The word geometry has eight letters. Three letters are chosen at random. What is the probability that two consonants and one vowel are chosen?
Answer: [tex]\dfrac{15}{28}[/tex]
Step-by-step explanation:
The given word : geometry
Total letters in the above word = 8
Number of vowels (a e i o u) in word =3
Number of consonants = 5
Number of ways to choose two consonant and one vowel is given by :-
[tex]F=^5C_2\times^3C_1\\\\=\dfrac{5!}{2!(5-2)!}\times (3)\ [ \because ^nC_1=n]\\\\=5\times2\times3=30[/tex]
Number of ways to choose any three letters from the 8 alphabets:-
[tex]T=^8C_{3}=\dfrac{8!}{3!(8-3)!}=8\times7=56[/tex]
Now, the probability that two consonants and one vowel are chosen :-
[tex]=\dfrac{F}{T}\\\\=\dfrac{30}{56}=\dfrac{15}{28}[/tex]
Hence, the required probability = [tex]\dfrac{15}{28}[/tex]
if f(x)=5x-2, and g(x)=2x+1, find (f+g)(x)
Suppose you are given that a=5 and 4a + b=6. What can you prove by using these statements and the substitution property?
Using the values given for 'a' and the equation '4a + b = 6', we applied the substitution property to prove that the value of 'b' is -14.
Given that a=5 and 4a + b=6, we can use the substitution property to find the value of b. The substitution property allows us to replace a with 5 in the second equation.
Performing the substitution, we have:
Substitute a with 5 in 4a + b = 6, giving 4(5) + b = 6.This simplifies to 20 + b = 6.To find b, subtract 20 from both sides of the equation; b = 6 - 20.Hence, b = -14.By substituting and manipulating the equation, we prove that b equals -14 when a equals 5 and 4a + b equals 6.
Subtract x/x^2-36-6/x^2-36
Answer:
x + 6; where x ≠ -6, +6
Step-by-step explanation:
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth. 5x+2y=7 -2x+6=9
Answer:
y = 1.7
Step-by-step explanation:
Given : 5x+2y=7 and - 2x+6=9.
To find : Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.
Solution : We have given
5x + 2y = 7 --------(1)
- 2x + 6y = 9 -------(2).
To make the y coefficient same multiply the equation 1 by 3.
15 x + 6y = 21 .
(+)-2x +(-) 6y = (-)9 .
______________ ( On subtracting both the equations )
17 x + 0 = 12 .
17 x = 12 .
On dividing both sides by 17
x = [tex]\frac{12}{17}[/tex].
x = 0.705
Plug x = 0.705 in equation 2 .
- 2 ( 0.705) + 6y = 9.
-1.41 + 6y = 9 .
On adding both sides by 1.41.
6y = 9 + 1.41
6 y = 10. 41
On dividing both sides by 6.
y = [tex]\frac{10.41}{6}[/tex].
y = 1.735.
Nearest tenth = 1.7
Therefore, y = 1.7.
In your US History class, you have scores of 78, 89, 87 and 96 on the first four tests. To get a B, the average of the five tests must be greater than or equal to 80 and less than 90. Solve an inequality to find the range of the scores needed on the fifth test to get a B
Quadrilateral WILD is inscribed in circle O.
WI is a diameter of circle O.
What is the measure of angle D?
Thye given Quadrilateral WILD is inscribed in circle O. The measure of angle D is 135 degrees.
Since the quadrilateral is inscribed inside the circle,
Where the four vertices are on the circle itself,
What is the addition opposite angle?The opposite angle addition is 180 degrees.
Angle I and Angle D are opposite angles.
They add to 180 degrees
(angle I) + (angle D) = 180
(45 degrees) + (angle D) = 180
(angle D) + 45 = 180
(angle D) + 45 - 45 = 180 - 45 ... subtract 45 from both sides.
angle D = 135
The measure of angle D is 135 degrees.
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A particle moves according to the equation x = 10t 2 where x is in meters and t is in seconds
on a map with a scale 1:100,000 the distance between two cities is 12cm. what would be the distance between these two cities on a different map with a scale 1:300,000?
Part 1)
we have
the scale is [tex]1:100,000[/tex]
the distance on a map is [tex]12\ cm[/tex]
we know that
The scale is equal to the distance on a map divided by the real distance
Let
x------> distance on a map
y-------> real distance
S-------> scale
[tex]S=\frac{x}{y}[/tex]
In this part we have
[tex]S=\frac{1}{100,000}[/tex]
[tex]x=12\ cm[/tex]
Find the value of y
[tex]y=\frac{x}{S}[/tex]
Substitute the values
[tex]y=\frac{12}{(1/100,000)}[/tex]
[tex]y=1,200,000\ cm[/tex]
Convert to kilometers
[tex]y=12\ Km[/tex]
Part 2)
In this part we have
[tex]S=\frac{1}{300,000}[/tex]
[tex]y=12\ km[/tex]
Find the value of x
[tex]x=S*y[/tex]
Substitute the values
[tex]x=(1/300,000)*12[/tex]
[tex]x=0.00004 Km[/tex]
Convert to centimeters
[tex]x=4\ cm[/tex]
therefore
the answer is
The distance is [tex]4\ cm[/tex]
(2h-4)11 (use the distributive property to simlify each expression)
Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below. 3x + 2y = 36.50 2x + 5y = 50.00 At which job does Percy earn the greater hourly wage? How much does Percy earn each hour at this job?
A) Percy earns a greater hourly wage of $7.00 at the library.
B) Percy earns a greater hourly wage of $7.00 at the coffee cart.
C) Percy earns a greater hourly wage of $7.50 at the library.
D) Percy earns a greater hourly wage of $7.50 at the coffee cart.
A rare bacterial culture is being grown in a lab. As time passes, the cells multiply in a specific pattern.After 1 day, there is only 1 cell.After 2 days, there are 9 cells.After 3 days, there are 20 cells.After 4 days, there are 34 cells.How many cells will there be after seven days?
a.149B.120C. 98D.94
the equation is,
a_n = a_(n–1) + 3 * n + 2
Substituting the values
for day 4,
20 + 3*4 + 2 = 34
Thus the equation is correct
Therefore to calculate for a_n at n = 7 or a_7, we must calculate a_5 and a_6 first.
a_5 = 34 + 3*5 + 2 = 51
a_6 = 51 + 3*6 + 2 = 71
Hence,
a_7 = 71 + 3*7 + 2 = 94
Answer: D. 94
If the distance between the 2 and the 3 and the 6 and the 7 on a scale are equal, the scale would likely be at least:
how much is 81% of 403? find the missing element in the following base-rate-percentage problem. round the answer to the nearest hundredth.
Find 81% of 403 by converting the percentage to a decimal (0.81) and then multiplying it by 403, which equals to 326.43 when rounded to the nearest hundredth.
Explanation:The student is asking for the solution to determine the value of 81% out of 403. This is a simple proportional math problem and could be solved with the following steps:
Convert the percentage (81%) to its decimal equivalent. This is done by dividing the percentage by 100. So, 81 divided by 100 equals 0.81.Multiply the given total number (403) by the decimal equivalent of the percentage. So, 0.81 times 403 equals 326.43.So, 81% of 403 is approximately 326.43, rounding to the nearest hundredth.
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What are the x and y intercepts of the graph of 3x + 4y = -36?
a) x-intercept = -9, y-intercept = 12
b) x-intercept = -12, y-intercept = -9
c) x-intercept = 12, y-intercept = -9
d) x-intercept = 9, y-intercept = -12
Answer:
d
Step-by-step explanation:
The Volume of a cube is 343ft cubed. What is the length of one side
davis printed 24 photos in 8 minutes. how many photos did he print per minute
340 decreased by 20%
What's the answer ????
Stephanie read 72 page on sundy and 83 pages on monday about haw many pages did stephanie read during the two days
The new york yankess sell an avergae of 42362 tickets for each of their 81 home games about how many tickts do they sell for an entire seasone of home games
multiply the number of games by the number of seats
42362 x 81 = 3,431,322 total seats
Two coins are knocked off a table at the same time by different forces. which coin will hit the ground first?
Final answer:
Two coins knocked off a table by different forces will hit the ground simultaneously because gravity affects each coin equally, and the horizontal and vertical components of their motion are independent. This is consistent with the universality of free fall and has been empirically demonstrated by repeated experiments.
Explanation:
Do Different Forces Affect Gravity's Impact on Falling Objects?
When two coins are knocked off a table simultaneously with different horizontal forces, their subsequent motion comprises both horizontal and vertical components. However, gravity acts only on the vertical motion, and it does so equally on both coins regardless of their horizontal velocities. According to the laws of physics, specifically Galileo's theory of falling bodies, both coins will hit the floor at the same time because the horizontal and vertical motions are independent of each other. This phenomenon is due to the universality of free fall, which states that all objects accelerate at the same rate under gravity's influence, ignoring air resistance.
An important point to note is that factors such as air resistance can affect the time it takes for objects with different shapes and surface areas to hit the ground. However, in the case of the coins, since they are identical and their shapes do not change as they fall, air resistance does not play a significant role, and thus they hit the ground simultaneously. This was demonstrated by Galileo and can be observed in everyday life, such as by dropping a shoe and a coin side by side.
The sum of the measures of the angles of any triangle is 180 degrees. in triangle abc, angles a and b have the same measure, while the measure of angle c is 72 degrees larger than each of a and
b. what are the measures of the three angles?
is the open sentence 3z=2z+5 true or false when z=5?
A. True
B. False
steven wants to buy a $565 bicycle. Steven has no money saved, but will be able to deposit $30 into a saving account when he receives his paycheck each Friday. However, before steven can buy the bike,he must give his sister $65 that he owes her. For how many weeks will steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
Suppose that the sample space is s = {a, b, c, d, e, f, g, h} and that outcomes are equally likely. find the probability of the event e = {b, f, h}.
The probability of the event E = {b, f, h} with the sample space S = {a, b, c, d, e, f, g, h} is 3/8 or 0.375.
Explanation:The student has asked to find the probability of the event E = {b, f, h} given the sample space S = {a, b, c, d, e, f, g, h} where all outcomes are equally likely. To calculate the probability, we need to use the formula for theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes in the sample space.
We see that the event E has 3 outcomes (b, f, h) and the sample space S has 8 outcomes. So the probability of event E is given by:
P(E) = Number of outcomes in E / Number of outcomes in S = 3 / 8 = 0.375
Susie scored 85, 84,and 78 on three of the four math tests. if her average score for the four tests was 86. what was her score on the fourth test?
PLEASE HELP: Why does the AA similarity Theorem only need to identify the measurement of 2 congruent angles? Why is it not necessary to find the measurement of the third angle and show that it is also congruent to the corresponding third angle of a similar triangle?
What are the 3 consecutive integers of 135?
Three consecutive integers can be represented as followed.
X → first integer
X + 1 → second integer
X + 2 → third integer
Since the sum of our three consecutive integers is 135, we can set up an equation to represent this.
X + X + 1 + X + 2 = 135
-Simplify on the left-
3x + 3 = 135
-3 -3
3x = 132
÷3 ÷3 ← divide both sides by 3
X = 44
X + 1 = 45
X + 2 = 46
Therefore, the three consecutive integers are 44, 45, and 46.
Marcus bought a shirt that was marked $28, but it was on sale for 15% off the marked price. what was the price of the shirt after the discount
Final answer:
To find the sale price of the shirt after a 15% discount on the marked price of $28, calculate the discount, subtract it from the original price, resulting in a sale price of $23.80.
Explanation:
Marcus bought a shirt that was marked $28, but it was on sale for 15% off the marked price. To calculate the price of the shirt after the discount, you first need to determine the amount of the discount. To do this, convert the percentage to a decimal by dividing by 100 (15% = 0.15) and then multiply this by the original price.
Discount amount = Original price × Discount rate
= $28 × 0.15
= $4.20.
Subtract the discount amount from the original price to find the sale price of the shirt:
Sale Price = Original price - Discount amount
= $28 - $4.20
= $23.80.
Therefore, the price of the shirt after the 15% discount is $23.80.