The probability that they each have a different tens digit is 0.047.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The probability of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Solution:- The collection contains 50 integers, hence there are [tex]^{50}C_5[/tex] different ways to select 5 different integers.
Sample space = [tex]^{50}C_5[/tex]
Each of the five numbers must correspond to one of the five available tens-digits, which are 2 through 6. There are a total of 105 ways to choose the five numbers that satisfy these properties because there are 10 ways to choose a number with a particular set of ten digits (such as 30, 31, or 39).
Therefore,
probability that each have a different tens digit = [tex]\frac{10^5}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{(50-5)!5!} }[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{45!5!} }[/tex]
= 0.047
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In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T (a,0). What are the coordinates of S
Based on the coordinates of the vertices of the parallelogram ORST, the coordinates of S can be found to be (a + b, d).
What are the coordinates of point S?As this is a parallelogram, the horizontal distance between O and R would be the same as the horizontal distance between S and T.
The horizontal distance between O and R is represented by "b".
The horizontal distance between T and S would therefore be:
= a + b
The fact that R and S are on the same plane would mean that the y-value of S is the same as that of R which is d.
The coordinates of S is:
( a + b, d).
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Hodaya is drawing a map of the trails in the canyon near her house. she knows that the distance from the first creek crossing to the second creek crossing is 1.8 miles. if every 3 inches on the map represents 0.75 of a mile, how far apart will the two creek crossings be on the map, to the nearest tenth of an inch? 2.3 4.1 5.4 7.2
The correct answer is 7.2 inch.
What is meant by distance?The length of the path joining two points determines their distance from one another.The entire journey that an object has taken can be used to define distance. An illustration. If an automobile drives 5 km east, then turns and drives 8 km further north, the total distance driven by the car is 13 km.'Distance' can be a verb or a noun, as was said above. He set himself apart from the remarks made by several of his coworkers. Thirty miles separate Peterborough from the nearest point. He had pledged to complete this duty but fell short of his commitment.The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance between two points can be computed by measuring the length of the line segment connecting the two points.The nearest tenth of a 7inch.
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1. Solve for x.
12
10
X
5
Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function?
Answer:
Step-by-step explanation:
Equation
f(x) = (8x + 1) / (2x + 9)
Notice the brackets. They are necessary to show what comes before the division sign, and what comes after.
Behavior
The best way to state the behavior is to get something like a graphing program to show you what the curve looks like -- where it's critical points are for example. I use Desmos for this kind of question, Just do a search for Desmos and bookmark it. You will use it quite often.
So you want to know the behavior.
Right Curve
Crosses the x axis at (-0.125, 0)
Crosses the y axis at (0,0,111)
The right curve has a domain of -∞ < x < ∞
The right curve has a range of -∞ < x < ∞
The range is going to have to go out quite a ways before you see any dramatic decrease in the way it is drawn.
Left Curve.
The right hand curve never crosses either the x or y axis. Nor does it just touch the x or y axis.
The domain is -∞ <x < 0
The range is 0<x<∞
In a study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration. What is the experimental probability the placebo pill induced better concentration on the student exams?
The experimental probability the placebo pill induced better concentration on the student exams is 0.64
The question has to do with probability.
What is probability?Probability is the likelihood of an event occurring.
The probability of an event A is given by
P(A) = number of occurrences of event A/total number of occurrences of all events.
What is the experimental probability the placebo pill induced better concentration on the student exams?Given that in the study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration.
The event A = students performing better.
Since 64 students performed better, the number of occurrences of event A = 64.
Since there were 100 students, the total number of occurrences = 100.
So, P(A) = P(students perform better)
= number of occurrences of event A/total number of occurrences of all events.
= 64/100
= 0.64
So, the experimental probability the placebo pill induced better concentration on the student exams is 0.64
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Dave is helping his grandmother make trail mix. His grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts.
Answer:
dave needs 3/5
Step-by-step explanation:
Step-by-step explanation:
what is the question ?
what problem needs to be solved ?
is it to find the ratio between fruit and nuts ?
then remember, a ratio is a fraction.
so, the ratio fruit : nuts is
1/5 / 1/3 = 1×3 / 5×1 = 3/5 or 3 : 5
or is it about any fraction problems and we need to bring them to the same denominator to add our compare them ?
to compare the 1/5 cup of fruit with the 1/3 cup of nuts, the smallest common multiple of 5 and 3 is 15. so we need to bring all to .../15.
how to make 15 out of 5 ? by multiplying 5 by 3. and we need to do this on the top of the fraction as well to keep the original value of the fraction.
1/5 = 1/5 × 3/3 = 3/15.
and with the same line of thinking :
1/3 = 1/3 × 5/5 = 5/15.
so, when mixing 1/5 cup of fruit with 1/3 cup of nuts, we get 3/15 + 5/15 = 8/15 cup of trail mix.
here you can clearly see the ratio again : 3/15 : 5/15 = 3:5
the first solution to get only full cups of trail mix is
3 cups of fruit and 5 cups of nuts = 8 cups of trail mix.
anything less will always end up with parts of cups (since 3/5 can't be simplified anymore).
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 can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.
How to determine the solution that can be eliminated?The equation is given as:
h(t)) = -16t^2 + 40t + 7
From the question
When h(t) = 0, the values of t are
t = -0.2 and t = 2.7
The t in the function h(t) represents time
As a general rule, time cannot be negative.
This means that the solution t = -0.2 can be eliminated
Hence, the solution that can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.
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Solve:
8(3 + a) = 64
A =
Answer: 8
Step-by-step explanation:
PEMDAS
pls help asap screenshot also posted- Which expression is equivalent to the given expression? 180‾‾‾‾√⋅230‾‾
The expression √180 * 2√30 is equivalent to the expression 60√6
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The square root is a factor of a number that, when multiplied by itself, gives the original number.
Given the expression √180 * 2√30
Collecting like terms give:
= 2√(180 * 30)
Simplifying:
= 60√6
The expression √180 * 2√30 is equivalent to the expression 60√6
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Which of the following is an example of the associative property of multiplication?
07-(3+5)=21+35
7-(3-5)=(7-3)-5
7-(3-5)=7-(5-3)
Answer:
think its number 2 7-(3-5)=(7-3)-5
Step-by-step explanation:
What is the difference between the smallest 7-digit number and the largest 6-digit number?
Answer:
the greatest 7 digit no.is = 999,99,99 the smallest 6 digit no.is= 1,00,000
Step-by-step explanation:
Sorry if I'm wrong I tried.
Se the laplace transform to solve the given initial-value problem. y'' − y' = et cos t, y(0) = 0, y'(0) = 0
The solution to this problem is (s2+1)Y(s)−2s−1=2s2+4 .
We let L[y(t)]=Y(s) . With that, tabular Laplace-transform laws entail
L[y′]=sY(s)−y(0)=sY(s)−2
L[y′′]=s2Y(s)−sy(0)−y′(0)=s2Y(s)−2s−1
∴L[y′′+y]=(s2+1)Y(s)−2s−1 .
Since the Laplace transform of sin(kt) is ks2+k2 , we have
(s2+1)Y(s)−2s−1=2s2+4 .
This equation readily solves to Y(s)=2s3+s2+8s+6(s2+1)(s2+4) . We compute its partial fraction decomposition as Y(s)=2s+53s2+1+−23s2+4 .
Our final step is to use tabular Laplace-transform laws ( sin(kt)↦ks2+k2 , and cos(kt)↦ss2+k2 ) to get y(t)=2cost+53sint−13sin(2t) . One can check that this indeed satisfies the initial value problem.
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pls solve if u can <3 much appreciated
Step-by-step explanation:
that is only possible, if we don't need to use a 2 and a 5 (but especially the 2) to create the 1 in the middle (log(10) = log(2×5) or log (5×2) = 1).
in other words, if the 1 in the middle is just a given, and does not use any of our digits for is creation, then a solution is possible.
first of all, the upper left corner has to be log(0⁰). we cannot use the digit 0 for anything else. and 0^n (except for n = 0) is not a valid argument for a logarithm.
log(0⁰) = 0 log(2×1) = 0.3... log(9/4) = 0.35...
log(1×2) = 0.3... 1 log(3×6) = 1.26...
log(7/3) = 0.37... log(4×5) = 1.3... log(6⁹) = 7.0...
but as soon as we need to build the center 1 by log(10), which takes then away one of the 2s (as the only way to build 10 by multiplication is 2×5 or 5×2), there is no possible solution.
Answer:
Please see attachment.
Step-by-step explanation:
There are many possible solutions to this problem.
A few things to note:
[tex]\log_a1=0[/tex]The log of a number smaller than its base is less than 1.The log of a number larger than its base is more than 1.[tex]\log_a0\:\:\textsf{is und\;\!efined}[/tex]There are 8 red boxes and 8 blue boxes, so we do not have to use every digit from 0 to 9.
Place zero in the blue box in the top left of the grid, since any number raised to zero is 1 and [tex]\log_a1=0[/tex]. Leave the red box blank for the moment, and fill it with any number not used at the end.
The value of the product of the red and blue boxes in the top-middle and left-middle of the grid should be less than 10. It is advisable to place the lowest numbers in these boxes, i.e. 1 and 2.
The value of the product of the red and blue boxes in the bottom-middle and right-middle of the grid should be more than 10.
It is advisable to place some of the highest numbers in the bottom right corner of the grid, as this is the box with the greatest value.
Please see the attached image for one possible way of filling the grid. The actual values of the logarithms (to 3 decimal places) have been placed in the bottom right corners of each box of the grid for verification.
The following formula relates three quantities: Force (F), mass (m), and acceleration (a). F = ma
F = ma is [tex]a=\frac{F}{m}[/tex]
Why is the formula F=ma?The equation for Newton's Second Law of Motion is F = ma. Force is equal to the rate of change of momentum, according to the definition of Newton's Second Law of Motion. Force is defined as mass times acceleration for a constant mass.The following formula relates three quantities: Force (F), mass (m), and acceleration (a). F = ma
F = ma
F= force
m= mass
a= acceleration
[tex]F = ma[/tex]
Divide both sides by the mass
[tex]a=\frac{F}{m}[/tex]
F = ma is [tex]a=\frac{F}{m}[/tex]
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Hey can someone help me with this?
Answer:
Step-by-step explanation:
A. a = $1350 b. b= 89%
B. 1350(.89)^t = 675
t = 5.9 years
A central angle is an angle whose vertex is at center of a circle. Find measure angle ACC
Part 1
[tex]m\angle AOB=m\angle BOC[/tex]
Part 2
Since [tex]m\angle AOB=m\angle BOC[/tex] from part 1, we know that since [tex]m\angle AOB=53^{\circ}[/tex], by the transitive property of equality, [tex]m\angle BOC=53^{\circ}[/tex].
Part 3
[tex]m\angle AOC=m\angle AOB+m\angle BOC=53^{\circ}+53^{\circ}=106^{\circ}[/tex]
how do you know if two line segments are perpendicular
Answer:
Step-by-step explanation:
Measure the angle between the lines
It should be 90 degrees,
trị tuyệt đối(x+1) = 3*x
u need first to understand the thing
Numbers that are divisible by 2 4 6 8 and 10 have to be?
Answer:
Even
Step-by-step explanation:
if g(x)=4x^2-16 were shifted 9 units to the right and 1 down, what would the new equation be?
The answer is g'(x) = 4x² - 72x + 307.
If shifted 9 units right, substitute (x - 9) in place of x.
g'(x) = 4(x - 9)² - 16If shifted 1 unit down afterwards, subtract 1.
g'(x) = 4(x - 9)² - 16 - 1g'(x) = 4(x - 9)² - 17g'(x) = 4x² - 72x + 324 - 17g'(x) = 4x² - 72x + 307Answer:
h(x)=4(x-9)^2-17
Step-by-step explanation:
Find the missing side. Round your answer to the nearest tenth.
What are the steps to finding missing sides
Answer:
23.6
Step-by-step explanation:
→ Identify length not given
Opposite
→ Find a formula without opposite
Cos = Adjacent ÷ Hypotenuse
→ Rearrange
Adjacent = Cos × Hypotenuse
→ Substitute
cos 38 × 30 = 23.6
Answer:
[tex]x = 23.6[/tex]
Step-by-step explanation:
To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.
In this case:
• The side adjacent to the given 38° angle is [tex]x[/tex] (required).
• The hypotenuse is 30 units.
The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:
[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].
Substituting into the formula:
[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]
⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]
⇒ [tex]x = 23.6[/tex]
Could I get some help with this?
Answer:
Step-by-step explanation:
base=b=7.2yd
height =h=7yd
area of parallelogram = b x h
. =7.2yd x 7yd
=50.49[tex]yd^{2}[/tex]
The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes.
The interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the slope?From the table of values, we have the following points
(x, y) = (5, 5.5) and (10, 5)
The slope of the table of values is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (5 - 5.5)/(10 -5)
Evaluate the difference
m = -0.5/5
Evaluate the quotient
m = -0.1
This means that the slope is -0.1
From the table of values, we have
x represents the elapsed time and y represents the volume of helium
So, the interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute
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Find an equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0)
The equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16
Equation of a straight lineFrom the question, we are to determine the equation of the line parallel to the given equation and that passes through the given point
Lines that are parallel to each other will have the same slope.
First, we will determine the slope of the line in the given equation.
The given equation of the line is
8x − 3y = 1
Express the equation in the slope-intercept form of a line, y = mx + b
Where m is the slope and
b is the y-intercept
That is,
8x − 3y = 1
8x -1 = 3y
3y = 8x - 1
y = 8/3(x) - 1/3
By comparing,
∴ The slope of the line is 8/3
Since we are to find the equation of a line parallel to this, the slope of the line will also be 8/3
Now, find the equation of a line containing the point (-2, 0) and that has a slope of 8/3
Using the point-slope form of a line
y - y₁ = m(x - x₁)
x₁ = -2
and y₁ = 0
∴ y - 0 = 8/3(x - -2)
y = 8/3(x +2)
3y = 8(x +2)
3y = 8x + 16
8x -3y = -16
Hence, the equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16
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what is 1016/86.89 include all your steps
Answer:
11.692945103
Step-by-step explanation:
take out a calculator divide 1016 by 86.89
If 8x + 6y = 24, what is y in terms of x ?
Step-by-step explanation:
8x+6y=24
6y=24-8x
y=24/6 - 8/6x
y=4-4/3x
5. If a, s are the zeroes of 2 -8x +λ ,such that a – s = 2, then λ=
The value of λ = 8s + 6
What are the zeroes of a function?The zeroes of a function f(x) are the values of x at which f(x) = 0.
How to find λ?Given that a, s are the zeroes of 2 - 8x + λ ,such that a - s = 2.
Since we require λ,
So, let f(x) = 2 - 8x + λ.
At x = a, f(x) = 0.
So, substituting the value of x = a into f(x), we have
f(a) = 2 - 8a + λ
Since f(a) = 0, we have
2 - 8a + λ = 0
2 + λ = 8a (1)
Also, x = s, f(x) = 0.
So, substituting the value of x = s into f(x), we have
f(s) = 2 - 8s + λ
Since f(s) = 0,we have
2 - 8s + λ = 0
2 + λ = 8s (2)
Since a - s = 2
Making a subject of the formula, we have
⇒ a = s + 2
So, substituting the value of a into equation (1), we have
2 + λ = 8a (1)
2 + λ = 8(s + 2) (1)
2 + λ = 8s + 16
- 14 + λ = 8s (3)
Adding equation (2) and (3), we have
-14 + λ = 8s (3)
+
2 + λ = 8s (2)
-12 + 2λ = 16s
2λ = 16s + 12
Dividing through by 2, we have
2λ/2 = (16s + 12)/2
λ = 4(4s + 3)/2
λ = 2(4s + 3)
λ = 8s + 6
So, the value of λ = 8s + 6
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Legs: The two ________ sides of a right triangle; the sides that meet at ___ degrees.
4|a| + 8 -a, if a = -2
PLEASE HELP!!!!!!!!!!!!!! I'm stuck on this!!
4|a| + 8 - a, if a = -2
What we're doing here is plugging in the given value of a for every instance of a in the expression.
4|-2| + 8 - (-2)
---The absolute value of a number is its distance from 0. -2 is 2 units away from 0, so the absolute value of -2 is 2. And, remember two negatives make a positive!
4(2) + 8 + 2
8 + 8 + 2
16 + 2
18
Hope this helps!
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?
The area of the trapezoidal tarp in the hotel is 47.3 square inches.
What is a trapezoid?A trapezoid is a quadrilateral having one pair of parallel opposite sides. It can have right angles (a right trapezoid) and congruent sides (isosceles), but neither is needed.How do determine the area of the trapezoid?
The area of a trapezoid is calculated using:Area = 0.5 × (Sum of parallel sides) × HeightFrom the complete question, the parallel sides are 10ft and 12ft.
So, Area = 0.5 × (10 + 12) × hEvaluate,
Area = 11 × hThe height (h) is computed using the cosine function shown below:
cos(120 - 90) = h/5This gives
cos(30) = h/5Make h the subject:
h = 5cos(30)Evaluate:
h = 4.3So, we get:
Area = 11 × 4.3Evaluate:
Area = 47.3Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.
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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?
to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.