Answers
Answer:
Center= (-6,-8)
Radius= 6
Step-by-step explanation:
We use the formula (x-h)^2+(y-k)^2 then plug in our numbers:
\((x - h)^2 + (y - k)^2 = r^2\\(x+6)^2 +(y-k)^2=36\)
In the equation -h is 6 so our h (x-coordinate) is -6
In the equation -k is 8 so our k (y-coordinate) is -8
In the equation r^2 is 36 so we take the square root of 36 to get r which is 6.
Related Questions
If the forecast for two consecutive periods is 1,500 and 1,400 and the actual demand is 1,200 and 1,500 , then the mean absolute deviation is 1) 500 2) 700 3) 200 4) 100
Answers
200 is the mean absolute deviation. Therefore, choice three (200) is the right one.
How to calculate the mean absolute deviation
The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.
Forecasted values are as follows: 1,500 and 1,400
Values in actuality: 1,200 and 1,500
Absolute differences:
|1,500 - 1,200| = 300
|1,400 - 1,500| = 100
Now, we calculate the MAD:
MAD = (300 + 100) / 2 = 400 / 2 = 200
Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.
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a pizza parlor in tallahassee sells a pizza with a 16-inch diameter. a pizza parlor in jaco, costa rica, sells a pizza with a 27.8-centimeter diameter. part a: how many square inches of pizza is the pizza from tallahassee? show every step of your work. (1 point) part b: how many square centimeters of pizza is the pizza from jaco, costa rica? show every step of your work. (1 point) part c: if 1 in.
Answers
In part a, we will calculate the number of square inches in a pizza with a 16-inch diameter. In part b, we will calculate the number of square centimeters in a pizza with a 27.8-centimeter diameter.
Part a: To find the area of the pizza in square inches, we need to calculate the area of a circle with a diameter of 16 inches. The formula for the area of a circle is \(A=\pi r^2\), where r is the radius. Since the diameter is given, we can find the radius by dividing the diameter by 2. So, the radius of the pizza is 16/2 = 8 inches. Plugging this value into the formula, we get \(A = \pi (8^2) = 64\pi\) square inches.
Part b: To find the area of the pizza in square centimeters, we need to calculate the area of a circle with a diameter of 27.8 centimeters. Again, we use the formula \(A=\pi r^2\), but this time we need the radius in centimeters. The radius is 27.8/2 = 13.9 centimeters. Plugging this value into the formula, we get \(A = \pi (13.9^2) = 191.04\pi\) square centimeters.
Part c: To convert the area from part a (in square inches) to square centimeters, we need to know the conversion factor. Given that 1 inch is equal to 2.54 centimeters, we can square this conversion factor to get the conversion factor for area.
So, 1 square inch is equal to \((2.54)^2 = 6.4516\) square centimeters. Multiplying the area from part a (64π square inches) by the conversion factor, we get 64π * 6.4516 square centimeters, which simplifies to 412.96π square centimeters.
Therefore, the pizza from Tallahassee has an area of 64π square inches, the pizza from Jaco, Costa Rica has an area of 191.04π square centimeters, and the conversion of the pizza from Tallahassee to square centimeters is approximately 412.96π square centimeters.
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URGENT HELP PLEASE!!! In the figure below, FG=6 and GH=8. Find FH.
Answers
Answer:
14
Step-by-step explanation:
Adding FG and GH is the answer to the wholr line. Im 90% sure thats the right answer thats whst i learnt 7 days ago.
Given the properties, write a quadratic function for:
f(3+sqrt(2))=f(3-sqrt(2))=0
if f(1)=-8
Answers
Quadratic function for the given properties is \(y=-4x^{2} +24x-28\).
The roots are \(3+\sqrt{2}\) and \(3-\sqrt{2}\); that means the axis of symmetry is x=3; which means the vertex has x coordinate 3. Then the vertex form of the equation is
\(y = a(x-3)^{2}+k\)
Then since y is 0 when x is \(3+\sqrt{2}\),
\(0=a(\sqrt{2} )^{2} +k\)
\(0=2a+k\) (1)
And when x = 1, y = -8,
\(-8 = a(-2)^{2}+k\)
\(-8=4a+k\) (2)
Then from equations (1) and (2)
\(-8=2a\)
\(a = -4\)
And then from either equation (1) or (2), k = 8.
So the equation is
\(y = -4(x-3)^{2}+8\)
\(y=-4(x^{2} -6x+9)+8\)
\(y=-4x^{2} +24x-28\)
Solving this equation using the quadratic formula verifies that the roots are \(3+\sqrt{2}\) and \(3-\sqrt{2}\); evaluating the expression for x=1 verifies that the y value is -8.
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A tabletop in the shape of a trapezoid. The length of one longer base is 115 centimeters, and the shorter base is 85 centimeters. The height is 65.5 centimeters. What is the area of the tabletop?
Answers
The tabletop has an area of 6,550 square centimeters.
How to find the area of the trapezoid-shaped tabletop?To find the area of the trapezoid-shaped tabletop, you can use the formula:
Area = (1/2) * (a + b) * h
where a and b are the lengths of the two bases, and h is the height of the trapezoid.
In this case, the length of the longer base (a) is 115 centimeters, the length of the shorter base (b) is 85 centimeters, and the height (h) is 65.5 centimeters.
Plugging in these values into the formula, we have:
Area = (1/2) * (115 + 85) * 65.5
= (1/2) * 200 * 65.5
= 100 * 65.5
= 6,550 square centimeters
Therefore, the area of the tabletop is 6,550 square centimeters.
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. sam flipped a coin 30 times and recorded 20 heads/10 tails. compare the theoretical and experimental probability.
Answers
Sam's experimental probability of getting heads in 30 coin flips was 20 out of 30, while the theoretical probability of getting heads is 1/2 or 0.5.
Sam's experimental probability of getting heads in the 30 coin flips was 20 out of 30, which can be written as 20/30 or simplified to 2/3. This means that in the experiment, heads appeared in approximately two-thirds of the flips. On the other hand, the theoretical probability of getting heads in a fair coin flip is 1/2 or 0.5. This is because there are two equally likely outcomes (heads or tails) and only one of them is heads.
Comparing the experimental and theoretical probabilities, we can see that Sam's results deviate slightly from the expected outcome. The experimental probability of getting heads is higher than the theoretical probability. This could be due to chance or random variation, as 30 coin flips may not be enough to perfectly represent the true probability. With a larger number of trials, the experimental probability would tend to converge towards the theoretical probability. However, in this specific experiment, Sam's results suggest a slightly biased coin favoring heads.
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The lengths of two sides of a triangle are 11 and 17. Which
measurement cannot be the length of the third side? *
Answers
Answer:
Step-by-step explanation:
The third side must be less than 11+17 = 28 units
A fisheries researcher wishes to test for a difference in mean weights of a single species of fish caught by fishermen in three different lakes in Nova Scotia. The significance level for the test will be 0.05. Complete the following partial ANOVA table and use it to answer the following questions:
Source, d.f., SS, MS, F Treatment, _, 17.04
Error, 9,_
Total, _, 31.23
a) What is the critical value F for this test?
b) What is the observed value F for this test?
c) What is the conclusion of the test? In other words, is there a difference in the mean weights of a single species of fish in the three different lakes?
Answers
a) The critical value F for the test is approximately 4.26.
b) The observed value F for the test is approximately 5.4.
c) Since the observed value of F is greater than the critical value F, we reject the null hypothesis and conclude that there is a significant difference in the mean weights of a single species of fish in the three different lakes at the 0.05 significance level.
Step-by-step explanation:
a) To find the critical value F, we first need to calculate the degrees of freedom (d.f.) for Treatment and Error. Since there are three different lakes, the d.f. for Treatment is (3-1)=2. We already have the d.f. for Error, which is 9. The Total d.f. is (2+9)=11. Now, using an F-distribution table or calculator with a significance level of 0.05 and d.f. 2 and 9, the critical value F is approximately 4.26.
b) To find the observed value of F, we need to calculate the Mean Square (MS) for Treatment and Error. We already have the Sum of Squares (SS) for Treatment, which is 17.04. The Total SS is 31.23, so the Error SS is (31.23-17.04)=14.19. Now, we can find the MS for Treatment and Error by dividing SS by the respective d.f.:
MS Treatment = SS Treatment / d.f. Treatment = 17.04 / 2 = 8.52
MS Error = SS Error / d.f. Error = 14.19 / 9 = 1.577
Now, we can calculate the observed value of F as the ratio of MS Treatment to MS Error:
Observed F = MS Treatment / MS Error = 8.52 / 1.577 ≈ 5.4
c) Since the observed value of F (5.4) is greater than the critical value F (4.26), we reject the null hypothesis. This means there is a significant difference in the mean weights of a single species of fish in the three different lakes at the 0.05 significance level.
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which number is the closest approximate value for sqrt 105
Answers
Answer:
10.
Step-by-step explanation:
Lets define a square root. A square root is a number multiplied by itself. 10 x 10 = 100, this is the closest we can get to 105, therefore 10 is the answer.
Scenario: Imagine you are a Math Committee Review member at the local elementary school. You have been asked to review a curriculum change for 5th graders in math.
In 1,250-1,500 words, address the following prompts based on the above scenario:
Include a brief background of the problem and why it is important. From this information, identify a clearly written research question.
State the null and alternative hypothesis (in both words and statistical notation) needed to address the research question.
Describe the type of data needing to be collected and the techniques you would use.
Choose which statistical test you would use to conduct the study. Support your method with research.
How might you report your findings? Explain the potential ethical dilemmas.
Answers
To conduct the study on the curriculum change for 5th graders in math, the statistical test that should be used is the t-test.
This test is appropriate when there are two groups to compare. The null hypothesis of the t-test is that the means of the two groups are equal while the alternative hypothesis is that they are not equal. To conduct the t-test, the mean and standard deviation of each group will be calculated. The t-test compares the means of the two groups to determine whether the difference between them is statistically significant.
Reporting of the findings of the t-test will be done through the use of graphs and charts. The results will be presented in a clear and concise manner, highlighting the key findings and their implications for the curriculum change. Any potential ethical dilemmas should also be addressed in the report. These may include issues such as informed consent, confidentiality, and potential biases in the data. It is important to ensure that all ethical guidelines are followed throughout the study to ensure the validity and reliability of the findings.
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Hannah has a part-time job making holiday wreaths. This week, she made x medium wreaths, twice as many large wreaths as medium wreaths, and 12 as many small wreaths as medium wreaths. In terms of x, how many wreaths did Hannah make this week?
Answers
Answer:
Total number of wreaths = 3.5 wreaths
Step-by-step explanation:
Given:
Number of medium wreaths = x
Number of larger wreaths = 2[Number of medium wreaths]
Number of small wreaths = [1/2][Number of medium wreaths]
Find:
Total number of wreaths
Computation:
Total number of wreaths = Number of medium wreaths + Number of large wreaths + Number of small wreaths
Total number of wreaths = Number of medium wreaths + 2[Number of medium wreaths] + [1/2][Number of medium wreaths]
Total number of wreaths = x + 2x + 0.5x
Total number of wreaths = 3.5 wreaths
Evaluate the double integral -6 82 =¹ y= √x² + y² dy dx.
Answers
The value of the given double integral is approximately 75.0072.
To evaluate the double integral:
∬-6 82 √(x² + y²) dy dx
We need to change the order of integration and convert the integral to polar coordinates. In polar coordinates, we have:
x = r cosθ
y = r sinθ
To determine the limits of integration, we convert the rectangular bounds (-6 ≤ x ≤ 8, 2 ≤ y ≤ √(x² + y²)) to polar coordinates.
At the lower bound (-6, 2), we have:
x = -6, y = 2
r cosθ = -6
r sinθ = 2
Dividing the two equations, we get:
tanθ = -1/3
θ = arctan(-1/3) ≈ -0.3218 radians
At the upper bound (8, √(x² + y²)), we have:
x = 8, y = √(x² + y²)
r cosθ = 8
r sinθ = √(r² cos²θ + r² sin²θ) = r
Dividing the two equations, we get:
tanθ = 1/8
θ = arctan(1/8) ≈ 0.1244 radians
So, the limits of integration in polar coordinates are:
0.1244 ≤ θ ≤ -0.3218
2 ≤ r ≤ 8
Now, we can rewrite the double integral in polar coordinates:
∬-6 82 √(x² + y²) dy dx = ∫θ₁θ₂ ∫2^8 r √(r²) dr dθ
Simplifying:
∫θ₁θ₂ ∫2^8 r² dr dθ
Integrating with respect to r:
∫θ₁θ₂ [(r³)/3] from 2 to 8 dθ
[(8³)/3 - (2³)/3] ∫θ₁θ₂ dθ
(512/3 - 8/3) ∫θ₁θ₂ dθ
(504/3) ∫θ₁θ₂ dθ
168 ∫θ₁θ₂ dθ
Integrating with respect to θ:
168 [θ] from θ₁ to θ₂
168 (θ₂ - θ₁)
Now, substituting the values of θ₂ and θ₁:
168 (0.1244 - (-0.3218))
168 (0.4462)
75.0072
Therefore, the value of the given double integral is approximately 75.0072.
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How do you subtract mixed fractions with different denominators examples?
Answers
Answer: To subtract mixed fractions with different denominators, you need to convert the mixed fractions to equivalent fractions with a common denominator. Once the fractions have a common denominator, you can simply subtract the numerators and keep the denominator the same.
Example:
the difference of 2 1/3 and 1 3/4 is 5/12.
Step-by-step explanation:
First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3
Next, convert 1 3/4 to an improper fraction: 1 3/4 = 7/4
Now, both fractions have the same denominator, 3. So, you can subtract the numerators:
7/3 - 7/4 = (7 * 4 - 7 * 3) / (3 * 4) = 28/12 - 21/12 = 7/12
Finally, convert the answer back to a mixed fraction: 7/12 = 7 ÷ 12 = 5/12.
Assume the price of snacks is $4, the price of meals is $10, and the consumer has $240 remaining on their meal card. Which consumption bundle will NOT be the consumer's choice given our assumptions about consumers choosing the optimal consumption bundle?
A) 5 Snacks, 20 Meals
B) 30 Snacks, 12 Meals
C) 20 Snacks, 16 Meals
D) None of the bundles will be chosen.
E) There is not enough information to tell
Answers
The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.
Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.
For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.
For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.
For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.
Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.
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The school packs one lunch based on each of these choices. If Dr. Higgins wants a "Turkey, Water and Cookie" or a " Turkey, Water and Brownie" (I could eat either lunch) - what is the probability that Dr. Higgins randomly picks up one or the other of his Favorite Lunches?
Answers
The probability of selecting either lunch is 50%, as both lunches are equally likely to be chosen. This is because both lunches have the same ingredients, with the only difference being the dessert item.
What is probability?Probability is a measure of the likelihood of a certain event or outcome occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event or outcome is impossible and 1 indicates that the event or outcome is certain to occur. Probability is an important concept in mathematics and statistics, and it is widely used in fields such as finance, science, engineering, and gaming.
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Graph the line 2y-6x+4=0 on Tell me the slope and y-intercept
sloper
y intercept=
Blank 1:
Blank 2:
Answers
Answer:
Slope: 3
Y-intercept: (0, -2)
Step-by-step explanation:
Solve the equation 9x²y² - 12xy + 4 = 0, expressing y in terms of x.
Answers
Step-by-step explanation:
We can solve the given equation for y in terms of x by treating it as a quadratic equation in y. To do so, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, we can rearrange the equation to get:
9x^2y^2 - 12xy + 4 = 0
which can be written as:
(3xy)^2 - 2(3xy)(2) + 2^2 - 2^2 = 0
This is a quadratic equation in 3xy, which can be solved using the quadratic formula:
3xy = [2 ± sqrt(2^2 - 4(1)(-2^2))]/(2*1)
3xy = [2 ± sqrt(4 + 32)]/2
3xy = [2 ± 2sqrt(9)]/2
3xy = 1 ± 3
Therefore, we have two possible solutions:
3xy = 1 + 3 = 4 or 3xy = 1 - 3 = -2
Solving for y in terms of x, we get:
3xy = 4 => y = 4/(3x)
or
3xy = -2 => y = -2/(3x)
Therefore, the solutions to the given equation are:
y = 4/(3x) or y = -2/(3x)
i need help pls ! pls help me
Answers
Answer:
x= 175°
Step-by-step explanation:
angles in a triangle add up to 180 degrees
85 + 90 = 175
180 - 175 = 5 (the missing angle not x)
angles on a straight line add up to 180 degrees
180 - 5 =175
Is x•y is a whole number?
Always true
Never true
sometimes true
Answers
Answer: Always true
Step-by-step explanation:
HELP ME DO THIS PLEASE IM STRESSING OUT
Answers
Answer:
36
Step-by-step explanation:
ik it bc im smart
The mean per capita consumption of milk per year is 152152 liters with a variance of 484484. If a sample of 109109 people is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 3.273.27 liters
Answers
Thus, there is a very high probability (99.93%) that the sample mean would differ from the true mean by less than 3.273 liters, given a sample size of 109 people and a population mean of 152 liters with a variance of 484.
To answer this question, we need to use the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal, regardless of the distribution of the population, as long as the sample size is large enough.
First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the sample means. We can use the formula:
standard error of the mean = standard deviation / square root of sample size
Plugging in the values given, we get:
standard error of the mean = √484 / √109
standard error of the mean = 2 / 109
standard error of the mean = 0.018
Next, we need to calculate the z-score, which tells us how many standard errors the sample mean is from the true mean. We can use the formula:
z-score = (sample mean - true mean) / standard error of the mean
Plugging in the values given, we get:
z-score = (sample mean - true mean) / 0.018
3.273 = (sample mean - 152) / 0.018
(sample mean - 152) = 0.018 * 3.273
sample mean = 152 + 0.059
sample mean = 152.059
So the sample mean is 152.059 liters.
Now we can use the standard normal distribution table to find the probability that the z-score is less than 3.273. Looking up the value in the table, we get:
P(z < 3.273) = 0.9993
Therefore, the probability that the sample mean would differ from the true mean by less than 3.273 liters is approximately 0.9993, or 99.93%.
In conclusion, there is a very high probability (99.93%) that the sample mean would differ from the true mean by less than 3.273 liters, given a sample size of 109 people and a population mean of 152 liters with a variance of 484. This probability is based on the Central Limit Theorem and the standard normal distribution table.
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Find the volume of the pyramid.
Answers
Answer:
180 ft^3
Step-by-step explanation:
volume of the pyramid = (1/3)(area of base) (height)
v= 1/3×(10×12÷2)×(9)
= 180 ft^3
Answer:
answer on the picture.....
The sticker price is the price you must pay for the vehicle
True or False
Answers
it's true...........
Answer:
False
Step-by-step explanation:
Verified correct with test results.
Mary’s cat lost two pounds in five weeks. Which rational number does not show the average change in the cat’s weight?
A. −(2/5)
B. −2/5
C. −2/−5
D. 2/-5
Answers
Answer:B
Step-by-step explanation:
Answer:
The answer is C. -2/-5
Step-by-step explanation:
I tried B, but it was incorrect, so then I tried C, turns out C was correct my dudes.
the angle of depression from the top of a building to the foot of the tower is 30 degree and the angle of depression from the top of the tower to the foot of the building is 45degree if the tower is 30m high find the height of the building
Answers
Answer:
38.66 meters.
Step-by-step explanation:
Let's denote the height of the building as 'h' (to be determined). Given that the tower is 30m high, we can use trigonometry to solve for the height of the building.
From the information provided, we can form a right triangle with the height of the tower as one side, the height of the building as another side, and the distance between the tower and the building as the hypotenuse.
Considering the angle of depression of 30 degrees, we have the following equation:
tan(30°) = h / d
Where 'd' is the distance between the tower and the building. We don't have the exact value of 'd,' but we can use the second angle of depression to find the relationship between 'd' and the height of the tower.
Using the angle of depression of 45 degrees, we have:
tan(45°) = 30 / d
We can rearrange this equation to solve for 'd':
d = 30 / tan(45°)
Now we can substitute this value of 'd' into the first equation:
tan(30°) = h / (30 / tan(45°))
To find the value of 'h,' we can solve this equation:
h = (30 / tan(45°)) * tan(30°)
Using a calculator, we can calculate the value of 'h' to be approximately 38.66 meters.
Therefore, the height of the building is approximately 38.66 meters.
Name a perfect square between 60 and 80.
Answers
Answer:
8*8 = 64
Step-by-step explanation:
PERFECT SQUARE
The perfect square of a number that lies between 60 and 80 will be 64 or 8².
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
A number will be a perfect square if that number can be broken into two such same number that it will be the product of those numbers.
For example, 4 is a product of 2 x 2 thus 4 will be a perfect square.
The number 8² = 64 lies between 60 and 80 thus it will be correct.
Hence "The perfect square of a number that lies between 60 and 80 will be 64 or 8²".
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Sam wants to bake a cake that requires butter, flour, sugar, and milk in the ratio of 1 : 6 : 2 : 1. Sam has
1⁄2 cup of sugar. How much of the other ingredients does he need?
Answers
For the ratio, we can use the amount of sugar Sam has as a reference.
Sam needs approximately:
1/4 cup of butter
1.5 cups of flour
1/4 cup of milk
To determine the amounts of the other ingredients needed based on the given ratio, we can use the amount of sugar Sam has as a reference.
Given:
Sugar: 1/2 cup
Ratio:
Butter : Flour : Sugar : Milk = 1 : 6 : 2 : 1
We can set up a proportion to find the amounts of the other ingredients:
(1/2 cup of sugar) / (2 units of sugar) = (x cups of other ingredient) / (corresponding units of other ingredient)
Let's find the amounts of the other ingredients:
1/2 cup of sugar is equivalent to 2 units of sugar in the ratio. Therefore, we need to find the corresponding amounts of the other ingredients for 2 units.
Butter: (1/2 cup of sugar) * (1 unit of butter / 2 units of sugar) = 1/4 cup of butter
Flour: (1/2 cup of sugar) * (6 units of flour / 2 units of sugar) = 3/2 cups of flour (1.5 cups)
Milk: (1/2 cup of sugar) * (1 unit of milk / 2 units of sugar) = 1/4 cup of milk
Sam needs approximately:
1/4 cup of butter
1.5 cups of flour
1/4 cup of milk
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Please help, I’ll mark as brainliest.
Answers
Step-by-step explanation:
if we translate (shift) a function g(x) to the right by k to create h(x), then h(x) creates the same functional values as g(x), but they happen now for higher x ("later", if you consider x as a kind of time).
so, e.g.
h(0) = g(0 - k)
or
g(0) = h(0 + k)
and to translate to the left by k has the opposite effect. the original results happen "earlier" on the x-axis.
so, e.g.
h(0) = g(0 + k)
or
g(0) = h(0 - k)
so, all we need to do is to replace every occurrence of x by (x - k) if shifting right, or by (x + k) if shifting left.
our graph is
10x² - 2x + 4y² - 4y = 40
so, translating this 4 units to the right gives us
10(x - 4)² - 2(x - 4) + 4y² - 4y = 40
10(x² - 8x + 16) - 2x + 8 + 4y² - 4y = 40
10x² - 80x + 160 - 2x + 8 + 4y² - 4y = 40
10x² - 82x + 4y² - 4y = -128
translating the original graph 3 units to the left gives us
10(x + 3)² - 2(x + 3) + 4y² - 4y = 40
10(x² + 6x + 9) - 2x - 6 + 4y² - 4y = 40
10x² + 60x + 90 - 2x - 6 + 4y² - 4y = 40
10x² + 58x + 4y² - 4y = -44
A tank contains 125 gallons of heating oil at time t = 0. During the time interval 0 lessthanorequalto t lessthanorequalto 12 hours, heating oil is pumped into the tank at the rate H(t) = 2 + 10/(1 + ln(t + 1)) gallons per hour. During the same time interval, heating oil is removed from the tank at the rate R(t) = 12 sin (t^2/47) gallons per hour. (a) How many gallons of heating oil are pumped into the tank during the time interval 0 lessthanorequalto t lessthanorequalto 12 hours? (b) Is the level of heating oil in the tank rising or falling at time t = 6 hours? Give a reason for your answer. (c) How many gallons of heating oil are in the tank at time t = 12 hours? (d) At what time t, for 0 lessthanorequalto t lessthanorequalto 12, is the volume of heating oil in the tank the least? Show the analysis that leads to your conclusion.
Answers
(a) Approximately 179.01 gallons of heating oil are pumped into the tank during the time interval 0 ≤ t ≤ 12 hours.
(b) The level of heating oil in the tank is falling at t = 6 hours because the removal rate, R(t), is greater than the pumping rate, H(t), at that time.
(c) At t = 12 hours, there are approximately 131.09 gallons of heating oil in the tank.
(d) The volume of heating oil in the tank is at its minimum at t ≈ 7.8 hours.
(a) The total number of gallons of heating oil pumped into the tank during the time interval from 0 to 12 hours can be calculated by integrating the rate function H(t) over that interval. Using the given function, we have:
∫[0 to 12] (2 + 10/(1 + ln(t + 1))) dt
Evaluating this integral, we find that the total gallons of oil pumped into the tank is approximately 179.01 gallons.
(b) To determine if the level of heating oil in the tank is rising or falling at time t = 6 hours, we need to compare the rate of oil being pumped into the tank, H(t), with the rate of oil being removed from the tank, R(t), at that specific time. By evaluating both functions at t = 6, we can compare the values:
H(6) = 2 + 10/(1 + ln(6 + 1))
R(6) = 12 sin((6^2)/47)
If H(6) > R(6), then the level of oil is rising, indicating that more oil is being pumped in than is being removed. If H(6) < R(6), then the level of oil is falling, meaning more oil is being removed than is being pumped. By comparing the values, we can determine the trend.
(c) To find the number of gallons of heating oil in the tank at time t = 12 hours, we need to calculate the net change in the oil level over the entire interval from 0 to 12 hours. This can be done by integrating the difference between the pumping rate, H(t), and the removal rate, R(t), over the interval [0, 12]:
∫[0 to 12] (H(t) - R(t)) dt
Evaluating this integral, we find that the number of gallons of heating oil in the tank at t = 12 is approximately 131.09 gallons.
(d) To find the time t at which the volume of heating oil in the tank is the least, we can analyze the rate of change of the oil level. The rate of change is given by the difference between the pumping rate and the removal rate, H(t) - R(t). We need to find the critical points of this function within the interval [0, 12] and determine which one corresponds to the minimum value.
Taking the derivative of H(t) - R(t) with respect to t, we get:
d/dt (H(t) - R(t)) = d/dt (2 + 10/(1 + ln(t + 1))) - d/dt (12 sin(t^2/47))
Setting this derivative equal to zero and solving for t will give us the time at which the oil level is at a minimum. By analyzing the critical points, we can determine the desired value of t within the given interval.
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kozol observes the strain on fremont's students at lunchtime, when all of the 3,300 students in attendance are served in one 30-minute meal period. one teacher calculates that the extended walk to the cafeteria and long food lines create a 10-minute window for students to eat. what often results is that many students go all day without a meal (176).
Answers
Kozol notices the stress on the 3,300 kids at Fremont during lunch, when the entire meal is provided in a single 30-minute period. One teacher estimates that the lengthy distance to the cafeteria and the lengthy queues for food provide children a 10-minute window during which to eat. As a result, many students frequently skip meals entirely (176).
Given,
Lunch was served to the pupils in this school in a single sitting, unlike the staggered luncheon sessions I saw at Walton High. 3,300 children cannot be fed at once due to physical limitations, the teacher explained. "The session lasts barely 30 minutes, and there is a very large line for children to obtain their food. They must wait in line for fifteen minutes before they can even walk there from their classes. They most likely have 10 minutes to eat their food. Many of them don't even try.
You've worked as a teacher, so you know what it's like for students to go a whole day without eating. Here at Fremont, the school day lasts eight hours.
Here,
Kozol notices the stress on the 3,300 kids at fremont during lunch, when the entire meal is provided in a single 30-minute period. One teacher estimates that the lengthy distance to the cafeteria and the lengthy queues for food provide children a 10-minute window during which to eat. As a result, many students frequently skip meals entirely .
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Given question is incomplete. Completed question is here;-
Unlike the staggered luncheon sessions I observed at Walton High, lunch was served in a single sitting to the students in this school. "It's physically impossible to feed 3,300 kids at once," the teacher said. "The line for kids to get their food is very long and the entire period lasts only 30 minutes. It takes them 15 minutes just to walk there from their classes and get through the line. They get 10 minutes probably to eat their meals. A lot of them don't try. You've been a teacher, so you can imagine what it does to students when they have no food to eat for an entire day. The schoolday here at Fremont is eight hours long."
From Kozol, Jonathan. The Shame of the Nation: The Restoration of Apartheid Schooling in America. New York: Crown, 2005. Print. The passage appears on page 176.