How many 4-sequences on {0..9} do not begin with 0?

Answers

Answer 1

I take a [tex]n[/tex]-sequence to mean any permutation of the digits 0-9 of length [tex]n[/tex]. Furthermore, I'm assuming no number can be repeated.

If that's the case, then for any 4-sequence, the first digits place (leftmost) has 9 possible choices (1-9). Once that number is used up, we have 9 numbers left in the pool of digits, from which we select a 3-sequence. The number of possible 3-sequences would be [tex]\dfrac{9!}{3!}=60,480[/tex]. Multiply this by 9 (to account for the first digit's possibilities) and we get a grand total of [tex]\dfrac{9\times9!}{3!}=544,320[/tex] possible 4-sequences on [tex]\{0,\ldots,9\}[/tex].

Answer 2

There are 9000 possible 4-sequences that do not begin with the digit 0.

The question asks how many 4-sequences on the set {0..9} do not begin with 0. To solve this, we need to consider the number of possible options for each of the four positions in the sequence, knowing that the first digit cannot be 0.

For the first position, there are 9 options (1-9), since 0 is not allowed. For the next three positions, each can be any of the 10 digits (0-9), since there are no restrictions. Thus, the total number of such sequences is the product of the number of options for each position.

9 options (1st position) x 10 options (2nd position) x 10 options (3rd position) x 10 options (4th position) = 9 x 10 x 10 x 10 = 9000.

So, to find how many 4-sequences do not begin with 0, multiply the number of choices for each position: 9 (first position, cannot be 0) x 10 (second position) x 10 (third position) x 10 (fourth position), resulting in 9000 such sequences.

Related Questions

On a standardized test raw answer the first 22 questions in 5 minutes there are 77 questions on the test if he continues to answer questions at the same rate how long will it take him to complete the test from start to finish

Answers

Hello!

If you answered 22 questions on the test in 5 minutes, there will be an unequal time amount. 22 x 3 = 15 minutes (66 questions) 22 x 4 = 20 minutes (88 questions).
Therefore, it would take you 17.5 minutes to finish all the questions on your test.
Enjoy.

Answer:

Step-by-step explanation:

17.5

the function f(x)=a^x-4 will never cross the x-axis. true or false

Answers

Answer: False

Solution:

The exponential functions with the form y=a^x never cross the x-axis (x-axis is an asymptote), but in this case we have the exponential function translated 4 units downward, then this function crosses the x-axis.

As it is not given a is positive real number or negative real number.

By supposing a is any real number, we will draw the graph of the curve

[tex]a^x-4[/tex] by taking different values of x.

As i have taken different values of a ,

I found that for a< 0, the graph of the curve [tex]y=a^x-4[/tex] does not exist.

For any other value of a, the curve cuts the x axis at one point.

For values of 1<a<0, the curve will cut negative side of X axis.

For value of a, a≥1, the curve will cut positive side of X axis.

For , a=0, the curve will not cut the x axis.

So, The function , f(x)=[tex]a^x -4[/tex] will cuts the x axis at one point for a >0 and for negative values of a, and for a< 0 ,it will not cut the x axis.

How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number. The large tire has a diameter of 60 inches. The small tire has a radius of 9 inches.

Answers

Final answer:

For the large tire with a diameter of 60 inches, it would make 38 rotations after traveling 600 feet. The small tire with a radius of 9 inches would make 127 rotations in the same distance.

Explanation:

First, let's convert the feet into inches since the tire measurements are given in inches. There are 12 inches in a foot, so 600 feet is equal to 7200 inches. Now, we need to determine the circumference of each tire, which we can find using the formula for the circumference of a circle which is 2πr (twice the product of pi and the radius).

For the large tire, the diameter is 60 inches, so the radius (r) is half the diameter, which is 30 inches. Thus, the circumference of the large tire would be 2π*30, which is about 188.5 inches. The large tire would therefore make about 7200/188.5 = 38 rotations.

The small tire has a radius (r) of 9 inches, so its circumference is 2π*9, which is about 56.55 inches. The small tire would hence make about 7200/56.55 = 127 rotations.

Please note that the numbers are rounded off to the nearest whole number as requested.

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Final answer:

The large tire makes approximately 38 rotations, and the small tire makes approximately 128 rotations when each travels a distance of 600 feet.

Explanation:

To find the number of rotations a tire makes, you first need to know the circumference of the tire, which represents the distance the tire would cover in one full rotation. The circumference of a circle (or tire, in this case) is calculated as 2πr, where r is the radius of the circle.

For the large tire with a diameter of 60 inches (which makes the radius 30 inches because the radius is half the diameter): The circumference is 2π × 30 = 188.5 inches. Convert this to feet because the distance given is in feet. So, 188.5 inches is about 15.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 15.7 feet = approximately 38 rotations.

For the small tire with a radius of 9 inches: The circumference is 2π × 9 = 56.5 inches, which is about 4.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 4.7 feet = approximately 128 rotations.

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How many ways can Hannah give three of her eight T-shirts to her younger sister?

Answers

If Hannah gives her younger sister 3 shirts, it does not matter what order she hands them to her. No matter the order, it will still be the same group of 3 shirt. Since order is not important this problem can be solved using a combination.

Specifically we are asked to find 8C3 (sometimes called "8 choose 3"). This is a fraction. In the numerator we start with 8 and count down 3 numbers. In the denominator we start with 3 and count all the way down to 1. Thus we obtain,

[tex] \frac{(8)(7)(6)}{(3)(2)(1)}=(8)(7)=56 [/tex]

The city transportation commission surveys a random sample of licensed drivers, asking the question, "Do you favor increasing the number of bus routes within the city limits?" Which shows how bias might have affected the results of the survey? A. The question is biased in favor of bus riders. B. The question is biased against bus riders. C. Surveying only licensed drivers creates a bias against people who don't have driver's licenses. D. Since the survey used random sampling, it is unlikely to be biased.

Answers

C) this shows bias against people without a license.

It stands to reason that someone without a driver's license is more likely to ride the bus; therefore their input should be received as well.

Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of vector PQ.

Answers

the magnitude of the vector is
[tex] \sqrt{2 {}^{2} + 5 {}^{2} } = \sqrt{29} [/tex]
the component form is
<2,5>

To find the component form, <x2-x1, y2-y1>
We have P(2,9) meaning, x1=2, y1=9
And, Q(4,14) meaning, x2=4, y2=14
Now PQ = <4-2, 14-9> = <2, 5>

Now to find the magnitude, we use the distance formula aka the Pythagorean Theorem. a^2 + b^2 = c^2 and we have, x=2, y=5
So, 2^2 + 5^2 = c^2 =29
Therefore, the magnitude is c = sqrt of 29.

The lifetimes of batteries produced by the juicy battery company are normally distributed with a mean of 100 hours and a standard deviation of 10 hours. find the number of hours where at least 90% of the batteries will continue to operate at.

Answers

The z-score associated with 90% is:
P(0.9)=1.28
sup[pose the number of hours whereby at least 90% of the batteries will continue to operate is x.
the z-score is given by:
z=(x-μ)/σ
where:
μ is the mean
σ is the standard deviation
substituting the values we shall have:
1.28=(x-100)/10
solving for x we get:
x=112.8 hours

find the area of the right triangle with the base length 30 inches and height 3 feet

Answers

A = (1/2)bh
.. = (1/2)(2.5 ft)*(3 ft) . . . . . . 30 inches = 2.5 feet
.. = 3.75 ft^2

Johnson Certified bought a fiber optic cable for $975,000. The estimated life of the cable is 20 years, after which its salvage value is estimated to be $5,000. Using the straight-line method, what is the annual depreciation to the nearest cent?

Answers

Remember that straight line depreciation can be calculated using the formula:
[tex]D_{a}= \frac{C-R}{U} [/tex]
where
[tex]D_{a}[/tex] is the annual depreciation
[tex]C[/tex] is cost
[tex]R[/tex] is the salvage value
[tex]U[/tex] is the estimated life in years.

For our problem we know that [tex]C=975000[/tex], [tex]R=5000[/tex], and [tex]U=5000[/tex]. Lets replace those values in our formula to find [tex]D_{a}[/tex]:
[tex]D_{a}= \frac{975000-5000}{20} [/tex]
[tex]D_{a}= \frac{970000}{20} [/tex]
[tex]D_{a}=48500[/tex]

We can conclude that the annual depreciation of the optic fiber cable is $45,000

At a grocery store a four-pack of yogurt costs $3.95. How much does each container of yogurt cost

Answers

99 cents if you round up the 7.

about 99 cents or exactly 0.9875

During the two hours of the morning rush from 8
a.m. to 10
a.m., 100 customers per hour arrive at the coffee shop. the coffee shop has a capacity of 80 customers per hour. what is the number of customers waiting at 10
a.m.

Answers

80 customers per hour

Suppose 60% of the people in a town will get exposed to flu in the next month. if you are exposed and not inoculated then the probability of your getting the flu is 80%, but if you are inoculated that probability drops to 15%. of two executives at beta company, one is inoculated and one is not. what is the probability at least one will not get the flu? assume that the events that determine whether or not they get the flu are independent.

Answers

P(Inoculated getting flu) = 0.6*0.15 = 0.09
P(Non-inoculated getting flu) = 0.6*0.8 = 0.48
P(Both getting flu) = 0.09*0.48 = 0.0432
P(Atleast 1 not getting flu) = 1-0.0432 = 0.9568

A light bulb consumers 1800 watt-hours per day. How long does it take to consume 9450 watt-hours?

Answers

Final answer:

To find out how long it takes for a light bulb to consume 9450 watt-hours, when it uses 1800 watt-hours per day, divide 9450 watt-hours by 1800 watt-hours per day, which equals 5.25 days.

Explanation:

The question involves calculating how long it takes for a light bulb to consume a certain amount of energy (9450 watt-hours) given its daily consumption rate (1800 watt-hours per day).

To find the duration, you simply divide the total energy by the daily consumption rate:

Total energy to be consumed = 9450 watt-hours

Daily energy consumption = 1800 watt-hours per day

Duration = Total energy ÷ Daily energy consumption

Duration = 9450 watt-hours ÷ 1800 watt-hours/day = 5.25 days

Therefore, it will take 5.25 days for the light bulb to consume 9450 watt-hours of energy.

Suppose that after he makes his first shot, he shoots exactly 5 more shots. what is the probability that, out of these 5 attempts, he makes an even number of shots?

Answers

The probability of making 2 of 5 shots is 0.31250. The probability of making 4 of 5 shots is 0.15625. So, the probability of making an even number of shots is
.. 0.31250 +0.15625 = 0.46875

_____
p(2 of 5) = (5C2)/2^5 = 10/32
p(4 of 5) = (5C4)/2^5 = 5/32

For the above, we have assumed the probability of success is 1/2.

Rachel jogged along a trail that was 1/4 (fraction) of a mile long. She jogged along the trail 8 times. How many miles did Rachel jog in all??

Answers

1/4+1/4+1/4+1/4+1/4+1/4+1/4+1/4 = 8 Miles

1/4+1/4 = 1/2 Mile

1/2+1/2 = 1 Mile

1+1 = 2 Miles

2 miles because 8 divided by 1/4 is 2

Gavin's mean score on 3 math tests is 87. What equation can be solved to find x, the score he needs on his next test to bring his mean score up to 90?

Answers

Final answer:

To find the score Gavin needs on his next test to have an average of 90, we understand that the sum of his first three tests and the fourth test, divided by four, must equal 90. Translating this understanding to an equation gives: (261 + x4) / 4 = 90, which can be solved for x4.

Explanation:

The subject posed deals with the understanding of mean averages and algebra. The mean, or average, is calculated by adding up all the values and dividing by the total number of values. In Gavin's case, his mean score of 87 over three tests can be represented algebraically as (x1 + x2 + x3) / 3 = 87. The challenge is to find out what Gavin needs to score in his next test (let's call this x4) to have a new mean score of 90.

To set up the equation we need to understand that now the average is calculated over four tests, and it must equal 90. Thus, the equation to solve is ((x1 + x2 + x3) + x4) / 4 = 90. As we know that the sum of his first three test scores is 87 * 3 (because (x1 + x2 + x3) / 3 = 87), we substitute that sum (261) into the equation:

(261 + x4) / 4 = 90. Solving this equation for x4 will give the score Gavin needs on his next test to achieve an average of 90.

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i dont get this. can you explain

Answers

The rightmost column is the product shown in the middle column. From top-to-bottom, those numbers will be 83.1, 831 (given), 8310.

The middle column is a re-write of the first column and is equal to the third column. You can figure the numbers there from either direction. In the center row, you need 8.31 × ___ = 831. It should not be difficult for you to figure out the number in the blank is 100. (It is also the power of 10 between 10 in the first row and 1000 in the third row.)

The divisor in the first column is the inverse of the multiplier in the second column. 0.1 = 1/10, 0.01 = 1/100, and in the third row, 0.001 = 1/1000. The missing number in the first column is 0.001.

_____
The four missing numbers are 83.1, 100, 0.001, 8310. (top to bottom, left to right)

There were three trains made of the cars with exactly the same number of passenger's seats. The first train had 418 seats, the second 456, and the third 494. How many cars were in each train, if it is known that each train had not more than 50 cars?

1 train=?

2 train=?

3 train=?

Answers

1 train=418 2 train=456 3train=494 add them all together and divide by 3 418+456+494=1368/3=456 i hope this helps you and each train has more than 50 cars

You apparently need to find the greatest common divisor of (418, 456, 494). You can start by looking at the differences between these numbers. They are
.. 456 -418 = 38
.. 494 -456 = 38
So, if 38 divides these numbers evenly, that is the number of seats in each car. (It does).

train 1 had 418/38 = 11 cars
train 2 had 456/38 = 12 cars
train 3 had 494/38 = 13 cars

_____
The number of seats in each car could be a sub-multiple of 38, say 19. In that case, the number of cars in each train would be twice the number shown above. It is slightly unusual for a train car to have an odd number of seats, but is not unheard of.

A snail traveled 3 over 8, of an inch in 3 minutes. How many inches can the snail travel in 9 minutes? Express the answer as a decimal

Answers

So, first of all, let's convert the fraction [tex] \frac{3}{8} [/tex] into a decimal, which would be 0.375 (3 divided by 8)

The snail travels this far in 3 minutes. To find out how far it travels in nine minutes, we have to find out how many times 3 goes into 9.

9 / 3 = 3

Now. we simply multiply our decimal by three in order to get our answer!

0.375 x 3 = 1.125 inches

The answer is 1.125 inches!

Patricia pays $1.19 each to download songs to her MP3 players. If n is the number of downloaded songs, which equation represents the cost C in dollar?

Answers

C=1.19n or C=1.19 X n
Because each song costs 1.19, you just multiply it by the number of songs downloaded. So if I downloaded 2 songs the cost would be $2.38.

Hope this Helps

A recipe for bread calls for 4 1/4 cups of flour. Which expression gives the number of cups of flour needed if you want to make 3 1/2 batches of this recipe?

A. 3 1/2 + 4 1/4
B. 3 1/2 x 4 1/4
C. 4 1/4 ÷ 3 1/2
D. 4 + 1/2 + 3 + 1/2

Answers

the answer to this question is B

the answer is B must multiply

Help! I’ve been stuck for like minuteeesss!!!

Answers

a. For each mile, you use 14.5/348=0.0417 gallons of gas. If you drive 2163 miles, you will use 0.0417*2163=90.2 gallons.

b. For each gallon, you can drive 348/14.5=24 miles. If you have 132 gallons, you can drive 132*24=3168 miles.

In △ABC, AB = 7 and AC = 17. Find m∠B to the nearest degree
68
38
21
87

Answers

Answer:

The m∠B is 68°

Step-by-step explanation:

Given the right angled triangle ABC in which right angled is at A.

AB = 7 units and AC = 17 units

we have to find the measure of ∠B.

By trigonometric ratios,

[tex]cot \angle B=\frac{AB}{AC}[/tex]

[tex]cot \angle=\frac{7}{17}[/tex]

[tex]\angle B=cot^{-1}(\frac{7}{17})[/tex]

[tex]\angle B=67.619864948\sim 68^{\circ}[/tex]

Hence, the m∠B is 68°

Option 1 is correct

2) Suppose 3x + 4y = 52 and 5x + y = 30. What is the value of 8x − 2y?

Answers

Try this solution, note, the suggested option is not the shortest way.

Answer:

Step-by-step explanation:

One side of a triangle is increasing at a rate of 8 cm/s and a second side is decreasing at a rate of 3 cm/s. if the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 24 cm long, the second side is 35 cm, and the angle is π/6?

Answers

A = (1/2)ab*sin(θ)
A' = (a'*b*sin(θ) +a*b'*sin(θ) +a*b*cos(θ)*θ')/2
0 = (8 cm/s)*(35 cm)*sin(π/6) +(24 cm)*(-3 cm/s)*sin(π/6) +(35 cm)*(24 cm)*cos(π/6)*θ'
0 = 140 cm^2/s -36 cm^2/s +420√3 cm^2*θ'
θ' = -104/(420√3) . . . . rad/s
.. = -26(√3)/315 . . . . . . rad/s
.. ≈ -8.19°/s

_____
The figure offers a sort of sanity check on the numbers.

A rectangular prism has a length of 5 centimeters, a width of 5 centimeters, and a height of 10 centimeters. The surface area of this prism is 250 square centimeters.

True or False

Answers

that is true because if you use the surface area formula, 2(wl+hl+hw), you'll get 250.

Trigonometric Identities and Applications plz help

Answers

[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\\\\ -------------------------------\\\\ sin(A+B)=(0.35)(0.81)~~+~~(0.94)(0.58) \\\\\\ sin(A+B)=0.2835+0.5452[/tex]

Edgar has a bird bath that holds 2 gallons of water. He only want to fill it 3/4 full. How much water in gallons should Edgar put in the bird bath?

Answers

In order to solve this problem, we need to multiply the total gallons the bath can hold with the amount he wants it full.

2 × 3/4 = 6/4 = 1 1/2

Edgar should put 1 1/2 gallons of water in the bath.

Hope this helps!

Bella Sandino failed to pay her cell phone bill in the amount of $85.14 by the due date of March 4. Calculate the amount Bella must pay on March 20 if the company charges 20% interest on late payments. Assume a 365-day year.

Answers

$85.14/ 100= 0.8514 x 20= 17.028 + 85.14 = $102.168

85.14*(1 +0.20*16/365) = 85.89

Let j and k stand for two different rational numbers. If ∣j∣>∣k∣, then what else must be true?
A) j is farther from 0 than k is. B) j is less than k. C) On a number line, j is to the right of k.
D) the opposite of j is less than the opposite of k

Answers

A is the correct answer trust me

Answer:

A) j is farther from 0 than k is

Step-by-step explanation:

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