Answer:
We can add any rational number to 1/5 to get a rational number.
Step-by-step explanation:
Given: We have given a rational number 1/5.
To find: We need to find a number which is added to 1/5 gives a rational number.
Solution: We know that,
Rational number + Rational number = Rational Number
Rational number + Irrational Number = Irrational Number
Irrational Number + Irrational Number = Irrational Number.
As we know that given fraction 1/5 is a rational number.
So, when we add any rational number to 1/5 would give a rational number.
Let us we take an example,
[tex]\frac{1}{5} +\frac{2}{3} = \frac{3+10}{15}= \frac{13}{15}[/tex]
We can see in above example that a rational number 2/3 is added to 1/5 gave us 13/15 which is also a rational number.
Therefore, we can add any rational number to 1/5 to get a rational number.
For tax reasons, i need to create a rectangular vegetable patch with an area of exactly 50 square feet. the fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. what are the dimensions of the vegetable patch with the least expensive fence?
Final answer:
The dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.
Explanation:
To find the dimensions of the vegetable patch with the least expensive fence, we can use the formula for the area of a rectangle: length x width = area.
Let's assume the length of the vegetable patch is 'x' and the width is 'y.'
So, xy = 50.
The cost for the east and west sides is $4 per foot, and the cost for the north and south sides is $2 per foot.
Therefore, the cost of fencing the east and west sides would be 4x, and the cost of fencing the north and south sides would be 2y.
For the least expensive fence, we want to minimize the cost, which means minimizing the sum of 4x and 2y.
We can rewrite the equation as:
y = 50/x.
Now substitute the value of y in the cost equation:
cost = 4x + 2(50/x).
To find the minimum cost, we need to find the derivative of the cost equation and set it equal to zero.
Calculating the derivative and solving for x, we find x = √100 = 10.
Therefore, the dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.
Adams Clothing Store buys coats for $50 and sells them
for $80. What percent of increase is this?
Answer is provided in the image attached.
f the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be
Which would take up more space, a pound of granite or a pound of basalt?
Answer:
1 pound of granite
Step-by-step explanation:
The density of granite is 168.6 lb/ft³. The volume occupied by 1 pound of granite is:
1 lb × (1 ft³/168.6 lb) = 0.00593 ft³
The density of basalt is 188 lb/ft³. The volume occupied by 1 pound of basalt is:
1 lb × (1 ft³/188 lb) = 0.00532 ft³
As we can see, 1 pound of granite takes up more space than 1 pound of basalt.
A garden snail moves 1/6 foot in 1/3 hours. what is the unit rate?
How many years would it take Jim to earn interest equal to half of his original principal at 10% simple interest?
A. 6 months
B. 12 months
C. 5 years
D. 10 Years
Jim would need 5 years to earn interest equal to half of his original principal at a 10% simple interest rate.
To find out how many years it would take for Jim to earn interest equal to half of his original principal at a 10% simple interest rate, we use the formula for simple interest: I = PRT, where I is the interest, P is the principal, R is the rate of interest per year, and T is the time in years.
In this case, Jim wants the interest I to be half of the principal P. So the equation becomes :
[tex]\frac{P}{2} = P \times 0.10 \times T[/tex] or T
= [tex]\frac{P}{2 \times P \times 0.10}[/tex], which simplifies to T =[tex]\frac{1}{2 \times 0.10}[/tex]or T = 5 years. Therefore, the correct answer is C. 5 years.
four-fifths of a number minus two is greater than three-tenths of twice that number
Lacoste middle school surveyed its student population about their favorite mobile app. The 786 students who listed Facebook as their favorite app represened 32 fewer students than two times the number on Instagram as their favorite app. How many students listed Instagram as their favorite app?
Hence, the number of students who listed Instagram as their favorite app is 409
Step-by-step explanation:Let x denote the number of students who listed Instagram their favorite app.
Now the number of people who listed Fb as their favorite app is 32 less than two times number of students who have Instagram as their favorite app.
Hence, the equation so obtained is given by:
786 = 2x - 32
i.e. 2x = 818
i.e. x = 409
Hence, the answer is: 409
What is 8.675 as a mixed number in simplified formation
An international company has 26,900 employees in one country. If this represents 16.9% of the company's employees, how many employees does it have in total?
Answer:
89,349
Step-by-step explanation:
i just did this problem on aleks and this is the answer they gave me how it helps other in the future
Find the values of a, b, and c for which the quadratic equation ax^2 + bx + c = 0 has the solutions 8i and −8i.
The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integers.
Answer:
equation: (x-3) +(x-1) +(x+1) +(x+3) = -72values: -21, -19, -17, -15Step-by-step explanation:
When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...
(x-3) +(x-1) +(x+1) +(x+3) = -72
This simplifies to ...
4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.
x = -18 . . . . . . . . the middle number of the sequence
So, the numbers are:
-18-3 = -21-18-1 = -19-18+1 = -17-18+3 = -15_____
A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...
(x) +(x +2) +(x +4) +(x +6) = -72
and that simplifies to ...
4x +12 = -72 . . . . . collect terms
4x = -84 . . . . . . . . subtract 12
x = -21 . . . . . . . . . . divide by 4
Now, the other three numbers are found by adding 2, 4, and 6 to this one.
Which is greater 2.16 or 2.061
mulch to cover a rectangular garden costs 48. mulch is needed to cover a larger, similar garden. the ratio of dimensions is 2:3. how much would it cost to cover the larger
Answer: $108
Step-by-step explanation:
It would cost $288 to cover the larger rectangular garden.
What is ratio?"It is relationship between two numbers that describe how many times one value can contain another. "
What is proportion?"It is an equation in which two ratios are equal."
What is area of rectangle?[tex]A=l\times w[/tex], where 'l' is length of the rectangle and 'w' is width of the rectangle
For given question,
Let 'l' be the length of the rectangle and the 'w' be the width of the rectangle.
The ratio of dimensions of a rectangular garden would be w:l.
mulch is needed to cover a larger, similar garden.
The ratio of dimensions is 2:3
As both the gardens are similar, their dimensions must be in proportion.
[tex]\Rightarrow \frac{w}{2}= \frac{l}{3}[/tex]
[tex]\Rightarrow \frac{w}{l}= \frac{2}{3}[/tex]
So, the length of the larger rectangular garden would be [tex]3l[/tex]
and the length of the larger rectangular garden would be 2w
A mulch to cover the first rectangular garden costs $48.
This means, for the area of [tex]A_1=l\times w[/tex] it costs $48.
Using the formula for area of rectangle the area of the larger garden would be,
[tex]A_2=3l\times 2w\\A_2=6(l\times w)\\A_2=6\times A_1[/tex]
For the second garden it would costs,
6 × 48 = 288
Therefore, it would cost $288 to cover the larger rectangular garden.
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Find two values of b that will make 9 x 2 + b x + 9 a perfect square trinomial.
ABC preschool spun $1,475 on diapers this year.if the diapers cost $25 per box how many boxes did they used?
Marcus recorded the high temperature each day for a week. the daily high temperatures in degrees Fahrenheit were: 68,74,66,78,72,80, and 74 which best describes what 74 represents in this data set?
A. median only
B. mean and mode
C. median and mode
D. mode only
Answer:
The answer is C. median and mode.
Step-by-step explanation:
First, we have to ensure that the list of the set of data is from least to greatest: 66, 68, 72, 74, 74, 78, 80 .
The mean = (66 + 68 + 72 + 74 + 74 + 78 + 80) ÷ 7 = 512 ÷ 7 = 73.14 . (Note that the mean is not equal to 74.)
The median = middle number when the set of data is listed in order from least to greatest = the fourth number = 74.
The mode = the temperature that occurred the most = 74 .
These results prove that the median and mode best describe what 74 represents in the data set, because they are the same value.
Answer: C
I think its right. Was it for the I ready diagnostic?
A submarine is at the surface of the ocean, preparing to dive. It submerges and dives to −972 feet. Then, it ascends 308 feet to avoid hitting an undersea cliff. What integer represents the submarine's position in feet (depth) after it ascends to avoid the cliff?
Answer:
The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664
Step-by-step explanation:
It submerges and dives to −972 feet. Then, it ascends 308 feet.
Initially it goes down by 972 feet and then goes up by 308 ft.
Since depth is more than elevation.
Final position is below sea level.
Final depth = 972 - 308 = 664 ft
The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664
3942588 to the nearest thousand
The number of customers for a new online business can be modeled by y = 6x2 + 75x + 200, where x represents the number of months since the business started. Which is the best prediction for the number of customers in month 25?
A. 5825
B. 3791
C. 2936
D. 4754
Answer:
A. 5825
Step-by-step explanation:
Given: The number of customers for a new online business can be modeled by y = 6x^2 + 75x + 200, where "x" represents the number of months.
We are asked to find number of customers in month 25.
To find the number of customers in 25th month, we need to plug x = 25 in the given function.
y = 6([tex]25)^2[/tex] + 75(25) + 200
y = 6(625) + 1875 + 200
y = 3750 + 1875 + 200
y = 5825
Therefore, the answer is A. 5825
Find the area of a circle with radius 7cm
What is the price of $1000 face-value one year zero coupon discount bond that offers 1.5% yield?
a.$992.3
b.$1001.5
c.$998.5
d.$985.2?
What is the reason for each step in the solution of the equation?
3+4xâ’3x=4
Drag and drop the reasons into the boxes to correctly complete the table.
3+x=43+x=4
x=1
Distributive property
Subtraction property of equality
Combine like terms
Division property of equality
Given
A dentist is making identical dental care bags for patients using 56 tubes of toothpaste, 112 packets of floss, and 85 toothbrushes. What is the greatest number of identical dental care bags the dentist can make with the least amount of items leftover
Answer: There would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.
Step-by-step explanation:
Since we have given that
Number of tubes of toothpaste = 56
Number of packets of floss = 112
Number of toothbrushes = 85
We need to find the greatest number of identical dental care bags that dentist can make with the least amount of items leftover.
So, we will find "H.C.F." of 56, 112, 85 which is equal to 1.
So, there would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.
The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?
10x + 3y - 1 = 0
x + 3y + 10 = 0
x + 3y - 10 = 0
The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?
Answer:
x + 3y - 10 = 0
what is the difference? 5/3-1/2
A. 4
B. 7
C. 7/6
D. 7/0 = undefined
What is the area of trapezoid ABCD ? (Enter your answer as a decimal or whole number)
Area of the trapezoid ABCD is
[tex]62\frac{1}{2}[/tex]
Given :
The diagram of a trapezoid ABCD
Area of trapezoid is [tex]\frac{base1+base2}{2} \cdot height[/tex]
Lets find the length of base 1 and base 2 using distance formula
Base 1 is AD. find the distance AD
[tex]AD=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\AD=\sqrt{\left(-13-\left(-1\right)\right)^2+\left(-11-5\right)^2}\\AD=20[/tex]
Now we find out BD that is base 2
[tex]BD=\sqrt{\left(0-3\right)^2+\left(-2-2\right)^2}\\BD=5[/tex]
Now find out height AB
A is (-1,5) and B(3,2)
[tex]AB=\sqrt{\left(-1-3\right)^2+\left(5-2\right)^2}\\AB=5\\[/tex]
[tex]Area =\frac{AD+BC}{2} \cdot AB\\Area=\frac{20+5}{2} \cdot 5\\Area=\frac{125}{2}\\Area=62\frac{1}{2}[/tex]
Area of the trapezoid ABCD is
[tex]62\frac{1}{2}[/tex]
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A nail is 0.1875 inch thick. What is it’s thickness as a fraction? Is 0.1875 inch closer to 1/8 inch or 1/4 inch on a number line?
Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans. Plan A: Raise the price by $0.05 each week until the price reaches $8.00. Plan B: Raise the price by 10 percent each week until the price reaches $8.00. Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00. Plan D: Raise the price by $0.25 each week until the price reaches $8.00. Which plan will result in the price of the bagels reaching $8.00 fastest? plan A plan B plan C plan D
Answer:
Plan B
Step-by-step explanation:
Plan B and plan C start out at the same increase: 10% ($0.50) for the first week. The increase under plan C stays at 10% of the original value, but the increase under plan B increases according to the value the week before, which keeps getting larger.
Hence, plan B gets to $8.00 the fastest — after about 5 weeks.
"write the expression in radical form and then evaluate"