A recipe asks for 2 2/3 cups of raisins.
How many cups of raisins are needed to make 1/2 of a recipe?
Express the answer in simplest form.
The number of cups of raisins needed to make 1/2 of the recipe is equal to [tex]1\frac{1}{3}[/tex] cups of raisins.
What is the unitary method ?
The unitary method is a method in which you find the value of one unit and then the value of required no. of units.
It is given that a full recipe asks for [tex]2\frac{2}{3}[/tex] cups of raisins.
We have to find the number of cups of raisins needed to make 1/2 of the recipe.
1 full recipe needs = [tex]2\frac{2}{3}[/tex] cups of raisins.
So , the number of cups of raisins needed to make 1/2 of the recipe can be calculated by :
1/2 of recipe needs = [tex]2\frac{2}{3}[/tex] × [tex]\frac{1}{2}[/tex] cups of raisins
or
1/2 of the recipe needs :
= [tex]\frac{8}{3}[/tex] × [tex]\frac{1}{2}[/tex] cups of raisins
= [tex]\frac{4}{3}[/tex]
or [tex]1\frac{1}{3}[/tex] cups of raisins
Therefore , the number of cups of raisins needed to make 1/2 of the recipe is equal to [tex]1\frac{1}{3}[/tex] cups of raisins.
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The sum of the measures of two complementary angles is 90°. If one angle measures 24° more than twice the measure of the other, find the measure of the smaller angle.
passes through (-1,2), parallel to the graph of x-3y=14
Can you please help me!!
during the summer you work 30 hours per week at a gas station and earned $8.75 per hour. You also work as a landscaper for $11 per hour and your work as many hours as you want. You want to earn a total of $400 per week. How many hours mostly work as a landscaper?
To earn a total of $400 per week, considering you already earn $262.50 working 30 hours a week at a gas station, you need to make up the rest ($137.50) working as a landscaper. This equates to approximately 12.5 hours of work a week at an hourly rate of $11.
Explanation:The nature of the question is mathematical, specifically relating to linear equations. Initially, we know you're earning $8.75 per hour from your job at the gas station, working 30 hours a week, which gives you a total of $8.75 * 30 = $262.50 per week. Your goal is to earn $400 in total per week. Therefore, your earnings from the landscaping job need to make up the difference, which is $400 - $262.50 = $137.50.
Next, to find out how many hours you need to work as a landscaper, we divide that by the landscaper's hourly wage of $11, so $137.50 / $11 = 12.5 hours approximately. Hence to meet your target of $400 per week, you need to work about 12.5 hours as a landscaper, in addition to your 30 hours at the gas station each week.
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Which equation does the graph below represent? A coordinate grid is shown. The x axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y axis values are from negative 10 to positive 10 in increments of 2 for each grid line. A line is shown passing through the ordered pairs negative 4, negative 8 and 0, 0 and 4, 8.Please help as fast as possible!!!!!!
Answer:
The equation of line is y = 2x.
Step-by-step explanation:
Consider the provided information.
A coordinate grid is shown. The x axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y axis values are from negative 10 to positive 10 in increments of 2 for each grid line.
The slope intercept form of an equation of line is: y = mx + c
Where m is the slope and c is the y intercept.
[tex]Slope = m = \frac{Rise}{Run}[/tex]
Increments or decrements in x axis value represent the Run. Increments or decrements in y axis value represent the Rise.
It is given that "y axis values are from negative 10 to positive 10 in increments of 2 for each grid line."
Thus the Rise is 2 unit.
The x axis values are from negative 5 to positive 5 in increments of 1 for each grid line,
Thus the Run is 1 unit.
Hence the slope is: [tex] Slope=m=\frac{Rise}{Run}=2[/tex]
It is given that line passing through (0,0) it means the y intercept is 0.
Now substitute the value of m and y intercept in slope intercept form..
y = 2x + 0
y = 2x
Hence, the equation of line is y = 2x.
Give an example of the associative property of multiplication
what is the remainder when 864 is devided by 31? 6 27 4 ther is no remainder
r 27 is the answer....
how many 5 3/4 inch pieces of yarn can be cut from a roll that has 60 inches of yarn?
The number 'N' of cars produced at a certain factory in 1 day after 't' hours of operation is given by N(t)=100t-5t^2, 0< or equal t < or equal 10. If the cost 'C' (in dollars) of producing 'N' cars is C(N)=15,000+8000N, find the cost 'C' as a function of the time 't' of operation of the factory
Then Interpret C(t) when t=5 hours as a new function.
Answer:
We know that:
[tex]C_{(N)}=15000+8000N[/tex]
So first we need to substitute the next equation in the C(N) equation
[tex]N_{(t)} = 100t-5t^{2}[/tex]
And therefore we have:
[tex]C_{(t)}=15,000 + 8000*(100t-5t^{2})\\C_{(t)}=15,000 + 800000t-40000t^{2}[/tex]
Finally we replace at t = 5 in the equation above and we have:
[tex]C_{(5)}=15,000 + 800000*5-40000*5^{2}\\C_{(5)}= 3015000[/tex]
The interpretation is that after 5 hours of operation, we have wasted 3015000 dollars producing cars.
To calculate the cost of production as a function of time, substitute the production function N(t) into the cost formula C(N). After simplifying, the cost function is C(t) = 15,000 + 800,000t - 40,000t². At 5 hours, the cost is 3,015,000 dollars.
Explanation:To find the cost C as a function of the time t of operation of the factory, we first use the formula for the number of cars produced N(t) = 100t - 5t². Then we substitute the expression for N(t) into the cost function C(N) = 15,000 + 8000N.
Substituting N(t) into C(N), we get:
C(N(t)) = 15,000 + 8000(100t - 5t²)C(t) = 15,000 + 8000(100t) - 8000(5t²)C(t) = 15,000 + 800,000t - 40,000t²This is the cost C as a function of time t.
When t = 5 hours, the function becomes:
C(5) = 15,000 + 800,000(5) - 40,000(5²)C(5) = 15,000 + 4,000,000 - 1,000,000C(5) = 3,015,000 dollarsThis result means that the cost of production after 5 hours of operation is 3,015,000 dollars.
What's 149590 rounded to the nearest 100,000
370 is greater than or less than to 248
describe and correct the error in describing the relationship between the angles
20 Points!!!
When you add a negative and a positive the answer is: Neg/Pos
When you add numbers with with the same sign the answer is: Neg/Pos
When you subtract a negative and a positive the answer is: Neg/Pos
When you subtract numbers with the same sign, the answer is: Neg/Pos
There are 75 customers in the store at 1:00. The store must be emptied of customers when it closes at 5:00. How many customers must leave the store between 4:00 and 5:00?
The quotient of two negative integers results in an integer.How does the value of the quotient compare to the value of the original two integers?
list three ways to express 3 to the 5th power as a product of powers?
How much sleep does a Jaguar get in a year
A brick has a mass of 100g and a volume of 25cm3. what is the density of the brick
The density of the brick, calculated by dividing its mass of 100g by its volume of 25cm3, is 4 g/cm³.
Explanation:The density of a substance can be calculated using the formula density = mass/volume. In this case, the brick has a mass of 100g and a volume of 25cm3. Therefore, its density would be 100g / 25cm3 = 4 g/cm³. This means that the density of the brick is 4 grams per cubic centimeter.
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Number 46 please help
H+20=35-4h please help
PLZ HELP ME 50 POINTS
indicate whether the lines are parallel, perpendicular, or neither (for all of them this is NOT multiple choice
1)y=3/2x - 3 and -2x = 3y - 4
2)x+4y = -12 and 24y= -6x - 72
3)4x - 14y = -112 and 14x + 4y =16
A falling stone is at a certain instant 250 feet above the ground and 3 seconds later it is only 10 feet above the ground. From what height was it dropped?
Final answer:
By applying the equations of motion for an object in free fall, it's determined that the stone was dropped from 404 feet above the ground, considering its positions at two separate times and using the acceleration due to gravity.
Explanation:
To find the original height from which the stone was dropped, we can use the equations of motion under constant acceleration due to gravity. Since we are dealing with a vertical motion and we are given the stone's positions at two different times, the most appropriate equation to use is:
h = h0 + v0t - ½gt²
Where:
h is the final height of the object above the ground,h0 is the initial height of the object above the ground,v0 is the initial velocity (which is 0 for a dropped object),g is the acceleration due to gravity (approximately 9.8 m/s², but since we are using feet, we use 32 ft/s²), andt is the time in seconds.We know that the stone is 250 feet above the ground at a certain instant and 10 feet above the ground 3 seconds later. Thus, we can use these values to solve for h0 in two steps. Firstly, convert the given heights to the same unit of measurement if necessary (in this case, they are already in feet). Then, substitute the given values into the equation:
At t = 3 seconds, h = 10 feet:
10 = h0 - ½(32)(3)²
Solving this equation gives us:
h0 = 10 + ½(32)(3)² = 10 + 144 = 154 feet
However, this calculation only accounts for the latter part of the fall. To find the total height from which it was dropped, we need to consider the height above the 250 feet mark.
Since we initially observed the stone at 250 feet and then at 10 feet above the ground, it implies the stone was dropped from 250 feet + 154 feet = 404 feet above the ground.
A swimmer swam 48 kilometers in d days.What is the value of d if the swimmer swam a average of 3.2 kilometers a day
Find the number if 5/3% of it is 4.75
To find the number when 5/3% of it is 4.75, you can set up the equation (5/3%) x N = 4.75 and solve for N.
Explanation:To find the number when 5/3% of it is 4.75, we can set up the equation:
(5/3%) x N = 4.75
To solve for N, we need to convert the percentage to a decimal:
5/3% = 5/3 x 1/100 = 5/300 = 1/60
Now we can rewrite the equation:
(1/60) x N = 4.75
To isolate N, we can multiply both sides of the equation by 60:
N = 4.75 x 60 = 285
Therefore, the number is 285.
Above 1700 feet to 2500 feet write compound inequality
Is 3.6 repeating equal to 11/3?
Yes, 3.6 repeating is equal to 11 /3 .
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Number is,
⇒ 11 /3
Now, We know that;
⇒ 11 / 3
After divide we get;
⇒ 3.666666...
Thus, 3.6 repeating is equal to 11 /3 .
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how can you show that the ratios 10:4 abd 15:6 are equivalent
Answer:
10:4 On dividing both the number by 2 and 15 : 6
On dividing both the number by 3
Step-by-step explanation:
Given : ratios 10:4 and 15:6 .
To find : you show that the ratios 10:4 abd 15:6 are equivalent.
Solution : We have given 10:4 and 15:6 .
For 10 : 4
On dividing both the number by 2
5 : 2
For 15 : 6
On dividing both the number by 3
5 : 2.
So, we can see both are equal in ratio 5 : 2 .
Therefore, 10:4 On dividing both the number by 2 and 15 : 6
On dividing both the number by 3
Which property should Remus use to solve the equation below?
7q=49
Answer:
division property of equality
Step-by-step explanation:
7q= 49
To solve this equation we need to get 'q' alone
In order to get 'q' alone, we need to remove 7 from 'q'
Here 7 is multiplied with 'q'
To remove any number we always do opposite operation
Opposite operation of multiplication is division
So we divide both sides by 7
q= 7
Here we used division property of equality
y = mx + b (b) Your answer: b = y - mx b = x- ym b = y + mx b = mx-y