The trigonometric function equivalent to sec(-270) is -1.
The secant function is defined as the reciprocal of the cosine function, i.e., sec(x) = 1/cos(x). To find the value of sec(-270), we need to first find the cosine of -270 degrees. The cosine function has a period of 360 degrees, which means that cos(-270) is the same as cos(-270 + 360) = cos(90) = 0. Therefore, we have sec(-270) = 1/0, which is undefined.
However, we can determine the sign of sec(-270) by examining the quadrant in which the angle -270 degrees lies. Since -270 degrees is in the fourth quadrant, the cosine function is negative in that quadrant. Therefore, we can write sec(-270) = -1/0-, which is equivalent to -1. Hence, the trigonometric function equivalent to sec(-270) is -1.
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Norma and david crawled to the barn and then hopped back to the house. they crawled at 300 centimeters per minute and hopped at 400 centimeters per minute. if round took 7 minutes, hiw long did they crawl
Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.
Find time Norma and David spent crawling to barn if the round trip took 7 minutes. They crawled at 300 cm/min hopped back at 400 cm/min.Let x be the time (in minutes) that Norma and David spent crawling to the barn, and y be the time (in minutes) they spent hopping back to the house. We know that:
x + y = 7 (the total time they spent on the round trip was 7 minutes)
300x + 400y = distance to the barn and back (since their speeds are given in centimeters per minute, the product of their speeds and the time spent crawling or hopping gives the distance in centimeters)
We want to find x, the time they spent crawling to the barn. We can solve for x by rearranging the first equation as x = 7 - y, and substituting into the second equation:
300(7 - y) + 400y = distance to the barn and back
2100 - 300y + 400y = distance to the barn and back
100y = distance to the barn and back - 2100
y = (distance to the barn and back - 2100)/100
Now we need to find the distance to the barn and back. They crawled to the barn at 300 cm/min, so the distance they crawled is 300x cm. They hopped back to the house at 400 cm/min, so the distance they hopped is 400y cm. The total distance to the barn and back is:
distance to the barn and back = 300x + 400y
= 300x + 400[(distance to the barn and back - 2100)/100] (substituting the expression we found for y)
= 300x + 4(distance to the barn and back - 2100)
Simplifying and solving for distance to the barn and back, we get:
distance to the barn and back = 5400/7 cm
Finally, we can substitute this value into the expression we found for y, and solve for x:
y = (distance to the barn and back - 2100)/100
= (5400/7 - 2100)/100
= 24/7
x = 7 - y
= 7 - 24/7
= 37/7
Therefore, Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.
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Algebra 1. please help!!
Answer: f(t) = 2.4t - 500
Step-by-step explanation:
So first of all, we need how much she actually profits from each taco. She charges $3.25 per taco, but we cannot forget that it is not free to make a taco in the first place. It costs her $0.85 to make a taco. This means we have to subtract the 85 cents from the 3 dollars 25 cents, which means it ends up being $2.40, or as the answer choices have it, 2.4.
So now we know what the number of tacos is being multiplied by: 2.4.
2.4t is now the profit per taco multiplied by the number of tacos.
But we're not quite done yet.
She has a fixed expense of $500 a month, which means this has to be subtracted from her taco profits to find her true profit.
Putting all of this together, we get f(t)=2.4t - 500.
(t)= (profit per taco)(amount of tacos sold) - (fixed expenses)
Which set of ordered pairs does NOT represent a function?A) (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)B) (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)C) (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)D) (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
The set of ordered pairs that does NOT represent a function is option B) (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
What is the set of ordered pairs?A function is a term that do not have two different outputs that is (y) for the same input(x).
Note that
For option A: The x values are {0,2,4,-2,5} Here none of the x values are repeated, So, it represents a function.
For option B: The input value 2 is linked with two different output values (2 and 7), so this set of ordered pairs does not stand a function.
Based on the explanation of the function given above, if x=2, the 'y' can not be equal to 2, 7. So, this is not a function.
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A 6 in.
D
X
F 6 in. G
The calculated value of x in the right triangle is 6
Calculating the value of xfrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where we have
x/6 = 6/x
To solve this equation, we can use the property of cross-multiplication.
So for the equation x/6 = 6/x, we can cross-multiply as follows:
x/6 = 6/x
x * x = 6 * 6
x^2 = 36
To solve for x, we need to take the square root of both sides of the equation:
√(x^2) = √36
x = 6
The value of x is 6
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Calculate the derivative of the following function, 4 y=sin(cos (8x)) ) Find the critical points of the following function f(x) = xVx+6"
The critical points of f(x) are x = -3 and x = 4.
Derivative of 4y = sin(cos(8x)):
We can find the derivative of the given function using the chain rule of differentiation. Let u = cos(8x), then we have:
y = sin(u)
dy/du = cos(u) (derivative of sin(u))
du/dx = -8sin(8x) (derivative of cos(8x) using chain rule)
dy/dx = dy/du * du/dx = cos(cos(8x)) * (-8sin(8x))
Therefore, the derivative of 4y = sin(cos(8x)) is:
dy/dx = -32sin(8x)cos(cos(8x))
Critical points of f(x) = x√(x+6):
To find the critical points of f(x), we need to find where the derivative of the function is equal to zero or undefined.
f(x) = x√(x+6)
f'(x) = (√(x+6) + x/2√(x+6))
To find the critical points, we need to set f'(x) equal to zero and solve for x:
(√(x+6) + x/2√(x+6)) = 0
Multiplying both sides by 2√(x+6), we get:
2x + 6 = -x√(x+6)
Squaring both sides, we get:
4[tex]x^2[/tex] + 24x + 36 = [tex]x^3[/tex] + 6[tex]x^2[/tex]
Rearranging, we get:
[tex]x^3[/tex] + [tex]2x^2[/tex] - 24x - 36 = 0
We can solve this cubic equation using numerical methods or by factoring.
By testing values, we can see that x = -3 is a root of the equation. Dividing the equation by (x+3), we get:
[tex]x^2[/tex]- x - 12 = 0
This quadratic equation can be factored as (x-4)(x+3) = 0.
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80.0% complete
question
a customer wants you to enlarge a photo to 234 its current height. the photo’s current height is 314 inches. what should its enlarged height be, in inches?
If the photo’s current height is 314 inches, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.
To calculate the enlarged height, you need to find out the percentage increase in height from the current height to the desired height.
The desired height is 234 inches, which is 234/314 = 0.744 or 74.4% of the current height.
To find the actual enlarged height, you need to increase the current height by 74.4%.
Enlarged height = current height + (current height x percentage increase)
Enlarged height = 314 + (314 x 0.744)
Enlarged height = 314 + 233.616
Enlarged height = 547.616
Therefore, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.
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A triangular prism is 36 millimeters long and has a triangular face with a base of 36 millimeters and a height of 24 millimeters. The other two sides of the triangle are each 30 millimeters. What is the surface area of the triangular prism?
The surface area of the triangular prism is
5752 square millimetersHow to find the surface area of the triangular prismThe surface area of the triangular prism is
= area of the two side rectangles + area of the base rectangles + area of the 2 triangles
= 2 * 36 * 30 + 36 * 36 + 2 * 1/2 * 36 * 24
= 2160 + 1296 + 1296
= 5752 square millimeters
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a city department of transportation studied traffic congestion on a certain highway. to encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2 . the probability distribution of the number of people in passenger cars on the highway is shown in the table. number of people 1 2 3 4 5 probability 0.56 0.28 0.08 0.06 0.02 based on the probability distribution, what is the mean number of people in passenger cars on the highway?
The mean number of people in passenger cars on the highway is 1.7 (approximately 2).
The mean of a probability distribution function is also known as Expectation of the probability distribution function.
The mean number of people in passenger cars (or expectation of number of people in passenger cars ) on the highway can be denoted as E(x) where x is the number of people in passenger cars on the highway.
Thus E(x) can be calculated as,
E(x) = ∑ [tex]x_{i} p_{i}[/tex] ∀ i= 1,2,3,4,5
where, [tex]p_{i}[/tex] is the probability of number of people in passenger cars on the highway
⇒ E(x) = (1)(0.56) + (2)(0.28) + (3)(0.08) + (4)(0.06) + (5)(0.02)
⇒ E(x) = 1.7
Hence the mean number of people in passenger cars on the highway is 1.7, which is less than 2.
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how many times can 2 go into 1742? please its for my homework due tomorrow
Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 13 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. It is the manager's service goal to limit the waiting time prior to beginning the checkout process to no more than five minutes. After reviewing the waiting line analysis of his store, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Option 1: Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 30 customers per hour. (Note: Although we hire one more person, it is still an M/M/1 queueing system, Because we do not operate a second counter but only hire a person to help with the first cashier counter, the service rate of the cashier improves. ) What are the arrival and service rates in Option 1
In Option 1, the arrival rate remains constant at 13 customers per hour. This means that, on average, 13 customers arrive at the checkout lane every hour, following a Poisson probability distribution.
However, the service rate in Option 1 increases to 30 customers per hour. This improvement is achieved by hiring a second person to assist the cashier in bagging groceries while the main cashier is occupied with entering cost data and collecting money from the customer. This essentially speeds up the overall service process, allowing more customers to be served within the same time frame.
The service rate of 30 customers per hour indicates that, on average, the cashier and the assistant can complete the checkout process for 30 customers in an hour. The service times still follow an exponential probability distribution, but with a faster rate of service compared to the initial service rate of 20 customers per hour.
By implementing Option 1, the manager aims to reduce the waiting time prior to the checkout process to no more than five minutes, thereby improving overall customer satisfaction and efficiency at Pete's Market.
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Larry sold 300 items in his sports memorabilia shop. 5 of the items sold 6 were football items. 20% of the other items sold were baseball items. What percent of the total items sold were baseball items?
Approximately 21.3 percent of the total items sold were baseball items.
Out of the 300 items sold, 5 of them were football items, so the number of non-football items sold is:
300 - 5 = 295
We know that 20% of the non-football items sold were baseball items, so the number of baseball items sold is:
0.20 * 295 = 59
Therefore, the total number of baseball and football items sold is:
59 + 5 = 64
The percentage of total items sold that were baseball items is:
(64 / 300) * 100% = 21.3%
Therefore, approximately 21.3 percent of the total items sold were baseball items.
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9(x) = ln (3x+11) calculate gl (x) A) 2-3x + 11)-3 B) 3(-3x + 11)-1 C) -54(-3x +11)-3 D) -9(-3x +11)-?
Using given function 9(x) = ln(3x+11), gl (x) B) 3(-3x + 11)^-1.
We are given 9(x) = ln(3x+11) and we need to find gl(x).
First, we can use the chain rule to differentiate ln(3x+11):
d/dx [ln(3x+11)] = 1/(3x+11) * d/dx [3x+11] = 3/(3x+11)
Now, we can use the given equation 9(x) = ln(3x+11) to find d/dx [9(x)]:
d/dx [9(x)] = d/dx [ln(3x+11)] = 3/(3x+11)
Therefore, gl(x) = d/dx [9(x)] / 3(x) = 3/(3x+11) * 1/3 = (3(-3x+11))^-1.
Therefore, the correct answer is B) 3(-3x+11)^-1.
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In which of the following situations does order matter? Select all that apply
Answer:
Locker and Phone number
Step-by-step explanation:
Gym student grouped together with no thought doesnt matter, lunch menu doesn't need order, and a classroom seating chart doesn't really matter
are 4(5k – 3) and 14k – 8 equivalent
help please
Answer: No they are not
Step-by-step explanation:
Distribute the 4 from the left equation into the parenthesis.
you would get 20k - 12
that is not equivalent to 14k - 8
How much will 3. 75 kg of meat cost at ?190. 00 per kilogram?
a. ?71250 b. ?7. 125 0 c. ?712. 50 d. ?7125. 0
3.75 kg of meat will cost 712.50, The correct answer is option (c).To determine how much 3.75 kg of meat will cost at ?190.00 per kilogram, you'll need to perform a multiplication using the given weight and price per kilogram, we need to :
1. Identify the weight of the meat: 3.75 kg.
2. Identify the cost per kilogram: ?190.00.
3. Multiply the weight (3.75 kg) by the cost per kilogram (?190.00).
3.75 kg × ?190.00/kg = 712.50
So, 3.75 kg of meat will cost ?712.50, which corresponds to option (c) in your list of possible answers. Remember to always check your calculations and units when solving problems like this to ensure accuracy.
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(3^6-3^8)/(9^4 -9^2)
Answer:
Step-by-step explanation:
First, let's simplify the numerator:
3^6 - 3^8 = 729 - 6561 = -5832
Now, let's simplify the denominator:
9^4 - 9^2 = 6561 - 81 = 6480
So, the expression simplifies to:
(-5832) / 6480 = -0.9
Help with problem in photo
Check the picture below.
A rectangular mural measures 1 meter by 3 meters. Rebekah creates a new mural that is 0. 5 meters longer. What is the perimeter of Rebekah's new mural?
The perimeter of Rebakh's new mural is 9 meters.
Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.
So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.
Therefore, the perimeter of Rebakh's new mural is 9 meters.
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Kathleen made 29, 38, 45, 42, and 36 points on her assignments. What is the mean number of points Kathleen made?
The mean number of points Kathleen made is 38.
To calculate the mean number of points Kathleen made, we will use the following terms: mean, sum, and total number of assignments.
The mean is the average value of a set of numbers. To find the mean, we need to sum all the given values and then divide the sum by the total number of values in the set.
Kathleen's assignment scores are 29, 38, 45, 42, and 36 points. To find the sum, we add these numbers together: 29 + 38 + 45 + 42 + 36 = 190 points.
Now, we need to determine the total number of assignments. Kathleen has completed five assignments. So, we will divide the sum of her points (190) by the total number of assignments (5) to find the mean.
Mean = Sum / Total number of assignments
Mean = 190 / 5
Mean = 38
The mean number of points Kathleen made on her assignments is 38 points. This indicates that on average, she scored 38 points per assignment. Calculating the mean gives us a general idea of her performance across all assignments, allowing us to gauge her overall progress.
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1. A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.
(a) Write an equation to represent this situation.
(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?
1 pt for correct answer to part (b), 4 pts for showing steps you took to get the correct answer and showing the formula with variable x that you used in part (a).
Note: correct answer to part (a) has only one variable, the variable x. Need to set up a ratio and cross multiply to solve for x.
X represents how many more consecutive tries she needs to make in a row
to raise her overall average up to 60%
2.
Simplify the expression 3x-12/x^2-15x+44. Show your work.
(NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors. )
3.
1. Write the expression as a simplified rational expression. Show your work.
14x+4
-----------
2 1
----- + -----
3x 2x+1
Thank you for any help
She requires 55 consecutive successful throws to get a success rate of 60%
The number of successful throws she made is 8 out of 50
Now to calculate the percentage we will use the formula
[tex]\frac{8}{50} X 100 = 16[/tex]
According to the problem, she needs to make her success percentage 60% and for that, we need to estimate the number of consecutive successful throws. Hence the new equation will be
[tex]\frac{8+x}{50+x} X 100 = 60[/tex]
[tex]or, \frac{8+x}{50+x} = 0.6[/tex]
This is the equation concerned.
Now,to solve this, we will take the denominator on the other side will give us
[tex]or, 8+x = 0.6(50+x)[/tex]
[tex]or, 8+x = 30+ 0.6x[/tex]
[tex]or, x - 0.6x = 30 -8[/tex]
[tex]or, 0.4x= 22[/tex]
or, x = 55
Hence we see that she requires 55 consecutive successful throws to get a success rate of 60%
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Complete Question
A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.
(a) Write an equation to represent this situation.
(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?
Please help me with this question. I need a detailed explanation if possible. I am offering 25 points.
1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²), the power and multiplication law is not used correctly.
2. (y⁵/x²)*(y¹⁰/x³), the power and multiplication law is not used correctly.
3. y⁷/x⁴ * y¹⁰/x³, the multiplication law is not used correctly.
What is the simplification of the exponents?The exponents are simplified as follows; (using power exponents)
1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²)
= (x⁻⁴y¹⁰)*(x⁻⁹y¹⁰)
= x⁻¹³y²⁰
2. (y⁵/x²)*(y¹⁰/x³) (simplify using multiplication and division rule)
(y⁵/x²)*(y¹⁰/x³)
= (y⁵x⁻²)*(y¹⁰x⁻³)
= y¹⁵x⁻⁵
3. y⁷/x⁴ * y¹⁰/x³ (simplify using multiplication and division rule)
y⁷/x⁴ * y¹⁰/x³
= (y⁷x⁻⁴)(y¹⁰x⁻³)
= y¹⁷x⁻⁷
4. y¹⁷/x⁷ (This expression is simplified correctly)
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The sum of twice a nuber,n, and 14 is 30.
2x+14=30
2x =30-14
2x=16
x =8
Answer:
8
Step-by-step explanation:
Twice means 2 so twice a number,n, means 2 times n thus 2n
sum means add so, 2n + 14
"is" means equal so 2n + 14 = 30
Solve for n:
2n=16
N=8
Find the inverse for each relation: 4 points each 1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)}
How do I solve a Pythagorean triangle of 7 squared + 2 squared and then the number after what would it be when u square root it
To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:
7² + 2² = x²
Simplifying this equation, we get:
49 + 4 = x²
53 = x²
To find the value of x, we need to take the square root of both sides:
√53 = x
So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.
In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.
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The diagonals of quadrilateral ABCD intersect at E(0,2). ABCD has vertices at A(1,6) and B(-2,4). What must be the coordinates of C and D to ensure that ABCD is
a parallelogram?
Answer:
C = (-1, -2)
D = (2, 0)
Step-by-step explanation:
You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).
ParallelogramThe diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:
E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC
C = 2E -A = 2(0, 2) -(1, 6)
C = (-1, -2)
and
D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern
D = (2, 0)
It costs $50 a year to be member of an online gaming service. The membership allows you to play games online for free; however, you will still need to purchase games for $60 each. If you can purchase up to 6 games a year, which are the domain and range of this linear function?
A. Domain: All real numbers
Range: All real numbers
B. Domain: {50, 110, 170, 230, 280, 340}
Range: {0, 1, 2, 3, 4, 5, 6}
C. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {50, 110, 170, 230, 290, 350, 410}
D. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {60, 160, 210, 270, 320, 380}
The correct answer is C.
The cost of membership is fixed at $50 per year, and the cost of purchasing games is $60 each. If you purchase up to 6 games a year, the cost of each purchase will be $60, and the total cost of membership and games will be $50 + ($60 x number of games purchased).
The function that relates the number of games purchased to the total cost is:
Total cost = 50 + 60(number of games purchased)
Now, let's consider the options provided:
A. Domain: All real numbers
Range: All real numbers
This is not a valid option since the domain and range are not restricted to the given context.
B. Domain: {50, 110, 170, 230, 280, 340}
Range: {0, 1, 2, 3, 4, 5, 6}
This option does not represent the relationship between the number of games purchased and the total cost correctly.
C. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {50, 110, 170, 230, 290, 350, 410}
This option correctly represents the relationship between the number of games purchased and the total cost. The domain represents the number of games purchased (up to 6), and the range represents the total cost (membership fee + cost of games).
D. Domain: {0, 1, 2, 3, 4, 5, 6}
Range: {60, 160, 210, 270, 320, 380}
This option represents the cost of games purchased only, and does not include the cost of membership.
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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 13)(0,13) and (5, 416)(5,416)
The exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].
To write an exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416), follow these steps:
1. Use the point (0, 13) to determine the value of a. Since the x-coordinate is 0, we have y = a * b⁰, which simplifies to y = a. Therefore, a = 13.
2. Use the point (5, 416) to determine the value of b. Plug in the values for x and y, as well as the value of a we just found: 416 = 13 * b⁵.
3. Solve for b: b⁵ = 416 / 13 = 32. Taking the fifth root of both sides, we get b = 2.
So, the exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].
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PLS HELP ME WITH THIS 2. QUESTIONS, 50 POINTS
( The first 2 images are from the first question, the other one is from the second)
Answer: B g(x)=1/4f(x) odd
Step-by-step explanation:
First Page:
Points from the graph
Points from f(x) points from g(x)
(1,2) (1, 1/2)
(4, 16) (4, 4)
f(x) was multiplied by 1/4 to get to g(x)
Second Page:
Even functions are symmetrical about the y-axis: . Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).
lets test for even: does f(x)=f(-x) => f(1)=f(-1) no -2[tex]\neq[/tex]2
see image for plotted points
lets test for odd: does f(x)= -f(-x) => f(1) = -f(-1) yes -2 = -2
Answer:
[tex]\textsf{B)} \quad g(x)=\dfrac{1}{4}f(x)[/tex]
[tex]\textsf{B)} \quad \textsf{odd}[/tex]
Step-by-step explanation:
Functions f(x) and g(x) are exponential functions.
From inspection of the given points on both graphs:
f(4) = 16g(4) = 4When x = 4, the y-value of function f(x) is four times the y-value of function g(x). Therefore, function g(x) is ¹/₄ of function f(x):
[tex]g(x)=\dfrac{1}{4}f(x)[/tex]
[tex]\hrulefill[/tex]
And even function is symmetric about the y-axis:
f(x) = f(-x) for all values of x.According to the table, f(3) = -4 and f(-3) = 4.
Therefore, as f(x) ≠ f(-x), the function is not even.
An odd function is symmetric about the origin:
f(-x) = -f(x) for all values of x.According to the table, f(-3) = 4 and f(3) = -4. So -f(3) = -(-4) = 4.
Therefore, as f(-3) = -f(3), the function is odd.
[tex]\hrulefill[/tex]
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A man sets out to travel from A to C via B. From A he travels a distance of 8km on a bearing N30degreesE to B. From B he travels further 6km due east. Calculate how far is north of A, east of A
The displacement of the man from Noth east of A from C is 12.2 km.
What is the displacement of the man?
The displacement of the man is the distance between his initial position at A and final position at C.
The angle formed at position B is calculated as follows;
θ = 30⁰ + 90⁰
θ = 120⁰
The displacement of the man is calculated by applying cosine rule as follows;
d² = 8² + 6² - 2(8 x 6) cos (120)
d² = 148
d = √148
d = 12.2 km
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Set up a series of 10 tubes. Into the first tube place 4 milliliters of saline. In tubes 2
through 10 place 2 ml of saline. To the first tube add 1 ml of serum. Transfer
2 ml from tube 1 to tube 2 and do the same throughout the remaining tubes. Discard
the last 2 ml transferred. Give the following:
a. The tube dilution in tubes 1, 3 and 5
b. The solution dilution in tubes 1, 2 and 7
c. The total volume and solution dilution in tube 10 before transfer
d. The amount or volume of serum in tube 6 before transfer and after transfer
a. The tube dilution in tubes 1, 3, and 5:
- Tube 1: 1:5 (1 ml serum + 4 ml saline)
- Tube 3: 1:125 (1:5 dilution from Tube 1 x 1:5 dilution from Tube 2 x 1:5 dilution from Tube 3)
- Tube 5: 1:3125 (1:125 dilution from Tube 3 x 1:5 dilution from Tube 4 x 1:5 dilution from Tube 5)
b. The solution dilution in tubes 1, 2, and 7:
- Tube 1: 1:5
- Tube 2: 1:25 (1:5 dilution from Tube 1 x 1:5 dilution from Tube 2)
- Tube 7: 1:78125 (1:3125 dilution from Tube 5 x 1:5 dilutions for Tubes 6 and 7)
c. The total volume and solution dilution in tube 10 before transfer:
- Total volume: 3 ml (2 ml saline + 1 ml transferred from Tube 9)
- Solution dilution: 1:1953125 (1:78125 dilution from Tube 7 x 1:5 dilutions for Tubes 8, 9, and 10)
d. The amount or volume of serum in tube 6 before transfer and after transfer:
- Before transfer: 0.00064 ml (2 ml x 1:3125 dilution from Tube 5)
- After transfer: 0.00032 ml (1 ml x 1:3125 dilution from Tube 5, as half the volume was transferred to Tube 7)
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