Answer:
[tex]64=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2=2^6[/tex]
Step-by-step explanation:
Gabrielle and John each
wrote the prime factorization of 64.
64 can be break into 32 times 2
32 can be break into 16 times 2
16 can be break into 8 and 2
8 can be break into 4 times 2
4 can be break into 2 times 2
So 64 is equal to 2 times 2 times 2 times 2 times 2 times 2
[tex]64=2^6[/tex]
The question involves analyzing the prime factorization of the number 64, which should be 2¶. The correctness of Gabrielle and John's factorizations can be checked by ensuring the base is 2 and the power is 6. Any deviation from this would indicate a mistake in their factorization.
Explanation:The question concerns the prime factorization of the number 64. A prime factorization is the expression of a number as a product of prime numbers. For the number 64, which is a power of 2, the prime factorization should be 2¶ since 64 is 2 multiplied by itself 6 times (2 x 2 x 2 x 2 x 2 x 2).
If Gabrielle and John wrote their prime factorizations of 64 differently, at least one of them has made an error. To verify if their prime factorizations are correct, they should end up with the same base number, which is 2 in this case, raised to the same power, which should be 6 for the number 64. Any other combination of numbers in the factorization would be incorrect, since 64 is not divisible by any other prime numbers.
When analyzing their work, one should check if they thoroughly factored the number down to only prime numbers and did not mistakenly include a composite number or an incorrect exponent in the factorization. To correct errors, divide the number progressively by the prime number 2 until the quotient is 1. Each division step represents an exponent in the prime factorization of 64.
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what is the algebraic expression for 7 more than a number
Answer:
7 + n
Step-by-step explanation:
Blank DVDs are sold in packages of 50 for $17.95. If your
company will need 2,700 blank DVDs next year, how much money
must you budget for blank DVDs?
Answer:
$969.3
Step-by-step explanation:
The DVDs are sold in packages of 50
Divide the total number you need by 50, therefore 2700/50 = 54 packages are needed
The packages are sold at $17.95 for one, hence amount needed is 54 * 17.95 = $969.3
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours. After the leak is fixed, the height of the water is 4.75 feet. The equation 4.75 = x +(-0.25) can be used to find x, the original height of the water in a pool.
The original height of the water level in pool is 5 feet
Solution:Given that , A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.
After the leak is fixed, the height of the water is 4.75 feet.
The equation 4.75 = x + (- 0.25) can be used to find x, the original height of the water in a pool.
So by solving the given equation and finding value of "x" gives the original height of water in pool
We have to find the original height of the water level in the tank.
So, let us solve the given equation
[tex]\begin{array}{l}{\rightarrow 4.75=x+(-0.25)} \\\\ {\rightarrow 4.75=x-0.25} \\\\ {\rightarrow x=4.75+0.25} \\\\ {\rightarrow x=5}\end{array}[/tex]
Hence, the original height of the water level is 5 feet
Answer5 feet
Step-by-step explanation:
Find a negative real number such that the square of the sum of the number and 5 is equal to 1225. (
Find a negative real number such that the square of the sum of the number and 5 is equal to 1225. (If th
The number is -40
Step-by-step explanation:
Let x be the number that we have to find
Then according to the given statement
the square of the sum of the number and 5 is equal to 1225.
[tex](x+5)^2 = 1225[/tex]
Taking square root on both sides
[tex]\sqrt{(x+5)^2} = \sqrt{1225}\\x+5 = -35 and x+5 = -35\\[/tex]
Subtracting 4 from both sides
[tex]x+5-5 = 35-5\ and\\ x+5 = -35-5\\x = 30\ and\ x = -40[/tex]
As it is mentioned in the equation, that the number is a negative number
So,
x = -40
Keywords: Radicals, Linear equations
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Factor 1/10 out of 1/10x-7/10
Answer:
[tex]\large\boxed{\dfrac{1}{10}x-\dfrac{7}{10}=\dfrac{1}{10}(x-7)}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{10}x=\left(\dfrac{1}{10}\right)(x)\\\\\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(7)\\\\\dfrac{1}{10}x-\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(x)-\left(\dfrac{1}{10}\right)(7)=\left(\dfrac{1}{10}\right)(x-7)[/tex]
A firm producing 7 units of output has an average total cost of Rs. 150 and has to pay Rs.350 to its fixed factors of production whether it produces or not. How much of the average total cost is made up of variable costs?
Rs 100 of the average total cost is made up of variable costs.
Step-by-step explanation:
Given:
Number of output the firm produces= 7 units
Average cost of the output= Rs. 150
fixed factors of production = Rs.350
To Find:
How much of the average total cost is made up of variable costs=?
Solution:
we know that,
Average total cost= total cost/ number of output units produced
substituting the values, we get
[tex]150=\frac{\text{Total cost}}{7}[/tex]
Total cost= 1050
we know that Total fixed cost = 350
Total cost = Total fixed cost + Total variable cost
plug in the known values.
1050= 350 + Total variable cost
Total variable cost = 1050-350
Total variable cost =700
For 7th unit [tex]\frac{700}{7}[/tex] = 100
What is the answer to this?
Answer:
7^-12 or 1/7^12
Step-by-step explanation:
To divide exponents with the same base, subtract the second exponent from the first.
So:
7^-5/7^7 = 7^-5-7 = 7^-12
You can also write 7^-12 as 1/7^12.
if 20%of a length is 23cm. what the complete lenght
Answer:
The complete length is 115 cm.
Step-by-step explanation:
Given:
If 20%of a length is 23 cm.
Now, to find the complete length.
Let, the complete length be [tex]x[/tex].
So, according to question:
20% of [tex]x[/tex] = 23 cm
[tex]\frac{20}{100} \times x=23[/tex]
[tex]0.20\times x=23[/tex]
[tex]0.20x=23[/tex]
Dividing both sides by 0.20 we get :
[tex]x=115[/tex]
Therefore, the complete length is 115 cm.
To find the complete length when 20% is 23 cm, divide 23 cm by 0.20 to get 115 cm as the total length.
If 20% of a length is 23 cm, we want to find out what the complete length is. To do so, we recognize that 20% is the same as saying 20 per 100 or 0.20 in decimal form. If 0.20 of the length is 23 cm, it means that 23 cm represents 0.20 of the total length. We can set up the equation like this:
0.20 * Total Length = 23 cm
To find the Total Length, we divide both sides of the equation by 0.20:
Total Length = 23 cm / 0.20
Total Length = 115 cm
Therefore, the complete length is 115 cm.
Jessica made 619 cups of punch. Her
punch had two different types of juice in
it. If the punch had 4 cups of one type of
juice, how many cups of the other type of
juice did it have?
Answer:
The cups of other type of juice is 615
Step-by-step explanation:
Given as :
The total cups of punch made by Jessica = 619
The two different types of juice is x and y
Let The one type of juice = x = 4
And According to question
x + y = 619
So, 4 + y = 619
Or, y = 619 - 4
∴ y = 615
Hence The cups of other type of juice is 615 . Answer
One of the angles of an isosceles triangle is 46º.
Find ALL possible measures of the other angles. Also,
in the space below, draw an example of each scenario.
Answer:
The other 2 angles are 67 and 67 degrees OR 46 and 88 degrees.
Step-by-step explanation:
If the vertex angle is 46 degrees then , as the other 2 angles are congruent, they are (180 - 46) / 2 = 67 degrees.
The triangle has angles (46, 67 and 67).
If the 2 equal angles are both 46 then the other angles is 180 - 2(46) = 88 degrees.
The other triangle has angles (46, 46 and 88).
Miguel created the ratio table below to show how he uses the money he earns at work. How much money will he save if he earns 120.00?
Answer:
The money he will save if he earns $120.00 is $90.00.
Step-by-step explanation:
Given:
In the figure is the ratio of the savings and the earnings.
Now, to find out that how much savings will be if Miguel earns $120.00.
We need to get the percentage of the ratio of the earning and saving.
So, according to the table:
If he earns $10.00 then he saves $7.50.
[tex]\frac{7.50}{10}\times 100[/tex]
[tex]=0.75\times 100[/tex]
[tex]=75[/tex]
So, if Miguel earns $10.00 he save the 75% of it.
If he earns $50.00 then he saves $37.50.
As we calculate the percentage as the above process then the saving is 75% of the earning.
And, if he earns $150.00 and save $112.50 then it is also the 75% of the earning as mentioned above.
Now, to find the saving of the earning $120.00.
So, it will be 75% of the earning as we observe in the above case:
75% of $120.00
[tex]\frac{75}{100}\times 120[/tex]
[tex]=0.75\times 120[/tex]
[tex]=90[/tex]
Therefore, the money he will save if he earns $120.00 is $90.00.
A farmer planted 4 1/2 acres of land with 6 types of wheat. If she planted an equal amount of each type of wheat, how many acres of each type did she plant? Write your answer as a fraction or as a whole or mixed number.
(I just want to know how to set it up!)
She planted [tex]\frac{3}{4}[/tex] arcs of each type
Step-by-step explanation:
The given is:
A farmer planted [tex]4\frac{1}{2}[/tex] acres of land with 6 types of wheatShe planted an equal amount of each type of wheatWe need to find how many acres of each type she planted
∵ The farmer planted [tex]4\frac{1}{2}[/tex] arcs of land
∵ She planted 6 types of wheat
∵ She planted an equal amount of each type of wheat
- Divide the total number of arcs by 6 to find the number of arcs
for each type
To divide the total number of arcs change it from the mixed number
[tex]4\frac{1}{2}[/tex] to improper fraction
∵ [tex]4\frac{1}{2}=\frac{(4*2)+1}{2}=\frac{9}{2}[/tex]
∴ The total number of arcs = [tex]\frac{9}{2}[/tex]
∴ The number of arcs of each type = [tex]\frac{9}{2}[/tex] ÷ 6
- Change the division sign to multiplication sign and reciprocal
the number after the division sign
∴ The number of arcs of each type = [tex]\frac{9}{2}[/tex] × [tex]\frac{1}{6}[/tex]
∴ The number of arcs of each type = [tex]\frac{9*1}{2*6}[/tex]
∴ The number of arcs of each type = [tex]\frac{9}{12}[/tex]
- Reduce the fraction by dividing up and down by 3
∴ The number of arcs of each type = [tex]\frac{3}{4}[/tex]
She planted [tex]\frac{3}{4}[/tex] arcs of each type
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Students at Springfield Middle school are planning to rooftop a garden.They plan to plant flowers in 18 beds,which is 30% of the total number of garden beds. What is the total number of garden beds in the students plans?
Answer:
60
Step-by-step explanation:
Since 30%/3 is 10%, 6 is 10% of the total number of garden beds, since 18/3 is 6.
And 10% times 10 is 100%, or all of it, so 60 is the total amount of garden beds, since 6 times 10 is 60.
60 garden beds in the students plans.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Present flower bed= 18
This is 30% of the total number of garden beds.
let the total flower bed be x.
So, 30% of x= 18
30/100 x = 18
x= 1800/ 30
x= 60
Hence, 60 garden beds in the students plans.
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x(956÷14×66) simplify the expression.
Answer:
[tex]\frac{31548}{7} x[/tex]
Step-by-step explanation:
Answer:
31548/7 x
Step-by-step explanation:
Andy received a 25% discount on the book he bought at the book sale if he paid 17.40 what was the original price for the book
Answer:
$21.75
Step-by-step explanation:
Add 25% then subtract to get back to $17.40
a polyhedron has 6 vertices and 9 edges how many faces
Answer: 5 faces
Step-by-step explanation:
The Euler's polyhedron formula states that:
number vertices - number of edges + number of faces = 2
That is :
6 - 9 + F = 2
-3 + f = 2
f = 2 + 3
f = 5
Therefore , it has 5 faces
62 out of 74 students turned in their hw. What percent of students turned in their hw and what percent did not turn in hw
83.78% students turned in their homework and 16.22 percent students did not turn in their homework
Step-by-step explanation:
Percentage formula will be used for this problem
Given
Total students = 74
Students who turned their homework = 62
So the percentage of students who turned in their homework will be:
[tex]Percentage\ of\ students\ who\ turned\ in\ their\ hw = \frac{62}{74} *100\\=0.8378*100\\=83.78\%[/tex]
So the students who did not turn in their homework = 100-83.78
=16.22%
Hence,
83.78% students turned in their homework and 16.22 percent students did not turn in their homework
Keywords: Percent, percentage
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Write the following as an expression and evaluate . The sum of -6 and the quotient of -36 and 6
Answer:
(-36/6)+(-6)
Step-by-step explanation:
Answer:
[tex] \frac{ - 36}{6} + ( - 6)[/tex]
-12
Step-by-step explanation:
-36/6 = - 6
-6 + (-6) = -12
TEST SCORES Matthew's math test scores this
semester were 80, 76, 94, 90, 88, 92, 88, and 70.
Which measure of central tendency might
Matthew want to use to describe his test
scores? Explain.
Answer:
Average mark of the semester
EXPLANATION
This is done by adding the total score divided by the number of scores of the semester in that way Matthews average test score would be gotten
Graph the inequality.
4x - 4y > 28
Step-by-step explanation:
[tex]4 < x - 7[/tex]
It's a straight line so plug in two numbers and connect the points.
And the result is everything under the line. Expect the line because its only < instead of <=
To check your answer use Mathaway or something Desmos
in a group of 26 children, 50% have blue eyes. how many children have blue eyes?
Answer:
13
Step-by-step explanation:
26 * 50/100 = 26 * 1/2 = 13
Answer:
13
Step-by-step explanation:
50% = 50/100 = 1/2
That means that 1/2 of the children have blue eyes.
26*(1/2) or 26/2 = 13
4) Mark rented a bike from Jose's Bikes. It
cost $10 plus $6 per hour. If Mark paid
$22, then he rented the bike for how many
hours?
Answer: 2hrs
Step-by-step explanation:
paid 10 dollars at first and then 6 every hour he rode
so let x represent the # of hour rented
6x+10=22
x=2hrs
are you able to simplify 3/9?
Answer:
Yes
Step-by-step explanation:
3 and 9 are both divisible by 3. Divide 3 and 9 by 3. You would get the fraction 1/3. You cannot simplify this fraction anymore.
~Stay golden~ :)
How many 3/5 are in 15 3/5
Answer:
26
Step-by-step explanation:
15 3/5=78/5
(78/5)/(3/5)=(78/5)(5/3)=78/3=26
There are 26 three-fifths in fifteen and three-fifths.
To find out how many times [tex]\frac{3}{5}[/tex] is in [tex]15 \frac{3}{5}[/tex], we follow these steps:
Convert the mixed number [tex]15 \frac{3}{5}[/tex] into an improper fraction.
[tex]15 \frac{3}{5} = 15 + \frac{3}{5} = \frac{15 \times 5}{5} + \frac{3}{5} = \frac{75}{5} + \frac{3}{5} = \frac{75 + 3}{5} = \frac{78}{5}[/tex]
Divide [tex]\frac{78}{5}[/tex] by [tex]\frac{3}{5}[/tex].
To divide fractions, we multiply by the reciprocal:
[tex]\frac{78}{5} \div \frac{3}{5} = \frac{78}{5} \times \frac{5}{3} = \frac{78 \times 5}{5 \times 3} = \frac{390}{15}[/tex]
Simplify [tex]\frac{390}{15}[/tex].
Divide the numerator and the denominator by their greatest common divisor (GCD), which is 15:
[tex]\frac{390 \div 15}{15 \div 15} = \frac{26}{1} = 26[/tex]
Choose the correct statement about the graph of x - 1 ≤ 2
A.) Closed circle on 1 and all the numbers to the left shaded
B.) Open circle on 3 and all numbers to the left shaded
C.) Open on 1 and all numbers to the right shaded
D.) Closed circle on 3 and all the numbers to the left shaded
Answer:
B.) Open circle on 3 and all numbers to the left shaded
Each snack at the concession
stand is priced at $4.00. All of the
snacks cost a total of $86.56.
How many snacks will need to be
sold in order to make a minimum
profit of $100.00?
To make a minimum profit of $100 with each snack priced at $4.00, a total of 47 snacks need to be sold at the concession stand. This includes 22 snacks to cover the total cost of $86.56 and an additional 25 snacks to achieve the profit goal.
Explanation:The question is about finding out how many snacks need to be sold at a concession stand to achieve a minimum profit. To get the answer, we first need to determine how many snacks would make up the total cost, and then calculate how many additional snacks would be necessary to attain the profit goal.
Given that each snack at the concession stand costs $4.00 and that the total cost of the snacks is $86.56, we can find out how many snacks were initially purchased by dividing the total cost by the price of each snack: $86.56 ÷ $4.00 = 21.64 snacks. Since we can't sell a fraction of snack, we round up to 22 snacks to cover the total cost.
To calculate the number of additional snacks needed to attain a $100 profit, we divide the profit goal by the price of each snack: $100 ÷ $4 = 25 snacks.
Therefore, to cover the total cost and also make a minimum profit of $100, the concession stand needs to sell 22 snacks for the cost and additional 25 snacks for the profit, totaling 47 snacks altogether.
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Chloe is a high school basketball player. In a particular game, she made some three point shots and some two point shots. Chloe made a total of 9 shots altogether and scored a total of 22 points. Determine the number of three point shots Chloe made and the number of two point shots she made.
Chloe made 4 three-point shots and 5 two-point shots.
Explanation:Let's solve this problem using a system of equations.
Let x be the number of three-point shots Chloe made and y be the number of two-point shots she made.
We have the following equations:
x + y = 9 (equation 1)
3x + 2y = 22 (equation 2)
From equation 1, we can solve it for x:
x = 9 - y
Substitute this value of x into equation 2:
3(9 - y) + 2y = 22
27 - 3y + 2y = 22
-y = -5
y = 5
Substitute this value of y back into equation 1:
x + 5 = 9
x = 4
Therefore, Chloe made 4 three-point shots and 5 two-point shots.
I’m the expression 10a + 4, identify the coefficient
Answer:
2(5a+2)
Step-by-step explanation:
10a+4=2(5a+2)
Please help with b..
Answer:
First side: 12 feet, second side: 16 feet
Step-by-step explanation:
We know that the second side is 4 feet longer than the first side. If the first side is x, then the second side is x+4
b) The total amount of the border is 28 feet, so we can say that first side+second side=28, or
x+(x+4)=28
2x+4=28
2x=24
x=12 feet is the first side
x+4 = 16 feet is the second side
We can check that 12 feet + 16 feet = 28 feet as stated by the problem
The graph shows a proportional relationship between y (price) and x (number of pounds of rice).
A graph with a line running through coordinates (0,0) and coordinates (30,24)
What is the unit rate, expressed in price per pound?
a. $0.60
b. $0.80
c. $1.25
d. $1.67
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The unit rate, expressed in price per pound is $0.80.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is constant.
The slope of the line running through coordinates (0,0) and coordinates (30,24) is,
m= (24-0)/(30-0) = 0.8
Hence, the unit rate, expressed in price per pound is $0.80.
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