Consider all four-digit numbers that can be made from the digits 0-9 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is less than or equal to 5000
Answer: 0.44
Step-by-step explanation:
First, let's count the total number of four-digit numbers.
Let's think it as four empty slots:
_ _ _ _
In each slot, we can put a single digit.
In the first slot, we have 9 options {1, 2, 3, 4, 5, 6, 7, 8, 9}
The zero is not an option here, because if there was a 0, this would be a 3 digit number, then the 0 can not be in the first slot.
For the second slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
for the third slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
for the fourth slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
The total number of combinations is equal to the product between the numbers of options for each slot, this means that we have:
Combinations = 9*10*10*10 = 9000
So there are 9000 different 4 digit numbers.
Now we want to find the probability of selecting a number at random that is equal or smaller than 5000.
Let's see the number of 4-digit numbers that are equal or smaller than 5000.
The smallest 4-digit number is 1000.
Then the number of numbers between 1000 and 5000 is:
5000 - 1000 = 4000
This means that there are 4000 4-digit numbers that are equal or smaller than 5000.
Now, the probability of selecting one of them at random is equal to the quotient between the number of 4-digit numbers that meet the condition (4000) and the total number of 4-digits (9000)
Then te probability is:
P = 4000/9000 = 4/9 = 0.44
T
Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h. Use your model to predict the number of boxes in stock at the end of an 8 hour shift.
Question:
A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.
- How many boxes were in stock when they opened?
- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.
- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.
Answer:
1. [tex]Initial = 244[/tex]
2. [tex]b = 244 + 52h[/tex]
3. 660 boxes
Step-by-step explanation:
Given
[tex]Rate = 52\ per\ hour[/tex]
[tex]Total\ boxes\ in\ 3\ hours = 400[/tex]
Solving (a): Initial Number of boxes
First, we calculate the number of boxes made in 3 hours
[tex]Boxes = Rate * Hours[/tex]
[tex]Boxes = 52 * 3[/tex]
[tex]Boxes = 156[/tex]
If they had 400 boxes at the 3rd hour.
Then, the number of boxes when they opened is:
[tex]Initial = 400 - 156[/tex]
[tex]Initial = 244[/tex]
Solving (b): Linear function
[tex]b = boxes[/tex]
[tex]h = hours[/tex]
Since, we have the rate and the initial number of boxes.
The linear function is:
[tex]Boxes = Initial + Rate * Hours[/tex]
i.e.
[tex]b = 244 + 52 * h[/tex]
[tex]b = 244 + 52h[/tex]
Solving (c): Boxes at the end of the 8th hour
We have:
[tex]b = 244 + 52h[/tex]
In this case:
[tex]h = 8[/tex]
Substitute 8 for h
[tex]b = 244 + 52 * 8[/tex]
[tex]b = 244 + 416[/tex]
[tex]b = 660[/tex]
Hence, there are 660 boxes at the end of the 8th hour
what is the answer pls i need help
Answer:
A because you have to mutiply 3 x 2 and it gives you 6
3x-2y=1x+4y=33 elimination process
Answer:
x = 5 ; y = 7
Step-by-step explanation:
3x - 2y = 1 --------------------(I)
x + 4y = 33 ------------(II)
Multiply equation (II) by (-3) and then add. So, x will be eliminated and we can find the value of y
(I) 3x - 2y = 1
(II)*(-3) -3x -12y = -99 {Now add}
- 14y = -98
y = -98/14
y = 7
Plugin y = 7 in equation (I)
3x - 2*7 = 1
3x - 14 = 1
3x = 1 + 14
3x = 15
x = 15/3
x = 5
A department store is having a clothing sale. If a $35.00 pair of pants has a discount tag of 20% off, what is the sale price?
Answer:
$28.00
Step-by-step explanation:
You start with 35.00.
Now 10% of this is 3.5.
Multiply by 2 because it's 20%.
You get 7, so 7 is 20% of 35.00.
35.00 minus 7 is 28.00.
The pair of pants will be 28.00 dollars!
a) Two cards are dealt off a well-shuffled deck. You win $1 if the two cards are
of different suits. Find the probability of your winning?
b) A coin is tossed 5 times. What is the probability that the first toss is a head
or exactly 2 out of the five tosses are heads?
c) In a shuffled 52-card deck, what is the probability that neither the top nor
the bottom card is a heart?
d) A bag contains 20 red marbles, 20 green marbles and 20 blue marbles. You
reach in and grab 15 marbles. What is the probability that they are all the
same colour?
Answer:
A.) 0.7647 b.) 13/ 16 C.) 0.9412 D.) 8.743 * 10^-10
Step-by-step explanation:
A)
Number of cards per suit = 13
Nunber of suits = 4
Probability = required outcome / Total possible outcomes
P(1) = probability of picking a card from a certain suit
P(1) = 13 / 52
Hence, probability that 2nd card will be from a suit different from the first :
Total possible outcomes = (52 - 1) = 51
Required outcomes = (13 * 3) = 39
= 39 / 51
= 0.7647
B.)
First toss being head :
Required outcome = H = 1
Total possible outcomes = T or H = 2
P(H) = 1/ 2
For 5 tosses
Total possible outcomes = 2^n = 2^5 = 32
Exactly 2 heads = 10
P(exactly 2 heads) = 10/32 = 5/16
1/2 + 5/16 = (8 + 5) / 16 = 13/16
c)
1 - P(both top and bottom are hearts)
Number of hearts = 13 ; number of cards = 52
P(both are hearts) = 13/52 * 12/51 = 0.05882
1 - 0.05882
= 0.94117
= 0.9412
d)
Either all marbles are red OR all marbles are green OR all marbles are blue
Total number of marbles = (20 + 20 + 20) = 60
Probability that all 15 marbles are of a certain color :
(20/60 * 19/59 * 18/58 * 17/57 * 16/56 * 15/55 * 14/54 * 13/53 * 12/52 * 11/51 * 10/50 * 9/49 * 8/48 * 7/47 * 6/46)
(2.9146E−10) + (2.9146E−10) + (2.9146E−10)
= 8.7438E−10
= 8.743 * 10^-10
Which graph represents y = √ X
Explanation:
[tex]\displaystyle [9, 3] → 3 = \sqrt{9} \\ [4, 2] → 2 = \sqrt{4} \\ [1, 1] → 1 = \sqrt{1} \\ [0, 0] → 0 = \sqrt{0}[/tex]
**In this case, we want NON-NEGATIVE terms.
I am joyous to assist you at any time.
there are 56 tulips in a flowerbed. the ratio of tulips to daffodils is 3:5. how many tulips and how many daffodils are there in a flowerbed? (Pls answer correctly)
Answer:
96
Step-by-step explanation:
3x + 5x = 8x.
8 altogether --> 3 tulips and 5 daisies
16 altogether --> 6 tulips and 10 daisies
24 altogether ---> 9 tulips and 15 daisies
etc
etc
48 altogether --> 12 tulips and 20 daisies
96 altogether --> 15 tulips and 25 daisies
Answer:
55 : 56.6666666667
Step-by-step explanation:
3:5 ÷ 3 = 1 : 1.66666666667 + 55= 56.6666666667
suris age is 4 less than 3 times her cousins age. suri is 17 years old. which method can be used to find c, her cousins age?
Suzi starts her hike at 275 feet below sea level. When she reaches the end of the hike, she is still below sea level at −135 feet. What was the change in elevation from the beginning of Suzi's hike to the end of the hike?
Answer:
Have a nice day!
Step-by-step explanation:
Answer:
140
Step-by-step explanation:
Hi there!
This problem may seem tricky because of the negative sea level, os let’s set up an equation.
[tex]-275+x=-135[/tex] where x = the change in elevation.
Using orders of operations, add 275 to both sides and you will end with
x = 140
Her change in elevation is 140 feet.
I hope this helps!
A small business earns a profit of $4,500 in
March and $9,500 in July. What is the rate
of change in profit for this time period?
Answer:
$2750/month
Step-by-step explanation:
Find the value of N
9 : 10 = 54 : N
Answer:
I think Value of N is 60
Step-by-step explanation:
because 9 ×6 =54
therefore, 10×6=60
hope its correct and hope ti helps..
You have a square that has a side length of $1$ centimeter. Each minute, $2$ centimeters are added to the side length. After $10$ minutes, what will be the difference between the area of the last square and the area of the initial square in square centimeters (do not include the units in your answer)?
Answer:
Difference in area of the last square and the initial square = 440 cm²
Step-by-step explanation:
Length of the side of a square = 1 cm
Area of the square = (side)² = 1 cm²
Addition of side length every minute = 2 cm
After x minutes length of each side of the square = (1 + 2x) cm
If x = 10 minutes
Length of each side of the square = [1 + 2(10)]
= 21 cm
Area of the square after 10 minutes = (21)²
= 441 cm²
Therefore, difference in area of the last square and area of the initial square
= 441 - 1
= 440 cm²
Choose all equations for which x=2 is a solution.
A:x+3=5
B:x+2=8
C:x+1=1
D:x-2=4
Ex-7=5-
Delta Airlines' flights from Boston to Seattle are on time 70 % of the time. Suppose 6 flights are randomly selected, and the number on-time flights is recorded. 1.The probability that at least 4 flights are on time is
Answer:
P(at least 4) = 0.74431
Step-by-step explanation:
Here
Probability of the flights on time is = 70% = 70/100= 0.7
q= 0.3
n= 6
As the probability of success and failure is constant and the n is also fixed then the binomail probability distribution can be used to solve this.
P (x= 4) = 6c4 *(0.7)^4 (0.3)^2= 15*0.2401* 0.09= 0.324135
P (x= 5) = 6c5 *(0.7)^5(0.3)^1= 6*0.16807* 0.3=0.302526
P (x= 6) = 6c6 *(0.7)^6 (0.3)^0= 0.117649P
P (x= 0) = 6c0 *(0.7)^0 (0.3)^6= 0.000729
P (x= 1) = 6c1 *(0.7)^1 (0.3)^5=0.010206
P (x= 2) = 6c 2*(0.7)^2 (0.3)^4=0.059535
P (x= 3) = 6c3 *(0.7)^3 (0.3)^3=0.18522
Probability of at least 4 means that probability of greater than 4 inclusive of 4.
This can be obtained in two ways.
First is by subtracting the probabilities of less than 4.
Second is by adding probabilities greater than 4 including 4.
We get the same answer with any of the two methods used.
P(at least 4) = 1- P(x<4)
= 1- [ 0.000729+ 0.010206 +0.059535+ 0.18522]
= 1- 0.25569
= 0.74431
P (at least 4) = P(x=4) +P(X=5) + P(x=6)
=0.324135+ 0.302526+ 0.117649
=0.74431
Aniyah is driving home at a constant speed. After 20 minutes, she is 70 miles from
home. After 1 hour, she is 40 miles from home. What equation models her distance
from home, y, as a function of time, x? Show your work.
Answer:
Aniyah is driving home at a constant speed. After 20 minutes, she is 70 miles from
Step-by-step explanation:
home. After 1 hour, she is 40 miles from home. What equation models her distance
from home, y, as a function of time, x? Show your work.
ASAP PLS HELP
Which fraction is equivalent to 2 over negative 6 ? (5 points)
Select one:
a.
negative 2 over 6
b.
2 over 6
c.
negative 2 over negative 6
d.
6 over 2
Pls help urgently extra points and mark brainlist
Answer:
You got it right it is the second option
Step-by-step explanation:
I'm trying to level up and need 3 more brainliest so if possible can you mark me brainliest if not that's ok! :)
Answer: the last one
Step-by-step explanation:
Is 45 a multiple of 4? Explain your answer.
50
Write an equation in slope-intercept form that is perpendicular to y = -7x + 3 and passing through (14.1).
Answer:
y = 1/7x -1
Step-by-step explanation:
1) Find the slope.
- In this case, the equation given is in simplest form so you can easily come to the conclusion that '-7' is the slope. But, since the math question wants a slope-intercept form in perpendicular form, the slope would actually be 1/7.
2) Use the point-slope form and substitute the values available. Then solve.
m (slope) = 1/7
(a, b) = (14, 1)
y - b = m(x - a)
y - 1 = 1/7(x - 14)
y - 1 = 1/7x - 2
y = 1/7x - 1
The result is your answer.
Hope this helped (please tell me if I made a mistake or if you have any confusion and I will resolve it under the comments) ^^
Solve 2x + 2y = -28 2x - 2y = 26
Answer:
x=−y−14
Step-by-step explanation:
Answer:
x = none y = -27
Step-by-step explanation:
2x + 2y = -28 + 2x - 26
-2x -2x
__________________
2y = -28 - 26
2y = -54
y = -27
Which is the answer HELP PLEASE
A. 205°
B. 215°
C. 210°
D. 220°
Answer:
A lol
Step-by-step explanation:
illustrates whather the two ratios are equal or not using cross 3/27, 1/9
Answer:
They are equal
Step-by-step explanation:
Given
[tex]\frac{3}{27}\ and\ \frac{1}{9}[/tex]
Required
Determine if they are equal
We start by equating both:
[tex]\frac{3}{27} = \frac{1}{9}[/tex]
Cross Multiply
[tex]3 * 9 = 1 * 27[/tex]
[tex]27 = 27[/tex]
Because both sides of the equation are equal, then the ratios are equal
ldentify the center and radius of the circle
(x-5)^2 + (y+1)^2=4.
Answer:
[tex] {(x - 5)}^{2} + {(y + 1)}^{2} = 4 \\ {(x - a)}^{2} + {(y -b) }^{2} = {r}^{2} [/tex]
Comparing both the equation we get,
(C) Centre:(5,-1), r =2give a description of the rules for the order of operation in your own words
Answer:
Order of opoation is a techniqe that gives us a easier way to figure out work
Step-by-step explanation:
Please mark me as brainiset
Ignoring unwritten factors of 1, what is the sum of the numerical factors in the expression below?
−4(x−2)+(x−2)7−(x+5)(x−2)+(x−2)9+(−3)(x−2)
(1 point)
The sum is
.
Answer:
Step-by-step explanation:
Move
2x-3
x2+4x+3
to the left side of the equation by subtracting it from both sides.
x+2
x2-9
+
x-3
x2-2x-3
-
2x-3
x2+4x+3
=0
Simplify
x+2
x2-9
+
x-3
x2-2x-3
-
2x-3
x2+4x+3
Mark me brainless
Answer: the sum is 5
Step-by-step explanation:
6 times 7 is 42 6 times 5 is 30 if that's any help please help me out.
6 * 5 = 30
42 - 30 = 12
? * 2 = 12
? = 6
Which missing value would you add in to make a perfect square
I’ll give brainliest
Answer:
Step-by-step explanation:
Is it 25
5 actions a good friend would make.
Answer:
1. respect your opinion
2. defend you/stand up for you
3. support your passions and goals
4. keep stuff you tell them to themselves
5. make you feel comfortable and like you can be yourself
Step-by-step explanation:
19 - k = 4.
I need help
Answer:
15
Step-by-step explanation:
first you have to subtract 4 from 19 to get what k is. that should be your answer. good luck!