which pair of numbers below have 4 and 6 as common factors
The pair of numbers with 4 and 6 as common factors is option D) 36, 48.
To determine which pair of numbers have 4 and 6 as common factors, we need to find the factors of each pair of numbers and see if both 4 and 6 are factors.
A) Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
Both 4 and 6 are common factors.
B) Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 4
Both 4 and 6 are not common factors.
C) Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2
Both 4 and 6 are not common factors.
D) Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors: 1, 2, 3, 4, 6, 12
Both 4 and 6 are common factors.
Therefore, the pair of numbers with 4 and 6 as common factors is option D) 36, 48.
The probable question may be:
Which pair of numbers below have 4 and 6 as common factors?
A) 12, 18 B) 20, 24 C) 28, 30 D) 36, 48
the lake side marina charges a $35 rental fee for a boat in addition to charging $15 an hour for usage.The total cost y of renting a boat for x hours can be represented by the equation y=15x+35? graph the equation?
interpret the slope and the y-intercept?
Answer:
Slope is 15 and y-intercept is 35.
Step-by-step explanation:
Given : The lake side marina charges a $35 rental fee for a boat in addition to charging $15 an hour for usage.
The total cost y of renting a boat for x hours can be represented by the equation [tex]y=15x+35[/tex]
To find : Graph the equation and interpret the slope and the y-intercept?
Solution :
The general slope form is [tex]y=mx+c[/tex]
where, m is the slope and c is the y-intercept.
On comparing the equation [tex]y=15x+35[/tex]
The slope is m=15.
The y-intercept is c=35.
Now we plot the equation [tex]y=15x+35[/tex] in graphing tool.
The equation is in green line passing thorough (35,0) and (-2.333,0).
Refer the attached figure below.
Answer:
y=15x+35
Step-by-step explanation:
describe how you regroup when you find the sum 64+43
Mr. Gaster has $5 in his piggy bank and wants to put $45 every week into the piggy bank. Make you equation showing how much money he will have at any number of day. Solve your equation to show the total amount of money Mr.Gaster will have in 28 days in his piggy bank. Make sure to show your work.
Final answer:
To find out how much money Mr. Gaster will have after any number of days, we create an equation based on his initial savings and weekly contributions. For 28 days, the equation is T = ($45 × (28/7)) + $5, which simplifies to T = $185. Therefore, Mr. Gaster will have $185 in his piggy bank after 28 days.
Explanation:
To determine how much money Mr. Gaster will have in any number of days, we need to create an equation that accounts for the initial amount and the weekly savings. Because there are 7 days in a week, Mr. Gaster will save $45 for every 7 days. Therefore, to find the total amount in the piggy bank after a certain number of days (d), we divide the number of days by 7 (to get the full weeks), multiply it by the weekly saving amount, and then add the initial amount.
Forming the Equation
Let T be the total amount, and the equation representing the situation is:
T = ($45 \times \frac{d}{7}) + $5
Solving for 28 Days
To solve for the total amount in 28 days:
T = ($45 \times \frac{28}{7}) + $5
T = ($45 \times 4) + $5
T = $180 + $5
T = $185
Hence, after 28 days, Mr. Gaster will have $185 in his piggy bank.
about 3/5 of the students at Roosevelt Elementary live within 1 mile of the school. what percent of students live within one mile of the school
60% of students live within one mile of the school if about 3/5 of the students at Roosevelt Elementary live within 1 mile of the school.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
About 3/5 of the students at Roosevelt Elementary live within 1 mile of the school.
3/5 in percent
= (3/5)x100
= 3x20
= 60 %
Thus, 60% of students live within one mile of the school if about 3/5 of the students at Roosevelt Elementary live within 1 mile of the school.
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Which shows the correct word and standard forms for the decimal?
20 + 6 + 0.09
A.
twenty-six and nine tenths
26.9
B.
twenty-six and nine hundredths
26.09
C.
twenty-six and nine hundredths
26.9
D.
twenty-six and nine thousandths
26.009
Is it B?
how much does all the angles in a quadrilateral equal up to?
The sum of the interior angles in any quadrilateral is always 360 degrees.
The sum of the interior angles in a quadrilateral is always 360 degrees. This is a fundamental concept in geometry that applies to all quadrilaterals, regardless of their shape. To understand why this is the case, one can consider dividing a quadrilateral into two triangles. Since the sum of the angles in a triangle is always 180 degrees, adding the angles from both triangles within the quadrilateral gives us a total of 360 degrees. This rule is crucial when solving various geometrical problems involving quadrilaterals. For example, if a quadrilateral ABCD has an extended line CE creating two angles on a straight line, angles ACD and ACE would sum up to 180 degrees because angles on a straight line always sum up to 180 degrees.
It is also worth noting that if a quadrilateral has three right angles, the properties of the sides relative to the fourth angle can be determined based on whether that angle is right, acute, or obtuse. These principles are derived from the fundamental properties of angles in polygons and are used to deduce further geometric relationships.
Last year, Hong opened an investment account with $6200 . At the end of the year, the amount in the account had decreased by 29.5% . How much is this decrease in dollars? How much money was in his account at the end of last year?
Answer:
Step-by-step explanation:
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what percent of 92 is 23
23 is approximately 25 percent of 92.
To determine the percentage, we need to find what portion of 92 is represented by 23. We can set up a proportion to solve for the percentage.
Let's assume the unknown percentage is 'p'. We can write the proportion as:
23 is to 92 as p is to 100.
This can be expressed mathematically as:
23/92 = p/100
To solve for 'p', we can cross-multiply:
23 x 100 = 92 x p
2300 = 92p
To isolate 'p', we divide both sides of the equation by 92:
2300/92 = p
Simplifying, we find:
25 = p
Therefore, 23 is approximately 25% of 92. This means that 23 is 25% of the whole value of 92. To verify this, we can calculate 25% of 92:
(25/100) x 92 = 0.25 x 92 = 23
Hence, 23 is indeed 25% of 92.
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Identify the terms,like terms,coefficients, and constants in each expression
4b+7b+5
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.Variable: A variable is a symbol that doesn't have a fixed value.Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.Given expression:
4b+7b+5
As. term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Terms are 4b, 7b, 5
Now, coefficient is a number that is multiplied by a variable in an expression.
coefficient are 4 , 7
As a constant is a fixed numerical value,
So, constant = 4, 7 , 5
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Eight paper clips cost 12. cents.How much does 6 paper clips cost?
2. In the troposphere, as altitude increases, air temperature drops at a relatively uniform rate. At the top of the troposphere, an average depth of 11 km, the average temperature is -56.5°C. At the base of the troposphere, 0 km, the average temperature is 15°C. In a linear model of this situation, which of the following statements applies? An increase of 1 km in altitude corresponds to a increase of 3.8°C in temperature. An increase of 1 km in altitude corresponds to a decrease of 3.8°C in temperature. An increase of 1 km in altitude corresponds to a increase of 6.5°C in temperature. An increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.
Answer: An increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.
Step-by-step explanation: In a linear model of this situation, the y-intercept represents the temperature at the base of the troposphere, 15°C.
The rate of change, or slope, can be determined using two values: temperature at the base, (0 , 15), and temperature at the top, (11 , −56.5).
The linear model of this situation is y = 15 − 6.5x, where x represents the height of the troposphere, in kilometers.
The rate of change, or slope, indicates that an increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature. Hope this helps
Final answer:
In the troposphere, an increase of 1 km in altitude corresponds to a temperature decrease of 6.5°C, based on the given data of 15°C at sea level and -56.5°C at the top of the troposphere (11 km).
Explanation:
The question concerns the change of air temperature with altitude in the troposphere. From the information provided, we know that the temperature at the base of the troposphere (0 km) is 15°C and at the average top (11 km), it's -56.5°C. To find the rate at which temperature decreases with altitude, we can use the given temperatures at two different altitudes to calculate the lapse rate.
The difference in temperature from the base to the top is 15°C - (-56.5°C) = 71.5°C. Over a distance of 11 km, this gives us a lapse rate of 71.5°C / 11 km = 6.5°C/km. Therefore, an increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.
When mrs chang filled the gas tank in her truck, the gas gauge was at Empty. She spent 75$ for 20 gallons of gas. The next time the gas gauge was at Empty, dhe had driven over 480 miles. Write the ratios you can use to find the two unit rates that concerns most drivers: dollars per gallon and miles per gallon. Then find the unit rates. Explain your reasoning.
Mrs. Chang's truck runs at a unit rate of $3.75 per gallon of gas and 24 miles per gallon. These rates are found by dividing the total cost by gallons for the cost rate, and total miles by gallons for the efficiency rate.
Explanation:To find the unit rates of dollars per gallon and miles per gallon for Mrs. Chang's truck, we can use the ratios provided by the information given. First, to find the cost per gallon of gas, we divide the total amount spent by the number of gallons:
Cost per gallon = Total cost / Number of gallons = $75 / 20 gallons = $3.75 per gallon
To calculate the miles per gallon, we divide the number of miles driven by the number of gallons it took to fill the tank when it was empty again:
Miles per gallon = Total miles driven / Number of gallons = 480 miles / 20 gallons = 24 miles per gallon
By calculating these unit rates, drivers can determine both the price efficiency of their gasoline purchases and the fuel efficiency of their vehicle.
Kelly has 4 dimes and some nickels. Jonny has 33 nickels and some dimes. Kelly and Jonny each have $2.25 worth of change. Who has more nickels? How many more?
Which of the following numbers is irrational?
a fraction with numerator negative 9 and denominator 5, a fraction with numerator square root of 5, a fraction with numerator 7 and denominator 3, square root of 9
a) a fraction with numerator negative 9 and denominator 5
b) square root of 5
c) a fraction with numerator 7 and denominator 3
d) square root of 9
mr cho has twice as many dollar bills as quarters. his money in dollar bills and quarters totals $15.75. how many of each does he have?
Final answer:
Mr. Cho has 7 quarters and 14 dollar bills. We find this by setting up an equation considering that he has twice as many dollar bills as quarters and their total value is $15.75. Solving the equation, we find the number of quarters (q) to be 7 and the number of dollar bills to be twice that amount.
Explanation:
Mr. Cho has twice as many dollar bills as quarters, and their total value is $15.75. To find out how many of each he has, let's set up some equations based on this information. Let's call the number of quarters q and the number of dollar bills 2q (since he has twice as many dollar bills as quarters).
Since each quarter is worth $0.25, the total value of the quarters would be 0.25q. The total value of the dollar bills would just be 2q (since each dollar bill is worth $1). The combined value of the quarters and dollars is given as $15.75, so we can set up the following equation:
0.25q + 2q = 15.75
Combining like terms:
2.25q = 15.75
Dividing by 2.25:
q = 15.75 / 2.25
q = 7
Therefore, Mr. Cho has 7 quarters. Since he has twice as many dollar bills as quarters, he has:
2q = 2 * 7 = 14 dollar bills.
In summary, Mr. Cho has 7 quarters and 14 dollar bills.
5/8 teaspoon baking soda with 1/3 teaspoon of salt equals how many teaspoons together
6.1 in.+3in.+6.9in.+3.1in.=
Six times as many people voted in the 2012 election as in the 2008 election if 162 people voted in 2008, how many people voted in both elections?
Paul is making loaves of raisin bread to sell at a fundraising event. The recipe calls for 1/3 cups of raisins for each loaf, and Paul has 3 1/4 cups of raisins. I need help with b.
Answer:
a. [tex]9\frac{3}{4}[/tex], from which he can make 9 loaves.
b. [tex]\frac{3}{4}[/tex] is the remaining part.
Step-by-step explanation:
Givens
The recipe calls for 1/3 cups of raisins for each loaf.Pauls has 3 1/4 cups of raisins.To find then number loaves that Paul can make, we just need to divide the number of cups of raising he has, and the cups of raisins need it according to the recipe.
[tex]3\frac{1}{4} \div \frac{1}{3}[/tex]
But, we first need to transform the mixed numero into a fraction, then we solve
[tex]3\frac{1}{4} \div \frac{1}{3}=\frac{13}{4} \div \frac{1}{3}=\frac{13}{4} \times \frac{3}{1}= \frac{39}{4}[/tex]
If we divide this fraction, we obtain a mixed number, becuase the division is not exact
[tex]\frac{39}{4}= 9\frac{3}{4}[/tex]
So, Paul can make [tex]9\frac{3}{4}[/tex] number of loaves. But, he cannot make an incomplete loaf, that means Paul can only make 9 loaves, and the remaining is 3/4, that's the "excess". You can get this answer by subtracting
[tex]9\frac{3}{4} - 9= \frac{39}{4}-9=\frac{39-36}{4}=\frac{3}{4}[/tex]
Therefore, the answers are
a. [tex]9\frac{3}{4}[/tex]
b. [tex]\frac{3}{4}[/tex]
7/8 greater than 5/10
2. There are 14 bees in the hive and 17 bees in the garden. How many bees are there?
By adding the 14 bees in the hive to the 17 bees in the garden, we determine there are a total of 31 bees.
Explanation:To find out how many bees there are in total, we need to add the number of bees in the hive to the number of bees in the garden. The problem states that there are 14 bees in the hive and 17 bees in the garden. Adding these two quantities together gives us:
14 bees in the hive + 17 bees in the garden = 31 bees in total.
So, there are 31 bees altogether.
Final answer:
To find the total number of bees, you need to add the number of bees in the hive to the number of bees in the garden. The total number of bees is 31.
Explanation:
To find the total number of bees, you need to add the number of bees in the hive to the number of bees in the garden. In this case, there are 14 bees in the hive and 17 bees in the garden.
To find the total number of bees, add the number of bees in the hive and the number of bees in the garden: 14 + 17 = 31.
Therefore, there are 31 bees in total.
solve each system of linear equations by adding or subtracting
How to solve -3a + 52a
the fastest a human has ever run is 27 miles per hour. how many miles per minute did the human run
The three sides of a triangle measure 9.97 meters, 10.1 meters, and 0.53 meter. what is the distance around the triangle
What is 8.461785 rounded to the nearest hundredth tenths
what is the value represented by the digit 2 after 298 is divided by 10?
Answer: the answer is 20
Step-by-step explanation:
Use compatible numbers to estimate the quotient? 474÷9
Using compatible numbers (numbers that are easy to compute mentally), you can estimate that 474 divided by 9 is approximately 50 by substituting 474 with 450, a number that is easily divisible by 9.
Explanation:The question is asking you to use compatible numbers to estimate the quotient of 474 divided by 9. Compatible numbers are numbers that are easy to compute mentally. When we look at 474 and 9, one potential set of compatible numbers might be 450 and 9. So, let's divide 450 by 9 to get our estimate.
Step 1: Identify the compatible numbers. Here we can use 450 instead of 474 because it is easily divisible by 9.
Step 2: Perform the division. 450 divided by 9 equals 50.
Therefore, using compatible numbers, we can estimate that 474 divided by 9 is approximately 50.
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Jeandre said |3| equals |-3|. Is Jeandre correct? Use a number line and words to support your answer.
Jeandre is correct because the absolute value of a number represents its distance from zero on a number line. Both |3| and |-3| are three units away from zero, therefore they have the same value of 3.
Jeandre is correct when he says that |3| equals |-3|. In mathematics, the absolute value of a number is the distance of that number from zero on a number line, regardless of direction. Both 3 and -3 are three units away from zero. Therefore, the absolute value of 3 is 3, and the absolute value of -3 is also 3.
To visualize this on a number line: if you start at zero and move three units to the right, you reach +3. If you move three units to the left of zero, you reach -3. Since absolute value is concerned with distance only and not direction, both |3| and |-3| represent a distance of 3 units from the origin, hence both have a value of 3.
The equals sign is used to indicate that both expressions are the same in value. Additionally, the rules of algebraic signs help to understand that the negative sign indicates direction on a number line, but does not affect the absolute value.