Final answer:
There can be 900,000 unique 6-digit numbers formed using the digits 0-9 with repetitions allowed, considering the first digit cannot be 0.
Explanation:
Calculating 6-Digit Numbers with Repetitions
The question pertains to the number of unique 6-digit combinations that can be made from the digits 0-9 when repetitions are allowed. Since the first digit of a 6-digit number cannot be 0 (as it would make the number a 5-digit number), there are 9 possibilities for the first digit (1-9). For each of the five remaining positions, all 10 digits (0-9) are possibilities because we are allowing repetitions. Therefore, the total number of combinations is calculated by multiplying the possibilities for each digit place.
The solution is as follows: 9 possibilities for the first digit times 10 possibilities for each of the second, third, fourth, fifth, and sixth digits.
9 (first digit) * 10 (second digit) * 10 (third digit) * 10 (fourth digit) * 10 (fifth digit) * 10 (sixth digit) = 900,000 unique 6-digit numbers that can be formed.
What is the probability of getting exactly 2 heads, given that the first toss is a head?
there is a 1/2 probability of getting heads on any one flip
since the first one landed on heads you have a 1/2 probability f getting a 2nd one
Probability = 1/2
Give the degree and classify the polynomial by the number of terms- 3
A)degree 1, monomial
B)degree 1, binomial
C)degree 0, monomial
D)degree 0, binomial
Answer:
Step-by-step explanation:
the answer is a
Write the standard form of the equation of the line passing through the point (2,5) and perpendicular to the line 4x - y = 2. The answer key says that the answer is x + 4y = 22, but I'm confused on how to get there
To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.
To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.
The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.
Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.
In the figure, if AB ≅ CD, then
A. AB ⊥ CD
B. CE ≅ BE
C. ∠CEA ≅ ∠CEB.
D. arc AB ≅ arc CD.
Answer:
D. arc AB ≅ arc CD.Step-by-step explanation:
To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".
Applying this theorem, we have
[tex]AE \times EB = CE \times ED[/tex]
Where [tex]AB=AE+EB[/tex] and [tex]CD=CE+ED[/tex], also [tex]AB \cong CD[/tex], which means
[tex]AE+EB=CE+ED[/tex]
However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is
[tex]arc(AB) \cong arc(CD)[/tex]
Because an arc is defined by its chord basically, and in this case they are congruent.
Please help me,I need help understand so I can do my own! Worth 20 points!!
A security fence encloses a rectangular area on one side of a park in a city. three sides of fencing are? used, since the fourth side of the area is formed by a building. the enclosed area measures 392392 square feet. exactly 5656 feet of fencing is used to fence in three sides of this rectangle. what are the possible dimensions that could have been used to construct this? area?
the old price for school lunches is $5. The new price is $5.25. What is the percent increase in the cost if school lunches? Write answer as percent. The formula is p=b-a/a. b =new price for lunch. a=old price for lunch. P=percent increase
p=(5.25-5.00)/5.00
p=0.25/5.00
p=0.05
p = 5% increase
A high-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.07 inches per second, and that r = 36 inches at time t = 0. Determine the equation that models the volume V of the balloon at time t, and find the volume when t = 400 seconds.
Find the sum of the first 100 terms in the series
[tex] \frac{1}{(1*2)} + \frac{1}{(2*3)} + \frac{1}{(3*4)} + . . . \frac{1}{n*(n+1)} [/tex]
How to find the volume of a parallelepiped with 8 vertices?
The volume of parallelepiped with 8 vertices is 75 units.
What is Volume of Parallelepiped?A parallelepiped's volume is determined by multiplying its surface area by its height.
The area of the parallelogram base is the cross product's magnitude, ∥a×b∥ , according to its geometric specification, and the vector a×b direction is perpendicular to the base.
Given:
let the 8 vertices are (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6).
so, Volume = det [tex]|\left[\begin{array}{ccc}0&3&2\\5&0&0\\1&0&5\end{array}\right] |[/tex]
= |0( 0- 0) - 3(25- 0) + 2(0 - 0)|
= |0 - 75 + 0|
= |- 75|
= 75 units
Hence, the volume of parallelepiped with 8 vertices is 75 units.
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The length of a rectangle is five times its width. if the area of the rectangle is 320 feet, find its perimeter.
determine the slope of y=3x^2-8 at (x,y)
The first term of a geometric sequence is –2 and the common -1/4. What are the next three terms of the sequence?
HELP! Will give Brainliest! Using dimensional analysis, convert 293 cm into m. (1 m= 100 cm)
(and this is also a Chemistry Question)
I get how to work out the other question, but I'm confused on this one
What is the solution to the system of linear equations graphed below?
A. (3.5, -4)
B. (-4, 3.5)
C. (0,3)
D. (0,-4)
Look at the picture.
Answer: A. (3.5, -4)
Human iq scores are approximately normally distributed with mean 100 and standard deviation 15. determine the minimum iq scores for the top 5% of the population.
To solve this problem, we make use of the z statistic. A population of 5% means that we are looking for the population at >95%, P = 0.95. Using the standard distribution tables for z, a value of P = 0.95 indicates a value of z of z = 1.645
Now given the z and standard deviation s and the mean u, we can calculate for the value of IQ of the top 5% (x):
x = z s + u
x = 1.645 (15) + 100
x = 24.675 + 100
x = 124.675
Therefore the minimum iq score for the top 5% of the population is around 124.675
The minimum IQ score for the top 5% of the population, with a normal distribution mean of 100 and a standard deviation of 15, is approximately 124.7. This is found by using the z-score that corresponds to the 95th percentile, which is 1.645, and applying it to the formula for a score in a normal distribution.
To determine the minimum IQ score for the top 5% of the population, given that human IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution. Typically, the top 5% of values on a normal distribution lie above a certain z-score threshold. This z-score corresponds to the point on the distribution where the cumulative area to the left is 95% (100% - 5%), since we are looking for the score above which the top 5% of scores fall.
To find this z-score, we look up the value in a standard normal distribution table or use a statistical software or calculator. The z-score that corresponds to the 95th percentile is typically around 1.645. To find the actual IQ score, we can then apply the following formula:
IQ Score = Mean + (Z-score * Standard Deviation)
Plugging the values in:
IQ Score = 100 + (1.645 * 15)
IQ Score = 100 + 24.675
IQ Score = 124.675
Therefore, the minimum IQ score for the top 5% of the population is approximately 124.7 (since IQ scores are usually reported to the nearest whole number).
(02.03 LC)
Read the following statement:
Line segment AB is congruent to line segment CD.
Which of the following is an equivalent statement?
AB overbar similar to CD overbar
AB overbar congruent to CD overbar
AB overbar equal to CD overbar
AB overbar element to CD overbar
Answer:
AB overbar congruent to CD overbar
Explanation:
The question is asking whether Line segment AB is CONGRUENT to line segment CD.
The meaning of congruent is having the same shape and size.
Congruent ≅
Element ∈
Equal =
Similar ~
In conclusion, you could say:
AB ≅ CD
I cannot type the lines over the top AB and CD but they are there.
(I know this question is probably old, and i am also tying this so I remember as well, but the other answer didn't have a bit bigger explanation so if anyone comes across this i hope this helped. :)
If two or more objects are the same copy in length and shape then that will be said to be congruent thus AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent thus options (B) and (C) is correct.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
In other meaning, if you can copy a figure then that copy and the original figure will be congruent.
All line segments are in the same shape and have degrees as one in the equation therefore only one criterion which is length is needed to prove congruency.
So, congruent lines are lines whose lengths are the same.
The sign of congruency is ≅ so AB ≅ CD.
Hence " AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent to AB ≅ CD".
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Candis took out a payday loan with an effective interest rate of 15,400%. if she had 220 to invest for a year at this interest rate, how much would make in interest?
A. 3,388,000
B 338,800
C.. 3388
D 33,880
To find the interest Candis would make from a 15,400% interest rate on a $220 investment for one year, we calculate using the simple interest formula, resulting in $33,880.
Explanation:The question asks us to determine how much interest Candis would make from a payday loan with an effective interest rate of 15,400% if she invested $220 for a year. To calculate the interest earned, we can use the formula for simple interest which is I = Prt, where I is interest, P is principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.
Converting 15,400% to a decimal, we get 154. Then, apply the formula:
I = $220 × 154 × 1
This gives us:
I = $33,880
Therefore, Candis would make $33,880 in interest after one year, which corresponds to option D.
If Matrix A has dimensions 1x4 and Matrix B has dimensions 3x4, can these be multiplied?
When constructing a circle circumscribed about a triangle, what is the purpose of constructing perpendicular bisectors?
Do not use spaces in your answer. If f(x) = (-x)3, then f(-3) =
You are typing a paper. At 4:04pm you have typed 275 words. By 4:18pm you have 765 words. Find the rate of change in words per minute. Round your answer to the nearest whole number.
A). None of these
B). 20 words per minute
C). 43 words per minute
D). 35 words per minute
E). 55 words per minute
The rate of change in words per minute will be [tex]35[/tex] words per minute.
What is rate of change ?Rate of change is a rate that tells how one quantity changes in relation to another quantity.
i.e. Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]
We have,
At [tex]4:04[/tex] pm typed [tex]275[/tex] words,
By [tex]4:18[/tex] pm you have [tex]765[/tex] words.
So,
Change in type [tex]= 4:18\ PM -4:04\ PM=14[/tex]
So,
Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]
[tex]=\frac{765-275}{14}[/tex]
[tex]=\frac{490}{14}[/tex]
Rate of change [tex]=35[/tex] words per minute
So, the rate of change is [tex]35[/tex] words per minute which is given in option [tex](D)[/tex].
Hence, we can say that the rate of change in words per minute will be [tex]35[/tex] words per minute.
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Graph y < 1/3x + 1/2
please i need help....the question is.........
area = H/2*(b1+b2)
8.1 = 1.5/2*(6.7 +b2)
8.1=0.75*(6.7+b2)
10.8=6.7+b2
b2=10.8-6.7
b2=4.1m
Find the length of an arc that subtends a central angle of 135° in a circle of radius 2 mi
Find the equation of the line specified.
The slope is -7, and it passes through ( 5, -3).
a.
y = -7x - 3
c.
y = -14x + 32
b.
y = -7x + 32
d.
y = -7x - 38
Please select the best answer from the choices provided
Answer:
answer is b
Step-by-step explanation:
Part A: Solve -vp + 30 < 45 for v .. show your work.
Part B: Solve 3w - 6r = 30 for r .. show your work.
how many cups of grape punch containing 10% fruit juice and berry punch containing 20% fruit juice must be added together to create 12 cups of punch with 18% fruit juice?
A regular octagon has a radius of 6 ft and a side length of 4.6 ft. what is the approximate area of the octagon? 71 ft2 101 ft2 110 ft2 202 ft2
Answer:
Option B is correct.
The approximate area of regular octagon is, 101 square ft.
Step-by-step explanation:
Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.
To find the area of a regular octagon(A) of side length a is given by :
[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]
Given the length of side, a= 4.6 ft
Substitute the value of a=4.6 ft in the given formula of area:
[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or
[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or
[tex]A=(2+2.828)\cdot(21.16)[/tex]
Simplify:
[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.
therefore, the approximate area of regular octagon is, 101 square ft
Carmen hiked at Yosemite national park for 1.25 hours. Her average speed was 3.9 miles per hour. How many miles did she hike? Give the exact answer- do not round!