Answer:
a) 81
b) 83
c) science
Step-by-step explanation:
a)
f(x) = 0.5x + 80
gn x = 2 tests
⇒ f(2) = 0.5(2) + 80
= 1 + 80
= 81
b)
gn x = 2
g(2) = 83
c)
we have g(x) = mx + b
m = (y₂-y₁)/(x₂-x₁)
= (83 - 81)/(2 - 1)
m = 2
for g(1),
g(1) = m(1) + b
81 = 2(1) + b
b = 81 -2
b = 79
⇒ g(x) = 2x + 79
and f(x) = 0.5x + 80
for 4 tests, we have x = 4
g(4) = 2(4) + 79
= 8 + 79
g(4) = 87
f(4) = 0.5(4) + 80
= 2 + 80
f(4) = 82
g(4) = 87 > f(4) = 82
∴Science class has a higher average
Which notation describes this transformation?
OA. (r,y)=(s - 8,y - 8)
OB. (r,y)=(r= 4,y - 8)
O C. (r,y)=(-4,-y)
O D. (r',y) = (1, -y)
Answer: A. (r,y)=(s - 8,y - 8)
Step-by-step explanation: The notation that describes this transformation is A. This notation represents a translation of 8 units to the left and 8 units down. The notation (r,y) represents the original coordinates, while (s-8, y-8) represents the new coordinates after the transformation.
help me please i would appreciate it so so much
Answer:
w = 120
x = 60
y = 120
z = 60
Step-by-step explanation:
w = 120 (vertically opposite angles)
sum of co interior angles is 180
⇒ w + x = 180 and x + y = 180
w + x = 180
⇒ 120 + x = 180
⇒ x = 180 - 120
⇒ x = 60
x + y = 180
⇒ 60 + y = 180
⇒ y = 180 - 60
⇒ y = 120
z = x (corresponding angles)
z = 60
If Daniela graphed the function describing Mondays storm she would find that it is
Daniela's graph of the function describing Monday's storm depicted the storm's temporal evolution, showcasing the changing intensity of rainfall, intermittent spikes, shifting wind direction, and overall duration. Analyzing the graph allowed Daniela to gain insights into the storm's behavior and better understand its impact on the area.
Daniela graphed the function describing Monday's storm and observed several key features. The graph displayed a rapid increase in precipitation during the early morning hours, with rain intensifying steadily until reaching its peak around midday. Afterward, the precipitation gradually subsided, leading to a decline in rainfall amounts throughout the afternoon and evening.
The graph exhibited a distinct pattern of fluctuation, reflecting the storm's dynamic nature. Intermittent spikes in rainfall were visible, indicating periodic bursts of heavy precipitation throughout the day. These spikes were followed by brief periods of relative calm, during which the rainfall decreased temporarily before resuming its intensity.
Furthermore, Daniela noticed a gradual shift in wind direction as the storm progressed. Initially, the wind blew from the east, but it gradually veered towards the south as the storm system moved across the region. The change in wind direction was evident on the graph, showing a gradual rotation of the wind vector over time.
The graph also revealed the storm's duration, spanning from the early morning hours until late evening. The rainfall accumulation steadily increased during the storm's initial phase and reached a maximum before gradually tapering off towards the end of the day.
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HELPPPP!!! Ill give 25 points!
Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer.
Y axis is GPA and X axis is hours studied
The GPA of a student who studies for 15 hours a week is 3.125 GPA.
What is a regression equation?In Mathematics, the standard form of the equation of a regression line is represented or modeled by the following mathematical expression;
y = bx + c
Where:
b represent the gradient, slope, or rate of change.x and y represent the data points.c represents the y-intercept, vertical intercept, or initial value.Since the student would study for 15 hours a week, the predicted GPA can be calculated as follows;
y = 0.149x + 0.89
y = 0.149(15) + 0.89
y = 3.125 GPA.
In conclusion, we can logically deduce that a student who studies for 15 hours a week would most likely have a 3.125 GPA.
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Complete Question:
Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer. The equation for the predicted GPA is y=0.149x+0.89
Jacob wants to write a novel, but he's worried it might be so long that nobody will read it. Of course, he also doesn't want to make it so short that nobody's willing to pay for it. To figure out a good
length, Jacob uses sales and page count data for published books to create a model:
S=-0.2² +100P+ 1615
Where S is the number of books sold in the first week after its release and P is the book's page count
What should Jacob use as the target for the length of his book in order to maximize his first-week sales?
The target length for Jacob's book to maximize his first-week sales would be a page count of 250.
To determine the target length of his book that would maximize his first-week sales, Jacob can use the given model: S = -0.2P² + 100P + 1615, where S represents the number of books sold in the first week and P represents the book's page count.
To find the maximum value of S, we can look for the vertex of the quadratic equation. The vertex of a quadratic equation in the form y = ax² + bx + c is given by the formula x = -b/2a. In this case, the coefficient of the quadratic term is -0.2, and the coefficient of the linear term is 100.
Using the formula x = -b/2a, we can calculate the value of P that corresponds to the maximum sales:
P = -100 / (2 * -0.2)
P = -100 / (-0.4)
P = 250
It's important to note that this model is based on a quadratic equation derived from sales and page count data of published books.
However, there are several other factors that can influence book sales, such as genre, marketing, author reputation, and reader preferences. Jacob should consider these factors along with the page count when determining the optimal length for his book.
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(21 points) Differentiate:
(a) f(x) = (x5 — 5x³ + 2x)5
(b) g(x) = sin(4x^4 – 2x)
(c) h(x) = (3x² − 1)6 sec² x
The functions (a), (b), and (c) can be differentiated as follows:
(a) The derivative of f(x) = [tex](x^5 - 5x^3 + 2x)^5[/tex] is found using the chain rule and the power rule.
(b) The derivative of g(x) = [tex]sin(4x^4 - 2x)[/tex] involves applying the chain rule and the derivative of the sine function.
(c) The derivative of h(x) = [tex](3x^2 - 1)^6 sec^2(x)[/tex] requires applying the chain rule, the power rule, and the derivative of the secant squared function.
(a) To differentiate f(x) =[tex](x^5 - 5x^3 + 2x)^5[/tex], we apply the chain rule. Let's denote the inner function as [tex]u = x^5 - 5x^3 + 2x.[/tex] Then, f(x) can be rewritten as [tex]u^5[/tex].
The derivative of [tex]u^5[/tex] with respect to x is given by [tex]5u^4[/tex] * du/dx. To find du/dx, we differentiate u term by term: du/dx = [tex]d/dx(x^5) - d/dx(5x^3) + d/dx(2x)[/tex]. This results in du/dx = [tex]5x^4 - 15x^2 + 2[/tex]. Therefore, the derivative of f(x) is [tex]5(x^5 - 5x^3 + 2x)^4 * (5x^4 - 15x^2 + 2)[/tex].
(b) To differentiate g(x) = [tex]sin(4x^4 - 2x)[/tex], we apply the chain rule. The derivative of sin(u), where u =[tex]4x^4 - 2x[/tex], is given by cos(u) * du/dx. To find du/dx, we differentiate u term by term: du/dx = [tex]d/dx(4x^4) - d/dx(2x)[/tex]. This results in du/dx = [tex]16x^3[/tex] - 2.
Therefore, the derivative of g(x) is [tex]cos(4x^4 - 2x) * (16x^3 - 2)[/tex].
(c) To differentiate h(x) = [tex](3x^2 - 1)^6 sec^2(x)[/tex], we apply the chain rule and the power rule. Let's denote the inner function as u = [tex]3x^2 - 1[/tex]. Then, h(x) can be rewritten as [tex]u^6 * sec^2(x)[/tex].
The derivative of u^6 with respect to x is given by 6u^5 * du/dx. To find du/dx, we differentiate u term by term: du/dx = [tex]d/dx(3x^2) - d/dx(1)[/tex]. This results in du/dx = 6x. Therefore, the derivative of h(x) is[tex]6(3x^2 - 1)^5 * 6x * sec^2(x)[/tex].
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If OQ and RT are parallel lines and mQPS = 136°
Angle QPS and angle RTS are congruent, both measuring 136°. Additionally, since OQ and RT are parallel, angle PSQ and angle RTS are alternate interior angles and are also congruent.
If OQ and RT are parallel lines and m QPS = 136°, we can use the property that when a transversal intersects two parallel lines, the corresponding angles are congruent.
Therefore, angle QPS and angle RTS are congruent, both measuring 136°. Additionally, since OQ and RT are parallel, angle PSQ and angle RTS are alternate interior angles and are also congruent.
Hence, angle PSQ measures 136° as well. In summary, angles QPS, PSQ, and RTS all have a measure of 136°.
This is because when two lines are parallel and intersected by a transversal, the corresponding angles and alternate interior angles are congruent.
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The complete question is given below:
If OQ and RT are parallel lines and m QPS = 136°
The enrollment at East Valley High School over a six-year period is displayed in the scatterplot.
Student Enrollment at East Valley High School
On a graph, the x-axis is labeled year and the y-axis is labeled students. Points (2009, 1,330) and (2013, 1,492) are plotted.
Which is the equation of the line of best-fit for this scatterplot?
y = negative StartFraction 81 Over 2 EndFraction x + StartFraction 165,389 Over 2 EndFraction
y = negative StartFraction 2 Over 81 EndFraction x + StartFraction 111,748 Over 81 EndFraction
y = StartFraction 2 Over 81 EndFraction x + StartFraction 103,712 Over 81 EndFraction
y = StartFraction 81 Over 2 EndFraction x minus StartFraction 160,069 Over 2 EndFraction
giving 100 points for answer asap
The equation of the line of best-fit for this scatterplot is
y = (81/2)x - (160,069/2)
The correct answer is D.
To find the equation of the line of best fit for the scatterplot, we need to calculate the slope and y-intercept based on the given data points (2009, 1,330) and (2013, 1,492).
First, we calculate the slope (m) using the formula:
[tex]m= \frac{(y2 - y1)}{(x2 - x1)}[/tex]
Using the points (2009, 1,330) and (2013, 1,492):
[tex]m=\frac{(1492 - 1330)}{(2013 - 2009)}[/tex]
[tex]m = \frac{162 }{4}[/tex]
[tex]m=\frac{81}{2}[/tex]
Next, we determine the y-intercept (b) by substituting one of the points and the calculated slope into the equation
[tex]y = mx + b[/tex].
Let's use the point (2009, 1330):
[tex]1330 = (\frac{81}{2} )\times2009 + b[/tex]
To find b, we can rearrange the equation:
[tex]b = 1330 - (\frac{81}{2} )\times2009[/tex]
[tex]b = 1330 - \frac{163,089}{2}[/tex]
[tex]b = 1330 - 81,544.5[/tex]
[tex]b = -80,214.5[/tex]
Therefore, the equation of the line of best fit is:
[tex]y =(\frac{81}{2} )\times x-80,214.5[/tex]
Simplifying the equation further:
[tex]y= (\frac{81}{2} ) x - 40,107.25[/tex]
The closest option to this equation is:
[tex]y=(\frac{81}{2} )x-(\frac{160,069}{2} )[/tex]
So, the correct answer is:
[tex]y = (\frac{81}{2} )x-(\frac{160,069}{2} )[/tex]
The correct answer is D.
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you have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per kilometer.
write an inequality to determine the distance in kilometers, d, you can ride for $20
The distance that can be traveled with $20 is equal to or less than 6 km.
Given that the total amount available is $20. Hence, the amount spent on the ride will be equal to or less than $20.
Base fare= $5
Rate per km = $2.5
Expressing the above case in the form of inequality:
Base fare + (Rate per km x Distance) ≤ Total amount available
$5 + $2.5d ≤ $20
⇒$2.5d ≤ $15
⇒ d ≤ 6 km where d represents the distance traveled.
Hence the distance that can be traveled with $20 is equal to or less than 6 km.
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The foci of an ellipse are at $(2, -3 + \sqrt{5})$ and $(4,-8).$ If the ellipse is tangent to the $x$-axis, then find the length of the major axis.
The length of the major axis is: 2√{18 - 6√5}
How to solve the equation of an Ellipse?The foci of an ellipse are usually denoted by the coordinates:
(c, 0) and (-c, 0)
where c is the distance from the center of the ellipse to each focus.
We are given the coordinates of the foci as:
(2, -3 + √5) and (4,-8).
Let us now find the distance between the two foci:
d = √{(2 - 4)² + (-3 + √5 + 8)²}
d = √{4 + (√{5} - 3)² }
d = √{18 - 6√5}
The ellipse is tangent to the x-axis, and as such the major axis of the ellipse will be parallel to the x-axis. The vertices lie on the x-axis.
The length of the major axis is given by2a,
where a is the distance from the center of the ellipse to either vertex.
The distance between the two vertices is 2a = 2c, which is twice the distance between the center and either focus.
Therefore, the length of the major axis is:
2a = 2d = 2√{18 - 6√5}
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1. What is the standard deviation of the probability distribution below?
The standard deviation of the probability distribution is approximately 13703.91.
To calculate the standard deviation of a probability distribution, we need to follow these steps:
Calculate the expected value (mean) of the probability distribution. This is done by multiplying each value (x) by its corresponding probability (p(x)) and summing them up.
Expected value (mean) = (10 * 27) + (20 * 28) + (30 * 45) = 270 + 560 + 1350 = 2180.
Calculate the squared deviation for each value. This is done by subtracting the expected value from each value, squaring the result, and then multiplying by the corresponding probability.
Squared deviation for 10: (10 - 2180)^2 * 27 = 212080 * 27 = 5726160.
Squared deviation for 20: (20 - 2180)^2 * 28 = 1998800 * 28 = 55982400.
Squared deviation for 30: (30 - 2180)^2 * 45 = 2815200 * 45 = 126684000.
Calculate the variance of the probability distribution. This is done by summing up the squared deviations.
Variance = (5726160 + 55982400 + 126684000) = 187692560.
Calculate the standard deviation by taking the square root of the variance.
Standard deviation = sqrt(187692560) ≈ 13703.91.
As a result, the probability distribution's standard deviation is around 13703.91.
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A transformation of rectangle ABCD results in rectangle A’B’C’D
Which transformation maps the pre-image to the image
In a dilation, the size of the object can be changed while keeping its shape, which is the case in this scenario.
A transformation of rectangle ABCD results in rectangle A’B’C’D. We need to identify which transformation maps the pre-image to the image.Two-dimensional transformations can be classified into four main categories; translations, reflections, rotations, and dilations. We will evaluate each of these to determine which of them maps the pre-image to the image.
TranslationsA translation is a transformation that moves an object in a straight line without changing its shape or orientation. It involves moving an object by a fixed distance in a particular direction. The image is congruent to the pre-image. This transformation does not result in a rectangle ABCD being transformed to A’B’C’D.
It results in a rectangle that has the same size and shape as the pre-image being moved to a different location.ReflectionsA reflection is a transformation that flips an object across a line without changing its shape or orientation. A reflection through a line known as the x-axis, or the y-axis results in a mirror image of the object.
This transformation does not result in a rectangle ABCD being transformed to A’B’C’D.RotationsA rotation is a transformation that turns an object about a fixed point. The fixed point is known as the center of rotation. The angle through which the object is rotated is known as the angle of rotation. A rotation does not change the size or shape of an object, but it changes its orientation. This transformation does not result in a rectangle ABCD being transformed to A’B’C’D.
DilationsA dilation is a transformation that changes the size of an object. The size change is described by a scale factor. The scale factor is greater than 1 for an enlargement and between 0 and 1 for a reduction. The center of dilation is the point about which the object is enlarged or reduced. This transformation does not result in a rectangle ABCD being transformed to A’B’C’D.After evaluating each of the four types of transformations, we can conclude that the transformation that maps the pre-image rectangle ABCD to the image rectangle A’B’C’D is a dilation.
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Find the cardinal number for the given set.
A = {13,19,25,31,39}
The cardinal number is
The cardinal number of the set is 5.
The cardinal number of the given set A = {13, 19, 25, 31, 39} is 5.
Cardinal number is the number of elements present in a set, so counting the number of elements of the set will give us the cardinal number of the set.
In this case, we have the set A with 5 elements: 13, 19, 25, 31, and 39.
Thus, the cardinal number of the set is 5.
Hence, the answer is 5.
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HELP AS SOON AS POSSIBLE
The resulting triangle after a reflection of triangle NMO over the line x = 2 would be N'(9, 2), M'(6, 1) and O'(7, 3)
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
Reflection is a type of transformation that involves the flipping of a point or figure over a line.
Triangle NMO with vertices at N(-5, 2), M(-2, 1) and O(-3, 3) is reflected over the line x = 2
The resulting triangle would be N'(9, 2), M'(6, 1) and O'(7, 3)
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Which statement best describes the solution set to this inequality?
0<8+x<17
A.
B.
C.
D.
The solution set includes all values of x greater than -8 and less than 9.
The solution set includes all values of x less than 8 or more than 25.
The solution set includes all values of x less than -8 or more than 9.
The solution set includes all values of x greater than 8 and less than 25.
Reset
Next
The statement that best describes the solution set to the inequality 0 < 8 + x < 17 is:D. The solution set includes all values of x greater than 8 and less than 9.
Let's break down the inequality step by step to understand the solution set.
[tex]0 < 8 + x < 17[/tex]
First, subtract 8 from all parts of the inequality:
[tex]-8 < x < 9[/tex]
This inequality states that x is greater than -8 and less than 9. In other words, the solution set includes all values of x between -8 and 9, excluding the endpoints.
To illustrate this, consider a number line. Mark -8 and 9 as open circles, indicating that they are not included in the solution set. Then, shade the region between -8 and 9, representing all values of x that satisfy the inequality.
The shaded region on the number line will include all values greater than -8 and less than 9. Therefore, statement D accurately describes the solution set.
It's important to note that when working with inequalities, the inequality signs (>, <) are treated similarly to equations, except that they indicate a range of values instead of a single solution. In this case, the inequality specifies the range for x that satisfies the given conditions.
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a) (10 pts) Re-express the given differential equation as a first order differential equation by utilizing matrix
and vector notation and in accordance with ()
= () form.
b) (10 pts) Is the system obtained in (a) stable, neutrally stable of unstable? Determine this using matrix.
c) (10 pts) Compute the eigenvalues and eigenvectors of matrix.
d) (10 pts) Using the results computed in (c) find and matrices and show that =
−
relationship
(i.e., the diagonalization relationship) is a valid relationship.
a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:
[tex]x' = Ax[/tex]
where x is a vector and A is a square matrix.
b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.
If all eigenvalues have negative real parts, the system is stable.
If at least one eigenvalue has a zero real part, the system is neutrally stable.
If at least one eigenvalue has a positive real part, the system is unstable.
c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation
[tex]det(A - \lambda I) = 0[/tex],
where λ is the eigenvalue and I is the identity matrix.
By solving this equation, we obtain the eigenvalues.
Substituting each eigenvalue into the equation
[tex](A - \lambda I)v = 0[/tex],
where v is the eigenvector, we can solve for the eigenvectors.
d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:
[tex]A = PDP^{(-1)}[/tex]
where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.
To show that this relationship is valid, we can compute [tex]PDP^{(-1)}[/tex] and verify that it equals A.
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Six students write an exam. The average score obtained on the exam by the group of students is 71%. If the first two students each obtained a mark of 73%, while the next three students each obtained a mark of 68%, what was the mark obtained by the sixth student?
What set of transformations are applied to parallelogram ABCD to create A″B″C″D″?
Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at negative 2, 1. Second parallelogram transformed formed by ordered pairs A double prime at 1, negative 4, B double prime at 2, negative 3, C double prime at 2, negative 1, D double prime 1, negative 2.
The transformations applied to parallelogram ABCD to create A″B″C″D″ are translations
To determine the set of transformations applied to parallelogram ABCD to create A″B″C″D″, we can compare the coordinates of the corresponding vertices.
Let's analyze the transformation for each vertex:
1. A (−4, 1) to A″ (1, −4):
Horizontal translation of 5 units to the right.Vertical translation of 5 units downward.2. B (−3, 2) to B″ (2, −3):
Horizontal translation of 5 units to the right.Vertical translation of 5 units downward.3. C (−1, 2) to C″ (2, −1):
Horizontal translation of 3 units to the right.Vertical translation of 3 units downward.4. D (−2, 1) to D″ (1, −2):
Horizontal translation of 3 units to the right.Vertical translation of 3 units downward.In summary, the transformations applied to parallelogram ABCD to create A″B″C″D″ are translations. Each vertex is translated horizontally to the right by either 3 or 5 units, and vertically downward by the same amount.
The specific values and directions of these translations determine the new positions of the vertices in the transformed parallelogram.
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Use the drawing tools) to form the correct answer on the provided graph
The graph of the function g(x)=+3-4 is shifted 5 units to the left. Plot the zeros of the new function on the
Drawing Tools
Select
Point
Click on a tool to begin drawing
Reset
k
a
F
Unu
The zeros of the new function are x = -9 and x = -4
Ploting the zeros of the new functionfrom the question, we have the following parameters that can be used in our computation:
g(x) = x² + 3x - 4
The transformation rule is given as
Shifted 5 units to the left
So, we have
h(x) = (x + 5)² + 3(x + 5) - 4
Next, we plot the graph of h(x)
See attachment
From the graph, we have the zeros to be
x = -9 and x = -4
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When copying segments and angles, which step is the same?
O Draw a ray with one endpoint.
O Create a point outside of the original figure.
O Draw a ray from the vertex to another point.
O Create a point on the original figure.
The step that is the same when copying segments and angles is to draw a ray from the vertex to another point (option c).
1. Start by identifying the segment or angle that you want to copy from the original figure.
2. Draw a ray with one endpoint. This ray will serve as the starting point for copying the segment or angle.
3. Next, create a point outside of the original figure. This point will be used as a reference for constructing the copied segment or angle.
4. Draw a ray from the vertex of the original segment or angle to the newly created point. This ray will determine the direction and length of the copied segment or angle.
5. Finally, create a point on the original figure that lies on the copied segment or angle. This point will help define the exact location of the copied segment or angle in relation to the original figure.
It is important to be precise and ensure that the rays and points are correctly positioned to maintain the integrity of the copied segment or angle.
Thus, the correct choice is c.
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PLEASE HELP V=1/3a^2h solve for A!!
The formula is `V = 1/3 a²h` and you need to solve for A. You can do this by rearranging the formula so that A is on one side of the equation and everything else is on the other side. Here are the steps you can follow to solve for A:
Step 1: Multiply both sides of the equation by 3 to get rid of the fraction: `3V = a²h`.
Step 2: Divide both sides of the equation by h: `3V/h = a²`.
Step 3: Take the square root of both sides of the equation to solve for a: `sqrt(3V/h) = a`.So the solution for `a` is `sqrt(3V/h)`. You can substitute the given value of `V` and `h` into the equation and simplify it if necessary.
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Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
Please awnser asap I will brainlist
The number of each type of vehicle the company can buy is:
Commercial van = 100
Small truck = 50
Large truck = l60
How many of each type of vehicle can they buy?Let
Commercial van = v
Small truck = s
Large truck = l
v = 2s
v + s + l = 310
35000v + 70,000s + 50,000l = 15,000,000
2s + s + l = 310
35000(2s) + 70,000s + 50,000l = 15,000,000
3s + l = 310
140,000s + 50,000l = 15,000,000
Divide by 10,000
3s + l = 310
14s + 5l = 1500
Multiply (1) by 5
15s + 5l = 1550
14s + 5l = 1500
subtract
s = 50
Recall,
v = 2s
v = 2(50)
v = 100
Therefore,
v + s + l = 310
100 + 50 + l = 310
150 + l = 310
l = 310 - 150
l = 160
Hence, the company can buy 100 commercial vehicle, 50 small truck and 160 large truck.
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Why are the lines y = 5x − 1 and 10x + 2y = 0 perpendicular
What is the x-intercept y-intercept of 3x-2y=18
Answer:
x-intercept(s): (6,0)
y-intercept(s): (0,−9)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
12. A plot of land is used to grow flowers. of the land is allocated for orchids. 2 After the orchids have been planted, of the remaining land is allocated for roses. After orchids and roses have been planted, 0.75 of the remaining land is allocated for tulips. What fraction of the plot of land is not occupied by the flowers?
The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.
Let's calculate the fraction of the plot of land that is not occupied by the flowers.
Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.
After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.
Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.
Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.
To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:
1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.
Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.
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Identify the conclusion in the conditional statement below.
"If a shape is a quadrilateral, then it is has exactly four sides."
A."If"
B."a shape is quadrilateral"
The conclusion in the conditional statement "If a shape is a quadrilateral, then it has exactly four sides" is "it has exactly four sides." Option C
How to determine the conclusionFrom the information given, we have that the statement is;
"If a shape is a quadrilateral, then it is has exactly four sides."
The antecedent (if a shape is a quadrilateral) and the consequent (then it has exactly four sides) of the statement are in a conditional connection.
The precise assertion or claim based on this conditional relationship is the conclusion.
In this instance, the conclusion argues that a shape must logically have four sides in order to qualify as a quadrilateral.
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The complete question:
Identify the conclusion in the conditional statement below.
"If a shape is a quadrilateral, then it is has exactly four sides."
A."If it is a quadrilateral, it has four sides"
B."a shape is quadrilateral"
C. "It has exactly four sides"
A fence with 2 gates in it surrounds a lion enclosure.
Each gate is 4 m wide.
an image
What is the length of the fence around the enclosure not including the gates?
The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.
Let's assume the length of the rectangle is 'l' and the width is 'w'.
From the given data, we know that each gate is 4 m wide.
Therefore, the width of the rectangle is:
Width = w + (4 m + 4 m) = w + 8 m
The perimeter of the rectangle is:
P = 2l + 2(w + 8 m) = 2l + 2w + 16 m
Now, we need to subtract the combined length of the two gates from the perimeter:
P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m
So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
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The function f(x) is shown on the graph.
What is f(0)?
0 only
-6 only
–2, –1, 1, and 3 only
–6, -2,-1, 1 and 3 only
The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.
The correct answer is D.
The function f(x) has some specific characteristics as shown in the graph.
The graph of f(x) has five intercepts, as can be seen from the graph.
The intercepts of f(x) can be determined by observing where the graph of f(x) crosses the x-axis.
The function f(x) intercepts the x-axis at five different points: -6 only, -2, -1, 1, and 3 only.
At these points, f(x) = 0.
Furthermore, the graph of f(x) is increasing from -∞ to -6, then decreasing from -6 to -2.
The graph of f(x) then increases from -2 to -1, decreases from -1 to 1, increases from 1 to 3, and finally decreases from 3 to +∞.
Hence, we can deduce that the graph of f(x) has a local maximum point at x = -6, a local minimum point at x = -2, and another local minimum point at x = 3.
We can also conclude that f(x) is an odd function, meaning that f(-x) = -f(x).
This can be deduced from the symmetry of the graph about the origin.
Finally, we can see from the graph that the function f(x) is continuous everywhere except at x = -2 and x = 3.
At these points, f(x) is not defined.
The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.
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0.834
0.861
0.927
0.877
0.831
0.925
0.912
0.83
0.849
0.933
0.884
find mean, median, maximum, minimum, and mode
Mean ≈ 0.874
Median ≈ 0.877
Maximum = 0.933
Minimum = 0.83
Mode = None
To find the mean, median, maximum, minimum, and mode of the given numbers:
Mean: The mean is the average of a set of numbers.
To calculate the mean, add up all the numbers and divide the sum by the total count.
Mean = (0.834 + 0.861 + 0.927 + 0.877 + 0.831 + 0.925 + 0.912 + 0.83 + 0.849 + 0.933 + 0.884) / 11
Mean ≈ 0.874
Median: The median is the middle value when the numbers are arranged in ascending or descending order.
Since there are 11 numbers, the median would be the 6th number when arranged in order.
Arranging the numbers in ascending order:
0.83, 0.831, 0.834, 0.849, 0.861, 0.877, 0.884, 0.912, 0.925, 0.927, 0.933
Median ≈ 0.877
Maximum: The maximum is the largest value among the given numbers.
Maximum = 0.933
Minimum: The minimum is the smallest value among the given numbers.
Minimum = 0.83
Mode: The mode is the value(s) that appear most frequently in the given numbers.
If there is no value that appears more than once, there is no mode.
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