Answer:
The mean of the sampling distribution of the sample mean for the three observations each day is 132.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 132
Standard Deviation, σ = 5
Each observation behaves as a random sample.
a) Mean of the sampling distribution
[tex]\bar{x} = \mu = 132[/tex]
b) Standard deviation of the sampling distribution
Sample size,n = 3
[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{5}{\sqrt{3}} = 2.887[/tex]
Thus, the mean of the sampling distribution of the sample mean for the three observations each day is 132.
42. Which matrix represents the image of the triangle with vertices at (-2,0), (1,5), and (4,-8) when dilated by a scale factor of 3?
The second matrix [tex]\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex] represents the triangle dilated by a scale factor of 3.
Step-by-step explanation:
Step 1:
To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.
The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.
Step 2:
If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get
[tex]\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right][/tex]
The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.
Step 3:
The matrix that represents the triangle after dilation is given by
[tex]3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex]
This is the second option.
Which of the following is the cheapest route to visit each city using the "Brute Force Method" starting from A and ending at A.
Group of answer choices
ABCDA, $960
ACDBA, $900
ACBDA, $960
None of the Above
Answer:
ACDBA, $900
Step-by-step explanation:
The cheapest route will be the one with the lowest cost. Of the routes listed, the cost $900 is the lowest, so route ACDBA is the cheapest.
_____
The "Brute Force Method" requires you compute the costs of the possible routes and pick the lowest. The answer choices have done that for you.
The cost of ACDBA is AC +CD +DB +BA = 240 +230 +210 +220 = 900, as shown in the answer selections.
The three routes listed, and their reverses (which are the same cost), are the only possible routes starting and ending at A.
Nathaniel and Grant go to the movie theater and purchase refreshments for their friends . Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars. Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars. You may use decimals for this problem.
Answer:
A candy costs $6.75 and a bag of popcorn costs $7.25
Step-by-step explanation:
Let the cost of one 1 candy=$x
Let the cost of one bag of popcorn=$y
Now, Total Cost Per Item=Number of Item Bought X Price Per Unit Item.
If Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars.
4x+10y=99.50
Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars.
3x+5y=56.50
Solving the two equations simultaneously
4x+10y=99.50 (I)
3x+5y=56.50 (II)
Multiply Equation (I) by 3 and Equation (II) by 4 to eliminate x
12x+30y=298.5
12x+20y=226
Subtracting
10y=72.5
y=$7.25
Now, from (II)
3x+5y=56.50
3x+5(7.25)=56.50
3x+36.25=56.50
3x=20.25
x=20.25/3=$6.75
Therefore a candy costs $6.75 and a bag of popcorn costs $7.25
Answer:
candy costs - $6.75
a bag of popcorn costs - $7.25
Step-by-step explanation:
Which of the following functions have the ordered pair (2, 5) as a solution?
x + 3 = y
7 - x = y
4 + x = y
y = 2 x
Answer:
x + 3 = y and 7 - x = yStep-by-step explanation:
Put the value of x = 2 and the value of y = 5 from the given point to the equations and check the equality.
x + 3 = y
2 + 3 = 5
5 = 5 CORRECT
7 - x = y
7 - 2 = 5
5 = 5 CORRECT
4 + x = y
4 + 2 = 5
6 = 5 FALSE
y = 2x
5 = 2(2)
5 = 4 FALSE
Answer:
y 2x
Step-by-step explanation:
A group of 200 workers 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the --workers selected to participate in the survey.The population consist of-workers
Answer:
Sample=15 Workers
Population=200 Workers
Step-by-step explanation:
Out of a group of 200 workers, 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the 15 workers selected to participate in the survey.The population consist of 200 workers
SAMPLE: This is a representative part of a population on which a research is about the population is administered
POPULATION: This is the large collection of people or objects that is the focus of a scientific query or research. Often times, the logistics involved in reaching the entire population may be unavailable, so a sample is taken
Final answer:
A group of 200 workers is the population of interest for a survey, and 15 are chosen as a sample to determine the number of miles driven to work each week. The sample represents the subset from which data is collected, while the population encompasses all 200 workers. The effectiveness of the survey depends on the representativeness of the sample.
Explanation:
In the situation described, a group of 200 workers is the overall group of interest for a survey about the number of miles they drive to work each week. Out of these, 15 workers are chosen to participate in the survey. Here, the sample consists of the 15 workers selected to participate in the survey, whereas the population consists of all 200 workers. Sampling is a critical concept in statistics that allows researchers to gather data from a subset of individuals from a larger group to make inferences about the entire group without the need to analyze every individual.
The success of a statistical analysis mainly depends on how well the sample represents the population. In an ideal scenario, a random sample is preferred, where every person in the population has an equal chance of being chosen. This method helps ensure that the sample is representative of the population, allowing findings from the sample to be reasonably generalized to the larger group.
A company that manufactures flash drives knows that the number of drives x it can sell each week is related to the price
p, in dollars, of each drive by the equation x=1500−100p. a. Find the price p that will bring in the maximum revenue. Remember, revenue (R) is the product of price (p) and items sold (x), in other words, R=xp.
The price $____
will yield the max revenue.b. Find the maximum revenue.
The max revenue is $_____
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Answer:
$7.50$5625Step-by-step explanation:
Use the given equation, and use your understanding of quadratic functions to reason about the solution.
R = xp
R = (1500 -100p)p . . . . . substitute the given expression for x
This is q quadratic function in p. It has zeros where p=0 and p=15. (These are the values that make the factors be zero.) We know this function has a maximum (because we're told to find it, and because p^2 has a negative coefficient). That maximum is the vertex of the parabola, which is located on the line of symmetry, halfway between the zeros.
The maximum revenue is obtained when p = (0+15)/2 = 7.5. That value of revenue is R = (1500 -100·7.5)(7.5) = 5625.
The price $7.50 will yield the maximum revenue, $5625.
To find the price that will bring in the maximum revenue, substitute the given equation for x into the revenue equation. Use calculus to find the value of p that yields the maximum revenue. Substitute the value of p into the revenue equation to find the maximum revenue.
Explanation:To find the price that will bring in the maximum revenue, we need to determine the value of p that maximizes the revenue function R = xp. We can substitute the expression for x into the revenue function to get R = (1500 - 100p)p. To find the p that yields the maximum revenue, we can use calculus by finding the critical points of the revenue function. Taking the derivative and setting it equal to zero, we can solve for p. After finding the value of p, we can substitute it back into the revenue function to find the maximum revenue.
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In 2/3 Of a minute aaron 5 Liter mountain bike tire loss 8/9 of a liter of air is the tie continues to lose air at this rate how long will it take for the tire to be completely flat
Answer:
3.75 minutes
Step-by-step explanation:
For every 2/3 minutes, Aaron's Tire loses 8/9 of a liter of air
Total Volume of Air in the Tyre = 5 liters
Now, we divide the total volume by volume of air lost every stated interval to know how many air loss it will take the Tyre to be empty
[tex]\dfrac{5}{8/9} =\dfrac{5X9}{8} =\dfrac{45}{8}[/tex]
Then, to get when the tire will be completely flat in:
[tex](\frac{2}{3}X\frac{45}{8}) minutes[/tex]=3.75 minutes=3 minutes 45 seconds
The tyre will be empty in 3 minutes 45 seconds
Mr. Couch noticed that one of his students was having trouble following directions during direct teach in his math class. He decided to take baseline data. How much time should he spend taking baseline data
Answer:
c. 3 to 5 observation periods
Step-by-step explanation:
The time that should he spend taking baseline data is 3 to 5 observation periods. The correct option is C).
What is baseline data?Data that analyzes conditions before the project begins for subsequent comparison is known as baseline data (or simply baseline). In other words, the baseline serves as the previous point of comparison for the subsequent project monitoring and assessment phases.
For instance, a business can use the number of units sold in the first year as a benchmark against which to compare subsequent annual sales in order to assess the success of a product line. The baseline acts as the benchmark against which all subsequent sales are evaluated.
The performance measurement baseline is the result of combining the three baselines. A baseline is a set timeline that serves as the benchmark against which the project's performance is evaluated.
Therefore, the correct option is C) 3 to 5 observation periods.
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The question is incomplete. Your most probably complete question is given below:
A) 30 minutes
B) 10 observation periods
C) 3 to 5 observation periods !!
D) immediately
Find the average rate of change for f(x) = x2 + 7x + 10 from x = −20 to x = −15.
Answer:
Step-by-step explanation:
This is a parabola. The only way you could find the actual rate of change at those x values is by finding the instantaneous rate of change at each of those points which requires calculus. The average rate of change is found when you find the slope of the line between the 2 points (-20, y) and (-15, y). To find y in each case, sub in the x values and solve for y:
[tex]f(-20)=(-20)^2+7(-20)+10[/tex] and
f(-20) = 270 and the resulting coordinate is (-20, 270).
Likewise for f(-15):
[tex]f(-15)=(-15)^2+7(-15)+10[/tex] and
f(-15) = 130 and the resulting coordinate is (-15, 130)
Applying the slope formula now will find the average rate of change between those 2 points:
[tex]m=\frac{130-270}{-15-(-20)}[/tex] which simplifies to
[tex]m=\frac{-140}{5}[/tex] so
m = -28
Very urgent.... Anyone please help me..
I need it with explanation!
Answer:
P(y) = 0.005y² -10y -10000003,200,000Step-by-step explanation:
a) Profit is the difference between revenue and cost.
P(y) = R(y) -C(y)
P(y) = (0.005y² +10y) -(20y +1000000) . . . . use the functions for revenue and cost
P(y) = 0.005y² -10y -1000000 . . . . . profit as a function of y
___
b) Evaluating this function for y=30,000, we get ...
P(30000) = 0.005(30000)² -10(30000) -1000000
= 3,200,000
The company will have a profit of 3,200,000 from the sale of 30,000 cars.
Graph the function f(x)=|x+1|+2. List the following values:a = __________. h = __________. k = __________. Vertex = ______
Answer:
a = 1
h = -1
k = 2
Vertex: (-1,2)
It's a V-shaped graph completely above the x-axis.
Vertex at (-1,2) and y-intercept at 3
For the function f(x)=|x+1|+2, a = 1, indicating no vertical stretch or compression and upward direction, h = -1 indicating a shift one unit to the left, and k = 2 indicates a shift two units up. The vertex of the function is at point (-1,2).
Explanation:The function f(x)=|x+1|+2 is a transformation of the base absolute value function |x|. Here, the 'a' refers to the vertical stretch/compression and reflection, 'h' refers to the horizontal shift, and 'k' refers to the vertical shift. The absolute value function is in the form f(x) = a|x-h|+k. For this specific function, a = 1 since the graph opens upward and is not stretched or compressed, h = -1 because the function is shifted 1 unit to the left, and k = 2 because the function is shifted 2 units up. As the vertex of an absolute value function is the point of its highest or lowest value, the vertex in this case is the point (-1,2).
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PLEASE ANSWER! WILL GIVE MANY POINTS
A zero gravity chamber simulates the weightlessness that astronauts experience in space. Which of the following will most likely happen to a person inside a zero-gravity chamber?
The person will feel energetic because the heart rate will increase.
The heart rate will slow down because the blood vessels will have less blood to circulate.
The person will feel dizzy because the heart will pump less blood per beat.
The heart will pump less blood per beat because the blood vessels will have less blood to circulate.
Answer:
The person will feel dizzy.
Answer:
Step-by-step explanation:
The person will feel energetic because the heart rate will increase. ... The heart will pump less blood per beat because the blood vessels will have less blood to circulate.
if a triangle has lengths of 27 m and 11 m, check all the possible lengths for the third side
The possible length of the third side of a triangle with sides of 27 m and 11 m, as per the Triangle Inequality Theorem, ranges between 16 m and 38 m.
Explanation:In mathematics, the possible length of the third side of a triangle, given the other two sides, is determined using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute value of the difference between those two sides.
Given side lengths of 27 m and 11 m, the possible length of the third side (let's call it 's') is between 27 m - 11 m and 27 m + 11 m.
Therefore, s > 16 m and s < 38 m. So, any value between 16 m and 38 m could be the length of the third side of the triangle.
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Give the values of a, b, and c from the general form of the equation (2x + 1)(x - 2) = 0.
a=2, b=-3, c= -2
a=2, b=5, C=-2
a=3, b=1, c= -1
[tex](2x+1)(x-2) = 0[/tex]
Multiplying the factors we obtain:
[tex]2x\cdot x+2x\cdot (-2)+1\cdot x+1\cdot (-2)=0[/tex]
[tex]2x^2-4x+x-2=0[/tex]
[tex]2x^2-3x-2=0[/tex]
The general form of quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
Therefore,
[tex]a=2[/tex]
[tex]b=-3[/tex]
[tex]c=-2[/tex]
The correct answer is the first one.
Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 4000/3∗π in3 . One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping. Hint: you may need to find the volume for both. One cup has a diameter of 4 in. And a height of 8 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work. One cup has a diameter of 8 in. And a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work. Answer:
Answer:
1. Carissa must scoop out of the sink 125 cups of water with the first cup to empty it.
2. Carissa must scoop out of the sink 31 cups of water with the second cup to empty it.
Step-by-step explanation:
1. Let's calculate the volume of the first cup, this way:
d = 4 ⇒ r =2
Volume of the first cup = π * r² * h /3
Volume of the first cup = π * 2² * 8 /3
Volume of the first cup = 32/3π in³
2. Let's calculate the volume of the second cup, this way:
d = 8 ⇒ r = 4
Volume of the second cup = π * r² * h /3
Volume of the second cup = π * 4² * 8 /3
Volume of the second cup = 128/3π in³
3. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the first cup to empty it, as follows:
Number of cups = Volume of the sink/Volume of the first cup
Number of cups = (4000π/3)/(32π/3)
Number of cups = 4,000π/3 * 3/32π (multiplying by the reciprocal)
We eliminated 3 and π in the numerator and denominator
Number of cups = 4,000/32 = 125
4. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the second cup to empty it, as follows:
Number of cups = Volume of the sink/Volume of the second cup
Number of cups = (4000π/3)/(128π/3)
Number of cups = 4,000π/3 * 3/128π (multiplying by the reciprocal)
Number of cups = 4,000/128 = 31.25
We eliminated 3 and π in the numerator and denominator
Number of cups = 31 (rounding to the next whole)
Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. A) Find the expected number of games that are played when (a) i= 2 and (b) i= 3. B) Find P(X = 4).
Answer:
Step-by-step explanation:
Please look at the 2 photos below, they may be your correct answers.
Mr. Davis borrowed $600 for 60 days at 9% annual interest. However he was able to repay the loan in 30 days. How much interest was he able to save by doing this?
Answer:
Thus he was able to save 4.438 dollars by paying 30 days before due.
Step-by-step explanation:
given that Mr. Davis borrowed $600 for 60 days at 9% annual interest.
Thus interest payable for 60 days = [tex]\frac{600*60*9}{365*100} \\=8.876[/tex]
Because he paid fully after 30 days his interest would have been only for 60 days
or half of interest for 60 days
So savings of interest = 50% of 8.876
=4.438 dollars
Thus he was able to save 4.438 dollars by paying 30 days before due.
Find an equation for the nth term of the arithmetic sequence.
-17, -13, -9, -5, ...
an = -17 + 4(n + 2)
an = -17 x 4(n - 1)
an = -17 + 4(n - 1)
an = -17 + 4(n + 1)
Answer:
it would be the the third one an=-17+4(n-1)
Step-by-step explanation:
i don't know the step by step explanation but if you were to like plug in, it checks.
Answer: an = - 17 + 4(n - 1)
Step-by-step explanation:
In an arithmetic sequence, the consecutive terms differ by a common difference.
The formula for determining the nth term of an arithmetic sequence is expressed as
an = a + d(n - 1)
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = - 17
d = - 13 - - 17 = - 9 - - 13 = 4
Therefore, the equation for the nth term of the arithmetic sequence is
an = - 17 + 4(n - 1)
Decide whether the relation defines a function.
{(-3, -2), (3, 6), (4, 6), (7, -7), (10, -1)}
A.Function
B.Not a function
This is a function because each input (x-value) has only one output (y-value). If an input (x-value) has more than one output (y-value) it is not a function. It is still a function if an output has more than one input.
Your answer is A
Which two values of x are roots of the polynomial below?
x2 + 3x + 5
Answer:
The answer to your question is below
Step-by-step explanation:
Data
x² + 3x + 5
Factor
- Solve using the formula
x = -b ±[tex]\sqrt{b^{2} -4 ac} / 2a[/tex]
- Substitution
x = -3 ± [tex]\sqrt{3^{2} - 4(1)(5)} /2[/tex]
- Simplification
x = -3 ± [tex]\sqrt{9 - 20} / 2[/tex]
x = -3 ± [tex]\sqrt{-11} / 2[/tex]
- Result
x₁ = -3+[tex]\sqrt{11} i / 2[/tex] x₂ = - 3 - [tex]\sqrt{11} i[/tex] / 2
The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting three girls and one boy (in any order ).
Answer:
¼
Step-by-step explanation:
BBBB
GGGG
BBBG
BBGB
BGBB
GBBB
GGGB
GGBG
GBGG
BGGG
BBGG
GGBB
GBGB
BGBG
GBBG
BGGB
3G and 1B
4/16 = 1/4
Using probability and sample space concepts, it is found that there is a 0.25 = 25% probability of getting three girls and one boy (in any order ).
-------------------------
The sample space is the set that contains all possible outcomes.A probability, calculated from a sample space, is the number of desired outcomes in the sample space divided by the number of total outcomes.-------------------------
For 4 children, the sample space is given by:
B - B - B - B
B - B - B - G
B - B - G - B
B - B - G - G
B - G - B - B
B - G - B - G
B - G - G - B
B - G - G - G
G - B - B - B
G - B - B - G
G - B - G - B
G - B - G - G
G - G - B - B
G - G - B - G
G - G - G - B
G - G - G - G
-------------------------
There are 16 outcomes.In 4, that are B-G-G-G, G-B-G-G, G-G-B-G and G-G-G-B, there are 3 girls and one boy.Thus:
[tex]p = \frac{D}{T} = \frac{4}{16} = 0.25[/tex]
0.25 = 25% probability of getting three girls and one boy (in any order ).
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Select the values of xxx that make the inequality true. x>\dfrac 12x> 2 1 x, is greater than, start fraction, 1, divided by, 2, end fraction Choose 2 answers: Choose 2 answers: (Choice A) A 2\dfrac132 3 1 2, start fraction, 1, divided by, 3, end fraction (Choice B) B 000 (Choice C) C -1\dfrac 12−1 2 1 minus, 1, start fraction, 1, divided by, 2, end fraction (Choice D) D 111 (Choice E) E -\dfrac34− 4 3 minus, start fraction, 3, divided by, 4, end fraction Report a problem 10 of 20
The values of x that make the inequality x > 1/2 true are Choice A (2 1/3) and Choice D (1).
Explanation:The inequality x > 1/2 means that we are looking for any values of x that are greater than 1/2. Looking at our choices, Choice A (2 1/3) and Choice D (1) are correct since these values are greater than 1/2. Choices B (0), C (-1 1/2) and E (-3/4) are all less than 1/2, so they do not make the inequality true.
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Can you help with this one? Given m = -1/5 and the point (1, 2), which of the following is the point-slope form of the equation?
y + 1 = -1/5(x + 1)
y + 2 = 1/5(x - 1)
y - 2 = -1/5(x - 1)
y + 2 = -1/5(x + 1)
Answer:
Its c because im quad-RAD-ic... PERIOD LUV
The voltage across the capacitor increases as a function of time when an uncharged capacitor is placed in a single loop with a resistor and a battery.
What mathematical function describes this behavior?
1. Exponential2. Linear 3. Quadratic 4. Power
Answer:
1. Exponential
Step-by-step explanation:
The simplest RC-Circuit, that is, a capacitor and a resistor in a series configuration can be modeled by using Ohm's Law and Kirchhoff's Circuit Laws:
[tex]C \cdot \frac{dV}{dt} + \frac{V}{R} = 0[/tex]
By rearranging the formula, an homogeneous linear first-order differential equation is found:
[tex]\frac{dV}{dt} + \frac{1}{R \cdot C} \cdot V = 0[/tex]
Whose solution has the form of a exponential model:
[tex]V(t) = V_{o} \cdot e^{-\frac{t}{R \cdot C} }[/tex]
HELP ASAP!! Write the direct variation function given that y varies directly with x, and y = 16 when x = 4.
Answer:
Step-by-step explanation:
X and y =4 so X+y is gonna be 4 X+y+16= and 16 times 4 is 64 so the answer is 64
Answer:
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.
Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes
y = kx
If y = 16 when x = 4, then
16 = 4k
k = 16/4 = 4
Therefore, the direct variation function is
y = 4x
Angle α lies in quadrant II , and tan α = [tex]-\frac{12}{5}[/tex] . Angle β lies in quadrant IV , and cosβ=3/5 .
What is the exact value of sin(α+β) ?
Enter your answer in the box.
sin(α+β) =
Since [tex]\alpha[/tex] lies in quadrant II and [tex]\beta[/tex] lies in quadrant IV, we expect [tex]\sin\alpha>0[/tex], [tex]\cos\alpha<0[/tex], and [tex]\sin\beta<0[/tex].
Recall the Pythagorean identities,
[tex]\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x[/tex]
It follows that
[tex]\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}[/tex]
[tex]\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}[/tex]
[tex]\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45[/tex]
Recall the angle sum identity for sine:
[tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha[/tex]
So we have
[tex]\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}[/tex]
The value of sin(α+β) is 56/65
Trigonometry identityGiven the following parameters
tan α = -12/5 = opposite/adjacent
Determine the hypotenuse using Pythagoras theorem:
hyp² = 12² + 5²
hyp² = 144 + 25
hyp² = 169
hyp = 13
Determine the value of sin α and cos α
sin α = opp/hyp
sin α = 12/13
cos α = adj/hyp = -5/13
Similarly if cosβ=3/5 = adj/hyp
opp^2 = 5^2 - 3^2
opp^2 = 16
opp = 4
sin β = opp/hyp = -4/5
Determine the value of sin(α+β)
sin(α+β) = sinαcosβ + cosαsinβ
sin(α+β) = 12/13(3/5) + (-5/13)(-4/5)
sin(α+β) = 56/65
Hence the value of sin(α+β) is 56/65
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The average (arithmetic mean) of three positive numbers is 10. One of the numbers is 12. The product of the other two numbers is 32. What is the greatest of the three numbers?
Answer:
16
Step-by-step explanation:
Let x and y be two numbers other than 12.
We have been given that the average (arithmetic mean) of three positive numbers is 10. We can represent this information in an equation as:
[tex]\frac{x+y+12}{3}=10[/tex]
We are also told that the product of the other two numbers is 32. We can represent this information in an equation as:
[tex]x\cdot y=32...(2)[/tex]
[tex]x=\frac{32}{y}[/tex]
Upon substituting this value in above equation, we will get:
[tex]\frac{\frac{32}{y}+y+12}{3}=10[/tex]
[tex]\frac{\frac{32}{y}\cdot y+y\cdot y+12\cdot y}{3}=10\cdot y[/tex]
[tex]\frac{32+y^2+12y}{3}=10y[/tex]
[tex]\frac{32+y^2+12y}{3}\cdot 3=10y\cdot 3[/tex]
[tex]32+y^2+12y=30y[/tex]
[tex]y^2+12y-30y+32=30y-30y[/tex]
[tex]y^2-18y+32=0[/tex]
[tex]y^2-16y+2y+32=0[/tex]
[tex]y(y-16)-2(y-16)=0[/tex]
[tex](y-16)(y-2)=0[/tex]
[tex]y=2, 16[/tex]
Since product of 2 and 16 is 32, therefore, the greatest of the three numbers would be 16.
Answer:
The greatest of the three number is 16.
Step-by-step explanation:
We are given the following in the question:
Let x and y be the two numbers.
[tex]\text{Mean} = \dfrac{12+x+y}{3} = 10\\\\12 + x + y = 30\\x + y = 18[/tex]
Also
[tex]xy = 32[/tex]
Puting values, we get,
[tex]x(18-x) = 32\\-x^2 + 18x - 32 = 0\\x^2 - 18x + 32 = 0\\(x-16)(x-2) = 0\\x = 16, x = 2[/tex]
When x = 16, y = 2
When x = 2, y = 16
Thus, the greatest of the three number is 16.
A tank of liquid has both an inlet pipe allowing liquid to be added to the tank and a drain allowing liquid to be drained from the tank.
The rate at which liquid is entering the tank through the inlet pipe is modeled by the function i(x)=3x^2+2 , where the rate is measured in gallons per hour. The rate at which liquid is being drained from the tank is modeled by the function d(x)=4x−1 , where the rate is measured in gallons per hour.
What does (i−d)(3) mean in this situation?
There are 18 gallons of liquid in the tank at t = 3 hours.
The rate at which the amount of liquid in the tank is changing at t = 3 hours is 40 gallons per hour.
There are 40 gallons of liquid in the tank at t = 3 hours.
The rate at which the amount of liquid in the tank is changing at t = 3 hours is 18 gallons per hour.
Answer:
Correct answer: First answer is true
Step-by-step explanation:
Where x is independently variable and refers to the elapsed time and
( i-d )(x) is a function or dependent variable and shows the number of gallons during that time.
f (x) = ( i-d )₍ₓ₎ = 3 x² + 2 - ( 4 x - 1) = 3 x² - 4 x + 3
( i-d )₍ₓ₎ = 3 x² - 4 x + 3
( i-d ) (3) = 3 · 3² - 4 · 3 + 3 = 27 - 12 + 3 = 18
( i-d ) (3) = 18 gallons after 3 hours in the tank
God is with you!!!
There are 18 gallons of liquid in the tank at t = 3 hours
How to elaborate the problem ?
The liquid tank has both an inlet pipe to add liquid and a drain pipe to drain liquid from the tank.
The modeled function of inlet pipe = i(x) = 3[tex]x^{2}[/tex]+2
The modeled function of drain pipe = d(x) = 4x-1 ,
where the rate is measured in gallons per hour in both functions.
What is the correct option ?(i-d)(x) = 3[tex]x^{2}[/tex]+2-(4x-1)
⇒ (i-d)(x) = 3[tex]x^{2}[/tex]+2-4x+1
⇒ (i-d)(x) = 3[tex]x^{2}[/tex]-4x+3
⇒ (i-d)(3) = 3×[tex]3^{2}[/tex]-4×3+3
⇒ (i-d)(3) = 27-12+3
⇒ (i-d)(3) = 18
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What is the purpose of a proof in Geometry? What is structure of a proof in Geometry?
Geometry (like any other branch of math) starts from a set of statements that we assume to be true, which we call axioms.
Then, we declare some rules that allow us to deduce true things from true things. For example, syllogism is one of this rules. So, if we know that [tex]A[/tex] is true, and it is also true that [tex]A\implies B[/tex], then we're allowed to deduce that [tex]B[/tex] is true as well.
So, the purpose of a proof is to show that a certain statement is true.
In its structure, you'll always start from some true facts, and you'll deduce new true facts by using allowed deductive methods.
In Geometry, a proof is used to demonstrate the validity of a statement or theorem. A proof consists of a statement, diagram, given conditions, logical reasoning, and a conclusion. It provides a convincing and rigorous argument.
Explanation:Purpose of a proof in Geometry
In Geometry, a proof is used to demonstrate the truth or validity of a statement or theorem. It provides a logical and systematic argument, using previously established statements (called axioms or postulates) and mathematical reasoning, to support the conclusion.
The main purpose of a proof is to build a convincing and rigorous argument, ensuring that the result can be trusted and applied in various mathematical contexts.
Structure of a proof in Geometry
A proof in Geometry typically consists of several components:
Statement: Start by clearly stating the theorem or statement to be proven.Diagram: Create a visual representation of the given information, including any relevant figures or shapes.Given: List the known information or conditions that are given in the problem.Proof: Utilize logical reasoning, postulates, theorems, and previously established facts to logically progress through the argument, step-by-step. Each step must be justified and clearly explained.Conclusion: Restate the theorem or statement and conclude that it has been proven based on the preceding logical steps.Bella earned the federal minimum wage in the year 2008. During that time, she worked 37.5 hours per week. How much money did she earn each week she worked in the year 2008? Round your answer to the nearest cent, Show your work.
Answer:
Belle's weekly earnings per week in 2008: $245.7
Step-by-step explanation:
The federal minimum wage in the year 2008 was: $6.55
She worked 37.5 hours per week.
She earn each week:
[tex]weekly earnings = 6.55*37.5=245.7[/tex]
Step-by-step explanation:
Below is an attachment containing the solution.