Omar is driving to Denver. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Omar has 55 miles to his destination after 44 minutes of driving, and he has 41.5 miles to his destination after 62 minutes of driving. How many miles will he have to his destination after 74 minutes of driving?
Answers
Answer:
After 74 minutes of driving, he still has 32.5 miles to his destination.
Step-by-step explanation:
A linear relationship can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that a line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Now let's go to the question.
We know that the distance to his destination is a linear function of his total driving time.
We know that he has 55 miles to his destination after 44 minutes of driving. We can write this as the point (44 min, 55mi)
We know that he has 41.5 miles to his destination after 62 minutes of driving, we can write this as (62 min, 41.5mi)
Then the slope of this equation will be:
a = (41.5mi - 55mi)/(62min - 44min) = -0.75 mi/min.
Then the linear equation is something like:
y = (-0.75 mi/min)*x + b
to find the value of b we can use the fact that this line passes through the point (44 min, 55mi)
This means that when x = 44 min, we must have y = 55mi
Then:
55mi = (-0.75 mi/min)*44min + b
55mi + (0.75 mi/min)*44min = b
88mi = b
Then the equation is:
y = (-0.75 mi/min)*x + 88mi
Now we want to know how many miles will he have to his destination after 74 minutes of driving, then we need to replace x by 74 min.
y = (-0.75 mi/min)*74min + 88mi
y = 32.5mi
After 74 minutes of driving, he still has 32.5 miles to his destination.
Related Questions
please and thank youuu
Answers
The 27th term of the arithmetic sequence with the first term \(\(a_1 = -13\)\) and a common difference of 4 is 91.
To find the 27th term of an arithmetic sequence, we can use the formula:
\(\[a_n = a_1 + (n - 1)d\]\)
where \(\(a_n\)\) represents the \(\(n\)\)th term, \(\(a_1\)\) is the first term, \(\(d\)\) is the common difference, and \(\(n\)\) is the term number.
Given that \(\(a_1 = -13\)\) and the common difference \(\(d = 4\)\), we will simply substitute these values into the given formula:
\(\[a_{27} = -13 + (27 - 1) \cdot 4\]\)
Simplifying the equation, we have:
\(\[a_{27} = -13 + 26 \cdot 4\]\)
Calculating the expression, we get:
\(\[a_{27} = -13 + 104\]\)
Finally, evaluating the sum, we find:
\(\[a_{27} = 91\]\)
Therefore, the 27th term of the arithmetic sequence with the first term \(\(a_1 = -13\)\) and a common difference of 4 is 91.
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If $3000 is put in a savings account that earns 2.5%
interest compounded semiannually.
a. Write a function A(t) to represent the money in
account after t years.
b. What is the total amount of money in the
account after 6 years?
HELPPPPP
Answers
the total amount of money in the account after 6 years is approximately $3,617.08.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
a. The formula for the amount A after t years, with an initial principal P, an annual interest rate r, and n times compounded per year is given by:
\(A = P(1 + r/n)^nt\)
In this case, P = $3000, r = 0.025 (2.5% expressed as a decimal), n = 2 (compounded semiannually), and t is the number of years. So the function A(t) can be written as:
\(A(t) = 3000(1 + 0.025/2)^2t\)
b. To find the total amount of money in the account after 6 years, we need to evaluate A(6):
\(A(6) = 3000(1 + 0.025/2)^{(16)\)
≈ $3,617.08
Therefore, the total amount of money in the account after 6 years is approximately $3,617.08.
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The area of a rectangular field is 8330M squared if the width of the field is 85 M what is its length
Answers
Answer:
length 98 meter
Step-by-step explanation:
Area=lw
Area=length times 85
8330=85 times l
divide by 85 it gives 98 meter
A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters. A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters. What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter. 282.6 mm3 271.3 mm3 553.9 mm3 836.5 mm3
Answers
Answer:
its b
Step-by-step explanation:
got it right on edge
The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.
What is the volume of the cylinder?A cylinder is a three-dimensional object. It is a prism with a circular base.
Volume of a cylinder = nr^2h
Where:
n = 22/7 r = radius = diameter / 2The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³
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Chase and Simon (1973) studied the memory of chess novices and experts for positions of chess pieces on a chessboard. Although experts generally have a far better memory for chess positions than do novices, they found that the novices performed as well or better than the experts when asked to recall random arrangements of chess pieces on the chessboard. The random arrangements included arrangements that could not possibly occur in a real game of chess. Why did novices do as well as experts when the pieces were arranged at random
Answers
Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.
One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.
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2 c) factorize : x² - 2xy + y²
Answers
Answer:
(x-y)²
Since, it's formula of (x+y)² ...
Hello!
This is an identity :
\(\boxed {(x - y)^2 = x^2 - 2xy + y^2}\)
∴ The factors are (x - y) and (x - y).
Please can anyone Help ASAP
Answers
Answer:
Jemima is wrong because perimeter is sum of all sides and the perimeter of this figure would be the outer sides of it and not the inner sides.
Answer:
See below.
Step-by-step explanation:
She is wrong because 3 times the perimeter of one triangle is the sum of 9 sides of the triangles.
In the shape we see that some of the sides of the triangles are 'shared' and dare not part of the perimeter of the shape, - the perimeter is only the length of 5 sides of a triangle.
So the perimeter is less than the sum of the sides of the 3 triangles.
The domain of f g consists of numbers x for which g(x) ____ 0 that are in the domains of ___________________.
Answers
The domain of f /g consists of numbers x for which g(x) does not equal to 0 that are in the domains of f and g.
According to the statement
we have given that the The domain of f /g consists of numbers x And we have to find the value of the g(x).
So, For this purpose, we know that the
Domain of a function is the set of all possible inputs for the function.
And according to definition it is clear that the , domain is the input value of the function,
And it is impossible that the function have a 0 zero input value in the functions f(x) and the g(x).
Every function have at least 1 domain or input value.
So, The domain of f /g consists of numbers x for which g(x) does not equal to 0 that are in the domains of f and g.
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Factor the quadratic inequality to find the x-intercept points.
y >= x ^ 2 - 2x - 3
Answers
Answer:
x = 3
x = -1
Step-by-step explanation:
First you wanna assume that y is 0: 0 \(\geq\) \(x^{2}\) - 2x - 3
now factor the right side like any other problem:
we know that we automatically have (x _ ?)(x_?), because there is an x squared
now we need to find a number that multiplies to -3 and adds up to -2
if take positive 1 and -3, we multiply it to get -3, and when you add the two numbers, you get -2
so now we can fill (x _ ?)(x_?), and turn it into (x - 3)(x + 1)
now we will take each parenthesis part and separate it and solve them for x individually:
(x - 3) = 0
x = 3
(x + 1) = 0
x = -1
so now we have our x intercepts
Question 7 (10 points] Find all distinct real or complex) eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvale For each eigenvalue, specify the number of basic eigenevectors corresponding to that eigenvalue
a=[8 -15]
[6 -10]
number of distinct eigenvalues=
number of vectors=
Answers
The basic eigenvector corresponding to λ₁ = 4 is v₁ = [3.75, 4], and the basic eigenvector corresponding to λ₂ = -3 is v₂ = [5, 6].
To find the eigenvalues of matrix A, we need to solve the characteristic equation:
|A - λI| = 0
where I is the identity matrix of the same size as A, and λ is the eigenvalue we are trying to find.
For matrix A given as:
a=[8 -15]
[6 -10]
we have:
|A - λI| =
|8 - λ -15 |
|6 -10- λ |
Expanding the determinant, we get:
(8 - λ)(-10 - λ) - (-15)(6) = 0
Simplifying the expression, we get:
λ² - 2λ - 12 = 0
Using the quadratic formula, we get:
λ₁ = 4
λ₂ = -3
Therefore, the distinct eigenvalues of A are λ₁ = 4 and λ₂ = -3.
Next, we find the eigenvectors corresponding to each eigenvalue. We do this by solving the system of equations:
(A - λI)x = 0
For λ₁ = 4:
A - λ₁I =
|8 - 4 -15 |
|6 -10 - 4 |
=
|4 -15 |
|6 -14|
RREF:
|1 -3.75|
|0 0 |
Thus, we have a free variable x₂. Setting x₂ = 4, we get the basic eigenvector:
v₁ = [3.75, 4]
Therefore, there is one basic eigenvector corresponding to eigenvalue λ₁ = 4.
For λ₂ = -3:
A - λ₂I =
|8 15 |
|6 7 |
RREF:
|1 -5/6|
|0 0 |
Thus, we have a free variable x₂. Setting x₂ = 6, we get the basic eigenvector:
v₂ = [5, 6]
Therefore, there is one basic eigenvector corresponding to eigenvalue λ₂ = -3.
In summary, the distinct eigenvalues of matrix A are λ₁ = 4 and λ₂ = -3. There is one basic eigenvector corresponding to each eigenvalue. The basic eigenvector corresponding to λ₁ = 4 is v₁ = [3.75, 4], and the basic eigenvector corresponding to λ₂ = -3 is v₂ = [5, 6].
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round 5,4268 to the nearest thousandth
Answers
the answer will be 5,427 because we need to round the six and since 8 is greater that 5, we aproximate 6 to 7
Amap is drawn so that every 1 inch on the map represents 50 actual miles. The table below can be used to record the actual distances between towns on the map. Actual Distances and Map Distances Actual Distance (mi.) Map Distance (in.) 1 50 What is the actual distance between two towns that are 4 inches apart on the map? O 54 miles 80 miles O 150 miles O 200 miles Save and Exit NO Submit Mark this and rotun
Answers
Answer:
200 miles
50x4
Step-by-step explanation:
Aaron’s class as 24 students. 1/6 of them play basketball. How many students in his class play basketball?
Answers
Answer:
4
Step-by-step explanation:
Indira buys 1250 square metres of land to build a hotel. Each square metre of land costs $12. Calculate the cost of the land. Answer(a) $ [1] (b) The cost of the land is 3% of the cost of the hotel. Calculate the cost of the hotel
Answers
Answer:
500000
Step-by-step explanation:
yeah boi
Simon spent 1/4 of his wages on rent.
He spent 20% of his wages on food.
He spent 0.15 of his wages on clothes
Work out the fraction of his wages that he had left.
Answers
Answer:
2x/5 wages is remaining.Step 1: Lets say 'x' is the total wage. Then we subtract 1/4 from the total wages.
=> 4x/4 - x/4
=> 3x/4 = Remaining Wages Left.
Step 2: Subtract 20% from 3x/4.
3x/4 - x/5 = Remaining Wages Left. [20% = 20x/100 = x/5]
=> 11x/20 = Remaining Wages Left.
Step 3: Subtract 0.15x from his remaining wages left.
=> 11x/20 - 3x/20 = Remaining Wages Left. [0.15 = 15/100 = 3/20]
=> 8x/20 = Remaining Wages Left.
Step 4: Simplify
8x/20 = 2x/5 = 0.40x
=> Simon has saved 2x/5 of the wages.
Please give me brainliest :)
Answer:
2/5 of wedgesStep-by-step explanation:
The total is 100% or 1.
Spent:
1/4 + 20% + 0.15 =0.25 + 0.2 + 0.15 = 0.6Left:
1 - 0.6 = 0.4 = 4/10 = 2/5if two lines form congruent adjacent angles, then the lines are
Answers
If two lines form congruent adjacent angles, it indicates that the lines are perpendicular to each other.
This is known as the Perpendicular Adjacent Angles Theorem. According to this theorem, if two lines intersect and the adjacent angles formed by the intersection are congruent, then the lines are perpendicular to each other.
Congruent adjacent angles are angles that have the same measure and share a common vertex and a common side. When two lines intersect to form congruent adjacent angles, it implies that the lines are forming a right angle at their point of intersection. Thus, the lines are perpendicular to each other.
In summary, if two lines form congruent adjacent angles, it indicates that the lines are perpendicular.
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With the increase in the use of social media, it is important to ________ those who don't follow the rules of ethical communication.
Answers
With increase in use of "social-media", it is important to diligently guard and defend against those who don't follow the rules of "ethical-communication", correct option is (c).
With increase in use of "social-media", it is important to diligently "guard and defend" against those who don't follow rules of "ethical-communication", which means actively monitoring and taking necessary actions to address unethical behavior on social media platforms.
It involves implementing measures to prevent and mitigate issues such as cyberbullying, hate speech, misinformation, and other forms of harmful or unethical communication.
By diligently guarding and defending against such behavior, individuals and organizations can contribute to creating a safer and more ethical online environment.
Therefore, the correct option is (c).
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The given question is incomplete, the complete question is
With the increase in the use of social media, it is important to ________ those who don't follow the rules of ethical communication.
(a) limit website access from
(b) not respond to
(c) diligently guard and defend against
(d) identify corporate policy for
f(0)=3, f(4) = 9
how do i find this
Answers
Answer:
Step-by-step explanation:
f(3) = 4 f(0) =9
Y = mx + b
m = (9 -4) / (0 - 3) = -5/3
b = 9
Y = - 5/3 X + 9
Find the answer to the following subtraction problem by using the Left to Right Algorithm. Do the work on paper then upload a picture. Make sure your drawing is clear. 3131 - 1641
Answers
I can explain how to solve the subtraction problem using the Left to Right Algorithm:
To perform the Left to Right Algorithm, we start from the leftmost digit of the numbers and subtract each corresponding digit until we reach the end of the numbers. If the digit being subtracted from is smaller than the digit being subtracted, we borrow from the next digit to the left.
Using this algorithm, we can solve the problem as follows:
3 1 3 1
- 1 6 4 1
---------
2 1 6 0
Therefore, 3131 - 1641 = 2160.
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TIME REMAINING
59:50
The table shows the mean number of basketball goals made by four random samples of players from the school team
during this year's season.
Sample #
Sample Mean
Number of Goals
7
1
4
2
3
5
4
8
Is a valid prediction for the mean of the population possible using these samples?
O No, there are not enough samples.
Yes, the sample means are all less than 10.
Yes, the variation of the sample means is small.
O No, the variation of the sample means is too great.
Mark this and retum
Save and Exit
Next
Submit
Answers
Answer:
I'd say yes, because you have a good variety of samples. (B.)
Step-by-step explanation:
The statement "P implies Q' is FALSE under which of the following conditions? Choose all that apply. a. P and Q are both true. b. P and Q are both false. c. P is true and Q is false. d. P is false and Q is true.
Answers
The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.
The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).
To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.
Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.
Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.
Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.
Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.
Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.
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if the distance from u to v equals the distance from u to v, then u and v are orthogonal. true or false
Answers
Answer:
This statement is FALSE
Step-by-step explanation:
If the distance from u to v equals the distance from u to v, it does not necessarily mean that u and v are orthogonal.
Distance is a scalar quantity and it measures the length between two points. Orthogonality, on the other hand, is a concept that relates to the angle between two vectors. Two vectors are orthogonal if their dot product is zero, which means that they are perpendicular to each other.
Therefore, it is possible for two vectors to have the same distance from a point without being orthogonal to each other.
When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.
Answers
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If 9 x 7 = 3545 and 4 x 3 = 1520 then 6 x 8 = ?
Answers
Answer:
4030 or 3040 I think 4030 though
Step-by-step explanation:
I think this is it but 6*8 is 48....I used a little logic so hopefully this is right
Answer:
4030
Step-by-step explanation:
if 9× 7 = 3545 then it 7 × 5, 9× 5 which gives 3545
4x3 = 3× 5, 4×5 which gives 1520
so 6× 8 will give 8×5, 6×5 = 4030
hi you can help me plis
Answers
Answer:
14
I hope it works for you
If f(x) = 2x2 + 4 and g(x) = x - 6, determine f(-5) - g(-5).
53
-49
55
65
which one is the answer
Answers
Answer:
65
Step-by-step explanation:
f(x) = 2x² + 4
g(x) = x - 6
f(-5) = 2 * (-5)² + 4
= 50 + 4
= 54
g(-5) = - 5 - 6
= - 11
f(-5) - g(-5) = 54 + 11 = 65
Hope it will help you :)
Question 19
By age 65 the number of Americans who experience hearing loss sufficient to affect communication is:
a. 1 in 2
b. 1 in 3
c. 1 in 4
d. 1 in 5
Answers
The number of Americans experience hearing loss sufficient to affect communication is: 1 in 4.
According to the National Institute on Deafness and Other Communication Disorders (NIDCD).
Approximately 1 in 4 adults in the United States aged 65 and older have hearing loss that is sufficient to affect communication.
This is based on data from a survey conducted by the NIDCD and the National Health Interview Survey.
NIDCD (National Institute on Deafness and Other Communication Disorders).
In the United States, 1 in 4 persons 65 and older suffer hearing loss severe enough to impair conversation.
This is based on information from surveys done by the National Health Interview Survey and the NIDCD.
The number of Americans who experience hearing loss sufficient to affect communication is: 1 in 4.
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14.
Write an equation in point-slope form for the line through the given point with the given slope.
(–3, –7); m = -6/5
A. y – 7 = -6/5(x + 3)
B. y + 3 = -6/5(x + 7)
C. y – 7 = -6/5(x – 3)
D. y + 7 = -6/5(x + 3)
Answers
Answer:
D. y + 7 = -6/5(x + 3)
Step-by-step explanation:
Answer:
B. y + 7 = -6/5 (x+3)
Step-by-step explanation:
Use the given slope and point to substitute into the point-slope formula y − y 1 = m ( x − x 1 ) .
Slope-intercept form: y = − 6 /5 x − 53 /5
Point-slope form: y + 7 = − 6 /5 ⋅ ( x + 3 )
point q is located at (4, 5). we want to shift it 6 units right. what would be the location of point q'?
Answers
Answer:
Point q would be located at (10,5)
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Find the 4th term in the sequencewith the following definition:aj = 0an = 2(an-1-3)
Answers
Answer:
-60
Explanation:
To find the 4th term we need to also find the 2nd and 3rd terms as follows:
\(\begin{gathered} a_n=2(a_{n-1}-3) \\ a_2=2(a_{2-1}-3) \\ a_2=2(a_1-3) \\ a_2=2(0-3) \\ a_2=2(-3) \\ a_2=-6 \end{gathered}\)\(\begin{gathered} a_3=2(a_{_2}-3) \\ a_3=2(-6-3) \\ a_3=3(-9) \\ a_3=-27 \end{gathered}\)Finally, we can calculate the value of the 4th term as:
\(\begin{gathered} a_4=2(a_3-3) \\ a_4=2(-27-3) \\ a_4=2(-30) \\ a_4=-60 \end{gathered}\)So, the answer is -60