Answer:
A sample of 151 cans must be selected.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation of fill volumes is 0.05 ounce.
This means that [tex]\sigma = 0.05[/tex]
How large a sample of cans must be selected to estimate the population mean fill volume with a 95% confidence interval that has a margin of error of 0.008 ounce?
We need a sample of n.
n is found when M = 0.008. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.008 = 1.96\frac{0.05}{\sqrt{n}}[/tex]
[tex]0.008\sqrt{n} = 1.96*0.05[/tex]
[tex]\sqrt{n} = \frac{1.96*0.05}{0.008}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.05}{0.008})^2[/tex]
[tex]n = 150.1[/tex]
Rounding up:
A sample of 151 cans must be selected.
teh velocity of a partilce in ft/s, moving along the x axis is given the function v(t) e^t te^t when 0
The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.
What is Acceleration ?
Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.
Given,
Velocity v= x² − 5x + 4
now, the acceleration
a = dv/dt
a = 2x (dx/dt) - 5x(dx/dt)
given that, v= dx/dt =0
so, a = 2x*0−5*0
a=0 m/sec²
so, the acceleration is zero ,when the velocity is zero.
Hence ,The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.
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Given question is incomplete , the complete question is given below:The velocity of a moving particle along the x-axis is given as v= x² − 5x + 4, where x denotes the x−coordinate of the particle in meters. Find the magnitude of the acceleration of the particle when the velocity of the particle is zero?5. (8.51) What is the equation of the line shown?
HELP PLEASE!!
Answer:
D
Step-by-step explanation:
D. If it's not D, C. It's a negative slope with a negative y-intercept of -1
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:
point
vertex
one
face
face
circular
length
area
volume
Find the perimeter of the figure shown above with aside length 5 unit
The perimeter of the figure with side length of 5 units is 50 units
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = rectangle
Smaller shapes = squares
Side lengths = 5 units
The perimeter of the figure is calculated as
Perimeter = Number of visible sides * Side length of the square shape
In this case, we have
Number of visible sides = 10
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 10 * 5
Evaluate the products
Perimeter = 50 units
Hence, the perimeter is 50 units
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Please help please and thank you
Answer:
Z
Step-by-step explanation:
Angle V is congruent to angle z because they have the same placement in the letter order.
Abdul was scuba diving 76 feet below the surface of the ocean. To get a closer look at a school of fish, he swam up 28 feet.
What is Abdul's position now relative to the surface of the ocean?
Answer:
-48 ft.
Step-by-step explanation:
-76+28= -48
Hope this helps! Had this on one of my quizzes
Answer:
-48 espero te sirva perdon por llegar tarde
As a hardworking student, plagued by too much homework, you spend all night doing math homework. By 6am, you imagine yourself to be a region bounded by
y = 8 x^2
x=0
x=4
y=0
As you grow more and more tired, the world begins to spin around you. However, according to Newton, there is no difference between the world spinning around you, and you spinning around the world. Unfortunately, you are so tired that you think the world is the x-axis. What is the volume of the solid you (the region) create by spinning about the x-axis?
The volume of the solid you (the region) create by spinning about the x-axis is V = 225units³
How is the volume of a solid object calculated?Depends whether it is a solid with sides, height, and depth. In this case it is the multiplicarion of the three to get the volume.
If it is an irregular shaped object it is done by water displacement. Fill a container with a known amount of water, immerse the object, and the difference in volume in the water is the volume of the object.
How do I find the volume of an irregular shape?Break the volume down into prisms and pyramids that you can calculate the volume of and sum the pieces up to get the total volume. If the shape has curved surfaces, it gets much more complicated.
This gives a y = 15
x = 3
The straight line equation will be y = 5x
The volume of a pyramid is given by the following equation:
where r = radius of the base
h= height of the cone
from the graph, roating about the x - axis gives h = 3, r = 15
Volume =
= 225 units³
Volume of cone formed is 225 units³.
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If cos 0= 3/5 what is the measure of the angle
Credit recovery
By using trigonometry, it can be calculated that The measure of the angle is 53.13° First option is correct.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. It is used to calculate lengths, angles, and other geometric figures. Trigonometry has applications in many fields, including engineering, astronomy, and navigation. The most common trigonometric functions are sine, cosine, and tangent. These functions are used to solve problems related to triangles, circles, and other geometric figures. Trigonometric identities are also used to solve algebraic equations. Trigonometry is an important tool for studying the physical world, as it allows us to calculate the position and motion of objects in space.
There are six trigonometrical functions. They are
[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\cos\theta = \frac{baser}{hypotenuse}\\tan\theta = \frac{perpendicular}{base}\\cot\theta = \frac{base}{perpendicular}\\sec\theta = \frac{hypotenuse}{base}\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]
Trigonometry is a very important tool in mathematics.
Here, the trigonometric function given is
[tex]cos\theta = \frac{3}{5}[/tex]
[tex]\theta = cos^{-1}(\frac{3}{5})[/tex]
[tex]\theta = 53.13^{\circ}[/tex]
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Find the value of x in the following equation:
1.2(3x + 5) = 3.6x + 6
A:Infinite solutions
b: No solution
c: x = 1.8
d: x = 0
Answer:
A:Infinite solutions
Step-by-step explanation:
1.2 ( 3x + 5 ) = 3.6x + 6
1.2 ( 3x ) + 1.2 ( 5 ) = 3.6x + 6
3.6x + 6 = 3.6x + 6
Answer: A
Step-by-step explanation:
what number do you get by adding 59 hundred to 31 thousandths?
im not sure if you made a mistake and meant hundredths or not but if you are adding hundreds it would be 59.031 but if you adding hundredths is would be 0.621.
PLEASE HELP ASAP
A line that passes through the points (-1, -4) and (4, 2) is shown.
Which equation is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7) ?
Answer:
D
Step-by-step explanation:
slope of the given line :
(-4-2)/(-1-4)
-6/-5
6/5
slope of a perpendicular line : -5/6
y-7 = -5/6 (x-(-3)
y -7 = -5/6 (x+3)
y -7 = -5/6 x - 5/2
5/6 x + y - 7 + 5/2 = 0
5/6 x + y + (-14 + 5)/2 = 0
5/6 x + y - 9/2 = 0
5x + 6y - 27= 0
5x + 6y = 27
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, - 4 ) and (x₂, y₂ ) = (4, 2 )
m = [tex]\frac{2-(-4)}{4-(-1)}[/tex] = [tex]\frac{2+4}{4+1}[/tex] = [tex]\frac{6}{5}[/tex] ← slope of graphed line
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{6}{5} }[/tex] = - [tex]\frac{5}{6}[/tex] , then
y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (- 3, 7 ) into the partial equation
7 = [tex]\frac{5}{2}[/tex] + c ⇒ c = 7 - [tex]\frac{5}{2}[/tex] = [tex]\frac{14}{2}[/tex] - [tex]\frac{5}{2}[/tex] = [tex]\frac{9}{2}[/tex]
y = - [tex]\frac{5}{6}[/tex] x + [tex]\frac{9}{2}[/tex] ← equation in slope- intercept form
multiply through by 6 ( the LCM of 6 and 2 ) to clear the fractions
6y = - 5x + 27 ( add 5x to both sides )
5x + 6y = 27 ← equation of perpendicular line in standard form
Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 6, 0 ≤ v ≤ 1.
Answer:
684.
Step-by-step explanation:
I need help with these problems
Step-by-step explanation:
whenever you see a variable ( a letter ) without a number in front of it, add a 1 ! It means the same thing...
y is the same as 1y
1). 3y + y = ?
Add that 1!
3y + 1y = ?
This problem is the same as 3 + 1
3y + 1y = 4y
2). b + b = ?
Add those 1's !
1b + 1b = ?
this is the same as 1 + 1
1b + 1b = 2b
Remember to keep the variable !
Part B is like a puzzle and the instructions give us hints.
It is telling us, when we see an r, we replace it with the number 3
and when we see t , we replace it with the number 9
Let's solve these puzzles!
8). [tex]\frac{r}{t} = ?[/tex]
We see and r and a t, let's plug in 3 and 9
Now we have ...
[tex]\frac{3}{9} = ?[/tex]
Divide using a calculator!
We get ....
[tex]\frac{3}{9} = \frac{1}{3}[/tex] or 0.33
9). [tex]rt = ?[/tex]
When variables are right next to each other, this means they are being MULTIPLIED!
Let's replace r and t with 3 and 9 and multiply them together!
[tex]rt =[/tex] 3 × 9
3 × 9 = 27
We do similar things for Part C
12). [tex]ab = ?[/tex]
It tells us a = 5 and b = -4
Let's plug it in
[tex]ab =[/tex] 5 × -4
5 × - 4 = -20
USE THESE EXAMPLES AND TIPS TO COMPLETE THE REST OF THE PROBLEMS AND I WILL CHECK THEM FOR YOU.
COMMENT THEM BELOW
If you are given an equation of a line
and a set of points, and are asked to find
an equation of a line parallel to Line #1,
what do you need to do?
If you wanted to make $798 by investing $6139 for 3 years in an account that pays simple interest, what interest rate you would need to achieve your goal?
Answer:
Below
Step-by-step explanation:
6139 * x * 3 = 798
x = 798/(3*6139) = .0433= 4.33%
Find the slope of the line graphed below
Answer: -5/3
Down -5
right 3
Step-by-step explanation: count the distance between the 2 dots looking from the y axis (up and down)and from the x axis (left to right)
Which graph represents the inequality y ≥ 2−2x?
I took a guess on this question. I just want to be sure my guess was right!
Answer:
Yes, your answer would be correct.
Step-by-step explanation:
That graph intersects at (0, 2), is a solid line, and the slope is -2.
Find the value of 3 - 12 by 5
Answer: 3/5
Step-by-step explanation:
Let x be the required solution:
so, x= 3- (12/5)
⇒ 5x = 15-12 (Multiplying both sides 5 so that the denominator is the same)
⇒ 5x = 3
∴ x = 3/5
What is the measure of ZE, in degrees? D 48 5 O A. Cannot be determined OB. 48° O C. 96° D. 84°. :)
Answer:
84
Step-by-step explanation:
EFD is an iscosilies triangle therefore angle F = angle D = 48
and therefore angle E= 180-48-48=84
Practice 21: Combine the like terms to make a simpler expression
A. -3n-7+6n + 1
B 7x+5-3x
D. 12x² -5+7x² - 11x
a)
C. 6x + 4 + 15-7x
E 6g + 11 + 8g² - 15w
1 point
The like terms to make a simpler expression is 19 x^2-6 x+9 n-6
Group like terms
What is simpler expression?
Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplication, dividing, adding, or subtracting to be done.
[tex]=12 x^2+7 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements[tex]: $12 x^2+7 x^2=19 x^2$[/tex]
[tex]=19 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements: [tex]$7 x-3 x-11 x=-7 x$[/tex]
[tex]=19 x^2-7 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements: [tex]$3 n+6 n=9 n$[/tex]
[tex]=19 x^2-7 x+9 n-7+1+5-5[/tex]
Add the numbers: [tex]$-7+1+5-5=-6$[/tex]
[tex]=19 x^2-7 x+9 n-6[/tex]
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If you are given an equation of a line
and a set of points, and are asked to find
an equation that is perpendicular to Line
#1, what do you need to do?
If you are given an equation of a line and a set of points, you should determine the slope of the equation that is perpendicular to the given equation of line. Lastly, you should use the set of points to write an equation for the perpendicular line.
How to determine an equation of this line?Mathematically, the slope-intercept or standard form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.In Mathematics, a condition that must be met for two lines to be perpendicular is given by this mathematical expression:
m₁ × m₂ = -1
Assuming the given equation of a line is y = 2x, the slope of the equation that is perpendicular to this line would be calculated as follows;
m₁ × m₂ = -1
2 × m₂ = -1
Slope, m₂ = -1/2.
In conclusion, you will use the newly calculated slope alongside the set of points to determine the equation for the perpendicular line either by using the slope-intercept form or point-slope form.
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In the figure below, R is between Q and S, and S is between R and T. If QS = 12, RT=9, and QT=17, find RS.
In the given figure QT is of 16 units.
What is a line segment ?A line segment has two end points unlike a line which can extend indefinitely in both the directions.
According to the given question S is between Q and T and R is the midpoint of QS. RS=4 And RT= 12 we have to find QT.
As R is the midpoint of QS It will be twice of RS which
= 8 units.
And if RS is 4 units then QR is also 4 unit as R is the midpoint.
QT = QR + RT.
QT = 4 + 12
QT = 16 units.
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This bar chart shows the numbers of pets owned by people
questioned in a survey. Note that the scale on the vertical
axis is missing.
The total number of pets
owned by the respondents
is 92.
How many people owned
exactly 2 pets?
Answer: C. The width of the bar representing dogs is more than the widths of the other bars.
Step-by-step explanation: The following statements describes how this Bar Chart misrepresents the data.
Find the value of x
Area of rectangle = 50
Answer:
x = 3.66
Step-by-step explanation:
Area of a rectangle = length * width
In this case:
(x+10)x = 50
x*x + x*10 = 50
x² + 10x - 50 = 0
x = {-10±√((10²) -(4*1*-50))} / (2*1)
x = {-10±√(10² + 200)} / 2
x = {-10±√(100+200)} / 2
x = {-10±√300} / 2
x = {-10±17.321} /2 aprox,
It is a geometric figure so only the positive value is taken.
x = {-10+17.321} / 2
x = 7.321/2
x = 3.66
Check:
3.66(3.66+10) = 50
3.66*13.66 = 50
Express 2678 as a product of prime numbers
Answer:
2, 13, 103
Step-by-step explanation:
These prime numbers are the ones.
2678 = 2 * 13 * 103
A prime number is a natural number that is greater than one and is not a product of smaller natural numbers. For example, 3 is a prime number and we can write it as a product, 1 * 3 or 3 * 1, which involves 3 itself.
So, prime numbers are those numbers that have only two factors, which are 1 and the number itself.
A natural number that is greater than 1 and is not a prime number, is called a composite number. Every natural number which is greater than 1, is either a prime itself or can be factorized as a product of primes that is unique up to their order.
The answer is -
2678 = 2 * 13 * 103
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Which ordered pairs are solutions to this system of inequalities?
x+5 y>8
4 x-y<6
Select each correct answer.
(2,-3)
(-1,5)
(10,2)
(-4,1)
(0,4)
(-6,7)
The ordered pairs to the system of linear inequality are (-1, 5), (0, 4), (-6, 7)
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
In the problem given;
x + 5y > 8 ...eq(i)
4x - y < 6 ...eq(ii)
From eq(i)
x + 5y > 8
x > 8 - 5y ...eq(iii)
however, this can easily be solved using a graph.
Plotting the inequality in a graph line;
The ordered pairs are (-1, 5), (0, 4), (-6, 7)
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David invests $800 into an account with a 2.3% interest rate that is compounded semiannually.
How much money will he have in this account if he keeps it for 5 years?
Round your answer to the nearest dollar.
To calculate how much money David will have in this account after 5 years, we first need to find out how much interest the account earns each year. To do this, we need to multiply the interest rate by the amount of money in the account. In this case, the interest earned each year would be $800 * 0.023 = $18.40.
Next, we need to calculate how much interest the account earns over the 5-year period. Since the interest is compounded semiannually, this means that the interest is earned twice per year. Therefore, the total amount of interest earned over 5 years would be $18.40 * 2 * 5 = $184.
Finally, we need to add the interest to the original amount of money in the account to find out how much money David will have after 5 years. In this case, the total amount of money David will have after 5 years is $800 + $184 = $984.
Therefore, if David keeps the money in this account for 5 years, he will have $984.
Answer:
$897
Step-by-step explanation:
We know:
P = 800
n = 2
r = 2.3
t = 5
Write Equation:
[tex]F = 800(1+\frac{\frac{2.3}{100} }{2} )^{2(5)}[/tex]
Evaluate:
896.9
Thus the answer is $897
Multiply. State the product in simplest form..
p²-4p-12
18p
6p+12 p²-9p+18
, p‡ - 2,3,6
The simplest form of [(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)] is 3p/ (p - 3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given expression is
[(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)]
Now factories p²- 4p -12, p²-9p+18, and 6p + 12:
p²- 4p -12
= p²- (6 - 2)p -12
= p²- 6p + 2p -12
= p(p - 6) + 2(p - 6)
=(p - 6)(p + 2)
p²- 9p + 18
= p²- (6 + 3)p + 18
= p²- 6p -3p + 18
= p(p - 6) -3(p -6)
=(p - 6)(p - 3)
6p + 12
=6(p+2)
Now putting p²- 4p -12 = (p - 6)(p + 2); p²- 9p + 18 = (p - 6)(p - 3); 6p + 12 = 6(p+2) in the given expression:
[ (p - 6)(p + 2)/6(p+2)] × [18p/(p - 6)(p - 3)]
Multiply the denominator with denominator and numerator with numerator:
= 18p (p - 6)(p + 2)/ 6(p+2)(p - 6)(p - 3)
Now cancel out (p+2)(p - 6) from denominator and numerator:
= 18p/ 6(p - 3)
Divide denominator and numerator by 6:
= 3p/ (p - 3)
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Last year at a certain high school, there were 56 boys on the honor roll and 135 girls on the honor roll. This year, the number of boys on the honor roll increased by 25% and the number of girls on the honor roll increased by 20%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
There is an effective change of 50% in the school.
What is Percentage?
A percentage is a relative figure that represents the hundredth part of any amount. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.
Solution:
To find the net/effective change we can the use the formula:
(a + b + ab/100)
here a and b are the rate of change
a = 25% and b = 20%
Net change = (25 +20 + 500/100) = 45 + 5 = 50%
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find the values of x in the following, giving brief reasons for your answers.
please help me, thank you.
Answer:
For the first one x= 60 degrees
Second one x= 125 degrees
Step-by-step explanation:
a) To figure out this we can see that the total of angles in a 5- angled shape is 540 degrees.
So (2x X 4) + x = 540 degrees
= 9x= 540
= x = 60
b) To figure out this we can see that the total of angles in a 7- angled shape is 900 degrees.
So 60+2x+x+x+x+x+90= 900
= 150 +6x= 900
= 6x= 750
= x= 125