Using the z-distribution, it is found that the 95% confidence interval is (0.46, 0.526), and it does not provide strong evidence against that belief.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We have that a random sample of 864 births in a state included 426 boys, hence the parameters are given by:
[tex]n = 864, \pi = \frac{426}{864} = 0.493[/tex]
Then, the bounds of the interval are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 - 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.46[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 + 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.526[/tex]
The 95% confidence interval estimate of the proportion of boys in all births is (0.46, 0.526). Since the interval contains 0.506, it does not provide strong evidence against that belief.
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help, I’m terrible with percentages
Bob has a 1% chance of getting a prize from a cereal box, while the other prizes have a 99% chance for him to get. How many cereal boxes does Bob have to buy in order to get the prize? Show your work.
I’m pretty sure you’re supposed to find out something like “one in a million chance!”
Answer:
99 boxes im sure
if a sum of money increased by 1/5 of itself every year and in 5 years amounts to Rs.8546,find the sum
Answer:
Answer :
Given : If a sum of money amounts to Rs 2200 in 5 years
Let sum of money = x
And as given : The interest is 3838 of the principal . So we get
x ( 3838 ) = 2200 - x
3x = 17600 - 8x
11x = 17600
x = 1600
So, Sum of money = Rs . 1600
Then interest = 2200 - 1600 = Rs . 600
Let Rate of interest = r %
And we know Simple interest = P × r × t100P × r × t100 , So we get
⇒1600 × r × 5100 = 600⇒16× r × 5100 = 6⇒80r = 600⇒r = 60080 = 152 = 712%⇒1600 × r × 5100 = 600⇒16× r × 5100 = 6⇒80r = 600⇒r = 60080 = 152 = 712%
So
Step-by-step explanation:
which graph represents the parabola with the equation y^2=-1/3x
Step-by-step explanation:
The graphs are not give but the graph looks like the above picture.
Fill in the blank
The composite figure shown is made up of a cylinder and a
12 cm
4 cm
20 cm
Answer: cone
Step-by-step explanation:
The bottom figure is a cylinder. A cylinder is basically a rectangle wrapped around two circles.
The top figure is a cone. A cone’s net looks like a triangle with a curved base wrapped around a circle. If you don’t believe the top figure is a cone, think about what ice cream cones look like. The top figure is a cone.
. Carlee surveyed customers as they left a convenience store. She asked them, “How many items did you
purchase?” The results are shown in the line plot.
(a) How many customers were surveyed?
(b) What was the greatest number of items purchased by a customer?
(c) How many customers purchased 9 items?
(d) How many customers purchased at least 5 items?
(e) What was the median number of items purchased?
Answer:
We need the line plot in order to solve the questions.
Step-by-step explanation:
8) A company sells small and large photo books. Each page of a small photo book costs
the same. The table below shows the relationship between the number of pages in a
small photo book and the total cost of the photo book.
Part A) What is the cost per page for a small photo book?
Small Photo Book
Number of Pages
Total Cost ($)
30
20
32
48
57
The cost per page is $1.5 and 38 pages of the book will cost $57
ProportionsData;
number of page = 20cost = $30To solve this question, we have to know the cost of one page of the book.
In the first scenario, 20 pages cost $30, let's find the cost of one page here.
[tex]20 page = \$30\\1 page = x\\x = \frac{30}{20}\\x = 1.5[/tex]
We can confirm our answer here by testing with the second scenario;
[tex]32 page = \$48\\1page = y\\y = \frac{48}{32} = 1.5[/tex]
Now can say that one page of the book cost $1.5, let's divide 57 by this to determine the number of pages
[tex]z = \frac{57}{1.5} \\z = 38[/tex]
From the calculations above, 38 pages of the book will cost $57.
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Prepare an amortization schedule for the first three months on a loan of $87,000 at 6% for 20 years.
Answer:
see attached
Step-by-step explanation:
An amortization schedule is conveniently prepared using a spreadsheet. It has the formula built in for computing the payment value.
__
The amount of the payment going to interest is the product of the outstanding balance and the monthly interest rate (=6%/12). In the attached, the amount of interest due is rounded to cents. The remaining amount of the payment reduces the outstanding balance.
The attachment shows the payment calculation and the amortization schedule for the first 5 payments.
Please help i will give brainliest to the right answer
Step-by-step explanation:
Jacinta is completely right while Tess made a mistake on the 3rd step.
she mistakenly plugged in the y value as X, and plugged in the X value as y.
so Tess is incorrect
A pet store has 11 puppies, including 5 poodles, 3 terriers, and 3 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement, find the probability that Aaron selects a retriever, given that Rebecka selects a poodle.
Answer: 0.2066
Step-by-step explanation:
Probability of Rebecka selecting a poodle = 5/11
Probability of Aaron selecting a poodle = 5/11
Both select one puppy at random with replacement, so their choices are independent.
Thus, probability that both select a poodle = [tex](5/11)\times(5/11)[/tex]
[tex]= 25/121 \approx 0.2066 \ $or 20.66\%[/tex]
solve this following equations. 1.x-2/5-x-4/2=2
Answer: hii
There are no values of x
that make the equation true.
Step-by-step explanation:
No solution.
hopefully this helps you.
- Matthew
What is the length of a rectangle formed from the lateral surface of a cylinder?
Answer:
B. 2[tex]\pi[/tex]r
Step-by-step explanation:
Pleasez help i have to complete this by the end of the 10 min
Answer:
Step-by-step explanation:
red shirt: 10%
green shirt: 20%
not choosing white 10%
not chosing black 20%
where orange shirt???
Write an equation of the line in slope-intercept form: y-intercept of 2, x-intercept of 4
Answer:
[tex]\sf y=-\dfrac12x+2[/tex]
Step-by-step explanation:
y-intercept is when x = 0, so (0, 2)
x-intercept is when y = 0, so (4, 0)
[tex]\sf slope=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{0-2}{4-0}=-\dfrac12[/tex]
Slope-intercept form of linear equation: [tex]\sf y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
Given:
[tex]\sf m=-\dfrac12[/tex]b = 2[tex]\sf \implies y=-\dfrac12x+2[/tex]
what is the median mean mode and range of 1,3,5,8,10?
Answer: median: 5
mode: 5.4
Range: 9
Step-by-step explanation:
Median: middle of the numbers
Mode: Add them all together and divide by number of terms
Range: Most minus least
I need help or my grade is going to go to a f-
Answer:
1
Step-by-step explanation:
65.751 = 6 x 10 + 5 x 1 + 7 x 1/10 + 5 x 1/100 + 1 x 1/1,000
6 x 10 = 60
5 x 1 = 5
7 x 1/10 = 0.7
5 x 1/100 = 0.05
1 x 1/1000 = 0.001
60 + 5 + 0.7 + 0.05 + 0.001 = 65.751
Can someone help me plssss!!!
The dimensions of a right rectangular prism are shown below.
How many cubes with side lengths of 1 over 6 inch are needed to fill the prism without gaps or overlaps?
show the work pls.
Answer:
a.
Step-by-step explanation:
open chormecanvis and draw little cubes on the side of the prisum, thats wahat i did
Which decimal is greater: 7.09 or 7.1?
Answer: 7.1
Step-by-step explanation:
7.09<7.10
7.10=7.1
sometimes adding a zero helps
The average mass of a grain of sand from
a certain beach is 9 × 10-8 kilograms.
What is this value in grams? Give your
answer in standard form.
Answer:
0.0009 grams
Step-by-step explanation:
The mass of the grain sand is:
[tex]9 \times {10}^{ - 8} \: Kg[/tex]
To convert kilograms to grams we divide by 1000 (1 × 10³)
[tex] \frac{9 \times {10}^{ - 8} }{1 \times {10}^{3} } [/tex]
Which gives us:
[tex]9 \times {10}^{ - 5} [/tex]
[tex]9 \times {10}^{ - 5} = 0.0009 \: g[/tex]
A right triangle has one angle that measures 60°. What is the measure of the other acute angle?
Answer:
30°
Step-by-step explanation:
The angle sum theorem tells you the sum of angles in any triangle is 180°. A right triangle has one angle that is 90°, so the sum of the remaining two acute angles is 180° -90° = 90°. That is, the acute angles in a right triangle are complementary.
__
The other acute angle is ...
90° -60° = 30°
A spinner with 10 equally sized slices has 2 blue slices, 4 yellow slices, and 4 red slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a blue slice? Write your answer as a fraction in simplest form.
Answer:
1/5
Step-by-step explanation:
the number of all slices is 10.. and you got 2 blue ones
so you get 2/10 and if you simplify it you get 1/5
Each hamburger patty is 1/8 pound. Drag the correct equation to each amount to show how many 1/8 pound hamburger patties can be made.
Answer:
For 3 pounds, 3 ÷ 1/8 = 54
For 7 pounds, 7 ÷ 1/8 = 56
Question 1a:
Compute the Laplace Transforms of
f(x) = { x² +2x +1 , x < 3
{ e⁻⁵ˣ , x ≥ 3
This is made easy if you know the Laplace transform pair
[tex]u(t - c) y(t - c) \mapsto e^{-cs} Y(s)[/tex]
where u(t) is the Heaviside step function and Y(s) is the Laplace transform of y(t).
We rewrite f, g, and h in terms of u :
[tex]f(x) = (x^2+2x+1) (u(x) - u(x-3)) + e^{-5x} u(x-3)[/tex]
[tex]g(x) = \sin(3x) (u(x-5) - u(x-10))[/tex]
[tex]h(x) = (u(x) - u(x-4)) + 2(u(x-4)-u(x-8)) + 3 (u(x-8)-u(x-16))[/tex]
and we also rearrange terms to get the right shift in argument:
[tex]f(x) = (x^2+2x+1) u(x) - ((x-3)^2+8(x-3)+16) u(x-3) + e^{-15} e^{-5(x-3)} u(x-3)[/tex]
[tex]g(x) = [\cos(15) \sin(3(x-5)) + \sin(15) \cos(3(x-5))] u(x-5) \\\\ ~~~~~~~~~~- [\cos(30) \sin(3(x-10)) + \sin(30) \cos(3(x-10))] u(x - 10)[/tex]
[tex]h(x) = u(x) + u(x-4) + u(x-8) - 3 u(x - 16)[/tex]
Now we can apply the known transform pair, along with
[tex]x^n \mapsto \dfrac{n!}{s^{n+1}}[/tex]
[tex]e^{ax} \mapsto \dfrac1{s-a}[/tex]
[tex]\sin(ax) \mapsto \dfrac{a}{s^2+a^2}[/tex]
[tex]\cos(ax) \mapsto \dfrac{s}{s^2+a^2}[/tex]
The transforms of f, g, and h are then
[tex]F(s) = e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-15} e^{-3s}}{s + 5} \\\\ = \boxed{e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-3(s+5)}}{s + 5}}[/tex]
[tex]G(s) = \dfrac{3\cos(15) e^{-5s}}{s^2+9} + \dfrac{s \sin(15) e^{-5s}}{s^2+9} - \dfrac{3\cos(30)e^{-10s}}{s^2+9} - \dfrac{s \sin(30) e^{-10s}}{s^2+9} \\\\ ~~~~~~~ = \dfrac{3(\cos(15)-\cos(30)) + s(\sin(15) - \sin(30))}{s^2+9} \\\\ ~~~~~~~ = \boxed{\dfrac{6\sin\left(\frac{45}2\right)\sin\left(\frac{15}2\right) - 2s \cos\left(\frac{45}2\right)\sin\left(\frac{15}2\right)}{s^2+9}}[/tex]
[tex]H(s) = \boxed{\dfrac{e^{-s} + e^{-4s} + e^{-8s} - 3 e^{-16s}}s}[/tex]
Resulting set please help !!!!
The union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.
What is ordered pair?The ordered pair is the pair of two numbers which represented in a manner that it provides a particular order.
In an order pair, the first term indicates the x-coordinate, while the second term indicate the y coordinates. The ordered pair are written in close bracket in the following way.
[tex](x,y)[/tex]
The given set is U(a,e,i,o,u), in which,
[tex]X=(a,i,o)\\Y=(o,e,u)\\Z=(i,o,u)[/tex]
[tex]X\cup Y[/tex]For the union, write all the terms of X and Y set.
[tex]X\cup Y=(a,e,i,o,u)[/tex]
[tex]X\cap Z[/tex]For the intersection, write all the common terms of X and Z set.
[tex]X\cap Z=(i,o)[/tex]
[tex]X\cap Y\cap Z[/tex]For the intersection, write all the common terms of X , Y and Z set.
[tex]X\cap Y\cap Z=(o)[/tex]
Hence, the union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.
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Samantha and Jeanie are each rolling a fair 6-sided die with the numbers 1 through 6. They are trying to see who can roll the most
number of odd numbers. Their rolls are shown in the given tables
Whose name experimental probability is closer to the theoretical probability of rolling an odd number
A.Samantha’s
B. Both Jeanie’s and Samantha’s experimental probability’s are very close to the theoretical probability
C. Jeanie’s
D. It can not be determined because there is not enough information
There are 3 odd numbers on the die so the theoretical probably of getting odd is 3/6 = 1/2
Samantha that rolled the die 4 times and got odd every time so her experimental probability was 4/4 = 1
Jeanie rolled the die 16 times and got 6 odds for an experimental probability of 6/16 = 3/8
3/8 is closer to 1/2
Answer: C. Jeanie’s
There are 8 ounces in a ½ pond. How many ounces are in 7¾ lbs
7 3/4 pounds contains 124 ounces
8 ounces = 0.5 pound
X ounces = 1 pound
X = 8 / 0.5 = 16 ounces
7 3/4 = 7.75
7.75 contains = 7.75 * 16
= 124 ounces
Rewrite each equation without absolute value for the given conditions. y=|x-3|+|x+2|-|x-5| if -2
The equation y = |x-3| + |x+2| - |x-5| is an absolute value equation
The equivalent equation of y = |x-3| + |x+2| - |x-5| if -2 < x < 3 is y = x
How to rewrite the absolute value equation?The equation is given as:
y = |x-3| + |x+2| - |x-5|
The condition is given as:
if -2 < x < 3
Split and solve each term of the absolute value equation.
|x-3| = -(x - 3) = 3 - x....... because x < 3
|x+2| = x + 2 because -2 < x
|x-5| = -(x - 5) = 5 - x....... because x < 5
So, we have:
y = |x-3| + |x+2| - |x-5|
This gives
y = (3 - x) + (x + 2) - (5 - x)
Open the brackets
y = 3 - x + x + 2 - 5 + x
Evaluate the like terms
y = x
Hence, the equivalent equation of y = |x-3| + |x+2| - |x-5| if -2 < x < 3 is y = x
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An ice cream store sells 2 drinks, in 4 sizes, and 6 flavors. In how many ways can a customer order a drink?
There are
ways that the customer can order a drink.
Answer:
Step-by-step explanation:
Drinks:
number of drinks - 2Number of sizes - 4Number of choices - 4 * 2 = 8Answer: 8
two examples of likely and unlikely events in mathematics probability
Answer:
what's likely is times or Addition less like likely is subtraction or rounding
Solve the equation for x. Assume a≠0. 4=ax−14
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve for x ~
[tex]\qquad \tt \dashrightarrow \:4 = ax - 14[/tex]
[tex]\qquad \tt \dashrightarrow \:ax = 4 + 14[/tex]
[tex]\qquad \tt \dashrightarrow \:ax = 18[/tex]
[tex]\qquad \tt \dashrightarrow \:x = \dfrac{18}{a}[/tex]
Jason and his three friends went bowling. They bowled all afternoon and each paid $3.25 per game. Jason had a coupon for one free game. Three of his friends paid $2.75 each to rent shoes. Using this information, Jason writes the expression 3.25\left(g-1\right)+2.75\left(3\right). What does Jason’s expression represent? the number of friends who bowled the number of friends who bowled the number of games Jason and his friends bowled the number of games Jason and his friends bowled the amount of money Jason saved using the coupon the amount of money Jason saved using the coupon the amount of money Jason and his friends spent that afternoon
The expression 3.25(g-1) + 2.75(3) by Jason and his friends is a linear expression
The number of friends who bowled is 3The number of games Jason and his friends bowled is gThe amount of money Jason saved using the coupon is 3.25 The amount of money Jason and his friends spent that afternoon is 3.25(g-1) + 2.75(3)How to interpret the expression?The expression is given as:
3.25(g-1) + 2.75(3)
The above expression means that:
-1 represents the coupon on one free game3.25 represents the amount paid per game2.75 represents the amount paid to rent a shoe3 represesents the number of shoes they rentRead more about linear expressions at:
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