Therefore, the other two zeros of the function are approximately -1.802 and -0.198.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.
by the question.
To find the zeros of the function, we need to solve the equation F(x) = 0. Since the given function has one known zero, which is 2 under the root, we can use this to simplify the expression.
Let's start by factoring out (x - 2^(1/2)) from the expression:
[tex]F(x) = (x - 2^(1/2))(6x^2 + 12x + 2^(1/2) - 4\sqrt{2})[/tex]
Now we need to find the zeros of the quadratic factor:
[tex]6x^2 + 12x + 2^(1/2) - 4\sqrt{2} = 0[/tex]
Using the quadratic formula, we get:
[tex]x = [-12±\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2}))]/(2(6))[/tex]
Simplifying the expression under the square root gives:
[tex]\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2})) = \sqrt(144 - 24\sqrt{2} - 96) = sqrt(48 - 24\sqrt{2})[/tex]
So, the zeros of the function are:
[tex]x = 2^(1/2), (-1 -\sqrt{6 + 3\sqrt{2}})/3, (-1 + \sqrt{6 + 3\sqrt{2}})/3[/tex]
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Two times the sum of x squared and y squared, increased by three times the sum of x squared and y squared. 7th grade
5 times the sum of x squared and y squared. This can be expressed as 5(x^2 + y^2).
What is express?Express is a web application framework for Node.js, released as free and open-source software under the MIT License. It is designed for building web applications and APIs and is the de facto standard server framework for Node.js. It provides a host of features to facilitate the development of web and mobile applications, including routing, templating, and a middleware system to handle requests and responses. Express is the backend component of the MEAN stack and enables the rapid development of dynamic web applications.
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If t has the terminal point P (-3/4 ,y) on the unit circle in
the second quadrant, find the value of tan t
tan t = -4/3
The equation for the unit circle is
x2 + y2 = 1
For the point (-3/4, y) we have
(-3/4)2 + y2 = 1
Rearranging this gives us
y2 = 1 - (3/4)2
Solving for y gives us
y = √ (1 - (3/4)2)
Now we can find tan t by using the equation
tan t = y / -3/4
Substituting in the value of y we found earlier gives us
tan t = √ (1 - (3/4)2) / -3/4
Finally, simplifying the equation gives us the answer
tan t = -4/3
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help me please and thank you
Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.
Explain volume.A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.
Here,
The capacity of a cylinder and a cone that are the same height and radius are not the same.
The formula V = πr²h,
where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation
=> V = (1/3)r²h gives the volume of a cone.
To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,
False we must first know the cylinder's radius and height.
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Guys please help My is assignment due tomorrow please guyyyysssss. Determine the value of k if g(x) = 4x+k is a tangent to f(x) = - x² + 8x +20
so, since we know that the derivative is simply the equation we use to get the slope at any point on the curve, thus df/dx will be that.
now, we know that g(x) is already in slope-intercept form, so it has a slope of "4", hmmm what's "x" at that instance?
[tex]f(x)=-x^2+8x+20\implies \cfrac{df}{dx}=-2x+8 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\stackrel{\stackrel{m}{\downarrow }}{4}x+k\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\\\ 4~~ = ~~-2x+8\implies 2=x[/tex]
well, now we know that x = 2, hmmm what's "y" at that instance? well, our "y" will be simply f(2) = g(x), because g(x) is touching f(x) at that point on the curve.
[tex]f(2)=-(2)^2+8(2)+20\implies f(2)=32 \\\\[-0.35em] ~\dotfill\\\\ g(x)=4x+k\implies 32=4(2)+k\implies 32=8+k\implies \boxed{24=k}[/tex]
Check the picture below.
What additional piece of information do you need to prove that ALKN-AKNM by the SAS similarity theorem?
A.
112
MN
B. MN=1
C
Option C, MN/LK||MN, is the additional piece of information required to demonstrate that ΔLKN ~ΔKNM by the SAS similarity theorem.
The SAS (Side-Angle-Side) similarity theorem: what is it?
According to the SAS (Side-Angle-Side) similarity theorem, two triangles are similar if they have two pairs of corresponding sides that are in proportion and the included angles are congruent.
In this example, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.
To clarify that MN is parallel to LK and forms a transversal with LN, we must first prove that MN/LK||MN.
To prove that the included angles between the matching sides are congruent, which is necessary for the triangles to be similar, this information is required.
Consequently, in order to demonstrate that ΔLKN~ΔKNM according to the SAS similarity theorem, option C is the correct additional piece of information.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
Step-by-step explanation:
[tex]m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{-12+(-8)}{2}, \frac{-7+(-4)}{2})[/tex]
[tex]=(-10,-5.5)[/tex]
Base on the given data uploaded, 1. Will you conclude that people can bargain price down when purchasing a house at 5% level of significance? 2. Will you conclude that the 3-bedroom houses is cheaper than 4-bedroom houses?
To know whether people can bargain the price down when purchasing a house at a 5% level of significance, we need to put a hypothesis test. The null hypothesis would be that people cannot bargain the price down
To determine whether 3-bedroom houses are cheaper than 4-bedroom houses, we would again give out a hypothesis test. The null hypothesis would be that there is no difference in price between 3-bedroom and 4-bedroom houses.
but the other hypothesis would be that 3-bedroom houses are cheaper than 4-bedroom houses. If the p-value is less than 0.05, we can reject the null hypothesis and say that 3-bedroom houses are more cheaper than 4-bedroom houses.
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Function g is the result of these transformations on the parent sine function: vertical stretch by a factor of 3 horizontal shift left units vertical shift down 4 units Substitute the values of A, C, and D to complete the equation modeling function g
The equation modeling function g after the given transformations on the parent sine function is:
g of (x) = A x sine(C(x minus D))+k
where A is the vertical stretch factor, C is the reciprocal of the horizontal stretch factor, D is the horizontal shift, and k is the vertical shift.
Substituting the given values, we get:
g of (x) = 3*sine((1/1)(x+1))+(-4)
Simplifying further, we get:
g of (x) = 3*sine of (x+1)-4
Therefore, the equation modeling function g is g of (x) = 3*sine(x+1)-4 after the given transformations on the parent sine function.
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One zero of the polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers f(x) = + ? + 3x + 3. zero: 3 = 1 One zero of the polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers. f(x) = ** - 3x + 8r - 18.6 +12; zero: 0 = 2 Due in 8 hours Construct a polynomial of least degree possible using the given information. Real roots: -1,4, - 3 and contain the point (1, 3). Construct a polynomial of least degree possible using the given information. Real roots: 4, 3 (with multiplicity 2 and 1) and (-1, f(-1)) = (1,1) Preview
One zero of the polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers.
Given: f(x) = x^2 + 3x + 3 and zero: 3
Here's how to approach this problem:
The polynomial f(x) has a root of 3.
f(x) can be expressed as a product of two factors, where the first factor contains (x-3) as one of its roots, as follows:
f(x) = (x-3)(ax + b)
We can obtain the values of a and b by equating the coefficients of this equation to that of the given polynomial:
a + 3 = 1 (since coefficient of x in the given polynomial is 3)
-3a + b = 3 (since the constant term in the given polynomial is 3)
Solving these equations gives us a=-2 and b=9.
f(x) can thus be expressed as:
f(x) = (x-3)(-2x + 9)
Hence, the expression for the polynomial is f(x) = -(x-3)(2x-9).
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Dani spends 5.20 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?
Answer:
13 for 5 bags.
Step-by-step explanation:
Dani spends 5.20 in total for 2 bags. You would do 5.20/2 to get 2.60 which tells us that 2.60 is the cost per bag. Then you would do 2.60 x 5 to get 13.
Evaluate the function for the given value of x. y = (1.2)^x ; x = 2
The solution, when x = 2, will be y = 1.44, according to the facts provided.
What are the definition and examples of value?Value refers to how little something is valuable, either financially or in terms of significance. It can also imply "determine how very much something that is worth," as in a reward with a $200 value. As a verb, it indicates "keeping something in high regard" (such "I value our friendship").
We can evaluate this function y = (1.2)ˣ at x = 2 by merely adding x = 2 to the formula for y.
y = (1.2)ˣ
y = (1.2)ˣ (substitute x = 2)
y = 1.44
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A rectangular prism. A is an edge, B is a vertex, and C is a face.
Label the highlighted parts of this prism.
A is
.
B is
.
C is
The volume of the rectangular prism can be calculated by using the formula V = lwh, where l is the length, w is the width, and h is the height.
The volume of a rectangular prism can be calculated by the formula V = lwh, where l is the length, w is the width, and h is the height. To calculate the volume of a rectangular prism, first measure the length, width, and height of the prism. Then, plug these measurements into the formula V = lwh and solve for V.
For example, if the length of the prism is 6 cm, the width is 5 cm, and the height is 4 cm, the volume can be calculated by plugging these values into the formula. V = 6 x 5 x 4 = 120 cm3. This means that the volume of this rectangular prism is 120 cm3.
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Complete question:
What are the labels for the highlighted parts of a rectangular prism: A, B, and C?
Answer:
A. is an edge
B. a vertex
C. a face
Step-by-step explanation:
I have this same question now and got this. If you need more proof then look at attachment.
6.02 line of best fit ms pre-algebra S2 v16.2/ patterns of association
The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot. It is also known as the regression line.
What is regression line?
In the context of MS Pre-Algebra S2 V16.2, the line of best fit is used to analyze patterns of association between two sets of data. For example, if we have data on the height and weight of a group of individuals, we can use a scatter plot to visualize the relationship between these two variables.
By drawing a line of best fit through the data points, we can see the general trend or pattern of association between height and weight. This line can then be used to make predictions about the weight of an individual based on their height, or vice versa. The line of best fit is a useful tool for analyzing patterns of association in a variety of fields, including statistics, economics, and social sciences.
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Complete question is: The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot.
A particle of mass 5 kg rests on a smooth
horizontal table. It is connected by a light
inextensible string passing over a smooth
pulley at the edge of the table to a particle
of mass 2 kg, which is hanging freely. Find the acceleration of the system
and the tension in the string.
5 kg
2 kg
The acceleration of the system is 0.83 m/s² and the tension in the string is 8.3 N.
The acceleration of the system can be calculated using Newton's second law of motion. The equation is F = ma, where F is the net force on the system, m is the total mass, and a is the acceleration. Since the two masses are connected by a light inextensible string, the net force acting on the system is equal to the tension in the string. Therefore, the equation becomes T = (5 kg + 2 kg)a, where T is the tension and a is the acceleration. Solving for a, the acceleration is found to be 0.83 m/s². The tension in the string can also be calculated using the equation above. Plugging in the acceleration, the tension is found to be 8.3 N.
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I need help with this now!
thank u.
6 hours and 57 minutes to fill the order if they work together.
Arrange these integers from smallest to greatest (ascending order): 2; -2; 3; -3; 6; -6; 0
Answer:
-6, -3, -2, 0, 2, 3, 6
Step-by-step explanation:
Normally the biggest number has the bigger value but in negative integers the smaller number has the bigger value.
Eg- If you have 2 dollars it is bigger that -2 dollars as then you will be going in dept.
-5 is smaller than -1
-1 is the greatest negative integer.
A company's circular logo, printed on a poster, has a radius of 1.25 feet and an area of about 5 square feet. The logo is being scaled up so it can be painted on a billboard. The equation k = √ A/5
shows the scale factor, k, that is needed to achieve an area A. A graph
of the equation is shown.
The company has 240 square feet worth of paint. If they want to use all their paint,
approximately what scale factor should they apply to the logo, and what will the dilated
logo's radius be?
The radius οf the dilated lοgο will be apprοximately 8.66 feet.
What is the scale factοr?The scale factοr is a number that represents the ratiο οf the cοrrespοnding side lengths οf twο similar figures. It can be used tο enlarge οr reduce the size οf a figure by a certain percentage οr factοr.
The area οf the lοgο is given as 5 square feet, and the radius οf the lοgο is 1.25 feet.
Therefοre, we can find the scale factοr as fοllοws:
k = √(A/5) = √(240/5) = √48 ≈ 6.93
Sο the scale factοr is apprοximately 6.93. Tο find the radius οf the dilated lοgο, we multiply the οriginal radius by the scale factοr:
r' = kr = 6.93(1.25) = 8.66
Hence, the radius οf the dilated lοgο will be apprοximately 8.66 feet.
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Which number line model represents the expression
2. 5
+
4. 5
The number line model begins at 2.5 and then adds 4.5 to it, resulting in the number 7 being plotted at the end of the line.
The number line model for the expression 2.5 + 4.5 is shown below. The equation for this expression is 2.5 + 4.5 = 7. This number line model illustrates this expression by starting at the number 2.5 and then adding 4.5 to it, which results in the number 7 being plotted at the end of the line. This is represented by the arrow extending from 2.5 to 7. Starting at 2.5, the arrow first passes through 3, then 4, then 5, then 6, before finally reaching 7. This is the result of adding 4.5 to 2.5, which is shown on the number line model.The expression 2.5 + 4.5 can also be written mathematically as 2.5 + 4.5 = 7. This equation is read as "2.5 plus 4.5 equals 7," and it is a statement that the sum of 2.5 and 4.5 is equal to 7. The number line model of this expression illustrates this mathematical equation by showing how 2.5 plus 4.5 equals 7. The number line model begins at 2.5 and then adds 4.5 to it, resulting in the number 7 being plotted at the end of the line.
|-----|-----|-----|-----|-----|-----|
0 1 2 3 4 5 6
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Which number line model represents the expression 2.5 + 4.5?
Identify the measurement as the diameter or radius of the circular object then find the circumference of the object 1 from the center to the edge of a dvd measures 60 mm
The diameter οr radius οf the circular οbject is 120mm, and the circumference οf the οbject 1 frοm the centre tο the edge οf a DVD is 380mm.
What is Circumference?A circle's οr an ellipse's circumference is its perimeter. In οther wοrds, if the circle were tο be straightened οut alοng a line segment, the length οf the arc wοuld be the circumference. The perimeter is mοre frequently used tο refer tο the length οf the curve surrοunding any defined figure.
The given infοrmatiοn is that a DVD's edge is 60 mm lοng.
The diameter, radius, and circumference οf the circular οbject must be determined in οrder tο determine the measurement.
We cοncluded that
Radius = 60mm
Diameter = 120mm
Circumference = 380mm
Hence, Diameter = 120mm
Circumference = 380mm
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can you factor this completely x^4-16x^3+15x^2
Answer:
(x-15)(x-1) x²
Step-by-step explanation:
x² (x²-16x+15)
a+b=-16
ab=15
a=-15
b=-1
x(x²-15)- (x-15)
(x-15)(x-1)
(x-15)(x-1) x²
Please Help Me!!!
The width of a rectangle measures (9. 8g-4. 5h) centimeters, and its length measures (1. 5g-3. 4h) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression that represents the perimeter of the rectangle in centimeters is 45.2g - 30.6h.
Let's start by finding the length of the top and bottom sides, which are equal to the width. The width is given by (9.8g - 4.5h) centimeters, so the length of the top and bottom sides is:
2(width) = 2(9.8g - 4.5h) = 19.6g - 9h
Next, we need to find the length of the left and right sides, which are equal to the length. The length is given by (1.5g - 3.4h) centimeters, so the length of the left and right sides is:
2(length) = 2(1.5g - 3.4h) = 3g - 6.8h
Now that we have the lengths of all four sides, we can find the perimeter of the rectangle by adding them together:
Perimeter = length + width + length + width
Perimeter = (3g - 6.8h) + (19.6g - 9h) + (3g - 6.8h) + (19.6g - 9h)
Perimeter = 45.2g - 30.6h
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The equation of line QR is x + 2y = 2. What is the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6)?
y = negative one halfx + seventeen halves
y = 2x − 4
y = negative one halfx + seven halves
y = 2x + 16
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]x+2y=2\implies 2y=-x+2 \\\\\\ x=\cfrac{-x+2}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1} \implies 2}}[/tex]
so we're really looking for the equation of a line whose slope is 2 and it passes through (5 , 6)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-6=2x-10\implies {\Large \begin{array}{llll} y=2x-4 \end{array}}[/tex]
The equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.
What is slope-intercept form of a line?y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line.
Given that a line QR has an equation is x+2y = 2, we need to find the equation of a line passing through (5, 6) and is perpendicular to the given line,
Converting the equation into slop-intercepts form,
y = -0.5x+1
Here, slope m = -0.5
We know that the slopes of the perpendicular lines are negative reciprocal of each other,
Therefore, the slope of the asked line is 2.
So, its equation =
y = 2x+c
To find c, put x = 5 and y = 6
6 = 2(5) + c
c = -4
Therefore, the final equation will be =
y = 2x-4
Hence, the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.
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How many rational numbers are there between 0 and 5
Answer: infinity technically the answer is infinity
nothing less nothing more
Step-by-step explanation:
The country of Sylvania has decided to reduce the number
3
of its illiterate citizens by
5 each year. This year there are
9000 illiterate people in the country. Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today
There will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.
We can write a function P(t) to represent the number of illiterate people in Sylvania t years from today, where t is the number of years after the current year.
Given that the country has decided to reduce the number of illiterate citizens by 5 each year, we can subtract 5 from the number of illiterate people each year.
The initial number of illiterate people in the country is 9000. So, the function can be written as:
P(t) = 9000 - 5t
where t is the number of years after the current year.
For example, if we want to find out how many illiterate people will be in Sylvania in 4 years from now, we can substitute t with 4:
P(4) = 9000 - 5(4) = 9000 - 20 = 8980
Therefore, there will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.
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Each box of Marco's favorite cookies costs $4. 0. Which is the dependent and independent variable?
In this scenario, the dependent variable is the cost of the boxes of cookies and the independent variable is the number of boxes of cookies being purchased.
The cost of the boxes of cookies depends on the number of boxes being purchased. The more boxes of cookies that are purchased, the higher the cost will be. Therefore, the cost of the boxes of cookies is the dependent variable, as it depends on the independent variable of the number of boxes being purchased.
Conversely, the number of boxes of cookies being purchased is the independent variable, as it is the variable that is being manipulated or changed. The cost of the boxes of cookies is not being changed, but rather is dependent on the number of boxes being purchased.
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2.5 m³ of granite has a mass of 6725 kg. a) Calculate the density of granite in kg/m³. b) Find the mass of 1.3 m³ of granite in kg.
The density of the granite is 2690 kg/m³ and the mass of 1.3 m³ of granite is 3497 kg.
How to calculate density?Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that;
Volume of the granite = 2.5 m³Mass = 6725 kgDensity p = ?Plug the given values into the above formula and solve for density of the granite.
p = m / v
p = 6725 kg / 2.5 m³
p = 2690 kg/m³
b) The mass of 1.3 m³ of granite in kg will be;
p = m / v
m = p × v
m = 2690 kg/m³ × 1.3 m³
m = 3497 kg
Therefore, the mass of 1.3 m³ of granite is 3497 kg.
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Which Rational Expression is undefined when x=0?
Answer:
Step-by-step explanation:
last one since if you plug in zero for the x in the denominator you get 0 and if you have 0 in the denominator it's always undefined
what is expressed in both units and dollars to show the number necessary to make enough money to keep going?
In the context of economics, the term “break-even point” is used to indicate the number necessary to make enough money to keep going, and it is expressed in both units and dollars.
What is the break-even point?Break-even point is a term used in cost accounting to describe the point at which total cost and total revenue are equal. At this point, there is no profit or loss; it is a neutral zone. At this point, a firm's revenue from the sale of products and services is just sufficient to cover the total costs of producing those products and services.
The break-even point can be expressed in terms of units sold or in terms of total revenue. The point at which the total revenue equals total cost is the break-even point in terms of dollars. The point at which the number of units sold equals the fixed costs divided by the contribution margin per unit is the break-even point in terms of units sold. Therefore, the break-even point is expressed in both units and dollars to show the number necessary to make enough money to keep going.
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I need to figure the code out
The function with the greatest rate of change are:
1. C = 3
2. A = 5
3. A = 1
4. B = 3
What is the Rate of Change of a Linear Function?The rate of change of a linear function, also known as the slope of the line, represents the amount by which the output (y) changes for a given change in the input (x). In other words, it is the measure of how steep the line is.
The formula for the rate of change, or slope, of a linear function is:
slope = (change in y) / (change in x)
1. Rate of change for function A = change in y / change in x = 4/3
For B = 1/2
For C = 3/1 = 3
The function with the greatest rate of change is C = 3
2. Rate of change for function A = change in y / change in x = (10 - 5)/(1 - 0) = 5
For B = (12 - 8) / (3 - 1) = 2
For C = (6 - 3)/(1 - 0) = 3
The function with the greatest rate of change is A = 5
3. Rate of change for function A = change in y / change in x = 2/2 = 1
For B = (3 - 2)/(2 - 0) = 1/2
For C = 1/3
The function with the greatest rate of change is A = 1
4. Rate of change for function A = change in y / change in x = -1/3
For B = (10 - 1)/(4 - 1) = 3
For C = 2
The function with the greatest rate of change is B = 3
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According to a survey on part-time workers (their monthly salaries can vary by different
months), the average base salary for women is higher than the average base salary for men. The
average base salary for women is $3000/month, and the average base salary for men is
$2750/month. Assume monthly salaries are normally distributed with a standard deviation of $300
for both men and women. Furthermore, assume salaries are independent across different months. How much would a woman have to make in a year to have a higher salary than 99% of her male
counterparts
To have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year
To find out how much a woman would have to make in a year to have a higher salary than 99% of her male counterparts, we need to find the salary level that corresponds to the 99th percentile of the male salary distribution.
First, we need to calculate the standard deviation of the annual salaries for both men and women. Since the standard deviation of the monthly salaries is $300, the standard deviation of the annual salaries can be calculated as:
σ_annual = σ_monthly * √12 = 300 * √12 = $1039.23
Next, we can calculate the salary level that corresponds to the 99th percentile of the male salary distribution using the standard normal distribution table.
z-score for the 99th percentile = 2.33
salary level for the 99th percentile of male salary distribution = mean + z-score * σ_annual
= $2750 + 2.33 * $1039.23 = $5229.48 (rounded to the nearest cent)
Therefore, to have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year (rounded to the nearest cent).
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