Answer:
8.8 minutes
Step-by-step explanation:
first we figure out how many liters are being lost
57 - 35 = 22
then divide that by 2.5
22 / 2.5 = 8.8
8.8 minutes
What is the range of possible values for x ?
The diagram is not to scale
The range of possible values for x is 0<x<20
What is Range?The Range is the difference between the lowest and highest values.
In any triangle, the smallest angle is opposite to the smallest side.
So, In ΔABD , the side which faces ∠ABD is AD whose length is 32 units.....(1)
And, in ΔCBD, the side which faces ∠CBD is CD whose length is 20 units....(2)
Now, from equations (1) and (2) We get,
∠ABD < ∠CBD
So, ∠ABD lies between 0° to 48°
0<4x+8<48
Subtract 8 on both sides
-8<4x<40
Divide by 4
-2<x<10
As ∠ABD lies between 0° to 48°, so 0<x<10 is the range.
Hence, 0<x<10 is the range of possible values for x.
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A study was made by a retail merchant to determine the relation between weekly advertising expenditures and sales. The following data were recorded: Advertising Costs ($) 40 Sales ($) 385 20 400 25 395 20 365 475 30 50 440 40 490 20 420 50 560 525 40 25 480 50 510 a) Plot a scatter diagram, you may use Excel. (5 marks) b) Find the equation of the regression line to predict weekly sales from advertising expenditures. (6 marks) c) Estimate the weekly sales when advertising costs are $35. (2 marks) d) Plot the residuals versus advertising costs. Comment. (5 marks) e) Using the t-test, test the hypothesis that 6 against the alternative that B< 6. Use a 0.025 level of significance. (10 marks) f) Construct a 95% confidence interval for the average weekly sales when $45 is spent on advertising. (5 marks) g) Construct a 95% prediction interval for the average weekly sales when $45 is spent on advertising (5 marks) h) What is the percentage of variations in weekly sales explained by the advertising costs? (2 marks)
For given data,
a) A scatter diagram is as shown below.
b) the coefficient of correlation is, r = 0.63
c) the linear regression equation (least-squares equation of the line) to predict weekly sales from advertising expenditures is : y = 3.2208x + 343.71, where x is the Advertising Costs and y be the Sales in dollars
d) when advertising costs are $32, the weekly sales would be 446.78 dollars.
In this question, we have been given that a retail merchant made a study to determine the relation between weekly advertising expenditures and sales.
The following data were recorded:
Advertising Costs, $ 40 20 25 20 30 50 40 20 50 40 25 50
Sales, $ 385 400 395 365 475 440 490 420 560 525 480 510
a) a scatter plot for the above data is as shown below.
b) the coefficient of correlation is:
r = √0.403
r = 0.63
c) the linear regression equation is:
y = 3.2208x + 343.71
where x is the weekly Advertising Costs and y be the Sales in dollars
d) the weekly sales when advertising costs are $32:
y = 3.2208(32) + 343.71
y = 446.78
So, when advertising costs are $32, the weekly sales would be 446.78 dollars.
Therefore, for given data:
a) A scatter diagram is as shown below.
b) the coefficient of correlation = 0.63
c) the linear regression equation: y = 3.2208x + 343.71
d) when advertising costs are $32, the weekly sales would be 446.78 dollars.
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PLEASSEEEE HEELPPP ASAPPPPP!!! (FOR 10 POINTS!)
For each system of equations below, choose the best method for solving
and solve. Show your work.
a. 3x+y=24
-x-y=-10
The solution to the system of equations 3x+y=24 and -x-y=-10 is x = 7, y = 3
How to determine the solution to the system?The system of equations is given as
3x+y=24
-x-y=-10
Make x the subject in the second equation
So, we have the following representation
x = 10 - y
Substitute x = 10 - y in the equation 3x+y=24
3(10 - y) +y=24
Expand the bracket
30 - 3y + y = 24
Evaluate the like terms
-2y = -6
Divide by -2
y = 3
Recall that
x = 10 - y
So, we have
x = 10 - 3
x = 7
Hence, the solution is x = 7, y = 3
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In gym class, a student can do 40 sit-ups in 60 seconds and 100 sit-ups in 150 seconds.
Graph the proportional relationship.
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 30
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
PLEASE HELP, its not D btw i did the test and got it wrong
D, graph with a line from 0 comma 0 to 90 comma 30 and an x axis labeled time seconds and a y axis labeled sit ups represents the proportional relationship.
How do graphs work?For the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate, a graph is a sort of chart that is frequently employed (y-axis).A straight line with data points passing through the origin characterizes the graph of any proportional relationship in mathematics (0, 0).In this situation, it is logically inferable that the values on the x- and y-coordinates of the provided graph are proportional and are represented by the following linear equation:Explanation:
y = 3x
where x is the passage of time.
y stands for how many sit-ups there were.
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If g(x)=f(x-3), then select all the statements that are true.
The value of g(1) is 3 .
The value of g(-1) is 1 .
The value of g(-1) is 8 .
The y-intercept of g(x) is at the point (0,1).
The true statement is The value of g(1) is 3 .
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
g(x)=f(x-3)
When x= 1
g(1) = f(-2)= 3
and, When x= -1
g(1) = f(-2)= -1
Hence, the true statement is The value of g(1) is 3 .
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I need help with this.
Answer:
Step-by-step explanation:
ax² + bx + c = 0
D = b² - 4ac
If D > 0 , then quadratic equation has 2 roots.
If D = 0 , then quadratic equation has 1 roots.
If D > 0 , then quadratic equation has No roots in the set of real numbers.
~~~~~~~~~~~~~~~~~~~~
2y² + 4y = 3
2y² + 4y - 3 = 0
a = 2 , b = 4 , c = - 3
D = 4² - 4(2)( - 3) = 40 > 0 ( 2 solutions )
[tex]y_{12}[/tex] = ( - 4 ± 2√10 ) ÷ 4
[tex]y_{1}[/tex] = [tex]\frac{-2+\sqrt{10} }{2}[/tex]
[tex]y_{2}[/tex] = [tex]\frac{-2-\sqrt{10} }{2}[/tex]
The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree.
Estimated volume of the tree as per given height and circumference using trapezoidal rule is equal to 30907.5 cubic inches.
As given in the question,
Given height 'x' and circumference 'y=f(x)',
Height (inches) 'x' : 0 15 30 45 60 75 90
Circumference (inches) 'y=f(x)': 31 28 21 17 12 8 2
Trapezoidal rule :
Δx = (b - a ) n
Here b = 90
a = 0
n =6
Δx = ( 90 - 0)/6
= 15
Substitute the value to get the volume using trapezoidal rule:
T₆=(Δx/2)[f(x₀)²+ 2{f(x₁)²+ f(x₂)²+f(x₃)² + f(x₄)²+f(x₅)²}+ f(x₅)²]
= (15/2)[ 31² + 2 (28² + 21² + 17² + 8²) + 2² ]
= ( 15/2) [961 + 2{ 784+ 441 + 289 + 64} + 4]
= 15 × 2060.5
= 30907.5 cubic inches
Therefore, the volume of the tree as per given given table using trapezoidal rule is equal to 30907.5 cubic inches.
The above question is incomplete , the complete question is:
The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree using the trapezoid rule. There needs to be six subdivisions in the trapezoid rule.
Height (inches) : 0 15 30 45 60 75 90
Circumference (inches): 31 28 21 17 12 8 2
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A man walks for 2 hours at a certain speed. He then cycles at three times that seed for
4 hours. He goes 77km altogether. Find the speed at which he walks.
5.5km/hr is the speed at which he walks.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given
w = walking speed
t = time walking = 2
Given, A man walks for 2 hours at a certain speed which is 2w
He then cycles at three times that seed for 4 hours.
We can form a equation by given data
2w + 3×w×4 = 77
2w+12w=77
14w = 77
Divide both sides by 14
w = 5.5 km/hr
Hence, 5.5km/hr is the speed at which he walks.
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what are two diffrent if-then statements implied by Theorem 2-13?
The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.What is the Parallel Lines & Perpendicular Lines?
Parallel Lines :Two or more lines that lie in the same plane and never intersect or meet each other are known as parallel lines,
Perpendicular Lines are formed when two lines meet each other at the right angle or 90 degrees.
Given: The theorem 2-13 is given.
We have to find what are two different if-then statements implied by Theorem 2-13.
The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.Hence, The two different if-then statements implied by Theorem 2-13 are:
If lines and are both not vertical then p || q if and only if the slope of the line p is equal to the slope of the line q.If lines p and q are both vertical then p || q.To learn more about the Parallel Lines & Perpendicular Lines visit,
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The width of the rectangle is 60% of its length of 40 ft. What is the area of the rectangle?
Answer:
24
Step-by-step explanation:
60% of 40 is 24 because to find a percentage, multiply the percent you are trying to find (60%) by the number you are trying to find percent of (40) and divide the answer of 60x40 by 100. 60x40 is 2,400. 2,400 divided by 100 is 24. The width of the rectangle is 24ft
Write the equation of the line in slope-intercept form (y = mx + b) based on the given information. 11. Passes through (12,-6) and perpendicular to y = 3x + 1
The equation of the line that is perpendicular to y = 3x + 1, in slope-intercept, is: y = -1/3*x - 2.
How to Write the Equation of a Perpendicular Line in Slope-intercept Form?If we are given a line that passes a point (12, -6) and is perpendicular to y = 3x + 1, we can find the equation of the line in slope-intercept form following the steps below.
First, find the slope of y = 3x + 1. The slope is 3. Since both lines are perpendicular to each other, therefore, the slope of the line that passes through (12, -6) would be the negative reciprocal of 3, which is m = -1/3.
Substitute m = -1/3 and (a, b) = (12, -6) into y - b = m(x - a):
y - (-6)) = -1/3(x - 12)
y + 6 = -1/3(x - 12)
Rewrite in slope-intercept form:
y + 6 = -1/3*x + 4
y + 6 - 6 = -1/3*x + 4 - 6
y = -1/3*x - 2
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At $4.20 per yd^3, how much will it cost to fill a container with dimensions of 3yd X 5yd X 7 1/3 yd?
Cost to fill the container = $ 462
The volume of the rectangular container:The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Various forms have various volumes.
The formula for the volume of a rectangular container is given by
Volume = Length × Width × Depth
Here we have,
Dimensions of a container are 3yd × 5yd × 7 1/3 yd
Here 7 1/3 = 22/3 yd
From the given formula,
Area of the container = 3yd × 5yd × 22/3 yd
= [tex](3 \times 5 \times \frac{22}{3} )yd^{3}[/tex]
= [tex]( 5 \times 22 )yd^{3}[/tex]
= 110 yd³
Given the cost per 1 yd³ = $ 4.20
=> cost of 110 yd³ = 110 × $ 4.20 = $ 462
Therefore,
Cost to fill the container = $ 462
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opinion 1: coefficient of x, coefficient of y, constant term
opinion 2: divide -105 by 3, divide 165 by 3, write the equation in slope-intercept form
opinion 3: -55, -35, 35, 55
Answer:
Coefficient of x
Write in the slope intercept form
35
Step-by-step explanation:
165 - 105x + 3y = 0 Subtract 165 from both sides and and 105x to both sides
3y = 105x - 165 Divide all the way through by 3
y = 35x - 55
The slope is the coefficient of x when the equation is written in the slope intercept form of the line.
The slope is 35
Let G(x) = -2(3x + 4)(x - 1)(x – 3)^2 be a polynomial function.
Find the Y intercept and state the end behavior of g(x).
The vertical intercepts is (4/3,0) (3,0) (1,0) and The horizontial intercepts is (0,72)
The end behavior is as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given the G(x) = -2(3x + 4)(x - 1)(x – 3)^2 as a polynomial function.
Since all the exponets will equal 0. The constant will just add to the term.
The leading degree is even. Thus Even Degree Polynomials like Quadratics tend to go approach positive infinity vertically as x approaches positive infinity, and as x approaches negative infinity, it approaches positive infinity vertically.
Our leading coefficient is negative which means our quadratic will get reflected across the x axis.
The end behavior is as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.
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Kaitlyn is trying to put in a water pipe underneath the
ground for her pool. The pipe will run from point G(c,6) to
point H(-5,d) on the coordinate grid. Which expression
represents the shortest distance between M and N in
units.
The shortest distance between the two points is √[(c + 5)² + (6 - d)²]
How to determine the shortest distance between the two points?From the question, we have the following points that can be used in our computation:
G = (c, 6) and H = (-5, d)
The distance between the two points can be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where
(x, y) = (c, 6) and (-5, d)
Substitute (x, y) = (c, 6) and (-5, d) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
distance = √[(c + 5)² + (6 - d)²]
Hence, the distance expression is √[(c + 5)² + (6 - d)²]
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What is the answer to -6v-1+v
Answer:
-6v-1+v
collect the like terms
-6v + v - 1
you have
-5v-1
Answer:
answer is 5v-1
Step-by-step explanation:
add the common varribles which are V,
does anyone know the answers?
Answer:
1. Supplementary
2. Alternate exterior
Step-by-step explanation:
1. ∠1 and ∠2 are complementary because they both lie on the same straight line. If you had the values of these angles, they would add up to 180°
2. ∠1 and ∠8 are alternate exterior angles because they are on opposite sides of the transversal (the diagonal line from the bottom left to the top right) and they are on the outsides of the parallel lines. (∠1 is above the top horizontal line and ∠8 is below the bottom horizontal line.)
a) The base of the pyramid is a Hexagon
b) The height of the pyramid is
c) The vertex of the pyramid is
Blank 1: Hexagon
Blank 2:
For the given hexagonal pyramid, the base of the pyramid is a Hexagon, The height of the pyramid is 13 units, and the vertex of the pyramid is 7.
What is a hexagonal pyramid?
A hexagonal pyramid features isosceles triangles as the faces that join the pyramid together at the top and a hexagonal-shaped base.
Given, for a hexagonal pyramid
a) The base of the pyramid is a Hexagon.
b) The height of the pyramid is 13 units.
c) The vertex of the pyramid is 7.
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Find sin2x,cos2x, and tan2x if sin x=12/13 and x terminates in quadrant II.
sin2x=
cos2x=
tan2x=
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
sin x= 12/ 13
So, B = √13² - 12² = √169 - 144 = √25 = 5
cos x= -5/ 13
So, sin 2x= 2 sin x cos x =2 (12/13)(-5/13) = -120/169
and, cos 2x= 1- 2 sin²x
= 1- 2( 144 / 169)
= -119/ 169
and, tan 2x = sin 2x/ cos 2x = 120/ 169 / (- 119/ 169)= 120/ 119
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Angela has 21 3/8 cups of flour. She uses 2 1/4 cups of flour to make each batch of cookies. Part A. How many batches of cookies can Angela make? Part B. Write an equation to model the solution to the problem.
Using proportions, Angela can make 9.5 batch of cookies and the equation to model the solution is y = 2.25x
What are ProportionsProportion is an equation that defines that the two given ratios are equivalent to each other. However, in this case, we can write out an equation that shows the number of cookies she can make with the number of cups of flour available.
To do this, we need to set up a proportional equation with a constant of proportionality.
This is often written as
y = kx
k = constant of proportionalityFor each batch, she needs 2 1/4 cups
Let's convert this into decimal which will give us 2.25 cups of flour.
y = 2.25x
A. The number of batch she can make will be
21 3/8 ÷ 2 1/4 = 9.5 batch
B) The equation to model the solution is y = 2.25x
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find the area of 10x^2+9x+2 when the the width is 2x+1
If the function g (« = f(a) + k, where k = 2, describe the changes to the slope and y-intercept of this transformation.
The changes to the slope and y-intercept of this transformation are
The slopes of the functions are the sameThe y-intercept of g(a) is 2 greater than the y-intercept of f(a)How to determine the changes to the slope and y-interceptFrom the question, we have the following parameters that can be used in our computation:
g(a) = f(a) + k
Also, from the question, we have
k = 2
Using the above as a guide, we have the following:
Substitute the known values in the above equation, so, we have the following representation
g(a) = f(a) + 2
This means that
Slope of f(a) = Slope of g(a)
Also, we have
y-intercept of g(a) = y-intercept of f(a) + 2
Hence, the y-intercept of g(a) is 2 greater than the y-intercept of f(a)
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Find the inverse function in slope-intercept form (mx+b): f(x)= -3x+3
The inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.
What is the inverse function?
The inverse function of a function f(x) is a function g(x) such that g(f(x)) = x for all x in the domain of f.
The given function is f(x) = -3x + 3. To find the inverse function, we can solve for x in terms of y:
y = -3x + 3
0 = -3x + y + 3
-y = -3x + 3
x = (-y + 3) / -3
The inverse function is then g(y) = (-y + 3) / -3. Rewriting this in slope-intercept form gives:
g(y) = (-1/3)y + 1
Hence, the inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.
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If R = {(x, y): y=x²-4 and y ≤5], then Find a) Domain and Range of R b) Inverse relation (R') c) Domain and Ranpe of R d) To Sketch the graphs of R. and Ro
a) The Domain is [-∞, 5]
And the range is [-∞, 3]
b) The area covered by a relation's inverse is the same as its domain. In other words, the relationship's x-values are its inverse's y-values.
c) The Domain is [-∞, 5]
And the range is [-∞, 3]
d) The graph of R is shown below:
What is meant by Domain?The set of inputs that a function will accept is referred to as the domain of the function in mathematics. It is important to note that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
The function f can be plotted in the Cartesian coordinate system in the special case where X and Y are both subsets of R. In this example, the graph's x-axis shows the domain as the projection.
Given,
R = {(x, y): y=x²-4 and y ≤5]
For x=0, y=-4
For x=1, y=-3
For x=2, y=0
For x=3, y=5
Therefore, the Domain is [-∞, 5]
And the range is [-∞, 3]
The area covered by a relation's inverse is the same as its domain. In other words, the relationship's x-values are its inverse's y-values.
The graph of R is shown below:
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In the diagram, the length of segment VS is 39 units. Line n is a perpendicular bisector of line segment T V. It intersects line segment T V at point R. Line n also contains points Q and S. Line segment Q V is 3 x + 4. Line segment R V is 2 x + 5. Line segment T S is 6 x minus 3. What is the length of segment TV? 14 units 19 units 38 units 50 units
On solving the provided question, by help of the Linear Equation we got that TV = 38 units.
what is linear equation?Any equation with a degree of 1 or above is considered linear. This shows that the exponent of the linear equation's variable is bigger than 1. A linear equation will always have a straight line as its graph.
RST and RSV, two equal right triangles, are shown in the illustration.
Notice that:
TS = VS
We know that,
TS = 6x - 3
VS = 39
6x - 3 = 39
6x = 42
[tex]x = \frac{42}{6}[/tex]
x = 7
Now, you can identify in the figure that:
RV = 2x + 5
The length of segment RV may be determined by substituting the above-calculated value of "x" into the equation and evaluating:
RV = 2(7)+ 5
RV = 19 units
Now,
TV = 19 + 19
TV = 38 units
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Type the 4letter code into the answer box. All CAPS, no spaces.
Answer:
HAEC
Step-by-step explanation:
You want the code letters associated with lines 1–4 on the graph.
Line 1Has a y-intercept of -4, and a rise/run if 1/4. The equation is ...
y = 1/4x -4 (H)
Line 2Has a y-intercept of -4, and a rise/run of 4/1 = 4. The equation is ...
y = 4x -4 (A)
Line 3Has a y-intercept of 3, and a rise/run of -2/1 = -2. The equation is ...
y = -2x +3 (E)
Line 4Has a y-intercept of +1 and a rise/run of 2/1 = 2. The equation is ...
y = 2x +1 (C)
The code is HAEC.
determine each feature of the graph of the given function
f(x)= -5/2x-1
horizontal asymptote: y =
vertical asymptote: x =
y intercept: ( _, 0)
x intercept: (0, _ )
hole: ( _ , _ )
Answer:
Step-by-step explanation:
HORIZONTAL ASYMPTOTE
lim x-> oo -5/(2x-1)
-5/(oo-1)
-5/oo
0
y = 0
VERTICAL ASYMPTOTE
2x - 1 = 0
2x = 1
2/2 x = 1/2
x = 1/2
y INTERCEPT
-5/(0-1)
-5/-1
5
(5,0)
X INTERCEPT
-5 = 0
Impossible
no x intercept
If A (2,2) and B is (-2, -2) what is the distance between AB?
The distance AB between the two points is 5.7 units
How to determine the distance AB between the two points?From the question, we have the following parameters that can be used in our computation:
A = (2, 2) and B =(-2, -2)
The distance between the two points can be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where
(x, y) = (2, 2) and (-2, -2)
Substitute (x, y) = (2, 2) and (-2, -2) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
distance = √[(2 + 2)² + (2 + 2)²]
Evaluate
distance = 5.7
Hence, the distance is 5.7 units
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Which answer choice correctly complete the sentence?
The Problem Solving Plan is a method to
OA) show all your work in math.
O B) give an example of a real-life problem.
OC) make solving a word problem easier.
OD) check to see if your answer is reasonable.
Answer: C
Step-by-step explanation:
The problem solving plan is a method to make solving a word problem easier.
Characteristics in common with 2 miles 72,000 inches and 3,000 feet
Answer:
Step-by-step explanation:
1 foot=12inch
3000 feet=12 ×3000=36000 inches
72,000 inches=2 miles
36000 inches=(2÷72,000)×36,000=1 mile