PLEASE HELP
The linear function f(x) = 0.9× + 79 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken.
Answers
The required answers are 80.8, 79,and g(42) > f(42).
How to find average of equation?Part A:
To determine the test average for the math class after completing test 2, we need to evaluate the function f(x) at x=2. That is,
[tex]$$f(2) = 0.9(2) + 79 = 80.8$$[/tex]
Therefore, the test average for the math class after completing test 2 is 80.8.
Part B:
To determine the test average for the science class after completing test 2, we need to find the equation of the linear function g(x) that passes through the given points (1,78) and (2,79). The slope of the line passing through these points is
[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{79-78}{2-1}=1$$[/tex]
We can use the point-slope form of a line to find the equation of the line passing through the point (1,78) with slope m=1. That is,
[tex]$$y-78 = 1(x-1)$$[/tex]
Simplifying, we get
y = x + 77
Therefore, the test average for the science class after completing test 2 is
g(2) = 2 + 77 = 79
Part C:
To determine which class had a higher average after completing test 42, we need to evaluate f(42) and g(42) and compare the results. We have
[tex]$$f(42) = 0.9(42) + 79 = 117.8$$[/tex]
To find (42), we need to extend the linear function g(x) beyond the given data points by assuming that the function is linear and continues with the same slope m=1. That is,
g(x) = x + 77
for all [tex]$x\geq 1$[/tex]. Therefore,
[tex]$$g(42) = 42 + 77 = 119$$[/tex]
Since g(42) > f(42), we conclude that the science class had a higher average after completing test 42.
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Related Questions
Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?
Answers
On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.
Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.
On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).
On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.
On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.
On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.
Finally, οn the first day, she sοld 15 tοmatοes.
Therefοre, Jοann had 71 tοmatοes tο begin with.
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Question 6
One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled
with 750 gal of water?
Question 7
1
Answers
Answer
6255 pounds
8.34×750=6255lbs
Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Answers
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
1. (Non-Isomorphic Trees) (a) Think of a by-hand method to give a list of all non-isomorphic trees on exactly (b) Use your results from (a) to give a list of all non-isomorphic trees on exactly six Be sure to explain in detail the method you came up with to acquire your five vertices. Display your results. vertices. Show you're results. lists in (a) and (b).
Answers
Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.
A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.
For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.
Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.
To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.
The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.
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I will mark you brainiest!
Given parallelogram STUV, what is the length of TV?
TW = y2
WV = 2y − 1
A) 2
B) 8
C) 4
Answers
The required value of TV is 2 units.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.
According to question:
We have given that;
TW = y²
WV = 2y − 1
We know that in parallelogram
TW = WV
y² = 2y − 1
y² - 2y + 1 = 0
y² - y - y + 1 =0
y(y - 1)-1(y - 1) = 0
(y - 1)(y - 1) = 0
(y - 1)² = 0
y - 1 = 0
y = 1
So;
TV = TW + WV
TV = y² + 2y − 1
TV = 1² + 2(1) - 1
TV = 1 + 2 - 1
TV = 2 units
Thus, required value of TV is 2 units.
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A box containing 5 balls costs $8.50. If the balls are bought individually, they cost $2.00 each. How much cheaper is it, in percentage terms, to buy the box as opposed to buying 5 individual balls?
Answers
Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.
The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.
To calculate the percentage difference, we can use the formula:
% difference = (difference ÷ original value) x 100%
In this case, the difference is $1.50, and the original value is $10.00.
% difference = ($1.50 ÷ $10.00) x 100%
% difference = 0.15 x 100%
% difference = 15%
Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.
Step-by-step explanation:
The scale on a map is 1:320000
What is the actual distance represented by 1cm?
Give your answer in kilometres.
Answers
By answering the presented question, we may conclude that Therefore, 1 expressions cm on the map corresponds to a real distance of 3.2 km.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Scale 1:
320000 means that 1 unit on the map represents his 320000 units in the real world.
To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.
1 kilometer = 100000 cm
So,
1 unit on the map = 320000 units in the real world
1 cm on the map = (1/100000) km in the real world
Multiplying both sides by 1 cm gives:
1 cm on the map = (1/100000) km * 320000
A simplification of this expression:
1 cm on the map = 3.2 km
Therefore, 1 cm on the map corresponds to a real distance of 3.2 km.
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generally, cold fronts move fast er than warm fronts generally, cold fronts have steeper slopes generally, precipitation cover s a much broader area with a cold front especially in winter, cumuliform clouds are more often associated with cold fronts
Answers
Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.
On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.
With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.
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can you help me to solve these two questions?
Answers
Case 1: The constant c of the piecewise function is equal to 1 / 7.
Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.
How to determine the value of a variable such that a piecewise function is continuous
A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:
g(a) = h(a)
Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7
c · a + 3 = c · a² - 3
c · (a² - a) = 6
c = 6 / (a² - a)
c = 6 / (7² - 7)
c = 6 / 42
c = 1 / 7
The value of the constant c is equal to 1 / 7.
Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5
b - 2 · a = - 150 / (a - b)
(b - 2 · a) · (a - b) = - 150
a · b - b² - 2 · a² + 2 · a · b = - 150
- b² + 3 · a · b - 2 · a² = - 150
b² - 3 · a · b + 2 · a² - 150 = 0
b² - 15 · b - 100 = 0
(b - 20) · (b + 5) = 0
b₁ = 20 or b₂ = - 5
The solution with the greater absolute value is b = 20.
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Consider two agents, Alice and Bob, who have utility functions 0.3x3 + 0.72A if xa > XB (0.314 +0.72B if XB > XA UA(2A, 2B) = UB(XA, XB) 4X A – 32B if XB > IA -0.32A + 1.3xB if x A > XB If Alice is the dictator in the dictator game with a $10 endowment, then she will offer Bob (A) $0; (B) $5; (C) $2; (D) $10.
Answers
The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.
Compare Alice's utility from each option and choose the one that maximizes her utility.
Let us consider each option,
If Alice offers Bob $0, her utility will be,
If XA > XB then
UA (XA , XB )= 0.3x3 + 0.72A
UA(10,0)
= 0.3(10)³ + 0.72(10)
= 307.2
If Alice offers Bob $5, Bob's utility will be,
UB(10,5)
= 0.314 + 0.72(5)
= 0.314 + 3.6
= 3.914
And Alice's utility will be,
UA(5,10)
= -0.32(5) + 1.3(10)
= 11.4
Total utility for both Alice and Bob will be,
UA(5,10) + UB(10,5)
= 11.4 + 3.914
= 15.314
If Alice offers Bob $2, Bob's utility will be,
UB(10,2)
= 0.314 + 0.72(2)
= 1.754
And Alice's utility will be,
UA(2,10)
= -0.32(2) + 1.3(10)
= 12.4
So the total utility for both Alice and Bob will be,
UA(2,10) + UB(10,2)
= 12.4 + 1.754
= 14.154
If Alice offers Bob $10, Bob's utility will be,
UB(10,10)
= 0.314 + 0.72(10)
= 7.514
And Alice's utility will be,
UA(10,10)
= 0.3(10)³ + 0.72(10)
= 307.2
So the total utility for both Alice and Bob will be,
UA(10,10) + UB(10,10)
= 307.2 + 7.514
= 314.714
Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.
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Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. He made a $4,330 partial payment at 2 months and another partial payment of $2,600 at 6 months. How much is due at maturity?
Answers
If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.
How to find the amount?To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.
To do this, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest
P = Principal (original loan amount)
r = Annual interest rate
t = Time (in years)
The interest for the first two months can be calculated as:
I1 = P * r * t1
= 24420 * 0.035 * (2/12)
= 142.45
So after the first two months, the amount owing on the loan is:
P1 = P + I1 - 4330
= 24420 +142.45 - 4330
= 20,232.45
The interest for the next four months can be calculated as:
I2 = P1 * r * t2
= 20,232.45 * 0.035 * (4/12)
= 236.05
So after six months, the amount owing on the loan is:
P2 = P1 + I2 - 2600
= 20,232.45 + 236.05- 2600
= 17868.50
Now we can calculate the interest for the remaining 18 months:
I3 = P2 * r * t3
= 17868.50* 0.035 * (18/12)
= 938.10
So the total amount owing at maturity (after 2 years) is:
Total amount owing = P2 + I3
= 17868.50 + 938.10
= 18806.6
Therefore, Andres Michael owes $18806.6 at maturity.
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solve this proportion: 5/a = 3/4
Answers
Answer:
[tex]a = \frac{20}{3}[/tex]
Step-by-step explanation:
Find the product of 3√20 and √5 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answers
Answer:
30, rational
Step-by-step explanation:
[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]
The result is rational because it can be written as a fraction of integers.
Find X using the picture below.
Answers
Answer: 37.5
Step-by-step explanation:
75 - 180 = 105
105 degrees = the obtuse angle, bottom triangle.
75/2= 37.5 (since both sides of the bottom triangle are equal angles)
A simple random sample of size n is drawn. The sample mean, x, is found to be 18.1, and the sample standard deviation, s, is found to be 4.1.
(a) Construct a 95% confidence interval about u if the sample size, n, is 34.
Lower bound: Upper bound:
(Use ascending order. Round to two decimal places as needed.)
Answers
In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
We use the following formula to create a confidence interval around the population mean u:
CI = x ± z*(s/√n)
where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.
Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.
CI = 18.1 ± 1.96*(4.1/√34)
CI = 18.1 ± 1.96*(0.704)
CI = 18.1 ± 1.38
Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.
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Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
Answers
The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.
The expression !(!(x < y) || (y != 5)) is equivalent to:
(x < y) && (y == 5)
To see why, let's break down the original expression:
!(!(x < y) || (y != 5))
= !(x >= y && y != 5) (by De Morgan's laws)
= (x < y) && (y == 5) (by negating and simplifying)
So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.
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Complete question:
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
(x < y) && (y != 5)
(x >= y) && (y == 5)
(x < y) || (y == 5)
(x >= y) || (y != 5)
QUESTION THREE (30 Marks) a) For a group of 100 Kiondo weavers of Kitui, the median and quartile earnings per week are KSHs. 88.6, 86.0 and 91.8 respectively. The earnings for the group range between KShs. 80-100. Ten per cent of the group earn under KSHs. 84 per week, 13 per cent earn KSHs 94 and over and 6 per cent KShs. 96 and over. i. Put these data into the form of a frequency distribution and obtain an estimate of the mean wage. 15 Marks
Answers
Answer:
the answer would be 100 I guess
can anyone help me with this question triangles?
Answers
The missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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1 On a map of scale 1:100 000, the distance between Tower Bridge
and Hammersmith Bridge is 12.3 cm.
What is the actual distance in km?
Answers
To calculate the actual distance in km, we need to use the scale factor of 1:100 000. This means that 1 cm on the map is equivalent to 100 000 cm in real life.
Therefore, 12.3 cm on the map is equivalent to 12.3 x 100 000 cm in real life.
Now, 1 km is equivalent to 100 000 cm.
Therefore, 12.3 x 100 000 cm is equivalent to 1.23 km.
Hence, the actual distance in km is 1.23 km.
Solve each proportion round to the nearest tenth
Answers
Answer:
[tex]v = \frac{7}{2}[/tex]
Step-by-step explanation:
Find any critical numbers of the function.
Answers
Answer:
(1, 2) and (-1, -2). or. (±1, ±2)
Step-by-step explanation:
[tex]{ \sf{f(x) = \frac{4x}{ {x}^{2} + 1 } }} \\ [/tex]
- Simply, a critical number or critical point is gotten by differentiating the function.
From Quotient rule;
[tex]{ \sf{ {f}^{l}(x) = \frac{4( {x}^{2} + 1) - (2x)(4x)}{ {( {x}^{2} + 1)}^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{ {4x}^{2} + 4 - {8x}^{2} }{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{f {}^{l}(x) = \frac{4(1 - {x}^{2}) }{ {( {x}^{2 } + 1) }^{2} } }}[/tex]
Then equate this derivative to zero;
[tex]{ \sf{0 = \frac{4(1 - {x}^{2} )}{ {( {x}^{2} + 1) }^{2} } }} \\ \\ { \sf{4(1 - {x}^{2} ) = 0}} \\ \\ { \sf{4 - {4x}^{2} = 0}} \\ \\ { \sf{4 {x}^{2} = 4}} \\ \\ { \sf{x = \sqrt{1} }} \\ \\ { \sf{ \underline{ \: x = \pm 1 \: }}}[/tex]
Substitute for x in f(x)
For x = 1
[tex]{ \sf{f(1) = \frac{4(1)}{ {(1)}^{2} + 1} = \frac{4}{2} = 2 }} \\ [/tex]
For x = -1
[tex]{ \sf{f( - 1) = \frac{4( - 1)}{ {( - 1)}^{2} + 1 } = \frac{ - 4}{2} = - 2 }} \\ [/tex]
Therefore points are;
(1, 2) and (-1, -2)
Select all the expressions that are equivalent to (12 + x)10.5.
It’s multiple choice and these are the answers
10.5(12x)
(10.5 + 12 + x)
10.5(12 + x)
126x
126 + 10.5x
22.5 + x
Answers
126+10.5x
Step-By-Step:
PLEASE HELP 30 POINTS!
Answers
Answer:
57
57
123
123
57
57
123
that's all.
Answer:
m<1 = 57°
m<2 = m<1 = 57°
m<3 = x = 123°
m<4 = x = 123°
m<5 = m<1 = 57°
m<6 = m<5 = 57°
m<7 = m<4 = 123°
Step-by-step explanation:
[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]
one ticket is drawn at random from each of the two boxes below: 1 2 6 1 4 5 8 find the chance that the both numbers are even numbers.
Answers
The chance that both numbers drawn are even numbers is 8/21.
The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.
The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.
By the multiplication rule of probability, the probability of drawing an even number from both boxes is
(4/7) × (2/3) = 8/21
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THE FIRST ANSWER GETS BRAINLIEST AND FIVE STARS!
Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
Answers
In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate percentage between 1985 and 2005? Assume that the value continued
to grow by the same percentage. What was the value of the house in the year 2010?
Answers
Answer:
To find the annual growth rate percentage, we can use the formula:
annual growth rate = [(final value / initial value)^(1/number of years)] - 1
where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.
Using the given values, we have:
annual growth rate = [(148,000 / 108,000)^(1/20)] - 1
= 0.0226 or 2.26%
So the house appreciated at an annual growth rate of 2.26%.
To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:
value in 2010 = 148,000 * (1 + 0.0226)^5
= $175,465.11 (rounded to the nearest cent)
Therefore, the value of the house in the year 2010 was $175,465.11.
Consider the initial value problem y⃗ ′=[33????23????4]y⃗ +????⃗ (????),y⃗ (1)=[20]. Suppose we know that y⃗ (????)=[−2????+????2????2+????] is the unique solution to this initial value problem. Find ????⃗ (????) and the constants ???? and ????.
Answers
The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.
To find the solution to the initial value problem, we first need to solve the differential equation.
Taking the derivative of y(t), we get:
y'(t) = -2t + a
Taking the derivative again, we get:
y''(t) = -2
Substituting y''(t) into the differential equation, we get:
y''(t) + 2y'(t) + 10y(t) = 20sin(3t)
Substituting y'(t) and y(t) into the equation, we get:
-2 + 2a + 10(-2t + a) = 20sin(3t)
Simplifying, we get:
8a - 20t = 20sin(3t) + 2
Using the initial condition y(0) = 2, we get:
y(0) = -2(0) + a = 2
Solving for a, we get:
a = 2
Using the other initial condition y'(0) = 21, we get:
y'(0) = -2(0) + 2(21) + B = 21
Solving for B, we get:
B = -21
Therefore, the solution to the initial value problem is:
y(t) = -t^2 + 2t + 3sin(3t) - 1
Thus, we have e(t) = y(t) - 8, so
e(t) = -t^2 + 2t + 3sin(3t) - 9
and a = 2, B = -21.
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_____The given question is incomplete, the complete question is given below:
Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =
Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
Answers
150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
Answers
Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
Marcia Gadzera wants to retire in San Diego when she is 65 years old. Marcia is now 50 and believes she will need $90,000 to retire comfortably. To date, she has set aside no retirement money. If she gets interest of 10% compounded semiannually, how much must she invest today to meet her goal of $90,000?
Answers
Answer:
Step-by-step explanation:
We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where:
FV = future value of the annuity
PMT = payment (or deposit) made at the end of each compounding period
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:
Marcia wants to retire in 15 years (when she is 65), so t = 15
The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2
Marcia wants to have $90,000 in her retirement account
Substituting these values into the formula, we get:
$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)
Simplifying the formula, we get:
PMT = $90,000 / [(1.025)^30 - 1] / 0.025
PMT = $90,000 / 19.7588
PMT = $4,553.39 (rounded to the nearest cent)
Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.
