Georgette created a factor tree and wrote the prime factorization of 72 shown here. A factor tree of 72. 72 branches to 8 and 9. 8 branches to 2 and 4. 4 branches to 2 and 2. 72 = 23 × 9 What is Georgette’s error? A. Georgette should have started the factor tree with 2 × 36. B. Georgette did not complete the factorization; 9 is a composite number. C. Georgette should have expressed 4 as 4 x 1, not 2 x 2. D. Georgette should have expressed 8 as 4 × 4, not 2 × 4.
Answer:
Georgette did not complete the factorization; 9 is a composite number.
Step-by-step explanation:
9 can be broken down to 3x3
So it the prime factorization of 72 should be 2x2x2x3x3
Georgette’s error is Georgette should have expressed 8 as 4 × 4, not 2 × 4.
The correct option is D.
The correct prime factorization of 72 is 2³ × 3², which means it can be expressed as the product of prime numbers raised to their respective exponents.
Analyzing the factor tree provided by Georgette, we can see that she made an error when branching from 72 to 8 and 9.
The prime factorization of 8 should be 2³, not 2 × 4, and the prime factorization of 9 should be 3², not 2 × 2.
Therefore, Georgette's error is that she have expressed 8 as 2³ × 1 or 4 × 2, not as 2 × 4.
The correct factor tree for 72 would be:
72
/ \
2 36
/ \
2 18
/ \
2 9
/ \
3 3
So, the prime factorization of 72 is 2³ × 3².
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1
GIVE ME BRAINLIEST MY GUY PLZ
1 problem
Because there are 13 problem and if she completed 12 of them yesterday .Only 1 will be left for today.
At a carnival game, you randomly throw two darts at the board and break two balloons. What is the probability that both the balloons you break are purple? Write your answer as a fraction or percent rounded to the nearest tenth. there are 15
Details are missing;
A board of 15 balloons. 4 are purple, 3 red, 4 blue, 2 yellow and 2 green
Answer:
the probability that both the balloons you break are purple = 2/35
Step-by-step explanation:
Since there are 15 balloons and 4 are purple. It means that probability of the first balloon being purple is;
4/15
Now, if the first balloon is purple, it means we have 3 purple left out of the remaining 14. Thus probability of the second being purple = 3/14
Thus;
the probability that both the balloons you break are purple = 4/15 × 3/14 = 2/35
What is the opposite value of -53 ?
Answer:
53
Step-by-step explanation:
Answer: Opposite of -53 = -(53) = 53
Step-by-step explanation: An opposite number of n is the exact same number as n on the other side of the number line. the opposite of n is n.
18 = 3(3x − 6) multi step equations show all steps pls
Answer:
x=4
Step-by-step explanation:
18 = 3(3x − 6)
Divide each side by 3
18/3 = 3( 3x-6)/3
6 = 3x-6
Add 6 to each side
6+6 = 3x-6+6
12 = 3x
Divide by 3
12/3 = 3x/3
4 =x
Answer: 4 = x
Step-by-step explanation: To solve this equation, we start by
distributing the 3 through the parenthses on the right side.
3(3x) is 9x and 3(-6) is -18.
So our equation now reads 18 = 9x - 18.
Our next step is to get the x term by itself on the right side.
So we add 18 to both sides to get 36 = 9x.
Now divide both sides by 9 to get 4 = x.
What is the arc length S what is shown below?
The angle in the image is a central angle în radians.
Answer:
14 cm
Step-by-step explanation:
The applicable formula is ...
s = rθ
s = (7 cm)(2) = 14 cm
square root of 87 to the nearest 10th
Answer:
9.3
Step-by-step explanation:
Step 1: Calculate. We calculate the square root of 87 to be: √87 = 9.32737905308882.
Step 2: Reduce. 9.32.
Step 3: Round. Round 9.32 so you only have one digit after the decimal point to get the answer: 9.3.
5. If median =137 and mean = 137.05, then find the value of mode. (2marks)
Answer:- 136.9
Step-by-step explanation:
3median=2mean+mode
3(137)=2(137.05)+mode
411=274.1+mode
411-274.1=mode
mode=136.9
Danny and 4 friend go to the movies. Each person buys a movie ticket for $10, a snack for $2 and a drink for $3. Write an expression which shows how much Danny and his friends spent.
8000647 dollars
Step-by-step explanation:
broggxtxycycuvuh8y7rtwh4w5iwutettixgdbf
Wyatt is training for a race. He will run 3
4
of a mile a day for 8 days. How far will Wyatt run altogether?
Answer: 6 OR 6/1
3 8 24 6
- x - = _ = - OR 6
4 1 4 1
Step-by-step explanation: Hope this helps! ~Pooch ♥
What is equivalent to 5.08 cm
Answer:
2 in
Step-by-step explanation:
-3(-9v-4)-2(v-2)????
A basketball team has 12 members who can play any position. How many different ways can the coach choose 5 starting players
This equation shows how the total cost of visiting the art museum as a member is related to the number of visits. c = v + 11 The variable v represents the number of visits to the art museum, and the variable c represents the total cost of those visits. What is the maximum number of visits a member of the art museum can make for a total cost of $14?
Answer:
6
Step-by-step explanation:
C=9.2v + 21.2
76.4 = 9.2v + 21.2
76.4 - 21.2 = 9.2v
55.2 = 9.2v
v= 55.2 / 9.2 = 6
True or false are confirmed angles have equal measures
Answer:
TRUE
Step-by-step explanation:
if the adjacent angles are equal, then they are right angles.
Write 8660 in scientific notation
Answer:
8.66 x 10^3
Step-by-step explanation:
8.66 * 1000 (10^3) = 8660
A thermometer comes with a guarantee that the stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit. Write an equation to represent the minimum and maximum actual temperatures when the thermometer states that the temperature is 87.4 degrees Fahrenheit.
Answer:
The equation is;
T = 87.4 ± 1.5
Maximum value of T = 88.9 °F
Minimum value of T = 85.9 °F
Step-by-step explanation:
We are given the stated temperature as 87.4 °F
Now, we are told that this stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit.
Thus, if the actual temperature is T, it means that T should either be 1.5 more than 87.4 or 1.5 less than 87.4.
Thus the equation is;
87.4 ± 1.5 = T
So maximum value of T = 87.4 + 1.5 = 88.9 °F
While minimum value of T = 87.4 - 1.5 = 85.9 °F
True or False: Segment AB is congruent to segment BC. A B C -2 0 1 3 Select one: True False
A bike shop rents bikes for $4.50 per hour, plus a $7.50 insurance charge. For how many hours can Peter rent a bike if he has $30?
Answer:
With $30, Peter can afford 5 hours
Step-by-step explanation:
Given
Insurance Charge = $7.5
Charges = $4.5 per hour
Required
Determine the number of hours $30 can afford
First, we need to determine the equation.
Total Charges = Charges per hour + Insurance Charge
Substitute values for Charges per hour and Insurance Charge
Total Charges = 4.5 per hour + 7.5
Let the number of hours be n;
So,
Total Charges = 4.5n + 7.5
To calculate Peter's; substitute 30 for total charges
[tex]30 = 4.5n + 7.5[/tex]
Subtract 7.5 from both sides
[tex]4.5n = 30 - 7.5[/tex]
[tex]4.5n = 22.5[/tex]
Divide both sides by 4.5
[tex]n = \frac{22.5}{4.5}[/tex]
[tex]n = 5[/tex]
Hence;
With $30, Peter can afford 5 hours
Point C is on line segment \overline{BD} BD . Given BC=x+4,BC=x+4, CD=5x,CD=5x, and BD=5x+7,BD=5x+7, determine the numerical length of \overline{CD}. CD .
Answer:
[tex]CD = 15[/tex]
Step-by-step explanation:
Given
[tex]BC = x + 4[/tex]
[tex]CD = 5x[/tex]
[tex]BD = 5x + 7[/tex]
Required
Determine CD
Since Point C is on segment BD, then we have
[tex]BD = BC + CD[/tex]
Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD
[tex]5x + 7 = x + 4 + 5x[/tex]
Collect Like Terms
[tex]5x - 5x - x = 4 - 7[/tex]
[tex]- x = -3[/tex]
Multiply both sides by -1
[tex]x = 3[/tex]
Substitute 3 for x in [tex]CD = 5x[/tex]
[tex]CD = 5(3)[/tex]
[tex]CD = 15[/tex]
Hence, the length of CD is 15 units
Answer:
Step-by-step explanation:
Given
Required
Determine CD
Since Point C is on segment BD, then we have
Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD
Collect Like Terms
Multiply both sides by -1
Substitute 3 for x in
Hence, the length of CD is 15 units
Step-by-step explanation:
1/2a+6b/7 Verbal Expression?
Answer:
one half of a plus six times b divided by seven
Step-by-step explanation:
(Giving Branliest)
The length of a desk is 3.5 feet. How many centimeters is the length? (There are 2.54 cm in an inch)
A. 60
B. 117.12
C. 120.23
D. 106.68
Answer:
106.68 cm
Step-by-step explanation:
Change ft to inches
3.5 ft * 12 inches / 1 ft = 42 inches
Change inches to cm
42 inches * 2.54 cm/ inch =106.68 cm
Answer:
106.68cm
Step-by-step explanation:
divide by feet untill you get inches
NEED HELP FAST!!! Determine the momentum: An electron (m= 9.1 x 10-31 kg) moving at 2.18 x 106 m/s (as if it were in a Bohr orbit in the H atom)
Answer:
p= (9.1 x 10^-31)(2.18 x 10^6) p = 1.9 x 10^-22kg*m/s
Step-by-step explanation:
for i said so
The momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.
Given, mass of electron is [tex]9.1\times 10^{-31}[/tex] kg.
And its velocity is [tex]2.18 \times 10^6[/tex] m per s.
We have to calculate its momentum.
We know that momentum is numerically equal to the product of mass and velocity of a particle and denoted by p.
So, [tex]p=mv[/tex]
[tex]p= 9.1\times10^{-31}\times2.18\times10^{6}[/tex]
[tex]p=19.838\times10^{25}[/tex]
[tex]p=1.9\times10^{26}[/tex]
Hence the momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.
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Solving the equation x + 2(x – 5) = 320
will need the following steps:
1. x + 2x + 10 = 320
II. 3x + 10 = 320
III.
3x = 310
310
IV.
x =
3
Which step above is incorrect?
A Step
B Step III
C Step IV
D All steps are correct
Lo
Answer:
A. Step I
Step-by-step explanation:
Appropriate application of the distributive property would give ...
x +2x -10 = 320 . . . . . . . does not match step I
Further solution steps would be ...
3x -10 = 320
3x = 330
x = 110
The transitive property of equality states that _____. if a = b, then b = a if a = b, then ac = bc if a = b and b = c, then a = c if a = b and c = c, then a + b = b + c
Answer:
If a = b and b = c, then a = c
Step-by-step explanation:
The transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.
Answer:
If a = b and b = c, then a = c
Step-by-step explanation:
i got it right on a test
- Suppose Q is the midpoint of PR. Use the information to find the missing value. PQ = 3x + 14 and QR = 7x - 10; Find x.
Answer:
x =6
Step-by-step explanation: Q is the midpoint of PR.
Therefore PQ = QR
3 x + 14 = 7 x -10
-14 -14
3 x = 7 x-24
-7x -7x
-4x = -24 Divide both sides by -4
x = 6
The value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.
What is midpoint of line segment?
The midpoint divides the line segment into two equal parts.
It is given that Q is the midpoint of PR which implies Q will divide PQ into two equal parts that is PQ (3x+14) equals QR (7x-10). now calculating x value :
[tex]\begin{aligned}PQ&=QR\\3x+14&=7x-10\\7x-3x&=14+10\\4x&=24\\x&=6\end{aligned}[/tex]
Therefore, the value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.
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5. What are the names of the segments ?
6. What are the names of the rays ?
Answer:
de ef and df
Step-by-step explanation:
Melissa worked to earn $20.00. Alan worked for $12.00 hours. If she earns $2.00 per hour, how many hours did Melissa work?
Answer: 10 hours
Step-by-step explanation: so if you do 10 times 2.00 it equals 20 dollars or you can divide 20 and 2
This is URGENT! Please help me solve this question with full solutions
Answer:
B
Step-by-step explanation:
Given
[tex]\frac{1}{(t-2)^2}[/tex] = 6 + [tex]\frac{1}{(t-2)}[/tex] ( multiply through by (t - 2)²
1 = 6(t - 2)² + t - 2 ← distribute parenthesis and simplify
1 = 6(t² - 4t + 4) + t - 2
1 = 6t² - 24t + 24 + t - 2
1 = 6t² - 23t + 22 ( subtract 1 from both sides )
6t² - 23t + 21 = 0 ← in standard form
(2t - 3)(3t - 7) = 0 → in factored form
Equate each factor to zero and solve for t
2t - 3 = 0 ⇒ 2t = 3 ⇒ t = [tex]\frac{3}{2}[/tex] ← p
3t - 7 = 0 ⇒ 3t = 7 ⇒ t = [tex]\frac{7}{3}[/tex] ← q
Thus
p × q = [tex]\frac{3}{2}[/tex] × [tex]\frac{7}{3}[/tex] = [tex]\frac{21}{6}[/tex] = [tex]\frac{7}{2}[/tex] → B
What is the circumference of this circle?
Answer:
B) 12.56
Step-by-step explanation:
The formula for circumference of a circle is 2πr.
Substitute r for 2 and it becomes 4π.
4π ≈ 12.56
Answer: is 12.56
Step-by-step explanation: