a) The least squares regression line for the given data is y = -3.5358x + 87.2857.
b) The slope of -3.5358 indicates that for each additional day absent, the final grade is expected to decrease by approximately 3.5358 points on average.
c) The y-intercept of 87.2857 represents the estimated final grade when the number of absences is zero, implying that a student who did not miss any classes is expected to have a final grade of approximately 87.2857.
a) To find the least squares regression line, we need to determine the equation of the line in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's calculate the necessary sums:
∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
∑y = 89.2 + 86.4 + 83.5 + 81.1 + 78.2 + 73.9 + 64.3 + 71.8 + 65.5 + 66.2 = 759.9
∑xy = (0 * 89.2) + (1 * 86.4) + (2 * 83.5) + (3 * 81.1) + (4 * 78.2) + (5 * 73.9) + (6 * 64.3) + (7 * 71.8) + (8 * 65.5) + (9 * 66.2) = 5079.6
∑[tex]x^2[/tex] = [tex](0^2) + (1^2) + (2^2) + (3^2) + (4^2) + (5^2) + (6^2) + (7^2) + (8^2) + (9^2)[/tex] = 285
[tex]\sum y^2 = (89.2^2) + (86.4^2) + (83.5^2) + (81.1^2) + (78.2^2) + (73.9^2) + (64.3^2) + (71.8^2) + (65.5^2) + (66.2^2) = 59718.63[/tex]
Using the formulas for the slope (m) and y-intercept (b):
m = (n∑xy - (∑x)(∑y)) / (n∑x^2 - (∑x)^2)
b = (∑y - m(∑x)) / n
Substituting the calculated values:
m = (10 * 5079.6 - (45 * 759.9)) / (10 * 285 - (45)^2)
b = (759.9 - m(45)) / 10
Calculating the values:
m ≈ -3.5358
b ≈ 87.2857
Therefore, the least squares regression line is y = -3.5358x + 87.2857.
b) The slope (-3.5358) represents the change in the final grade (y) for each additional day absent (x). This means that on average, for each additional day a student is absent, their final grade is expected to decrease by approximately 3.5358 points.
c) The y-intercept (87.2857) represents the estimated final grade when the number of absences (x) is zero. In other words, it is the predicted final grade for a student who did not miss any classes.
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Question
The following data represents the number of days absent, x, and the final grade, y, for a sample of college students at a community college.
No.of absences, x | 0 1 2 3 4 5 6 7 8 9
Final Grade, y | 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
a) Find the least squares regression line treating the number of absences as the explanatory variable and the final grade as the response variable.
b) Interpret the slope using complete sentences.
c) Interpret the y intercept using complete sentences.
In AMNO, the measure of 0=90°, ON = 15, MO = 8, and NM = 17. What is the value of the cosine of M to the nearest hundredth?
To find the value of the cosine of angle M in triangle AMNO, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides [tex]\displaystyle a[/tex], [tex]\displaystyle b[/tex], and [tex]\displaystyle c[/tex], and angle [tex]\displaystyle C[/tex] opposite side [tex]\displaystyle c[/tex], the following equation holds:
[tex]\displaystyle c^{2} =a^{2} +b^{2} -2ab\cos( C)[/tex]
In triangle AMNO, we have the following information:
[tex]\displaystyle AM=17[/tex] (side [tex]\displaystyle a[/tex])
[tex]\displaystyle MN=15[/tex] (side [tex]\displaystyle b[/tex])
[tex]\displaystyle AN=8[/tex] (side [tex]\displaystyle c[/tex])
Angle M = 90 degrees
We can apply the Law of Cosines to find the value of [tex]\displaystyle \cos( M)[/tex]:
[tex]\displaystyle AN^{2} =AM^{2} +MN^{2} -2\cdot AM\cdot MN\cdot \cos( M)[/tex]
Substituting the given values:
[tex]\displaystyle 8^{2} =17^{2} +15^{2} -2\cdot 17\cdot 15\cdot \cos( M)[/tex]
Simplifying:
[tex]\displaystyle 64=289+225-510\cdot \cos( M)[/tex]
[tex]\displaystyle 64=514-510\cdot \cos( M)[/tex]
Rearranging the equation:
[tex]\displaystyle 510\cdot \cos( M) =514-64[/tex]
[tex]\displaystyle 510\cdot \cos( M) =450[/tex]
Dividing both sides by 510:
[tex]\displaystyle \cos( M) =\frac{450}{510}[/tex]
Simplifying:
[tex]\displaystyle \cos( M) =\frac{15}{17}[/tex]
Therefore, the value of the cosine of angle M in triangle AMNO, to the nearest hundredth, is approximately [tex]\displaystyle 0.88[/tex].
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
Corelise has 3 wooden bookcases that contain all of her books. The first bookcase has 3 shelves with 22 books on each shelf. The second bookcase has 4 shelves with 18 books on each shelf. The third bookcase has 5 shelves with 17 books on each shelf.
Part A
Write an expression for how many books she has.
A.
(
3
×
22
)
+
(
4
×
18
)
+
(
5
×
17
)
B.
(
3
+
22
)
×
(
4
+
18
)
×
(
5
+
17
)
C.
(
3
+
22
)
+
(
4
+
18
)
+
(
5
+
17
)
D.
(
3
×
22
)
+
(
4
+
18
)
+
(
5
×
17
)
Part B
Stephan has 230 books. Does Corelise have more than Stephan?
Yes or no
, she has
2,7,13,23
more or fewer
than Stephan.
Answer:
A
Step-by-step explanation:
3x16
+
4x18
+
5x17
Solving for Side Lengths of Right Triangles
Quiz Active
1
2 3
O
4 5
с
Which relationship in the triangle must be true?
sin(B) = sin(A)
O sin(B) = cos(90 - B)
cos(B) = sin(180 - B)
O cos(B) = cos(A)
6
B
7 8
9
10
TIME REMAINING
12:30
Answer:
6 is the sin
Step-by-step explanation:
30+((-2×(25- (13-3)))
Hello,
Answer:
[tex]30+((-2\times(25- (13-3)))[/tex]
[tex]=30+((-2\times(25- 10))[/tex]
[tex]=30+(-2\times 15)[/tex]
[tex]=30+(-30)[/tex]
[tex]=30-30[/tex]
[tex]=\boxed{0}[/tex]
PLSS HELP ASAPPP
PLS HELP HURRYYY
I NEED HELP RIGHT NOW!!!
GEOMETRY 50POINTS
TY GUYS
Answer:
35.7 ft
Step-by-step explanation:
Given
Hypotenuse (length of the ladder) = 50 ft
Base (distance from the ladder to wall) = 35 ft
Height (of the wall) = [tex]\sqrt{50^{2}-35^{2} }[/tex] = [tex]\sqrt{1275}[/tex] = 35.7 ft
How many cubic centimeter blocks are in the bottom layer of the prism shown below? A rectangular prism with length of 3 centimeters, height of 5 centimeters, and width of 4 centimeters. 3 4 7 12
Answer:
There are 12 blocks in the bottom layer
Step-by-step explanation:
We see from the diagram that in the bottom layer,
length = 3 cm
width = 4 cm
And that there are 3 blocks for the 3 cm length,
Hence each block has a length of 1 cm (the 3 then make up 3 cm)
And there are 4 blocks for the 4 cm width
Hence the width is also 1 cm (4 of these make up 4 cm width)
Now, to find the total number of blocks,
we just multiply the length and width,
so, (3)(4) = 12
so there are 12 blocks in the bottom layer
An event with probability 3/4 is more likely to happen than an event with probability 4/5
True or False why?
The given statement "An event with probability 3/4 is more likely to happen than an event with probability 4/5" is true.
The reason why we say an event with a higher probability is more likely to happen is because probability is the measure of how often an event will occur during a large number of trials.
Therefore, when we compare the probabilities of two events, we can expect that the one with the higher probability will occur more often and therefore is more likely to happen.For instance, in the context of a coin flip, the probability of getting heads is 1/2 while the probability of getting tails is also 1/2.
Therefore, both events are equally likely to happen. On the other hand, if we were to compare the probability of rolling a six-sided die and getting a 1, which has a probability of 1/6, with the probability of rolling the die and getting a number less than or equal to 4, which has a probability of 4/6 or 2/3, we can say that the latter is more likely to happen since it has a higher probability.
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please answer ASAP I will brainlist
Answer:
(a) 10, $2088.81
(b) see attached
(c) B. increases at a slower rate
Step-by-step explanation:
Given the cost function g(x) = -1736.7 +1661.4·ln(x) for the average dollar cost of health insurance in year x after 2000, you want the cost in 2010, a graph for the years 2006 to 2015, and a description of the shape of the curve.
(a) Cost in 2010The value of x is years after 2000, so for the year 2010, the value of x is ...
x = 2010 -2000 = 10
Substituting 10 for x in the function will give the cost in 2010. That is ...
g(10) = -1736.7 +1661.4·ln(10) ≈ 2088.81
The cost in 2010 is about $2088.81.
(b) GraphThe second attachment shows a graphing calculator's rendition of the graph. We note it has positive slope everywhere, but does not intersect the lines y=1000 or y=3000. This eliminates choices A, C, and D, leaving choice B for the graph.
(c) ShapeThe logarithm function has positive and decreasing slope. The function here is a scaled and shifted version of the logarithm function, but it still has positive and decreasing slope. That is, ...
the average cost increases at a slower rate as time goes on
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What is the area of the shaded region?
Step-by-step explanation:
The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon
A students score is at the 16th percentile. This indicates that:
A. 16% of scores are at his/her score or below
B. 84% of scores are at his/her score or below.
Answer:
A. 16% of scores are at his/her score or below
Step-by-step explanation:
When a student's score is at the 16th percentile, it means that their score is equal to or better than 16% of the scores in the population. In other words, 16% of the scores are at their score or below.
Rotate point (-3, 2) about the origin 180 degrees clockwise. Where will the new point be?
Answer: the answer is (3,-2)
Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)
therefore
(-3,2) becomes (3,-2)
I'm pretty sure
Is f(x)=-x3-x an odd function
The function f(x) = -x³ - x is an odd function.
Is the given function odd, even, or neither?Given the function in the question:
f(x) = -x³ - x
To determine if a function is odd, we need to check if it satisfies the given property:
f(-x) = -f(x)
For all x in the domain of the function.
Given that:
f(x) = -x³ - x
Evaluate f(-x) for the given function f(x) = -x³ - x:
f(x) = -x³ - x
Replace x with -x
f(-x) = -(-x)³ - (-x)
f(-x) = -(-x³) + x
f(-x) = x³ + x
Now, check if -f(x) is equal to x³ + x:
-f(x) = -(-x³ - x)
-f(x) = x³ + x
Since -f(x) = x³ + x, f(x) = -x³ - x is an odd function.
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14x^(2n+1)+7x^(n+3)-21^(n+2)
100 points will be awarded
Answer:
Step-by-step explanation:
The given expression is: 14x^(2n+1) + 7x^(n+3) - 21^(n+2)
Unfortunately, it seems there is a missing exponent for the term "21" in the expression. Please provide the correct exponent for 21, and I'll be happy to help you further simplify the expression.
Henry deposited $150 in a bank Find the opposite quantity that makes Henry’s balance
Withdrawal: If Henry decides to withdraw money from his bank account, the opposite quantity would be the amount he withdraws.
Transfer: If Henry transfers money from his account to another account, the opposite quantity would be the amount of the transfer.
Debit/Credit: If there are debit or credit transactions on Henry's account, the opposite quantity would depend on whether it is a debit (negative) or credit (positive) entry.
To determine the opposite quantity that makes Henry's balance, we need to know the specific transaction or action that affects the balance. Without further information, it is not possible to provide an exact answer.
However, I can explain a few scenarios based on common banking transactions that could result in an opposite quantity affecting Henry's balance:
1. Withdrawal: If Henry decides to withdraw money from his bank account, the opposite quantity would be the amount he withdraws. For example, if Henry withdraws $50 from his account, the opposite quantity would be -$50.
2. Transfer: If Henry transfers money from his account to another account, the opposite quantity would be the amount of the transfer. For instance, if Henry transfers $100 to another account, the opposite quantity would be -$100.
3. Debit/Credit: If there are debit or credit transactions on Henry's account, the opposite quantity would depend on whether it is a debit (negative) or credit (positive) entry.
It's important to note that these scenarios are examples, and the opposite quantity would vary depending on the specific transaction or action affecting Henry's balance. To accurately determine the opposite quantity, we would need more information about the specific transaction or action taken by Henry that impacts his account balance.
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The cost of capsaicin arthritis rub is $21 for a
physical therapist who works with chronic arthritis patients, you need to buy
42 ounces of capsaicin. How many tubes will you need to purchase?
You will need to purchase approximately 1/42 of a tube, which is less than a full tube. In practical terms, you would need to purchase at least one tube to meet your requirement of 42 ounces of capsaicin arthritis rub.
To determine the number of tubes of capsaicin arthritis rub you will need to purchase, we can divide the total required quantity by the quantity in each tube.
Given that the cost of capsaicin arthritis rub is $21 and you need to buy 42 ounces, we need to find out how many ounces are in each tube.
Let's assume that each tube contains x ounces of capsaicin arthritis rub.
Now we can set up a proportion to solve for x:
42 ounces / x tubes = 1 tube / x ounces
Cross-multiplying gives us:
42x = 1 * x
Simplifying the equation:
42x = x
Dividing both sides of the equation by x (since x cannot be zero):
42 = 1
Since this equation is not true, it means that there is an error in our assumption. We need to revise our assumption.
Let's assume that each tube contains 1 ounce of capsaicin arthritis rub.
Now we can set up a new proportion:
42 ounces / x tubes = 1 tube / 1 ounce
Cross-multiplying gives us:
42x = 1 * 1
Simplifying the equation:
42x = 1
Dividing both sides of the equation by 42:
x = 1/42
As a result, you will need to buy less than a full tube—roughly 1/42 of a tube. In order to get the 42 ounces of capsaicin arthritis rub you need, you would essentially need to buy at least one tube.
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I just need help with the range domain is [-2,3)
Answer:
We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).
Step-by-step explanation:
4,5,6,8,9,9,10,12,12,12,17,17,18,18
which expression represents the product of x^3+2x-1 and x^4-x^3+3
Answer:
(x^3+2x-1) * (x^4-x^3+3)
Step-by-step explanation:
To simplify this expression, we can multiply each term in the first expression by each term in the second expression and combine like terms:
(x^3)(x^4) + (x^3)(-x^3) + (x^3)(3) + (2x)(x^4) + (2x)(-x^3) + (2x)(3) + (-1)(x^4) + (-1)(-x^3) + (-1)*(3)
Simplifying further:
x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x - x^4 + x^3 - 3
Combining like terms:
x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3
Therefore, the expression representing the product of (x^3+2x-1) and (x^4-x^3+3) is x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3.
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 11 yards long, and the height of the equilateral triangle is 9.5 yards. The pyramid's slant height is 17 yards. What is its surface area?
The surface area of the triangular pyramid is approximately 331.93 square yards.
To find the surface area of the triangular pyramid, we need to calculate the areas of its individual components and then sum them up.
The triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 11 yards long, and the height of the equilateral triangle is 9.5 yards. The formula to calculate the area of an equilateral triangle is:
Area = (√3/4) * [tex]side^2[/tex]
Plugging in the values, we get:
Area of the base equilateral triangle = (√3/4) * 11^2 ≈ 52.43 square yards
The triangular pyramid also has three triangular faces. Each face is an isosceles triangle, with two sides measuring 11 yards (same as the sides of the base equilateral triangle) and a slant height of 17 yards. We can use the formula for the area of an isosceles triangle:
Area = (1/2) * base * height
Since the base of the isosceles triangle is 11 yards and the height is 17 yards, the area of each triangular face is:
Area of each triangular face = (1/2) * 11 * 17 = 93.5 square yards
Now, we can calculate the total surface area of the triangular pyramid by summing up the areas of the base and the three triangular faces:
Surface area = Area of the base equilateral triangle + 3 * Area of each triangular face
Surface area = 52.43 + 3 * 93.5
Surface area ≈ 331.93 square yards
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help needed fast pleaseeeeeeee. Identify the solution of the system graphed below.
The solution to the system of equations is (a) (1, 0)
Identifying the solutions to the system of equationsFrom the question, we have the following parameters that can be used in our computation:
The graph
The point of intersection of the lines of the graph represent the solution to the system graphed
From the graph, we have the intersection point to be
(x, y) = (1, 0)
This means that
x = 1 and y = 0
Hence, the solution to the system of equations is (a) (1, 0)
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Cara used the order of operations to evaluate the expression below. StartFraction 4 (7 minus 13) over 3 EndFraction + (negative 4) squared minus 2 (6 minus 2) = StartFraction 28 minus 13 over 3 EndFraction + (negative 4) squared minus 2 (4) = StartFraction 15 over 3 EndFraction + 16 minus 18 = 5 + 16 minus 8 = 13. What was Cara’s first error?
Cara's first error occurred when she simplified the expression (negative 4) squared.
According to the order of operations (PEMDAS/BODMAS), exponentiation should be performed before any other operations. However, Cara incorrectly squared only the negative sign and not the entire number.
As a result, she obtained a value of positive 4 instead of 16.
To correct the error, Cara should have squared the entire value of -4. Squaring a negative number yields a positive result. Thus, (-4) squared is equal to 16. By failing to correctly apply this rule, Cara ended up with an incorrect value in her expression.
The correct evaluation of the expression should have been:
StartFraction 4 (7 minus 13) over 3 EndFraction + (negative 4) squared minus 2 (6 minus 2) = StartFraction 4 (-6) over 3 EndFraction + 16 minus 2 (4) = -8 + 16 - 8 = 0.
Therefore, Cara's first error was in incorrectly squaring only the negative sign and obtaining a value of 4 instead of 16.
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Function g is a transformation of the parent tangent function such that g(x) = tan(x-4) + 2 . Which graph represents function g?
Based on the given transformations, the correct graph that represents function g(x) = tan(x-4) + 2 is option c.
How to determine the graph that represents function g(x) = tan(x-4) + 2To determine the graph that represents function g(x) = tan(x-4) + 2, we can analyze the transformations applied to the parent tangent function.
The parent tangent function has the form f(x) = tan(x). The given function g(x) = tan(x-4) + 2 introduces two transformations:
1. Horizontal shift: The function is shifted 4 units to the right compared to the parent function f(x) = tan(x). This means the graph of g(x) will be shifted to the right by 4 units.
2. Vertical shift: The function is shifted 2 units up compared to the parent function f(x) = tan(x). This means the graph of g(x) will be shifted upward by 2 units.
Based on the given transformations, the correct graph that represents function g(x) = tan(x-4) + 2 is option c. The graph in option c shows a rightward shift of 4 units (horizontal shift) and an upward shift of 2 units (vertical shift), matching the transformations described for g(x).
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45% of the Walton High School student body are male. 90% of Walton females love math, while only 60% of the males love math. What percentage of the student body loves math?
Approximately 76.5% of the student body at Walton High School loves math.
To determine the percentage of the student body that loves math, we need to consider the proportions of males and females in the Walton High School student body and their respective percentages of loving math.
Given that 45% of the student body are males, we can deduce that 55% are females (since the total percentage must add up to 100%). Now let's calculate the percentage of the student body that loves math:
For the females:
55% of the student body are females.
90% of the females love math.
So, the percentage of females who love math is 55% * 90% = 49.5% of the student body.
For the males:
45% of the student body are males.
60% of the males love math.
So, the percentage of males who love math is 45% * 60% = 27% of the student body.
To find the total percentage of the student body that loves math, we add the percentages of females who love math and males who love math:
49.5% + 27% = 76.5%
As a result, 76.5% of Walton High School's student body enjoys maths.
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a die has red, blue and one white face. when the die is rolled, a red result wins, a blue result, and a white result. what is the "expected return" for one roll of this die.
A company Charting its profits notices that the relationship between the number of units sold,x, and the profit,P, is a linear. If 170 units sold results in $20 profit and 220 units sold results in $2820 profit, write the profit function for this company.
P=
Find the marginal profit
$
Step-by-step explanation:
a linear relationship or function is described in general as
y = f(x) = ax + b
Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".
here f(x) is P(x) :
P(x) = ax + b
now we are using both given points (ordered pairs) to calculate a and b :
20 = a×170 + b
2820 = a×220 + b
to eliminate first one variable we subtract equation 1 from equation 2 :
2800 = a×50
a = 2800/50 = 280/5 = 56
now, we use that in any of the 2 original equations to get b :
20 = 56×170 + b
b = 20 - 56×170 = 20 - 9520 = -9500
so,
P(x) = 56x - 9500
Which set of ordered pairs represents a function?
O {(6,-8), (2,-2), (6, -1), (8, -7)}
O {(-7,-8), (-3,9), (7,4), (-1,4)}
O {(1, -2), (-6, 2), (5,0), (1,6)}
{(3,8), (3, 6), (8,-6), (1, -7)}
Submit Answer
Answer:
{(-7, -8), (-3, 9), (7, 4), (-1, 4)} represents a function.
There are 12 containers containing various amounts of water, as shown below. ←+ 0 H ½ X X X X X X 1 X 1½ X X X 2 Cups If all of the water were dumped into one container, how many cups would be in the container?
Answer: it contains 12 containers
Step-by-step explanation: i dont know what the answer is but i know what i can help you with all you have to do is round the answer.
what is the graph of f(x) = 5(2)^x
The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.
The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.
As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:
When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).
As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.
For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.
The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.
Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.
The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.
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Which system of linear inequalities is represented by the graph?
y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x + 1
Answer:
The system of linear inequalities represented by the graph is:
y > x - 2 and y < x + 1
This system of inequalities indicates that y is greater than x - 2, which represents the upper boundary of the shaded region in the graph. Additionally, y is less than x + 1, which represents the lower boundary of the shaded region. The intersection of these two conditions is the region between the lines, satisfying both inequalities.