Answer:
1,576,800 minutes
Select the correct population parameter, null hypothesis, and alternative hypothesis., A nationwide poll revealed that 28% of teens said they seldom or never argue with their parents. Ralph wonders if this result would be different at his large high school, so he surveys a random sample of 175 students at his school.
The results from Ralph's survey are not statistically different from the national results.
Population Parameter: The percentage of teens who seldom or never argue with their parents in Ralph's large high school.
Null Hypothesis (H0): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is equal to the nationwide percentage of 28%.
Alternative Hypothesis (H1): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is not equal to the nationwide percentage of 28%.
H0: p = 0.28
H1: p ≠ 0.28
To calculate whether or not the results from Ralph's survey are significantly different from the national result, a one-sample z-test can be used. The z-score is calculated using the following formula: z = (x-µ)/(σ/√n). In this example, x is the sample proportion of teens who seldom or never argue with their parents (Ralph's survey), µ is the population proportion (the nationwide poll results of 28%), σ is the population standard deviation, and n is the sample size (175).
If the z-score is outside of the critical region, then it can be said that the results from Ralph's survey are statistically different from the national results. If the z-score is within the critical region, then it can be said that the results from Ralph's survey are not statistically different from the national results.
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Solve for x round to the nearest tenth
The solved for x round to the nearest tenth is x≈ 14.
What is meant by round ?
A spherical item. a circuitous or repetitive course; rounds in the hospital.A large-scale outburst at a gathering from a crowd of people.A song that is sung by multiple groups, each of which begins singing at a separate moment.Making a number simpler while maintaining a value that is close to what it was is known as rounding. Although less accurate, the outcome is simpler to utilize.For instance, 73 equals 70 when rounded to the closest 10, since 70 is closer to 73 than 80 is.Rounding numbers maintains the value of the original number while also making them "easier" to use or comprehend.Remember Sine of an angle is = opposite side /hypotenuse
So let the hypotenuse be x :
sin(54°) = opposite side / x
sin(54°) = 12 / x
To solve for x, divide sin(54°) by 12:
x = 12 / sin(54°)
x≈14
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Find the smallest integer n such that $$(x^2 + y^2 + z^2)^2 \leq n(x^4 + y^4 + z^4)$$ for all real numbers x, y, and z.
Using the expansion of inequality, The smallest integer , n is 3 .
What in math is an integer?
A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).
Integers include things like -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.
we have given in question that , n is an integer such that ,
(x²+y²+z²)²≤n(x⁴+y4⁴+z⁴)
Let us consider, a=x², b=y², and c=z² which are all nonnegative i.e a,b,c >0 , n>3 but we find least value of n
So, the above inequality become,
(a+b+c)² ≤ n (a²+b²+c²) ----(*)
by expanding both side of above equation we get, a² + b²+ c² + 2(ab + bc + ac) ≤n( a²+b²+c²)
2(ab + bc + ac) ≤ (n- 1) (a²+b²+c²)
=> (ab+bc+ac) ≤ (n- 1)/2 (a²+ b²+c²)
=> (xy)²+ (yz)²+(xz)²≤ (n-1)/2(x⁴+y⁴+z⁴)
If we put n=3− ∈ where ∈ >0 and x=y=z then
3 ≤ 2 or 1/2 which is wrong . Hence, the smallest value of n is 3.
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The complete question is -
Find the smallest integer n such that (x2+y2+z2)2≤n(x4+y4+z4)
for all real numbers x,y, and z.
A tumor is injected with 0.6
grams of Iodine-125, which has a decay rate of 1.15%
per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t
days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60
days.
Enter the exact answer.
Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*exp(h)
or c*ln(h)
.
Answer:
The exponential model representing the amount of Iodine-125 remaining in the tumor after t days would be:
Iodine-125(t) = 0.6 * e^(-0.0115t)
To find the amount of Iodine-125 that would remain in the tumor after 60 days, we would plug in t = 60 into the model:
Iodine-125(60) = 0.6 * e^(-0.0115(60))
= 0.6 * e^(-0.69)
= 0.6 * 0.5032
= 0.3019
So after 60 days, there would be approximately 0.3019 grams of Iodine-125 remaining in the tumor.
If I helped you, could you please make my answer best?
HELP PLEASE FAST!!!!!!!!
The value of x = 19 and the value of z = 70° in the figure given above.
How do you find the value of x and z?In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown.
" x is a variable in x + 2 = 7, but we can figure out its value if we try! A variable can be any letter, name, or symbol; it doesn't have to be "x"; examples include "y" and "w." Z-scores are calculated using the formula z = (x-)/, where x represents the raw score, the population mean, and the population standard deviation.
The z-score is simply the raw score less the population mean, divided by the population standard deviation, as the calculation demonstrates. A raw score's position relative to its distance from the mean is described by the z-score.
Using The property Vertically opposite angles are equal
110° = 9x - 61
⇒ 9x = 110 +61
⇒ 9x = 171
⇒ x = 171/9
⇒ x = 19
As all angles equal 360°
110° + 110° + 2z = 360°
⇒ 2z = 360° - (110° + 110°)
⇒ 2z = 140
⇒ z = 140/2
⇒ z = 140/2
⇒ z = 70°
Thus, The value of x = 19 and the value of z = 70° in the figure given above.
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let s represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait. the random variable s follows a geometric distribution with mean 4.66. which of the following is a correct interpretation of the mean?
In repeated sampling from the S distribution, the mean of the values will be close to 4.66, which is the appropriate interpretation of the mean.
What is mean?The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a set of findings from a survey, experiment, or observational study. The average of a group of values is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Here,
The average of the values will be close to 4.66 in repeated sampling from the S distribution, which is the correct interpretation of the mean.
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When given a circle with a radius of 4, how do you find the following? explain why.
a. Diameter
b. Circumference
Answer:
Diameter is 8
Circumference is 8pi ~= 25.13
Step-by-step explanation:
The diameter is double the radius. So the given radius is 4 and double is 8.
The Circumference is given by C = pi•d or C = 2pi•r
Both of these equations will give the circumference.
C = pi•d
= pi•8
= 8pi ~= 25.13
OR
C = 2pi•r
= 2pi•4
= 8pi ~= 25.13
For finding the diameter, I multiply the radius by 2:
Diameter = 2 × radius
= 2 × 4
= 8
So the diameter is 8. As for the circumference, we can use two ways : either multiply pi times the diameter, or multiply 2 times pi times the radius.
The formulas are
C = πd and C = 2πr
To find the circumference, stick in 8 for d:
C = π × 8
C = 25.13 units
Suppose that a wholesaler expects that his monthly revenue, in dollars, for an electronic game will be R(x) = 170x -0.13x^2, 0 < x < 800 where x is the number of units sold. Find his marginal revenue and interpret it when the quantity sold is the following. (a) X = 200 $ Interpret the marginal revenue. O This is the additional revenue from the 201st unit. O This is the additional revenue from the 200th unit. O The sale of the 200th unit results in a loss of revenue of this amount O The sale of the 201st unit results in a loss of this amount. (b) 800 $ Interpret the marginal revenue. O This is the additional revenue from the 101st unit. O This is the additional revenue from the 200th unit. O The sale of the 101st unit results in a loss of this amount O The sale of the 800th unit results in a loss of revenue of this amount
The total monthly revenue when 200 units were sold is $28800 and the monthly revenue when 800 units were sold is $52800.
Given,
The equation for monthly revenue, [tex]R(x)= 170x - 0.13x^{2}[/tex] [tex](0 < x < 800)[/tex]
where [tex]x[/tex] is the number of units sold
(a) Total number of units sold, [tex]x = 200[/tex]
Monthly revenue, [tex]R(200)= 170x- 0.13x^{2}[/tex]
[tex]= 170*200 - 0.13*200^{2}[/tex]
[tex]= 34000 - 0.13* 40000[/tex]
[tex]= 34000 - 5200[/tex]
[tex]= 28800[/tex]
Hence , monthly revenue = $28800
(b) Total number of units sold, [tex]x = 800[/tex]
Monthly revenue, [tex]R(800)= 170x- 0.13x^{2}[/tex]
[tex]= 170*800 - 0.13*800^{2}[/tex]
[tex]= 136000 - 0.13*640000[/tex]
[tex]= 136000- 83200[/tex]
[tex]= 52800[/tex]
Hence , monthly revenue = $52800
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what is the length q and r
The correct order of bond lengths P, Q, and R in the above diagram is P > Q > R. The correct option is A.
What is the bond length?The bond length is the distance between the centers of two bound atoms. Consider the fact that a homonuclear diatomic molecule's bonded atoms are separated by half their element's atomic radius (sometimes referred to as the covalent or bonding atomic radius).
Less percentage of s character in a bond means the length of orbitals of the molecule is more, and also the bond length is more.
Therefore, the correct option is A. P > Q > R.
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The question is incomplete. Your most probably complete question is given below:
Which is the correct order of bond lengths P, Q, and R in the above diagram?
P > Q > R
R > Q > P
Q > P > R
Q > R > P
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds (Morningstar Funds500, 2008).\begin{matrix} \text{Type of Fund} & \text{Number of Funds} & \text{Total Return (\\\%)}\\ \text{Domestic Equity} & \text{9191} & \text{4.65}\\ \text{International Equity} & \text{2621} & \text{18.15}\\ \text{Specialty Stock} & \text{1419} & \text{11.36}\\ \text{Hybrid} & \text{2900} & \text{6.75}\\ \end{matrix}Type of FundDomestic EquityInternational EquitySpecialty StockHybridNumber of Funds9191262114192900Total Return (%)4.6518.1511.366.75a. Using the number of funds as weights, compute the weighted average total return for the mutual funds covered by Morningstar.b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return for Morningstar in part (a)? Discuss. What else might be used for weights?c. Suppose you had invested $10,000 in mutual funds at the beginning of 2007 and diversified the investment by placing$2000 in Domestic Equity funds, $4000 in International Equity funds,$3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio?
The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories.
a. The weighted average total return for the mutual funds covered by Morningstar is 9.20%.
This is calculated by taking the sum of the products of the total return and the number of funds for each of the four categories:
(4.65 * 9191) + (18.15 * 2621) + (11.36 * 1419) + (6.75 * 2900) / (9191 + 2621 + 1419 + 2900) = 9.20%
b. Yes, there is a difficulty associated with using the number of funds as the weights in computing the weighted average total return for Morningstar. This is because the number of mutual funds in each category can fluctuate over time, and thus, the weights used to calculate the average total return may not accurately reflect the true performance of the mutual funds.
An alternative to using the number of funds as weights would be to use the dollar amount invested in each type of mutual fund as the weight. This would give a more accurate representation of the performance of the mutual funds.
c. The expected return on the portfolio is 9.63%.
This is calculated by taking the sum of the products of the total return and the amount invested in each of the four categories:
(4.65 * 2000) + (18.15 * 4000) + (11.36 * 3000) + (6.75 * 1000) / (2000 + 4000 + 3000 + 1000) = 9.63%
The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories. However, using the number of funds as weights may not accurately reflect the true performance of the mutual funds, and an alternative would be to use the dollar amount invested in each type of mutual fund as the weight. The expected return on the portfolio is 9.63%, calculated by taking the sum of the products of the total return and the amount invested in each of the four categories.
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find the exact value of each of the remaining trigonometric functions of . rationalize denominators when applicable. cot
A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.
What is meant by trigonometric functions?A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.
A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms.
Given that sin theta = √3/√7
Opposite = √3
Hypotenuse = √7
Get the adjacent
Adj² = (√7)²-(√3)²
simplifying the above equation, we get
Adj² = 7-3
Adj² = 4
Adj = √4
Adj = 2
Cos theta = adj/hyp = 2/√7
csc theta = 1/sin theta = 1/(√3/√7) = √7/√3
sec theta = 1/cos theta = 1/(2/√7) = √7/2
tan theta = opp./adj = √3/2
cot theta = 1/tan theta = 1/(√3/2) = 2/√3
= 2√3/3
The complete question is:
Find the exact value of each of the remaining trigonometric functions of theta. Rationalize denominators when applicable.
sin theta [tex]$=\sqrt{\frac{3}{7}}$[/tex] given that theta is in quadrant I.
cos theta=
csc theta =
sec theta =
tan theta =
cot theta =
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Harry is a computer programmer and he earns £14 per hour Monday to Friday. If he works on a Sunday, he earns 1.75 times the hourly rate.What is his hourly rate on a Sunday
Answer:
$24.50
Step-by-step explanation:
hourly rate on Sunday is 1.75 times his normal hourly rate, that is
1.75 × $14 = $24.50
hourly rate on a Sunday is $24.50
the distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. suppose the company hires a 28th employee at a salary of $120,000. which of the following claims about the new salary distribution is supported?
The range is not likely to vary, which is one of the claims regarding the new salary distribution that is supported.
What is standard deviation?Standard deviation is significant because it facilitates comprehension of measurements when data is scattered. The data's standard deviation will increase in proportion to how widely spread the data is. How dispersed the data is is indicated by the standard deviation. Any distribution will have roughly 95% of its values within two standard deviations of the mean. A large standard deviation doesn't necessarily mean something is wrong; rather, it only indicates that the group under study has a lot of variety, according to Rumsey in Statistics for Dummies.Therefore,
Given that a small company's salary distribution of 27 employees has a mean of $35,000 and a standard deviation of $2,000,
When a highly unusual value, such as 120000, is taken into account for the 28th employee, we discover that the mean increases.
The new median would be the average of items 14 and 15, as the prior median was the 14th item. Thus, the median may alter.
Because the maximum has been raised up to 120000, the range will undoubtedly vary.
so that we can say
Range changes, median changes, and mean increases.
Thus, we determine that Option B is correct.
The complete question is:
The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th
28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?
The median is not likely to change. I
The range is not likely to change. II
The mean is likely to increase. III
A) I only
B) III only
C) I and II only
D) I and III only
E) I, II, and III
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Factorise all of the questions.
Please answer a b c and d and please give an explanation on how to work each question out! It would really help ! It’s very urgent ty
Answer:
a.x (x + 1)
b. 3x (1 - 3x)
c. 7x (x² - 5)
d. 4x² (x + 6).
find $53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} 1\frac{2}{3} \right)$. express your answer as a mixed number.
The result of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex] is[tex]$-56\frac{13}{20}$[/tex]
A mixed number is a combination of a whole number and a fraction, like [tex]3\frac{1}{2}[/tex], expressing numbers greater than one whole unit. It can be converted to an improper fraction.
To find the solution of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex]
We can first simplify the inner parenthesis
[tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right)=53\cdot(-1\frac{1}{10})=-53\frac{11}{10}$[/tex]
Then simplify the denominator, The denominator is the bottom part of a fraction, which represents the total number of parts in the whole. It is used to indicate the size of the fraction's unit or whole. It is also used to divide the numerator (top part of a fraction) by in order to determine the fraction's value.
[tex]$2\frac{3}{4} - 1\frac{2}{3} = \frac{11}{4} - \frac{5}{3} = \frac{44}{12} - \frac{20}{12} = \frac{24}{12} = 2$[/tex]
Now we can divide -53 and 11/10 by 2
[tex]$-53\frac{11}{10} \div 2 = -53\frac{11}{20} = -\frac{1133}{20} = -56\frac{13}{20}$[/tex]
So, the answer is [tex]$-56\frac{13}{20}$[/tex]
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a wooden deck of a house needs paint. the function C(n)=24n+5 represents the cost of painting the deck as a function of the number of cans of paint used.The function n(A)=A/6 represents the number of cans of paint needed as a function of area in square ft of the deck. Write a function for the cost of painting the deck as a function of the area in square ft of the deck.
Answer: C(n)=24n+5 =24
(A)=A/6 =0
Step-by-step explanation:
Isabella is an artist who normally purchases her spray fixative in 6 2/3 ounce cans. If the economy size contains 1 2/5 as much spray, how many ounces will it contain?
Using multiplication operation, the number of ounces of Isabella's spray fixative contained in the economy size is 9¹/₃ ounces.
What is multiplication operation?Multiplication operation is one of the four basic mathematical operations, including addition, division, and subtraction.
The multiplication operation involves the multiplicand multiplied by the multiplier, resulting in a product.
The multiplication operand is depicted using (x), (*), or (of).
The normal spray fixative purchased by Isabella = 6²/₃ = 6.667 ounces
The relative size of the economy can = 1²/₅ of 6²/₃ ounces
The number of ounces in the economy can = 9¹/₃ ounces (1²/₅ x 6²/₃)
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Pick three answers for this question
Answer:
HOPE THIS HELPS YOUStep-by-step explanation:
0.25 L = 250 mL
12 000mL = 12 L
5 L 400mL = 5400mL
An equilateral triangle has sides of length (3x+7). Find the perimeter of triangle.
The perimeter of the equilateral triangle which has sides of length (3x+7) is 9x+21.
What is equilateral triangle?A triangle's three sides and angles must be equal for it to be considered an equilateral triangle.
An equilateral triangle is also referred to as an equiangular triangle because it has angles that are each 60 degrees in length. Because its sides and angles are equal, the equilateral triangle is regarded as a regular polygon or triangle.
Depending on how many sides a triangle has, there are three different types. These triangles are equilateral, isosceles, and scalene.
In an equilateral triangles all sides are equal
so,
perimeter = 3x+7 + 3x+7 + 3x+7
perimeter = 9x+21
Thus, perimeter of the equilateral trinagle which has sides of lenght (3x+7) is 9x+21.
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Complete the missing values in the solution to the equation.
[tex] \tt \: 4x + y = 10 ---- eqⁿ[/tex]
[tex] \: [/tex]
-6 is already given ,
[tex] \: [/tex]
so , put the value of y = -6 in the given eqⁿ ~
[tex] \: [/tex]
[tex] \tt \: 4x + y = 10[/tex]
[tex] \: [/tex]
[tex] \tt \: 4x + (-6) = 10[/tex]
[tex] \: [/tex]
[tex] \tt \: 4x = 10 + 6[/tex]
[tex] \: [/tex]
[tex] \tt \: 4x = 16[/tex]
[tex] \: [/tex]
[tex] \tt \:x = \cancel \frac{16}{4} [/tex]
[tex] \: [/tex]
[tex] \underline{\boxed { \red{\tt \large \: x = 4}} { \green✓}}[/tex]
[tex] \: [/tex]
missing value is 4!
hope it helps! :)
what is the y-intercept in the following equation y=-4x-5
Answer:
y intercepts : (0, -5)
Step-by-step explanation:
hope it helps<3Answer:
(0,-5)
Step-by-step explanation:
Without changing the order of the numbers, write an expression that is equivalent to -3 - 6?
Answer:
-2
Step-by-step explanation:
x-2y+z=9
2x + 3y - 2z = -12
x+y=3z = - 13
Answer:
what to find in this question ?
The following frequency data shows the number of states, including the District of Columbia, that
favored each party in the presidential popular vote in 1976 and in 2012.
What percent voted Republican in 1976? What type of frequency is this?
In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.
1976: Republican: 43 states, District of Columbia; Democrat: 6 states
2012: Republican: 24 states, District of Columbia; Democrat: 26 states
In 1976, 43/49 (including the District of Columbia) states voted Republican, which is 87.76%. This is a relative frequency.
1. Calculating the total number of states and District of Columbia in 1976: 43 + 6 + 1 = 50.
2. Calculating the percentage of states voting Republican in 1976: 43/50 (including the District of Columbia) = 0.87 or 87.76%.
3. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.
In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency.
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DUE REALLY SOON SOMEONE PLEASE HELP ME WITH THIS!
Factor
Will mark the brainliest! thanks
By distributive property, the polynomial (3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v² is equivalent to polynomial (1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²).
How to use distributive property to factor a polynomial
In this problem we find a polynomial that must be simplified by means of algebra properties, especially by distributive property. First, write the entire polynomial:
(3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v²
Second, use distributive property to simplify the polynomial thrice:
(1 / 2) · (3 · u² · v⁴ - 2 · u³ · v⁵ + u⁴ · v²)
(1 / 2) · u² · (3 · v⁴ - 2 · u · v³ + u² · v²)
(1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²)
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A scale on a hiking map shows that
3
33 inches represents
1.25
1.251, point, 25 miles.
What number of inches on the map represent
10
1010 actual miles?
If 3 inches on the map represents 1.25 miles, we can use that proportion to find how many inches represents 10 miles.
3 inches / 1.25 miles = x inches / 10 miles
We can cross multiply and divide to find x:
x = (3 inches * 10 miles) / 1.25 miles
x = 24 inches
So on the map, 24 inches represent 10 actual miles.
There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple?
According to the information, the probability that the next pice of fruit out of the bag will be an apple is 0.66.
How to calculate the probability that the next piece of fruit out of the bag will be an apple?To calculate the probability that the next piece of fruit out of the bag will be an apple we have to perform the following mathematical operation:
We have to calculate how many fruits there are in the bag.
4 apples, 3 peaches, and 2 plums less 2 plums and 1 peach = 4 apples, 2 peaches.So, we have 4 apples and 2 peaches, so we have 6 fruits in total. Now, we have to divide the number each fruit in the bag by the total number of fruits as shown.
4 / 6 = 0.66
2 / 6 = 0.33
According to the above, the probability that the next pice of fruit out of the bag will be an apple is 0.66.
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The proportional relationship between the number of inches a candle has burned away, b, at any time in hours, t, can be represented by the equation b = 1.5tb=1.5t. At what rate does the candle burn, in inches per hour?
The rate at which the candle burns is 1.5 inches per hour.
At what rate does the candle burn, in inches per hour?We know that the proportional relation between the number of inches that the candle has burned away, b, and the time in hours, t, is:
b = 1.5*t
The rate at which the candle burns is the amount burned in one unit of time, in this case, hours, then:
So, after t = 1 (one hour)
b = 1.5
In one hour, the candle burns 1.5 inches.
That is the rate at which the candle burns, it should be written as:
rate = 1.5 inches burned per hour.
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Find the point (x, y) on the unit circle that corresponds to the real number t. t = 7/4
The point on the unit circle that corresponds to the real number t = 7/4 is given as follows:
(-0.1782, 0.9840).
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
With parameter t, the coordinates of the point are given as follows:
(cos(t), sin(t)).
Hence the x-coordinate when t = 7/4 is given as follows:
cos(7/4) = -0.1782.
The y-coordinate when t = 7/4 is given as follows:
sin(7/4) = 0.9840.
Meaning that the coordinates are:
(-0.1782, 0.9840).
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