Rodney bought a 25-pound bag of dog food. His dog ate 10 2/5 pounds of the food in the first month and 10 4/5 pounds in the second month. How much dog food, in pounds, was remaining in the bag at the end of the two months?
Answer:
[tex]3\frac{4}{5}[/tex] pounds of food
Step-by-step explanation:
We have been given that Rodney bought a 25-pound bag of dog food. His dog ate [tex]10\frac{2}{5}[/tex] pounds of the food in the first month and [tex]10\frac{4}{5}[/tex] pounds in the second month.
Let us find the amount of dog-food eaten by dog in two months.
[tex]\text{Dog-food eaten in 2 months}=10\frac{2}{5}+10\frac{4}{5}[/tex]
[tex]\text{Dog-food eaten in 2 months}=\frac{52}{5}+\frac{54}{5}[/tex]
[tex]\text{Dog-food eaten in 2 months}=\frac{52+54}{5}[/tex]
[tex]\text{Dog-food eaten in 2 months}=\frac{106}{5}[/tex]
Now we will subtract amount of food eaten by dog from the amount of food initially to find the remaining amount of dog food.
[tex]\text{Remaining amount of dog-food}=25-\frac{106}{5}[/tex]
[tex]\text{Remaining amount of dog-food}=\frac{5*25}{5}-\frac{106}{5}[/tex]
[tex]\text{Remaining amount of dog-food}=\frac{125}{5}-\frac{106}{5}[/tex]
[tex]\text{Remaining amount of dog food}=\frac{125-106}{5}[/tex]
[tex]\text{Remaining amount of dog food}=\frac{19}{5}[/tex]
[tex]\text{Remaining amount of dog food}=3\frac{4}{5}[/tex]
Therefore, [tex]3\frac{4}{5}[/tex] pounds of food was remaining in the bag at the end of the two months.
What is the solution to this inequality? 17+x≥33
Name all pairs of vertical angles.
The two tables below show the success rates of several groups of businesses in a certain city. The first shows the number of businesses of several types started in Sharon’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category. Type Food Retail Financial Service Opened 3,193 2,280 1,898 5,045 Closed 1,977 1,626 1,443 3,548 Up to $25k $25-50k $50-75k $75-100k Over $100k Food 945 623 601 258 114 Retail 813 548 347 188 63 Financial 316 244 195 86 51 Service 979 739 432 174 124 Using the tables as experimental data, determine which of the following situations have a probability of at least 15.00%. I. a food establishment succeeding and earning $50,000 or more II. a service establishment succeeding and earning between $25,000 and $75,000 III. a retail establishment succeeding and earning no more than $50,000 a. I only b. I and II c. II and III d. III only
Answer:
The answer is D on edge 2020.
Step-by-step explanation:
A plot of 1/no2 versus time is linear. using this information, identify the factor by which the rate will increase in model (c) if the number of molecules is increased by a factor of 17.
i,ii,iii,iiii,iiiii what is the twentieth term?
A prism with a volume of 360yd^3 is scaled down to a volume of 45yd^3. What is the scale factor? Enter your answer, as a decimal or a fraction in simplest form, in the box.
the first term in an arithmetic sequence is 5. the foutth term in the sequence is -4. the tenth term is 22. which function can be used to find the nth term of the arithemetic sequence
Describe a real- world situation in which there is an additive or multiplicative relationship between two quantities . Make a table that includes at least three pairs of values. Then write an equation that models the relationship between the quantities
Final answer:
An example of a real-world situation with an additive relationship between two quantities is the distance traveled by a car and the time it takes. The equation that models this relationship is Distance = Time x Speed.
Explanation:
An example of a real-world situation with an additive relationship between two quantities is the distance traveled by a car and the time it takes. Let's say that the car travels at a constant speed of 60 miles per hour. We can create a table with three pairs of values:
Time (hours), Distance (miles)
1 60,
2 120,
3 180
In this case, the equation that models the relationship between the time and distance is Distance = Time x Speed. Since the car travels at a constant speed of 60 miles per hour, the equation can be simplified to Distance = 60 x Time.
On Monday 21 dvd's were checked out at the library. This is 3 less than half the amount of books check out that day. How many books were checked out?
The speed limit on a highway is 55 miles per hour. This means that vehicles cannot legally drive at speeds over 55 miles per hour. Write an inequality that is true only for speeds in miles per hour, x, at which vehicles can drive legally on the highway.
Ferdinand wrote a check for $96 to pay his monthly cable bill, but when balancing his checkbook, he accidentally recorded it as a credit rather than as a debit. How will his check register compare to his monthly bank statement when he receives it?
Answer:
$192 is over in his check-register.
Step-by-step explanation:
Ferdinand wrote a check to pay his monthly cable bill = $96.00
He accidentally recorded it as a credit in his check register rather than as a debit.
When he receives his bank statement he found his bank statement balance is less than his check register, he should compare it by debiting twice of the cable bill from balance of his check register.
96 × 2 = $192
Ferdinand would compare his check register to his monthly bank statement by subtracting $192 form his balance of check register.
Draw a number line and mark all described points.
x2=4
Question solved! please dont answer
Vanessa earns a base salary of $400.00 every week with an additional 5% percent commission on everything she sells. Vanessa sold $1650.00 worth of items last week.
What was vanessas total pay last week
A parallelogram has an area of 108 square centimeters. If the base measures 18 centimeters, what is the height?
The height of the parallelogram is 6cm.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
We have,
Area of parallelogram = 108 square cm
Base = 18 cm
So, Area of parallelogram
108 = base x height
108 = 18 x height
Height= 108/ 18
Height = 6 cm
Thus, the height is 6 cm.
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A bag of trail mix weighs 2 lb. By weight, 20% of the bag is oats. How many pounds is the
oats portion of the trail mix?
(a) Write an equation for the situation and label the “part,” “whole,” and “percent.”
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Write an inequality to represent the situation. Twelve times a number increased by four is no more thsn twenty-three.
Let x be the number.
Twelve times the number x is 12·x=12x.
The number 12x increased by four is 12x+4. This result is no more than twenty-three, then
12x+4≤23.
Answer: 12x+4≤23.
if a circle has a radius of 12 inches what is the arc length inside the interior angle 90 degrees
It took Eduardo 8 hours to drive from buffalo, NY to new York city, a distance of about 400 miles. Find his average speed.
Melinda needs 6 gallons of punch for her party. the grocery only sells quarts of punch. how many quarts will she need?
Which expression is equivalent to to the equivalent -1/2(-3/2x+6x+1)-3x
Answer:
Step-by-step explanation:
Bonjour
Which expression is equivalent to the equivalent -1/2(-3/2x+6x+1)-3x
= 3/4 x - 3x - 1/2 - 3x
= 3/4 x - 24/4 x - 1/2
= -21/4 x - 1/2
Use the graph of f(x) below to estimate the value of f '(3):
Based on the graph of f(x), the value of f '(3) is approximately 3.
Based on the graph of f(x) below, the value of f '(3) is approximately 3.
graph of f(x) with a tangent line drawn at x=3 and the slope of the tangent line labeled as 3.
To estimate the value of f '(3), we can approximate the slope of the tangent line to the graph at x=3. The slope of the tangent line represents the instantaneous rate of change of the function at that point, which is equal to the derivative of the function at that point.
To approximate the slope of the tangent line, we can choose two points on the line and use the rise-over-run formula. In this case, we can choose the points (2,2) and (4,4), which are two points on the tangent line that are close to x=3. The slope of the tangent line is then:
(4-2)/(4-2) = 2/2 = 1
Therefore, we can estimate that the value of f '(3) is approximately 1.
Note that this is just an estimate, since we are approximating the slope of the tangent line. If we were to calculate the exact derivative of f(x) at x=3, we might get a slightly different answer. However, this estimate is close enough for most practical purposes.
Write a general formula to describe the variation: M varies jointly with the cube root of the difference B and b.
The general formula to describe the variation: M varies jointly with the cube root of the difference B and b is [tex]M=k \sqrt[3]{(B-b)}[/tex]
What is joint variation?
When two (or more) other variables are held constant, joint variation occurs when one variable directly fluctuates as each of the other variables.
Given that;
M varies jointly with the cube root of the difference B and b
The difference of B and b (B-b)
let K be the the constant of proportionality
cube root of the difference B and b, [tex]\sqrt[3]{(B-b)}[/tex]
Then we have [tex]M=k \sqrt[3]{(B-b)}[/tex]
[tex]\[ M = k \cdot \sqrt[3]{B - b} \][/tex]
Explanation:In the given context, the formula [tex]\( M = k \cdot \sqrt[3]{B - b} \)[/tex] represents a joint variation between the variable M, the cube root of the difference between B and b, and a constant of proportionality (k).
Joint variation occurs when a variable is directly proportional to the product of two or more other variables, each raised to a specific power.
Breaking down the formula, [tex]\( \sqrt[3]{B - b} \)[/tex] signifies the cube root of the difference between B and b. This reflects the relationship where M is jointly influenced by both the magnitude and sign of the difference between B and b.
The constant of proportionality (k) is introduced to account for the specific numerical relationship between M and the cube root of the difference.
For a practical example, consider a scenario where M represents the volume of a gas, B is the initial pressure, and b is the final pressure. The formula captures how the volume varies jointly with the cube root of the pressure difference.
As the pressure difference increases, the cube root of the difference influences the volume of the gas, and the constant of proportionality ensures the appropriate scaling of this relationship.
The joint variation formula provides a concise representation of the complex relationship between the variables involved.
first find the estimate of the quotient then find the exact quotient 3 3/7 divide by 1 4/9
A rectangular prism has a length of 20 in a width of 2 in and a height of 3 1/4 in the prism is filled with cubes that have edge lengths of 1/4 in how many cubes are needed ro fill the rectangular prism
∠1 and ∠2 are a linear pair. m∠1 = x - 29, and m∠2 = x + 61. Find the measure of each angle.
a store received 500 containers of milk to be sold by Febuary 1. Each container the store sold $0.83 and sold for $1.67. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by Febuary 1. If 470 containers were sold bu February 1, how much profit did the store make?
if cos28 = x/4, find x(3sf)
The value of x when cos(28°) = x/4 is found by solving the equation, leading to x = 3.53 to three significant figures. This involves basic trigonometry and arithmetic operations.
Explanation:If cos(28°) = x/4, we are asked to find the value of x to three significant figures. This type of problem involves trigonometry, a branch of mathematics that deals with the relationships between the sides and angles of triangles. To solve for x, we use the equation given and manipulate it to isolate x.
Given that cos(28°) = x/4, we can find x by multiplying both sides of the equation by 4:
x = 4 * cos(28°)Using a calculator, cos(28°) approximately equals 0.8829. Therefore, x is equal to 4 * 0.8829, which simplifies to:
x = 3.5316To three significant figures, x = 3.53.
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Find the missing measures for the rectangle.
l = _?_
w = 2 cm
A = _?_
P = 25 cm
12.5 cm; 21 cm2
10.5 cm; 21 cm2
12.5 cm; 25 cm2
10.5 cm; 25 cm2
Find the zeros of f(x) = 4x 2 + 5x - 21.
The required zeros of the given polynomial equation are x = 7/4 and x = -3.
Zeros of an equation is defined as the value of the independent variable where the equation or function gives zero.
here,
Given expression,
f(x) = 4x² + 5x - 21.
Putting the above expression equal to zero,
4x² + 5x - 21 = 0
Factorizing the above equaiton gives,
(x - 7/4)(x + 3) = 0
Now,
x = 7/4 and x = -3
Thus, the required zeros of the given polynomial equation is x = 7/4 and x = -3.
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