Write the following decimal number in its equivalent fraction form. Show all work for full credit.
0.8(repeating)
To write the decimal number 0.8(repeating) as a fraction, use the concept of an infinite geometric series and convert it to an equation. Multiply both sides of the equation by 10 to eliminate the decimal point and subtract the original equation to eliminate the repeating part. Finally, divide by 9 to get the equivalent fraction form.
Explanation:To write the decimal number 0.8(repeating) as a fraction, we can use the concept of an infinite geometric series. Let's assume the repeating decimal as x: x = 0.8(repeating). Now, multiply both sides of the equation by 10 to remove the decimal point: 10x = 8(repeating). Next, subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 8(repeating) - 0.8(repeating). Simplifying these expressions gives us: 9x = 7.2. Finally, divide both sides of the equation by 9: x = 7.2/9. Therefore, the equivalent fraction form of 0.8(repeating) is 7.2/9.
The room measures 8 inches by 5 inches on the blueprint. If the scale on the blueprint is 1 inch by 4 feet, what is the actual area of the room
A manufacturer of drinking glasses ships his delicate stock in speical boxes that can hold 32 glasses. if 1714 glasses are manufactured, how many full boxes are filled? are there any glasses left over?
Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.
Noel is more likely to draw two cards with a sum that is greater than 13.
To determine which outcome is more likely, let's count the number of combinations that meet each criterion.
1. **Sum that is a multiple of 3**:
- Possible sums: 3, 6, 9, 12
- Counting the combinations:
- 3: 1 combination
- 6: 2 combinations
- 9: 3 combinations
- 12: 4 combinations
- Total combinations: 1 + 2 + 3 + 4 = 10 combinations.
2. **Sum greater than 13**:
- Possible sums: 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
- Counting the combinations:
- 14: 1 combination
- 15: 2 combinations
- 16: 2 combinations
- 17: 3 combinations
- 18: 2 combinations
- 19: 3 combinations
- 20: 2 combinations
- 21: 3 combinations
- 22: 1 combination
- 23: 1 combination
- Total combinations: 1 + 2 + 2 + 3 + 2 + 3 + 2 + 3 + 1 + 1 = 20 combinations.
Comparing the total combinations, we see that there are more combinations with a sum greater than 13 (20 combinations) than there are combinations with a sum that is a multiple of 3 (10 combinations). Therefore, Noel is more likely to draw two cards with a sum that is greater than 13.
The probable question may be:
Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.
3, 6, 7, 9, 1
1 = 4, 7, 8, 10, 12
4 = 7, 10, 11, 13, 15
6 = 9, 12, 13, 15, 17
8 = 11, 14, 15, 17, 19
12 = 15, 18, 19, 21, 23
Is Noel more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13?
Noel is more likely to draw two cards with a sum greater than 13, as there are 37 combinations compared to 11 combinations for multiples of 3.
To determine whether Noel is more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13, we can analyze the table provided.
1. Sum that is a multiple of 3:
- There are several combinations of card values that result in a sum that is a multiple of 3. We can count these combinations from the table:
- (3, 4), (3, 7), (3, 9), (3, 12)
- (6, 7), (6, 10), (6, 12)
- (7, 8), (7, 11)
- (9, 10), (9, 13)
- (11, 12)
2. Sum greater than 13:
- We need to count the combinations of card values that result in a sum greater than 13:
- (6, 8), (6, 10), (6, 11), (6, 12), (6, 13), (6, 15), (6, 17)
- (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 15), (7, 17), (7, 19)
- (9, 10), (9, 11), (9, 12), (9, 13), (9, 15), (9, 17), (9, 19)
- (11, 12), (11, 13), (11, 15), (11, 17), (11, 19)
- (12, 13), (12, 15), (12, 17), (12, 19)
- (13, 15), (13, 17), (13, 19)
- (15, 17), (15, 19)
- (17, 19)
After counting the combinations, we can compare the number of combinations in each category:
1. Sum that is a multiple of 3:
- Total combinations: 11
2. Sum greater than 13:
- Total combinations: 37
Comparing the totals, we can see that Noel is more likely to draw two cards with a sum that is greater than 13, as there are more combinations resulting in this outcome.
Complete Question:
I need help on this one.
A stained glass window is in the shape of an equilateral triangle. what is the measure of one interior angle of the triangle
Some one help me with this question!
One of the halves on the Hoover Dam releases 40,000 gallons of water per second. What is the rate, in gallons per minute?
If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year, what will be the balance of the savings account after all the interest is paid for the year?
A. $5300.00
B. $5127.03
C. $5100.00
D. $5370.30
Answer:
Option D - $5370.30
Step-by-step explanation:
Given : If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year.
To find : What will be the balance of the savings account after all the interest is paid for the year?
Solution :
First we find the interest he paid.
The interest formula is [tex]I=P\times R\times T[/tex]
Where, P is the principal P=$5100
R is the rate of interest R=5.3%=0.053
T is the time T=1 year
Substituting the values,
[tex]I=5100\times 0.053\times 1[/tex]
[tex]I=\$270.3[/tex]
The balance of the saving account is the sum of interest paid and principal value.
Amount = Interest +Principal
Amount = $270.3 +$5100
Amount = $5370.3
Therefore, Option D is correct.
Martin needs 60 meters of fence to go around a rectangular garden.
The length, l, of the garden is twice its width w.
Three of these equations give the correct value for w.
Which equation does NOT?
2 • w + 2 • 2w = 60
2 • (2w + w) = 60
w + 2w = 60
w + 2w + w + 2w = 60
Answer:
w + 2w = 60
Step-by-step explanation:
w + 2w = 60
This equation will not give you the correct value for W because W is the siez or represents the size of the smaller side, since you have 4 sides, 2 small and 2 big, the sum of this 4 sides will be the perimeter, or the total meters of fence needed, since the total meter of fence need is 60 and in the equation you just have 2 sides, the value for W will be double than the real.
Carlos’s hockey team has ten players, not counting the goalie.Five non goalie players need to be selected for a starting line-up.
A)How many different starting lineups are possible if positions are not assigned?
B)How many starting lineups are possible if positions are assigned?
Final answer:
There are 252 different starting lineups possible if positions are not assigned, and 30,240 starting lineups are possible if positions are assigned.
Explanation:
For part A of the question, where positions are not assigned, we can calculate the number of different starting lineup combinations by using the combination formula. Since we are choosing 5 players out of 10 without regard to order, we use:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of players to choose from, and k is the number of players we want to choose. Therefore, we have:
C(10, 5) = 10! / (5! (10-5)!) = 252
There are 252 different starting lineups possible if positions are not assigned.
For part B, where positions are assigned, we use the permutation formula because the order in which we select the players matters. This formula is:
P(n, k) = n! / (n-k)!
Since the order in which the players are chosen matters, we have:
P(10, 5) = 10! / (10-5)! = 30,240
There are 30,240 different starting lineups possible with positions assigned.
solve the system of equations by substitution y=5x-13 and 5x+2y=19
Help please !!!!!!! .......
If A2 = I, where I is the identity matrix, which matrix correctly represents matrix A?
We know that [tex] \boldsymbol{A^2}=\boldsymbol{A\times A} [/tex]
We also know that [tex] \boldsymbol{I}=\begin{bmatrix}
1 &0 \\
0&1
\end{bmatrix} [/tex]
Now, it has been given to us that [tex] \boldsymbol{A^2}=\boldsymbol{I} [/tex]
Therefore, we will have to find the correct [tex] \boldsymbol{A} [/tex] from the given options and we find that when:
[tex] \boldsymbol{A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix} [/tex]
then [tex] \boldsymbol{A^2}=\boldsymbol{A\times A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}\times \begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix} [/tex]
Therefore, from the above given options, Option C is the correct option.
Therefore, [tex] \boldsymbol{A}=\begin{bmatrix}
3 & -2\\
4 & -3
\end{bmatrix} [/tex] is the correct answer.
Answer:
C. [3, -2]
[4, -3]
Step-by-step explanation:
PLATOOOO
An after school club is building a clubhouse that has a rectangular floor that is 8 feet by 6 feet. What is the total floor area in square inches of the clubhouse?
A gardener crosses tall true-breeding pea plants with short true-breeding ones. Tall plants are dominant to short ones. He collects the seeds to grow F1 plants and then allows them to self-pollinate to form an F2 generation. Which of the following describes the traits of the offspring correctly?
Will someone please find the value of x for these questions
A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet is uniform. what is the x-coordinate of its center of mass?
How many 4-sequences on {0..9} do not begin with 0?
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.
New grass seeds grow rapidly. A grass seed has grown to 12 millimeters tall. tomorrow it will be 23 millimeters tall, the next day it will be 24 millimeters tall. and on the next day it will be 45 millimeters tall. write a rule to represent the height of the bean plant as an arithmetic sequence. how tall will the plant be in 15 days?
A) A(n) = 16 + (n-1) 11: 194 millimeters
B) A(n) = 12 + (n-1) 11: 166 millimeters
C) A(n) = 13n: 195 millimeters
D) A(n) = 12n; 180 millimeters
help please in eed answers asap
Answer:
74,088 cm³
Step-by-step explanation:
[tex]whl = V \\ \\ [4,2]^{3} = 74,088[/tex]
I am joyous to assist you anytime.
solve the system of equations 6X + 5 y equals 55 + 6 x + 5 y equals 60
Simplify (- 5/8) divided by (-3/4)
A: 20/24
B: -20/24
C: -15/32
D: 15/32
Assume that the poisson distribution applies and that the mean number of hurricanes in a certain area is 5.55.5 per year.
a. find the probability that, in a year, there will be 44 hurricanes.
b. in a 5555-year period, how many years are expected to have 44 hurricanes?
c. how does the result from part (b) compare to a recent period of 5555 years in which 88 years had 44 hurricanes? does the poisson distribution work well here?
after school, maurice walks 1/3 mile to the park and then walks 1/2 mile to his house. how far does maurice walk from school to his house?
There are four steps in solving one’s personal financial challenges:
1. considering opportunity costs
2. assessing risks and returns
3. setting short- and long-term goals
4. assessing needs and wants
Which of these is the correct order of these steps?
2, 3, 1, 4
1, 2, 3, 4
4, 1, 2, 3
3, 1, 4, 2
Answer: C. 4, 1, 2, 3.
I hope this helps :)
Answer: Third option is correct.
Step-by-step explanation:
Since there are four steps in solving one's personal financial challenges:
1) First he needs to assessing the needs and wants .
2) Then, he will consider opportunity costs, i.e. next best alternative.
3) Then, he will assessing the risks and returns associated with the opportunity costs.
4) Last, but not the least, he will be setting short and long term goals.
So, The correct order of these steps is 4,1,2,3.
Hence, Third option is correct.
If the side length of a square pyramid is triple and the slant height is divided by 5 what would be the formula to find the modified surface area
What number fills in the blank to complete the factorization of 3x + 24?
(x + 8)
Answer:
The factor form of given expression is 3(x+8) so the required number is 3.
Step-by-step explanation:
The given expression is
[tex]3x+24[/tex]
Write the factors of each term.
[tex]3x+24=3\times x+3\times 8[/tex]
In both terms, 3 is a common factor.
Take out the common factor 3.
[tex]3x+24=3(x+8)[/tex]
The factor form of given expression is 3(x+8). The factor (x+8) is given, therefore the required number is 3.
At what Kelvin temperature will a sample of gas occupy 12 liters if the same sample occupies 8 liters at 27 °C?
Question 11 options:
45.0K
450K
40.5K
405K
What is the slope of the line on the graph. I need help I!!!
Compute the area of the triangle ( express answer in cm2
Height =6 cm
Base= 12cm
Answer:
36 cm^2
Step-by-step explanation: