√87x = √(x * 87) = √(x * 3 * 29)
If x is a perfect square, say x = a^2, then we can rewrite the expression as:
√(a^2 * 3 * 29) = a√(3 * 29)
In this form, the expression is simplified further, because a is a constant and √(3 * 29) is a simplified radical.
Therefore, to simplify the expression √87x further, we need x to be a perfect square.
The expression √87x cannot be further simplified because the square root and the variable are multiplied together. However, it is possible that the expression was meant to be written as √(87x) with the entire expression under the square root symbol. In this case, the expression can be further simplified by evaluating the square root of 87 times x, but the value of x is not relevant to this simplification.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Mario's Pizza just received two big orders from customers throwing parties. The first customer, Karen, bought 6 regular pizzas and 7 deluxe pizzas and paid $226. The second customer, Malik, ordered 6 regular pizzas and 9 deluxe pizzas, paying a total of $270. What is the price of each pizza?
Each regular pizza costs blank $, and each deluxe pizza costs blank$.
The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. each regular pizza costs $41 and each deluxe pizza costs $22.
System of equations:
6r + 7d = 226
6r + 9d = 270
Solving:
6r + 7d = 226
6r + 9d = 270
-6r -6r
7d -9d = -44
d = -44/2
d = -22
6r + (-22) = 226
6r = 248
r = 248/6
r = 41
Each regular pizza costs $41, and each deluxe pizza costs $22.
The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. To solve this system of equations, we first subtracted 6r from both equations, leaving us with 7d and -9d on one side. We then divided both sides by -2, leaving us with d = -22. We then added 22 to the other equation, leaving us with 6r = 248. Finally, we divided both sides by 6, leaving us with r = 41. Thus, each regular pizza costs $41 and each deluxe pizza costs $22.
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While warming up at soccer practice, Ellie's teammate tosses the ball to Ellie. Ellie hits the ball upward with her head from a height of 1.6 meters at a velocity of 6 meters per second. The ball is in the air for some time until Ellie catches it at a height of 1 meter.
To the nearest tenth of a second, how long is the ball in the air before Ellie catches it?
The ball is in the air for approximately 0.8 seconds before Ellie catches it.
What is acceleration?The acceleration a body experiences as a result of gravity is known as the acceleration due to gravity. Its acceleration is around 9.81 metres per second squared close to the Earth's surface. In kinematics, many equations that describe how things move when affected by gravity include the acceleration caused by gravity as a constant.
Using kinematic equation to solve for the time (t):
Δy = vit + 0.5a*t²
Rearranging we have:
t = √((Δy - 0.5at²) / vi)
Substituting the values:
t = √((1 - 0.59.81t²) / 6)
t = 0.798 seconds
Hence, the ball is in the air for approximately 0.8 seconds before Ellie catches it.
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If a matrix A is 5 x 3 and the product AB is 5 x 7, what is the size of B?
Matrix Multiplication
Two matrices may be multiplied if and only if the first matrix has the same number of columns as there are rows in the second matrix. Suppose the first matrix has dimensions of a×b and the second matrix has dimensions of c×d, we can say that b=c and their product will have dimensions of a×d
Answer:
Matrix B is a 3 × 7 matrix.
PLEASE HELP! WILL TRY AND DO BRAINLYEST! INCLUDE SCRATCH AND CORRECT ANSWER. THANK YOU!
The Distance after 18 minutes travelled is calculated as: 19.8 miles
How to interpret Distance, speed and time relationship?In the distance, speed and time relationship, we know that:
Speed = Distance/Time
From the table, we see the distance the car travels in y miles after x minutes. Thus:
We can use slope formula to find the average speed which is:
Slope = (y2 - y1)/(x2 - x1)
Thus:
Constant speed = (22 - 11)/(20 - 10)
Constant Speed = 11/10 = 1.1 miles per minute
Thus, distance after 18 minutes is:
Distance = 1.1 * 18 = 19.8 miles
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help
im stuck on this question
Answer:
Step-by-step explanation:
Line A passes through (5,1) and (0,-2). So
gradient line A =[tex]=\frac{-2-1}{0-5} =\frac{3}{5}[/tex]
Since the lines are parallel they have equal gradients, so [tex]m=\frac{3}{5}[/tex].
The line passes through point P and so has y-intercept = 3 (so c=3).
So the equation of the new line is:
[tex]y=\frac{3}{5} x+3[/tex]
Apply the Cauchy-Goursat Theorem to show that Jc f(z) dz = 0 when the contour C is the unit circle with counterclockwise (positive) orientation, where (a) f(z) = ze-%, (b) f(2) (c) f(z) tan 2. 22 + 2 Let C1 be the positively oriented boundary of the square whose vertices lie On the lines I El and y = +l and Cz be the positively oriented circle |2| = 4. Explain why Jc f(2) dz Jc_ f(2) dz when + 2 (a) f(2) (6) f(2) (c) f(2) sin( 2/2)` Let C denote the positively oriented boundary of the square whose sides lie along I = 12 and y +2 Use a Cauchy Integral Formula (Generalised version Or not) to evaluate the following integrals: COS - dz cosh z d tan(2/2) d2 (6) (c) c 2 (22 (a) First show that for AnY real constant ( d= = 2t4. Using the parameterisation writo (ie integral in part (a) in terms of 0. Then with the aid of Euler icentitV lerive the formula 4C coska sin 0) d0 = x, Bonus: Use the following method to derive the integration formila (with b > OJ:
The Cauchy Integral Formula (Generalized version), we have: ∫C [tex]z^2[/tex] dz = ∫C[tex]z^2[/tex]/(z - 0) dz
To apply the Cauchy-Goursat Theorem, we need to check if the function f(z) is analytic inside the contour C, i.e., it should be differentiable everywhere inside C.
(a) Let f(z) =[tex]ze^(-z)[/tex]. Then, f(z) is entire, i.e., differentiable everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:
∮C f(z) dz = 0
(b) Let f(z) = 2. Since 2 is a constant, it is analytic everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:
∮C f(z) dz = f(0) × 2πi = 0 (since C does not enclose the origin)
(c) Let f(z) = z tan(2π/2). Since tan(2π/2) is not analytic at z = ±i, f(z) is not analytic inside the unit circle C. Hence, we cannot apply the Cauchy-Goursat Theorem directly to evaluate the integral ∮C f(z) dz.
To evaluate the integral ∮C f(z) dz, we can use the Cauchy Integral Formula (Generalized version) which states that for any analytic function f(z) and any closed contour C, we have:
∮C f(z)/(z - a) dz = 2πi f(a)
where a is any point inside the contour C.
For (a), let's use the Cauchy Integral Formula to evaluate the integral. We have:
f(z) = z[tex]e^{-z[/tex]
∮C f(z) dz = ∮C f(z)/(z - 0) dz (since f(0) = 0)
= 2πi f(0) = 0
For (b), we can use the Cauchy-Goursat Theorem as f(z) = 2 is analytic everywhere inside the circle |z| = 4. Hence, we have:
∮C2 dz = 2πi f(0) = 2πi × 2 = 4πi
For (c), we need to use the Cauchy Integral Formula to evaluate the integral. We have:
f(z) = z tan(π/2)
∮C f(z) dz = ∮C f(z)/(z - i) dz (since i is inside C)
= 2πi f(i) = 2πi × i × tan(π/2) = -2πi
Thus, we have:
∮C f(z) dz ≠ ∮C f(z) dz in general.
Now, let C be the positively oriented boundary of the square whose sides lie along x = ±2 and y = ±2.
(a) Using the Cauchy Integral Formula (Generalized version), we have:
∫C cos(z) dz = ∫C cos(z)/(z - π/2) dz
= 2πi cos(π/2) = 0
(b) Using the Cauchy Integral Formula (Generalized version), we have:
∫C cosh(z) dz = ∫C cosh(z)/(z - 0) dz
= 2πi cosh(0) = 2πi
(c) Using the Cauchy Integral Formula (Generalized version), we have:
∫C [tex]z^2[/tex]dz = ∫C [tex]z^2[/tex]/(z - 0) dz.
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At the beginning of spring, Samuel planted a small sunflower in his backyard. The sunflower's height in inches,h,after w weeks, is given by the equation h=3.25w+19. What could the number 3.25 represent in the equation?
In equation h=3.25w+19, the number 3.25 represents the rate of change in the height of the sunflower per week (w), and the constant term of 19 represents the initial height of the sunflower when it was first planted.
The equation h=3.25w+19 is in slope-intercept form, which means that it can be written as y=mx+b, where y represents the dependent variable (in this case, the height of the sunflower), x represents the independent variable (the number of weeks since the sunflower was planted), m represents the slope of the line, and b represents the y-intercept (the value of y when x=0).
In this equation, the slope is 3.25, which means that for each additional week that passes since the sunflower was planted, its height increases by an average of 3.25 inches. So, the number 3.25 represents the rate of change of the height of the sunflower with respect to time.
This means that for every additional week that passes since the sunflower was planted, the height of the sunflower increases by 3.25 inches on average.
The equation also includes a constant term of 19, which represents the initial height of the sunflower when it was first planted, before any weeks had passed.
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errors-in-variables bias a. is only a problem in small samples. b. arises from error in the measurement of the dependent variable. c. arises from error in the measurement of the independent variable. d. is particularly severe when the source is an error in the measurement of the dependent variable.
Errors -in -variables bias represents the option c. arises from error in the measurement of the independent variable.
In a regression model Errors -in -variables bias is not only a problem in small samples.
It can affect large samples as well.
This can lead to biased estimates of the regression coefficients.
This can lead to biased and inconsistent estimates of the regression coefficients and standard errors.
Even if the error in the dependent variable is zero-mean.
Even if the measurement error in the dependent variable is negligible.
The problem is not limited to small samples.
And can be particularly severe when the measurement error in the independent variable is large.
Therefore, the errors -in - variables bias arises from the option c. arises from error in the measurement of the independent variable.
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Which sequence of transformations will produce the same result?
Option C includes a 5 unit upshift, a mirror along the y-axis, and a 1.5 scale factor dilation. Therefore sequence of transformation in C will produce the same result. .
Which sequence of transformation will produce the same result?The ideal selection is B. Reflection along the y-axis, a 5 unit upshift, and a 1.5 scale factor for elongation
Option A says: 15-turn clockwise spin and 2 unit translation to the right
Rotation and translation are rigid transformations that create congruent as well as similar figures while preserving the measurements of matching sides and angles. Therefore, this series of transformations is incorrect because it will not result in a similar or congruent picture.
Option B involves 90-degree anticlockwise spin and reflection along the x-axis.
Reflection and rotation are rigid transformations that create congruent as well as similar figures while preserving the measurements of corresponding sides and angles. Consequently, this series of changes won't result in a similar Thus, it is untrue.
Option C includes a 5 unit upshift, a mirror along the y-axis, and a 1.5 scale factor dilation.
Translation and reflection are rigid transformations that create congruent as well as similar figures while preserving the measurements of matching sides and angles. The picture will no longer be congruent after dilation with a scale factor of 1.5, but it will still be similar because the measure of the angles remains constant. This series of transformations will therefore result in a similar but incongruent image, and is therefore accurate.
Option D calls for a scale factor of 2 followed by a scale factor of 0.5.
With a scale factor of 2, dilation results in the side widths of The picture will eventually grow to be twice as long as the preimage.
The side lengths of the picture with double side lengths will then be halved by dilation once more with a scale factor of 0.5.
The figure will eventually return to its initial condition, which is identical to and consistent with itself. Therefore, this series of transformations is incorrect because it won't result in a similar or congruent picture.
The best choice is C.
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Complete question:
Which sequence of transformations will produce the same result?
Option A says: 15-turn clockwise spin and 2-unit translation to the right
Option B: involves a 90-degree anticlockwise spin and reflection along the x-axis.
Option C: includes a 5-unit upshift, a mirror along the y-axis, and a 1.5 scale factor dilation.
Option D: calls for a scale factor of 2 followed by a scale factor of 0.5.
Determine if the two triangles are congruent. If they are, state how you know and write the congruent statement of each angles and sides
Therefore , the solution of the given problem of triangle comes out to be two triangles cannot be congruent because their side lengths and angle measurements vary.
A triangle is exactly what?If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
The diagram's two rectangles are not parallel to one another. Here's how we can figure that out:
The two triangles' side lengths and angle measurements vary, as is evident. Triangle DEF's side lengths are
=> DE = 5, EF = 4, and DF = 7,
while Triangle ABC's side lengths are
=> AB = 7, BC = 4, and AC = 8.
Triangle DEF has an acute angle at D, a right angle at E, and
an oblique angle at F,
whereas Triangle ABC has acute angles at A and B and a right angle
at C.
The two triangles cannot be congruent because their side lengths and angle measurements vary.
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please help with both and not just one
The solution to the inequality is:
x ∈ (-√2, 3/4) ∪ (√2, 4).
What is inequality ?
An inequality is a mathematical statement that compares two values or expressions using symbols such as <, >, ≤, or ≥. It indicates that one value or expression is less than or greater than the other. Inequalities can be solved by using various algebraic techniques to find the range of values that satisfy the inequality. Inequalities are commonly used in many areas of mathematics, such as in algebra, geometry, and calculus, as well as in real-world applications such as economics, physics, and engineering.
According to the question:
To solve the inequality f(4x-3)/(2-x²)>0, we first need to find the critical values of x where the function is equal to zero or undefined.
For f(4x-3) to be zero, we have 4x-3 = 0, which gives us x = 3/4.
For 2-x² to be zero, we have 2-x² = 0, which gives us x = ±√2.
We also need to check where the function is undefined, which is where the denominator (2-x²) is equal to zero. This occurs at x = ±√2.
So, we have critical values at x = -√2, 3/4, and √2.
We can use a sign chart to determine the intervals where the function is positive.
x -√2 3/4 √2
f(x)
(4x-3)/(2-x²) - + -
sign - + -
From the sign chart, we see that the function is positive on the intervals (-√2, 3/4) and (√2, 4). Therefore, the solution to the inequality is:
x ∈ (-√2, 3/4) ∪ (√2, 4).
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Determine whether the table represents a linear or an exponential function.
Does this table represent an linear or exponential function?
La tabla representa una función exponencial, ya que la razón entre los términos consecutivos es constante y no varía como en una función lineal.
simplify the question: √256÷2√8
Answer:
1) Since 16 x 16 = 256, the square root of 256 is 16.
16÷2√8
2) Simplify 18 to 2√2.
16 ÷ 2 × 2√2
3) Simplify 16÷2 to 8.
8 × 2√2
4) Simplify.
16√2
Done
Decimal Form: 22.627417
Answer:
22.6 (approx)
Step-by-step explanation:
[tex] \sqrt{256} = 16[/tex]
[tex] \sqrt{8} = 2 \sqrt{2} [/tex]
[tex] \sqrt{2} = 1.41 \: approx[/tex]
16 ÷ 2×(2×1.41)
16 ÷ 2×2.82
8 × 2.82
Therefore, answer is 22.56
Given: QS bisects PR at T, QR is parallel to PS. Prove PQRS is a parallelogram
The proof involves showing that the bisecting line QS and the parallel sides QR and PS create pairs of congruent angles, which then proves that opposite sides are parallel. Therefore, PQRS is a parallelogram.
Proof:
Since QS bisects PR at T, we know that PT = RT and QT = TS.
Also, QR is parallel to PS. Therefore, angle QTS is congruent to angle RPT (alternate interior angles).
Using the same reasoning, we can show that angle PST is congruent to angle QRP (alternate interior angles).
Now, we have two pairs of congruent angles in the quadrilateral PQRS, which means that the opposite sides are parallel.
Therefore, PQRS is a parallelogram.
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A disk is shaped like a flat circular plate. Its radius is 4.25 inches. What is the area of 5/6 of the disk? Write your answer in terms of pi.
Answer:
5/6π(4.25 in)^2
Step-by-step explanation:
Step 1: Calculate the full area of the disk using the formula for the area of a circle: A = π × r2
A = π × (4.25 inches)2
A = 56.41π inches2
Step 2: Calculate 5/6 of the full area.
A = (5/6) × 56.41π inches2
A = 47.01π inches2
Therefore, the area of 5/6 of the disk is 47.01π inches2.
\If the three hoses are used to start filling the pool at 10 a.m. on Tuesday, when will the pool be completely filled?
8 p.m. on Tuesday
10 p.m. on Tuesday
4 a.m. on Wednesday
6 a.m. on Wednesday
Answer: C OR 4 a.m. on Wednesday
Step-by-step explanation:
Lauren receives a discount on each book she purchases. the original price of each x dollars. she purchase 4 books for a total of (4x-12) dollars. Factor the expression. what can you conclude about the discount?
The discount that she receives in total is 12 dollars.
What is a factor?Factors are integers (whole numbers) greater than 1 that are multiplied together to produce a given product.
The expression 4x-12 can be factored to (4x - 4) - (4-8).
This means that the discount that Lauren receives on each book is 4 dollars. So, for each book, the price is reduced by 4 dollars.
This means that if the original price of each book is x dollars, then Lauren pays x-4 dollars for each book.
In total, she pays 4(x-4) = 4x-16 dollars for 4 books.
This means that the discount that she receives in total is 12 dollars.
Therefore, we can conclude that Lauren receives a 4 dollar discount on each book she purchases and a total discount of 12 dollars when she purchases four books.
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Which linear equations have an infinite number of solutions? Check all that apply.
(x – 3\7) = 2\3 (3\2x – 9\14 )
8(x + 2) = 5x – 14
12. 3x – 18 = 3(–6 + 4. 1x)
1\2(6x + 10) = 7(3\7x – 2)
4. 2x – 3. 5 = 2. 1 (5x + 8)
the linear equations that have an infinite number of solutions are (x – 3/7) = 2/3 (3/2x – 9/14), 3x – 18 = 3(–6 + 4.1).
To determine which linear equations have an infinite number of solutions, we need to check if the equations are equivalent. Two linear equations are equivalent if they have the same slope and y-intercept, or if they represent the same line.
Let's check each of the given equations:
(x – 3/7) = 2/3 (3/2x – 9/14)
Multiplying both sides by 14, we get:
14x - 6 = 28/3x - 6
Multiplying both sides by 3, we get:
42x - 18 = 28x - 18
Subtracting 28x and adding 18 to both sides, we get:
14x = 0
Dividing both sides by 14, we get:
x = 0
Substituting x = 0 into the original equation, we get:
(-3/7) = (-9/14)
The left-hand side is equal to the right-hand side, which means the equation is true for all values of x. Therefore, this equation has an infinite number of solutions.
8(x + 2) = 5x – 14
Expanding the left-hand side, we get:
8x + 16 = 5x - 14
Subtracting 5x and subtracting 16 from both sides, we get:
3x = -30
Dividing both sides by 3, we get:
x = -10
Substituting x = -10 into the original equation, we get:
8(-8) = 5(-10) - 14
-64 = -64
The left-hand side is equal to the right-hand side, which means the equation is true for x = -10. Therefore, this equation has exactly one solution.
3x – 18 = 3(–6 + 4.1x)
Expanding the right-hand side, we get:
3x - 18 = -18 + 12.3x
Subtracting 3x and adding 18 to both sides, we get:
0 = 0.3x
Dividing both sides by 0.3, we get:
x = 0
Substituting x = 0 into the original equation, we get:
-18 = -18
The left-hand side is equal to the right-hand side, which means the equation is true for all values of x. Therefore, this equation has an infinite number of solutions.
1/2(6x + 10) = 7(3/7x – 2)
Expanding both sides, we get:
3x + 5 = 3x - 14
This equation simplifies to 5 = -14, which is not true for any value of x. Therefore, this equation has no solutions.
2x – 3.5 = 2.1(5x + 8)
Expanding the right-hand side, we get:
2x - 3.5 = 10.5x + 16.8
Subtracting 2x and adding 3.5 to both sides, we get:
0 = 8.5x + 20.3
This equation simplifies to 0 = 0, which is true for all values of x. Therefore, this equation has an infinite number of solutions.
Therefore, the linear equations that have an infinite number of solutions are (x – 3/7) = 2/3 (3/2x – 9/14), 3x – 18 = 3(–6 + 4.1).
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what is the geometric mean of 4 and 29
Answer: between 4 and 9 is
4 *9=36=6
Arrange these number card to make the smallest possible number that rounds to 3 when rounding to the nearest whole number 3250
Answer: What number cards??
Step-by-step explanation:
What are the 4 basic steps that should be followed to a attain a structured analysis of transactions? describe each briefly.
The four basic steps that should be followed to attain a structured analysis of transactions are identifying and analyzing transactions, recording transactions to a journal, posting journal entries to ledger accounts, and preparing a trial balance.
There are different variations of the steps involved in the accounting cycle or transaction analysis, but here are four basic steps that are commonly used:
Identify and analyze transactions: This involves identifying the financial transactions that have occurred and analyzing them to understand their nature, purpose, and effect on the business.
Record transactions to a journal: After analyzing the transactions, they need to be recorded in a journal. The journal entries should include the date, accounts involved, amounts, and a brief description of the transaction.
Post journal entries to ledger accounts: Once the transactions are recorded in the journal, they need to be posted to the corresponding ledger accounts, which are used to summarize and organize the transactions for each account.
Prepare a trial balance: After the transactions have been recorded and posted to the ledger accounts, a trial balance should be prepared to ensure that the debits and credits balance. This involves adding up all the debit balances and credit balances in the ledger accounts to see if they are equal.
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(a) If a matrix A is 5 x 3 and the product AB is 5x7, what is the size of B?
If a matrix A is 5 x 3 and the product AB is 5x7, the size of B is 3x7.
The product of two matrices A and B, denoted as AB, is possible only if the number of columns of A is equal to the number of rows of B. In this case, A is 5x3, which means it has 3 columns.
And since the product AB is 5x7, it means the resulting matrix has 7 columns. Therefore, the number of columns of B must be equal to 7. And since A has 3 columns, the number of rows of B must be equal to 3 for the product to be possible.
Thus, the size of B is 3x7.
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6x1/2=
PLEASE HELP MEEEEEEEEEEEEEEE IT DO TOMORROW SO PLEASE I WILL GIVE U 10 POINTS!!!!!!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation:
The expression 0. 15c-0. 072 factored is
0.15c - 0.072 = 0.078c = (0.15 - 0.072)c = 0.078 times the coefficient c.
To factor 0.15c - 0.072, the first step is to find the greatest common factor (GCF) of the terms. In this case, the GCF is 0.072. This means that 0.072 can be divided out of both terms.
The next step is to divide out 0.072 from both terms. This gives 0.15c/0.072 = 0.208 and -0.072/0.072 = -1.
After this, we can combine the terms by multiplying the coefficients: 0.208 x -1 = -0.208.
Therefore, 0.15c - 0.072 can be factored as -0.208c. This means that 0.15c - 0.072 is equal to -0.208 times the coefficient c.
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Anyone know how to do these
There are 1300 Roman coins in the museum's collection in total.
How to determine the total number of Roman coins ?
To determine the total number of Roman coins in the museum's collection, we need to use the information given in the histogram. We know that there are 108 coins with a weight between 8 g and 17 g.
We can find the total frequency of all the coins by integrating the frequency density over the entire range of masses. To do this, we need to first find the width of each mass interval, which is given by the difference between the upper and lower mass values of each interval.
From the histogram, we can see that the width of each interval is 5 g.
So, the frequency of the coins between 8 g and 17 g can be calculated as:
Frequency = frequency density × interval width
Frequency = 10 × 5 = 50
This means that there are 50 coins in the museum's collection with a mass between 8 g and 17 g.
To find the total number of coins in the collection, we need to sum up the frequency of all the intervals.
To do this, we can calculate the area of each rectangle formed by the interval width and frequency density, and then sum up all these areas.
The total number of coins in the collection is given by:
Total number of coins = sum of frequencies over all intervals
Total number of coins = 50 + (15 × 15) + (20 × 20) + (25 × 25)
Total number of coins = 50 + 225 + 400 + 625
Total number of coins = 1300
Therefore, there are 1300 Roman coins in the museum's collection in total.
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Twice Jill's Age Added To Three Times Tony's Age Is 44. Jill's Age Equals Tony's Age Plus 2 Years. Find Jill's And Tony's Age
the age of jill and tony is 10 and 8 respectively
Twice Jill's Age Added To Three Times Tony's Age Is 44
2m + 3n = 44
Jill's Age Equals Tony's Age Plus 2 Years
m = n + 2
by solving the both equation we get
2(n + 2) + 3n = 44
5n + 4 = 44
5n = 44 - 4
n = 40/5
n = 8
again
m = 8 + 2
m = 10
so the age of jill and tony is 10 and 8 respectively
There are numerous methods to define a mathematical equation. A model is just a mathematical statement that says two theoretical results are equal. For instance, in the equation 3x + 5 = 14, the terms 3x + 5 and 14 are two different formulations that are separated by the symbol "equal." The simplest and most fundamental algebraic equations in mathematics contain one or more parameters.
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Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 10 dollars.
The profit for a selling price of $10 is approximately $64,692. To find the quadratic regression equation for this set of data, we can use the method of least squares to fit a quadratic function to the given data points.
The equation of a quadratic function is y =[tex]ax^2[/tex] + bx + c, where a, b, and c are constants. We will use column A for the widget selling price (x) and column B for the total profit earned at that price (y). Using calculator with regression capabilities, we can obtain the following quadratic regression equation for the given data:
y = -180.69[tex]x^2[/tex] + 4623.75x + 1423.64
To find the profit for a selling price of 10 dollars, we can simply substitute x = 10 into the equation and evaluate:
y =[tex]-180.69[/tex][tex](10)^2[/tex] + 4623.75(10) + 1423.64
y = -18069 + 46237.5 + 1423.64
y = 64692.14
Therefore, the profit for a selling price of 10 dollars is approximately $64,692.
The complete question is:
Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 10 dollars.
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State what each variable may be so that the equation is true. You must have at least one negative number. Explain how you chose the values for a and b. 2^a • 2^b = 2^0
We can solve [tex]2^{a}[/tex] x[tex]2^{b}[/tex] = [tex]2^{0}[/tex] by recognizing that [tex]2^{0}[/tex]equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1.
EquationsTo solve [tex]2^{a}.2^{b}=2^{0}[/tex] for a and b, we must first recognize that 2^0 equals 1, which means that the equation can be rewritten as [tex]2^{a}.2^{b}=1[/tex]. Therefore, we can simplify the equation to [tex]2^{a+b}[/tex] = 1.
Since 2 raised to any negative power is a fraction, we need at least one of the exponents to be negative.
We could also choose other values that make either a or b negative, such as a = -2 and b = 2, or a = -3 and b = 3. The key is to have one negative exponent and one positive exponent so that their sum equals zero.
In summary, we can solve [tex]2^{a}.2^{b}=1[/tex]by recognizing that [tex]2^{0}[/tex] equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1. We must have at least one negative exponent to satisfy the equation, and we can choose various values for a and b as long as their sum equals zero.
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Find the cross product a ⨯
b. A = 4, 5, 0 , b = 1, 0, 3 verify that it is orthogonal to both a and
b. (a ⨯
b. · a = (a ⨯
b. · b =
The cross product a ⨯b: A = 4, 5, 0 , b = 1, 0, 3
cross product {15, -12, -5}
dot products with 'a' and 'b': 0 and 0
For vectors a = {4, 5, 0} and b = {1, 0, 3}, you want the cross product and verification that the cross product is orthogonal to both 'a' and 'b'.
Cross product:
The cross product of 4i+5j+0k and 1i+0j+3k is the determinant :
[tex]\left[\begin{array}{ccc}i&j&k\\4&5&0\\1&0&3\end{array}\right][/tex]
= 15i - 12j -5k
As a list of coefficients, the cross product is c = {15, -12, -5}.
Orthogonal
Vectors are orthogonal if their dot product is 0.
a· c = {4, 5, 0}·{15, -12, -5} = (4·15) -(5·12) +(0·(-5)) = 60 -60 = 0
b· c = {1, 0, 3}·{15, -12, -5} = (1·15) +(0·(-12)) +(3·(-5)) = 15 -15 = 0
The dot products are both zero, so the cross product is orthogonal to both of the vectors that created it.
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simplify: |x-120| when x<-120
Answer: If x is less than -120, then x-120 will be less than zero, so we have:
|x-120| = -(x-120)
And since x is less than -120, we have:
|x-120| = -(x-120) = -x + 120
Therefore, the simplified expression for |x-120| when x<-120 is -x + 120.
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