Answer:
81.7 mpg
Step-by-step explanation:
"miles per gallon" means the number of miles is divided by the number of gallons.
(425 mi)/(5.2 gal) = (425/5.2) mi/gal ≈ 81.7 mpg
Use the distributive property to solve the equation 3x=15?
Answer:
x = 5
Step-by-step explanation:
Ordinarily, one would not need the distributive property to solve this equation. It is quickly and easily solved by making use of the multiplication property of equality: multiply both sides of the equation by 1/3.
3x(1/3) = 15(1/3)
x = 5
___
To use the distributive property, we need the sum of two terms that have a common factor. We can get that form by subtracting 15 from both sides of the equation (subtraction property of equality):
3x - 15 = 15 - 15 . . . . subtract 15
3x -15 = 0 . . . . . . . . .simplify
Now, we can apply the distributive property to remove a factor of 3:
3(x -5) = 0
And we can use the multiplication property of equality to multiply by 1/3:
3(1/3)(x -5) = 0(1/3)
x -5 = 0 . . . . . . . . . . simplify
Finally, we can add 5 to both sides of the equation (addition property of equality):
x -5 +5 = 0 +5
x + 0 = 5 . . . . . . simplify
x = 5 . . . . . . . . . .simplify more
Answer:
X=5
Step-by-step explanation:
i believe this is the correct answer!
Which statements accurately describe Earth’s magnetic field? Check all that apply. The magnetic field lines flow from Antarctica to northern Canada. The magnetic field is created by magnetic rocks on the surface. The magnetic poles line up exactly with Earth’s geographic poles. The magnetic field is generated in Earth’s core. The magnetic field is similar to the magnetic field of a bar magnet.
Answer:
It’s A, D, and E
The magnetic field lines flow from Earth’s geographic South Pole to Earth’s
geographic North Pole.
The magnetic field is generated in Earth’s core.
The magnetic field is similar to the magnetic field of a bar magnet.
thank youhave a good day
Answer:
It’s A, D, and E.
Step-by-step explanation: Try and find out :)
Jk Jk it's right.
The graph below shows a system of equations: y = -x + 5 and y = x - 1.
The x-coordinate of the solution to the system of equations is __________. Answer for Blank 1:
Answer:
3
Step-by-step explanation:
I don't see the graph.
So I'm going to do algebra and should be x-coordinate of the intersection you see in front of you.
If y=-x+5 and y=x-1, then -x+5=x-1.
-x+5=x-1
Add x on both sides:
5=2x-1
Add 1 on both sides:
6=2x
Divide 2 on both sides:
6/2=x
Simplify
3=x
You should see them cross when x is 3.
The y there should by 3-1=2.
They should cross at the ordered pair (3,2).
Answer:
3
Step-by-step explanation:
If a graph shows a system of equations: y = -x + 5 and y = x - 1, the x-coordinate of the solution to the system of equations is 3.
y=-x+5
y=x-1
-x+5=x-1
The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the
lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.
Answer:
Step-by-step explanation:
Let the other leg = x
x^2 + 4^2 = (3x)^2
x^2 + 4^2 = 9x^2
4^2 = 9x^2 - x^2
16= 8x^2
16/8 = x^2
x^2 = 2
x = sqrt(2)
The lengths of the sides
x = sqrt(2)
other side =4
hypotenuse = 3*sqrt(2)
x = 1.4
other side= 4
hypotenuse = 3*1.4142
hypotenuse = 4.2
Answer:
4 feet, 1.4 feet, 4.2 feet
Step-by-step explanation:
We are looking for the lengths of the three sides of a right triangle. We are given that one leg has length 4ft. Let x be the length of the other leg. Since the hypotenuse of the right triangle is three times the length of this leg, we can represent the hypotenuse as 3x. This is a right triangle, so we can use the Pythagorean Theorem to find x.
42+x216+x2=(3x)2=9x2
Subtracting x2 from both sides, then dividing by 8 to isolate the x, we have
8x2x2x=16=2=±2–√
Considering only the positive value for x, the lengths of the three sides of the triangle are approximately 4 feet, 2–√≈1.4 feet, and 32–√≈4.2 feet.
These long term behaviors are very hard to understand.
the first one
the degree of the polynomial in the numerator is 2.
the degree of the polynomial in the denominator is 2.
when the top and bottom have the same degree, like in this case, the horizontal asymptotes that that can afford us is simply the value of their coefficients.
[tex]\bf \cfrac{x^2-16}{x^2+2x+1}\implies \cfrac{1x^2-16}{1x^2+2x+1}\implies \stackrel{\textit{horizontal asymptote}}{y=\cfrac{1}{1}\implies y=1}[/tex]
for the second one
well, the degree of the numerator is 3.
the degree of the denominator is 2.
when the numerator has a higher degree than the denominator, there are no horizontal asymptotes, however, when the degree of the numerator is exactly 1 degree higher than that of the denominator, the rational has an oblique or slant asymptote, and its equation comes from the quotient of the whole expression, check the picture below, the top part.
for the third one
this one is about the same as the one before it, the numerator has exactly one degree higher than the denominator, so we're looking at an oblique asymptote, check the picture below, the bottom part.
Translate the given statement into propositional logic using proposition provided :
You can see the movie only if you are over 18 years old or you have the permission of a parent. Express your answer in terms of m: “You can see the movie,” e: “You are over 18 years old,” and p: “You have the permission of a parent.”
Final answer:
In propositional logic, the statement translates to ‘m → (e ∨ p)’, which denotes that seeing the movie 'm' can happen if the person is over 18 'e' or has parental permission 'p'.
Explanation:
The student is asking to translate a given statement into propositional logic. The statement in question is "You can see the movie only if you are over 18 years old or you have the permission of a parent." Using the propositions provided, where m represents "You can see the movie," e represents "You are over 18 years old," and p represents "You have the permission of a parent," we can express the logical relation in the following way:
In terms of logic, the statement can be written as a conditional: if you can see the movie (m), then you are over 18 years old (e) or you have the permission of a parent (p). This can be expressed as:
m → (e ∨ p)
This states that seeing the movie is the consequence of the condition of being over 18 years old or having parental permission. The conditional statement here establishes a necessary and sufficient relationship, while the use of or indicates that at least one of the conditions (being over 18 or having permission) must be met for the consequence (seeing the movie) to be true.
Identify the polygon with vertices A(5,0), B(2,4), C(−2,1), and D(1,−3), and then find the perimeter and area of the polygon. HELP ASAP!
Answer:
Part 1) The polygon is a square
Part 2) The perimeter is equal to [tex]20\ units[/tex]
Part 3) The area is equal to [tex]25\ units^{2}[/tex]
Step-by-step explanation:
we have
[tex]A(5,0), B(2,4), C(-2,1),D(1,-3)[/tex]
Plot the points
see the attached figure
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
[tex]A(5,0),B(2,4)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-0)^{2}+(2-5)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]AB=5\ units[/tex]
Find the distance BC
[tex]B(2,4), C(-2,1)[/tex]
substitute in the formula
[tex]d=\sqrt{(1-4)^{2}+(-2-2)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]BC=5\ units[/tex]
Find the distance CD
[tex]C(-2,1),D(1,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-1)^{2}+(1+2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]CD=5\ units[/tex]
Find the distance AD
[tex]A(5,0),D(1,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-0)^{2}+(1-5)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]AD=5\ units[/tex]
we have that
AB=BC=CD=AD
Find the distance BD (diagonal)
[tex]B(2,4),D(1,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-4)^{2}+(1-2)^{2}}[/tex]
[tex]d=\sqrt{(-7)^{2}+(-1)^{2}}[/tex]
[tex]BD=\sqrt{50}\ units[/tex]
Verify if the polygon is a square
If the triangle BDA is a right triangle, then the polygon is a square
Applying the Pythagoras theorem
[tex]BD^{2}=AD^{2}+AB^{2}[/tex]
substitute
[tex](\sqrt{50})^{2}=5^{2}+5^{2}[/tex]
[tex]50=50[/tex] -----> is true
so
The triangle BDA is a right triangle
therefore
The polygon is a square
Find the Area of the polygon
The area of a square is equal to
[tex]A=b^{2}[/tex]
we have
[tex]b=5\ units[/tex]
[tex]A=5^{2}=25\ units^{2}[/tex]
Find the perimeter of the polygon
The perimeter of a square is equal to
[tex]P=4b[/tex]
we have
[tex]b=5\ units[/tex]
[tex]P=4(5)=20\ units[/tex]
Find the area of the circle.
Use 3.14 for t.
Help Resources
d = 4 m
A = [?] m2
A=Tr2
Answer:
The area of the circle is A = 12.56 m²
Step-by-step explanation:
* Lets explain how to solve the problem
- The area of any circle is A = π r² , where r is the radius of the circle
- In any circle the length of the radius is half the length of its diameter
* Lets solve the problem
- The diameter of the circle is 4 meters
∵ The radius of the circle = 1/2 diameter
∵ The diameter = 4 meters
∴ The radius = 1/2 × 4 = 2 meters
- The area of the circle is A = π r²
∵ The value of π = 3.14
∵ The length of r = 2 meters
- Substitute the value of r in the rule of the area
∵ A = π r²
∴ A = 3.14 × (2)²
∴ A = 3.14 × 4 = 12.56 meters²
* The area of the circle is A = 12.56 m²
Need help with this
Answer:
Answer choice C is the correct answer.
Step-by-step explanation:
Answer choice A, 4/9, is equal to roughly .44.
Answer choice B, 2/5, is equal to exactly .4.
Answer choice C, 3/6, is equal to exactly .5.
Answer choice D, 5/12, is equal to roughly .42.
A proportion implies that the fractions will equal each other in value. The fraction 7/14 is equal to 1/2 or .5. Answer choice C, when simplified, is equal to 1/2 or .5, making it the correct answer.
A 50-foot ladder leans against a wall 15 feet from the base of the wall. What is the measure of the angle formed by the ladder and the wall? Please show all work.
Answer:
72.5°
Step-by-step explanation:
This is a right triangle problem. The ladder is the hypotenuse, and we have a length for that of 50 feet. We also have the distance along the ground that the ladder's base is from the wall against which it is leaning. This is the side adjacent to the angle for which we are seeking, so it the side adjacent to the angle, and it measures 15 feet.
We need a trig ratio that relates the side adjacent to the hypotenuse. That will be the cosine. Setting up:
[tex]cos\theta =\frac{adjacent}{hypotenuse}[/tex] and then filling in:
[tex]cos\theta=\frac{15}{50}[/tex]
Use the 2nd button on your calculator, and then press cos and you will get a display on your screen that looks like this:
[tex]cos^{-1}([/tex]
After that open parenthesis enter the fraction 15/50 and hit enter and you'll get the angle of 72.5 degrees, rounded.
just an addition to that superb reply above by @Luv2Teach
to the risk of sounding redundant.
Check the picture below.
make sure your calculator is in Degree mode.
The perimeter of a triangle with two equal sides is 50 cm. If its base were lengthened by 3 cm and each leg were shortened by 4 cm, all three sides would be equal. Find the length of the base of the original triangle.
Answer:
Base of the original triangle is 12 cm.
Step-by-step explanation:
Let base of triangle be x
two equal legs of triangles by y
therefore perimeter of triangle
x+y+y = 50 or x+2y =50
according to the question
if base is x+3 and leg is y-4
then both are equal
that is x+3 = y-4
y-x = 7 or y =x+7
x+2y =50
x+2(x+7) = 50
x+2x +14 =50
3x +14 =50
3x = 50 -14
3x = 36
x = 12
therefore base of the original triangle is 12 cm
What remainder does the sum 2222+2333 leave after division? Each one has an answer! Need answer quickly! 18 points!
by 4?
by 6?
by 9?
by 12?
2222 = 2220 + 2 = 555 * 4 + 2
2333 = 2332 + 1 = 583 * 4 + 1
Then
2222 + 2333 = (555 + 583) * 4 + 3
leaving a remainder of 3.
Dividing by 62222 = 2220 + 2 = 370 * 6 + 2
2333 = 2328 + 5 = 388 * 6 + 5
Then
2222 + 2333 = (370 + 388) * 6 + 7 = (370 + 388 + 1) * 6 + 1
leaving a remainder of 1.
Dividing by 92222 = 2223 - 1 = 741 * 3 - 1
2333 = 388 * 6 + 5 = (388 * 2) * 3 + 5 = (388 * 2 + 1) * 3 + 2
Then
2222 + 2333 = (741 + 388 * 2 + 1) * 3 + 1
leaving a remainder of 1.
Dividing by 122222 = 555 * 4 + 2 = 185 * 3 * 4 + 2 = 185 * 12 + 2
2333 = 2400 - 67 = 2400 - 60 - 7 = (200 - 5) * 12 - 7
Then
2222 + 2333 = (185 + 200 - 5) * 12 - 5
leaving a remainder of -5, or 7. (because 12 - 5 = 7)
Need some help with this
Answer:
y = 5x - 11
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 )
here slope m = 5, hence
y = 5x + c ← is the partial equation
To find c substitute (1, - 6) into the partial equation
- 6 = 5 + c ⇒ c = - 6 - 5 = - 11
y = 5x - 11 ← equation of line
A baseball team plays in a stadium that holds 58,000 spectators. With ticket prices at $12, the average attendance had been 23,000. When ticket prices were lowered to $10, the average attendance rose to 29,000.
(a) Find the demand function (price p as a function of attendance x), assuming it to be linear.
(b) How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.)
Answer: the lower the price the more people want to come to the baseball game.
Step-by-step explanation:
Answer:
a) p = -x/3000 + 19 2/3
b) $9.83
Step-by-step explanation:
a) The 2-point form of the equation for a line can be used with the two given points. The attendance is said to be the independent variable.
y = (y2 -y1)/(x2 -x1)(x -x1) + y1
Here "y" is the price (p), and "x" is the attendance, so we have ...
p = (10 -12)/(29000 -23000)(x -23000) +12
p = -1/3000(x -23000) +12
p = -x/3000 + 19 2/3 . . . . price as a function of attendance
__
b) Revenue is the product of attendance and price. We can find the attendance associated with maximum revenue, then find the corresponding price.
R(x) = x·p = x(-x/3000 +19 2/3)
This has zeros at x=0 and x=3000(19 2/3) = 59,000. The maximum revenue corresponds to attendance halfway between these values, at x = 29,500. The demand function tells us the ticket price should be ...
p = -29500/3000 +19 2/3 = 9.83 . . . . dollars
_____
Comment on the problem working
I might have written the "demand function" to use price as the independent variable. Then the price is what you know when you find the maximum revenue; you don't have to do an extra step to find it.
x = 3000(19 2/3 -p)
xp = 3000p(19 2/3 -p) is maximized at p = (19 2/3)/2 = 9 5/6 ≈ 9.83
Expected Value (50 points)
Game: Roll two dice. Win a prize based on the sum of the dice.
Cost of playing the game: $1
Prizes:
Win $10 if your sum is odd.
Win $5 if you roll a sum of 4 or 8.
Win $50 if you roll a sum of 2 or 12.
1.Explain HOW to find the expected value of playing this game. What is the expected value of playing this game? Show your work. (30 points)
2.Interpret the meaning of the expected value in the context of this game. Why should someone play or not play this game. Answer in complete sentences. (20 points)
Answer:
the expected value is if your sum is odd because half of the values you could roll are odd witch means you have 50% chance to get odd
because their are not high odds of getting something good
Can someone help with this!? :)
The system of equations provided consists of a circle and a line:
1. [tex]\( x^2 + y^2 = 49 \)[/tex] (This represents a circle with a radius of 7, centered at the origin.)
2. [tex]\( y = -x - 7 \)[/tex] (This is a linear equation.)
The first equation has already been graphed, showing a circle with a radius of 7. To find the intersection points of the circle and the line, which are the solutions of the system, we can substitute the expression for y from the second equation into the first one:
[tex]\[ x^2 + (-x - 7)^2 = 49 \][/tex]
[tex]\[ x^2 + x^2 + 14x + 49 = 49 \][/tex]
[tex]\[ 2x^2 + 14x + 49 - 49 = 0 \][/tex]
[tex]\[ 2x^2 + 14x = 0 \][/tex]
[tex]\[ x(2x + 14) = 0 \][/tex]
This gives us two solutions for x:
[tex]\[ x = 0 \quad \text{or} \quad 2x + 14 = 0 \][/tex]
[tex]\[ x = 0 \quad \text{or} \quad x = -7 \][/tex]
Now we can substitute these x-values into the second equation to find the corresponding y-values:
For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = -0 - 7 \][/tex]
[tex]\[ y = -7 \][/tex]
For [tex]\( x = -7 \)[/tex]:
[tex]\[ y = -(-7) - 7 \][/tex]
[tex]\[ y = 7 - 7 \][/tex]
[tex]\[ y = 0 \][/tex]
Therefore, the system of equations has two solutions where the line intersects the circle:
[tex]\[ (0, -7) \quad \text{and} \quad (-7, 0) \][/tex]
These calculations provide us with the step-by-step solution to the system of equations. The graphical solution would show the line [tex]\( y = -x - 7 \)[/tex] intersecting the circle [tex]\( x^2 + y^2 = 49 \)[/tex] at these two points.
Here is the graph showing the system of equations:
- The circle represented by [tex]\( x^2 + y^2 = 49 \)[/tex].
- The line represented by [tex]\( y = -x - 7 \).[/tex]
The red points indicate where the line intersects the circle, which are the solutions to the system of equations. These points are at (0, -7) and (-7, 0).
Find the value of x. Then find the measure of each labeled angle.
Answer:
20
4x will be 80
5x will be 100
Step-by-step explanation:
So those two how pink arrows means those opposite sides are parallel.
The side at the bottom is acting as a transversal through the parallel lines.
The angle that has measurement 5x and the one that has 4x are actually same-side interior angles; some people like to call it consecutive angles.
These angles add up to be 180 degrees when dealing with parallel lines.
So we have 5x+4x=180
which means 9x=180
Divide both sides by 9 giving us x=180/9
x=180/9=20.
The angle labeled 4x will then be 4(20) which is 80.
The angle labeled 5x will then by 5(20) which is 100.
To solve for x in vector problems, identify the axes, decompose each vector into its components using trigonometric functions, combine the components to find the resultant vector, and ensure that the solution is reasonable. Be sure to use radians for angles in calculations.
Explanation:To find the value of x, we need to follow specific steps when dealing with vectors and their components. The given information suggests we have vectors A and B with specific magnitudes and angles relative to the x-axis. Here's how to proceed:
Identify the x- and y-axes that will be used in the problem.Find the components of each vector to be added along the perpendicular axes using the equations: Ax = A cos θ and Ay = A sin θ, where A is the magnitude of vector A and θ is the angle it makes with the x-axis. Repeat this for vector B to obtain Bx and By.Substitute the known values into the equations and solve for the components.Combine the x-components (Ax and Bx) and y-components (Ay and By) to find the resultant vector's components.To get the resultant vector's magnitude, use the Pythagorean theorem.To get the direction of the resultant, measure the angle it makes with the reference frame or use trigonometric relationships to determine this angle.Check your answer to see if it is reasonable, ensuring the units and the magnitude of the resultant make sense.For example, given A = 53.0 m, θA = 20.0°, B = 34.0 m, and θB = 63.0°, we can find the x-components as Ax = A cos θA. It is important to use radians when calculations involve angles.
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Suppose the circumference of a crop circle is 150.7968 hectometers (hm). What's the radius of the circle? (Use π = 3.1416.)
A. 24 hm
B. 96 hm
C. 48 hm
D. 16 hm
Answer:
A. 24 hm
Step-by-step explanation:
The formula for the circumference of a circle is ...
C = 2πr
Fill in the given values and solve.
150.7968 hm = 2×3.1416×r
(150.7968 hm)/6.2832 = r = 24 hm . . . . . divide by 2π
The radius of the circle is 24 hm.
The product of (a − b)(a − b) is a2 − b2.
A. Sometimes
B. Always
C. Never
The correct option is C. Never The product of (a - b)(a - b) is always equal to a² - 2ab + b².
The product of (a - b)(a - b) can be expanded using the distributive property:
(a - b)(a - b) = a(a) - a(b) - b(a) + b(b)
Simplify by multiplying the terms:
= a² - ab - ab + b²
Combine like terms:
= a² - 2ab + b²
As you can see, the product of (a - b)(a - b) is a² - 2ab + b², not a² - b².
However, there is a well-known algebraic identity called the difference of squares, which states that a² - b² can be factored as (a + b)(a - b). So, the correct statement is:
(a - b)(a - b) is equivalent to a² - 2ab + b², not a² - b².
Therefore, the answer is C. Never the product of (a - b)(a - b) is always equal to a² - 2ab + b².
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Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip.(A) 35(B) 40(C) 45(D) 50(E) 55
Answer:
The correct option is B.
Step-by-step explanation:
It is given that Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 60 miles/hr for the remaining 30 miles of the trip.
[tex]Time=\frac{Distance}{Speed}[/tex]
Time taken by Susan in first 30 miles is
[tex]T_1=\frac{30}{30}=1[/tex]
Time taken by Susan in remaining 30 miles is
[tex]T_2=\frac{30}{60}=0.5[/tex]
Total distance covered by Susan is
[tex]D=30+30=60[/tex]
Total time taken by susan to complete 60 miles trip is
[tex]T=T_1+T_2[/tex]
[tex]T=1+0.5=1.5[/tex]
Susan's avg speed in miles/hr for the entire trip is
[tex]S=\frac{60}{1.5}=40[/tex]
The average speed of susan for entire trip is 40. Therefore the correct option is B.
What is tan 11pie/6 ?
Answer:
1/root 3
Step-by-step explanation:
pi =180degrees
11×180/6
11×30
330
tan 330=tan (360-30)
=-tan30
=1/root3
i have answered ur question
An article reported that for a sample of 40 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 165.23.
Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)
=(_________,__________) ppm
(b) Suppose the investigators had made a rough guess of 167 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 57ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
=__________ kitchens
Answer: (a) (602.95,705.37)
(b) 33
Step-by-step explanation:
(a) Given : Sample size : [tex]n=40[/tex]
Sample mean : [tex]\overline{x}=654.16[/tex]
Standard deviation : [tex]\sigma= 165.23[/tex]
Significance level :[tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The confidence interval for population mean is given by :-
[tex]\mu\ \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=654.16\pm(1.96)\dfrac{165.23}{\sqrt{40}}\\\\\approx654.16\pm51.21\\\\=(654.16-51.21,\ 654.16+51.21)=(602.95,705.37)[/tex]
Hence, the 95% (two-sided) confidence interval for true average [tex]CO_2[/tex] level in the population of all homes from which the sample was selected.
(b) Given : Standard deviation : [tex]s= 167\text{ ppm}[/tex]
Margin of error : [tex]E=\pm57\text{ ppm}[/tex]
Significance level :[tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The formula to calculate the sample size is given by :-
[tex]n=(\dfrac{z_{\alpha/2}s}{E})^2\\\\\Rightarrow\ n=(\dfrac{(1.96)(167)}{57})^2=32.9758025239\approx33[/tex]
Hence, the minimum required sample size would be 33.
Please help with this question
Explanation:
1. Sine and Cosine are never greater than 1 because they are the ratio of the leg of a right triangle to the hypotenuse. The hypotenuse is never shorter than one of the legs of a right triangle, so the ratio is at most 1.
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2. Secant and cosecant are the reciprocals of the cosine and sine (respectively), so are the reciprocals of numbers that are at most 1. Therefore, they can never be less than 1 (in magnitude).
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3. Tangent and cotangent (and secant and cosecant) are sometimes undefined because they are the ratios of triangle side lengths. The side length used in the denominator may be zero, causing the ratio to be undefined.
A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed aa. uniform probability distributionb. binomial probability distributionc. hypergeometric probability distributiond. normal probability distribution
Answer: binomial probability
Step-by-step explanation:
A binomial probability indicates to the probability of having exactly x successes on n repeated trials in an particular binomial experiment which has only two possible outcomes.
If the probability of success on an single trial is b (which does not change) , then , the probability of failure will be (1-b) .
The binomial probability for success in x trials out of n trials is given by :-
[tex]^nC_x\ b\ (1-b)^{n-x}[/tex]
Final answer:
The distribution called for a fixed number of independent trials with a constant success probability is the binomial probability distribution, defined by the equation P(X = x).
Explanation:
The probability distribution that shows the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a binomial probability distribution. The key characteristics of a binomial distribution include a fixed number of independent trials with two possible outcomes (success or failure) and a constant probability of success in each trial.
Mathematically, the binomial distribution is defined using the equation P(X = x) = (n choose x) * px * qn-x, where p is the probability of success, q = 1 - p is the probability of failure, and (n choose x) is the combination of n taken x at a time.
Tina, the owner of a home and garden store, lends $8,000 to Lana to help her open an art shop. Lana plans to repay Tina at the end of eight years with interest compounded semiannually at 8%. Using the tables found in the textbook, you can determine that at the end of eight years, Tina will receive A. $14,484. B. $14,984. C. $16,587. D. $16,857.
Answer:
B. $14,984
Step-by-step explanation:
The multiplier is ...
(1 +r/n)^(nt) . . . . where r is the nominal annual rate, n is the number of times interest is compounded per year, and t is the number of years.
Here, that multiplier is ...
(1 +.08/2)^(2·8) = 1.04^16 ≈ 1.87298
Then Lana will be paying Tina ...
$8000×1.87298 ≈ $14984
at the end of 8 years.
Can someone help me with this math question it involves transformation
Answer:
ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])
Step-by-step explanation:
* Lets explain the reflection and the translation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is (x , y - k)
* Now lets solve the problem
∵ The vertices of ABCD are:
A = (-5 , 2) , B = (-3 , 4) , C = (-2 , 4) , D = (-1 , 2)
- If ABCD reflected over the y-axis we will change the sign of the
x-coordinate of all the points
∴ The image of A = (5 , 2)
∴ The image of B = (3 , 4)
∴ The image of C = (2 , 4)
∴ The image of D = (1 , 2)
∴ The image of ABCD after reflection over the y-axis will be at
the first quadrant
- The figure EHGF is left and down the image of ABCD after
the reflection over the y-axis
∴ The image is translate to the left and down
∵ E = (1 , -2) and E is the image of A after reflection and translation
∵ The image of a after reflection is (5 , 2)
- That means 5 became 1 and 2 became -2
∵ 1 - 5 = -4
∴ The image of A after reflection translate 4 units to the left
∵ -2 - 2 = -4
∴ The image of A after reflection translate 4 units down
∴ ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])
* You can check the rest of points
# B with H
∵ B = (-3 , 4) after reflection over y-axis is (3 , 4) after translation is
(3 + [-4] , 4 + [-4]) = (-1 , 0) the same with point H = (-1 , 0)
# C with G
∵ C = (-2 , 4) after reflection over y-axis is (2 , 4) after translation is
(2 + [-4] , 4 + [-4]) = (-2 , 0) the same with point G = (-2 , 0)
# D with F
∵ D = (-1 , 2) after reflection over y-axis is (1 , 2) after translation is
(1 + [-4] , 2 + [-4]) = (-3 , -2) the same with point F = (-3 , -2)
Certainly! In order to assist you effectively with your math question involving transformation, please provide me with the specific details or instructions regarding the transformation problem you're facing.
Are you looking to translate, rotate, reflect, or dilate a geometric figure? Please provide the specifics such as the type of transformation, the figure involved, and any parameters (like the direction and distance of a translation, the angle and direction of a rotation, the line of reflection, or the scale factor and center of dilation for a dilation).
Once you provide these details, I'll be able to guide you through the mathematical process to solve your transformation problem step by step.
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 92.6-cm and a standard deviation of 2-cm. For shipment, 12 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm. Enter your answer as a number accurate to 4 decimal places.
Answer: 0.2140
Step-by-step explanation:
Given : A company produces steel rods. The lengths of the steel rods are normally distributed with
[tex]\mu=92.6 \text{ cm}[/tex]
[tex]\sigma=2\text{ cm}[/tex]
Sample size : [tex]n=12[/tex]
Let x be the length of randomly selected item.
z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For x=92 cm
[tex]z=\dfrac{92-92.6}{\dfrac{2}{\sqrt{12}}}\approx-1.04[/tex]
For x=92.4 cm
[tex]z=\dfrac{92.4-92.6}{\dfrac{2}{\sqrt{12}}}\approx-0.35[/tex]
The probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm by using the standard normal distribution table
= [tex]P(92<x<92.4)=P(-1.04<z<-0.35)=P(z<-0.35)-P(z<-1.04)[/tex]
[tex]= 0.3631693-0.14917=0.2139993\approx0.2140[/tex]
Hence, the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm is 0.2140.
For the pair of triangles below, determine whether or not the triangles are similar. If they are similar, show your reasoning in a flowchart. If they are not similar, explain how you know.
Answer:
The triangles are similar
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
step 1
In the right triangle FED
Find the length of side FD
Applying the Pythagoras Theorem
[tex]FD^{2}=FE^{2}+DE^{2}[/tex]
substitute the given values
[tex]FD^{2}=3^{2}+4^{2}[/tex]
[tex]FD^{2}=25[/tex]
[tex]FD^{2}=5\ units[/tex]
step 2
In the right triangle BUG
Find the length of side GU
Applying the Pythagoras Theorem
[tex]BG^{2}=BU^{2}+GU^{2}[/tex]
substitute the given values
[tex]10^{2}=6^{2}+GU^{2}[/tex]
[tex]GU^{2}=100-36[/tex]
[tex]GU^{2}=8\ units[/tex]
step 3
Find the ratio of its corresponding sides
If the triangles are similar
[tex]\frac{FD}{BG}=\frac{FE}{BU}=\frac{DE}{GU}[/tex]
substitute the given values
[tex]\frac{5}{10}=\frac{3}{6}=\frac{4}{8}[/tex]
[tex0.5=0.5=0.5[/tex] -----> is true
therefore
The triangles are similar
Proportions in Triangles (10)
DOES ANYONE KNOW HOW TO DO THIS??????????
Donna's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Donna $4.20 per pound, and type B coffee costs $5.30 per pound. This month, Donna made 145 pounds of the blend, for a total cost of $659.90. How many pounds of type B coffee did she use?
Answer:
She used 49 of type B
Step-by-step explanation:
4.20 x 96 = 403.25.3 x 49 = 259.7403.2 + 259.7 = 659.9Step-by-step explanation:
Same steps, different problem.
x - pounds of type A coffee for current month
y - pounds of type B coffee for current month
x+y=145
4.2x+5.3y=659.9
x+y=145 -> multiply both sides by 4.2
4.2x+5.3y=659.9
4.2x+4.2y=609
1.1y=50.9