the probability that a positive integer less than 100 picked at random has all distinct digits is 90.
He has 99 positive integers less than 100.
The integers that do not have all distinct digits have the same digit twice.
11, 22, 33, 44, 55, 66, 77, 88, 99
There are 9 integers that do not have distinct digits, therefore there are 99-9 integers that do.
Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.
A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final results of an experiment. Getting a Heads whilst tossing a coin is an event.
Simple probability is the calculation of an outcome or the chance of an event ever taking place. coverage companies use possibility statistics to determine the possibilities of having to pay out a declare. A simple chance is calculated by way of dividing a particular outcome through all of the feasible outcomes.
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A tennis tournament has 2n contestants. We want to pair them up for the first round of singles matches. Show that the number of different ways in which first round matches can be conducted is
There are
[tex]\dbinom{2n}2 = \dfrac{(2n)!}{2! (2n-2)!}[/tex]
ways of pairing up any 2 members from the pool of [tex]2n[/tex] contestants. Note that
[tex](2n)! = 1\times2\times3\times4\times\cdots\times(2n-2)\times(2n-1)\times(2n) = (2n-2)! \times(2n-1) \times(2n)[/tex]
so that
[tex]\dbinom{2n}2 = \dfrac{(2n)\times(2n-1)\times(2n-2)!}{2! (2n-2)!} = \boxed{n(2n-1)}[/tex]
The number of different ways in which first-round matches can be conducted is n (2n - 1).
We have,
Number of contestant = 2n
Number of contestants in each match = 2
Now,
The number of different ways in which first-round matches can be conducted.
A combination formula is used.
= [tex]^{2n}C_2[/tex]
= 2n! / 2! (2n - 2)!
= 2n (2n - 1)(2n - 2)! / [2 x (2n - 2)!]
= 2n (2n - 1) / 2
= n (2n - 1)
Thus,
The number of different ways in which first-round matches can be conducted is n (2n - 1).
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True or False? If ab<0, then a<0, b>0 or a>0, b<0
Answer:
True
Step-by-step explanation:
If ab < 0, then ab = negative #.
In order for ab to be a negative #, one of them has to be negative while the other one needs to be positive.
Example:
a = -2, b = 1
ab < 0
(-2)(1) < 0
-2 < 0, TRUE
a < 0
-2 < 0, TRUE
b > 0
1 > 0, TRUE
If I switch a = -2 to 1 and b = 1 to -2, a > 0 and b < 0 is true too.
from two points one on each leg of an isosceles triangle perpendicular are drawn to the base prove that the triangles formed are similar
The description below proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
How to prove an Isosceles Triangle?Let ABC be an isosceles triangle such that AB = AC.
Let AD be the bisector of ∠A.
We want to prove that BD=DC
In △ABD & △ACD
AB = AC(Thus, △ABC is an isosceles triangle)
∠BAD =∠CAD(Because AD is the bisector of ∠A)
AD = AD(Common sides)
By SAS Congruency, we have;
△ABD ≅ △ACD
By corresponding parts of congruent triangles, we can say that; BD=DC
Thus, this proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
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change the unit of length 6ft 2in= ___ft?
Answer:
Step-by-step explanation:
Comment
You don't have to do anything to the 6 feet. It already is in feet. It's the 2 inches you have to worry about.
2 inches = 2/12 of a foot.
2/12 = 1/6 = 0.167 feet
Answer
6 feet 2 inches = 6.167 feet
Step-by-step explanation:
The equation y = ax describes the graph of a line. If the value of a is negative,
the line:
Answer:
The line has a downward slope
Step-by-step explanation:
If y = ax, it means that a represents the slope of the line. So, if A is negative, the line has a downward slope. In other words, for every increase in the value of x, there is a decrease in the value of y (increase in the negative direction). You can imagine the line y = -x, where the value of a is -1. When x is 1, y is -1; when x is 2, y is -2; when x is 5, y is -5. You can imagine that the graph looks like a diagonal line, much like y = x, except the function values are positive in the second quadrant and negative in the fourth (it slants downward to the right side). I hope that answers your question.
The formula for the perimeter of a rectangle is P=2(l+w). Part A. Rewrite the formula for the perimeter of a rectangle in terms of the width, w. In your final answer, include all of your work. Part B. In two or more complete sentences, describe the process you followed while isolating the variable w in the equation P=2(l+w).
The expression that represents the width is w = (P-2l)/2
Subject of formulaGiven the formula for calculating the perimeter of a triangle expressed as:
P = 2(l + w)
where
l is the length
w is the width
Make w the subject of the formula
Given
P = 2(l + w)
Expand
P = 2l + 2w
Subtract 2l from both sides
P - 2l = 2w
Divide both sides by2
2w/2 = (P-2l)/2
w = (P-2l)/2
Hence the expression that represents the width is w = (P-2l)/2
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The formula s = startroot startfraction s a over 6 endfraction endroot gives the length of the side, s, of a cube with a surface area, sa. how much longer is the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters? startroot 30 endroot minus 4 startroot 5 endroot meters m startroot 30 endroot minus 2 startroot 5 endroot meters m startroot 10 endroot meters m 2 startroot 15 endroot meters m
Step-by-step explanation:
so, let me get this straight :
s = sqrt(sa/6)
this is because the surface area of a cube consists of 6 squares (as everybody knows that dice have 6 equal sides).
and the area of a single square is side².
for a cube with sa = 180 m² we have
s = sqrt(180/6) = sqrt(30)
for a cube with sa = 120 m² we have
s = sqrt(120/6) = sqrt(20) = sqrt(4×5) = 2×sqrt(5)
so, the side length of the larger cube is
sqrt(30) - 2×sqrt(5) meters
longer than the side length of the smaller cube.
in other words, the difference between both side lengths.
Answer:
answer above is correct, its B
Step-by-step explanation:
Researchers at a food company are interested in how a new ketchup made from green tomatoes (and green in color) will compare to their traditional red ketchup. They randomly assign participants to either the green or red ketchup condition. Participants indicate the tastiness of the sauce on a 20-point scale. Tastiness scores tended to be skewed (not normal). What statistical test should be used to analyze that data
The statistical test which can be used to analyze the data is chi square test.
Given two categories of tomatoes , one is red and other one is green.
When we want to compare more than two categorical variables, we can use the chi-square test. The main objective of chi square test is to compare the distribution of responses or the proportions of participants in each response category. This test does not require mean, standard deviation or anything. In the given problem we have not given sample mean, population mean, population standard deviation, etc. So we cannot use z test, t test, f test because they require sample mean, population mean , standard deviation in their calculation. The formula to be use in chi square test is as under:
[tex]X^{2}=[/tex]∑[tex](f_{0} -f_{e}) ^{2} /f_{e}[/tex]
where [tex]f_{0}[/tex]= observed frequency of each of response category.
[tex]f_{1}[/tex]=expected frequency in each of the response categories.
We can find the critical value in a table of probabilities for the chi square distribution with degree of freedom df=K-1.
Hence we can use chi square test to analyze the data.
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Determine the number of possible solutions for a triangle with b = 37, a = 32, and b = 27.
There are two(2) possible solutions for the given parameters of a triangle. Using the law of cosines, the parameters of the triangle are calculated.
What is the law of cosines?The law of cosines is used to relate the angles and side lengths of a triangle.
They are given as follows:
a² = b² + c² -2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)
Calculation:The given triangle has B = 37°, a = 32 and b = 27
So, using the law b² = a² + c² - 2ac cos(B)
On substituting,
27² = 32² + c² - 2(32)c cos(37°)
⇒ c² - 50.56 c + 1024 = 729
⇒ c² - 50.56 c + 295 = 0
Since the obtained equation is quadratic, it has 2 solutions.
Using quadratic formula the solutions are calculated.
c = [50.56 ± [tex]\sqrt{50.56^2-4(1)(295)}[/tex]]/2(1)
On simplifying,
c = 43.8 and c = 6.7
Therefore, there are 2 possible solutions for the given triangle.
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A courier travels due North at an average speed of 40km/h for 6 minutes to collect a parcel, before travelling 10km due East to deliver it. He then travels due South at an average speed of 30km/h for 12 minutes to collect another parcel. Find the shortest distance between the courier and his starting point.
Answer:
Step-by-step explanation:
Answer:10.2km
He took the route eastwards then southwards
Point Z is equidistant from the vertices of ΔTUV.
Point Z is equidistant from the vertices of triangle T U V. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C.
Which must be true?
Line segment T A is-congruent-to line segment T B
Line segment A Z is-congruent-to line segment B Z
AngleBTZ Is-congruent-to AngleBUZ
AngleTZA Is-congruent-to AngleTZB
An isosceles triangle is one with two equal-length sides. The correct option is C.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
The diagram as per the given conditions is drawn below.
In ΔUTZ, since the sides UZ and TZ are equal because the point z is equidistance from T and U, therefore, the triangle is an isosceles triangle. Thus, ∠BTZ≅TZB.
Hence, the correct option is C.
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help asap 20 points
Select the correct answer from each drop-down menu.
Answer: (99/13, 150/13)
Step-by-step explanation:
I'm too lazy to explain so here's a screen shot from desmos.
2. A map is drawn so that every 1 inch on the map represents 50 actual miles. The table below can be used to record the actual distances between towns on the map. Actual Distance (mi.) Map Distance (in.) Actual Distances and Map Distances 50 1 Complete the table. What is the actual distance between two towns that are 4 inches apart on the map? 2. A map is drawn so that every 1 inch on the map represents 50 actual miles . The table below can be used to record the actual distances between towns on the map . Actual Distance ( mi . ) Map Distance ( in . ) Actual Distances and Map Distances 50 1 Complete the table . What is the actual distance between two towns that are 4 inches apart on the map ?
Answer:
200miles
Step-by-step explanation
4 x 50 = 200
As for the table, just multiply each inch by 50.
For example; 7in = 350 miles because 7x50 = 350
Please help? I’ve been stuck on this question
Answer:
y-intercept = -3
another point on the line = (6,-1)
Step-by-step explanation:
1. Underline important parts of the question (slope of 1/3, point (3, -2))
2. mark the point that is given (3, -2)
3. slope form is rise over run which basically means that the number one is how much the line rises, and the number three is how much the line goes to the right (since the slope is positive then it runs to the right, if it was negative it would go to the left.) Basically 1/3 = rise over run
4. put your pencil on the point (3, -2) and go up one point and over three points. continue doing so from each new point (two or three points is good enough)
5. take a ruler and draw a line that connects all three and keep it going until it crosses the y- axis (which is the vertical line)
6. the point that crosses through the y -axis is the y-intercept.
7. now you can go and look at your points that you have made and choose one of them to answer the question with
(I hope this cleared it up a bit I'm not very good at explaining things this is the best I can do)
helllppppppppppp please
Answer:
No, it will not pass specifications.
Step-by-step explanation:
It says that the max slope of the wheelchair ramp should be 1/12.
To calculate slope, you do rise over run or y values over x values. In this case, the rise over run is 5/50. 5/50 simplifies to 1/10.
1/10 > 1/12, meaning that it is more than the maximum slope.
If B=3n-10B=3n−10 and C=n^{2}-6n-6,C=n
2
−6n−6, find an expression that equals 2B-3C2B−3C in standard form.
The expression of 2B - 3C in standard form is -3n^2 + 24n - 2
Functions and valuesGiven the following expressions
B = 3n - 10
C = n^2-6n-6
Required
2B - 3C
Substitute
2B - 3C = 2(3n -10) - 3(n^2-6n-6)
2B - 3C = 6n - 20 -3n^2+18n+18
2B - 3C = -3n^2 + 24n - 2
Hence expression of 2B - 3C in standard form is -3n^2 + 24n - 2
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You design a logo for your soccer team. The logo is 3 inches by 5 inches. You decide to dilate the logo to 1.5 inches by 2.5 inches. What is the scale factor of this dilation?
Answer:
1/2
Step-by-step explanation:
The dimensions are cut in half ....scale factor 1/2
URGENT PLEASE ANSWER THESE
Answer:
1A) 2 gallons of 20% solution and 3 gallons 15% solution needed
1B) 4 gallons of 20% solution and 1 gallons 15% solution needed
Step-by-step explanation:
1A) adding 20% salt and 15% water making 5 gallons of 17%
20% salt + 15% salt = 5 gallons of 17% salt
0.20x + 0.15(5 - x) = 0.17(5)
0.20x + 0.75 - 0.15x = 0.85
0.20x + 0.75 - 0.75 - 0.15x = 0.85 - 0.75
0.20x - 0.15x = 0.10
0.05x = 0.10
0.05x/ 0.05 = 0.10/0.05
x = 2 gallons (amount of 20% solution needed)
5 - x = 5 - 2 = 3 gallons (amount of 15% solution needed)
1B)
0.20x + 0.15(5 - x) = 0.19(5)
0.20x + 0.75 - 0.15x = 0.95
0.20x + 0.75 - 0.75 - 0.15x = 0.95 - 0.75
0.20x - 0.15x = 0.20
0.05x = 0.20
0.05x / 0.05 = 0.20/0.05
x = 4 gallons (amount of 20% solution needed)
5 - x = 5 - 4 = 1 gallons (amount of 15% solution needed)
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Independent Practice
An image on a slide is similar to its projected image. A slide is 35 mm wide and 21 mm high. Its projected image is 85 cm wide. To the nearest centimeter, how high
is the image?
A. 51 cm
B. 5.1 cm
C.
D.
142 cm
9 cm
Answer:
Projected height = (85 *21) / 35 = 51 cm
Step-by-step explanation:
Since the images are similar, we can set up the proportional equation like this:
Slide width / Slide height = Projected width / Projected height
35 mm / 21 mm = 85 cm / Projected height (in cm)
Projected height = (85 *21) / 35 = 51 cm
Which exponential equation is equivalent to this logarithmic equation? log x = 4
Answer:
[tex]x=10^{4}[/tex]
Step-by-step explanation:
Switching from Logarithmic to Exponential form:An exponential base is the inverse of a logarithm with the same base. Given the equation log x = 4, note that the base of the logarithm isn't written in (it has no subscript). By default, the base of the logarithm function is base-10. So, to rewrite the equation using an exponential, we need to undo the logarithm with an exponential of the same base.
[tex]\log(x)=4[/tex]
[tex]10^{\log{(x)}}=10^{4}[/tex]
[tex]x=10^{4}[/tex]
Analogies with Addition/SubtractionThink about the equation x + 7 = 10.
I could tell you this is the equation in "addition form". What if I asked you to write an equation in "subtraction form"? While neither "addition form" nor "subtraction form" have been defined explicitly, one could undo the addition, and get an equation with subtraction in it, which one could argue is a "subtraction form" of the equation.
[tex]x+7=10[/tex]
Subtracting 7 from both sides to undo the addition...
[tex](x+7)-7=(10)-7[/tex]
Simplifying the left side since the "+7" and "-7" cancel...
[tex]x=10-7[/tex]
This is arguably in a "subtraction form" (there's a subtraction in it), whereas the original equation had addition in it.
While we could simplify this particular equation's right-hand side, we might not always be able to (what if the 10 had been a "y"... then the "y" and the "7" aren't like terms, and they would have to remain separate)
Similarly, in the logarithm problem, one could simplify 10^4 (it's 10,000), but one doesn't have to, and one won't always be able to.
For the logarithm problem, x=10^4 is the exponential form, as requested.
Solve the questions by factoring! Please help asap!
Answer:
Step-by-step explanation:
A group of summer campers went on a trip.
22 campers rode in cars with their parents
while the rest filled four buses. How many
campers were on each bus if a total of 150
campers went on the trip?
Answer:
Answer is 32
Step-by-step explanation:
150-22=128
128÷4=32
Explain weather this equation is a linear equation
4. y = 1 - x
Answer:
Yes, it is a linear equation.
Step-by-step explanation:
Linear equation:An equation of the form ax + by +c = 0, where x and y are two variables and a, b,c are the non-zero real numbers is called a linear equation and the degree of the equation is 1.
y = 1 - x
x + y - 1 = 0
Where a = 1 ; b=1 and c = -1
So, y = 1 -x is a linear equation.
Kirsten is knitting and hates to donate to a local charity. Each hat takes 3 hours to make. If Kirsten knitted 3 hats and a third of another hat. how many hours did she spend knitting?
Simplify the expression to a polynomial in
standard form:
(3x-1)(3x^2+3x+8)
Answer:
9x^3+6x^2+21x-8
Step-by-step explanation:
(3x-1) (3x ^ 2 + 3x + 8) =3x(3x ^ 2 + 3x + 8) +(-1)(3x ^ 2 + 3x + 8) =9x^3+9x^2+24x-3x^2-3x-8 = 9x^3+6x^2+21x-8
Answer:
[tex]\huge\boxed{\sf 9x^3+6x^2+21x-8}[/tex]
Step-by-step explanation:
Given expression:= [tex](3x-1)(3x^2+3x+8)[/tex]
[tex]Expand[/tex]
[tex]= 3x(3x^2+3x+8)-1(3x^2+3x+8)\\\\Multiply\\\\=9x^3+9x^2+24x-3x^2-3x-8\\\\Combine \ like \ terms\\\\= 9x^3+9x^2-3x^2+24x-3x-8\\\\= 9x^3+6x^2+21x-8\\\\\rule[225]{225}{2}[/tex]
Line I has a slope of 13/7. The line through which of the following pair
of points is perpendicular to l?
Answer:
Step-by-step explanation:
You need to find the set of points that will yield a slope that is the negative reciprocal of the slope of Line L because perpendicular lines have negative reciprocal slopes. The negative reciprocal of 13/7 is -7/13. Which set of points will produce this result? The formula for finding the slope is:
m = (y2 - y1)/(x2 - x1)
Consider the second set of coordinates.
(2 - (-5))/(-7 - 6) = (2 + 5)/(-13) = -7/13
The second set of coordinates satisfy the condition.
how to solve part ii and iii
(i) Given that
[tex]\tan^{-1}(x) + \tan^{-1}(y) + \tan^{-1}(xy) = \dfrac{7\pi}{12}[/tex]
when [tex]x=1[/tex] this reduces to
[tex]\tan^{-1}(1) + 2 \tan^{-1}(y) = \dfrac{7\pi}{12}[/tex]
[tex]\dfrac\pi4 + 2 \tan^{-1}(y) = \dfrac{7\pi}{12}[/tex]
[tex]2 \tan^{-1}(y) = \dfrac\pi3[/tex]
[tex]\tan^{-1}(y) = \dfrac\pi6[/tex]
[tex]\tan\left(\tan^{-1}(y)\right) = \tan\left(\dfrac\pi6\right)[/tex]
[tex]\implies \boxed{y = \dfrac1{\sqrt3}}[/tex]
(ii) Differentiate [tex]\tan^{-1}(xy)[/tex] implicitly with respect to [tex]x[/tex]. By the chain and product rules,
[tex]\dfrac d{dx} \tan^{-1}(xy) = \dfrac1{1+(xy)^2} \times \dfrac d{dx}xy = \boxed{\dfrac{y + x\frac{dy}{dx}}{1 + x^2y^2}}[/tex]
(iii) Differentiating both sides of the given equation leads to
[tex]\dfrac1{1+x^2} + \dfrac1{1+y^2} \dfrac{dy}{dx} + \dfrac{y + x\frac{dy}{dx}}{1+x^2y^2} = 0[/tex]
where we use the result from (ii) for the derivative of [tex]\tan^{-1}(xy)[/tex].
Solve for [tex]\frac{dy}{dx}[/tex] :
[tex]\dfrac1{1+x^2} + \left(\dfrac1{1+y^2} + \dfrac x{1+x^2y^2}\right) \dfrac{dy}{dx} + \dfrac y{1+x^2y^2} = 0[/tex]
[tex]\left(\dfrac1{1+y^2} + \dfrac x{1+x^2y^2}\right) \dfrac{dy}{dx} = -\left(\dfrac1{1+x^2} + \dfrac y{1+x^2y^2}\right)[/tex]
[tex]\dfrac{1+x^2y^2 + x(1+y^2)}{(1+y^2)(1+x^2y^2)} \dfrac{dy}{dx} = - \dfrac{1+x^2y^2 + y(1+x^2)}{(1+x^2)(1+x^2y^2)}[/tex]
[tex]\implies \dfrac{dy}{dx} = - \dfrac{(1 + x^2y^2 + y + x^2y) (1 + y^2) (1 + x^2y^2)}{(1 + x^2y^2 + x + xy^2) (1+x^2) (1+x^2y^2)}[/tex]
[tex]\implies \dfrac{dy}{dx} = -\dfrac{(1 + x^2y^2 + y + x^2y) (1 + y^2)}{(1 + x^2y^2 + x + xy^2) (1+x^2)}[/tex]
From part (i), we have [tex]x=1[/tex] and [tex]y=\frac1{\sqrt3}[/tex], and substituting these leads to
[tex]\dfrac{dy}{dx} = -\dfrac{\left(1 + \frac13 + \frac1{\sqrt3} + \frac1{\sqrt3}\right) \left(1 + \frac13\right)}{\left(1 + \frac13 + 1 + \frac13\right) \left(1 + 1\right)}[/tex]
[tex]\dfrac{dy}{dx} = -\dfrac{\left(\frac43 + \frac2{\sqrt3}\right) \times \frac43}{\frac83 \times 2}[/tex]
[tex]\dfrac{dy}{dx} = -\dfrac13 - \dfrac1{2\sqrt3}[/tex]
as required.
what is the decimal of 1/2
Answer:
0.5
one divide by two is zero point five
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
We need to find the decimal form of [tex]\boldsymbol{\sf{\displaystyle\frac{1}{2}}}[/tex].
But first we need to convert it into a fraction whose
denominator is 10, or 100, or 1,000, etc.
The closest number that's divisible by 2 is 10.
So that's the new denominator of the fraction.
Now we should also multiply the top times the number
that we multiplied the bottom by. See how this works?
[tex]\boldsymbol{\sf{\displaystyle\frac{1\times5}{2\times5}}}[/tex]. This yields
[tex]\boldsymbol{\sf{\displaystyle\frac{5}{10}}}[/tex]. And 5/10 in decimal-form yields
[tex]\boldsymbol{\sf{0.5}}[/tex].
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\LARGE\boldsymbol{\sf{calligraphy}}[/tex]
Area=
Help me please thanks
The area of the shaded region shown in the figure is 80π unit²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Area of the shaded region = area of semicircle IL - area of semicircle JK + area of semicircle IJ + area of semicircle KL
Area of the shaded region = area of semicircle IL + area of semicircle IJ = (0.5 * π * 12²) + (0.5 * π * (12/3)²) = 80π
The area of the shaded region shown in the figure is 80π unit²
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Suzanne walks four miles every third day. What is the fewest number of miles she can walk in February
36 miles is the fewest number of miles she can walk in February
There are 28 days in February.
Every third day is 28/3 = 9.333 = 9 days of walking.
since she walks four miles,
9*4 = 36
Hence, 36 miles is the fewest number of miles she can walk in February
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