Find an equation of the tangent line to the curve
y = 8x sin x at the point (π/2, 4π).
y'=8(sinx)+8xcosx
8(sinπ)+8π(cosπ)
0+(-8π)
In a group of 10 batteries, 3 are dead. You choose 2 batteries at random.
Create a probability model for the number of good batteries.
The probability model for the number of good batteries when selecting 2 out of 10 with 3 dead is calculated as combinations of selecting good and dead batteries for each scenario. The probabilities are always divided by the total ways of drawing 2 from 10.
Explanation:This question is a typical problem related to probability. Firstly, we need to identify the number of ways we can draw 2 batteries randomly from this given set. We know there are 10 batteries in total with 3 dead ones. That leaves us with 7 good batteries.
Assuming 'X' is the number of good batteries we could select when drawing two batteries at random, 'X' could be 0, 1, or 2. Here are the three possible cases:
Both batteries are good (X = 2): The number of ways to select 2 batteries from 7 is combination of 7 by 2, denoted as C(7, 2). One battery is good and one is not (X = 1): The number of ways for this case can be calculated as the combination of picking 1 good battery from 7 and 1 dead battery from 3, denoted as C(7, 1)*C(3, 1). None of the batteries are good (X = 0): The number of ways for this case can be calculated as the combination of picking 2 dead batteries from 3, denoted as C(3, 2).To find out the probability of each scenario, we would have to divide by the total number of ways of drawing 2 batteries from 10, which equals to C(10, 2).
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Which of the following is not equivalent to the formula for the circumference of a circle, C = 2pir ?
A) C over r equals 2 times pi
B) C over pi equals 2 times r
C) C over the quantity of r times pi equals 2
D) Cr = 2pi
Answer:
the answer is d. Cr= 2 pi
Step-by-step explanation:
The correct answer that is not equivalent to the formula for the circumference of a circle is: Cr = 2pi. (Option D).
How to get the Circumference of a Circle?To prove the options, it is important to test the formulas given:
In option A, C over r equals 2 times pi:
C/r = 2 * pi
This equation is equivalent to the formula for the circumference of a circle, C = 2 * pi * r, as you can simply multiply both sides by 'r' to get the standard formula.
In Option B, C over pi equals 2 times r:
C/pi = 2 * r
This equation is equivalent to the formula for the circumference of a circle as pi can be multiplied on both sides
In Option C, C over the quantity of r times pi equals 2:
C / (r * pi) = 2
This equation is equivalent to the formula for the circumference of a circle since you can multiply both sides by (r * pi) to get C = 2 * (r * pi).
In option D, This equation is not equivalent to the formula for the circumference of a circle. It is missing the division by 'r' on the right side of the equation.
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Use the three steps to solve the problem.
A "Local" train leaves a station and runs at an average rate of 35 mph. An hour and a half later an "Express" train leaves the station and travels at an average rate of 56 mph on a parallel track. How many hours after it starts will the Express overtake the Local?
Which of the following sets represents the range of the function shown?
{(–3, 4), (5, 11), (9, –1), (10, 13)}
{–3, 5, 9, 10}
{–1, 4, 11, 13}
{(4, –3), (11, 5), (–1, 9), (13, 10)}
{–3, –1, 4, 5, 9, 10, 11, 13}
Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l.
w ≥ 0.5l
2l + 2w ≤ 180
Answer:
The length of the blanket should be less than or equal to 60 inches.
The width should be greater than or equal to 30 inches.
Step-by-step explanation:
Let the length of the blanket be = l
Let the width of the blanket be = w
Charlene wants the width, w, to be at least half its length, l. This can be shown as :
[tex]w\geq 0.5l[/tex]
She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches.
This can be shown as :
[tex]2l+2w\leq 180[/tex]
[tex]2l+2(0.5l) \leq 180[/tex]
[tex]2l+1l \leq 180[/tex]
[tex]3l \leq 180[/tex]
[tex]l\leq 30[/tex]
So, we get length of the blanket should be less than or equal to 60 inches.
And the width should be greater than or equal to 30 inches.
MULTIPLE CHOICE PLEASE HELP FAST!!!!!!!
in one study it was found that the correlation coefficient between two variables is -0.32. which statement is true?
A. There is a weak positive association between the variables
B. There is a weak negative association between the variable
C. There is a strong positive association between the variable
D. There is a strong negative association between the variable
A study of several cities shows a positive correlation between the percent of people biking to work and that percent of people spending their vacation time at home.
Which statement is most likely true?
A. Bike riding makes people want to vacation at home
B. Vacationing makes people want to rife their bikes
C. The correlation is due to a third variable: cost of milk
D. The correlation is due to a third variable: cost of gas
Answer:
Just took the test and got an 100% so the answers are in fact,
in one study it was found that the correlation coefficient between two variables is -0.32. which statement is true?
B. There is a weak negative association between the variable
A study of several cities shows a positive correlation between the percent of people biking to work and the percent of people spending their vacation time at home.
Which statement is most likely true?
A. Bike riding makes people want to vacation at home
Have a wonderful day if you need any other questions from this test let me know!!!!!!!
Final answer:
The correct answer for the correlation coefficient of -0.32 is B. There is a weak negative association.
For the correlation between biking and vacationing at home, the likely third variable is cost of gas, choice D: The correlation is due to a third variable: cost of gas
Explanation:
The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient is -0.32, which indicates a weak negative association between the variables. A negative correlation means that as one variable increases, the other variable tends to decrease. So, option B - There is a weak negative association between the variables - is true.
For the second question, based on the information given, it is most likely that option D - The correlation is due to a third variable: cost of gas - is true. This means that the positive correlation between the percent of people biking to work and the percent of people spending their vacation time at home is likely influenced by the cost of gas as a third variable.
calculated a = 8³³ ÷ [4³² × 2³⁴ (2⁵ × 2²⁰)⁵ ÷ (16 × 2²³) (7⁵ ÷ 7⁵- 1)³² × 4]b = [(11 - 0¹¹) × (3³-3²) 1²⁰²⁰] × (3²-2³) - 3² × 2.
What is the lcm of 6,15?
solve
3x + 2y + 5x - y
Answer: 8x+y
Step-by-step explanation:
you always combine your like terms, a trick is to put a line infront of your equation signs making it look like 3x/+2y/+5x/-y. This makes it easier to see if your terms are positive or negative. Now you have 5x+3x and 2y-y giving you 8x+y because its still positive.
The difference between 6 thirty-sixes and 4 thirty-sixes?
Which best describes the solution to 4-7?
Answer:
the answer is the second option; because 4+(-7) is an equivalent expression the answer Is -3
The simplified value.
4^0 + 2 ⋅ 3 - 2
1
2
5
8
14
26
Answer: option c.) 5
Step-by-step explanation: you must always follow PEMDAS
so first step would be parentheses but there are none so you move on to exponents. 4^0=1. so now you have 1+2x3-2.
Next step is multiplication. 2x3 is 6 so now you have 1+6-2.
Now we only have addition and subtraction so you move from left to right. 1+6=7
7-2=5
giving you option c. 5
In forming a contract, the “meeting of the minds” is _____. a. an agreement between all parties involved in the contract of the details of the contract. b. a formal meeting of the parties involved in a contract that may or may not result in a signed agreement. c. a phrase used to describe a verbal contract or a contract made without signatures from the parties involved. d. a mental exercise used by a person involved in a contract to try to guess the contract requests of the other parties and offer a compromise
Answer: (a) an agreement between all parties involved in the contract.
Step-by-step explanation: While forming a contract, we generally use the phrase "meeting of the minds" , which implies that both the parties which are involved in the contract agree to the terms and conditions mentioned in the contract and are aware of the commitments made by each of the parties. Out of the four given options, only option (a) is acceptable, because the other three do not match with our requirement.
Thus, the correct option is (a).
An agreement between all parties involved in the contract. The correct option is A.
What is a “meeting of the minds”?While forming a contract, we generally use the phrase "meeting of the minds", which implies that both the parties which are involved in the contract agree to the terms and conditions mentioned in the contract and are aware of the commitments made by each of the parties. Out of the four given options, only option (a) is acceptable, because the other three do not match with our requirements.
Therefore, an agreement between all parties involved in the contract. The correct option is A.
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Solve for u
3(2u+5)=33
Simplify your answer as much as possible.
What are the common factors of 30 and 300?
The ballpark made a total of $15,000 from ticket sales at Wednesday's game. The ballpark charges $20 for each adult ticket and $10 for each child's ticket. They sold 3 times as many children's tickets as adult tickets. Write a system of equations that can be used to determine the number of adult and child tickets sold.
To determine the number of adult and child tickets sold, we can set up a system of equations based on the given information. By solving the system of equations, we find that the number of adult tickets sold is 300, and the number of children's tickets sold is 900.
Explanation:Let's assume that the number of adult tickets sold is represented by 'x'.
Since the number of children's tickets sold is three times the number of adult tickets, the number of children's tickets sold can be represented as '3x'.
The total revenue from ticket sales is $15,000, so we can create the following equation:
20x + 10(3x) = 15,000
Simplifying this equation, we get:
20x + 30x = 15,000
Combining like terms, we have:
50x = 15,000
Dividing both sides by 50, we find:
x = 300
So, the number of adult tickets sold is 300, and the number of children's tickets sold is 3 times that, which is 900.
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What is the negative reciprocal of 3/4 or three over 4
Final answer:
The negative reciprocal of 3/4 is -4/3. This is found by inverting the fraction to get 4/3 and then applying the negative sign.
Explanation:
The negative reciprocal of a number refers to the value that, when multiplied by the original number, results in -1. For the fraction 3/4 (three over four), taking the reciprocal involves flipping the numerator and the denominator, which gives us 4/3. Making this reciprocal negative results in -4/3. The concept of reciprocals relates to the broader mathematical principles of multiplication and division, where negative exponents indicate the inverse of the corresponding positive exponent. For example, x to the power of -1 is equal to 1 divided by x to the power of 1, which demonstrates how negative exponents introduce division into the operation.
general admission to the americanmuseum of natural history is $19. if a group of 125 students visits the museum how much will the group's tickets cost
Please check answer. Will Upvote.
Evaluate the function rule for the given value.
y = 15 • 3x for x = –3
Is the answer -135?
Answer: Yes
Step-by-step explanation:
Hi, to answer this question we have to substitute x =-3 on the function given, and solve for the variable y.
y = 15 • 3x
Replacing the value of the variable x by -3:
y = 15 • 3(-3)
Multiplying
y = 15 .-9
y = -135
It is correct, the answer is y= -135
Feel free to ask for more if needed or if you did not understand something.
Bob gets paid an annual salary of $30,000 and earns 5% commission on all sales he makes. If Bob wants to make $6,000 this month, how much in sales does he need to have?
Answer: Correct answer is 70,000 just took the test
how do i find this answer....
215.4% of 55= 118.47...
I have a TEAS test tomorrow and i cant figure out how to find this answer! ...?
Use the graph to determine and interpret the solution. A 4 cm bean plant grows at a rate of 1/2cm per week. A 5.5 cm flower grows at a rate of 1/4cm per week. If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:
h = 1/2t + 4
h = 1/4t + 5.5
The solution to the system,___?___
, means that the plants will both be ___?___ centimeters tall after__?___weeks.
The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.
Given that
A 4 cm bean plant grows at a rate of 1/2cm per week.
A 5.5 cm flower grows at a rate of 1/4cm per week.
If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:
h = 1/2t + 4
h = 1/4t + 5.5
According to the question
The solution of the system of equation is;
h = 1/2t + 4
h = 1/4t + 5.5
Substitute the value of h from equation 1 in equation 2
[tex]\rm h = \dfrac{1}{4}+5.5\\\\\dfrac{1}{2}t +4 = \dfrac{1}{4}t +5.5\\\\\dfrac{1}{2}t-\dfrac{1}{4}t = 5.5-4\\\\\dfrac{2t-t}{4} = 1.5\\\\\dfrac{t}{4} = 1.5\\\\t = 4\times 1.5\\\\t = 6[/tex]
Substitute the value of t in equation 1
[tex]\rm h = \dfrac{1}{2}\times 6+4\\\\h = 3+4\\\\h = 7[/tex]
Hence, The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.
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How much less would a 25 year old male pay for a $50,000 policy of 20 y life insurance @ $5.84 per $1000, than a straight life policy @ $15.66 per $1000?
A 25-year-old male would pay $491 less for a $50,000 policy of 20-year life insurance at $5.84 per $1,000, than for a straight life policy at $15.66 per $1,000. This is calculated by first determining the total cost of each policy and then finding the difference between the two.
Explanation:To calculate the cost difference between the 20-year life policy and the straight life policy, we first need to calculate the cost of each policy. The cost of the policies is given per $1,000, and the policies provided are worth a total of $50,000.
The 20-year life policy costs $5.84 per $1,000. Therefore, we calculate 50 (as $50,000 divided by $1,000 gives 50) multiplied by $5.84, which equals to $292. The straight life policy costs $15.66 per $1,000. Therefore, we calculate 50 multiplied by $15.66, which equals to $783.
To find out how much less a 25-year-old male would pay for the 20-year policy than the straight life policy, we subtract the cost of the 20-year policy from the cost of the straight life policy: $783 - $292 = $491.
So, a 25-year-old male would pay $491 less for a $50,000 20-year policy than a straight life policy.
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How do you solve this problem
58=(2/3)w
Write log3 6 as a logarithm of base 2.
1) (log2)3/(log2)6
2) (log2)6/(log2)3
3) (log3)2/(log6)2
4) (log6)2/ (log3)2 ...?
The correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).
To express log₃ 6 as a logarithm of base 2, we can use the change of base formula. The change of base formula states that logb x = (logc x) / (logc b), where c is any positive value other than 1.
Applying the change of base formula to log3 6:
log₃ 6 = (log₂ 6) / (log₂ 3)
Therefore, the correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).
To calculate it properly, we need to find the decimal approximation of this expression:
Using the appropriate logarithmic functions, we have:
(log₂ 3) / (log₂ 6) ≈ 1.58496 / 2.58496 ≈ 0.6124
Thus, log₃ 6 as a logarithm of base 2 is approximately 0.6124.
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If ON = 5x – 4, LM = 4x + 7, NM = x – 7 and OL = 2y – 6, find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale. ...?
Opposite sides of parallelogram LMNO must be equal. By setting the equations for opposite sides equal and solving, we find x = 11 and y = 5.
Explanation:To determine the values of x and y for which LMNO is a parallelogram, we can use the properties of a parallelogram which state that opposite sides are equal in length. Since ON and LM are opposite sides, as well as OL and MN, we set their equations equal to each other:
ON = LM means 5x - 4 = 4x + 7.OL = NM means 2y - 6 = x - 7.Solving the first equation gives us x = 11. Substituting x = 11 in the second equation gives 2y - 6 = 4, which simplifies to y = 5. Therefore, the values are x = 11 and y = 5 for LMNO to be a parallelogram.
Turn 357 centimeters into meters
What is the measure of ∠XYZ
The measure of angle ∠XYZ is 66°.
Given:
∠W + ∠X = ∠XYZ (Sum of opposite interior angles is equal to the exterior angle)
Let's solve for x:
2x + 12 + 2x + 14 = 5x + 16
4x + 26 = 5x + 16
26 - 16 = 5x - 4x
10 = x
Now substitute the value of x into the equation for ∠XYZ:
∠XYZ = 5x + 16
∠XYZ = 5 * 10 + 16
∠XYZ = 50 + 16
∠XYZ = 66°
Therefore, the measure of ∠XYZ is 66°.
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What is meant by "transposing a term"?