a) The equation that models the server's earnings as a function of the number of hours the server works is A. y = 20x.
b) The interpretation of the slope and the y-intercept of the line of fit is A. The slope of 20 means that the server’s earnings increase by about $20 per hour. The y-intercept of 0 means that the server makes $0 if she does not work.
What is the slope?The slope of the line of fit is the quotient of the rise and the run.
The rise is the difference between y2 and y1 while the run is the difference between x2 and x1.
The slope shows the constant rate of change or the unit rate.
The y-intercept is the product of the slope and x-intercept.
The rate of earnings per hour, which is the slope = $20
The y-value or intercept depends on the x-value.
For instance, if the server works 4 hours, her total earnings (y) will be $80 (4 x $20).
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Question Completion:Table of Total Earnings, y (in dollars) and x hours:
x 0 1 2 3 4 5 6
y 0 20 40 60 80 100 120
What should be the remainder of the polynomial function for the divisor to be a factor?
Answer:
zero
Step-by-step explanation:
You want to know the remainder of the polynomial function for the divisor to be a factor?
DivisionA divisor is a factor of the dividend in any division problem if and only if the remainder is zero (0).
The divisor will be a factor of a polynomial function if division of the function by that divisor has a remainder of zero.
On a number line, 3.4 would be located. Choose all answers that make a
true statement.
3.4
A. to the left of 3.53
B. to the right of 3.69
C. to the right of 3.33
D. between 3.4 and 3.5
An airplane flying into a headwind travels the 1800-mile flying distance between New York City and Albuquerque, New Mexico in 4 hours. On the return flight, the same distance is traveled in 3 hours and 36 minutes. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
Answer:
speed of the airplane is 520 miles per hour and the speed of the wind is 20 miles per hour.
I need help!! What is the value of x in this triangle?
Answer:
33.49 degrees
Step-by-step explanation:
The sine of the angle is 32/58 (Opposite over Hypotenuse from SOH CAH TOA), so the angle measure is the arcsine or sin^-1 of 32/58 on a calculator which is approximately 33.49 in degrees. An issue you could be having is your calculator being in radian instead of degree mode by default.
how many solutions are there to this nonlinear system
There is only one solution to the nonlinear system.
What is Nonlinear system?
A nonlinear system is a system in which the change of the output is not proportional to the change of the input.
The solutions of a nonlinear system of equations are in the form of x and y values and these are the points at which the graphs intersect. Such systems have no solution, or one or more solutions.
So, here function 1 is a parabola and function 2 is a straight line. The parabola is touching the straight line at one point only, so this has one solution.
Hence the answer is there is only one solution to the nonlinear system.
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Digitalis is a technology company that makes high-end computer processors. Their newest processor, the luteA, is going to be sold directly to the public. The processor is to be sold for $2800 , making Digitalis a profit of $452 . Unfortunately there was a manufacturing flaw, and some of these luteA processors are defective and cannot be repaired. On these defective processors, Digitalis is going to give the customer a full refund. Suppose that for each luteA there is an 12% chance that it is defective and an 88% chance that it is not defective. If Digitalis knows it will sell many of these processors, should it expect to make or lose money from selling them? How much?
The correct option regarding the expected profit of the company is given as follows:
Dugitalis can expected to make money from selling these processors.
In the long run, they should expect to make $116 on each processor sold.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome multiplied by it's respective probability.
The distribution of profits in this problem is given as follows:
P(X = 452) = 0.88 -> non-defective processors sold.P(X = -2348) = 0.12 -> defective processors.For the second probability, we have the number 2348, which is the cost of manufacturing each processor, as 2800 - 452 = $2,348.
Then the expected profit over time is given as follows:
E(X) = 0.88 x 452 - 2348 x 0.12 = $116.
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What are the coordinates of B′ after the pentagon is rotated 90° about the origin?
Assuming that the rotation is anticlockwise (as it is not defined) the coordinates of B after the rotation are (-5, 1), so the correct option is C.
What are the coordinates of B' after the rotation?If the pentagon is rotated 90°, then all the vertices are also rotated 90° about the origin.
Here we don't know if the rotation is clockwise or anticlockwise, so we assume it is anticlockwise, as this is the standard rotation.
The orignal coordiates of point B are (1, 5)
This is on the first quadrant, a rotation of 90° anticlockwise will:
Interchange the x-value and the y-value.Add a negative sign to the new x-value.So we will go from a point (x, y) to (-y, x)
Then the new coordinates of B' are (-5, 1)
Thus, the correct option is C.
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Hello Help me, please with this Hw
The net investment for Feinstein's Finest's new pub is $2,200,000.
Given in the question:Building cost = $1.5 million
Fixtures + installation Cost =$200,000
Stocking Inventory =$ 100,000
Land( Old cost ) =$300,000
Land( New cost ) = $1,000,000
Calculating The net investment for Feinstein's Finest's new pub:Net investment =Building cost + (Fixtures + installation Cost) +Stocking Inventory + Land( Old cost )
Net investment = $1.5 million + $200,000 +$ 100,000 +$ 100,000 + $300,000
The net investment =$2,200,000
Note: The New land cost was not included in the calculation because the land has been bought previously at $300,000. But the land's present cost is $1,000,000
Hence,
The net investment for Feinstein's Finest's new pub is $2,200,000
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If TU = 4x, UV = x + 2, and TV = 7, what is TU?
===========================================================
Explanation:
Assuming points T, U, and V are all on the same straight line, then we can say the following:
TU + UV = TV
(4x) + (x+2) = 7
5x+2 = 7
5x = 7-2
5x = 5
x = 5/5
x = 1
Now we can determine the length of each piece.
TU = 4x = 4*1 = 4UV = x+2 = 1+2 = 3as a check: TU + UV = 4+3 = 7 which matches perfectly with TV = 7. The answer is confirmed.
Once again, this assumes that points T, U, and V are collinear (i.e. on the same straight line). It also assumes that U is between T and V.
what is the center of a circle represented by the equation x52y624265565665
According to the equation (x-5)²+(y+6)2=4², the center of a circle is (5,-6).
What are circles?A circle is, to put it simply, a rounded shape devoid of any edges or line segments.
Its geometric form is that of a closed curve.
Following a moving point in a plane while keeping a fixed distance from another point will result in the closed shape of a circle.
The word circle derives from the Greek word kirks, which means hoop or ring.
So, the equation we have is (x-5)²+(y+6)2=4².
The circle equation's center radius form is:
(x - h)² + (y - k)² = r²
Considering the information we have:
(x - 5)² + (y + 6)² = 4²
Where the radius is 4 and the center is (5, -6).
Therefore, according to the equation (x-5)²+(y+6)2=4², the center of a circle is (5,-6).
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Correct question:
What is the center of a circle represented by the equation (x-5)²+(y+6)2=4²?
I6
Researchers measured the data speeds for particular smartphone carrier at 50 airports. The highest speed measured was
75.5 Mbps. The complete list of 50 data speeds has a mean of ) 15.59 Mbps and a standard deviation of s = 23.85 Mbps.
What is the difference between carrier's highest data speed and the
mean of all 50 data speeds?
b. How many standard deviations is that [the difference found in part (a)]?
. Convert the carrier's highest data speed to a z score.
d. If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly high,
is the carrier's highest data speed significant?
Answer:
66 es pero que te ayude ■■♤♤
are the triangles congruent why or why not brainly
∠C is not congruent to any angle in DEF. Hence, option C is the correct answer.
From the given figure below,
In ΔABC,
∠A=33° and ∠C=88°
By angle sum property of triangles,
∠A+∠B+∠C=180°
33°+∠B+88°=180°
∠B=180°-33°-88° [subtracting 33° and 88° from both sides]
∠B=59°
Now, In ΔDEF,
∠D=33° and ∠E=58°
By angle sum property of triangles,
∠D+∠E+∠F=180°
33°+58°+∠F=180°
∠F=180°-33°-58° [subtracting 33° and 58° from both sides]
∠F=89°
Thus, ΔABC is not congruent to Δ DEF as∠C and ∠B are not congruent to any angle of the Δ DEF .
Hence, ∠C is not congruent to any angle in DEF."
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The complete question is -
Are the triangles congruent? Why or why not?
A) Yes, ∠A ≅∠D and AB ≅ DE.
B) Yes, they are congruent by either AAS or ASA.
C) No,∠C is not congruent to any angle in ΔDEF.
D) No, the congruent sides do not correspond.
Which ordered pair is a solution to the inequality y + 2 < 2x
The ordered pairs are of the form (x, y < 2x - 2), some examples of solutions are (0, -3) and (0, -4)
Which ordered pair is a solution of the inequality?An ordered pair will be a solution if, when we replace the values of the ordered pair on the inequality, the inequality becomes true.
Here the inequality is:
y + 2 < 2x
Isolating one of the variables we get:
y < 2x - 2
Now let's assume we impose x = 0, then the inequality becomes:
y < 2*0 - 2
y < -2
So y can be any value smaller than -2, then for example:
(0, -3), (0, -4)...
All of these are solutions of the inequality.
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Mia is 1.65 meters tall. At 3 p.m., she measures the length of a tree's shadow to be
26.45 meters. She stands 21.4 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
The height of the tree to the nearest hundredth of a meter is 8.64 meters
What are equivalent ratios?"Two or more ratios that reflect the same relation or comparison of numbers are known as equivalent ratios," according to the definition of the equivalent ratio in mathematics. The idea of corresponding fractions is comparable. The term "proportion" also refers to the equivalence of two ratios. Even if the values of the antecedent and the consequent are different, if we simplify them, we will still arrive at the same value.
How to solve?
Mia's height=1.65 m
Tree's equivalent height=26.45m
Mia's height w.r.t. the tree's shadow=26.45-21.40 =5.05m
Ratio of the equivalent height w.r.t original height=5.05:1.65 =3.06
Tree's original height= tree's equivalent height: ratio of Mia's height
= 26.45:3.06 =8.64m
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Based on the given statement, and the image, what is the value of a?
Enter your answer as a decimal, like this: 42.25
Answer:
$5.80
Step-by-step explanation:
Based on the given statement, and the image, what is the value of a?
Box 2 has 7 circles:
$10.15 / 7 = $1.45 per circle
box 1 has 4 circles:
1.45 * 4 = $5.80
25/24 as a decimal rounded to the nearest tenth
Answer:
1.0
Step-by-step explanation:
Hope this helps! :)
The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
here, we have,
given that, 25/24
now, we have to rounded to the nearest tenth
as decimal, so, we have to divide 25 by 24
i.e. 25/24 = 1.041
we get, 1.041 => 1.0
so, it is 1.0 a decimal rounded to the nearest tenth
Hence, The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .
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Given Ray BA bisects ∠CBD and the diagram below, what is m∠ABD?
The measure of the angle ∠ABD is 64 degrees
How to determine the measure of the angle?From the question, we have the following parameters:
Ray BA bisects ∠CBD
∠CBD = 5x + 18
∠ABC = 3x - 2
Because of the bisection, we have
∠ABC = ∠ABD
∠ABC * 2 = ∠CBD
Substitute the known values in the above equation, so, we have the following representation
(3x - 2) * 2 = 5x + 18
Open the brackets
6x - 4 = 5x + 18
Evaluate the like terms
x = 2
Recall that
∠ABC = ∠ABD
So, we have
∠ABD = 3x - 2
This gives
∠ABD = 3 x 22 - 2
Evaluate
∠ABD = 64
Hence, the angle is 64 degrees
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What is LCD and how do I do it in math??
Answer:
LCD is the abbreviation for Least Common Denominator.
Step-by-step explanation:
To find the LCD of two numbers, you list out the multiples of each number. Then you look for the smallest multiple of both numbers and there you have it!
For example, if we had to find the LCD of 4 and 3, we'll first list out the multiples of both.
4: 4, 8, 12, 16, 20, ...
3: 3, 6, 9, 12, 15, ...
The first least multiple we found in those two numbers is 12.
Therefore, the LCD would be 12.
What is the formula V Lwh used for?
The formula V = Lwh used to calculate the volume of rectangular prisms.
Volume is generally defined as the amount of space that a substance or object occupies, or that is enclosed within a container.
The the formula V = Lwh used for calculation of the volume of rectangular prisms.
Where, the L represents the length of the rectangular prism
the W represents the width of the rectangular prism
the H represents the height of the rectangular prism.
Therefore, The formula V Lwh used to calculate the volume of rectangular prisms.
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Dasan is participating in a traditional cornstalk archery competition hosted by the Chickasaw
Nation. He is using a custom bow and arrow, handmade by a Chickasaw bowmaker. The quadratic
expression below represents the height of an arrow, in feet, a seconds after Dasan launches it
toward the cornstalks.
What is the linear term of the quadratic expression?
-16x² +50x+4
The algebraic systems of equations that contain one linear equation and one quadratic equation are known as linear and quadratic equations.
What Is the Linear Expression?If each term is a constant or a variable raised to the first power, an algebraic statement is referred to as a linear expression. That is to say, no exponent can be greater than 1.A variable raised to the first power is referred to as x, whereas a variable raised to the second power is referred to as x2.Five is an illustration of a constant.Keep in mind that the coefficients put in front of the variables have no real meaning. Let's take a look at a few instances of these polynomials, which are merely expressions with two or more terms.In a linear formulation,
-16x² +50x+4
-2(8x² - 25x - 2)
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If l 1m, then <1 is a right angle
Right angle is an angle of 90 degrees while complementary angles add up to 90 degrees.
What are complementary angles and right angles?When the sum of two angles is 90°, then the angles are known as complementary angles.
A right angle is an angle of 90°.
Perpendicular lines are lines that intersect at a 90° angle. Perpendicular lines forms a right angle.
The complementary angle theorem states, "If two angles are complementary to the same angle, then they are congruent to each other".
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The width of a rectangular slab of concrete is 10m less than the length. The area is 24 m ^2
The width and the length of the slab are 2 meters and 12 meters, respectively
How to determine the dimensions of the slab?From the question, we have the following parameters that can be used in our computation:
Width of a rectangular slab of concrete = 10m less than the length.
Area = 24 m²
These parameters can be represented as
Width = Length - 10
Area = Length * Width
So, we have
w = l - 10
A = lw
Also, we have
A = 24
Substitute w = l - 10 in A = lw
A = l(l - 10)
So, we have
l(l - 10) = 24
Expand
l² - 10l = 24
This gives
l² - 10l - 24 = 0
Expand
l² + 2l - 12l - 24 = 0
Factorize
(l + 2)(l - 12) = 0
So, we have
l = -2 and l = 12
The length cannot be negative
So, we have
l = 12
Recall that
w = l - 10
So, we have
w = 12 - 10
Evaluate
w = 2
Hence, the dimensions are 2 meters and 12 meters, respectively
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Possible question
The width of a rectangular slab of concrete is 10m less than the length. The area is 24 m ^2
Compute the dimensions of the slab
What is always true about an isosceles triangle?
In an isosceles triangle, two angles and two sides are always equal.
What do we mean by an isosceles triangle?In geometry, an isosceles triangle is one with at least two sides of equal length.
It can be defined as having exactly two equal-length sides or as having at least two equal-length sides, with the equilateral triangle being an exception to the second definition.
Isosceles Triangle: A triangle is referred to as being isosceles if any of its two sides is equal.
if the triangle has X, Y, and Z as its three sides.
The triangle is isosceles when X = Y, X = Z, or Y = Z.
Scalene triangles are recognized as triangles without equal sides.
Therefore, in an isosceles triangle, two angles and two sides are always equal.
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2x y 6 y 3x 4 what is the resulting equation
The solution of the equations are x = 0.4 and y = 5.2.
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Given equations are
2x + y = 6 .....(i)
y = 3x + 4 .....(ii)
Solve the equation by using substitution method:
Put y = 3x + 4 in equation (i)
2x + 3x + 4 = 6
5x + 4 = 6
5x = 2
x = 2/5
x = 0.4
Putting x = 0.4 in equation (ii)
y = 1.2 + 4
y = 5.2
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Question 3 (2 points)
Find the area of the composite figure. Show work to get bonus points.
The area of the shaded portion of the composite figure could be easily 25*25 - 1/2*13*10 that is 625 - 65 = 560 feet
What is meant by the term Area?When referring to a two-dimensional space or points, in mathematics, the term "area" is used. It refers to a region's or a flat object's size, such a square or rectangle. The area of a form is determined in geometry by dividing the length by the breadth. For example, the area of a square with a side length of 4 units is 4 x 4 = 16 square units. Square units, such as square inches, square feet, or square meters, are used to measure area. Triangles (1/2 x base x height), circles ( x radius squared), and trapezoids (1/2 x (base 1 + base 2) x height) are other basic geometric forms with associated area calculations.
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Solving a tax rate or interest rate problem
The cost of each computer before the finance charges is of:
Desktop: $2,761.Laptop: $2,411.What is the system of equations?The variables to the system of equations are given as follows:
Variable x: cost of the desktop.Variable y: cost of the laptop.The laptop costs $350 more than the laptop, hence:
x = 350 + y.
Considering the interest rates, the finance charges were of $400 for one year, hence:
0.075x + 0.08y = 400.
Replacing the first equation into the second, the cost of the laptop is of:
0.075(350 + y) + 0.08y = 400.
0.155y = 373.75
y = 373.75/0.155
y = $2,411.
Then the cost of the desktop is obtained as follows:
x = 350 + y = 350 + 2411 = $2,761.
(which is 350 more than the laptop).
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for a fishing trip, debra is going to choose lures to put in her tackle box. she has 4 lures that are jigs and 9 that are spinnerbaits. In how many waits can she choose 6 lures if more than 4 must be spinnerbaits?
Answer:
1680
Step-by-step explanation:
Multiply and write a fraction or mixed numbers in its simplest form
2/5 x 6/7
A right triangle has side lengths 9,40, and 41 as shown below . Use these lengths to find tanY, Sin Y, and cosY
Using the trigonometric ratio of sin, cos and tan of Y, the values are 12.7, 12.7 and 12.4 degrees respectively
Trigonometric RatioThis involves using ratios of sine, cosine, tangent, cot, cosec, sec to find the missing sides of a right angle triangle.
In the triangle given;
Using angle Y as a reference point;
hypothenuse = 41opposite = 9adjacent = 40Sin Y = opposite / hypothenuse
sin Y = 9 / 41
Y = sin⁻¹ (9/41)
Y = 12.7°
The cosine value of Y
cos Y = adjacent / hypothenuse
cos Y = 40 / 41
Y = cos⁻¹(40 / 41)
Y = 12.7°
The tangent value of Y is
tan Y = opposite / adjacent
tan Y = 9 / 41
Y = tan⁻¹(9/41)
Y = 12.4°
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Explore
A 100-unit-long line is split in half.
Half of the line is used to form one large circle.
The other half forms two identical smaller circles.
Which is larger?
The larger circle is, half of the line is used to form one large circle.
What is split in half?
To split or cause to split, especially violently, by cleaving into distinct pieces, typically into two nearly equal ones.
To split into a lesser number of things neatly or equally. The mirror collapsed and broke into three almost identical pieces.
Here, a 100-unit-long line is split in half.
That means a line is divided into two equal part with length 50 unit each.
Also, half of the line is used to form one large circle. The other half forms two identical smaller circles.
From this we can see that half of the line is used to form one large circle is always a lager circle.
And other half forms two identical smaller circles are the smaller circles.
Hence, the larger circle is, half of the line is used to form one large circle.
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