Prime Factorization *Student A stated that the PRIME FACTORIZATION of 96 is 2x3x5x5. *Student B said that the PRIME FACTORIZATION of 96 is 2x2x2x2x2x3. Mr. Hrenko asks three students to find the PRIME FACTORIZATION of 96. *Student C stated that the PRIME FACTORIZATION of 96 is 2x2x3x3x5. Which student is correct? Prove your answer by making a factor tree. O Student B Studnet C O None of the students are correct O Student A
The student that is correct with regards to the prime factorization of 956 is student B.
Which student is correct?A factor is a number that divides another number without leaving any remainder. For example, 10 is a factor of 100. A prime number is a number that is perfectly divisible by 1 and that number only.
For example, a prime number is 7. A prime factor is the factor of a number that is a prime number. For example, a prime factor of 28 is 2.
In order to determine the prime factorization of a number, express the number as its prime factors.
Prime factors of 92 = 2 x 2 x 2 x 2 x 2 x 3
Thus, it is only student B that is correct. 5 is not a factor of 96.
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Write a directed number suggested by the following :
A 14 degrees below zero
B altitude 200 metres
The directed number suggested by the following will be:
A 14 degrees below zero = -14°
B altitude 200 metres = +200
How to illustrate the information?It should be noted that the directed number simply means the numbers that had both size and direction. It should be noted that the direction can either be positive or negative.
A measurement of altitude or height is the distance between a location or item and a reference datum, typically in the vertical or "up" direction. Although the term "altitude" is frequently used to refer to a location's height above sea level, the term "elevation" is frequently preferred in the context of geography. The term "depth" often refers to vertical distance measurements taken in the "down" direction. Globally, the research team discovered that the pace of temperature change frequently quickens as altitude increases.
Therefore, the directed number suggested by 14 degrees below zero will be negative 14 and this will be -14°
Also, altitude 200 metres will be positive 200 and this will be +200
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Last year you mowed grass and shoveled snow for 12 houses. You earned $225 for each lawn you mowed
and $200 for each house you shoveled for a total of $2600. How many lawns did you mow? How many
driveways did you shovel?
1800 lawns were mowed. 800 driveways were shoveled.
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Given Data
Let mowed grass be x
Let shoveled snow be y
Last year you mowed grass and shoveled snow for 12 houses
x + y = 12
y = 12 -x
You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.
225x + 200y = 2600
Equating value of y
225x + 200(12-x) = 2600
225x + 2400 - 200x = 2600
225x - 200x = 2600 - 2400
25x = 200
x = 8
For value of y,
y= 12 -x
y = 12 - 8
y = 4
Lawn mowed = 225(8)
Lawn mowed = 1800
Shoveled snow = 200(4)
Shoveled snow = 800
1800 lawns were mowed. 800 driveways were shoveled.
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Bonnie measured a city and made a scale drawing. a neighborhood park is 115 inches long in the drawing. the actual park is 138 yards long. what is the scale of the drawing? 5 inches : _ yards
The scale of drawing of Bonnie's drawing is 5 inches : 6 yards.
How to solve scale drawing?She measured a city and made a scale drawing.
The neighbourhood park is 115 inches long in the drawing. The actual park is 138 yards long.
Therefore, the scale of the drawing can be calculated as follows:
Hence,
115 inches = 138 yards
5 inches = ?
cross multiply
scale of the drawing = 5 × 138 / 115
scale of the drawing = 690 / 115
Therefore,
scale of the drawing is 5 inches : 6 yards
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There are 25 students competing in a volleyball tournament.
They are all wearing school colors. There are 4 students with blue shirts, 11 students with white shirts, and 10 students with yellow shirts.
A student is selected at random to be the captain. Match each probability to an outcome.
The captain has a blue shirt
The captain has a red shirt
The captain has a blue or white shirt.
impossible unlikely
neither unlikely nor likely
likely certain
Probability when a student is selected at random to be the captain. Probability the captain has a blue shirt is unlikely. Probability the captain has a red shirt is impossible. Probability the captain has a blue or white shirt is likely certain.
The total number of students is 15.
4 students are wearing blue shirt.
11 students are wearing white shirt.
10 students are wearing yellow shirt.
Only any one student can be captain.
The total outcomes are 25.
Probability that the student has blue shirt B is,
Total favorable outcomes = 4
P(B) = 1/25.
Probability that the student has red shirt R is,
Total favorable outcomes = 0
P(B) = 0/25.
P(B) = 0
Probability that the student has blue or white shirt B and W is,
Total favorable outcomes = 15
P(B&W) = 15/25.
P(B&W) = 3/5.
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The mean number of people per day visiting a museum in July was 160. If 20
more people each day visited the museum in August, what was the mean
number of people per day visiting in August?
• A. 640
• B. 160
• C. 620
• D. 180
The mean number of people per day visiting in August will be equal to option (D) 180.
Mean number of students in July = 160
20 more people visited the people each day in the month of August.
As, there is a constant increase in the number of who are visiting the museum in August each day that is 20 people, the mean will also increase by the same number that is 20 and will be:
Mean number of people per day visiting in August = 160 + 20
Mean number of people per day visiting in August = 180
Therefore, we get that, the mean number of people per day visiting in August will be equal to option (D) 180.
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una tuberia tiene 7 tramos iguales de 0.75 m. ¿cual es la longitud de la tuberia?
Answer: la respuesta es 5.25
Step-by-step explanation: 0.75 x 7 = 5.25
Is the relation represented in this table a function?
Is the relation in this set of points a function?
Answer:
the relation in the table is a function
the relation in the set of points is not a function
Step-by-step explanation:
the definition of a function is that one input (x) can only have one output (y). In the set of points, the input 4 appears twice, which means it is not a function.
27 ÷ 9 = 3, therefore 27 ÷ 0.9 = 30.
True
False
Answer: True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
. (4, 9) and (1, 6) the slope between the two points
Answer: the slope is 1
Step-by-step explanation:
Sandra has twenty seven coins, made up of nickels and quarters. The total is $5.35, how many nickles and quarters are there?
Answer: 21 quarters and 2 nickels.
Step-by-step explanation: $0.25(one quarter) x 21 = $5.25. $0.05(one nickel) x 2 = $0.10. $5.25 + $0.10= $5.35.
what 3 numbers can equal 20 and 300 in multiplication trying to help sister
Answer:
Here are all 3 number combinations that you can multiply to get 300: 300 × 1 × 1 = 300 150 × 2 × 1 = 300 150 × 1 × 2 = 300 100 × 3 × 1 = 300:
HELPPPPPPPPPPPPPPPP PLEASE
Answer:
use v for the value
Step-by-step explanation:
???? Help asap pls. ……
The expression equivalent to (3x²z⁻³)² is 9x⁴z⁻⁶.
What is meant by the term indices/index?In mathematics, an index (indices) is indeed the power or exponent raised to a number or variable. A constant is a value that cannot be altered. An index can be assigned to a number or a variable. A variable's index (or constant) is a value raised to a power of the variable. The indices are also referred to as powers or exponents.For the given question;
The expression is given as;
= (3x²z⁻³)²
Squaring each term individually.
= (3)²(x²)²(z⁻³)²
As the property of the index, the power will be multiplied.
= 9x⁴z⁻⁶.
Thus, the expression equivalent obtained for the given expression (3x²z⁻³)² is 9x⁴z⁻⁶.
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Explain how you can represent a proportional relationship using an equation.
The proportional relationship can be represented by using an equation y = kx
Proportional relationship defined as the relationships between two variables where their ratios are equivalent. We can say that , in a proportional relationship, one variable is always a constant value times the other. That constant is called as the "constant of proportionality"
Consider y and x are in direct proportional relationship
y ∝ x
We can write this proportional relationship as
y = kx
Where y and x are the two variables
K is the constant of proportionality
In this equation we can see that the variable y is a constant value times the other variable x
Hence, the proportional relationship can be represented by using an equation y = kx
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Solve for that value of x which makes like m and n parallel
Answer:
x = 300°
Step-by-step explanation:
If m and n are parallel, then m∠4x is equal to 120, since they are congruent angles.
Solve for x:
4x = 1200
Divide both sides by four
x = 300
rectangle QRST has coordinates Q(-8,5), R(-8,7), S(-5,7), and T(-5,5). dilate the rectangle by a scale factor of 4 with a center of dilation at the origin. write a rule to describe this transformation and use the rule to determine the coordinates of rectangle Q'R'S'T'
The rule to describe the transformation, dilation by a scale factor of 4 with center of dilation at the origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' is are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .
In the question ,
a rectangle QRST with coordinates Q(-8,5), R(-8,7), S(-5,7), and T(-5,5) is given ,
and to dilate the rectangle by a scale factor of 4 with center of dilation at the origin , we multiply coordinates of the original shape with the dilation factor
so the rule to describe the dilation will be
(x,y)→(4x,4y)
Using this rule to find the new coordinates of the rectangle Q'R'S'T' .
When Q = (-8,5)
Q' = (4*(-8),4*5)
Q' = (-32,20)
When R = (-8,7)
R' = (4*(-8),4*7)
R' = (-32,28)
When S = (-5,7)
S' = (4*(-5),4*7)
S' = (-20,28)
When T= (-5,5)
T' = (4*(-5),4*5)
T' = (-20,20)
So the coordinates of the rectangle Q'R'S'T' is Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .
Therefore , the rule to describe the transformation, dilation by a sale factor of 4 with center of dilation at the origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .
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7x-15= where x=3
[tex]222[/tex]
A bag contains 3 green, 4 blue, 2 red, 1 black, 6 yellow and 4 brown marbles. Suppose you randomly select a marble, replace it in the bag, and randomly pick a second
marble. What is the probability you pick a blue marble and then another blue marble?
Select the correct answer.
Choose the system of inequalities that best matches the graph below.
O A. y 22 +1
y ≤ 2+2
OB. y
-3
FI
≤z + 1
y ≥ 2x + 2
2z + 1
2+2
y2 2z+1
y2z+2
O D.
O c. y ≤
y ≥
Answer: The answer is C. You start off by first thinking about your slope equation, being y=Mx+b. Remember b equals your y- intercept. In this case one of your y-intercepts is positive 1 and the other is positive 2. Now you have the “b” part of the equation. Looking for slope or your “mx” part of the equation is next. All this is going to be is the rise over the run from your y intercept. How much did you rise and how much did you run to get to the next point. Both of these slopes are going up therefore both slopes will be positives. For the first one it rises 2 and runs 1 to get to the next point, however you do not need to write the one at the bottom of the 2 and can leave it as “2x+1”, because it is shaded below the red line the inequality will be less than or equal to
. The blue slope rises 1 and runs 2, it is written as
and because it is shaded above the blue one it will be greater than or equal to
.
Step-by-step explanation:
Considering the linear functions on the graph, the inequality that matches the situation is:
B. y ≥ x/2 + 2
y ≤ 2x + 1
What is a linear function?A linear function is modeled by:
y = mx + b, In which: m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
here, we have,
The lower bound of the interval is a linear function with
y-intercept of b = 2,
that also passes through (2,3), hence the slope is:
m = (3 - 2)/(2 - 0)
= 1/2.
Hence the inequality is:
y ≥ x/2 + 2
The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:
m = (5 - 1)/(2 - 0) = 2.
Hence the inequality is:
y ≤ 2x + 1
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The value of the inequality expression given as –3(2x – 5) < 5(2 – x) are x < 5 and number line (4)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the inequality expression?The inequality expression is given as
–3(2x – 5) < 5(2 – x)
Open the brackets
So, we have
-6x + 15 > 10 - 5x
Collect the like terms
So, we have
5x -6x > 10- 15
Evaluate the like terms
So, we have
-x > -5
This gives
x < 5
When represented on a number line, it can be represented as the number line in option (4)
Hence, the equivalents of the inequality are x < 5 and number line (4)
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F = G(m1m2/d2)
Solve for m1
Answer:
[tex]m_1=\frac{Fd^2}{Gm_2}[/tex]
Step-by-step explanation:
[tex]F=G \left(\frac{m_1 m_2}{d^2} \right) \\ \\ \frac{F}{G}=\frac{m_1 m_2}{d^2} \\ \\ \frac{Fd^2}{G}=m_1 m_2 \\ \\ m_1=\frac{Fd^2}{Gm_2}[/tex]
you repeatedly roll a fair six-sided die until you roll a 1 (and then you stop). every time you roll a 3, you win a points, and every time you roll a 6, you lose b points. you do not win or lose any points if you roll a 2, 4 or a 5. what is the expected number of points (as a function of a and b) you will have when you stop?
The expected number of points as a function of a and b is C = b+a.
In this questions what we are been asked is for the expected value C, to solve the problem we need to recognize the random variables and their respective probability.
x1 = roll a 1 -> P1 = 1/6
x2 = roll a 2 -> P2 = 1/6
x3 = roll a 6 -> P3 = 1/6
x4 = roll a 1, 4 or 5 -> P4 = 1/2
E = P1*x1 + P2*x2 + P3*x2 + P4*x4
x1 is equal to zero (no points and the game stop), x2 is equal to C+b (win a points, affecting the expected value), x3 is equal to C-a (win b points, affecting the expected value) and x4 is equal B (no points are lost and the game continues, therefore the expected value is not affected)
C = 1/6*0 + 1/6*(C+b) + 1/6*(C-a) + 1/2*(C)
1/6*C = 1/6*b + 1/6a
Solving for C
C = b+a
Conclusion: If you get a "2, 4 or 5, this means the game will be unaffected (in terms of points), you need to pay special attention to x1 and x2 (all with the same probability) that are the results that are going to affect your game.
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0.80divide by 50.i need help
The correct answer to the task 0.80 divided by 50 given above is 0.016
Division of numbersWhen we are trying to find the number of times a number can be obtained in another number, we use the term "division" to describe the mathematical expression. The division can be represented as ÷
For instance, the division of 0.80 by 50 is represented and solved below:
0.80 ÷ 50 = 0.016
It can also be represented like this:
0.80 / 50 = 0.016.
Another example of division of numbers is:
8/4 = 2
10 ÷ 2 = 5
So therefore, from the explanation given above we can confirm that when 0.80 ÷ 50, the answer is 0.016.
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Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?
y = –3(x + 2)2 + 10
y = –3(x – 2)2 + 10
y = –3(x + 2)2 – 14
y = –3(x – 2)2 – 2
Answer:
y = -3(x + 2)^2 + 10.
Step-by-step explanation:
y = –3x2 – 12x – 2
Divide first 2 terms by -3:
y = -3(x^2 + 4x) - 2 Now complete the square on x^2 + 4x:-
y = -3(x^2 + 4x + 4 - 4) - 2
y = -3[(x + 2)^2 - 4] - 2
y = -3(x + 2)^2 + 12 - 2
y = -3(x + 2)^2 + 10.
Solve for x (6x+5) 86
Answer:
x = -5/6
Step-by-step explanation:
First, set the equation (6x + 5) * 86 equal to 0. The equation is now (6x + 5) * 86 = 0. Next, simplify (6x + 5) * 86 by multplying 86 to 6x and 5. This will turn the equation into 516x + 430 = 0. Next, subtract 430 from both sides, cancelling out the 430 on the left side. After that, get the x value by itself by dividing 516 on both sides, cancelling out the 516 on the left side. Now, x = -430/516. From here, find the common factor of both the numerator and denominator; this turns out to be 86. Since 86 is the common factor, divide the numerator and denominator by 86 and you get x = -5/6.
HELPPPPPP
You are selling concessions at a local swim meet. Hot dogs are being sold for $1.00 and soda is being sold for $0.50. At the end of the day you made $150. Let x represent the number of hotdogs sold and y represent the number of sodas sold. Write an equation that can be used to find the number of hotdogs and sodas sold at the swim meet.
a. Standard Form:
b. Slope-Intercept Form:
c. If you sold 40 hot dogs how many sodas did you sell?
d. Using the Standard Form, identify the x - intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sold.
e. Using the Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the number of hot dogs and sodas sold.
d. Using the Standard Form, identify the x - intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sol
Maybe sorry if i got it wrong
please help me fasttt need to find the equation
The equation of the linear graph is expressed in slope intercept form as; y = 20x
What is the equation of the Linear Graph?The equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept (which is the point where the line crosses the y-axis)
From the graph given we can see that the line crosses the y-axis at 0. Thus; c = 0
Now, we can pick two coordinates to find the slope;
Slope = (y2 - y1)/(x2 - x1)
Slope = (40 - 20)/(2 - 1)
Slope = 20
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During the 2021 winter storm in texas, snow fell at a constant rate. in 3 hours, 19.5 centimeters of snow fell. how many centimeters of snow fell per hour?
Answer:
19.5/3=6.5 centimeters
Step-by-step explanation:
If I bought a scooter and it dropped by 24% in the FIRST year and after every year it drops by 13% for 7 years. I payed £850. How much is it worth now
Step-by-step explanation:
850÷100=17/2=8.5
8.5×24=204
850-204=646
646÷100=6.46
6.46×13=83.98 1st
646-83.98=562.02
562.02÷100=5.6202 2nd
5.6202×13=73.0626
562.02-73.0626=488.9574
488.9574÷100=4.889574 3rd
4.889574×13=63.564462
4.889574×13=63.564462
488.9574-63.564462=425.392938
425.392938÷100=4.25392938 4th
4.25392938×13=55.30108194
425.392938-55.30108194=370.0918561
370.0918561÷100=3.700918561 5th
3.700918561×13=48.11194129
370.0918561-48.11194129=321.9799148
321.9799148÷100=3.219799148 6th
3.219799148×13=41.85738893
321.9799148-41.85738893=280.1225259
280.1225259÷100=2.801225259 7th
2.801225259×13=36.41592836
280.1225259-36.41592836=243.7065975
I spent waaaaay to much time typing this
answer out I swear if it is incorrect I am done
£243.71