To apply the Integral Test, we need to find a function f(x) that is continuous, positive, and decreasing such that f(x) = 1/(5√x).
Taking the integral of f(x) from 1 to infinity, we get:
∫1 to infinity (1/(5√x)) dx = 2/5
Since this integral is a finite number, the series is convergent by the Integral Test.
To determine whether the series is convergent or divergent, we will apply the Integral Test as requested. The given series is:
Σ (from n=1 to infinity) of (1 / (5√n))
First, let's consider the function f(x) = 1 / (5√x). This function is positive, continuous, and decreasing for x ≥ 1, which are the necessary conditions for applying the Integral Test.
Now, we evaluate the improper integral:
∫ (from x=1 to infinity) of (1 / (5√x)) dx
To solve this integral, we'll first rewrite the integrand:
1 / (5√x) = 1 / (5x^(1/3))
Now integrate:
∫(1 / (5x^(1/3))) dx = (3/2) * (1/5) * x^(2/3) + C = (3/10) * x^(2/3) + C
Evaluate the improper integral:
lim (t -> infinity) [∫(from x=1 to t) of ((3/10) * x^(2/3)) dx]
= lim (t -> infinity) [(3/10) * (t^(2/3) - 1)]
Since the exponent (2/3) is less than 1, the limit converges to a finite value:
lim (t -> infinity) [(3/10) * (t^(2/3) - 1)] = -(3/10)
Since the improper integral converges, by the Integral Test, the given series is convergent as well.
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A student is buying a shirt that has a regular price of $18. After using a coupon, the price of the shirt is 0. 75x, where x is the regular price of the shirt. The clerk includes 6% sales tax on the price of the shirt. How much change should the student receive if the student pays for the shirt using a $20 bill?
The student should receive $5.69 in change.
How to find the price?The price of the shirt after the coupon is applied is 0.75 times the regular price, so:
Price of the shirt = 0.75x
If x = $18, then the price of the shirt is:
Price of the shirt = 0.75($18) = $13.50
The clerk adds 6% sales tax to the price of the shirt:
Sales tax = 6% of $13.50 = 0.06($13.50) = $0.81
So the total cost of the shirt is:
Total cost = $13.50 + $0.81 = $14.31
If the student pays with a $20 bill, the change the student should receive is:
Change = $20 - $14.31 = $5.69
Therefore, the student should receive $5.69 in change.
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Craig needs to measure 2 3/8 cups. How many times must he fill a 1/3 cup measuring cup?
First, we need to convert the mixed number 2 3/8 to an improper fraction:
2 3/8 = (2 x 8 + 3) / 8 = 19/8
To find out how many times Craig needs to fill a 1/3 cup measuring cup, we can divide 19/8 by 1/3:
(19/8) / (1/3) = (19/8) x (3/1) = 57/8
Therefore, Craig needs to fill a 1/3 cup measuring cup 57/8 times to measure 2 3/8 cups.
Ed
8. A watering can holds 3 liters of water.
If Patricia waters her vegetable garden
5 times a day and uses one full can in
all, how many milliliters of water does
she use each time she waters?
~ 60 mL
B 3,000 mL
© 600 mL
D 300 ml
SNO
9. Find 4-5.
8. Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct option is A © 600 mL.
9. 4-5 =-1
For first question:
8. A watering can holds 3 liters of water, and Patricia waters her vegetable garden 5 times a day using one full can in total. To find out how many milliliters of water she uses each time, you need to first convert the 3 liters to milliliters (1 liter = 1,000 milliliters) and then divide by 5.
3 liters × 1,000 milliliters/liter = 3,000 milliliters
3,000 milliliters ÷ 5 = 600 milliliters
So, Patricia uses 600 milliliters of water each time she waters her vegetable garden. The correct answer is 600 mL.
9. For second question, the calculation is as follows:
4 - 5 = -1
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1. In a nation centre, the administrative fee is RM30 per student. The tuition fee is RM45 per subject for language subjects and RM40 per subject for other subjects.
(a) Express the total payment. J. for a student who registers for m language subjects and n other subjects.
(b) Zaleha registers for 3 language subjects and 2 other subjects. How much does she have to pay?
(c) Chan pays RM280 when she registers for 2 language subjects and p other subjects. Find the value of p.
2. The diagram shows a right pyramid with a square base.
(a) Form a formula by using the surface area of the pyramid, L,as the subject of the formula.
(b) Calculate the surface area of the pyramid if a 10 and b = 12.
(c) If L=192 and a=b, find the value of a
Answer:
Step-by-step explanation:
(a) The total payment for a student who registers for m language subjects and n other subjects can be expressed as:
Total payment = Administrative fee + Tuition fee for language subjects + Tuition fee for other subjects
Total payment = RM30 + RM45m + RM40n
Total payment = RM30 + 45m + 40n
(b) For Zaleha who registers for 3 language subjects and 2 other subjects, the total payment can be calculated as:
Total payment = RM30 + (3 x RM45) + (2 x RM40)
Total payment = RM30 + RM135 + RM80
Total payment = RM245
(c) Chan pays RM280 when she registers for 2 language subjects and p other subjects. We can use the formula derived in part (a) to find the value of p:
Total payment = RM30 + (2 x RM45) + (p x RM40)
RM280 = RM30 + RM90 + RM40p
RM280 - RM120 = RM40p
RM160 = RM40p
p = 4
Therefore, Chan registers for 2 language subjects and 4 other subjects.
(a) The surface area of a right pyramid with a square base can be calculated as:
L = base area + 1/2 x perimeter of base x slant height
The base of the pyramid is a square, so its area can be expressed as:
Base area = a^2
The perimeter of the base can be calculated as:
Perimeter of base = 4a
The slant height can be calculated using the Pythagorean theorem:
slant height = sqrt(h^2 + (a/2)^2)
where h is the height of the pyramid.
Substituting these values in the surface area formula, we get:
L = a^2 + 1/2 x 4a x sqrt(h^2 + (a/2)^2)
L = a^2 + 2a x sqrt(h^2 + (a/2)^2)
(b) If a = 10 and b = 12, then the surface area of the pyramid can be calculated as:
L = 10^2 + 2 x 10 x sqrt(h^2 + (10/2)^2)
L = 100 + 20sqrt(h^2 + 25)
Given that L = 192, we can solve for h:
192 - 100 = 20sqrt(h^2 + 25)
92 = 20sqrt(h^2 + 25)
4.6 = sqrt(h^2 + 25)
4.6^2 - 25 = h^2
h^2 = 2.76
h = sqrt(2.76)
h ≈ 1.66
Substituting these values in the surface area formula, we get:
L = 10^2 + 2 x 10 x sqrt(1.66^2 + (10/2)^2)
L ≈ 314.9
Therefore, the surface area of the pyramid is approximately 314.9 square units.
(c) If L = 192 and a = b, then the surface area formula can be simplified as:
L = a^2 + 2a x sqrt(h^2 + (a/2)^2)
192 = a^2 + 2a x sqrt(h^2 + (a/2)^2)
We also know that the height of the pyramid is equal to the side length of the triangular faces. Since the pyramid is a right pyramid, the height and slant height are related by the Pythagorean theorem:
h^2 + (a/2)^
What would the balance be after 5 years if you deposited $1,000 in an account compounded monthly if the interest rate is 3. 7%?
$5,000. 00
$1,199. 21
$1,185. 00
$1,202. 88
PLS HELP ME WITH THIS 50 POINTS!
Answer: The transformation is up one and to the left 5
(-5, 1)
Step-by-step explanation:
Please Give brainliest, have a great night!
Answer: h(x) = g(x+5)+1
Step-by-step explanation:
h(x) = g(x+5)+1
You went 5 in the negative direction x direction; take the opposite sign
Also went up 1 in the y direction so add 1 to equation
Ayo can people who read team katsudon sus mangas rate my favorite ones. Number 1 : life with my cat kacchan. Number 2: whatever my pets say. Rn rate them only if you read then
The quality of a manga is subjective and it varies from person to person.
Quality of a manga is depending on their interests, preferences, and tastes.
Therefore,If anything favourite of one person that not mean another person also like the thing.
Manga ratings can be found on various online platforms such as MyAnimeList, MangaUpdates and Goodreads.
These all websites have a community of users who rate and review manga based on their own opinions and experiences.
If we want to get a rating for our favorite manga,
We can try posting your question on manga-related forums, social media groups, or other online communities where manga enthusiasts gather.
We can also ask your friends who are into manga to share their thoughts on the series we like.
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Mathetmatics
Class - 6 question
Topic - Roman Numerals :-
Question:-
The number VCX is incorrect. Explain why?
Answer as fast as you can. I'l mark you as brainliest
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
The number VCX is incorrect in Roman Numerals because V (5) cannot be subtracted from X (10) to make 5, and C (100) cannot be subtracted from X (10) to make 90.
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
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Chris had a collection of 1,000 records at the beginning of the summer. After the summer, Chris had traded some of his records and now he has only 870 records.
What is the percent decrease of his record collection?
Please help worth 50 points if right.
Answer:
Step-by-step explanation:
git
A department store buys 200 shirts at a cost of $ 3600 and sells them at a selling price of $ 20 each. Find the percent markup.
The value of the calculated percent markup of the shirt is 11.1%
Finding the percent markup of the shirtFrom the question, we have the following parameters that can be used in our computation:
A department store buys 200 shirts at a cost of $ 3600 and sells them at a selling price of $ 20 each.
This means that
Cost price = 3600/200
Evaluate
Cost price = 18
The percent markup of the shirt is then calculated as
Percentage = (20 - 18)/18
Evaluate
Percentage = 11.1%
Hence, the percent markup of the shirt is11.1%
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Kimi wants to teach her puppy 4 new tricks. in how many different orders can the puppy learn the tricks?
Answer:
3! = 6
Step-by-step explanation:
Once she teaches the puppy one trick there are 3 possible tricks left. After teaching the second trick there are 2 and after the third there is 1. Therefore, we multiply these numbers together to get 3(2)(1)=6 which is 3!.
I NEED HELP ON THIS ASAP! PLEASE IT'S DUE TODAY, I WILL GIVE BRAINLIEST!!
Answer:
Function A: f(x) = -8^x
Function B: f(x) = 2^x
Function A has a greater horizontal asymptote. As x approaches negative infinity, Function A approaches y = 0 faster than Function B.
PJ conducts an experimental study on the effects of soft music during high stakes science testing. He randomly assigns students at the school. In one condition he does not provide music for testing while in the other group he does provide the music. He administers a pretest at the beginning of the year and a posttest at the end of the year. PJ's design is best described as a:
PJ's design is best described as a randomized controlled trial (RCT), which is a type of experimental study that randomly assigns participants to a control group or an intervention group.
In this case, the control group did not receive the soft music during high stakes science testing, while the intervention group did. By administering both a pretest and a posttest, PJ was able to measure any differences in performance between the two groups. The use of randomization helps to ensure that any differences observed between the groups can be attributed to the intervention (soft music) rather than to other factors that may have influenced the results. Overall, PJ's RCT design is a rigorous way to test the effects of a specific intervention on a particular outcome.
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Can you guys help pls
Copy and complete the table of values for y=x2+x
What numbers replace A B and C?
X -2 -1 0 1 2
Y 2 A B 2 C
The value of A, B and C from the given equation are 0, 0 and 6 respectively.
The given equation is y=x²+x.
Here, the table is
X -2 -1 0 1 2
Y 2 A B 2 C
When x=-1
y=(-1)²-1
y=0
So, A=0
When x=0
y=(0)²+0
y=0
So, B=0
When x=2
y=(2)²+2
y=6
So, C=6
Therefore, the value of A, B and C are 0, 0 and 6 respectively.
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if you borrow $1,400 for 3 years at an annual interest rate of 20% what the total amount of money you will pay back
Answer:
$2,240
Step-by-step explanation:
1400×3=4,200
4200×20=84,000
84,000÷100=840
840+1400=2,240
Please mark me the brainliest
what are the first three terms of the sequence 40-2n
Answer:
1 term-38. ,2nd term-36. ,3rd tern is34
A little more difficult question.
8) John went to a vending machine and bought 2 bags of chips and 2 Powerades for
$3. 50. He then went back to the same vending machine and bought another bag of
chips and 3 Powerades for $3. 75. How much does a bag of chips cost, how much
does a Powerade cost?
The cost of a Powerade is $0.75 if 2 bags of chips and 2 Powerades cost $3.50 and one bag of chips and 3 Powerades cost $3.75.
Let the cost of one Powerade be x
The cost of one bag of chips be y
Cost of 2 bags of chips and 2 Powerades = $3.50
Cost of 2 bags of chips = 2y
Cost of 2 Powerades = 2x
2x + 2y = 3.50 ----(i)
Cost of one bag of chips and 3 Powerades= $3.75
Cost of 1 bag of chips = y
Cost of 3 Powerades = 3x
x + 3y = 3.75
Multiply the above equation by 2
2x + 6y = 7.50 -----(ii)
Subtract (ii) and (i)
4y = 4
y = $1
The cost of one bag of chips is $1
x + 3 = 3.75
x = $0.75
The cost of one Powerade is $0.75
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Ten sixth-grade students reported the hours of sleep they get on nights
before a school day. Their responses are recorded in the dot plot. Looking
at the dot plot, Lin estimated the mean number of hours of sleep to be 8. 5
hours. Noah's estimate was 7. 5 hours. Diego's estimate was 6. 5
hours. Which estimate do you think is best? Solve for the mean to figure out
who was closer. *
Lin
ООО
Noah
Diego
Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.
We have,
Compare the estimates given by Lin, Noah, and Diego.
Lin's estimate is 8.5 hours.
Noah's estimate is 7.5 hours.
Diego's estimate is 6.5 hours.
The average of these three estimates:
(8.5 + 7.5 + 6.5) / 3
= 22.5 / 3
= 7.5
It appears that Noah's estimate of 7.5 hours is the closest.
Therefore,
Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.
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The complete question:
Which estimate of the mean number of hours of sleep reported by the ten sixth-grade students is closest to the actual mean: Lin's estimate of 8.5 hours, Noah's estimate of 7.5 hours, or Diego's estimate of 6.5 hours?
Dmitri practices his domra for 98 min during
the school week. this is 70% of the time he
must practice his instrument in one week.
The total or actual time he needs to practice is 140 min whereas he practiced for 98 min during the school week.
We need to find the total time he must practice for a week. To find the total time we assume that the total time is x min.
Given Data:
Dmitri practices time during the school week = 98 min
Dmitri practices amount of time = 70% of his total time
Total time = x
Then the equation is given as
70% × (x) = 98
0.70 × (x) = 98
x = 98 / 0.70
x = 140
Therefore, The total time of the practices is 140 min
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You deposit $2,500 in an investment
account. The rate of growth is 4. 55% a year.
If you make no further deposits or
withdrawals, and the investment is allowed
to grow uninhibited, how long will it take for
your investment to reach $5,000? Round to
the nearest tenth.
It will take approximately 15.27 years for your investment to reach $5,000 at a growth rate of 4.55% per year.
Using the compound interest calculation, we can determine how long it will take for your investment to grow to $5,000 at a growth rate of 4.55% per year:
[tex]A = P(\frac{1 + r}{n} )^(^n^t^)[/tex]
Where:
A = the final amount ($5,000)
P = the initial deposit ($2,500)
r = the interest rate (4.55%)
n = the number of times interest is compounded per year (assuming yearly compounding, n=1)
t = the number of years
Plugging in the values, we get:
[tex]\$5,000 = \$2,500(\frac{1 + 0.0455}{1} )^(^1^t^)[/tex]
Simplifying, we get:
[tex]2 = (1.0455)^t[/tex]
Taking the natural logarithm of both sides, we get:
ln(2) = t ln(1.0455)
Solving for t, we get:
t = ln(2) / ln(1.0455) = 15.27 years
Therefore, it will take approximately 15.27 years for your investment to reach $5,000 at a growth rate of 4.55% per year.
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ASAP plis i need an answer and explanation
Answer: Z=21, Y=9, X=1
Step-by-step explanation:
Z---------
Since 3z and 63 are equal angles, then 3z must equal 63 as well. So 3 times what is 63? 3 times 21. Z=21.
X------1
2 times 1 is 2.
3 times 1 is 3. 3-1 is 2.
x=1
Y----
Same concept as Z. Since the length 13 and Y+4 are equal sides (definition of the kite figure I forget the proper name) then 13-4 is your answer. 9.
The triangle above has the following measures.
s = 29 m
r= 63 m
Find the m/Q.
Round to the nearest tenth and include correct units.
Show all your work.
The value of m∠Q as shown in the right-angled triangle below is 62.59°.
What is a right-angled triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
To calculate the value of m∠Q, we use the formula below
Formula:
m∠Q = cos⁻¹(s/r)........................ Equation 1Where:
s = 29 mr = 63 mSubstitute these values into equation 1
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find the perimeter of the equilateral triangle whose area is 16root3/4
The perimeter of the equilateral triangle whose area is 16root3/4 is 15.9[tex]\sqrt{3/4} cm[/tex]
What is an equilateral triangle?You should understand that a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted
An equilateral triangle is a special case of an isosceles triangle in which all three sides have the same length
Let the sides of the triangle be a
a + a + a = 16root3/4
3a = 16[tex]\sqrt{3/4}[/tex]
a = 5.3[tex]\sqrt{3/4}[/tex]
Therefore the perimeter of the equilateral triangle is
5.3[tex]\sqrt{3/4} + 5.3\sqrt{3/4} +5.3\sqrt{3/4}[/tex]
Therefore, the perimeter is 15.9[tex]\sqrt{3/4} cm[/tex]
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Winston drew a scale drawing of the elementary school. He used the scale 8 centimeters=10 meters. What is the scale factor of the drawing?
The scale factor of Winston's drawing of the elementary school is 0.008. The scale factor represents the relationship between the measurements on the drawing and the corresponding actual measurements.
To find the scale factor of Winston's drawing that has a scale of 8 centimeters = 10 meters,
Convert both units to the same unit. In this case, we will convert meters to centimeters.Since 1 meter = 100 centimeters, 10 meters = 10 * 100 = 1000 centimeters.Divide the drawing's unit by the actual unit.So, the scale factor of Winston's drawing of the elementary school is 0.008.
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Ryann is filing Chapter 7 bankruptcy. She will be able to include $10,148.22 of her total debt of $112,758.00Calculate what percent of Ryann's total debt is included in the bankrup
Answer:
Step-by-step explanation:
To calculate the percentage of Ryann’s total debt that is included in the bankruptcy, you can divide the amount of debt included in the bankruptcy by the total debt and then multiply by 100.
So, the calculation would be: ($10,148.22 / $112,758.00) * 100 = 9%.
This means that 9% of Ryann’s total debt is included in the bankruptcy.
Benjamin went shopping for a new phone
because of a sale. The price on the tag was
$28, but Benjamin paid $15. 40 before tax.
Find the percent discount
The percent discount on the phone because of a sale is 45%.
To find the percent discount, we need to calculate the difference between the original price and the discounted price, and then express that difference as a percentage of the original price.
First, let's find the difference between the two prices: $28 - $15.40 = $12.60. This means that Benjamin saved $12.60 on the phone.
Now, let's find the percent discount. We can do this by dividing the savings by the original price, and then multiplying the result by 100: ($12.60 / $28) * 100 = 45%.
So, Benjamin received a 45% discount on the phone before tax. This calculation shows that the sale allowed him to save a significant amount on his purchase. It's important to compare original and discounted prices to determine if a sale provides good value.
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Help with problem in photo
Answer:
(x-6)²+(y+3)²=17²
Step-by-step explanation:
The equation of a circle with center (a,b) and radius r is given by the formula:
(x - a)² + (y - b)² = r²
In this case, the center of the circle is (6,-3), and it passes through the point (-9,5). To find the radius of the circle, we need to calculate the distance between the center and the point on the circle. Using the distance formula, we get:
r = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(-9 - 6)² + (5 - (-3))²]
= √[225 + 64]
= √289
= 17
So, the radius of the circle is 17. Now we can plug in the values for the center and radius into the equation of a circle:
(x - 6)² + (y + 3)² = 17²
PLEASE WRITE THE EXPRESSION IN FORM OF |x-b|=c
Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either number or an expression) that have the following solution sets:
Please do both problems
All numbers such that x≤−14.
All numbers such that x≥ -1. 3
The vertical distance the Mars Rover Curiosity has traveled is approximately 84.954 meters.
What will be the absolute value equations in the form |x-b|=c for x ≤ -14 and x ≥ -1.3?An absolute value equation is an equation that contains an absolute value expression, which is defined as the distance of a number from zero on the number line. The equation |x-b|=c represents the distance between x and b is c units. To write the absolute value equations in the form |x-b|=c, we need to determine the values of b and c based on the given solution sets.
For the solution set "All numbers such that x ≤ -14", we know that the distance between x and -14 is always a non-negative value. Therefore, the absolute value of (x-(-14)) or (x+14) is equal to the distance between x and -14. Since we want x to be less than or equal to -14, we can set the absolute value expression to be equal to -c, where c is a positive number. Hence, the absolute value equation is |x+14|=-c.
Similarly, for the solution set "All numbers such that x ≥ -1.3", the distance between x and -1.3 is always a non-negative value. Therefore, the absolute value of (x-(-1.3)) or (x+1.3) is equal to the distance between x and -1.3. Since we want x to be greater than or equal to -1.3, we can set the absolute value expression to be equal to c, where c is a positive number. Hence, the absolute value equation is |x+1.3|=c.
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The graph of a quadratic function f is shown on the
grid. Which of these best represents the domain of f?
-4
Oy≥-12.25
All real numbers
All real numbers less than -4 or greater than 5
All real numbers will be the function's domain. D is the right answer in this case.
What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set(x).
A function's range is the collection of values it can take as input.
After we enter an x value, the function outputs this sequence of values.
The range refers to all potential values of y, and the domain refers to all conceivable values of x.
Let a be the leading coefficient and the parabola's vertex be the point (h, k).
The parabola's equation will then be provided as,
y = a(x - h)² + k
The graph shows where the vertex of the parabola will be. (-1.5, -4.5). The equation is then presented as:
y = a(x + 1.5)² - 4.5
Therefore, all real numbers will be the function's domain. D is the right answer in the case.
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Correct question:
The graph of the quadratic function f is shown in the grid. Which of these best represents the domain of f?
A: y>=4.5
B: All real numbers less than -4 or greater than 1
C: -4<=x<=1
D: All real numbers
Casey bought an 100 pound bag of dog food . He gave his dogs the same amount of dog food each week. the dog food lasted eight weeks. How much dog food did Cassie give his dogs each week? give the answer as a fraction or a mixed number