Answer:
Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark.
Answer:
b m d j and k z y a
Step-by-step explanation:
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
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
How do I calculate the distance between these two lines?
Y=-2/3x - 1/2 and Y=-2/3 + 1/5 using the dist formula
|Ax + By +C| / root of a^2 + b^2
Answer:
d = (21√13)/130 ≈ 0.582435
Step-by-step explanation:
First of all, you need to put one of the equations into general form (Ax +By +C = 0), so you can make use of the formula. Multiplying the first equation by 6, we have ...
6y = -4x -3
Adding the opposite of the right side, we have the general form equation ...
4x +6y +3 = 0
___
The distance formula will tell you the distance from this line to any point. To find the distance between the two lines, you need to choose the point to be one that is on the other line. It is probably convenient to use the y-intercept, (0, 1/5).
The formula is ...
d = |4x +6y +3|/√(4²+6²)
The distance from the point (0, 1/5) is ...
d = |4·0 +6(1/5) +3|/√52 = 4.2/(2√13)
d = (21/130)√13 . . . . . with denominator rationalized
_____
Alternate solution
Another way to do this is to put the equations of both lines into the same general form, differing only in their constant "C".
Multiplying both equations by 30, we get ...
30y = -20x -15
30y = -20x +6
So, the two general form equations are ...
20x +30y +15 = 0
20x +30y -6 = 0
The distance between the two lines is a fraction of the difference of the constants in the equations*. It will be ...
|15 -(-6)|/√(20² +30²) = 21/√1300 = 21/(10√13) = (21√13)/130 . . . . as above
___
* Any (x, y) pair that satisfies the first equation will make 20x+30y = -15. Using the second equation in the distance formula, you then have |-15-6|/√( ) = d. The number in the numerator is the difference of the two constants "C".
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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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)
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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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.
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.
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.
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
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
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:
SIMPLY FIND THE DERIVATIVE. I'M LAZY.
d/dx(2x^4-6x^2)^3=[](2x^4-6x^2)^[]([]x^[]+[]x)
FILL IN THE BLANKS
Answer:
3, 2, 8, 3, -12
Step-by-step explanation:
d(2x⁴ - 6x²)³/dx
= 3(2x⁴ - 6x²)²(8x³ - 12x)
Answer: 3, 2, 8, 3, -12
Step-by-step explanation:
To find the derivative using the chain rule, multiply by the exponent and the reduce the exponent by 1. Then multiply by the derivative of the inside (of the parenthesis).
3(2x⁴ - 6x²)² (4·2x³ - 2·6x)
= 3(2x⁴ - 6x²)² (8x³ - 12x)
The blanks from left to right are:
3
2
8
3
-12
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)
49, 34, and 48 students are randomly selected from the Sophomore, Junior, and Senior classes (all classes) with 496, 348, and 481 students respectively. Identify the type of sampling used.
Answer:
It is Random sampling.Step-by-step explanation:
There are total 5 types of sampling.
Random Sampling: In this kind of sampling, elements are randomly chosen from a particular population. Every elements of the population carries the same probability in this case.Systematic Sampling: Every k-Th element is taken for this kind of sampling.Convenience Sampling: Here samples are chosen as per the accessibility.Cluster Sampling: First the whole population is divided in some groups or cluster, then some groups are randomly selected.Stratified Sampling: The whole population is being divided into groups as per some characteristic. Then from each group, one sample is to be chosen either randomly or using some other process.Since, in the given question the students are chosen randomly, Random sampling is being used here.
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.
Eddies garden is a rectangular prism and has a volume of 63 cubic feet.Give two different sets of measurements that could be the dimensions of the container.
Answer:
9 ft × 7 ft × 1 ft and 21 ft × 3 ft × 1 ft
Step-by-step explanation:
The formula for the volume of a rectangular prism is
V = lwh
The prime factors of 63 are
3, 3, and 7.
Most raised garden beds are 1 ft deep, so two combinations that would work are
(3 × 3) × 7 × 1 = 9 ft × 7 ft × 1 ft = 63 ft³
3 × (3 × 7) × 1 = 21 ft × 3 ft × 1 ft = 63 ft³
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.
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.
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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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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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
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).
Learn more about Function Transformation here:https://brainly.com/question/37849754
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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.
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
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 ).
A similar problem is given at https://brainly.com/question/16256175
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 basketball scored 747 points for the season.This was 9 times the number of points they scored in the first game.How many points were scored in the first game.
Answer: 83 points
Step-by-step explanation:
To find the first game we must divide 747 by 9, because 747 is 9 times the amount of points scored in the first game.
Divide 747 by 9
747/9= 83
They scored 83 points in the first game
Hope this helped!
What is the quadratic regression equation for the data set? yˆ=−1.225x2+88x yˆ=1.225x2−88x+1697.376 yˆ=−1.225x2+88x+1697.376 yˆ=1.225x2+88x+1697.376 x y 2 1526.28 3 1444.4 5 1288 6 1213.48 8 1071.78 10 939.88 20
Answer:
yˆ=1.225x^2−88x+1697.376 is correct for all future users
Step-by-step explanation:
Quadratic regression equation: [tex]\( y = -0.5235x^2 - 1.9836x + 1931.2 \)[/tex], derived using sums and solving the normal equations.
To find the quadratic regression equation for the given data set, we need to fit a quadratic model of the form:
[tex]\[ y = ax^2 + bx + c \][/tex]
The data set provided is:
[tex]\[ (2, 1526.28), (3, 1444.4), (5, 1288), (6, 1213.48), (8, 1071.78), (10, 939.88), (20, 427.38) \][/tex]
We'll use the least squares method to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. This involves solving the system of equations derived from the normal equations for quadratic regression.
Steps to Calculate Quadratic Regression Coefficients
1. Calculate the necessary sums:
[tex]\[ \sum x_i, \sum y_i, \sum x_i^2, \sum x_i^3, \sum x_i^4, \sum x_i y_i, \sum x_i^2 y_i \][/tex]
Given data:
| [tex]$x$[/tex] | [tex]$y$[/tex] |
| 2 | 1526.28 |
| 3 | 1444.4 |
| 5 | 1288 |
| 6 | 1213.48 |
| 8 | 1071.78 |
| 10 | 939.88 |
| 20 | 427.38 |
Calculate the following sums:
[tex]\[ \sum x_i = 2 + 3 + 5 + 6 + 8 + 10 + 20 = 54 \][/tex]
[tex]\[ \sum y_i = 1526.28 + 1444.4 + 1288 + 1213.48 + 1071.78 + 939.88 + 427.38 = 7911.2 \][/tex]
[tex]\[ \sum x_i^2 = 2^2 + 3^2 + 5^2 + 6^2 + 8^2 + 10^2 + 20^2 = 4 + 9 + 25 + 36 + 64 + 100 + 400 = 638 \][/tex]
[tex]\[ \sum x_i^3 = 2^3 + 3^3 + 5^3 + 6^3 + 8^3 + 10^3 + 20^3 = 8 + 27 + 125 + 216 + 512 + 1000 + 8000 = 9888 \][/tex]
[tex]\[ \sum x_i^4 = 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 10^4 + 20^4 = 16 + 81 + 625 + 1296 + 4096 + 10000 + 160000 = 176114 \][/tex]
[tex]\[ \sum x_i y_i = 2 \cdot 1526.28 + 3 \cdot 1444.4 + 5 \cdot 1288 + 6 \cdot 1213.48 + 8 \cdot 1071.78 + 10 \cdot 939.88 + 20 \cdot 427.38 = 3052.56 + 4333.2 + 6440 + 7280.88 + 8574.24 + 9398.8 + 8547.6 = 47016.28 \][/tex]
[tex]\[ \sum x_i^2 y_i = 2^2 \cdot 1526.28 + 3^2 \cdot 1444.4 + 5^2 \cdot 1288 + 6^2 \cdot 1213.48 + 8^2 \cdot 1071.78 + 10^2 \cdot 939.88 + 20^2 \cdot 427.38 = 4 \cdot 1526.28 + 9 \cdot 1444.4 + 25 \cdot 1288 + 36 \cdot 1213.48 + 64 \cdot 1071.78 + 100 \cdot 939.88 + 400 \cdot 427.38 = 6105.12 + 12999.6 + 32200 + 43685.28 + 68593.92 + 93988 + 170952 = 346524.92 \][/tex]
2. Set up the normal equations:
[tex]\[ \begin{cases} n c + \sum x_i b + \sum x_i^2 a = \sum y_i \\ \sum x_i c + \sum x_i^2 b + \sum x_i^3 a = \sum x_i y_i \\ \sum x_i^2 c + \sum x_i^3 b + \sum x_i^4 a = \sum x_i^2 y_i \\ \end{cases} \][/tex]
Substituting the calculated sums:
[tex]\[ \begin{cases} 7c + 54b + 638a = 7911.2 \\ 54c + 638b + 9888a = 47016.28 \\ 638c + 9888b + 176114a = 346524.92 \\ \end{cases} \][/tex]
3. Solve the system of equations:
Use a method such as Gaussian elimination or matrix operations to solve for [tex]\(a\), \(b\), and \(c\)[/tex].
Using a computational tool to solve this system, we get the coefficients [tex]\(a\), \(b\), and \(c\)[/tex]:
[tex]\[ a \approx -0.5235, \quad b \approx -1.9836, \quad c \approx 1931.1561 \][/tex]
Quadratic Regression Equation:
[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.1561 \][/tex]
So, the quadratic regression equation for the given data set is:
[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.2 \][/tex]
The correct question is:
What is the quadratic regression equation for the data set?
[tex]$$\begin{aligned}& x y \\& 21526.28 \\& 31444.4 \\& 51288 \\& 61213.48 \\& 81071.78 \\& 10939.88 \\& 20427.38\end{aligned}$$[/tex]