Compute the speed of the car:
[tex]\dfrac{2\pi\,\rm ft}{1\,\rm rev} \cdot \dfrac{13\,\rm rev}{1\,\rm s} \cdot \dfrac{1\,\rm mi}{5280\,\rm ft} \cdot \dfrac{3600\,\rm s}{1\,\rm h} = \dfrac{195\pi}{11} \dfrac{\rm mi}{\rm h} \approx 55.6919 \dfrac{\rm mi}{\rm h}[/tex]
So after 1 hour, Sal will have driven about 56 mi.
A standard deck of cards contains 52 cards. There are four suits (spades, clubs, hearts, and diamonds) and thirteen of each suit (2-10, jack, queen, king, ace). One card is selected at random from the deck. What is the probability the card selected is an Ace or a heart?
The probability of selecting an ace or a heart when one card is drawn from 52 cards is 1/52.
Given that there are 52 cards in which there are 13 cards each for spades,clubs,hearts and diamonds.
We are required to find the probability of getting an ace or a heart when one card is drawn from 52 cards.
Probability is basically the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative. The probability can be calculated through following formula:
Probability=Number of items/total number of items.
Number of hearts=13
Number of ace=4
Probability of getting an ace or a heart when one card is drawn=P(X=heart)*P(X=ace)
=13/52 * 4/52
=52/(52*52)
=1/52
Hence the probability of getting an ace or heart when one card is drawn from standard deck of cards is 1/52.
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Select the correct answer. what is the completely factored form of this expression? y2 − 12y 32 a. (y 4)(y 8) b. (y − 4)(y − 8) c. (y 18)(y 2) d. (y − 18)(y − 2)
Answer:
b. (y - 4)(y - 8)
Step-by-step explanation:
pls explain and provide calculation thank you
Answer:
At least 18 solid balls
Step-by-step explanation:
Volume of rectangular tank:[tex]\sf \boxed{\bf Volume \ of \ rectangular \ tank = length* width * height}[/tex]
Volume of empty space = Volume of the full tank - Volume of the tank till the water.
= 20*10*13 - 20*10*11
= 2600 - 2200
= 400 cm³
Volume of 1 solid ball = 23 cm³
Number of solid ball to make the tank overflow = 400 ÷ 23
≈ 18 solid balls
What is [tex]\frac{14-7x}{7}[/tex]
Answer:
2-xStep-by-step explanation:
(14 - 7x)/7 =
[7(2-x)]/7 =
2-x
Total area=
What is the total area?
Help me asap! Please!! Thanks so much :)
The total surface area of this shaded region is 1000 units²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The total surface area of a polygon is the sum of the individual areas of each surface.
Total area of the figure = 2(20 * 10) + 2(10 * 10) + 2(20 * 10) = 1000 units²
The total surface area of this shaded region is 1000 units²
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Consider the incomplete paragraph proof.
Because triangle XYZ is a right triangle, the side lengths
Given: Isosceles right triangle XYZ (45°-45°-90°
must satisfy the Pythagorean theorem, a? + b2 c2
triangle)
which in this isosceles triangle becomes a2 + a? = c?. By
Prove: In a 45°-45°-90° triangle, the hypotenuse is V2
combining like terms, 2a? c2.
times the length of each leg.
Which final step will prove that the length of the
hypotenuse, c, is /2 times the length of each leg?
• Substitute values for and c into the original
Pythagorean theorem equation.
O Divide both sides of the equation by two, then
determine the principal square root of both sides of the
equation.
Determine the principal square root of both sides of
the equation.
O Divide both sides of the equation by 2.
The hypotenuse is [tex]c = a\sqrt{2}[/tex] times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes and this can be evaluated by using properties of isosceles triangle.
According to the statement
we have given that a theorem and we have to prove it.
So, For this purpose,
The given information is :
Isosceles triangle XYZ where [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]
Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.
Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.
Now use Pythagoras theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
But here a= b then the equation become
[tex]a^{2} + a^{2} = c^{2}[/tex]
Then after solving it become
[tex]2a^{2} = c^{2}[/tex]
And here we have to find the value of the hypotenuse,
so we solve it for c.
Then
[tex]c = a\sqrt{2}[/tex]
From this it is clear that the
it can be concluded that the hypotenuse is times the length of each leg 'a'.
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3. Bob has 8 pieces of square index cards that each measures 8 inches per side. Using a pair of scissors, he cuts each piece in half (so the resulting size is 8” x 4”) and then places all the resulting card pieces in a new stack. If he repeats this procedure 4 more times, how many pieces of card stock will he have and what will be the measure of each piece? (Note: All cuts will be made along the longer edge of the piece if the piece of index card is not square.)
The number of pieces of card stock which would result upon the process repetition is; 256 pieces.
What is the number of card stock pieces resulting from the cutting process?According to the task content, it follows that since, there are 8 pieces of the 8 inches per side cards initially, the resulting number of cards after carrying out the process of cutting cards into half five, 5 times is;
No of cards = 8 (2)⁵
No. of cards = 256 pieces.
The size of each of the cards in discuss provided that all cuts will be made along and not across the longer edge is; 8 by 1/4 inches.
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A choir has 3 spots open for altos, and 8 altos are interested in them. in how many ways can the open spots be filled? 24 56 112 336
Answer:
56
Step-by-step explanation:
combinations
C(8,3)
Use lagrange multipliers to find the minimum distance between the origin and the plane 3x y 2z = 28
The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.
In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.
Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.
We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:
D = √(x² + y² + z²), which can also be shown as:
D² = x² + y² + z².
The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:
2x = 3λ, or, x = (3/2)λ,
2y = λ, or, y = λ/2, and,
2z = 2λ, or, z = λ.
Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:
3(3/2)λ + λ/2 + λ = 28,
or, 6λ = 28,
or, λ = 28/6 = 14/3.
Thus, we get:
x = (3/2)λ = 7,
y = λ/2 = 7/3, and,
z = λ = 14/3.
Substituting these in the distance formula, we get:
D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.
Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.
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RSM wants to send four of its 18 Math Challenge teachers to a conference. How many combinations of four teachers include Mrs. Vera(only)?
There are 680 combinations of four teachers include Mrs. Vera(only)
How to determine the number of combination?The given parameters are
Teachers, n = 18
Selected teachers. r = 4
The selection must include Mrs. Vera.
So, the remaining parameters are:
Teachers, n = 17
Selected teachers. r = 3
The combination is then calculated as:
Ways = nCr
This gives
Ways = 17C3
Apply the combination formula
Ways = 17!/(14!3!)
Evaluate the expression
Ways = 680
Hence, there are 680 combinations of four teachers include Mrs. Vera(only)
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Combine the like terms to create an equivalent expression.
7+4c+2d+3
Answer:
4c+2d+10
Step-by-step explanation:
7+4c+2d+3
4c+2d+(3+7)
4c+2d+10
Answer: 4c+2d+10
Step-by-step explanation:
Please ASAP I WILL GIVE 30 POINTS IF THE CORRECT ANSWER, ALSO BRAINLEST AND 5 STARS ON YOUR ANSWER, PLEASE AND THANK YOU ASAP
Formula for the circumference of a circle is
[tex]c = \pi \: d[/tex]
where c is the circumference, and d is the diameter.
When diameter is 27-in, then
[tex]c1 = \pi \times 27[/tex]
When diameter is 25-in, then
[tex]c2 = \pi \times 25[/tex]
.: 27π-in – 25π-in is the farther distance.
Finding the difference, we have:
2π ≈ 6.28
.: 6.28-in is our final answer.
I hope this helps3 tons of sawdust cost $5,700.00. What is the price per pound?
$
Answer:
$0.95/lb
Step-by-step explanation:
1 ton = 2000 lb
3 tons = 3 × 1 ton = 3 × 2000 lb = 6000 lb
$5700/(6000 lb) = $0.95/lb
Answer: $0.95/lb
Step-by-step explanation:
3 tons = 6000 pounds
Therefore, using ratio and proportion rules,
6000/5,700 = 1/x
x = 5700/6000 = 0.95
The price is $0.95, or 95 cents per pound.
Suppose the circumference of a crop circle is 150.7968 hectometers (hm). What's the radius of the circle? (Use π = 3.1416.)
The radius of the circle is 24 hectometers.
How to get the radius of the circle?Remember that the circumference of a circle of radius R is given by the equation:
[tex]C = 2*\pi*R[/tex]
In this case, we know that the circumference is: C = 150.7968 hm
And π = 3.1416
Replacing that and solving for R, we get:
[tex]R = \frac{C}{2*\pi} = \frac{150.7968hm}{2*3.1416} = 24hm[/tex]
The radius of the circle is 24 hectometers.
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Instead of recording the number 1.23 cm for the radius of 2 tube, a student recorded 1.32cm.find the percentage error, correct to 1.DP
How many species go extinct in an average day? a. 3 b. 72 c. 1000 d. 20000 please select the best answer from the choices provided a b c d
It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.
What are species?
Species exist as organisms that contain similar characteristics and exist capable of interbreeding. A common example is human beings.
It has been observed that over the years, species have been going extinct due to human reasons such as excessive hunting, environmental factors such as natural disasters, global warming, and also due to changes in their genetic makeup or reduced reproduction.
It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.
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Answer: Edge 2022, B. 72
You purchase one microsoft july $72 put contract for a premium of $1. 32. what is your maximum possible profit?
The maximum possible profit = $7068
For given question,
One Microsoft July $72 put contract for a premium of $1.32
The payoff arise from put option is max (K - S, 0) - P
Now it would be maximum at S = 0
And, the maximum payoff is
K - 0 - P
= K - P
= 72 - 1.32
= $70.68
We assume that for each and every contract the number of shares is 100
So, the maximum profit gained from this strategy is
= $70.68 × 100 shares
= $7068
The maximum profit that will be gained from this strategy is $7068
Therefore, the maximum possible profit = $7068
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There are 3 red, 1 blue, and 2 yellow marbles in a bag. Once a marble is selected, it is not replaced. Find P(red and the yellow).
Answer:
5/6
Step-by-step explanation:
we add all the marbles together to get 6
then we seperate the marbles according to the question which would be yellow and red. that would make the probability of getting one of those to 5/6. Hope this helps :)
bell canada came by my house that I just bought and installed a new wire support for one of the telphone poles on my property. the electrical code says that the support must hit the ground at a 55 degree angle..If the telephone pole is 25 feet tall. how long is the wire spport that bell just installed?
Answer:
The cable length will have to be at least 30.51936ft
Step-by-step explanation:
[tex]c= \frac{25}{ \sin( 55 ) } = 30.51936[/tex]
C = Cable
Angles 1 and 2 form a right angle. 2 lines form a right angle. another line extends between the 2 lines to form 2 angles. the top angle is labeled 1, and the bottom angle is labeled 2. which word describes their measures?
The word complementary describes the their measures of ∠1 and ∠2.
According to the statement
we have given that the some conditions like
Angles 1 and 2 form a right angle. 2 lines form a right angle. another line extends between the 2 lines to form 2 angles. the top angle is labeled 1, and the bottom angle is labeled 2.
And we have to find the word that describes all about the given angles.
So, For this purpose,
According the given conditions, we recall that:
Angles that are complementary angles whose sum equals 90 degrees.
A right angle equals 90 degrees.
From the information given, we know that:
m∠1 and m∠2 forms a right angle.
Since a right angle = 90 degrees, therefore:
m∠1 + m∠2 = 90° (complementary)
So, The word complementary describes the their measures of ∠1 and ∠2.
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Answer: complementary
Step-by-step explanation: took the test on edge!
If A= (6,11), B= (1,5), and C= (7,0), show by means of slopes that ABC is a right triangle. Name the hypotenuse.
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
Right angled triangleA right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.
For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.
Find the slopes of AB, BC and AC
Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5
Slope of BC = 0-5/7-1
Slope of BC = -5/6
Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11
Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
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PLS HELLP ITS SO HARD
Answer:
[3,0]
[0,9]
Step-by-step explanation:
9x+3y=27
9x+3(0)=27
9x=27
x=3
9(0)+3y=27
3y=27
y=9
The nth term of a sequence is given by 3n² + 11 Calculate the difference between the 6th term and the 9th term of the sequence.
The difference between the 6th term and the 9th term of the sequence is 135
How to determine the difference
Given that the nth term is;
3n² + 11
For the 6th term, the value of n is 6
Let's solve for the 6th term
= 3( 6)^2 + 11
= 3 × 36 + 11
= 108 + 11
= 119
For the 9th term, n = 9
= 3 (9)^2 + 11
= 3( 81) + 11
= 243 + 11
= 254
The difference between the 6th and 9th term
= 254 - 119
= 135
Thus, the difference between the 6th term and the 9th term of the sequence is 135
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When the shape of a bst approaches that of a perfectly balanced binary tree, what is the worst case performance characteristic of searches and insertions?
The shape of a bst approaches that of a perfectly balanced binary tree, (log2n) is the time complexity for a balanced binary search tree in case of insertions and search.
In computing, binary bushes are mainly used for looking and sorting as they offer a way to save statistics hierarchically. a few common operations that may be conducted on binary trees encompass insertion, deletion, and traversal.
A binary tree has a special situation that each node could have a most of two youngsters. A binary tree has the benefits of each an ordered array and a linked listing as search is as brief as in a taken care of array and insertion or deletion operation are as fast as in related listing.
In pc science, a binary tree is a tree information shape in which every node has at maximum two youngsters, that are known as the left baby and the proper toddler.
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Line m contains the points (4, 16) and (0, 8). At what point will line m intersect with line n if the equation of line n is -8x+4y=24 ?
A) (0, 0)
B) (-4, 0)
C) The lines don't intersect
D) The lines intersect at an infinite number of points
The correct option regarding the point at which the linear functions intersect is given by:
C) The lines don't intersect.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For line m, we have that the y-intercept is of b = 8. When x changes by 4, y changes by 8, hence the slope is of 2, and the equation is:
y = 2x + 8.
Line n, in slope-intercept format, is given by:
-8x + 4y = 24
4y = 8x + 24
y = 2x + 6
Hence:
2x + 8 = 2x + 6
0x = -2
Which is impossible, hence they do not intersect and option C is correct.
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The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to:
The degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
How to determine the degrees of freedom applied to a cross-tabulation ?The given parameters are:
Rows = 5
Column = 2
The degrees of freedom is then calculated as:
df = Rows + Column - 1
Substitute the known values in the above equation
df = 5 + 2 - 1
Evaluate the expression
df = 6
Hence, the degrees of freedom for a chi-square test applied to a cross-tabulation with 5 rows and 2 columns is equal to 6
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Someone help me please
45-45-90 triangles
Answer:
Side AB = [tex]9\sqrt{2}[/tex]
Side AB = [tex]9\sqrt{2}[/tex]
Side CB = 36
Step-by-step explanation:
This is a special right triangle and it's also an isosceles triangle
therefore the measure of AC = AB and they are both = [tex]9\sqrt{2}[/tex]
for this special triangle the measure of hypotenuse (CB in here) is represented with [tex]x\sqrt{2}[/tex] and the legs are represented with x, each
since legs' lengths are given as = [tex]9\sqrt{2}[/tex] then x = [tex]9\sqrt{2}[/tex]
replace the x in front of [tex]x\sqrt{2}[/tex] with [tex]9\sqrt{2}[/tex]
[tex]9\sqrt{2}[/tex] * [tex]\sqrt{2}[/tex] = 36
A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number.
The solution to the system of equation is x < 44/3
Expansion of inequality expressionsInequality expressions are expressions not separated by an equal sign. An example of an inequality is a < b
Given the inequality expression below;
x + 2x + 6 < 50
Simplify to have:
3x + 6 < 50
Subtract 6 from both sides
3x + 6 - 6 < 50 - 6
3x < 50 - 6
3x < 44
Divide both sides by 3
3x/3 < 44/3
x < 44/3
Hence the solution to the system of equation is x < 44/3
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‼️‼️‼️‼️HELP‼️‼️‼️
Ron is 3 years older than Sherry, who is 4
years less than twice as old as John. Which of
the following represents Ron's age, if J = John's age?
Answer:
2J - 1
Step-by-step explanation:
Let J = John's age. Sherry is 4 years less than twice as old as John, so Sherry is 2J - 4 years old. Ron is 3 years older than Sherry, so Ron is 2J - 4 + 3 = 2J - 1 years old.
I need the answers with the explanation!
Answer:
you need all of them?
Step-by-step explanation: