The value of Σxy = 12016, Σx²y = 547608 and (Σxy)² = 144384256.
We must make some calculations using the provided data in order to determine the necessary numbers.
x: 90, 76, 16, 28, 46, 52, 14, 48
y: 33, 6, 91, 35, 63, 25, 17, 41
In order to determine xy (the total of the product of x and y):
Σxy = x₁y₁ + x₂y₂ + x₃y₃ + ... + x₈y₈
Σxy = (90 × 33) + (76 × 6) + (16 × 91) + (28 × 35) + (46 × 63) + (52 × 25) + (14 × 17) + (48 × 41)
Σxy = 2970 + 456 + 1456 + 980 + 2898 + 1300 + 238 + 1968
Σxy = 12016
Consequently, 12016 is equivalent to xy.
Calculate x2y (the sum of x2 and y) as follows:
Σx²y = x₁²y₁ + x₂²y₂ + x₃²y₃ + ... + x₈²y₈
Σx²y = (90² × 33) + (76² × 6) + (16² × 91) + (28² × 35) + (46² × 63) + (52² × 25) + (14² × 17) + (48² × 41)
Σx²y = 267300 + 34656 + 23296 + 34300 + 77376 + 67600 + 4012 + 97968
Σx²y = 547608
Therefore, Σx²y is equal to 547608.
Finally, to calculate (Σxy)² (the square of the sum of xy):
(Σxy)² = (12016)²
(Σxy)² = 144384256
Therefore, (Σxy)² is equal to 144384256.
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The complete question is:
Use the data below to complete the following calculations.
x 90 76 16 28 46 52 14 48
y 33 6 91 35 63 25 17 41
Σxy =
Σx²y =
(Σxy)² =
A brand of cereal had 1. 21. 21, point, 2 milligrams (\text{mg})(mg)left parenthesis, start text, m, g, end text, right parenthesis of iron per serving. Then they changed their recipe so they had 1. 8\,\text{mg}1. 8mg1, point, 8, start text, m, g, end text of iron per serving. What was the percent increase in iron?.
The percent increase in iron content after the recipe change for the cereal is approximately 35.56%.
To calculate the percent increase in iron content, we need to find the difference between the new iron content (1.8 mg) and the original iron content (1.21 mg). The difference is 1.8 - 1.21 = 0.59 mg. Then, we divide this difference by the original iron content (1.21 mg) and multiply by 100 to get the percentage increase: (0.59 / 1.21) × 100 ≈ 35.56%.
This means that the iron content of the cereal increased by approximately 35.56% after the recipe change. To calculate the percent increase, we compare the difference between the new and original values to the original value. In this case, the original iron content was 1.21 mg, and the new iron content is 1.8 mg. The difference between these two values is 1.8 - 1.21 = 0.59 mg. To find the percentage increase, we divide this difference (0.59 mg) by the original value (1.21 mg) and multiply by 100.
The resulting value, 0.59 / 1.21 ≈ 0.4876, represents the proportion of increase. Multiplying it by 100 gives us the percentage increase, which is approximately 48.76%. Therefore, the iron content increased by approximately 48.76% after the recipe change.
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It is 185 miles to Fort Worth if vangs drives 2 hours at 65 miles per hour how far will he be from Fort Worth
If Vangs drives for 2 hours at a speed of 65 miles per hour, we can calculate how far he will be from Fort Worth. Vangs will be 125 miles away from Fort Worth.
Given that Vangs drives at a speed of 65 miles per hour for 2 hours, we can calculate the distance traveled using the formula Distance = Speed × Time.
Distance = 65 miles/hour × 2 hours = 130 miles.
Since Vangs started 185 miles away from Fort Worth and traveled a distance of 130 miles, we subtract the distance traveled from the initial distance to find how far he will be from Fort Worth.
Distance from Fort Worth = Initial distance - Distance traveled = 185 miles - 130 miles = 55 miles.
Therefore, Vangs will be 55 miles away from Fort Worth after driving for 2 hours at a speed of 65 miles per hour.
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Gunther's starting weight is 248 pounds, and he plans to lose 2 pounds each week. Use a linear equation to determine Gunther's weight after 10 weeks. Do not include units in your answer
To determine Gunther's weight after 10 weeks, we can use a linear equation. Given that he plans to lose 2 pounds each week, we can represent his weight after 10 weeks as a linear function of time. Therefore, Gunther's weight after 10 weeks would be 268 pounds.
1. The equation would be: weight = starting weight - (rate of weight loss * number of weeks). Substituting the given values, we find Gunther's weight after 10 weeks.
2. Gunther's weight after 10 weeks can be determined using a linear equation. Let's denote Gunther's starting weight as W₀ and the rate of weight loss as R. Since he plans to lose 2 pounds each week, the rate of weight loss R is -2 (negative because it represents a decrease in weight).
3. The equation for Gunther's weight after 10 weeks would be: weight = W₀ - (R * number of weeks).
Substituting the given values, we have weight = 248 - (-2 * 10).
4. Simplifying further, weight = 248 + 20 = 268. Therefore, Gunther's weight after 10 weeks would be 268 pounds.
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Select the correct answer.
Solve the exponential equation for X.
216 6(41 +11)
OA.
I = 2
OB.
I = -2
OC.
I = 3
OD.
= -3
The given equation is I = -2OD where I is the intensity of light, O is the aperture of the lens and D is the distance between the lens and the object. This equation is known as the Inverse Square Law of Light.
The equation states that the intensity of light decreases as the square of the distance between the object and the ens increases. This means that if we double the distance between the object and the lens, the intensity of light becomes 1/4th of its original value.Similarly, if we triple the distance between the object and the lens, the intensity of light becomes 1/9th of its original value. This law is applicable to all types of light sources, including natural light sources like the sun and artificial light sources like bulbs.One practical application of this law is in photography. If a photographer wants to capture an image of a subject that is far away, they need to use a lens with a larger aperture to let in more light. This will ensure that the image is bright and clear even when the distance between the subject and the camera is large.Similarly, if a photographer wants to capture an image of a subject that is close to the camera, they need to use a lens with a smaller aperture to reduce the amount of light that enters the camera. This will prevent the image from being overexposed and washed out.Overall, the Inverse Square Law of Light is an important principle that governs the behavior of light in various applications, including photography, cinematography, and physics.For such more question on Square Law
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Jewelers consider weight, cut grade, color, and clarity when pricing diamonds. In researching jewelry prices, Yvonne makes the following statements based on her observations. Which of the statements are statements of causation?
The correct answer is 'statement missing.'Causation refers to the relationship between an event and a possible cause that is inferred from the past events or historical records.
Statements of causation are one of the several types of causal relationships.Jewelers consider weight, cut grade, color, and clarity when pricing diamonds. In researching jewelry prices, Yvonne makes the following statements based on her observations.No statement has been given in the question.The given statements are missing.Therefore, it is impossible to determine the statements of causation.In simple words, no information has been given regarding any statement. Hence, the correct answer is 'statement missing.'
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The dimensions of a right recutangular prism are 0.25m, 0.36m, and 0.14mWhat is the volume of the prism? use the formula v=1xwxh
The volume of the given right rectangular prism is 0.0126 m³.
The volume of a right rectangular prism can be calculated using the formula:
V = l × w × h,
where l, w, and h are the dimensions of the prism.
The given dimensions of the right rectangular prism are 0.25m, 0.36m, and 0.14m.
Volume of the prism = l × w × h
= 0.25 × 0.36 × 0.14
= 0.0126 m³
Therefore, the volume of the prism is 0.0126 m³.
We have used the formula:
V = l × w × h to find out the volume of the prism.
This is because the given prism is a right rectangular prism.
The formula for finding the volume of a right rectangular prism is
V = l × w × h,
where l, w, and h are the dimensions of the prism.
A right rectangular prism is a three-dimensional figure with six rectangular faces.
It has three pairs of congruent faces that are parallel to each other.
The opposite faces of the right rectangular prism are identical in size and shape.
The right rectangular prism is a type of prism, which is a three-dimensional figure with two identical and parallel faces called bases.
A prism can be named by the shape of its base. In this case, the right rectangular prism has a rectangular base.
Conclusion: The volume of the given right rectangular prism is 0.0126 m³, which was found using the formula V = l × w × h.
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if the intrest earned on a account after 2 years is $15, how much would it be after 10 year? Why?
The amount after 10 years with a principal of $100 and interest rate of 7% compounded annually would be $196.72.
The term "amount" refers to the quantity or total of something. It is a general term used to describe the measure or magnitude of a particular quantity. The specific context in which "amount" is used determines what it is referring to.
For example:
In finance and accounting, "amount" often refers to a monetary value or sum of money. It can represent the total of a bill, an invoice, a balance, or a transaction.
In mathematics, "amount" can be used to describe the result of a calculation or the value of a quantity. For instance, the amount of money in a bank account after a series of deposits and withdrawals.
In everyday language, "amount" can refer to a general quantity or measure of something, such as the amount of food in a recipe, the amount of time spent on a task, or the amount of rainfall in a particular area.
Given that the interest earned on an account after two years is $15. We need to find out how much it would be after 10 years, assuming the interest rate is constant over time.
The formula for compound interest is given by [tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A = final amount,
P = principal amount,
r = annual interest rate (as a decimal),
n = number of times the interest is compounded per year, and t = time in years.
Substituting the given values in the formula, we get A = P (1 + r/n)^(nt)
Since we are not given the principal amount, we can assume it to be any value. Let us assume the principal amount to be $100 for simplicity. Therefore, P = $100After two years, the interest earned is $15.
Therefore, the final amount after two years would be $100 + $15 = $115.t = 2 years
[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
115 = 100(1 + r/1)²
115/100 = (1 + r)²
1.15 = (1 + r)²
Taking square root on both sides, we get1.07 = 1 + rr = 0.07. Thus, the annual interest rate is 7%.
Now, substituting the given values in the formula, [tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
We get, A = 100(1 + 0.07/1)¹⁰ˣ¹
A = $196.72
Therefore, the amount after 10 years with a principal of $100 and interest rate of 7% compounded annually would be $196.72.
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Fill in the blanks using each of the numbers 0-7 exactly once, so that the percent, decimal, and fraction below are ordered from least to greatest._4._%, _.3_, _/7
The correct arrangement is 4.5%, 0.3, and 1/7.
To order the percent, decimal, and fraction from least to greatest, we need to find the appropriate value for each of the blanks using the numbers 0-7 exactly once.
Starting with the percent, we can see that 4.5% is the smallest possible value. Moving to the decimal, 0.3 is the next smallest value. Finally, for the fraction, the only remaining option is 1/7.
Therefore, the correct arrangement from least to greatest is 4.5%, 0.3, and 1/7.
It's important to note that the order may not be unique since there could be other valid combinations using the numbers 0-7. However, based on the given information, 4.5% is the smallest, followed by 0.3, and then 1/7.
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A business advertises that everything in the store is an additional 10% off the already reduced prices. Marcus picks out 2 shirts that are on a 30% off rack. If the shirts are originally priced at $28. 99 and $30. 29 and there is 6% sales tax, how much does Marcus end up paying for them? a. $39. 59 b. $37. 70 c. $37. 35 d. $35. 57.
Marcus picks out 2 shirts that are on a 30% off rack. If the shirts are originally priced at $28.99 and $30.29 and there is 6% sales tax, the amount Marcus has to pay for them is $37.70.Option (b) $37.70 is the correct answer.
How to calculate the final price Marcus has to pay?Let us begin with calculating the 30% discount Marcus gets for picking out 2 shirts that are on a 30% off rack.30% discount means Marcus gets to save (30/100) × (28.99 + 30.29) = $17.63Marcus' savings = $17.63The original price of the 2 shirts = $28.99 + $30.29 = $59.28Now, Marcus gets 10% off on the already reduced prices,
which means he gets an additional discount of (10/100) × $41.65 = $4.17Therefore, the new discounted price = $41.65 - $4.17 = $37.48The sales tax is 6% of $37.48Sales tax = 6/100 × $37.48 = $2.25Therefore, Marcus has to pay $37.48 + $2.25 = $39.73This is the amount Marcus has to pay.
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Darren lives in Wrexham and works in Corwen.
a) Use the chart to find the road distance
between Wrexham and Corwen.
(a) The road distance between Wrexham and Oswestry is 15 miles.
(b) The number of miles Sarah travels to and from work each week is 330 miles.
Given a chart of the road distances between various towns and cities.
(a) From the chart,
Distance the corresponds to Wrexham and Oswestry = 15 miles
Road distance between Wrexham and Oswestry is 15 miles.
(b) Distance between Ruthin and Oswestry = 33 miles
Total distance travelled to and from work in a day = 33 × 2 = 66 miles
She works 5 days a week.
Total distance travelled for 5 days = 66 × 5 = 330 miles
Hence, the number of miles travelled by Sarah in a week is 330 miles.
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The chart is given below.
"Your question is incomplete, probably the complete question/missing part is:"
The chart shows the distances, in miles, between some towns and cities.
Toby lives in Wrexham and works in Oswestry.
Wrexham
18
Ruthin
a) Use the chart to find the road distance
between Wrexham and Oswestry.
15
21
12
Corwen
15
33
23
Oswestry
Sarah lives in Ruthin and works in Oswestry for
5 days a week. Each day she travels to and
from work using the route shown on the map.
MOLD
ROTHEN
WRESTHAM
b) How many miles, in total, does she travel to
and from work each week? 231 miles
CORNEN
OSWESTRY
Choose CI
There are
128
128128 ounces in a gallon. There are
4
44 quarts in a gallon.
How many ounces are in a quart?
There are 32 ounces are in a quart
How to determine how many ounces are in a quart?From the question, we have the following parameters that can be used in our computation:
128 ounces in a gallon
Also, we have
4 quart in a gallon
using the above as a guide, we have the following:
128 ounces = 4 quart
Divide both sides by 4
So, we have
32 ounces = 1 quart
Hence, there are 32 ounces are in a quart
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A photon has a frequency of 2. 9 × 10–16 Hz. Planck’s constant is 6. 63 × 10–34 J•s. The energy of the photon, to the nearest tenths place, is × 10–49 J.
Using the equation E = hf, where f = 2.9 × 10^(-16) Hz and h = 6.63 × 10^(-34) J·s, the energy of the photon is approximately 1.9 × 10^(-49) J.
To calculate the energy of a photon, you can use the equation:
E = hf
where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon.
Given:
Frequency (f) = 2.9 × 10^(-16) Hz
Planck's constant (h) = 6.63 × 10^(-34) J·s
Now, substitute the values into the equation:
E = (6.63 × 10^(-34) J·s) × (2.9 × 10^(-16) Hz)
Multiply the values:
E = 1.9207 × 10^(-49) J
To the nearest tenths place, the energy of the photon is approximately 1.9 × 10^(-49) J.
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What is the most likely outcome when trade barriers between two nations, such as quotas and tariffs, are removed
When trade barriers such as quotas and tariffs are removed between two nations, the most likely outcome is an increase in international trade and economic integration. Here are some key potential outcomes:
Increased Exports and Imports: Removal of trade barriers allows businesses in both nations to freely export and import goods and services, leading to an expansion of trade volume between the two countries. Economic Growth: Increased trade often leads to economic growth as businesses have access to larger markets, enabling them to increase production, create jobs, and generate more revenue. Consumer Benefits: Removal of trade barriers can result in greater consumer choice and lower prices. With increased competition from foreign markets, domestic industries may need to become more efficient and offer competitive prices and quality to attract customers.
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Rory joins the game for the second round and wins that round what can you say about where his score would appear on the number line explain
If Rory joins the game for the second round and wins that round, we can conclude that his score for the second round would be higher than his score for the first round.
However, without knowing the specific scores or the scoring system of the game, we cannot determine the exact position of Rory's score on the number line.
The number line represents a continuous range of numbers, and the positioning of a score on the number line depends on various factors such as the range of possible scores, the distribution of scores, and the specific scoring system used in the game. Without additional information about these factors, we cannot accurately determine the exact position of Rory's score on the number line.
However, we can infer that Rory's score for the second round would be greater than his score for the first round, which implies that his score would be located to the right of his first round score on the number line.
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Here are 5 numbers 2 5 7 8 9 one of the numbers is removed meaing the avarge of the remainnig four numbers is 6 which card removed numbers
We can conclude that the missing number is 7. To find out which number was removed from the list, we can first calculate the sum of the remaining four numbers and
then find the missing equation by comparing it with the average.
Given numbers: 2, 5, 7, 8, 9
Step 1: Calculate the sum of the remaining four numbers.
Sum = 2 + 5 + 7 + 8 + 9 = 31
Step 2: Calculate the average of the remaining four numbers.
Average = Sum / 4 = 31 / 4 = 7.75
Step 3: Compare the average with each number to find the missing number.
- If the missing number is 2:
(2 + 5 + 7 + 8) / 4 = 22 / 4 = 5.5 (not equal to 6)
- If the missing number is 5:
(2 + 7 + 8 + 9) / 4 = 26 / 4 = 6.5 (not equal to 6)
- If the missing number is 7:
(2 + 5 + 8 + 9) / 4 = 24 / 4 = 6 (equal to 6)
- If the missing number is 8:
(2 + 5 + 7 + 9) / 4 = 23 / 4 = 5.75 (not equal to 6)
- If the missing number is 9:
(2 + 5 + 7 + 8) / 4 = 22 / 4 = 5.5 (not equal to 6)
Based on the calculations, we can conclude that the missing number is 7.
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Alli has $382. 45 in her checking account and $450 in her savings account. She writes a check for $400. Alli’s bank automatically takes money from her savings to cover the amount of a check if the money in the checking account is not sufficient. Unfortunately for Alli, the bank also withdraws $25 from her savings account for this service. Once the check has cleared, how much money does Alli have in her savings account?
$17. 55
$17. 55
$42. 55
$42. 55
$407. 45
$407. 45
$442. 55
$442. 55
Once the check has cleared, Alli has $17.55 in her savings account. Finally, the amount of money Alli has in her savings account after the check has cleared is $25, so the answer is option A: $17.55.
Initial amount in Alli's checking account = $382.45
Initial amount in Alli's savings account = $450
Amount Alli withdrew from checking account = $400
Amount the bank withdrew from Alli's savings account = $25
Total cost of the check = 400+25
=425
Since the initial amount in her checking account was insufficient, the bank automatically withdrew $25 from her savings account to cover the cost of the check. This means that Alli has a total of $425 - $400 = $25 left in her savings account.After the withdrawal from her savings account, Alli's remaining savings balance is $450 - $25 = $425. However, she spent $400 to cover the check, so her final savings balance is $425 - $400 = $25.
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the price of a watch was increased by 20% to 144 what was the price before the increase
The price of the watch before the increase was $120. The price of a watch was increased by 20% to 144.
To find the original price of the watch, we can use the concept of reverse percentage change.
Let's assume the original price of the watch is P dollars. The price of the watch was increased by 20%, which means the final price is 120% (100% + 20%) of the original price.
We can set up the equation:
1.2P = 144
To solve for P, we divide both sides of the equation by 1.2:
P = 144 / 1.2 = $120
Therefore, the price of the watch before the increase was $120.
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On Monday, 238 students and 10 teachers went on a trip to the zoo. If a bus can hold 58 people each, how many busses are needed? (Hint: remember you cannot have part of a bus and you must have enough to fit all people
we would need a total of 5 buses to accommodate all the students and teachers on the trip.To determine the number of buses needed, we divide the total number of students and teachers by the capacity of each bus, which is 58 people.
238 students + 10 teachers = 248 people
To calculate the number of buses needed, we divide 248 people by 58 people per bus:
248 people ÷ 58 people/bus ≈ 4.276 buses
Since we cannot have a fraction of a bus, we round up to the nearest whole number. Therefore, we would need a total of 5 buses to accommodate all the students and teachers on the trip.
It's important to note that rounding up ensures that there are enough buses to accommodate all the individuals, even if there are some empty seats on each bus.
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Leila, trey and Justin have a total of 125$ in their wallets trey has 3 times what Justin has. Leila has 10$ more than Justin. How much does each have
Let's represent the amount of money Justin has as [tex]\(x\).[/tex]
According to the given information, Trey has 3 times what Justin has, so Trey has [tex]\(3x\)[/tex] dollars.
Leila has 10 dollars more than Justin, so she has [tex]\(x + 10\)[/tex] dollars.
The sum of the amounts of money they have is 125 dollars:
[tex]\(x + 3x + (x + 10) = 125\)[/tex]
Combining like terms, we have:
[tex]\(5x + 10 = 125\)[/tex]
Subtracting 10 from both sides:
[tex]\(5x = 115\)[/tex]
Dividing both sides by 5:
[tex]\(x = 23\)[/tex]
So Justin has 23 dollars.
Trey has 3 times that amount:
[tex]\(3 \times 23 = 69\)[/tex]
Leila has 10 dollars more than Justin:
[tex]\(23 + 10 = 33\)[/tex]
Therefore, Justin has 23 dollars, Trey has 69 dollars, and Leila has 33 dollars.
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An elephant weighs 1200 pounds, which is 3/4 the weight of a whale. A giraffe weighs 1/8 of the weight of the whale or 5/6 of the weight of 12 deer. How much does 12 deer weigh?
Answer:
240 pounds
Step-by-step explanation:
Let the variables:
e = lbs of elephant
w = lbs of whale
g = lbs of giraffe
d = lbs of 12 deer
e = 1200 and a whale is 3/4 of this weight so:
1200 / 4 = 400 which means 1/4 of the weight is 400
Multiply by 4 and get the total weight of 1600
w = 1600
g = 1600(1/8)
g = 200
200 is 5/6 of the weight of 12 deer so each 1/6 is 40
multiply 6 * 40
240
sam spins a spinner 24 times at a speed of 10 mph. how much times did the spinner spin
The spinner spins for a total of 2.4 hours when Sam spins it 24 times at a speed of 10 mph.
If Sam spins the spinner 24 times at a speed of 10 mph, we can calculate the total time the spinner spins by dividing the distance traveled by the speed.
Let's assume that each spin of the spinner covers a distance of 1 revolution. The total distance covered by the spinner would then be 24 revolutions.
To calculate the time the spinner spins, we divide the distance by the speed:
Time = Distance / Speed
Distance = 24 revolutions
Speed = 10 mph
Time = 24 revolutions / 10 mph = 2.4 hours
Therefore, the spinner spins for a total of 2.4 hours when Sam spins it 24 times at a speed of 10 mph.
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A sporting goods manager was selling a ski CERT for a certain price the manager offered the markdowns sound to the right making the one day sale price for the ski CERT $328 funny original selling price of the ski set
The sporting goods manager initially priced the ski set at a certain amount. By offering markdowns and holding a one-day sale, the manager reduced the price to $328. We need to determine the original selling price of the ski set.
To find the original selling price of the ski set, we know that the one-day sale price is $328. This means the markdown or discount was applied to the original price.
Let's assume the original selling price of the ski set is "x." The markdown or discount applied to x results in a sale price of $328.
Mathematically, we can represent this as:
x - markdown = $328
The markdown amount can be calculated as the difference between the original price and the sale price:
markdown = x - $328
However, the exact markdown amount or percentage is not provided in the given information. Therefore, we cannot determine the original selling price of the ski set without additional information.
In summary, based on the given information, the one-day sale price for the ski set is $328, but the original selling price cannot be determined without knowing the specific markdown or discount applied by the sporting goods manager.
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complete question:
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $328. Find the original selling price of the ski set.
An item originally costs $175. 0. The item is now on sale for $99. 75. What percent
is the sale price of the original price? Is this an example of percent increase or
decrease? Explain how you know. *
It is percentage decrease by 43 percent.
Given that, the original cost of item = $175.00 and the sale price of item = $99.75.
Percentage increase or decrease = (Original Price - Sale Price)/Original Price ×100
= (175.00-99.75)/175.00 ×100
= 75.25/175.00 ×100
= 0.43×100
= 43%
Therefore, it is percentage decrease by 43 percent.
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a cone with equal height and radius has volume 1234 cm³. what is the height of the cone to the nearest tenth of a centimetre?
The height is equal to the radius, the height of the cone to the nearest tenth of a centimetre is 14.98 cm. A cone with equal height and radius has volume 1234 cm³. To find the height of the cone, we will use the formula for the volume of a cone: V = 1/3πr²h
A cone with equal height and radius has volume 1234 cm³. To find the height of the cone, we will use the formula for the volume of a cone: V = 1/3πr²h
where: V is the volume of the cone, π is pi (3.14), r is the radius of the cone, h is the height of the cone
We are given that the height and radius of the cone are equal, so we can substitute r for h. Also, we know the volume of the cone is 1234 cm³. So:
1234 = 1/3πr²h
1234 = 1/3πr²(r)
1234 = 1/3πr³ (since r = h)
Now we can solve for r: 1234 * 3 / π = r³
3747.22 = r³
r ≈ 14.98 cm
Since the height is equal to the radius, the height of the cone to the nearest tenth of a centimetre is 14.98 cm.
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Square root of 1/961 is?
Square root of -361 is ?
Square root of 625 i s?
The answers are:Square root of 1/961 is 1/31Explanation:We can write the square root of 1/961 as √1/961. Simplifying this,
we get:√1/961=√1/√961=1/31Therefore, the main answer is 1/31.Square root of -361 is not real:As we know, the square root of a negative number is not real.
herefore, the square root of -361 is not real. Hence, the main answer is "not real".Square root of 625 is 25:We can write the square root of 625 as √625. Simplifying this, we get:√625=25Therefore, the main answer is 25.
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6. At a medical convention, there are 7 pediatricians, 5 cardiologists, 3 nurses and
4 dermatologists. If a participant is selected at random, what is the probability
of selecting a pediatrician or a cardiologist?
The probability of selecting a pediatrician or a cardiologist at a medical convention can be found by adding the probabilities of selecting each. The probability is 12/19 or approximately 0.63.
The total number of participants at the medical convention is 7 + 5 + 3 + 4 = 19.
The probability of selecting a pediatrician is 7/19, since there are 7 pediatricians out of 19 participants.
The probability of selecting a cardiologist is 5/19, since there are 5 cardiologists out of 19 participants.
Since we are looking for the probability of selecting a pediatrician or a cardiologist, we can add these probabilities together:
P(pediatrician or cardiologist) = P(pediatrician) + P(cardiologist)
P(pediatrician or cardiologist) = 7/19 + 5/19
P(pediatrician or cardiologist) = 12/19
Therefore, the probability of selecting a pediatrician or a cardiologist is 12/19, or approximately 0.63 (rounded to two decimal places).
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For 100/300 bodily injury limits and $100,000.00 property damage limits, Stephanie Ambrose's base premium is $292.50. Her base premium is $75.90 for $50-deductible comprehensive insurance and $225.79 for $50-deductible collision insurance. What is Stephanie's annual base premium?
To calculate Stephanie Ambrose's annual base premium, we need to sum up the costs of her bodily injury, property damage, comprehensive, and collision insurance.
Given that the bodily injury limits are $100/300 and the property damage limits are $100,000, we can calculate the cost of bodily injury and property damage insurance. The cost for bodily injury insurance is $100 for every $100,000 of coverage, and the cost for property damage insurance is $100 for every $100,000 of coverage.
For bodily injury insurance, the cost is calculated as:
(100/300) * 100 = $33.33
For property damage insurance, the cost is:
(100,000/100,000) * 100 = $100
Adding up the costs of bodily injury, property damage, comprehensive, and collision insurance:
Base premium: $292.50
Comprehensive insurance: $75.90
Collision insurance: $225.79
Bodily injury insurance: $33.33
Property damage insurance: $100
Total annual base premium = Base premium + Comprehensive insurance + Collision insurance + Bodily injury insurance + Property damage insurance
Total annual base premium = $292.50 + $75.90 + $225.79 + $33.33 + $100 = $727.52
Therefore, Stephanie Ambrose's annual base premium is $727.52.
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janine spends 1 tenths hour making the bed 1 fiths hour getting dressed and 1 half hour eating breakfast what fraction of an hour does she spend doing these activitys
Therefore, Janine spends 4/5 of an hour doing these activities.
To determine the fraction of an hour that Janine spends doing the given activities, we need to convert the given times to fractions of an hour. We know that 1 hour is equivalent to 1 whole, which means that half an hour would be equivalent to half of a whole.
Similarly, one-fifth of an hour would be equivalent to 1 ÷ 5, which is 0.2, and one-tenth of an hour would be equivalent to 1 ÷ 10, which is 0.1.
Now, let's add the three times together to find the total time:
1/10 hour making the bed + 1/5 hour getting dressed + 1/2 hour eating breakfast = 1/10 + 2/10 + 5/10= 8/10 (which can be simplified to 4/5).
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A basketball team has won 70% of the 20 games they have played. If they win all their remaining games, how many would they have to play to increase their win percentage to 80%. Please explain your answer and show your reasoning.
To increase their win percentage from 70% to 80%, the basketball team needs to win a specific number of remaining games.
Let's first determine the number of games the team has won out of the 20 games played. Since they have won 70% of the games, we can calculate that as 0.7 * 20 = 14 games won.
Now, let's assume the team has to play 'x' remaining games to achieve an 80% win percentage. If they win all the remaining games, they will have a total of 20 + x games played and 14 + x games won.
To find the win percentage, we divide the total number of games won by the total number of games played and set it equal to 80% or 0.8:
(14 + x) / (20 + x) = 0.8
We can solve this equation to determine the value of 'x':
0.8 * (20 + x) = 14 + x
16 + 0.8x = 14 + x
0.8x - x = 14 - 16
0.2x = -2
x = -2 / 0.2
x = -10
Since we cannot have a negative number of remaining games, it is not possible for the team to increase their win percentage to 80% by winning all their remaining games.
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A group of 5 friend were bowling one Saturday night. There are 10 pins in bowling and 10 frames for each bowler. If every bowler knocked every pin down every frame, how many pins would be knocked down?
250 pins would be knocked down.
In bowling, a single bowler would knock down all ten pins in every frame; thus, a total of 10 frames will result in 100 knocked down pins for each bowler. So, five bowlers each knocking down 100 pins would result in a total of 500 pins knocked down. Consequently, all 50 pins would be knocked down in total (100 pins per bowler × 5 bowlers), which amounts to 250 knocked down pins.
Therefore, the main answer is 250 pins would be knocked down.
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