To divide 300 by a ratio of 3:7, calculate the value of each part by dividing 300 by the sum of the ratio parts (10) and then multiply by each part of the ratio to get 90 and 210, respectively.
Explanation:To divide 300 in a ratio of 3:7, first add the parts of the ratio together to determine how many parts you will split 300 into.
In this case, 3 + 7 equals 10 parts.
Then, you divide 300 by 10 to find out how much one part is worth.
This gives 300 ÷ 10 = 30. Now, to find the amounts corresponding to the ratio, multiply the single part value by the numbers in the ratio. For the first part (ratio 3), multiply 30 by 3 to get 90.
For the second part (ratio 7), multiply 30 by 7 to get 210.
So, 300 divided in a ratio of 3:7 gives us 90 and 210, respectively.
Rodrigo is starting his own part time business. He plans to earn $25 per hour. He has the following expenses each month, $750 for overhead, $110 for phone and fax and $75 for materials. a. Write an equality that describes the number of hours h he must work to earn a profit of $625. b. How many hours should he have worked to earn a profit of at least $625?
The equality that describes the number of hours h he must work to earn a profit of $625 is h = 62.4 hours and The inequality that describes the number of hours h he must work to earn a profit of atleast $625 is [tex]\rm h \geq 62.4\;hours[/tex] and this can be determine by using arithmetic operations.
Given :
Rodrigo plans to earn $25 per hour.Total expenses each month - $750 for overhead, $110 for phne and fax and $75 for materials.a). Let the total number of hours be 'h'. The equality that describes the number of hours Rodrigo needs to work to earn a profit of $625 is given by:
25h - (750 + 110 + 75) = 625
25h = 1560
h = 62.4 hours
b). Then the inequality that describes the number of hours Rodrigo needs to work to earn a profit of atleast $625. is given by:
[tex]\rm 25h -(750+110+75)\geq 625[/tex]
[tex]\rm 25h - 935 \geq 625[/tex]
[tex]\rm 25h \geq 625+935[/tex]
[tex]\rm 25h \geq 1560[/tex]
[tex]\rm h \geq 62.4\; hours[/tex]
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Round 8473227 to the nearest 100000
Over a 6 week period, the price of an MP3 player dropped steadily, from $82 to $34. What is the average weekly change in the price of the MP3 player over this period?
A washer and dryer cost $815 combined. The washer cost $85 less than the dryer. What is the cost of the dryer?
what is the complete factorization of the polynomial below. x^3-3x^2+x-3
Answer:
(x-3)(x+i)(x-i)
Step-by-step explanation:
[tex]x^3-3x^2+x-3[/tex]
We apply grouping method
We group first two terms and last two terms
[tex](x^3-3x^2)+(x-3)[/tex]
Take out GCF x^2 from first group. Also take out 1 from second group
[tex]x^2(x-3)+1(x-3)[/tex]
[tex](x-3) (x^2+1)[/tex]
Now we factor x^2 + 1
We use difference of square formula
a^2 - b^2 = (a+b)(a-b)
x^1 + 1 can be written as [tex]x^2 - (-1)[/tex], the value of -1 is i^2
[tex]x^2 +1 = x^2 -(-1) = x^2 - i^2[/tex]
x^2 - i^2 = (x+i)(x-i)
Final answer is (x-3)(x+i)(x-i)
The complete factorization of the polynomial x^3 - 3x^2 + x - 3 is (x - 3)(x^2 + 1). The process involves grouping and factoring out common terms.
The question asks for the complete factorization of the polynomial x^3 - 3x^2 + x - 3. To factor this polynomial, we are looking for factors of the lowest possible order that will multiply together to give us the original polynomial. Let's first look for a common factor in all the terms. In this case, there isn't a common factor except for 1, so we move on to finding factors through other means such as grouping.
We can attempt to group terms to facilitate the factoring process:
First, consider the polynomial in two parts (x^3 - 3x^2) and (x - 3).Within the first group (x^3 - 3x^2), we can factor out an x^2, which gives us x^2(x - 3).The second group is already in the form (x - 3), mirroring the (x - 3) factor we found in the first group.We then combine these to get the full expression x^2(x - 3) + (x - 3).Next, we can factor out the common (x - 3) term from both groups, obtaining (x - 3)(x^2 + 1).The polynomial x^3 - 3x^2 + x - 3 can now be expressed as the product of (x - 3) and (x^2 + 1). This represents the polynomial in its factored form using real coefficients.
Factor 3x^3-24x^2+36x
Put these decimals in order from least to greatest.
7.0,0.07,0.7,0.077
a triangle has two sides that are 2 inches and 12 inches what could be the length of the third side of the triangle
Answer:18
Step-by-step explanation:6+12>x
18>x
A man has 24 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 345 cents, how many dimes and how many quarters does he have?
The man has 17 dimes and 7 quarters.
A system of equations was set up, using the total number of coins and their total value, to determine the quantity of each coin type.
Let's denote the number of dimes as d and the number of quarters as q. We are given two facts: (1) the man has a total of 24 coins, and (2) the total value of the coins is 345 cents. Thus we have two equations:
d + q = 24 (since the total number of coins is 24)10d + 25q = 345 (since the value of each dime is 10 cents and each quarter is 25 cents, and their total value is 345 cents)We can solve this system of equations to find the values of d and q.
Subtracting the first equation from the second (multiplied by 10) to eliminate the variable d:
10d + 25q = 345
-(10d + 10q = 240)
-------------------------
15q = 105
Dividing by 15 to solve for q, we get q = 7. This means the man has 7 quarters. Substituting q = 7 into the first equation:
d + 7 = 24
d = 24 - 7
d = 17
So, the man has 17 dimes.
Therefore, the man has 17 dimes and 7 quarters.
−20≤10n i need a solution.
Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding, how much should her employer withhold from her check for social security?
0.65
6.50
2.60
26.01
Out of 106 total sophomores, there were forty-eight boys who received either an a, b, or c on their first math test. out of the twenty-eight total a’s, sixteen girls received a’s. out of the total fifty-four b’s, thirty girls received b’s. twelve boys received a c out of the twenty-four total c’s on the test. which two-way table represents this information
The two-way table that represents this information correctly is: Table B.
What is a Two-Way Table?A two-way table is used to demonstrate the frequencies for two variables collated from a single group. Rows and columns are used to represent information. The pieces of information stated above are well represented by chart B.
For instance, in the horizontal row, the total number of boys that had a, b, and c was shown to be 48. This means that there were forty-eight boys who received either an a, b, or c on their first test.
Learn more about two-way tables here:
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Express 192 as a prime factors in order
Which of the following is the inverse of y=3^x
Please hurry
A. y= 1/3^x
B. y=log3x
C. y=(1/3)^x
D. y=log1/3x
Answer:
[tex]y=log_3x[/tex]
Step-by-step explanation:
We want to find the inverse of [tex]y=3^x[/tex].
We interchange [tex]x[/tex] and [tex]y[/tex] to obtain,
[tex]x=3^y[/tex].
We now make y the subject by taking logarithm of both sides to base 3 to get,
[tex]log_3x=log_33^y[/tex].
[tex]log_3x=y\:log_33[/tex].
[tex]\Rightarrow log_3x=y\:(1)[/tex].
[tex]\Rightarrow y=log_3x[/tex]
The correct answer is B.
What is the value of the digit 8 in Alaska's population
To receive a C grade, a student must average more than 77 but less than or equal to 85 . If Ethan received a C in the course and had five grades of 78 , 79 76 , 64 , and 85 before taking the final exam, what were the possible grades for his final if there were 100 points possible?
Nick can read 3 pages in 1 minute. Write the ordered pairs (number of minutes, number of pages read) for Nick reading 0,1,2,and 3 minutes.
Which graph represents a reflection across the x-axis of g(x) = (3)x?
Answer:
the answer is B
Step-by-step explanation:
the curve starting at -4 all the way down.
Just did this on edge hope this helps :)
A container holds 7 quarts of water. How much is this in gallons?
To convert 7 quarts to gallons, divide 7 by 4, as there are 4 quarts in a gallon. The result is that 7 quarts equal 1.75 gallons.
To convert quarts to gallons, one must understand the unit equivalence between the two. One gallon is equivalent to 4 quarts. To find out how many gallons are in 7 quarts, divide the number of quarts by the number of quarts in a gallon.
Using the equivalence provided:
1 gallon = 4 quartsYou would perform the following calculation:
7 quarts
4 quarts per gallon = 1.75 gallons
Therefore, 7 quarts is equal to 1.75 gallons.
Answer:
7 quarts of water is equivalent to 1.75 gallons.
Explanation:
To convert quarts to gallons, you can use the conversion factor that 1 gallon is equal to 4 quarts.
Given that the container holds 7 quarts of water, you can use the conversion factor to find out how many gallons that is:
[tex]\[ \text{Number of gallons} = \frac{\text{Number of quarts}}{4} \][/tex]
[tex]\[ \text{Number of gallons} = \frac{7 \text{ quarts}}{4} \][/tex]
[tex]\[ \text{Number of gallons} = 1.75 \text{ gallons} \][/tex]
A copy machine makes
105
copies in
3
minutes and
45
seconds. How many copies does it make per minute?
Dr. Black is standing 15 feet from a streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the street lamp 50 degrees. To the nearest foot, the streetlamp is about
1 point) the solution of a certain differential equation is of the form y(t)=aexp(3t)+bexp(4t), y ( t ) = a exp ( 3 t ) + b exp ( 4 t ) , where a a and b b are constants. the solution has initial conditions y(0)=3 y ( 0 ) = 3 and y′(0)=3. y ′ ( 0 ) = 3 . find the solution by using the initial conditions to get linear equations for a a and
Your car is skidding to a stop from a high speed. you may want to review ( pages 112 - 114) . part a identify all forces acting on the object.
The forces acting on a car which is skidding to a stop are its weight due to gravity, a normal force coming from the ground, and the friction force due to the relative movement between the tires and the ground. Theoretically, we should also consider the friction force due to air viscosity, however practically we can neglect this force since it's contribution is very small in comparsion to the others (specially at low speeds).
Further explanationBy making the free body diagram of the car, we can observe 3 things:
The car has a certain mass, therefor due to the effect of gravity, it will have certain weight pointing towards the ground. It is important to remember that the weight always points downwards, even if the car would be on an inclined plane.Even though weight pulls the car down, the floor excerts a force over the car upward which keeps it in place. This is called the normal force and it is always perpendicular to the ground.Due to the roughness of the tires and the concrete, there will be a friction force do the relative movement between them. This friction force always goes in the opposite direction in which the car is moving (so if the car is heading to the right, the friction force aims towards the left, thus slowing it down).As a reference you can check the attached image, which shows how the forces would be in case the car would brake on a horizontal street. In case the car would be slowing on a floor which is not horizontal, like on a hill, the forces would have different directions.
Learn moreForces acting on a body: https://brainly.com/question/4230804Difference between kinetic and static friction: https://brainly.com/question/1714663Newton's second law: https://brainly.com/question/254316KeywordsForces, acceleration, friction
What number is needed to complete the pattern below?
66 73 13 21 52 __ 10 20
All of the following are true statements except _____. |56| = 56 -|56| = 56 |-56| = 56 -|56| = -56
Which symbol correctly compares these fractions? 13 20 ___ 7 10
Answer:
[tex]\frac{13}{20} < \frac{7}{10}[/tex]
Step-by-step explanation:
[tex]\frac{13}{20} \ and \ \frac{7}{10}[/tex]
Now we compare both the fractions
To compare both the fractions, we make the denominators same
LCD is 20
To make the denominators same we multiply the denominator of second fraction by 2
[tex]\frac{7 \cdot 2}{10 \cdot 2}[/tex]
[tex]\frac{14}{20}[/tex]
[tex]\frac{13}{20}[/tex] and [tex]\frac{14}{20}[/tex]
13/20 is smaller than 14/20
[tex]\frac{13}{20} < \frac{14}{20}[/tex]
How do you rename 5400 as hundred
Jordan and Manuel are on the track and field team at school.running around the track one day, Jordan ran 444m and Manuel ran 777 m. They both ran an even number of times around the track. How far is the track
Answer:
The track is 111 m
Step-by-step explanation:
The easiest way to calculate the meters in the track is to find the Greatest Common Divisor (GCD). This method is used to find the largest number to exactly divide both numbers 444 and 777, which are the meters both guys ran. The resulting number will give us the longest distance the track could have.
There are various techniques used to find the GCD. One of the is to find all divisors of both numbers and then look for the biggest one they have in common.
D 444 = { 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444 }
D 777 = { 1, 3, 7, 21, 37, 111, 259, 777 }
As we can see, the only divisors they have in common are 1, 3 ,37 and 111. The greatest of them is 111 ----> GCD(444,777) = 111.
This means the track has 111 m.
(Actually, the track could have been as long as any of the other common divisors, but it wouldn't have been realistic for the track to be 1, 3 or 37 meters).
Write 125.06 million 4 different ways.
Answer:
125.0600 million
[tex]\frac{6253}{50} million[/tex]
125,060,000
125 million 60 thousand
Step-by-step explanation:
It does not matter how many zeroes we add to the right end after the decimal, it does not change the value of the number.
Thus, 125.06, 125.060, 125.0600,.... all have the same values.
Similarly 125.06 can be change into the rational form
Thus, [tex]125.06=\frac{6253}{50} =\frac{12506}{100} \text{all have same values}[/tex]
We can also write the word "million" into the digits.
Thus, 125.06 million = 125,060,000 = 125 million 60 thousand
Jessica earned $13.50 babysitting one night. After babysitting the next day, she had a total of $31.75. How much did she earn babysitting the next day? Equation: 13.50 + x = 31.75