used to determine the product of two or more numbers. The sign that represent division is ÷. Division is a mathematical operations. Other mathematical operations include addition, subtraction and multiplication. Division entails grouping a number into equal groups using another number.
Rate = number of products ÷ time
1 ÷ 1/2
1 x 2 = 2 products per second
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