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Answer:

  2y^2 +7y +11

Step-by-step explanation:

The remaining length is the difference between the original and the length cut off:

  remaining = whole length - piece length

  remaining = (3y^2 +7y +1) -(y^2 -10)

  = 3y^2 +7y +1 -y^2 +10  = (3 -1)y^2 +7y +(1 +10)

  remaining = 2y^2 +7y +11

Answer:

1/2

Step-by-step explanation:

Pick two points on the graph that are easy to read. A point is easiest to read if it lies on the intersection of grid lines.

For example, pick (10, 50) and (30, 60) which are easy to read.

slope = rise/run

rise = change in y

run = change in x

To go from (10, 50) to (30, 60), you go 20 units right. "20 units right" is a change of +20 units in x. The run is 20.

To go from (10, 50) to (30, 60), you go 10 units up. "10 units up" is a change of +10 units in y. The rise is 10.

slope = rise/run = 10/20

slope = 1/2

Answer: 2 inches

Step-by-step explanation:

14 inches

Step-by-step explanation:

Length of the hole = 16(½) inches

Length of the dirt = 8(¾)inches

The distance between the top of the pile to the bottom of the hole = ?

Since the dirt is beside the hole and not inside the hole, we can find it's length using addition.

Distance from the top to the bottom = length of dirt + length of the hole

Length of dirt = 8×¾ = 6 inches

Length of the hole = 16 × ½ = 8 inches

Distance from the top of the dirt to the bottom of the hole = (6 + 8) inches

Distance from the top of the dirt to the bottom of the hole = 14 inches

Note: the only way we can use subtraction here is if the hole was filled with dirt, what's the distance that's left

Distance left = length of hole - length of dirt

Distance left = 8 - 6 = 2 inches .

Answer:

\( x = \sqrt {40}\)

Step-by-step explanation:

Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:

\( {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ \)

Answer:

D. x = sqrt(52).

Step-by-step explanation:

Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.

a^2 + b^2 = x^2

4^2 + 6^2 = x^2

16 + 36 = x^2

52 = x^2

x = sqrt(52)

x = sqrt(2 * 2 * 13)

x = 2sqrt(13)

x = 7.211102551.

Hope this helps!

Answer:

500,000

Step-by-step explanation:

If the number is under 5 it rounds down and over 5 rounds up

Answer:   I'm gonna go with B. hours worked; weekly pay; 30 to 35 hours; $360 to $420, because I had something similar to this

Wendy is paid $9 per hour and plans to work between 20 and 25 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.

weekly pay; hours worked; 20 to 25 hours; $180 to $225

hours worked; weekly pay; 20 to 25 hours; $180 to $225

weekly pay; hours worked; $180 to $225; 20 to 25 hours

hours worked; weekly pay; 20 to 25 hours; $9 to $225

Step-by-step explanation:

The independent quantity is her pay and the dependent quantity is the hours she works in a week.

I believe the range would be 30 to 35 hours and the domain would be $360 to $450.

...................................................................................................................................................

Answer:

Part a) The independent quantity is the variable x (the number of hours) and the dependent quantity is the variable y (total paid)

Part b) Domain  

Part c) Range  

Step-by-step explanation:

Let

x------> the number of hours

y-----> total paid

The linear equation that represent this situation is

so

Part a)

The independent quantity is the variable x (the number of hours)

The dependent quantity is the variable y (total paid)

Part b) Find the domain

The domain is the interval-------->  

All real numbers greater than or equal to  hours and less than or equal to  hours

Part c) Find the range

For  

find the value of y

For  

find the value of y

The range is the interval------->  

All real numbers greater than or equal to  and less than or equal to  

...............................................................................................................................................

The dependent quantity would be the $12 per hour, while the independent quantities are 30 hrs/ week to 35 hours/ week.

The $12 per hour would become $360/week to $420/week.

The domain of the problem, with the unit of hrs/week, would be :30,31,32,33,34,35.

The Range of the problem, with the unit of $/week, would be : 360, 372, 384, 396, 408, 420.

...............................................................................................................................................

Answer:

E = 100M/L

Step-by-step explanation:

we could cross-multiply to get:

E·L = 100M

now divide each side by L to get:

E = 100M/L

The coefficient of determination is a value between 0 and 1 (option a).

The coefficient of determination, denoted as \(R^{2}\) , is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model. It ranges from 0 to 1, where 0 indicates that the independent variable(s) cannot explain any of the variability in the dependent variable, and 1 indicates that the independent variable(s) can completely explain the variability in the dependent variable.

\(R^{2}\)  represents the goodness-of-fit of a regression model. A value close to 1 indicates a strong relationship between the independent and dependent variables, suggesting that the model provides a good fit to the data. On the other hand, a value close to 0 suggests that the model does not effectively explain the variability in the dependent variable.

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The general solution is y(x) = c_1x + c_2x ln(x) + c_3x^-4 + (1/8)x, where c_1, c_2, and c_3 are constants.

To find the general solution to the Cauchy-Euler equation x^3y" - 7x^2y"' +8xy' - 8y = x, we first need to find a particular solution to the non-homogeneous equation.

We can try a particular solution of the form y_p(x) = Ax + B. Substituting this into the equation, we get:

x^3(0) - 7x^2(0) + 8x(1) - 8(Ax + B) = x

Simplifying this, we get:

8Ax - 8B = x

Comparing coefficients, we see that A = 1/8 and B = 0. Therefore, our particular solution is y_p(x) = (1/8)x.

Now, we can find the general solution by adding the particular solution to the homogeneous solution.

Since (x, 4x ln(4x), x^r) is a fundamental solution set for the corresponding homogeneous equation, we can write the homogeneous solution as:

y_h(x) = c_1x + c_2x ln(x) + c_3x^-4

where c_1, c_2, and c_3 are constants.

Therefore, the general solution is:

y(x) = y_h(x) + y_p(x)
y(x) = c_1x + c_2x ln(x) + c_3x^-4 + (1/8)x

where c_1, c_2, and c_3 are constants.

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Answer:

C. x - 5y - 30 = 0

Step-by-step explanation:

Y = x/5 - 30

y + 30 = x/5

you multiply both sides by 5

5y + 30 = x

you subtract x from both sides

- x + 5y + 30 = 0

which is the same as

x - 5y - 30 = 0

The probability of getting 3 is P(A) = 1/216. The probability that sum being 3 is 1 / 216.

When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. A dice can show a minimum of one and a maximum of six dots, for a total of six sides, giving it a total of 6 * 6 * 6 = 216 possible outcomes.

:When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. The probability can be calculated as follows:

Let A be the event that the sum is 3. The number of ways to get 3 is 1, i.e., (1, 1, 1). The total number of possible outcomes is 6³,

since each die can have 6 possible outcomes.

Therefore, the probability of getting 3 is P(A) = 1/216.

In conclusion, the probability that sum being 3 is 1 / 216.

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Answer:

342.938 cm²

Step-by-step explanation:

Area of shaded region = area of rectangle - area of circle

= (length*width) - (π*radius²)

= (32*17) - (π8²)

= 544 - 201.06192983

= 342.93807017 ≈ 342.938 cm²

Answer:

B

Step-by-step explanation:

Answer:

2n² + n

Step-by-step explanation:

Given sequence:

3, 10, 21, 36, ...

Work out the first differences between terms:

\(3 \underset{+7}{\longrightarrow} 10 \underset{+11}{\longrightarrow} 21 \underset{+15}{\longrightarrow} 36\)

As the first differences are not the same, work out the second differences.

\(7 \underset{+4}{\longrightarrow} 11 \underset{+4}{\longrightarrow} 15\)

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of n² is always half of the second difference. Therefore, as the second difference is 4, the coefficient of n² is 2.

To work out the nth term of the sequence, write out the numbers in the sequence 2n² and compare with the given sequence:

\(\begin{array}{|l|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4 \\\cline{1-5} 2n^2 & 2 & 8 & 18 & 32\\\cline{1-5} \sf Operation & +1 & +2& +3& +4\\\cline{1-5} \sf Sequence & 3 & 10 & 21 & 36\\\cline{1-5}\end{array}\)

Therefore, we need to add n to 2n² to match the sequence.

Therefore, the nth term of this sequence is 2n² + n.

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The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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The relationship in the triangle that must be true is sin B = cos (90 - B).

option B.

Complementary angles are two angles that add up to 90 degrees. In other words, if you have two angles that are complementary, the measure of one angle added to the measure of the other angle will equal 90 degrees.

In the given diagram, angle A is complementary to angle B.

90 - B = A

From the diagram, Sin B = b/c

Cos (90 - B) = Cos A = b/c

So Cos (90 - B) is equal to sin B because the two angles are complementary.

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Answer:

XV = 16

Step-by-step explanation:

Triangle VWX is an isosceles triangle. Since the base angles are the same, the sides opposite the angle are also the same. See image. They gave VW so XV is the same as VW.

Answer:

0% chance

Step-by-step explanation:

there are no green marbles

Marbles no

There is no green marbles

So it will never occur(impossible event)

Answer:

y = 410

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

y = 23x - 4

x = 18

Step 2: Evaluate

Answer:

y = 410

Step-by-step explanation:

y = 23x - 4    If x = 18

y = (23*18) - 4

y = 414 - 4

y = 410

The expressions below represent the price of the lunch special are:

A. p-0.25p

D. 0.75p

A term in an algebraic expression that is referred to as a linear expression is either a constant or a variable raised to the first power. The fundamental equation used to represent and solve for an unknown quantity is a linear expression in one variable. It is simply depicted graphically and is always a straight line. A simple way to convey a mathematical assertion is with a linear expression.

In the given question,

The original total price of a lunch order be the variable p.

Now 25% off the original price = 25% × p

= 0.25p

Now after the discount the price of the lunch special is:

p-0.25p

= 0.75p

Therefore, the expressions below represent the price of the lunch special are:

A. p-0.25p

D. 0.75p

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Answer:

https://socratic.org/questions/a-card-is-drawn-from-a-standard-deck-a-second-card-is-drawn-without-replacing-th-1#131182

Step-by-step explanation:

:)

Answer:

[-1.8,0.03]

Step-by-step explanation:

This is how you use interval notation, square brackets means including the numbers, circular brackets means not including

Answer:

(-1.3,1.8]

Step-by-step explanation:

The inequality −1.3<x≤1.8 means "all numbers between −1.3 and 1.8." In interval notation, we express this as (−1.3,1.8]. Notice that we use a parenthesis to show that the number −1.3 is not included and a bracket to show that the number 1.8 is included.

The average temperature of the coffee between t = 0 and t = 10 minutes is approximately 146 degrees.

Option C is the correct answer.

We have,

To find the average temperature of the coffee between t = 0 and t = 10 minutes, we need to calculate the average value of the temperature function F(t) over that interval.

The formula for the average value of a function f(x) over an interval [a, b] is given by:

Average value = (1 / (b - a)) x ∫[a to b] f(x) dx

In this case,

We want to find the average temperature over the interval [0, 10] minutes, so our formula becomes:

Average temperature = (1 / (10 - 0)) x ∫[0 to 10] F(t) dt

To find the integral of F(t), we need to calculate the antiderivative of F(t):

∫ F(t) dt = ∫ \((72 + 118e^{-0.093t}) dt\)

Using the power rule of integration and the fact that the integral of \(e^x\) is \(e^x\), we can evaluate the integral:

∫ F(t) dt =\(72t - (118 / 0.093) \times e^{-0.093t}\)

Now,

Average temperature = (1 / 10) x ∫[0 to 10] F(t) dt

Average temperature = (1 / 10) x (72(10) - (118 / 0.093) x \(e^{-0.093(10)}\) - (72(0) - (118 / 0.093) x \(e^{-0.093(0)}))\)

Simplifying further:

Average temperature = (1 / 10) x (720 - (118 / 0.093) x \(e^{-0.93}\) - 0)

Using a calculator, we find:

Average temperature ≈ 146 degrees

Therefore,

The average temperature of the coffee between t = 0 and t = 10 minutes is approximately 146 degrees.

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Two scenarios that create right angle are 3 and 4.

In both the situations, Pythagoras theorem get satisfy with the sides which theorem is only applicable when there is right angle in the triangle.

Here's the explanation using 3 as an example :

From the statement we can assume that height of the window as the perpendicular(P) and distance from base(B) of the building to William as base of the triangle and line distance from Tom to William as hypotenuse(H) of the triangle.

Therefore, H = 130, B= 36.4 and P = 124.8

By Pythagoras theorem,

H² = P² + B²;

130² = 124.8² + 36.4²,

16900 = 15575.04 + 1324.96,

16900 = 16900

Hence satisfy the Pythagoras theorem, therefore triangle is right angle.

Similarly for the 4 statement.

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The given parametric curve x=cost, y=et; 0≤t≤π/2, intersects the line y=1 at t=0, and intersects the line x=0 at t=π/2. Therefore, we need to find the area bounded by the curve and the lines y=1 and x=0, between t=0 and t=π/2. We can use the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. In this case, we need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The final result is A=e-1/2.

The given parametric curve x=cost, y=et; 0≤t≤π/2, intersects the line y=1 at t=0, and intersects the line x=0 at t=π/2. Therefore, we need to find the area bounded by the curve and the lines y=1 and x=0, between t=0 and t=π/2. To do so, we can use the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. In this case, we need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The final result is A=e-1/2.

The area bounded by the parametric curve x=cost, y=et; 0≤t≤π/2, and the lines y=1 and x=0 is e-1/2. This can be found using the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. We need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The curve intersects the line y=1 at t=0 and the line x=0 at t=π/2, which defines the boundaries for the integral.

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Answer:

answer is cm² ok

Step-by-step explanation:

because it is saying area ,in area we have to put cm2

Answer:

16.49

Step-by-step explanation:

21^2 - 13^2 = 272

square root 272 = 16.49

Answer:

Dear user,

Answer to your query is provided below

Pages full = 13

Card on last page = 1

Step-by-step explanation:

Rafael has 118 baseball cards.

Each album can hold 9.

So, using multiples of 9 or by dividing 118/9

That 1 is remainder.

So, cards on last page is 1

Verify ,

Pages full = (118-1)/9 = 13