Examination writing skills refer to a set of abilities that are essential for effective and successful writing in an exam context.
These skills include reading the question carefully, planning your response, writing a clear and concise answer, using appropriate terminology, providing evidence to support your argument, and presenting your answer in a logical and organized manner.
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Complete question:
State one way in which each of the examination writing skills below could effectively assist you when writing your examinations:
Read the questionPlan the responseAnswer the questions10 POINTS!! ASAP please help me find the area and also the outer perimeter!!!
Answer:
area of semi circle =pi r^2/2
3.14*6*6/2=56.2
area of rectangle=lb
=20*12=240
240+56.2=296.2
rounding it it will become 300 ft sqr
perimeter of rectangle without including 4th side=20+12+20=52
perimeter of semicircle=pi r+d (d is not needed here)
3.14*6=18.84
so total perimeter=52+18.84=70.84ft
Step-by-step explanation:
C Select the correct answer. Which equation is equivalent to the given eq -4(x - 5) + 8x = 9x - 3
Answer:
-4(x - 5) + 8x = 9x - 3
Simplifying the left side:
-4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
Subtracting 4x from both sides:
20 = 5x - 3
Adding 3 to both sides:
23 = 5x
Dividing both sides by 5:
x = 23/5
Therefore, the equation equivalent to the given equation is:
5x - 23 = 0
Homer's car weighs 4,000 pounds. How many tons does
Homer's car weigh?
Answer:2
Step-by-step explanation:
Answer:
2 Tons
Step-by-step explanation:
Homer’s car weighs 2 tons because there are 2,000 pounds in a ton and 4,000 divided by 2,000 equals 2
A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $9 the average attendance has been 23000. When the price dropped to $7, the average attendance rose to 30000. Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue?
Answer:
Step-by-step explanation:
We can start by assuming that the relationship between the ticket price and attendance is linear, so we can write the equation for the line that connects the two data points we have:
Point 1: (9, 23000)
Point 2: (7, 30000)
The slope of the line can be calculated as:
slope = (y2 - y1) / (x2 - x1)
slope = (30000 - 23000) / (7 - 9)
slope = 3500
So the equation for the line is:
y - y1 = m(x - x1)
y - 23000 = 3500(x - 9)
y = 3500x - 28700
Now we can use this equation to find the attendance for any ticket price. To maximize revenue, we need to find the ticket price that generates the highest revenue. Revenue is simply the product of attendance and ticket price:
R = P*A
R = P(3500P - 28700)
R = 3500P^2 - 28700P
To find the ticket price that maximizes revenue, we need to take the derivative of the revenue equation and set it equal to zero:
dR/dP = 7000P - 28700 = 0
7000P = 28700
P = 4.10
So the ticket price that would maximize revenue is $4.10. However, we need to make sure that this price is within a reasonable range, so we should check that the attendance at this price is between 23,000 and 30,000:
A = 3500(4.10) - 28700
A = 5730
Since 23,000 < 5,730 < 30,000, we can conclude that the ticket price that would maximize revenue is $4.10.
The weight of a miniature Tootsie roll is normally distributed with a mean of 3.30 grams and standard deviation of .13 gram
We can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams for standard deviation of 0.13 gram.
What is a normal distribution?A normal distribution is a symmetric, bell-shaped continuous probability distribution that is defined by its mean and standard deviation. The majority of the data in a normal distribution is located close to the mean, and the number of data points decreases as you deviate from the mean in either direction. Because many real-world events, like human height or test scores, have a tendency to follow a normal distribution, the normal distribution is frequently utilised in statistics. A helpful technique for determining the range of values within a normal distribution based on the mean and standard deviation is the empirical rule, commonly known as the 68-95-99.7 rule.
Given that, the mean of 3.30 grams and standard deviation of 0.13 gram.
Using the empirical formula the range that falls in 95% is associated to two standard deviations.
Mean + 2 standard deviations = 3.30 + 2(0.13) = 3.56 grams
Mean - 2 standard deviations = 3.30 - 2(0.13) = 3.04 grams
Hence, we can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams.
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Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment..
The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
Explain about the sample space of an event?A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.
When this happens, we want to give each event—like rolling a two—a number that represents the likelihood of the occurrence and describes how probable it is that it will occur. Similar to this, we would like to give any event or group of outcomes—say rolling an even number—a probability that reflects how possible it is that the occurrence will take place if the experiment is carried out.Martin features a spinner with four compartments marked A, B, C, and D.
To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.
Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
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? Answer the question below. Type your response in the space provided. What do you call the materials that help you achieve your goals?
Answer:
Acquired resources
Step-by-step explanation:
Acquired resources
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 9 feet. Container B has a diameter of 8 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Step-by-step explanation:
the volume of container B is Travers from A to B.
so, the volume of the empty space in A is exactly the volume of container B.
the volume of a cylinder is
base area × height = pi×r² × height.
the reside is as always half of the diameter.
r = 8/2 = 4 ft
the volume of the empty space in A = the volume of container B =
= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈
≈ 1,005.3 ft³
BRAINEST IF CORRECT! 25 POINTS.
What transformation of Figure 1 results in Figure 2?
Select from the drop-down menu to correctly complete the statement.
A ______ of Figure 1 results in Figure 2.
Answer:
its reflection
Step-by-step explanation:
a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Answer:
It is Reflection. Check if it is in the list.
You are crossing two pea plants. One is heterozygous for yellow. The second pea plant is homozygous for green. Use "G/g" as the letter to represent the gene for this problem.
The result of the cross breeding between the heterozygous and homozygous pea plant is the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
What is the result of crossbreeding?In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).
When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).
The possible combinations of alleles that the offspring can inherit from their parents are:
Gg x gg
Gametes from the Gg plant: G, gGametes from the gg plant: g, gPossible genotypes of offspring: Gg, gg (50% chance for each)Possible phenotypes of offspring: yellow (Gg) or green (gg) in a 1:1 ratioTherefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
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Question 4 X Suppose that starting today, you make deposits at the beginning of each quarterly period for the next 40 years. The first deposit is for 400, but you decrease the size of each deposit by 1% from the previous deposit. Using an nominal annual interest rate of 8% compounded quarterly, find the future value (i.e. the value at the end of 40 years) of these deposits. Give your answer as a decimal rounded to two places (i.e. X.XX).
if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
The first step in solving this problem is to calculate the amount of each quarterly deposit. We know that the first deposit is $400, and each subsequent deposit decreases by 1% from the previous deposit. This means that each deposit is 99% of the previous deposit. To calculate the size of each deposit, we can use the following formula:
deposit_ n = deposit_(n-1) * 0.99
Using this formula, we can calculate the size of each quarterly deposit as follows:
deposit_1 = $400
deposit_2 = deposit_1 * 0.99 = $396.00
deposit_3 = deposit_2 * 0.99 = $392.04
deposit_4 = deposit_3 * 0.99 = $388.12
...
We can continue this pattern for 40 years (160 quarters) to find the size of each quarterly deposit.
Next, we need to calculate the future value of these deposits using an nominal annual interest rate of 8% compounded quarterly. We can use the formula for compound interest to calculate the future value:
[tex]FV = PV * (1 + r/n)^(n*t)[/tex]
where FV is the future value, PV is the present value (which is zero since we are starting with deposits), r is the nominal annual interest rate (8%), n is the number of times the interest is compounded per year (4 since we are compounding quarterly), and t is the number of years (40).
We can substitute the values into the formula and solve for FV:
[tex]FV = $400 * (1 + 0.08/4)^(440) + $396.00 * (1 + 0.08/4)^(439) + $392.04 * (1 + 0.08/4)^(4*38) + ... + $1.64 * (1 + 0.08/4)^4[/tex]
After solving this equation, we get a future value of $143,004.54, rounded to two decimal places. This means that if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
This calculation highlights the power of compound interest over long periods of time. By making regular contributions and earning interest on those contributions, our investment grows exponentially over time. It also shows the importance of starting early and consistently contributing to an investment over time in order to achieve long-term financial goals.
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in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a)
The bases for the row space and null space of A, we put A into reduced row echelon form and solve for the null space. The dot product of basis vectors shows they are orthogonal.
To find the bases for the row space and null space of A, we perform row operations on A until it is in reduced row echelon form:
[ 1 -1 3 | 5 ] [ 1 -1 3 | 5 ]
[ 2 1 -5 | -9 ] -> [ 0 3 -11 | -19]
[-1 -1 2 | 2 ] [ 0 0 0 | 0 ]
[ 1 1 -1 | -1 ] [ 0 0 0 | 0 ]
The reduced row echelon form of A tells us that there are two pivot columns, corresponding to the first and second columns of A. The third and fourth columns are free variables. Therefore, a basis for the row space of A is given by the first two rows of the reduced row echelon form of A:
[ 1 -1 3 | 5 ]
[ 0 3 -11 | -19]
To find a basis for the null space of A, we solve the system Ax = 0. Since the third and fourth columns of A are free variables, we can express the solution in terms of those variables. Setting s = column 3 and t = column 4, we have:
x1 - x2 + 3x3 + 5x4 = 0
2x1 + x2 - 5x3 - 9x4 = 0
-x1 - x2 + 2x3 + 2x4 = 0
x1 + x2 - x3 - x4 = 0
Solving for x1, x2, x3, and x4 in terms of s and t, we get:
x1 = -3s - 5t
x2 = s + 2t
x3 = s
x4 = t
Therefore, a basis for the null space of A is given by the vectors:
[-3 1 1 0]
[ 5 2 0 1]
To verify that every vector in the row space of A is orthogonal to every vector in the null space of A, we compute the dot product of each basis vector for the row space with each basis vector for the null space:
[ 1 -1 3 | 5 ] dot [-3 1 1 0] = 0
[ 1 -1 3 | 5 ] dot [ 5 2 0 1] = 0
[ 0 3 -11 | -19] dot [-3 1 1 0] = 0
[ 0 3 -11 | -19] dot [ 5 2 0 1] = 0
Since all dot products are equal to zero, we have verified that every vector in the row space of A is orthogonal to every vector in the null space of A.
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_____The given question is incomplete, the complete question is given below:
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a). a = [ 1 -1 3 5 2 1 0 1 -2 -1 -1 1]
A contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answer:
I'm pretty confident that the answer is E
Synthetic Division to Find Zeros
if f(x)=x^3−3x^2+16x+20 and x+1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answer:
Step-by-step explanation:
Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.
We set up synthetic division as follows:
-1 | 1 -3 16 20
| -1 4 -20
|_____________
1 -4 20 0
The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:
x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))
= (4 ± sqrt(-64)) / 2
= 2 ± 2i√2
Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.
can you find c and b?
c=?
b=?
The value of the constant c that makes the following function are c = 0.
What is constant ?Constant is a term used to describe a value that remains unchanged or fixed throughout a program or process. It can be a numeric value, a character value, a string, or a Boolean (true/false) value. Common examples of constants include physical constants, mathematical constants, and programming-language keywords.A constant is a value that does not change, regardless of the conditions or context in which it is used. Common examples of constants include mathematical values such as pi (3.14159), physical constants such as the speed of light (299,792,458 m/s), and other constants such as the universal gravitational constant (6.67408 × 10−11 m3 kg−1 s−2).
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Therefore, c must equal 0 in order for the two sides of the function to be equal. and The one with the greater absolute value is b = 10.
What is function?A function is a block of code that performs a specific task. It is a subprogram or a set of instructions that can be used multiple times in a program.
27. For the function to be continuous at x = 7, the limit of the function as x approaches 7 from the left must equal the limit of the function as x approaches 7 from the right.
This means that the value of y as x approaches 7 must be the same on both the left and right sides of the point.
Since the left side of the function is y = c*y + 3, the right side of the function must also be equal to y = c*y + 3.
Therefore, c must equal 0 in order for the two sides of the function to be equal.
28. In order for the function to be continuous at x = 5, the value of y at x = 5 must be the same on both the left and right sides of the point.
Since the left side of the function is y = b - 2x, the right side of the function must also be equal to y = b - 2x.
Therefore, b must equal 10 in order for the two sides of the function to be equal.
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Complete Question:
Find the center and radius of the circle whose equation is x^2+y^2+4y=32
Answer:
center: (0, -2)
radius: 6
Step-by-step explanation:
You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.
see image.
Dividing sin^2Ø+cos^2Ø=1 by ____ yields 1+cot^2Ø=csc^2Ø
a.cot^2Ø
b.tan^2Ø
c.cos^2Ø
d.csc^2Ø
e.sec^2Ø
f.sin^2Ø
To obtain the required equation we divide the equation by sin²Ø.
What are trigonometric functions?The first six functions are trigonometric, with the domain value being the angle of a right triangle and the range being a number. The angle, expressed in degrees or radians, serves as the domain and the range of the trigonometric function (sometimes known as the "trig function") of f(x) = sin. Like with all other functions, we have the domain and range. In calculus, geometry, and algebra, trigonometric functions are often utilised.
The given equation is:
sin²Ø+cos²Ø=1
To obtain the required equation we divide the equation with sin²Ø:
sin²Ø/sin²Ø +cos²Ø/ sin²Ø = 1/sin²Ø
1 + cot²Ø = csc²Ø
Hence, to obtain the required equation we divide the equation by sin²Ø.
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It is known that the area of a triangle can be calculated by multiplying the measure of the base by the measure of the height. Let the triangle measure 5m, 12m and 13m. Determine your area
The area of this triangle is 30 m².
What area?Area is a surface measure, that is, it is the amount of space that a geometric figure occupies on a flat surface.
To calculate the area of a triangle, we can use the formula:
Area = (base x height) / 2
In the case of the given triangle, we can choose the measure of 5m as the base and the measure of 12m as the height, since the height forms a right angle with the base and is perpendicular to it.
So, we have:
Area = (b*h)/2
Area = (5m * 12m) / 2
Area = 30m²
Suppose that, for budget planning purposes, the city in Exercise 24 needs a better estimate of the mean daily income from parking fees.
a) Someone suggests that the city use its data to create a confidence interval instead of the interval first created. How would this interval be better for the city? (You need not actually create the new interval.)
b) How would the interval be worse for the planners?
c) How could they achieve an interval estimate that would better serve their planning needs?
d) How many days' worth of data should they collect to have confidence of estimating the true mean to within
a) As per the given budget, the amount of interval that would be better for the city is 95% confidence interval.
b) The interval that be worse for the planners is depends on sample size
c) They achieve an interval estimate that would better serve their planning needs is depends on margin of error
d) The number of days worth of data should they collect to have confidence of estimating the true mean to 30 days
To obtain a better estimate, the city can create a confidence interval, which is a range of values that is likely to contain the true population mean with a certain degree of confidence.
However, there are also some disadvantages to using a confidence interval. The interval estimate may be wider than a point estimate, which means that the budget planners may have to allocate a larger budget to account for the uncertainty in the estimate.
To achieve a better interval estimate, the city could increase the sample size or reduce the variability of the data. Increasing the sample size reduces the margin of error and increases the precision of the estimate.
Finally, to determine how many days' worth of data the city should collect to estimate the true mean with a certain degree of confidence, the city would need to consider the desired level of precision, the variability of the data, and the desired level of confidence.
Typically, a larger sample size will provide a more accurate estimate, but this also depends on the variability of the data. In general, a sample size of at least 30 is recommended for a reasonably accurate estimate.
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The lunch special at Maria's Restaurant is a sandwich and a drink. There are 2 sandwiches and 5 drinks to choose from. How many lunch specials are possible?
Answer:
the question is incomplete, so I looked for similar questions:
There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.
the answer = 3 x 4 x 2 = 24 possible combinations
Explanation:
for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich
since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24
If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.
For this question's answer, there are 2 x 5 = 10 lunch specials are possible.
The number of lunch specials possible are 10.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
We are given that;
Number of sandwiches=2
Number of drinks=5
Now,
To find the total number of lunch specials, we need to multiply the number of choices for sandwiches by the number of choices for drinks.
Number of sandwich choices = 2
Number of drink choices = 5
Total number of lunch specials = 2 x 5 = 10
Therefore, by combinations and permutations there are 10 possible lunch specials.
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The function f(x) is represented by this table of values.
x f(x)
-5 35
-4 24
-3 15
-28
-1
3
0
0
1 -1
Match the average rates of change of fx) to the corresponding intervals.
-8
-7
(-5, -1]
(-4,-1]
[-3, 1]
(2, 1)
HELPPP ASAP
Answer:
-8: (-4, -3]
-7: (-3, -1]
(-5, -1]: (-5, -1]
(-4, -1]: (-4, -1]
[-3, 1]: [-3, 1]
(2, 1): (1, 2]
please assist with this question...
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
(a)
the experimental probability is just using the actual experience to predict any future results.
the total number of cases was 20, and the number of desired cases (yellow) was 12.
so, the experimental probability of landing on yellow is
12/20 = 3/5 = 0.600
(b)
the theoretical probability of a totally fair spinner landing on yellow is 2 out of 5 possibilities, so
2/5 = 0.4000
(c)
the correct statement is the first one.
with a more or less balanced (fair) spinner the experimental numbers should get closer and closer to the theoretical numbers, the more spins we make.
At a certain instant, the base of a triangle is 5 inches and is increasing at the rate of 1 inch per minute. At the same instant, the height is 10 inches and is decreasing at the rate of 2.5 inches per minute. Is the area of the triangle increasing or decreasing? Justify your answer.
Using differentiation, the area of the triangle is decreasing at the given time.
Is the area of the triangle increasing or decreasing?The formula for the area of a triangle is:
A = (1/2)bh
where b is the base and h is the height.
Differentiating both sides of the equation with respect to time t, we get:
[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]
Substituting the given values, we get:
[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]
Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.
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(b) Write 5 as a percentage.
Answer:
5 as a percentage of 100 is 5/100 which is 5%
please find the midpoint of the following line and arc using straightedge-compass-construction method
The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.
To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.
To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.
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--The question is incomplete, answering to the question below--
"find the midpoint of a line and arc using straight edge-compass-construction method"
PLEASE HELP !!!! HELP!!label each equation is proportionality or non proportional Help
y=9/x
y=x-12
h=3d
f=1/3e
Answer:
y=9/x => proportional
y = x - 12 ==> non-proportional
h = 3d ==> proportional
f = 1/3 e = proportional
Step-by-step explanation:
A proportional equation is of the general form
y = kx (directly proportional) or
y = k/x (inversely proportional)
k is known as the constant of proportionality
y = 9/x ==> k = 9 proportional
y = x - 12 cannot be expressed as y = kx or y = k/x
h = 3d ==> k = 3 proportional
f = 1/3 e ==> k = 1/3 proportional
In a survey of 124 pet owners, 44 said they own a dog, and 58 said they own a cat. 14 said they own both a dog and a cat. How many owned neither a cat nor a dog?
Step-by-step explanation:
See Venn diagram below
Alexander and Rhiannon left school at the same time. Alexander travelled 14 km home at an average speed of 20 km/h. Rhiannon travelled 10 km home at an average speed of 24 km/h. a) Who arrived home earlier? b) How much earlier did this person arrive at home? Give your answer to the nearest minute.
Rhiannon arrived home approximately 17 minutes earlier than Alexander.
What is the average?This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
According to the given information:To solve this problem, we can use the formula:
time = distance / speed
a) The time it took Alexander to get home is:
time_Alexander = 14 km / 20 km/h = 0.7 hours
The time it took Rhiannon to get home is:
time_Rhiannon = 10 km / 24 km/h = 0.41667 hours
Since Rhiannon's time is smaller than Alexander's, Rhiannon arrived home earlier.
b) The time difference between their arrivals is:
time_difference = time_Alexander - time_Rhiannon = 0.7 hours - 0.41667 hours = 0.28333 hours
To convert this to minutes, we can multiply by 60:
time_difference_in_minutes = 0.28333 hours x 60 minutes/hour ≈ 17 minutes
Therefore, Rhiannon arrived home approximately 17 minutes earlier than Alexander.
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fine the exact value of sin(45-30)
a cliff diver plunges from a height of 81 ft above the water surface. the distance the diver falls in t seconds is given by the function d(t)
(a) Therefore after t = 1.75 seconds the diver will hit the water.
(b) The velocity the diver hit the water is 56 ft/s.
From the given condition we have d(t) = 16t²
and the height is 49ft
(a) Now when the diver hit the water the equation become
16t² = 49
t² = 49/16
t = ±7/4
t = ±1.75
since time can not be negative so t = 1.75
Therefore after t = 1.75 seconds the diver will hit the water.
(b)
Now differentiating d(t) with respect to t we get
d'(t) = 32t
now putting t=7/4 we get
the velocity d'(7/4) = 32*7/4
d'(7/4) = 56ft/s
Therefore the velocity the diver hit the water is 56 ft/s.
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The complete question is :
A cliff diver plunges from a height of 49ft above the water surface. The distance the diver falls in t seconds is given by the function d(t)=16t²ft
(a) After how many seconds will the diver hit the water?
(b) With what velocity (in ft/s ) does the diver hit the water?
