What is the GCF of 72, 90, and 162?
Answers
Answer:
18
Step-by-step explanation:
Prime factorization of the numbers:
72 = 2 × 2 × 2 × 3 × 3
90 = 2 × 3 × 3 × 5
162 = 2 × 3 × 3 × 3 × 3
GCF(72, 90, 162)
= 2 × 3 × 3
= 18
Answer: 18
Step-by-step explanation:
Factors for 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Factors for 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Factors for 162: 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162
Related Questions
BRAINLISET BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST
number 16 and 17
justify each step
please answer quickly thank you
Answers
Then you divide each side by 3 to figure out that x=6.
17: multiply each side by 4 then divide each side by nine to figure out that x= -4
Sixty-four percent of voters in a very large electorate support candidate Smith in an upcoming election. A student employee working the evening shift at a telephone survey facility calls voters at random and asks them which candidate they prefer. a. What is the probability that, among five voters the student calls, exactly one supports candidate Smith? b. What is the probability that, among five voters the student calls, at least one supports candidate Smith? c. What is the probability that the first voter supporting candidate Smith is reached on the fifth call, i.e., what is the probability that it takes the student five calls to reach the first voter who supports candidate Smith? d. What is the probability that the third voter supporting candidate Smith is reached on the fifth call, i.e., what is the probability that it takes the student five calls to reach three voters who supports candidate Smith?
Answers
The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.
a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:
\[
P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4
\]
The calculation results in approximately 0.369, or 36.9%.
b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:
\[
P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5
\]
The calculation results in approximately 0.997, or 99.7%.
c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):
\[
P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64
\]
The calculation results in approximately 0.014, or 1.4%.
d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):
\[
P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64
\]
The calculation results in approximately 0.147, or 14.7%.
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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.
a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:
[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]
The calculation results in approximately 0.369, or 36.9%.
b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:
[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]
The calculation results in approximately 0.997, or 99.7%.
c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):
\[
P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64
\]
The calculation results in approximately 0.014, or 1.4%.
d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):
\[
P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64
\]
The calculation results in approximately 0.147, or 14.7%.
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how many bit strings of length 8 start with a 11 or end with 000? (you do not need to compute the final value. you just need to write down the combination, e.g., x^a y^b)
Answers
There are 92 bit strings of length 8 that start with a 11 or end with 000.
We can solve this problem using the principle of inclusion-exclusion. Let A be the set of bit strings of length 8 that start with 11, and let B be the set of bit strings of length 8 that end with 000. We want to find the size of the union of A and B.
The number of bit strings of length 8 that start with 11 is 2^6, since there are 6 remaining bits that can be either 0 or 1. The number of bit strings of length 8 that end with 000 is also 2^5, since there are 5 remaining bits that can be either 0 or 1.
However, we have counted the bit strings that both start with 11 and end with 000 twice. To correct for this, we need to subtract the number of bit strings of length 8 that start with 11000, which is 2^2.
Therefore, the number of bit strings of length 8 that start with a 11 or end with 000 is:
|A ∪ B| = |A| + |B| - |A ∩ B|
= 2^6 + 2^5 - 2^2
= 64 + 32 - 4
= 92
So there are 92 bit strings of length 8 that start with a 11 or end with 000.
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There are 88 bit strings of length 8 that start with "11" or end with "000."
To determine the number of bit strings of length 8 that start with "11" or end with "000," we can use the principle of inclusion-exclusion.
Let's consider the two conditions separately:
Bit strings that start with "11":
In this case, the first two bits are fixed as "11." The remaining 6 bits can be either 0 or 1, giving us 2^6 = 64 possibilities.
Bit strings that end with "000":
Similarly, the last three bits are fixed as "000." The first 5 bits can be either 0 or 1, resulting in 2^5 = 32 possibilities.
However, we have counted some bit strings twice because they satisfy both conditions (start with "11" and end with "000"). These bit strings have a length of at least 5 (3 bits in the middle), and there are 2^3 = 8 possibilities for these middle bits.
By using the principle of inclusion-exclusion, we can compute the total number of bit strings satisfying either condition as follows:
Total = Bit strings starting with "11" + Bit strings ending with "000" - Bit strings satisfying both conditions
= 64 + 32 - 8
= 88
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Help needed ASAP please
Answers
Answer:
19. 0•7431
20. 1•2800
21. 0•4850
Solve for x.
(x−2)^2+2=38
x= ___ or x= ___
Answers
Step-by-step explanation:
\(( {x - 2)}^{2} + 2 = 38 \\ {x }^{2} + 4 - 2 {x}^{2} + 2 = 38 \\ x = 38 - 2 - 4 \\ x = 32\)
Discuss 02 dissociation curve details.
Answers
The dissociation curve is a graphical representation of the relationship between the fractional saturation of hemoglobin (Y-axis) and the partial pressure of oxygen (X-axis) under specific conditions. It provides important information about the binding and release of oxygen by hemoglobin.
The dissociation curve for hemoglobin exhibits a sigmoidal (S-shaped) shape. At low partial pressures of oxygen, such as in tissues, hemoglobin has a low affinity for oxygen and only binds a small amount. As the partial pressure of oxygen increases, hemoglobin's affinity for oxygen increases, resulting in a rapid increase in the binding of oxygen molecules. However, once the hemoglobin becomes nearly saturated with oxygen, the curve levels off, indicating that further increases in partial pressure have minimal effects on oxygen binding.
To calculate the fractional saturation of hemoglobin at a given partial pressure of oxygen, you can use the Hill equation:
Y = [O2]^n / ([O2]^n + P50^n)
Where:
Y is the fractional saturation of hemoglobin,
[O2] is the partial pressure of oxygen,
P50 is the partial pressure of oxygen at which hemoglobin is 50% saturated,
n is the Hill coefficient, which represents the cooperativity of oxygen binding.
To determine the P50 value experimentally, the partial pressure of oxygen at which hemoglobin is 50% saturated, you can plot the dissociation curve and identify the point where the curve reaches 50% saturation.
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Need help with this ASAP!!
Answers
Answer:
64
Step-by-step explanation:
40x1.6
Chase ordered a set of beads. He received 4,000 beads in all. 3,000 of the beads were green. What percentage of the beads were green?
Answers
75% of the beads are green in color.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Chase ordered a set of beads
He received 4,000 beads in all.
3,000 of the beads were green.
We need to find the percentage of the beads were green of 4000.
x/100×4000=3000
40x=3000
Divide both sides by 40
x=75%
Hence, 75% of the beads are green in color.
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The population of an island was 2 million in 1950. The population grew in an exponential trend for 63 years and became 6.5 million in 2013. It is estimated that the carrying capacity of the island is 10 million. Assuming the population growth rate in the future remains the same as in the last 50 years, what will be the population of the island in 2050? (Assume constant carrying capacity and consumption/capita.)
Answers
The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.
If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050
The population is given to be increasing exponentially, which means it will follow the equation:
\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.
We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:
\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)
Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.
Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:
\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)
where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)
where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)
Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)
To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):
\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.
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What number, when divided by 6, is equivalent to 15?
n=90
n=5/2
n=4
n=15
Answers
Answer:
90
Step-by-step explanation:
15+15=30
3x30=90
Therefore, the answer to what divided by 6 equals 15 is 90. You can prove this by taking 90 and dividing it by 6, and you will see that the answer is 15. Tip: For future reference, when you are presented with a problem like "What divided by 6 equals 15?", all you have to do is multiply the two known numbers together.
Therefore, n=90 is your correct answer
Let the vector
�
v have an initial point at
(
7
,
−
6
)
(7,−6) and a terminal point at
(
6
,
−
3
)
(6,−3). Determine the components of vector
�. V
Answers
The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:
(6, -6) to (3, -6)(7, -6) to (6, -6)How to find the components of the vectorThe components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).
This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle
From the graph, the coordinates are:
component 1: (6, -6) to (3, -6)
component 2: (7, -6) to (6, -6)
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Tong loaned Jody $50 for a month. He charged 5% simple interest for the month. How much did Jody have to pay Tong?
Answers
Answer:
$50(1.05) = $52.50
Jody had to pay $52.50 to Tong for the month.
Parallelogram MNOP with vertices M(1, 7),
N(8, 5), O(4, 2), and P(-3, 4): and it rotates 180° What will be the new coordinates
Answers
The new coordinates are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)
What is a 180 degrees rotation?A 180 degrees rotation denoted by R(180, 0) is a rotation that has the same effect as the 180 degrees counterclockwise of a figure.
And it has the algebraic rule of its rotation to be changed from (x, y) to (-x, -y) i.e (x, y) ⇒ (-x, -y)
How to determine the image of the rotation?The coordinates of the parallelogram are given as
M(1, 7), N(8, 5), O(4, 2), and P(-3, 4)
The rotation is given as 180° rotation
As mentioned above,
We have (x, y) ⇒ (-x, -y)
Substitute M(1, 7), N(8, 5), O(4, 2), and P(-3, 4) in (x, y) ⇒ (-x, -y)
So, we have
M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)
Hence, the coordinates of the image are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)
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Drag the point on the coordinate plane to the solution of the system of equations shown below: y=-2x-1 y = x + 2
Answers
Answer:
(1,-1)
Step-by-step explanation:
-2x-1 = x+2
-3x = 3
x = -1
substitute
y = (-1) + 2
y = 1
point: (1,-1)
A panther runs at the speed of 80 km/h. What distance will it cover in 90 min?
Answers
Answer:
120 km
distance = speed * time
90 minutes can be converted to 1.5 hours
speed given 80 km/h and time given 1.5 hours
so distance = 80 * 1.5 = 120 km
Answer:
The panther will run 120 km in 90 mins
Step-by-step explanation:
An hour is 60 mins and you know in 1 hour the panther can run 80km
all you need to do is figure out how many miles an xtra 30 mins will be
60 minutes divided by 2 = 30 minutes and 80 km divided by 2 = 40km
Therefore 30 minutes = 40km
just add this to the original statement and you're good
60 mins + 30 mins = 90 mins
80km + 40km = 120km
The panther will run 120km in 90 mins
Joey hid them in bunches of 24 and in all he hid 503 bunches how many did he hide in all
Answers
503*24=12,072
Is y=4/x-3 linear or non-liner
Answers
Trust me it is
Is 4/3=8/6 equivalent
Answers
Answer:
Yes
Trust me it is right!Good Luck:)NEED EXPLINATION PLEASE COMMENT BELLOW
Answer:
yes 4/3 is equivalent to 8/6
Step-by-step explanation:
8/6 divided both the numerator and the denominator by 2 you get 4/3.thus 8/6 is equivalent to 4/3
describe the pattern. Then give the next two numbers
1,1,2,3,5,8
Answers
Answer:
the next two numbers will be 13, then 21
Step-by-step explanation:
the next number is the sum of the last two numbers.
1 + 1 = 2
2 + 3 = 5
etc etc
the next two numbers will be 13, then 21
what letter goes with number 1
Answers
The solutions to the given algebraic expressions are;
1) 3x + 4 = 7x - 8; Letter C
2) 2x = 7x - 5; Letter E
3) 5x - 8 = 5x + 12; Letter D
How to solve Algebraic expressions?1) We are given the algebraic expression as;
3x + 4 = 7x - 8
Add 8 to both sides to get;
3x + 12 = 7x
Subtract 3x from both sides to get;
12 = 4x
divide both sides by 4 to get;
x = 3
2) 2x = 7x - 5
Add 5 to both sides to get;
2x + 5 = 7x
Subtract 2x from both sides to get;
5x = 5
divide both sides by 5 to get;
x = 1
3) 5x - 8 = 5x + 12
Subtract 5x from both sides gives;
-8 = 12
Thus, no solution
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what is the answer to simplify 5^-4/5^3
Answers
Answer:69
Step-by-step explanation:ejwndj wdedwedew
Answer:
1/ 5^7
Step-by-step explanation:
5^-4 / 5^3 is the same as (5^-4 / 1) * (1/5^3)
5^-4 turns into 1 / 5^4
So you have 1/ (5^4 * 5^3)
When multiplying two of the same numbers you add the exponents giving you 1/ (5^7)
Tyson has a $50 gift card to use at a store. He does not have any additional money to spend at the store. Tyson will purchase a belt that costs $8 and x
number of shirts that cost $15 each. The function f(x) = 42 - 15x models the balance on the gift card after Tyson makes the purchases. What is the mo
appropriate domain of the function?
(A) all integer values of
B
all positive integer values of x
©
0 x< 2 where x is an integer
D
0<x<3 where x is an integer
First
Back Pause I
Next
Review I
Answers
0 ≤ x < 2, where x is an integer. Option C
The appropriate domain for the function f(x) = 42 - 15x in the given context can be determined by considering the constraints of the problem.
Tyson has a $50 gift card, and he wants to purchase a belt that costs $8 and x number of shirts that cost $15 each. The function f(x) represents the balance on the gift card after Tyson makes the purchases.
The number of shirts Tyson can purchase depends on the remaining balance on the gift card. Since each shirt costs $15, the maximum number of shirts he can buy is limited by the amount of money left on the gift card.
If we subtract the cost of the belt ($8) and the cost of x shirts ($15x) from the initial balance ($50), we should get a non-negative result, indicating that Tyson has enough money on the gift card to make the purchases.
Therefore, we can set up the inequality:
50 - 8 - 15x ≥ 0
Simplifying, we have:
42 - 15x ≥ 0
Now, we can solve for x:
-15x ≥ -42
Dividing by -15 (remembering to flip the inequality sign), we get:
x ≤ 42/15
x ≤ 2.8
Since x represents the number of shirts Tyson can buy, it should be a whole number. Therefore, the appropriate domain for the function f(x) is:
0 ≤ x ≤ 2, where x is an integer.
Option C.
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a sample of 90 adult randolph county residents showed that 59 own a home. what is the risk of owning a home?
Answers
The risk of owning a home in Randolph County based on the given sample can be calculated as:
Risk of owning a home = Number of residents who own a home / Total number of residents in the sample
Risk of owning a home = 59 / 90
Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.
Find the volume. Worth 20
Answers
Answer: 475
Step-by-step explanation: i am in middle school so I think its this
Which of the following are possible side lengths for a triangle?A. 5,7,9 B. 1,8,9 C. 5, 5, 12
Answers
Answer:
A. 5, 7, 9
Step-by-step explanation:
in a regular triangle the sum of any 2 sides must always be greater than the third side.
A.
5+7 = 12 > 9
5+9 = 14 > 7
9+7 = 16 > 5
yes, this can be a triangle.
B.
1+8 = 9 = 9
that violates the condition. both sides together are equally long as the third side, so the triangle would be only a flat line with the top vertex being squeezed flat onto the baseline.
no triangle.
C.
5+5 = 10 < 12
that violates the condition. the sides cannot even connect all around.
no triangle.
The diameter of a circle is 16 ft. Find its area in terms of π.
Answers
Answer:
201.14
Step-by-step explanation:
diameter=16
r=d/2
= 16/2
= 8
now,
A= πr^2
= 22/7*8^2
= 201.14
Answer: 64 pi !!
Step-by-step explanation:
Simplify x/4 + x/6 help please
Answers
Answer:
5/12x
Step-by-step explanation:
Mary has 92 blouses. She has 20% fewer than Susan. How many blouses does she have?
Answers
Answer:
115
Step-by-step explanation:
20% is one fifth. If Mary has one fifth fewer than Susan, then she has 4 fifths of what Susan has. So 92 is 4 fifths of some number.
To find out what one fifth is, you can divide 92 by 4 because it is four fifths.
92/4 = 23
So one fifth of the number of blouses Susan has is 23. Now you can multiply 23 by 5 to get the total number of blouses Susan has.
23 * 5 = 115
suppose that each party must select a speaker and a vice speaker. how many ways are there for the speaker and vice speaker to be selected in the demonstrators party?
Answers
There are n x (n-1) number of ways for the speaker and vice speaker to be selected in the demonstrator's party, where n is the number of members in the party.
For the demonstrator's party, the first position of the speaker can be filled by any of the n members. After the speaker is chosen, there are n-1 members left to select from for the position of vice speaker. Therefore, the total number of ways the speaker and vice speaker can be selected is n x (n-1).
For example, if the demonstrator's party has 4 members, there are 4 choices for the speaker position. After the speaker is chosen, there are 3 choices left for the position of vice speaker. So, the total number of ways to select a speaker and vice speaker in the party is 4 x 3 = 12.
This formula can be applied to any size of the party to determine the total number of possible ways to select a speaker and vice speaker.
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She dilated the outdoor stage by a scale factor of four with the center of dilation at the origin. Which ordered pair
will be the coordinates of one of the new vertices?
Answers
Answer:
(32, 16)
Step-by-step explanation:
Since the scale factor is 4, you always multiply both coordinate places (x and y) by this number.
The coordinates of one of the new vertices is (32, 16). Therefore, option D is the correct answer.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
Given that, rectangle with vertices A(-6, 4), B(8, 4), C(8, -2) and D(-6, -2).
Here, the scale factor is 4
So,
(-6,4) by a scale factor of 4(-6, 4)=(-24, 16)
(8, 4) by a scale factor of 4(8, 4)= (32, 16)
(-6, -2) by a scale factor of 4(-6, -2)= (-24, -8)
(8, -2) by a scale factor of 4(8, -2)= (32, -8)
Therefore, option D is the correct answer.
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