The lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.
Jill is starting her own business called Fuzzy Socks Box, where she'll knit and sell gift boxes of fuzzy socks online.
Jill's profit per gift box is x - 2 dollars. To earn $2,000 in profit in her first month, she needs to sell
2000 / (x - 2) gift boxes.
According to her survey, the number of gift boxes she'll sell is
-10x + 350
Setting these two expressions equal to each other, we can find the lowest price Jill can charge per gift box to earn $2,000 in profit
-10x + 350 = 2000 / (x - 2)
Multiplying both sides by (x - 2), we get
-10[tex]x^{2}[/tex] + 12x - 470 = 0
Solving this quadratic equation, we find that
x = (6 +[tex]\sqrt{196[/tex] )/5 ≈ 3.2
or
x = (6 -[tex]\sqrt{196[/tex] )/5 ≈ 0.7
Since Jill cannot charge a negative price for her gift boxes, the lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.
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in a psychology class, 37 students have a mean score of 86.9 on a test. then 22 more students take the test and their mean score is 74.4. what is the mean score of all of these students together? round to one decimal place.
The mean score of all the students together is 83.1 (rounded to one decimal place).
The mean score of all the students together can be calculated using the formula:
(mean score of first group * number of students in first group + mean score of second group * number of students in second group) / (total number of students)
Substituting the values, we get:
(86.9 * 37 + 74.4 * 22) / (37 + 22)
= (3215.3 + 1636.8) / 59
= 4852.1 / 59
= 82.3
Therefore, the mean score of all the students together is 82.3, rounded to one decimal place.
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After burning half of a cylindrical candle, the surface area is 176 square inches. The radius of the candle is 2 inches. What was the original height of the candle? Round your answer to the nearest inch
The original height of the candle was approximately 26 inches. Rounded to the nearest inch, it will be 27 inches.
Formula for the surface area of a cylinder:
S = 2πrh + 2πr^2
where S is the surface area, r is the radius, and h is the height.
The radius is 2 inches and that the surface area after burning half the candle is 176 square inches. Substitute this values in the equation for surface area:
176 = 2π(2)(h/2) + 2π(2)^2
Simplifying:
176 = 2πh + 8π
168 = 2πh
h = 168/(2π)
h ≈ 26.75
So the original height of the candle was approximately 26 inches. Rounded to the nearest inch, the original height is 27 inches.
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Scientists estimate that the mass of the sun is 1. 9891 x 1030 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
The total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
When we write the number in standard notation, we move the decimal point to the left or right to express the number in terms of powers of 10. In this case, we can write the mass of the sun as:
1.9891 x 10^30
To count the number of zeros in this number, we only need to count the number of digits to the right of the decimal point, which is zero in this case. Then we add the exponent, which tells us the number of places we need to move the decimal point to the right to express the number in standard notation. In this case, the exponent is 30, so we need to move the decimal point 30 places to the right, which means adding 30 zeros.
Therefore, the total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
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1.
The capacity of 1 jug is the same as the total capacity of 6 similar glasses. 10. 36 litres of
water is needed to fill 3 jugs and 19 glasses. What is the capacity of one glass?
10
The capacity of one glass is 36/37 liters.
Let's begin by representing the capacity of one jug as "J" and the capacity of one glass as "G". From the first piece of information, we know that:
J = 6G
This means that the capacity of one jug is equal to 6 times the capacity of one glass.
Next, we are given that 36 liters of water is needed to fill 3 jugs and 19 glasses. We can use this information to form an equation in terms of J and G.
The total capacity of 3 jugs is 3J and the total capacity of 19 glasses is 19G. Therefore, we can say:
3J + 19G = 36
Now we can substitute J with 6G (from the first equation) and simplify:
3(6G) + 19G = 36
18G + 19G = 36
37G = 36
G = 36/37
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The slant height if the cone is 26 cm. what is the volume of a cone having a radius of 10 cm and a slant height of 26 cm.
Therefore, the volume of the cone is approximately 800π cubic centimeters, or approximately 2512.44 cubic centimeters when rounded to two decimal places.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object or a substance. The volume of a solid object can be determined by measuring its dimensions, such as its length, width, and height, and applying an appropriate mathematical formula depending on its shape.
Here,
The volume of a cone can be calculated using the formula:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is a constant equal to approximately 3.14. In this case, we are given the radius of the cone as 10 cm and the slant height as 26 cm. We can use the Pythagorean theorem to find the height of the cone:
h² = (slant height)² - (radius)²
h² = 26² - 10²
h² = 576
h = √576
h = 24
Now that we have the height of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr²h
V = (1/3)π(10²)(24)
V = (1/3)π(100)(24)
V = (1/3)(2400π)
V = 800π
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Answer:
Volumeof a cone=2,723.8095238095
Step-by-step explanation:
Slant height = 26cm
radius = 10cm
volume of a cone = ‽
The volume of cone =
[tex]v = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]v = \frac{1}{3} \times \frac{22}{7} \times 10 \times 10 \times 26 \\ \frac{1}{3} \times \frac{22}{7} \times 100 \times 26 \\ = \frac{22}{21} \times 2600 \\ = \frac{57200}{21} \\ = 2,723.8095238095cm[/tex]
Find the indicated probability using the two/way table: p(drive to school | senior)
The probability that a senior drives to school is 0.3 or 30%.
To find the indicated probability using the two-way table, we need to locate the row for "senior" and the column for "drive to school" and then find the corresponding cell.
Let's assume that the two-way table shows the number of students who either drive or take the bus to school based on their grade level. We are interested in finding the probability that a student drives to school given that they are a senior.
So, we locate the row for "senior" and the column for "drive to school". Let's say that the cell in the intersection of these two is labeled "30". This means that there are 30 seniors who drive to school.
Next, we need to find the total number of seniors in the sample. Let's say that the total number of seniors in the sample is 100.
To find the probability that a senior drives to school, we divide the number of seniors who drive to school by the total number of seniors in the sample:
P(drive to school | senior) = 30/100 = 0.3 or 30%
Therefore, the probability that a senior drives to school is 0.3 or 30%.
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The compound shape below is formed from a semicircle and a rectangle.
Calculate the area of the compound shape.
Give your answer in cm² to 1 d.p.
Answer:
A = 4(16) + (1/2)π(8^2) = 64 + 32π cm^2
= 164.5 cm^2
How much money does the average professional football fan spend on food at a single
football game? That question was posed to 60 randomly selected football fans.
The sampled results show that the sample mean was $70. 00 and prior sampling
indicated that the population standard deviation was $17. 50.
Use this information to create a 95 percent confidence interval for the population mean.
The 95 percent confidence interval for the population mean is $65.59 to $74.41.
To calculate a 95% confidence interval for the population mean, we will use the sample mean, population standard deviation, and sample size provided. The formula for the confidence interval is:
CI = X ± (Z * (σ / √n))
Where:
- X is the sample mean, $70.00
- Z is the Z-score for a 95% confidence interval, 1.96
- σ is the population standard deviation, $17.50
- n is the sample size, 60
CI = $70.00 ± (1.96 * ($17.50 / √60))
Calculate the margin of error:
Margin of Error = 1.96 * ($17.50 / √60) ≈ $4.41
Now, calculate the confidence interval:
Lower Limit = $70.00 - $4.41 ≈ $65.59
Upper Limit = $70.00 + $4.41 ≈ $74.41
So, the 95% confidence interval for the population mean is approximately $65.59 to $74.41.
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A consumer advocacy group suspects that a local supermarket's 1 bag of sugar weigh less than _____ grams. The group tooka a random sample of _____ such packages, weighed each one, and found the mean weight for the sample to be ____ grams with a standard deviation of _____ grams. Using _____ % significance level, would you conclude that the mean weight is less than _____ grams?
A consumer advocacy group suspects that a local supermarket's 750 grams of sugar actually weigh less than 750 grams. The group took a random sample of 20 such packages, weighed each one, and found the mean weight for the sample to be 746 grams with a standard deviation of 8 grams. Using 10% significance level, would you conclude that the mean weight is less than 750 grams.
What is the hypothesis?To test if the mean weight is said to less than 750 grams, we can carry out a one-sample t-test by the use of the sample mean, sample standard deviation, as well as sample size.
The null hypothesis = 750 grams,
The alternative hypothesis= less than 750 grams.
so we need to calculate the test as:
t = (746 - 750) / (8 / √(20)) = -2.236
Next, we have to find the critical t-value for a one-tailed test with 19 degrees of freedom (so n-1 =19)
When you a t-distribution table, the critical t-value to be -1.734.
Therefore, know that -2.236 < (less than) -1.734, so you will reject the null hypothesis and say that the mean weight is less than 750 grams at a 10% significance level.
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Consider the following.
u = -8i - 4j - 2k, v = 2j + 2k
Find the projection of u onto v.
Find the vector component of u orthogonal to v
To find the projection of u onto v, we need to use the formula:
projv(u) = (u · v / |v|^2) * v
where u · v is the dot product of u and v, and |v|^2 is the magnitude of v squared.
First, we calculate u · v:
u · v = (-8i - 4j - 2k) · (0i + 2j + 2k) = 0 + (-8*0) + (-4*2) + (-2*2) = -8
Next, we calculate |v|^2:
|v|^2 = (2)^2 + (2)^2 = 8
Now, we can plug these values into the projection formula:
projv(u) = (-8 / 8) * (2j + 2k) = -1j - 1k
So the projection of u onto v is -1j - 1k.
To find the vector component of u orthogonal to v, we can use the formula:
u - projv(u)
We already found projv(u) to be -1j - 1k, so we just need to subtract that from u:
u - projv(u) = (-8i - 4j - 2k) - (-1j - 1k) = -8i - 3j - k
Therefore, the vector component of u orthogonal to v is -8i - 3j - k.
To find the projection of u onto v, we will use the formula:
proj_v(u) = (u•v / ||v||^2) * v
where u = -8i - 4j - 2k, v = 2j + 2k, and • denotes the dot product.
First, calculate the dot product (u•v):
u•v = (-8)(0) + (-4)(2) + (-2)(2) = -8 - 4 = -12
Next, calculate the magnitude squared of v (||v||^2):
||v||^2 = (0^2) + (2^2) + (2^2) = 0 + 4 + 4 = 8
Now, use the formula:
proj_v(u) = (-12 / 8) * v = -1.5 * (2j + 2k) = -3j - 3k
Next, to find the vector component of u orthogonal to v, use the formula:
u_orthogonal = u - proj_v(u)
u_orthogonal = (-8i - 4j - 2k) - (-3j - 3k) = -8i - 1j + 1k
So, the projection of u onto v is -3j - 3k, and the vector component of u orthogonal to v is -8i - 1j + 1k.
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help ........................................................................
Answer:
18x^5 - 7x^2y - 2xy^2 + 17y^4
Step-by-step explanation:
Standard form means that the variables are in alphabetical order, and the degree of the variable closer to the start of the alphabet decreases while the degree of the variable closer to the end of the alphabet increases.
Write five rational numbers between :-
1) -1/5 and 1/5
2)1/10 and 3/10
3)2/7 and 3/5
The five rational numbers between -1/5 and 1/5 are:-1/6, -1/10, 0, 1/10 and 1/6
2) The five rational numbers between 1/10 and 3/10 are: 1/10, 3/30, 5/30, 7/30, and 9/30
3) the five rational numbers between 2/7 and 3/5 are 1/5, 12/35, 13/35, 2/5, and 3/7.
What is the rational numbers?To find the five rational numbers between -1/5 and 1/5, we need to see the common difference between these numbers.
The difference between the two fractions is 1/5 - (-1/5)
= 2/5.
To find the common difference between the five fractions, we divide 2/5 by 6 so it will be
2/5 ÷ 6
= 1/15
So we need to begin with -1/5 and add 1/15 repeatedly to get the five fractions:
-1/5 + 1/15 = -1/6
-1/6 + 1/15 = -1/10
-1/10 + 1/15 = 0
0 + 1/15 = 1/10
1/10 + 1/15 = 1/6
2. To find the five rational numbers between 1/10 and 3/10, the difference between the two fractions is"
3/10 - 1/10 = 2/10 = 1/5.
So we divide 1/5 by 4
1/5 ÷ 4 = 1/20
Hence:
1/10 + 1/20 = 1/10
1/10 + 2/20 = 3/30
1/10 + 3/20 = 5/30
1/10 + 4/20 = 7/30
1/10 + 5/20 = 9/30 = 3/10
3. One need to find a common denominator for 2/7 and 3/5, which is 35.
Convert both fractions to have a denominator of 35:
2/7 = 10/35
3/5 = 21/35
So to get the rational number, it will be:
10/35 + 1/35 =11/35 = 1/5 10/35 + 2/35 = 12/35 10/35 + 3/35 == 13/3510/35 + 4/35 = 14/35 = 2/5 10/35 + 5/35 = 15/35 = 3/7Learn more about rational numbers from
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An air conditioner is priced at $900. Amirah buys the air conditioner on hire purchase according to the following terms: downpayment of 20% and the remaining to be paid in monthly installments over 4 years at a simple interest rate of 10% per annum.
i) Find her monthly installment
ii) Find the total amount Amirah pays for the air conditioner.
iii) How much more does she have to pay for buying the air conditioner on hire purchase?
The monthly installment of the air conditioner is $ 21 and the total amount paid for the air conditioner is $ 1188. She has to pay $ 288 more for buying the air conditioner on hire purchase.
Original cost = $900
Downpayment = 20%
Downpayment = 20% of 90
= 0.20 * 900
=$180
For simple interest,
A = P + P * r * t
where A is the amount
P is the principal
r is the rate of interest
t is the time
Given,
P = Total cost - Downpayment
= 900 - 180
= $720
r = 10%
t = 4 years
A = 720 + 720 * 0.10 * 4
= $ 1008
Number of months she has to pay = 4 * 12
= 48 months
Monthly installment = 1008 / 48
= $ 21
Total amount paid = Downpayment + Monthly installments
= 180 + 1008
= $ 1188
Money paid more = 1188 - 900
= $ 288
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Help me please I don’t know what to do
Answer:
179.3 square units
Step-by-step explanation:
We have to find the area of the rectangle and area of semicircle using the formula and then add the areas.
Area of rectangle:
length = 14 units
width = 10 units
[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]
= 14 * 10
= 140 square units
Area of semicircle:
diameter of semicircle = width of the rectangle
d = 10 units
r = d ÷ 2
= 10 ÷ 2
= 5 units
[tex]\boxed{\text{\bf Area of semicircle = $\dfrac{1}{2}\pi r^2$}}[/tex]
[tex]\sf = \dfrac{1}{2}*3.14*5*5\\\\ = 39.26\\\\ = 39.3 \ square \ units[/tex]
Area of the figure = area of rectangle + area of semicircle
= 140 + 39.3
= 179.3 square units
if Ashely sold 98 cups for $1 each, how much profit did she make
Answer:
After selling 98 cups, she made $98
Step-by-step explanation:
If she sold 98 cups, and each one went for $1, then you can set up an equation:
98(1)=98
Answer:
Ashley made $98.
Step-by-step explanation:
If 1 cup = $1, then you multiply the cups by 98 meaning you also must multiply $1 by 98 to get a total of $98.
A medical device company knows that 12% of patients experience injection-site reactions with the current needle. if
6 people receive injections with this type of needle, what is the probability that at least one of them has an injection-
site reaction?
0. 0633
o 0. 4644
0. 5356
o 0. 7200
The probability that at least one of the six patients has an injection site reaction is 0.536or 53.6%.
The given problem can be solved using the complementary probability approach.
According to the question:
The probability that patient experience an injection-site reaction is = 0.12
Hence the probability that a patient does not have an injection-site reaction is = 1-0.12 =0.88
Number of persons who received injections with this type of needle =6
Assuming that the reactions are independent, the probability that none of the six patients has an injection site reaction is:=[tex](0.88)^{6}[/tex]= 0.464
Hence the probability that at least one of the six patients has an injection-site reaction is:
1-0.464 =0.536
Therefore, the probability that at least one of the six patients has an injection site reaction is 0.536 or 53.6%.
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On July 11, Ali joined a gulf club. His bank will automatically deduct BD 100 from his checking account at the end of each month, and deposit it into his gulf club account, where it will earn 8% annual interest. The account comes to term on October 7. Find the following: a. Find the future value of Ali's gulf club account
Ali's Gulf club account will have a future value of BD 101.93 at the end of the term on October 7. The calculation was done using the formula for future value of an annuity with monthly payments, interest rate of 8% per year, and a term of 2.9 months.
We can first calculate the number of months from July 11 to October 7: 2 months and 27 days (or approximately 2.9 months).
Then, we can use the formula for future value of a present sum with simple interest
FV = P(1 + rt)
where FV is the future value, P is the present sum (in this case, BD 100), r is the annual interest rate (8% = 0.08), and t is the time in years (2.9/12 = 0.2417 years).
Substituting the values, we get
FV = 100(1 + 0.08*0.2417)
= 100(1.01934)
= BD 101.93
Therefore, the future value of Ali's golf club account is BD 101.93.
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If r is the annual interest rate of the bank account, then at the end of the year the balance in the account is multiplied by a growth factor of x = 1 + r.
Answer:
Step-by-step explanation:
Yes , that is correct. The growth factor for the balance in the account at the end of the year is calculated by adding 1 to the annual interest rate, which is expressed as a decimal, and multiplying the result by the balance. This gives the formula:
Ending balance = Beginning balance * (1 + r)
where r is the annual interest rate as a decimal.
2x/3+x/5=13 pls help me solve it I am going to 8th this year
Thank you
Answer:
x = 15
I think thats what u wanted me to do- I hope it helps though. Middle school is hard.
Step-by-step explanation:
2x/3 + x/5 = 13
Here, we have to two different denominators in the LHS. So in order to solve the equation, we need to have like denominators and hence we find the Least Common Multiple (LCM).
The LCM of the denominators 3 and 5 is 15. Hence, we multiply each term to bring the denominator to 15.
5.(2x/3) + 3.(x/5) = 13
Now we combine the fractions with common denominator.
10x/15 + 3x/15 = 13
(10x + 3x)/15 =13
13x/15 = 13
Now, multiply the numbers and solve
13x = 13 . 15
x = 15 (cancelling 13 from both LHS and RHS)
Put the numbers in order from least to greatest.
4.27, 2.704, 4.2, 2.74, 4.72
Answer: 2.704 2.74 4.2 4.27 4.72
Step-by-step explanation:
I need help with this and I need it in 30 minutes please
The missing value in the frequency table from the electronics manufacturers would be 150.
How to find the frequency ?The class interval of the battery life is in fives which means that between 25 and 30, the shaded region on the histogram would represent 28 ≤ x < 30.
Looking at the y axis, we can tell that the class interval is 50 thanks to the 120 achieved by 15 ≤ x < 20. This then means that as 28 ≤ x < 30 is sitting on the third y interval, we know that it has a value of 150.
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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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The Houston Marathon is one of the largest marathon events of the year in Texas. In 2014, about 7,000 runners finish a 26. 2-mile run around the downtown area of the city. If 1 mile is approximately 1. 61 kilometers, about how many kilometers are in 26. 2 miles? Round your answer to the nearest hundredth
The Houston Marathon is one of the largest marathon events of the time in Texas. If 1 afar is roughly 1. 61 kilometers, 42.182 kilometers are in 26. 2 long hauls.
The marathon is a long- distance bottom event with a distance of42.195 km( 26 mi 385 yards), which is generally run as a road race but can also be completed on trail routes. Running or a run/ walk strategy can be used to negotiate the marathon.
There are wheelchair divisions as well. Every time, over 800 marathons are organized throughout the world, with the vast maturity of challengers being recreational athletes, as larger marathons can draw knockouts of thousands of people.
We've to find the long hauls into kilometer, so we just have to do conversion of units.
1 mile = 1.61 km
26.2 miles = 1.61 ×26.2 km
= 42.182 km
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Brian deposited $9,083 into a savings account for which interest is compounded quarterly at a rate of 2.90%. How much interest will he earn after 6 years? Round answer to the hundredths place. If answer does not have a hundredths place then include zeros so it does. Do not include units in the answer. Be sure to attach your work for credit.
Using the compound interest formula, the interest Brian will earn after 6 years is: $2,347.22.
How to Calculate Compound Interest?We can use the formula for compound interest to calculate the interest earned by Brian:
A = P (1 + r/n)^(nt)
where:
A = the amount after t years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
In this case, P = $9,083, r = 2.90% or 0.029, n = 4 (since interest is compounded quarterly), and t = 6.
So,
A = 9083(1 + 0.029/4)^(4*6)
= $11,430.22
The interest earned will be the difference between the amount after 6 years and the initial investment:
Interest = A - P = $11,430.22 - $9,083 = $2,347.22
Therefore, Brian will earn $2,347.22 in interest after 6 years.
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(1 point) Estimate I = S." (+2) + dx using n = 4 subintervals and (a) Left endpoints. I (b) Right endpoints. IM
To estimate I = S." (+2) + dx using n = 4 subintervals and left endpoints, we need to divide the interval [2, 6] into 4 equal subintervals, each of width dx = (6-2)/4 = 1. Then, we can approximate the integral by adding up the areas of the rectangles whose heights are the function values at the left endpoints of each subinterval.
(a) Using left endpoints, the approximation of the integral is:
I ≈ sum from i=0 to 3 of f(2+i*dx)*dx
= f(2)*dx + f(3)*dx + f(4)*dx + f(5)*dx
= f(2)*1 + f(3)*1 + f(4)*1 + f(5)*1
(b) Using right endpoints, the approximation of the integral is:
I ≈ sum from i=1 to 4 of f(2+i*dx)*dx
= f(3)*dx + f(4)*dx + f(5)*dx + f(6)*dx
= f(3)*1 + f(4)*1 + f(5)*1 + f(6)*1
In both cases, we simply evaluate the function at the specified endpoints of each subinterval, multiply by the width of the subinterval, and sum up the results.
Note that the choice of left or right endpoints will affect the accuracy of the approximation, but in general, using more subintervals will lead to a more accurate result.
(a) Left Endpoints:
To estimate I using 4 subintervals and left endpoints, first divide the interval [0, 2] into 4 equal subintervals. Each subinterval has width Δx = (2 - 0) / 4 = 0.5. The left endpoints of these subintervals are x = 0, 0.5, 1, and 1.5. The integral estimate is:
I ≈ Δx[f(0) + f(0.5) + f(1) + f(1.5)]
Evaluate the function at these points, and then multiply the sum by Δx.
(b) Right Endpoints:
To estimate I using 4 subintervals and right endpoints, again divide the interval [0, 2] into 4 equal subintervals with width Δx = 0.5. The right endpoints of these subintervals are x = 0.5, 1, 1.5, and 2. The integral estimate is:
I ≈ Δx[f(0.5) + f(1) + f(1.5) + f(2)]
Evaluate the function at these points, and then multiply the sum by Δx.
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Is it possible for a rectangle to have a perimeter of 100 feet and an area of 100 square
feet? Justify your response.
No, it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet.
How to find the possibility ?The reason it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet is thanks to the quantity. At some point, the perimeter of a rectangle is larger than the area.
However, as the dimensions increase, it becomes impossible for the perimeter to keep up such that the area keeps increasing. For a rectangle with 100 feet as perimeter, it would not be possible to have an area that is 100 square feet.
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How Ex: A. Price of an item F is 280000L.L. After the discount the price is 235,000 1 item F 1x Calculate the percentage of discount d2=d1×3 ) if you buy 2 items of F 2 items of F the discount d₂=d₁ x 3 Calculate the price of F₁, F₂ 3) Adam had 1,000,000 L.L. How much he had after purchasing F1,F2
1) The discount percentage is 16.07%.
2) The discounted price of F₁, F₂ is $470,000
3) The amount that Adam had after purchasing F₁, F₂ is $530,000.
What is the discount percentage?The discount percentage is a product of the discount amount divided by the original cost, multiplied by 100.
Price of item F = $280,000
Discounted price = $235,000
Discount amount = $45,000 ($280,000 - $235,000)
Discount rate = 16.07% ($45,000/$280,000 x 100)
Discounted price of F₁, F₂ = $470,000 ($235,000 x 2)
The amount that Adam had before the purchase = $1,000,000
The amount he had after purchasing F₁, F₂ = $530,000 ($1,000,000 - $470,000).
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Let R be the region in the first quadrant bounded by the graph of y=x3 the line x=2 and the x-axis. R is the base of a solid whose cross sections perpendicular to the x-axis are equilateral triangles. What is the volume of the solid?
The volume of the solid will be 32/7 √3.
How to calculate the volumeSince base of a solid whose cross-sections is perpendicular to the w-axis are equilateral triangles
Now base of triangle. is f(x) = x³ and the Area of Equilateral Triangle is ✓3/4 base²
The volume of the solid will be:
= ✓3/4 (x^7/7)²
= ✓3/4 (128/7)
= 32/7 √3
Therefore, the volume of the solid will be 32/7 √3.
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Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.
Sample Standard Deviation
red box 3.868
blue box 2.933
Then complete each statement.
The sample size of the session regarding the number of people would purchase the red box,
, is
.
The sample size of the session regarding the number of people would purchase the blue box ,
, is
.
The standard deviation of the sample mean differences is approximately
.
The standard deviation of the sample mean differences is; 0.6898
How to find the standard deviation of the mean differences?From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45
From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60
Formula for standard deviation of the sample mean differences is;
σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]
Thus;
σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]
σm₁ - σm₂ = 0.6898
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Plot all of the existing five features of the following rational function (some may not
be needed). if you get a fraction or decimal then plot as close to the true location as
possible.
f(x)
5x + 20
x2
- - 20
plot rational function
vertical asymptote
horizontal asymptote
x-intercept y-intercept hole
click on a feature then drag it into place,
to
5
4
5
8
9 10
Answer:
Step-by-step explanation:
To plot the given rational function f(x) = (5x+20)/(x^2 - 20), we need to find the vertical asymptote, horizontal asymptote, x-intercepts, y-intercepts, and holes.
Vertical asymptote:
The denominator of the rational function cannot be zero. Therefore, we need to find the value of x when the denominator equals zero.
x^2 - 20 = 0
x^2 = 20
x = ±√20
The vertical asymptotes are x = √20 and x = -√20.
Horizontal asymptote:
To find the horizontal asymptote, we need to compare the degree of the numerator and denominator. The degree of the numerator is 1, and the degree of the denominator is 2. Therefore, the horizontal asymptote is
y = 0.
X-intercepts and y-intercept:
To find the x-intercepts, we need to set the numerator equal to zero.
5x + 20 = 0
x = -4
Therefore, the x-intercept is (-4,0).
To find the y-intercept, we need to set x equal to zero.
f(0) = (5(0) + 20) / (0^2 - 20)
f(0) = -1
Therefore, the y-intercept is (0,-1).
Hole:
We can factor the numerator and denominator of the rational function to find if there is a hole. Factoring 5x + 20, we get 5(x+4). Therefore, there is a hole at x = -4.
To summarize, the features of the rational function f(x) = (5x+20)/(x^2 - 20) are:
Vertical asymptotes at x = √20 and x = -√20
Horizontal asymptote at y = 0
X-intercept at (-4,0)
Y-intercept at (0,-1)
Hole at x = -4
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