How many integers are there from 1,000 through 9,999? (b) How many odd integers are there from 1,000 through 9,999? (c) How many integers from 1,000 through 9,999 have distinct digits? (d) How many odd integers from 1,000 through 9,999 have distinct digits? (e) What is the probability that a randomly chosen four-digit integer has distinct digits? What is the probability that a randomly chosen four-digit integer has distinct digits and is odd?

Answers

Answer 1

Answer:

(a) [tex]Total= 9000[/tex]

(b) [tex]Total = 4500[/tex]

(c) [tex]Total = 4536[/tex]

(d) [tex]Total = 2240[/tex]

(e) [tex]Pr = 0.5040[/tex] --- Probability of distinct digits

[tex]Pr = 0.2489[/tex] --- Probability of odd distinct digits

Step-by-step explanation:

Solving (a): Integers from 1000 to 9999

To do this, we simply add 1 to the range.

i.e.

[tex]Total= Range +1[/tex]

Range is the difference between the given interval.

[tex]Total= 9999 - 1000 +1[/tex]

[tex]Total= 9000[/tex]

Solving (b): Odd integers

This implies that the last digit must be any of 1, 3, 5, 7 and 9 (i.e. 5 digits)

The first digit can not be 0 (i.e any of the remaining 9 digits)

There is no restriction to other digits

Numbers from 1000 to 9999 are 4 digits, so the possible selection are:

[tex]First= 9\\Second = 10\\Third = 10\\Last = 5[/tex]

Total selection is:

[tex]Total = 9 * 10 * 10 * 5[/tex]

[tex]Total = 4500[/tex]

Solving (c): Distinct digits

This implies that all 4 digits are different and the first can not be 0.

So, we have:  

[tex]First = 9[/tex] i.e. (1 - 9)

[tex]Second = 9[/tex] i.e. (0 - 9) minus the first digit

[tex]Third = 8[/tex]

[tex]Fourth = 7[/tex]

Total selection is:

[tex]Total = 9*9*8*7[/tex]

[tex]Total = 4536[/tex]

Solving (d): Odd digits that are distinct

This implies that the last digit must be any of 1, 3, 5, 7 and 9 (i.e. 5 digits)

The first digit can not be 0 and must be different from the last (i.e 8 digits)

The second digit must be different from the first and the last(i.e. 8 digits)

The third digit must be different from the three other digits (i.e. 7 digits)

So,

[tex]Total = 5 * 8 * 8 * 7[/tex]

[tex]Total = 2240[/tex]

Solving (e): Probability that a number is distinct

In (a), total possible digits is 9000

In (c), total distints are 4536

So, the probability is:

[tex]Pr = \frac{4536}{9000}[/tex]

[tex]Pr = 0.5040[/tex]

In (d), total odd distinct digits are 2240

So, the probability is:

[tex]Pr = \frac{2240}{9000}[/tex]

[tex]Pr = 0.2489[/tex]


Related Questions

David’s watch broke. He decides to get it fixed instead of replacing it. The total cost to repair the watch can be represented by 0.07(45h) + 45h, where h represents the number of hours it takes to repair the watch. What part of the expression represents the amount of tax David has to pay? Explain.

Answers

0.07

45h represents how much it costs per hour to get it fixed and how long it takes to get it fixed
0.07(45h) would represent the tax because it is 7% of the cost pretax

Hii!! Please help me out. To help me understand the answer just say exactly which part I'm putting the number in and stuff.

Answers

Answer:

y = 4;

y = 7;

x = 6

Step-by-step explanation:

Given the rule, y = x/2, find the missing values as shown below:

✔️For the first row, to find y, substitute x = 8 into y = x/2,

y = 8/2

y = 4

✔️For the second row, to find y, substitute x = 14 into y = x/2,

y = 14/2

y = 7

✔️For the third row, to find x, substitute y = 3 into y = x/2,

3 = x/2

3*2 = x

6 = x

x = 6

Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
Click twice to plot each segment.
Click a segment to delete it.


Answers

I can't plot it for you, but the slope will be the y/x or the rise/run.

You can find the slope by using 2 points of the line and subtracting the (y1-y2)/(x2-x1)

Choose the sentence that is out of sequence.

Mary Jo began reading The Alphabet Book.
Mother put Jimmy to bed.
Jimmy helped read.
Jimmy fell asleep.

Answers

Answer:

C.

Step-by-step explanation:

⚠️ Mhanifa, can you help me, please? This is due asap and I will mark brainliest :)

The image is attached. Thanks! (There are two questions.)

Answers

Answer:

The domain is the set of x-values:

x = [-4, 4]

The range is the set of y-values:

y = [-1, 2]

How do I do number 2 and 4 please help

Answers

Answer:

2: 176.8mm

4: ?

Step-by-step explanation:

2: 56 times 3.14 = 175.84 --> Nearest tenth: 176.8

4: I can't see the problem, sorry :(

Answer:

2. 2461.8

4. 86.6

Explanation:

your formula for area is pi×radius^2

you are using 3.14 for pi

and your radius is half way across the circle or half the diameter.

2. 3.14×(28)^2

3.14×784

=2461.8

4.This one shows the diameter so you have to divide it by 2 first.

10.5/2=5.25

radius=5.25

3.14×(5.25)^2

3.14x27.5625

=86.6

I ROUNDED BOTH ANSWERS AT THE END

Melody paid for a scarf with a ten dollar bill her change was two dollar three quarters and two dimes how much was the scarf

Answers

Answer:

Step-by-step explanation:

10 -2.95 = 7.05

the scarf cost $ 7.05

Answer:

4456646

Step-by-step explanation:

its that bc we add

need help w this thanks

Answers

Answer:

a

Step-by-step explanation:

) Jolie draws a map of her neighborhood on a
coordinate plane. She draws her house at a point in
Quadrant II.
OU
Select all the points that could represent the location of
Jolie's house?
a.) (0,5)
b.) (1, -4)
c.) (-2, 0)
d.) (-4.71
Pls help and explain if you can

Answers

omg omg omg omg omg omgg omg

A box contains paper clips of three different sizes. The numbers of each size of paper clip are listed below.
· 100 small paper clips.
· 250 medium paper clips.
· 150 large paper clips.
One paper clip is randomly selected from the box. What is the probability that the paper clip selected is either small of medium?

Answers

Answer:

[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

Add all paper clip sizes together:

[tex]100 + 250 + 150 = 500[/tex]

They want the probability of either a small or medium being chosen, so you add both paper clips sizes together.

[tex]100 + 250 = 350[/tex]

Now put the number of small and medium paper clips together over the total number of paper clips to find the probability.

Can divide 350 and 500 by 50, which simplifies it down to 7/10.

[tex]\frac{350}{500} = \frac{7}{10}[/tex]

The probability that the paper clip selected is either small or medium is 7/10.

What is the probability that the paper clip is either small or medium?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the paper clip selected is either small or medium = (number of small paper clip / total number of clips) + (number of medium paper clip / total number of clips)

= 100/500 + 250 / 500 = 350 / 500 = 7/10

To learn more about probability, please check: https://brainly.com/question/13234031

Marking as brainliest



So basically I need u to in ur on words for the reasoning to explain to me how I got my answer. An the answer is in the second box I circled it btw this is 9th grade algebra!

Answers

you knew that it had to be a total of $60.60 and that the flat cost of the plan is $48. so you subtracted the flat cost from the total cost to get the amount that could be spent on gigabytes of data. since you knew that the gigabytes cost $3 each, you divided the remaining budget (12.60) by $3 and got the number of gigabytes that she can get.

sorry if that's confusing or wordy! hope it helps!

Which of the following terms correctly describe the object below?
Check all that apply.
A. Polygon
B. Pyramid
C. Triangle
D. Prism
E. Polyhedron
F. Square

Answers

Answer:

pyramid,  solid, polyhedron

Step-by-step explanation:

The given figure is a pyramid.

What is a pyramid?

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point. A pyramid is formed by connecting the bases to a vertex. Each edge of the base is connected to the vertex, and forms the triangular face, called the lateral face.

The given figure is a square pyramid, since it has a square base where all the edges are joined at a common vertex by four triangular faces. A square pyramid characterized by a square base is a three-dimensional shape having five faces, thus called a pentahedron. The most famous example of such a square pyramid is the Great Pyramid of Giza.

Learn more about pyramid here

https://brainly.com/question/13057463

#SPJ2

Find h.
10 cm
h = ✓ [?] cm
8 cm

Answers

Answer:

√86 cm

Step-by-step explanation:

radius² + h² = slope²            slope = 10       radius = 4

               h² = slope² - radius²

               h  =  √(slope² - radius²)

                   =  √(10² - 4²)

                   =  √ 86

                   =

Answer: 84

...........

PLS HELP WILL GIVE BRAINLESS

Given 4 < a < 5, 2 < b < 4 Find: a / b

Answers

Answer:

I hope this helps!

Step-by-step explanation:

4<a<5

2<b<4   multiply

4x2 < axb < 5x4

8<ab < 20

Answer:

1<a/b<2.5

Step-by-step explanation:

bro you're gonna give me brainless ://

We are given 4<a<5 and 2<b<4 and are asked to find a/b.

Since there is a wide range of values of numbers from 4 to 5 and 2 to 4, there is no definite answer to this. However, we can take the most extreme values here and write them on the opposite ends of the inequality.

For example, the lowest value here is >4/4 (>1) because that is the smallest value from the first inequality divided by the largest value from the second inequality. The other extreme is the biggest value possible, which is <5/2 (<2.5).

Given these extremes, we can now rewrite the inequality.

(smallest value)<a/b<(largest value)

1<a/b<2.5

Neeed help plz urgent need to turn in this assignment

Answers

Answer:

The area of the shaded region of the figure in the exercise is:

27.98 [tex]in^{2}[/tex]

Step-by-step explanation:

To obtain the area of irregular shapes, you can divide that shape in figure you know and you can obtain the area, first, we're gonna calculate the area of the right side and the left side with the formula below:

Area of a rectangle = base * height.Area of right rectangle = 1.6 in * 5.2 inArea of right rectangle = 8.32 [tex]in^{2}[/tex]

How the left rectangle and the right rectangle have the same measurements, we can say:

Area of left rectangle = 8.32 [tex]in^{2}[/tex]

You can see in the center there is a rectangle too, but you need just a half formed by a triangle, you can use two form for this: calculating the area of the triangle or calculating the area of the whole rectangle and next to divide in 2, we're gonna use the first:

Area of triangle = (base * height) / 2

In the exercise, the base of the shaded triangle is 2.7 inches, and the height you must add the measurements in the right side:

Height of the triangle = 1.6 in + 5.2 in + 1.6 inHeight of the triangle = 8.4 in

Now we replace in the formula:

Area of triangle = (2.7 in * 8.4 in) / 2Area of triangle = 22.68 [tex]in^{2}[/tex] / 2Area of triangle = 11.34 [tex]in^{2}[/tex]

By last, you must add all the calculated areas from the shaded regions:

Area of the shaded region = 8.32 [tex]in^{2}[/tex] + 8.32 [tex]in^{2}[/tex] + 11.34 [tex]in^{2}[/tex]Area of the shaded region = 27.98 [tex]in^{2}[/tex]

Plzzzzzzzzzzzzzzzzzzz help

Answers

Answer:

25

Step-by-step explanation:

1/2 b h

1/2×10×5=25

so i guess the ans is 25 thats all I know

u take 1/2 base ×height

1/2 * 5 * 10
Answer = 25

What is the value of the second quartile

Answers

Answer:

the value is 20 out of 100

Step-by-step explanation:

What’s the answer to this ?

Answers

Answer:

Step-by-step explanation:

[tex]0.25=\frac{x}{140} \\140*0.25=\frac{x}{140}*140\\35=x[/tex]

1st box: 140

2nd box: 140

3rd box: 35

A:Consecutive interior angles
B:Vertical angles
C:Alternate exterior angles
D:Corresponding angles

Answers

Answer:

D: corresponding angle

hope it helps.

Answer:

corresponding angles

Step-by-step explanation:

hope it is helpful ><

Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the letters of the word DANCER be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is . (b) How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit? (c) How many ways can the letters of the word DANCER be arranged in a row if the letters NCE must remain together (in order) as a unit?

Answers

Answer:

(a) 720 ways

(b) 120 ways

(c) 24 ways

Step-by-step explanation:

Given

[tex]Word = DANCER[/tex]

[tex]n =6[/tex] --- number of letters

Solving (a): Number of arrangements.

We have:

[tex]n =6[/tex]

So, the number of arrangements is calculated as:

[tex]Total =n![/tex]

This gives:

[tex]Total =6![/tex]

This gives:

[tex]Total =6*5*4*3*2*1[/tex]

[tex]Total =720[/tex]

Solving (b): DA as a unit

DA as a unit implies that, we have:

[DA] N C E R

So, we have:

[tex]n = 5[/tex]

So, the number of arrangements is calculated as:

[tex]Total =n![/tex]

This gives:

[tex]Total =5![/tex]

This gives:

[tex]Total =5*4*3*2*1[/tex]

[tex]Total =120[/tex]

Solving (c): NCE as a unit

NCE as a unit implies that, we have:

D A [NCE] R

So, we have:

[tex]n = 4[/tex]

So, the number of arrangements is calculated as:

[tex]Total =n![/tex]

This gives:

[tex]Total =4![/tex]

This gives:

[tex]Total =4*3*2*1[/tex]

[tex]Total =24[/tex]

Box Plot for Problem #12​

Answers

I don’t see an image for this.

A couple's anniversary dinner bill was $126.50. They tipped their waiter 20% of the bill. What was the total bill including tip?

Answers

Answer:

$151.80 was the total bill including tip.

Step-by-step explanation:

$126.50 x 20% = $25.30

$126.50 + $25.30 = $151.80


$151.80

$126.5•1.2=$151.8


[tex]\boxed {\boxed {prove : \: 3 \: is \: greater \: than \: 5​ }} [/tex]

Answers

3 has more letters than 5. Hence 3 is greater than 5

Write the equation of the circle with the given information.
Center: (5, -13)
Radius: 11

Answers

Answer:

(x - 5)² + (y + 13)² = 121

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (5, - 13 ) and r = 11 , then

(x - 5)² + (y - (- 13))² = 11² , that is

(x - 5)² + (y + 13)² = 121

Miguel is staining a wooden box. To determine how much stain he needs, he'll need to find the surface area of the box. True False

Answers

Answer:

True

Step-by-step explanation:

Miguel is staining a wooden box. he needs to find the surface area of the box

We have given that,

Miguel is staining a wooden box.

To determine how much stain he needs, he'll need to find the surface area of the box.

We have to determine statement is true or false.

What is the surface area of the box?

To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Therefore he needs to find the surface area of the box

and it is a true statement.

To learn more about the box visit:

https://brainly.com/question/26161002

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For which situation could flipping a coin be used to generate a random sample

A: To predict if a machine will be defective or not. B: To predict student performance on an exam. C: To predict the number of peanuts in a container. D: to predict which of four players will win a gold tournament.

I put A but Im not sure.

Answers

Answer: B

because its 50/50 chance you'll have heads or tails

Use the graph of the polynomial function. What are the zeros
Of the polynomial
A{-2}
B{3,-1,4}
C{-3,1,4}
D{2}

Answers

Answer:

B

Step-by-step explanation:

Whenever the curved line touches the x-axis that will be the zeros of the function.

Carmen runs each lap in 4 minutes. She will run less than 28 minutes today. What are the possible numbers of laps she will run today?

Answers

Answer:

# of laps < 28, the number of laps will be less than 28.

1 lap = 4 minutes

28 laps = 112 minutes

Because we want less than 28 laps,

27 laps = 108 minutes

She can run any amount of laps less than 28.

assume that the total surface area of the cuboid is 200cm^2 work out the volume of the cuboid

Answers

Answer: 187.5

Step-by-step explanation:

200 - 2 x 5 x 5 = 50

200 - 50 = 150

150/ 4  = 37. X 5 = 187.5

- hope this helps

Pls help ! Find the value of x .

Answers

Answer:

101

Step-by-step explanation:

180-79=101

have a great day

Answer:

the value of x is 101 degrees

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