question 1 options: what is the common difference in the sequence 7, 12, 17, 22, 27, ...? put the just the number in the blank.

The value of the expression when w = 3, x = -2, y = 6, and z = 0.5 is -1.

We have,

Substituting the given values in the expression.

(yz) / w + 2x

= (6 x 0.5) / (3) + 2(-2)

= 3 - 4

= -1

Therefore,

The value of the expression when w = 3, x = -2, y = 6, and z = 0.5 is -1.

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The complete question.

Evaluate the Expression when W = 3, x = -2, y = 6, and z = 0.5.

(y z) / w + 2x

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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The Maclaurin series for given function f(x) = x cos(8x) is f(x) = x - 8x^2 - 85.333x^3 + ...

The Maclaurin series expansion for a function f(x) can be obtained by finding the derivatives of f(x) at x=0 and evaluating them at x=0. The general formula for the Maclaurin series is:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

To find the Maclaurin series for f(x) = x cos(8x), we need to take the derivatives of f(x) and evaluate them at x=0.

f(x) = x cos(8x)

f'(x) = cos(8x) - 8x sin(8x)

f''(x) = -16 sin(8x) - 8x cos(8x)

f'''(x) = -128 cos(8x) + 24x sin(8x)

Evaluating at x=0, we get:

f(0) = 0

f'(0) = 1

f''(0) = -16

f'''(0) = -128

Plugging these into the Maclaurin series formula, we get:

f(x) = 0 + 1x - 16x^2/2! - 128x^3/3! + ...

f(x) = x - 8x^2 - 85.333x^3 + ...

Therefore, the Maclaurin series for f(x) = x cos(8x) is:

f(x) = x - 8x^2 - 85.333x^3 + ...

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Complete question is:

Use a Maclaurin series to obtain the Maclaurin series for the given function

f(x) = x cos(8x)

Let's assume that x represents the number of square feet in the garden, and y represents the number of carrots that can be grown at a time.

We are given that when the garden is 2 square feet, she can grow 8 carrots at a time. This suggests a linear relationship between x and y.

To find the equation, we can use the concept of proportionality. Since the number of carrots grown is directly proportional to the area of the garden, we can set up a proportion:

x/y = 2/8

Cross-multiplying, we have:

8x = 2y

Dividing both sides by 2, we get:

4x = y

So, the equation for the relationship between x and y is y = 4x.

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The measure of the angle JKL as per the attached diagram is equal to 97 degrees.

As per in the question,

Diagram is attached.

Angle JKL is linear pair angle with given angle of measure 83 degrees.

Sum of the pair of linear pair is always equal to 180 degrees.

Let 'x' be the measure of angle JKL, we get,

83° + m ∠JKL = 180°

Subtract 83° from both the side of the equation we get,

⇒ 83° - 83° + m ∠JKL = 180° - 83°

⇒ m ∠JKL = 97°

Therefore, the measure of the angle JKL as per the attached diagram is equal to 97 degrees.

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Answer: d. No, because the study was not taken from a random sample of scholarship athletes.

Step-by-step explanation:

Since the study only focuses on basketball players, the sample may not be representative of all scholarship athletes in the university. This can cause bias in the results and make it difficult to generalize the findings to the larger population of scholarship athletes. Therefore, the university administration should not fully trust the results of this study.

Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression.

What is an expression?

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Finding the value of f(x) =... or y =... that corresponds to a specific value of x is what it means to evaluate a function.

Simply swap out all instances of x with the value of x to accomplish this. For instance, x has been given the value 4 if we are asked to evaluate f(4).

We use the given number to replace the expression's variable before using the order of operations to simplify the expression.

Hence, finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression.

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Answer:

x=15

Step-by-step explanation:

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Answer:

\(y = 1.4\)

Step-by-step explanation:

Given

\(y = width\)

\(x = length\)

\(y = 3;\ when\ x = 14\)

Required

Find y when x = 30

Being an inverse variation, we have:

\(y\ \alpha\ \frac{1}{x}\)

Convert the variation to an equation

\(y = \frac{k}{x}\)

First, we solve for k

Make k the subject to solve for k

\(k = xy\)

\(y = 3;\ when\ x = 14\)

So, the value of k is:

\(k = 14 * 3\)

\(k = 42\)

To solve for y when x = 30

Substitute 30 for x and 42 for k in \(k = xy\)

\(42 = 30 * y\)

Make y the subject

\(y = \frac{42}{30}\)

\(y = 1.4\)

The width of the rectangle would be as follows:

\(1.4\)  inches

Inverse proportion occurs when one value increases and the other decreases.

The width, \(y\), of a rectangle with a fixed area varies inversely with its length, \(x\).

So, \(y=\frac{k}{x}\) where \(k\) is the constant.

The width is \(3\) inches when the length is \(14\) inches.

So,

\(3=\frac{k}{14} \\k=42y=\frac{42}{x}\\Put x=30\)

Therefore, \(y=\frac{42}{30}=1.4\) inches

Thus, Width is \(\boldsymbol{1.4}\) inches when the length is \(30\) inches.

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Increasing data collection and streamlining the model are the answers to overfitting.

Given statement;

If your model performs great on the training data but generalizes poorly to new instances.

The possible solutions for the given condition is,

A model is probably overfitting the training data if it performs well on the training data but poorly on new examples (or we got extremely lucky on the training data). Obtaining more data, simplifying the model (choosing a simpler technique, reducing the amount of parameters or features utilized, or regularizing the model), or lowering the noise in the training data are all potential remedies for overfitting.

Hence, the solutions to overfitting are getting more data, simplifying the model.

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The seventh term of the geometric sequence is -7/32. The nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term

To find the seventh term of a geometric sequence, we can use the formula:

\(an = a1 * r^(n-1),\)

where an represents the nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.

In this case, we are given a2 = -7 and r = 1/2.

Using the formula, we can find a1 by substituting n = 2:

a2 = a1 * (1/2)^(2-1).

We know that a2 = -7, so we can rewrite the equation:

-7 = a1 * (1/2)^1,

-7 = a1 * (1/2).

Now, let's solve for a1:

a1 = -7 * (2/1),

a1 = -14.

We have found that the first term, a1, is equal to -14.

Now, we can find the seventh term, a7, by substituting n = 7 into the formula:

a7 = (-14) * (1/2)^(7-1),

a7 = (-14) * (1/2)^6,

a7 = (-14) * (1/64),

a7 = -14/64,

a7 = -7/32.

Therefore, the seventh term of the geometric sequence is -7/32.

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Answer:

Step-by-step explanation:

1. 13/15

2.17/15

3.15/13

4.

5.

60.2

Step-by-step explanation:

a^2 + b^2 = c^2

40^2 + 45^2 = c^2

1600 + 2025 = c^2

3625 = c^2

the square root of 3625 is 60.2

Answer:

60.2 metres

Step-by-step explanation:

Pythagoras formula = square of b plus squar of c = square of a

let b be 40 and let c be 45

40^2 + 45^2 = a^2

1600 + 2025 = a^2

3625 = a^2

square root of 3625 = a

60.2 meters = a

The original selling price would be approximately $ 512.69.

Let x be the original selling price ( in dollars ),

After marking down 10%,

New selling price = x-10% of x = x-0.1x = 0.9x

Again after marking down 30%,

Final selling price = 0.9x - 30% of 0.9x

Final selling price = 0.9x - 0.3 * 0.9x

Final selling price = 0.63x

According to the question,

0.63x = 323

x = 323/ 0.63

x =  512.69

Hence, the original selling price would be approximately $ 512.69.

Complete question:

A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns​ shown, making the​ one-day sale price of the ski set ​$325. Find the original selling price of the ski set. It was marked down 10% and 30%.

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The expression that will help determine the amount of money Anthony earned for his cub scout troop is 6.00x.

To determine the amount of money Anthony earned for his cub scout troop, we can follow these steps:

Identify the number of boxes Anthony sold, represented by x.

Determine the price per box, which is $6.00.

Multiply the number of boxes (x) by the price per box ($6.00) to calculate the total amount of money earned.

So, the expression that helps us determine the amount of money Anthony earned is 6.00x.

By multiplying the number of boxes by the price per box, we can find the total earnings because each box is sold for $6.00. The variable x represents the number of boxes sold, and multiplying it by $6.00 gives us the total amount of money earned.

For example, if Anthony sold 10 boxes of popcorn, the expression would be: 6.00 * 10 = $60.00. Therefore, Anthony would have earned $60.00 for his cub scout troop.

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For both acute angles in the given isosceles right triangle with legs of length 2, the sin, cos, and tan are all equal to 1.

sin(45°) = cos(45°) = tan(45°) = 1, and sin(π/4) = cos(π/4) = tan(π/4) = 1.

In an isosceles right triangle with legs of length 2, we know that both acute angles are 45 degrees or π/4 radians.

To find the sine, cosine, and tangent of these angles, we can use the definitions of these trigonometric functions.

Since the triangle is isosceles, the hypotenuse is also of length 2.

For the angle of 45 degrees or π/4 radians:

Sine (sin) = opposite / hypotenuse = 2 / 2 = 1

Cosine (cos) = adjacent / hypotenuse = 2 / 2 = 1

Tangent (tan) = opposite / adjacent = 2 / 2 = 1

For both acute angles in the given isosceles right triangle with legs of length 2, the sin, cos, and tan are all equal to 1.

So, sin(45°) = cos(45°) = tan(45°) = 1, and sin(π/4) = cos(π/4) = tan(π/4) = 1.

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Answer:

Step-by-step explanation:

Yes it is a rational number

Yes, the decimal number is a rational number.

If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

The decimal number is 0.258.

A number decimal number is a terminating number. So, the decimal number is a rational number.

Yes, the decimal number is a rational number.

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Answer:

Step-by-step explanation:

its subtracting 4 each time

a. The person who wrote more words in total will be Hudson.

b. Hudson wrote 80 more words

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Isabelle worked for 55 minutes and wrote an average of 16 words per minute. The total words would be:

= 55 × 16

= 880

Hudson worked for 80 minutes and wrote an average of 12 words per minute. The total words will be:

= 80 × 12

= 960

The difference will be:

= 960 - 880

= 80

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Answer:

1. Equation: x/-9=-16

solution: x=144

2. Equation:15*x=-75

solution: x=-5

3.Equation:0.75n=36

solution: n=48

Step-by-step explanation:

Answer:

(a) -1

(b) -2

Step-by-step explanation:

(a) Replace the a's with 1 and the b's with 3 to get 1*3 = 1-3+1 = -1

(b) We already figured out that (1*3) equals -1 so we just need to find -1*2. Using same strategy as part a, replace a and b with -1 and two, respectively. -1*2 = -1-2+1= -2. Hope this helps and sorry if I made a mistake. :)

The value of 1 cm : 1 km is 6.66666667e-7

The ratio expression is given as:

1 cm : 15 km

Convert km to cm

So, we have

1 cm : 1 km = 1 cm : 1500000 cm

Express as quotient

1 cm : 1 km = 1 cm/1500000 cm

Evaluate the quotient

1 cm : 1 km = 6.66666667e-7

Hence, the value of 1 cm : 1 km is 6.66666667e-7

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Answer:

b = 10.06 in

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (10.5)² = b² + (3)²

→ 110.25 = b² + 9

→ b² = 110.25 - 9

→ b = √101.25

→ [ b = 10.06 in ]

Hence, value of b is 10.06 in.

Answer:

\( \cos \bigg( \frac{7\pi}{12} \bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } \)

Step-by-step explanation:

\( \cos \bigg( \frac{7\pi}{12} \bigg) \\ \\ = \cos \bigg( \frac{7 \times 180 \degree}{12} \bigg)\\ \\ = \cos \bigg( {7 \times 15 \degree} \bigg)\\ \\ = \cos \bigg( {105 \degree} \bigg)\\ \\ = \cos \bigg( {60\degree + 45 \degree} \bigg) \\ \\ = \cos {60\degree .\cos 45 \degree} - \sin {60\degree .\sin 45 \degree} \\ \\ = \frac{1}{2} . \frac{1}{ \sqrt{2} } - \frac{ \sqrt{3} }{2} .\frac{1}{ \sqrt{2} } \\ \\ = \frac{1}{2 \sqrt{2} } - \frac{ \sqrt{3} }{2 \sqrt{2} } \\ \\ \huge \purple{ \boxed{ \cos \Bigg( \frac{7\pi}{12} \Bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } }}\)

The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

We have to given that,

An equation is,

⇒ cos (7 pi/12)

Now, WE can change it into degree as,

⇒ cos (7 pi/12)

⇒ cos (7 × 180 / 12)

⇒ cos (7 × 15)

⇒ cos 105°

⇒ cos (90 + 15)°

⇒ - sin 15°

⇒ - (√3 - 1) / 2√2

⇒ - 0.2588

Thus, The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

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For Car A, we have that:

a. The function is exponential.

b. The definition of the function is: \(y = 18500(0.94)^x\)

c. When x = 9, the numeric value of the function is given as follows: 10,600.

For Car B, we have that:

a. The function is linear.

b. The definition of the function is: y = -750x + 18500.

c. When x = 9, the numeric value of the function is given as follows: 11,750.

The general format of an exponential function is presented as follows:

y = ab^x.

In which the parameters are defined as follows:

For Car A, the function is exponential, as the rate of change is a constant quotient, as follows:

b = 16346.60/17390 = 15365.80/16345.60 = 0.94.

Hence:

\(y = a(0.94)^x\)

The initial value is calculated as follows:

a = 17390/0.94

a = 18500.

Hence the function is:

\(y = 18500(0.94)^x\)

The numeric value at x = 9 is given as follows:

\(y = 18500(0.94)^9 = 10,600\)

A linear function has the general format given as follows:

y = mx + b.

In which the parameters are explained as follows:

For Car B, the function is linear, as the difference between consecutive terms is the same, as follows:

m = 17000 - 17750 = 16250 - 17000 = -750.

Hence the intercept is:

b = 17750 + 750 = 18500.

Then the function is:

y = -750x + 18500.

The numeric value at x = 9 is given as follows:

y = -750(9) + 18500 = 11,750.

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Answer:

4

Step-by-step explanation:

Answer:

g(f(-9))=4

Step-by-step explanation:

This is a composite function so we need to first find the value of the function on the inside in order find the value of the composite function

f(-9)=x+7=-9+7=-2

we can put -2 instead of f(-9) in the composite function

g(-2)=(-2)^2=4

The function of differentiable parameterization of arc length 2 in space is ∫√(1)² + (2t)² + (cos(t))² dt.

To set up a differentiable parameterization of arc-length 2 in space, we can use the arc-length formula:

s = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

where s is the arc length, t is the parameter, and (x, y, z) is the position vector.

We want the arc length to be 2, so we can set up the following equation:

2 = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

We can then choose a function for each component of the position vector, such as:

x = t

y = t²

z = sin(t)

We can now find the derivatives with respect to t:

dx/dt = 1

dy/dt = 2t

dz/dt = cos(t)

We can substitute these into the arc-length formula:

2 = ∫√(1)² + (2t)² + (cos(t))² dt

Solving this integral for t will give us the desired parameterization of arc-length 2 in space. However, this integral may not have a closed-form solution, so numerical methods may need to be used to approximate the solution.

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The question is -

Differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?

Answer:

6.75

Step-by-step explanation:

6 is equivalent to 6

3/4 is equivalent to 0.75

Answer:

It is 6.75

Step-by-step explanation:

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Atmosphere and temperatures of 273 Kelvin and 298 Kelvin, along with a pressure of 1 kilopascal and a temperature of 273 Kelvin.


Standard conditions refer to a specific set of conditions, usually including a pressure of 1 atmosphere and a temperature of 0 degrees Kelvin, that are used to measure enthalpy changes. Under these conditions, the enthalpy change of a given reaction is known as the standard enthalpy of reaction (ΔH°). Other standard conditions used to measure enthalpy changes include a pressure of 1 atmosphere and temperatures of 273 Kelvin and 298 Kelvin, along with a pressure of 1 kilopascal and a temperature of 273 Kelvin.

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