When analyzing a resultant vector, the equation to find the magnitude of the vector is the Pythagorean theorem. This equation states that the magnitude of the resultant vector is equal to the square root of the sum of the squares of its components.
To find the direction of the resultant vector, the trigonometric function of inverse tangent or arctan can be used. This involves taking the inverse tangent of the vertical component divided by the horizontal component, which gives the angle of the vector with respect to the positive x-axis.
Alternatively, the direction can also be found using the trigonometric functions of sine and cosine by dividing the vertical and horizontal components of the vector by its magnitude.
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15 Carousel
A carousel has three rings of wooden horses fixed to a circular platform,
which rotates anticlockwise around a central pole. The inner ring of
horses is 1.5 metres from the pole, and the middle ring of horses is 2.41
metres from the pole. (Distances are between the centre of the pole and
the centres of the horses.) Sisters Etsuko and Bachico sit on horses next
to each other on
The ride starts slowly but reaches maximum speed during the first rev
olution. At the end of the first revolution, the siblings wave to their
mother who is then directly alongside them. The carousel continues to
rotate at the maximum speed until they have passed their mother a
further 16 times. The carousel then slows down and stops without the
siblings passing their mother again. The time between the first and last
time the siblings passed their mother was 6 minutes.
a Etsuko sits on a horse on the inner ring. Calculate Etsuko's maximum
speed in metres per second to 2 decimal places.
b Bachico sits on a horse on the middle ring. Calculate how many times
faster she is travelling compared to Etsuko.
e The safety regulations for carousels state that the maximum speed at
which it is safe for a child to sit on a horse without flying off is 1.5
metres per second. Find the maximum distance from the pole to the
outer ring of horses to the nearest centimetre.
d In the UK and Australia carousels are typically called merry-go-rounds.
and rotate clockwise. There is a merry-go-round near the carousel
that Bachico and Etsuko are riding. Bachico's friend Sakura is riding
the merry-go-round, which travels at 2 revolutions per minute. At
certain times they were as close as possible, that is, simultaneously
both on the imaginary straight line joining the two poles. Each time
this happened they screamed 'yay'. Find the time in seconds between
consecutive yays.
a) Etsuko's maximum speed is 4.19 m/s.
b) Bachico is traveling 1.61 times faster than Etsuko.
c) The maximum distance from the pole to the outer ring of horses is 3.56 meters.
d) The time between consecutive "yays" is 7.5 seconds.
How to solveLet's call the maximum speed of the carousel V. Then, the circumference of the circular path traveled by the outermost ring of horses is:
C = 2πr, where r is the distance between the pole and the outermost ring of horses.
The time it takes for the carousel to complete one revolution is:
T = C/V
We can use the information given in the problem to set up an equation for the total time it takes for the siblings to pass their mother 17 times:
T = T₁ + 16T₂ = 6 minutes = 360 seconds
So, the time it takes for Etsuko's horse to complete one revolution is:
T₁ = C₁/V
The distance that Etsuko's horse travels between consecutive passes of the mother is equal to the difference in the distances traveled by the innermost and middle rings of horses during one revolution, which is:
Δd = 2.41 - 1.5 = 0.91
So, the time it takes for the carousel to complete one revolution between subsequent passes of the mother is:
Solving for V, we get:
V = 4.19 m/s
Therefore, Etsuko's maximum speed is 4.19 m/s.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on red, P(not red).
0.125
0.250
0.675
0.875
The probability of not getting red is 87.5%.
Hence, The correct option is C.
We know that;
Probability = Number of favorable outcomes / Number of samples
Given that;
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red .
You only have one of eight (1/8) evenly divided orange sections.
The rest is not red,
P = (1 - 1/8
P = 7/8
P = 0.875
P = 87.5%
Therefore, spinning once will yield 7/8 odds of not landing on red are,
⇒ 0.875 or 87.5%.
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expand each logarithm
Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148. We may answer this question by using the definition of logrithmic.
Describe logrithmic.Mathematical operations that relate to a number's logarithm are known as logarithmic functions. The power that a given basis must be increased in order to obtain a particular number is known as the logarithm of the number.
Although 10 (also known as the common logarithm) is the base that is most frequently used, logarithms can be calculated in relation to any positive base higher than 1. If the base is 10, the logarithm of such an integer x with regard to a base b is written by log(base b)(x), or just log(x).
We can compress the given logarithm via the logarithmic identity log(base a)(bc) = c * log(base a)(b):
Sqrt(3.5.11) = Log((3.5.11)(1/2), 9) = Log((3.5.11)*(1/2), 9) = (1/2) * Log (3.5.11, 9)
We must now calculate that logarithm of 9 in base 3.5.11. This can be changed to a log with a more recognisable column, such as base 10 or base e, using the change-of-base formula. Using the base 10 scale
3.5.11, 9) = 9)/log (3.5.11)
We can calculate this using a calculator:
log(9) = 0.9542 (reduced to 4 decimal places)
log(3.5.11) = log(3) + log(5) + log(11) = 0.4771, 0.6978, and 1.0414, respectively, yielding 2.2174. (rounded to 4 decimal places)
Therefore:
sqrt(3.5.11),9 = (1/2) log(3.5.11,9) = (1/2) log(9)/log(3.5.11)) = (1/2) log(0.9542/2.2174) = 0.2148 log(3.5.11,9) = (1/2) log(3.5.11, 9) = (1/2)
Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148.
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The expanded form of the logarithm is:
log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)
What is logarithm?
A logarithm is a mathematical function that tells us what exponent is needed to produce a given number, when that number is expressed as a power of a fixed base. In other words, logarithms tell us how many times we need to multiply the base by itself to get the desired number.
We can use the property of logarithms that says:
log base b (a * c) = log base b (a) + log base b (c)
to expand the logarithm.
Therefore, we have:
log base 9 √(3.5.11) = log base 9 √(3 * 5 * 11)
= log base 9 (3) + log base 9 (5) + log base 9 (11)
So, the expanded form of the logarithm is:
log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)
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17.match graph to what motion is occurring
1. The object is accelerating at an increasing rate
2. The object is moving at a constant velocity
3. The object is not moving
4 The object moved at a constant speed, then stopped. It returned to the beginning. Then it
moved back in the original direction at a very fast constant speed.
Type here tot
paads
Distance
Distance
Time
Time
Time
The solution is : the velocity of the person on the walk way with respect to the observers on the ground is D 1.7 m/s.
Here, we have,
In order to find the velocity of the person on the walk way with respect to the person on the ground we have to apply relative velocity concept.
Consider the observer on the ground as B and the person walking on the pathway as A.
The relative velocity is the velocity that the body A would appear to an observer on the body B and vice versa.
Mathematically speaking the relative velocity is the vector difference between the velocities of two bodies.
Relative velocity = Velocity of Body A- Velocity of Body B.
Velocity of the person walking on the walkway (A)= 1.5 m/s.(given)
Velocity of the observer on the ground (B)= -0.2 m/s(given).
Relative velocity of object A with respect to B = 1.5 - (-0.2)= 1.7 m/s.
Thus the velocity of the person on the walk way with respect to the observers on the ground is 1.7 m/s.
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complete question:
A person is strolling along a moving walkway at a constant velocity of +1.00 m/s with respect tot he walkway, which moves at a constant velocity of +0.50 m/s with respect to the ground. An observer on the ground is walking at a constant velocity of -0.2 m/s. what is the velocity of the person on the walk way with respect to the observers on the ground?
A - 0.7 m/s
B + 1.3 m/s
C - 0.3 m/s
D + 1.7 ms
The expression 1500 (1.085)^3 represents an account balance in dollars after three years with an initial deposit of $1,500. The account pays 8.5% interest, compounded annually for three years.
A. Explain how the expression would change if the bank had compounded the interest quarterly for the three years.
B. Write a new expression to represent the account balance, in dollars, if interest is compounded quarterly.
A. If the bank had compounded the interest quarterly for the three years, the interest rate would be divided by 4 (since there are 4 quarters in a year) and the number of compounding periods would be multiplied by 4. This is because the interest would be calculated and added to the account balance every quarter, rather than just once a year.
B. To represent the account balance if interest is compounded quarterly, we need to use the formula for compound interest with quarterly compounding:
A = P(1 + r/n)^(nt)
where A is the account balance, P is the principal (initial deposit), r is the annual interest rate (8.5%), n is the number of times the interest is compounded per year (4 for quarterly compounding), and t is the number of years (3).
Substituting the given values into the formula, we get:
A = 1500(1 + 0.085/4)^(4×3)
A = 1500(1.02125)^12
A ≈ $1,969.36
Therefore, the new expression for the account balance, in dollars, if interest is compounded quarterly is:
$1,969.36 = 1500(1 + 0.085/4)^(4×3)
Find the value of x.
Answer:
80°
Step-by-step explanation:
the sum of the internal angles of a regular or irregular pentagon is 540°, we remove the known angles and we will have the answer
540 - 110 - 110 - 120 - 120 =
80°
Golf Tournament In a golf tournament, the top 6 men's scores are 65, 68, 70, 72, 73, 75. The top women's scores are 69, 71, 73, 74, 77, 80. Compare the spread of the data for the two sets of scores using (a) the range and (b) the mean absolute deviation.
Answer:
Range: Men: 10, Women: 11
MAD: Men: 2.833333 (17/6), Women: 3
Step-by-step explanation:
The range of the men's scores is 75-65 (highest-lowest), which is 10.
The range of the woman's scores is 80-69, which is 11.
The MAD is the mean of the absolute difference between the terms and the mean, which is very painful to do, but in the sake of the problem, I will be doing.
Men's MAD:
The mean is [tex]\frac{65+68+70+72+73+75}{6}[/tex], which is 70.5.
Sigh.
Now, we find the difference of each term to the mean.
[tex]70.5-65= 5.5[/tex]
[tex]70.5-68=2.5[/tex]
[tex]70.5 - 70 = 0.5[/tex]
[tex]72-70.5=1.5[/tex]
[tex]73-70.5=2.5[/tex]
[tex]75-70.5=4.5[/tex]
wow. Now, we find the mean of these numbers.
[tex]\frac{5.5 + 2.5 + 0.5 + 1.5 + 2.5 + 4.5}{6}[/tex]= 17/6=2.8333333333 This is the MAD.
For the Women's, I'll speed over it.
The mean is 74.
The MAD is 3.
It is the end of the semester and Kyle has one test left. His 5 test grades were 90, 83, 75, 84, 96. What does he need to make on the sixth test to have a mean test grade of 90
Answer:
Kyle needs 112 marks on his sixth test for the mean test grade to be 90.
Step-by-step explanation:
Let the marks Kyle needs for the sixth test be x.
The mean of all tests is given as 90. The formula for mean would be: (sum of marks obtained in each test)/(total number of tests)
which implies,
(90+83+75+84+96+x)/6 = 90,
(428+x)/6 = 90,
428+x = 540,
x = 112
Therefore, Kyle needs 112 marks on his sixth test for the mean test grade to be 90.
The sum of all values divided by the total number of values determines a dataset's mean (also known as the arithmetic mean, which differs from the geometric mean). It is the most widely applied central tendency measure and is frequently called the "average."
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a coin is biased so that the probability a head comes up when it is flipped is 0.6. what is the expected number of heads that come up when it is flipped 10 times
A coin is biased so that the probability a head comes up when it is flipped is 0.6. Therefore, we can expect to get 6 heads when a biased coin with a probability of 0.6 for heads is flipped 10 times.
To find the expected number of heads when a biased coin is flipped 10 times, we can use the formula:
Expected number of heads = Probability of getting a head × Number of times the coin is flipped
In this case, the probability of getting a head is 0.6 and the coin is flipped 10 times. So the expected number of heads is:
Expected number of heads = probability of getting a head x number of times flipped
Expected number of heads = 0.6 x 10
Expected number of heads = 6
Therefore, the expected number of heads when the coin is flipped 10 times is 6.
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For which value of x is the inequality −2x≥6
true?
A. -3
B. -2
C. -1
D. 0
E. 4
Answer:
-2x > 6, so x < -3
So A is correct.
If events E and F are disjoint (mutually exclusive) and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion. Choose the correct answer below.A.Yes, events E and G must be disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G= {6,7,8} show that E and F are disjoint events, F and G are disjoint events, and E and G are also disjoint events.B.No, events E and G are not necessarily disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.C.Yes, events E and G must be disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are also disjoint events.D.No, events E and G are not necessarily disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {6,7,8} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.
The correct answer is D. No, events E and G are not necessarily disjoint. The mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.
The example provided in option D shows that events E and F are disjoint, events F and G are disjoint, but events E and G are not disjoint. This is because they share the element 2.
For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} .
Therefore, the mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.
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If f(x) = x³ 3x² - 22x + 24 and x - 6 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answer:
x = (3 ± sqrt(-47)) / 2.
Step-by-step explanation:
If x - 6 is a factor of f(x), then we know that (x - 6) must divide evenly into f(x), which means that there is another factor of f(x) that we can find by polynomial long division or synthetic division.
Using synthetic division:
We start by writing the coefficients of f(x) in order:
1 3 -22 24
We then write the factor (x - 6) to the left of the coefficients, and draw a line:
6 | 1 3 -22 24
We bring down the first coefficient: 1
1 3 -22 24
1
We multiply 6 by the first coefficient and write the result under the second coefficient: 1
6 | 1 3 -22 24
-6
-3
If x - 6 is a factor of f(x), then we know that (x - 6) must divide evenly into f(x), which means that there is another factor of f(x) that we can find by polynomial long division or synthetic division.
Using synthetic division:
We start by writing the coefficients of f(x) in order:
1 3 -22 24
We then write the factor (x - 6) to the left of the coefficients, and draw a line:
6 | 1 3 -22 24
We bring down the first coefficient:
Copy code
1
6 | 1 3 -22 24
1
We multiply 6 by the first coefficient and write the result under the second coefficient:
Copy code
1
6 | 1 3 -22 24
-6
Copy code
-3
We add the second and third coefficients to get -19, then multiply by 6 and write the result under the third coefficient:
1
6 | 1 3 -22 24
-6
-3
42
66
We add the last two numbers to get 90. This means that we can write f(x) as:
f(x) = (x - 6)(x² - 3x + 14)
To find the zeros of f(x), we need to solve the equation (x - 6)(x² - 3x + 14) = 0.
The first factor gives us x = 6.
To solve the quadratic factor, we can use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = -3, and c = 14. Substituting these values into the formula, we get:
x = (3 ± sqrt(3² - 4(1)(14))) / 2(1)
x = (3 ± sqrt(-47)) / 2
Since the square root of a negative number is not a real number, the quadratic factor does not have any real zeros.
Therefore, the zeros of f(x) are x = 6, and the complex numbers x = (3 ± sqrt(-47)) / 2.
two similar solids have surface areas of 45 in.^2 and 80 in.^2. the volume of the larger solid is 320 in.^3. what is the volume of the smaller solid?
The volume of the smaller solid is 292 in³ under the condition that two similar solids have surface areas of 45 in² and 80 in². The volume of the larger solid is 320 in³.
Given the two solids are similar, so their corresponding sides are proportional. Let us consider them calling the ratio of the corresponding sides k. The ratio regarding their surface areas is k² and the ratio of their volumes is k³.
Let us consider the volume of the smaller solid V. It is given the surface area of the smaller solid is 45 in² and that of the larger solid is 80 in²
k² = 80/45 = 8/9
k = √(8/9)
= 0.94 (approx.)
It is given the volume of the larger solid is 320 in³.
k³ = 320/V
0.94³ = 320/V
V = 320/(0.94³)
= 292 in³ (approx.)
The volume of the smaller solid is 292 in³.
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Alyssa is tracking the growth of a plant. The plant grows c inches in the first week and n inches in the second week. Enter an equation to show that the plant grows 2 inches more in the second week than in the first week
The equation is given as n = c + 2
How to derive the equationThe plant grows c inches in the first week.
The plant grows n inches in the second week.
mаthеmаticаlly, the equаtion requires that wea rea to to show thе relаtionship between thе growth in thе first wееk (c) and thе growth in thе seсond wееk (n).
thе growth in thе seсond wееk (n) is said to be 2 inсhes more than thе growth in thе first wееk (c) from the given question.
The equation would be
n = c + 2
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John has 8 boxes of apples. Each box holds 10 apples. If 5 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?
Answer:
65 apples
Step-by-step explanation:
We Know
John has 8 boxes of apples.
Each box holds 10 apples.
If 5 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?
Let's solve
5 boxes are full: 5 x 10 = 50 apples
3 boxes are half full = 3(1/2 · 10) = 15 apples
50 + 15 = 65 apples
So, John has 65 apples.
Fill in the missing words
Lex has opened a savings account with $1,200. His account has an annual interest rate of 6.8%
compounded annually. How much money will Lex have after 6 years?
Answer:
$1780.77------------------------------
Use the formula for compound interest :
[tex]A = P(1 + r/n)^{nt}[/tex]Where:
A = the future value' P = the principal investment amount,r = the annual interest rate,n = the number of compounds,t = the number of years.In this problem, we have:
P = $1,200, r = 6.8% = 0.068, n = 1, t = 6Now, let's plug these values into the formula:
[tex]A = 1200(1 + 0.068/1)^{1*6} = 1200(1 + 0.068)^6 = 1200(1.068)^6 = 1780.77[/tex]After 6 years, Lex will have approximately $1780.77 in his savings account.
HELP! Image attached
The data distribution is skewed and the mean of the emails is less than the median number of emails.
The median is 22 and the mean is 20.2.
How to find the mean and median ?The mean can be found by adding up the number of emails and dividing it by the number of days :
= ( 15 + 16 + 18 + 19 + 22 + 22 + 22 + 22 + 23 + 23 ) / 10
= 20. 2
The median is the number in the middle. As there are 10 numbers, the median would be:
= (Position 5 + Position 6) / 2
= ( 22 + 22 ) / 2
= 22
The mean is less than the median.
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21. Select Yes or No to indicate whether each ordered pair is a point of intersection between the line y = 2x + 4 and the parabola y = x² + 4x + 1
Ordered Pairs
(-3,-2)
(1,6)
(0,4)
Yes (-3,-2) is true.
No (1,6) is false
No (0,4) is false
How to determine the ordered pairTo determine if an ordered pair is a point of intersection between the line and the parabola, we need to check if the coordinates satisfy both equations.
(-3, -2)
y = 2x + 4 => -2
= 2(-3) + 4 => -2 = -2 (True)
y = x² + 4x + 1 => -2
= (-3)² + 4(-3) + 1 => -2 = -2 (True)
Answer: Yes
(1, 6)
y = 2x + 4 => 6
= 2(1) + 4 => 6 = 6 (True)
y = x² + 4x + 1 => 6
= (1)² + 4(1) + 1 => 6 ≠ 6 (False)
Answer: No
(0, 4)
y = 2x + 4 => 4
= 2(0) + 4 => 4 = 4 (True)
y = x² + 4x + 1 => 4
= (0)² + 4(0) + 1 => 4 ≠ 1 (False)
Answer: No
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help me with this, this is for my 10-year-old brother he kept bugging me
The mean is 89, the median is 89, the mode is 89, and the range is 22.
The mean is 72.6, the median is 76, there is no mode, and the range is 25.
The mean is 60.5, the median is 57.5, there is no mode, and the range is 55.
What are the mean, median, mode, and range of the following data?The mean, median, mode, and range of the given data are calculated as follows:
Mean = sum of values/ number of values
The median is the middle score when the scores are arranged in order from lowest to highest
Mode is the number that occurs most
The range is the difference between the largest and smallest values
1. Mean = (98 + 89 + 76 + 93 + 89) / 5
Mean = 89
76, 89, 89, 93, 98
The median is 89.
The mode is also 89.
Range = 98 - 76
Range = 22
2. Mean = (59 + 63 + 84 + 76 + 81) / 5
Mean = 72.6
Median: 59, 63, 76, 81, 84
The median is 76.
There is no mode for this set of score
Range = 84 - 59
Range = 25
3. Mean = (36 + 48 + 67 + 91) / 4
Mean = 60.5
Median: 36, 48, 67, 91
Median = (48 + 67) / 2
Median = 57.5
The data has no mode
Range = 91 - 36
Range = 55
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Keisha runs 8 miles in 84 minutes. At the same rate, how many minutes would she take to run 6 miles?
Answer: 63 minutes
Step-by-step explanation:
Use proportions:
8/84 = 6/x
Cross multiply to get:
8x = 504
Simplify by dividing by 8 on both sides.
x = 63.
HELP !!!! HELP ASAPPPP
Determine if the relation is a function and explain your reasoning.
Day of the week Whether I went for a walk
Monday
No walk
Tuesday
Walked
Wednesday
No walk
Thursday
Walked
Friday
No walk
Saturday
Walked
Sunday
Walked
O The relation is a function because all of the input values have different output values.
O The relation is not a function because the output value Walking has different input values, and the same with No walk.
O The relation is not a function because some of the input values have different output values.
O The relation is not a function because there are 7 different input values.
Is the relation a function and explain your reasoning: B. The relation is not a function because the output value Walking has different input values, and the same with No walk.
How to determine whether or not the relation represent a function?In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).
This ultimately implies that, an input value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the output value on the y-coordinate of a cartesian coordinate.
Based on the table, we can logically deduce that the relation does not represent a function because each of its input value (domain) has more than one dependent value (range) i.e Walked and No Walk.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
what is a polynomial of the 5th degree with a leading coefficient of 7 and a constant term 6
Answer: A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 can be expressed in the following form:
f(x) = 7x^5 + ... + ... + ... + ... + 6
Step-by-step explanation: Since the polynomial has a degree of 5, it will have 6 terms in total, including the constant term. However, the other coefficients are unknown, so we need more information to determine them. For example, we could be given additional roots or points on the curve.
Without any further information, the polynomial can only be expressed in this general form.
47. For a certain type of computers, the length of time between charges of the battery is normally
distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of
these computers and wants to know the probability that the length of time will be between
40 and 70 hours.
A. .344
B. .656
C. .748
D. .908
The probability that the length of time between charges will be between 40 and 70 hours is 0.656.
To solve this problem, we need to standardize the values of 40 and 70 using the given mean and standard deviation, and then use the standard normal distribution table to find the probability.
Standardizing 40: z = (x - mu) / sigma z = (40- 50)/15 z = -2/3
Standardizing 70: z = (x-mu) / sigma z = (70- 50)/15 z 4/3
Now we look up the probabilities associated
with the standardized values -2/3 and 4/3 in the
standard normal distribution table.
Using the table, we find that the probability of z being less than -2/3 is 0.2525 and the probability of z being less than 4/3 is 0.9082.
So the probability of the length of time being between 40 and 70 hours can be found by subtracting the probability of z being less than -2/3 from the probability of z being less than 4/3:
P(40 < x <70) = P(-2/3 <z < 4/3) = P(z < 4/3) - P(z< -2/3)
P(40 < x < 70) = 0.9082-0.2525 P(40 < x <70) = 0.6557
Therefore, the probability that the length of time between charges will be between 40 and 70 hours is approximately 0.656, which is closest to option B.
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Select the correct answer. Which equation represents circle W? A. (x − 6)2 + (y + 4)2 = 4 B. (x − 6)2 + (y + 4)2 = 16 C. (x + 6)2 + (y − 4)2 = 4 D. (x + 6)2 + (y − 4)2 = 16
(the twos on the side are exponents, they're being squared)
Answer:
I believe the answer is C. (x + 6)2 + (y − 4)2 = 4
Step-by-step explanation:
Hope this helps :)
Please let me know if its incorrect
A certain quadratic function has a graph which contains the points (1, 7), (2, 16), and (3, 29). Using a quadratic regression (or a system of linear equations), find the equation for this function in standard form. As your answer, give the coefficient on x2 (that is, a).
Group of answer choices
–2
2
–1
1
The required coefficient on x² is 2, so the answer is 2. Option B is correct.
We can start by assuming that the quadratic function has the form:
y = ax² + bx + c
where a, b, and c are unknown coefficients to be determined. We can use the three given points on the graph to set up a system of three equations in three unknowns:
7 = a(1)² + b(1) + c
16 = a(2)² + b(2) + c
29 = a(3)² + b(3) + c
Simplifying each equation, we get:
a + b + c = 7
4a + 2b + c = 16
9a + 3b + c = 29
We can solve this system of equations using any method of our choice, such as elimination or substitution. One possible approach is to subtract equation 1 from equation 2 and equation 2 from equation 3, which gives:
a + b + c = 7
3a + b = 9
5a + b = 13
a = 2; b = 3; c = 2
Therefore, the equation for the quadratic function in standard form is:
y = 2x² + 3x + 2
The coefficient on x² is 2, so the answer is 2.
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What is the unit for force? Give the equation for gravitational force- make sure to include units too. Does gravitational force increase or decrease as you move away from earth? Using the equation, what would happen if the radius between centers were to be cut in half?
The unit for force is the Newton (N). The equation for gravitational force is given by Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where: F is the gravitational force (in Newtons, N) G is the gravitational constant (approximately 6.674 × 10^-11 N·m²/kg²) m1 and m2 are the masses of the two objects (in kilograms, kg) r is the distance between the centers of the masses (in meters, m)
Gravitational force decreases as you move away from Earth because the force is inversely proportional to the square of the distance (r^2) between the objects. If the radius between the centers (r) were to be cut in half, the gravitational force would increase by a factor of 4, since the force is inversely proportional to the square of the distance.
So if r becomes (1/2)r, the force would be inversely proportional to (1/4)r^2, leading to a 4 times increase in force.
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2y-2.3=4.1 answer that
To solve the equation 2y − 2.3 = 4.1 for y, we can use algebraic manipulation.
Step 1:In order to remove the constant term on the left-hand side of the equation, we first add 2.3 to both sides of the equation:
2y - 2.3 = 4.1
+2.3 +2.3
2y = 6.4
Step 2:Now, we divide both sides by 2 to isolate y:
2y = 6.4
÷2 ÷2
y = 3.2
So, the solution to this equation is y = 3.2
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SummaryWe need to isolate the variable on one side of the equation in order to solve an equation like this. By carrying out the same method on both sides of the equation, we can do this. In this example, we divided both sides by 2 to isolate y after adding 2.3 to both sides to remove the constant term on the left-hand side.
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FAQWhat is a constant term?- A term in an algebraic equation that has no variables and is steady is known as a constant term in mathematics. A constant is a fixed, unchanging value. A constant in algebra can be a number on its own or sometimes a letter like a, b, or c to show a fixed integer.
What isolating y mean, in this case?- To separate y from all other terms in an equation, the equation must be rewritten so that y is on one side and all other terms are on the other side. It allows us to calculate the value of y and solve for it.
What is algebraic manipulation?- Mathematical operations including addition, subtraction, multiplication, and division are used to rearrange algebraic expressions or equations to try to simplify or solve them. This process is known as algebraic manipulation. By doing the opposite operations (undoing) to any equation, algebraic manipulation tries to isolate a variable or simplify an expression in order to solve for a certain variable.
a dice game involves rolling 2 dice. if you roll a 2,3,4,10,11 or a 12 you win $5.00. if you roll a 5,6,7,8 or 9 you lose $5.00. how would you setup the problem to determine the expected value you win (or lose) per game?
The expected value represents the losing amount per game equals to $0.55.
Number of dice rolled = 2
To win $5.00 ,
Roll 2,3,4,10,11 or a 12
To lose $5.00 ,
Roll 5,6,7,8 or 9
Probability of winning or losing on a single roll of 2 dice.
There are 36 possible outcomes when rolling 2 dice.
Since each die has 6 possible outcomes.
Out of these 36 possible outcomes.
There are 6 ways to roll a 7 which is a loss.
And 10 ways to roll a 6 or an 8 also a loss.
Total of 16 losing outcomes.
Similarly, there are 5 ways to roll a 2 or a 12 which is a win.
4 ways to roll a 3 or an 11 also a win.
and 3 ways to roll a 4 or a 10 another win.
Total of 12 winning outcomes.
The probability of winning is 12/36 = 1/3
= 0.3333 approximately.
The probability of losing is 16/36 = 4/9
= 0.4444 approximately
The amount of money you can expect to win or lose on a single game,
If you win, you receive $5.00.
If you lose, you lose $5.00.
The expected value you win or lose per game is
Expected value
= (Probability of winning x Amount won) - (Probability of losing x Amount lost)
⇒ Expected value = (1/3 x $5.00) - (4/9 x $5.00)
⇒ Expected value = ($1.67) - ($2.22)
⇒ Expected value = -$0.55
Therefore, on average expected value to lose $0.55 per game.
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Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Among 2094 passenger cars in a particular region, 227 had only rear license plates. Among 330 commercial trucks, 46 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level to test that hypothesis.a. Test the claim using a hypothesis test.b. Test the claim by constructing an appropriate confidence interval.
Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Since the confidence interval does not contain 0, it supports the alternative hypothesis that commercial trucks have a higher proportion of violations than passenger cars.
a. Hypothesis Test:
Null Hypothesis: The proportion of passenger cars with only rear license plates is equal to or greater than the proportion of commercial trucks with only rear license plates.
Alternative Hypothesis: The proportion of commercial trucks with only rear license plates is greater than the proportion of passenger cars with only rear license plates.
Let p1 be the proportion of passenger cars with only rear license plates, and p2 be the proportion of commercial trucks with only rear license plates.
The test statistic for comparing two proportions is the z-test.
z = ((p1 - p2) - 0) / √(p_hat * (1 - p_hat) * (1/n1 + 1/n2))
where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of successes (only rear license plates) in the two samples, and n1 and n2 are the sample sizes.
Plugging in the values, we get:
p1 = 227/2094 = 0.1084
p2 = 46/330 = 0.1394
p_hat = (227 + 46) / (2094 + 330) = 0.1116
n1 = 2094
n2 = 330
z = ((0.1084 - 0.1394) - 0) / √(0.1116 * (1 - 0.1116) * (1/2094 + 1/330))
= -1.68
The p-value for this one-tailed test is P(Z < -1.68) = 0.0475.
Conclusion: The data provides sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
b. Confidence Interval:
We can also construct a confidence interval to estimate the difference in proportions with a specified level of confidence.
A 90% confidence interval for the difference in proportions can be calculated as:
(p1 - p2) ± z√(p1(1-p1)/n1 + p2*(1-p2)/n2)
Plugging in the values, we get:
(p1 - p2) ± 1.645√(0.1084(1-0.1084)/2094 + 0.1394*(1-0.1394)/330)
= (-0.0499, 0.0094)
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Karim and ali looked at the following expression and made a comment: 2-3= (-1) karim:whole numbers are not closed under subtraction. Ali: integers are closed under subtraction. Why do they have different conclusions about the closure property for the whole numbers and integers
The closure property for subtraction holds for integers, but not necessarily for whole numbers.
Closure property is an important concept in mathematics. It refers to the property of a set of numbers to produce a result within the same set when a mathematical operation is performed on any two numbers in that set.
Whole numbers are a subset of integers and include only non-negative numbers, whereas integers include both positive and negative numbers along with zero.
When we subtract two whole numbers, the result may not always be a whole number. For instance, if we subtract 3 from 2, the result is -1, which is not a whole number. This is why Karim concluded that whole numbers are not closed under subtraction.
On the other hand, when we subtract two integers, the result will always be an integer. For example, if we subtract 3 from 2, the result is -1, which is an integer. This is why Ali concluded that integers are closed under subtraction.
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