Your professor asks you to get up in front of the class and repeat a long list of numbers that she reads to you. If you are not given a chance to repeat the numbers to yourself as she reads them, what is the longest list of numbers you will most likely to be able to remember

Answers

Answer 1

The longest list of numbers that an average person can remember without any repetition is around 7 ± 2, according to Miller's Law.

What is the longest list of numbers an average person can remember without repetition?

Miller's Law suggests that the capacity of human short-term memory is limited to around 7 ± 2 items, or "chunks" of information. This means that if the professor reads a list of numbers to you without giving you a chance to repeat them, the longest list you are likely to remember is around 7 ± 2 numbers.

However, this capacity can be increased through the use of various memory strategies such as chunking, which involves grouping pieces of information into meaningful units. Additionally, the ability to remember numbers or any other type of information can vary greatly between individuals depending on factors such as age, cognitive ability, and previous experience with the material.

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Related Questions

Aemilus rids his bike for 2 hours. for how many seconds does Aemilus ride his bike​

Answers

120 sec beacause 60+60 is 120 this is how beacause 1 hour has 60 minits in it and thrte is 2 hours so 60+60=120

Answer:

Step-by-step explanation:

1 dk=60 saniye 1 saat=60 dk 60x60=3600 saniye 1 saat eder. 2 saat istediği için      2x3600=7200 saniyedir                                                                                                                     cevap= 7200

PLEASE HELP!!!!! I WILL GIVE BRAINLIEST!!!!


The following dot plot shows the pulse rates of runners after finishing a marathon:


dot plot with title of Pulse Rates of Marathon Runners, Pulse Rate on the x axis, and Number of Runners on the y axis with 6 dots over 140, 5 dots over 165, 2 dots over 170, 4 dots over 180


Which of the following data sets is represented in the dot plot?


a. {6, 5, 2, 4}

b. {140, 165, 170, 180}

c. {140, 140, 140, 140, 140, 140, 165, 165, 165, 165, 165, 170, 170, 180, 180, 180, 180}

d. {140, 141, 142, 145, 145, 149, 150, 151, 152, 160, 165, 170, 170, 172, 178, 179, 180, 180}

Answers

c. {140, 140, 140, 140, 140, 140, 165, 165, 165, 165, 165, 170, 170, 180, 180, 180, 180} is the data sets represented in the dot plot

How to get the data set

The dot plot represents the pulse rates of runners after finishing a marathon. It shows the number of runners with specific pulse rates. Based on the given dot plot, we have:

6 dots over 140, which means 6 runners have a pulse rate of 140.

5 dots over 165, which means 5 runners have a pulse rate of 165.

2 dots over 170, which means 2 runners have a pulse rate of 170.

4 dots over 180, which means 4 runners have a pulse rate of 180.

The data set represented in the dot plot is:

c. {140, 140, 140, 140, 140, 140, 165, 165, 165, 165, 165, 170, 170, 180, 180, 180, 180}

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What is the charge qenc that is enclosed by the cylinder (cross-sectional area A=2.00×10-2 m2) if the charge is only on one surface?

Answers

The charge enclosed by the cylinder is simply equal to the total charge Q on the surface of the cylinder.

If the charge is only on one surface of the cylinder, then we can assume that the charge is uniformly distributed on that surface. Let's denote the surface charge density by σ.

The charge enclosed by the cylinder is given by qenc = σA, where A is the cross-sectional area of the cylinder.

We are not given the surface charge density σ, but we can relate it to the total charge Q on the surface of the cylinder as follows:

Q = σA

We can solve for σ to get:

σ = Q/A

Substituting this expression for σ into our equation for qenc, we get:

qenc = σA = (Q/A)A = Q

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What is the circumference of the following circle?
Use 3.14 for πpi and enter your answer as a decimal.

Answers

The circumference of the given circle will be 6.28 units.

The circumference of a circle is given by the formula:

C = 2πr

where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14159.

If the radius of the circle is 1 unit, then we can substitute this value into the formula to get:

C = 2π(1)

Simplifying the expression, we get:

C = 2π

Using a calculator or rounding π to 3.14, we can evaluate this expression to find the circumference:

C ≈ 6.28 units (using π ≈ 3.14)

Therefore, the circumference of a circle with a radius of 1 unit is approximately 6.28 units.

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What is the intermediate step in the form (x+a)^2=b(x+a)
2 =b as a result of completing the square for the following equation?
x²-4x=-29

Answers

The required equation is (x+2)² = -25

Given is an equation, x²-4x = -29, we need to simplify it,

So,

x²-4x = -29

x²-2×2×x+4 = -29+4

(x+2)² = -25

Hence, the required equation is (x+2)² = -25

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Please help I’ll give brainliest!!

Answers

The solution of the graph of the system of equations is:

x = 1, y = 2

How to solve the system of equations graphed on the coordinate axes?

To solve the system of equations graphed on the coordinate axes, we need to look for the point of intersection of the two lines.

Looking at the graph, you will notice that the two lines meet at a point with the coordinate values of (1, 2) as indicated (check attached image).

Thus, the x and y values of the point of intersection is the solution of the graph of the systems of equation. Thus:

x = 1, y = 2

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If cos ϕ = 0.4626 and 3π/2 < ϕ < 2π, find decimal approximations for sin ϕ and tan ϕ

Answers

Answer: We can use the identity sin^2 ϕ + cos^2 ϕ = 1 to find sin ϕ:

cos^2 ϕ + sin^2 ϕ = 1sin^2 ϕ = 1 - cos^2 ϕsin ϕ = ±√(1 - cos^2 ϕ)

Since 3π/2 < ϕ < 2π, we know that sin ϕ < 0. Therefore, we can take the negative square root:

sin ϕ = -√(1 - cos^2 ϕ)sin ϕ = -√(1 - 0.4626^2)sin ϕ ≈ -0.8865

To find tan ϕ, we can use the identity tan ϕ = sin ϕ / cos ϕ:

tan ϕ = sin ϕ / cos ϕtan ϕ = -0.8865 / 0.8861tan ϕ ≈ -0.9996

Therefore, the decimal approximations for sin ϕ and tan ϕ are approximately -0.8865 and -0.9996, respectively.

A slice is made perpendicular to the base of a right rectangular pyramid through the vertex. What is the area of the resulting two-dimensional cross section?

Enter you answer in the box. Cm²

The figure is a square pyramid. Two sides of the square base are labeled 5 centimeters. A plane intersects the pyramid through the pyramids vertex and base. The plane is perpendicular to the pyramids base. A shaded triangle appears in the interior of the pyramid and lies on the intersecting plane. The height of this triangle is labeled 11 centimeters and is equal to the height of the pyramid. The base of the triangle is equal to the side length of the pyramids square base

Answers

The area of the resulting two-dimensional cross section is 27.5 cm².

The resulting two-dimensional cross section is a triangle. To find its area, we need to calculate the area of the triangle.

The height of the triangle is given as 11 centimeters, which is also the height of the pyramid. The base of the triangle is equal to the side length of the pyramid's square base, which is given as 5 centimeters.

The formula to calculate the area of a triangle is: Area = (1/2) * base * height.

Substituting the values into the formula, we have:

Area = (1/2) * 5 cm * 11 cm

Area = 27.5 cm²

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A slice is made perpendicular to the base of a right rectangular pyramid through the vertex. What is the area of the resulting two-dimensional cross section?

Enter you answer in the box. Cm²

The figure is a square pyramid. Two sides of the square base are labeled 5 centimeters. A plane intersects the pyramid through the pyramids vertex and base. The plane is perpendicular to the pyramids base. A shaded triangle appears in the interior of the pyramid and lies on the intersecting plane. The height of this triangle is labeled 11 centimeters and is equal to the height of the pyramid. The base of the triangle is equal to the side length of the pyramids square base

I need helppppp nowww

Answers

The description for the function would be D. As the value of x increases, f(x) exceeds g(x) because g(x) is a quadratic function and f(x) is an exponential function with a base greater than 1.

What are exponential functions like ?

As x advances, exponential functions escalate more rapidly compared to quadratic functions. This is especially viable when the base of such functions lies with a range above 1. Here, f(x) possesses a prime value estimate of 3 exceeding this limit and inevitably outshines g(x).

Contrarily speaking, as compared to exponential functions; g(x), which acts as a quadratic function undergoes a slower growth rate in correlation to x advancement time period. Henceforth, over time, the estimation of f(x) supersedes the assessment given to g(x).

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A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?

Answers

The solid that could have resulted in a two-dimensional cross section in the shape of a rectangle is a rectangular pyramid.

How to explain the information

A prism is a solid figure with two parallel, congruent faces called bases. The other faces of a prism are rectangles. If a plane is passed through a prism parallel to one of its bases, the resulting cross section will be a rectangle.

A rectangular pyramid could indeed have a rectangular base and therefore could have resulted in a cross section in the shape of a rectangle.

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A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?

Rectangle

Trapezoid

Cylinder

Rectangular pyramid.

The tangent to the curve y=ax^2 -5x + 2 at the point where x=2 has equation y =7x+b. find the values of the constants a and b​

Answers

Answer:

To find the values of a and b, we need to find the equation of the tangent to the curve at x=2.

We begin by finding the derivative of the function y=ax^2 -5x + 2:

y' = 2ax - 5

Next, we can substitute x=2 into the derivative to find the slope of the tangent at x=2:

y'(2) = 2a(2) - 5 = 4a - 5

We know that the equation of the tangent line at x=2 is y=7x+b. To find b, we can substitute x=2 and solve for y:

y=7x+b

y=7(2)+b

y=14+b

Now that we know that the point (2, 14+b) lies on the curve and the tangent, we can set the derivative of the curve equal to the slope of the tangent at x=2:

4a - 5 = 7

Solving for a, we get:

4a = 12

a = 3

Now we can substitute a=3 into the equation of the derivative to find the slope of the tangent at x=2:

y'(2) = 4a - 5 = 7

Therefore, the equation of the tangent to the curve y=ax^2 -5x + 2 at the point where x=2 is y=7x+0.

So, the values of the constants are a=3 and b=0.

Final answer:

The values of constants 'a' and 'b' are determined based on the properties of the tangent line at a given point. By taking the derivative to find the slope of the tangent and substituting the given X-value, we find that a = 3. By comparing the Y-values in both original and tangent line equations, we find that b = -10.

Explanation:

To find the values of the constants a and b, you should first take the derivative of the equation of the curve to find the slope of the tangent at any point. Here, the equation is y = ax^2 - 5x + 2. The derivative is y' = 2ax - 5. We substitute the given value of x=2 into this equation to find the slope of the tangent at this point, which is stated to be 7. So, 2a*2 - 5 = 7, solving for a we get a = 3.

Next, we need to find the value of b. We know the equation of the tangent line is y = 7x + b and we also know that the tangent line touches the curve at the point where x = 2. Thus, we substitute x = 2 into both equations to find the corresponding y value. That must be equal in both equations since it's the same point. So, we substitute x=2 in the curve's equation to find y, we get y = 3*2^2 - 5*2 + 2 = 4. But, from the tangent's equation y = 7*2 + b, solving for b gives us b = 4 - 14 = -10.

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For what values of x is ((log(3-x)/(sqrt(x-1)) defined?

Answers

Answer: 1<x<3

Step-by-step explanation:

There are 3  rules in one that are needed for this problem

1st:  you can never get a 0 at the bottom of a denominator so x [tex]\neq[/tex] 1

[tex]\sqrt{x-1}=0\\ x-1=0\\x=1[/tex] would make a value of 0 on the bottom of a denominator which is not allowed.

2nd:  you can never get a - under the square root so x cannot be less than 1

3rd.  you can never get a log that is equal to 0 or less than 0 so x

3-x=0

-x=-3

x=3

so x cannot =3 or be greater than 3

the values that x CAN be are  1<x<3

For Positive Acute Angles A And B, It Is Known That Tan A= 60/11 And Cos B= 24/25. Find The Value Of Sin A+B In the Simplest Form. 50 Answer: X=Frac Square Square Hit Answer

Answers

We can use the trigonometric identity sin(A+B) = sinAcosB + cosAsinB to find sin(A+B).

First, we need to find sinA and sinB. We can use the Pythagorean identity to find sinA:
sin^2 A + cos^2 A = 1
sin^2 A + (60/11)^2 = 1
sin^2 A = 1 - (60/11)^2
sin A = sqrt(1 - (60/11)^2)

Similarly, we can use the Pythagorean identity to find sinB:
sin^2 B + cos^2 B = 1
sin^2 B + (24/25)^2 = 1
sin^2 B = 1 - (24/25)^2
sin B = sqrt(1 - (24/25)^2)

Now we can use the identity sin(A+B) = sinAcosB + cosAsinB:
sin(A+B) = sinAcosB + cosAsinB
sin(A+B) = sqrt(1 - (60/11)^2) * (24/25) + (60/11) * sqrt(1 - (24/25)^2)

We can simplify this expression by using the fact that 60/11 = (120/22) = (240/44) and 24/25 = (48/50) = (96/100):
sin(A+B) = sqrt(1 - (240/121)^2) * (96/100) + (240/121) * sqrt(1 - (96/100)^2)
sin(A+B) = (sqrt(14561) / 121) * (24/25) + (240/121) * (7/25)
sin(A+B) = (576 * sqrt(14561) + 1680) / 3025

Therefore, sin(A+B) = (576 * sqrt(14561) + 1680) / 3025.

Hope this helps

Josh has c, coins. Nick has 4 fewer than three times as Josh

Answers

The requried, total number of coins between Josh and Nick is 4c - 4.

Let's say Josh has c coins, and Nick has 4 fewer than three times as many coins as Josh. We can express this mathematically as:

Nick's coins = 3 * Josh's coins - 4

Now, if we add the number of coins Josh and Nick have, we get the total number of coins between them:

Total coins = Josh's coins + Nick's coins

Total coins = c + (3c - 4)

Total coins = 4c - 4

Therefore, the total number of coins between Josh and Nick is 4c - 4.

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Let U= {1, 2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 5, 7}, and B= {2, 3, 4} Find the set A ∩ B.
A ∩ B={____}

Answers

The set A ∩ B = {2}.

To find the set A ∩ B, given that U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 5, 7}, and B = {2, 3, 4}.

A ∩ B represents the intersection of sets A and B, which means we need to find the elements that are common to both sets A and B. The intersection of two sets are sets that are common to both sets.

To do this, compare the elements of sets A and B:
A = {1, 2, 5, 7}
B = {2, 3, 4}

The only common element in both sets is 2.

Therefore, A ∩ B = {2}.

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How is 1/2 x 1/4 and 1⁄2 ÷ 4 related?

Answers

Answer:It is relates because 1/4 is the reciprocal of 4 so if you multiply by the reciprocal it will be the same answer as dividing by the first number.

Step-by-step explanation:

Answer:

it is equal

Step-by-step explanation:

since whenever you divide fractions basically the number on the right gets reciprocated and the division sign changes to a multiplication sign,

For example 2÷4 = 2 × 1/4

in this question we have

1/2 × 1/4 and 1/2 ÷4

4 is on the right so we reciprocate it

hence

1/2 x 1/4 = 1/2 × 1/4

TRUE/FALSE. Lambda and r are related; specifically the natural log of lambda is equal to r.

Answers

The given statement "Lambda and r are related; specifically the natural log of lambda is equal to r." is False because lambda and r are not necessarily related in such a way.

Lambda and r are both parameters that can be used to model exponential decay or growth, but they have different interpretations and units of measurement.

Lambda, denoted as λ, is the decay constant or the rate at which a quantity decreases over time in an exponential decay model. It has units of inverse time (e.g., per second, per year). The natural logarithm of λ is not equal to r, but rather to the negative of the decay rate: ln(λ) = -k, where k is the decay rate.

On the other hand, r is the growth rate or the rate at which a quantity increases over time in an exponential growth model. It has units of inverse time (e.g., per second, per year) like lambda. The natural logarithm of the base of the exponential growth function is equal to r: ln(b) = r, where b is the base of the exponential function.

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The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides?

Explain how you know. Provide at least one reason for your answer.

Answers

The other two sides of the triangle will be 8 cm.

Let's call the length of each of the other two sides "x".

Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as:

perimeter = 6 + x + x

Simplifying this equation, we get:

perimeter = 2x + 6

We know that the perimeter is 22 cm, so we can set up an equation and solve for x:

22 = 2x + 6

Subtracting 6 from both sides, we get:

16 = 2x

Dividing both sides by 2, we get:

x = 8

So the other two sides could both be 8 cm long in order to make an isosceles triangle with a perimeter of 22 cm.

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Answer:

8 cm

Step-by-step explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get 2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get  16 = 2x Dividing both sides by 2, we get x=8

You spin the spinner twice.
What is the probability of landing on a factor of 2 and then landing on a number less than 47
Simplify your answer and write it as a fraction or whole number.
Submit
Probability of simple events
Work it out
Not feeling ready yet? These can help:
Identify inds
Que
ans
Ti
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PAU
Smart
out of
6.

Answers

The probability of landing on a factor of 2 and number less than 4 is 1/3

Calculating the probability of landing on a factor of 2 and number less than 4

From the question, we have the following parameters that can be used in our computation:

Spinner

On the spinner, we have

Sections = 1, 2 and 3

This means that

Factor of 2 = 1 i.e. 2

Number less than 4 = 3 i.e 1, 2 and 3

So, we have

P(Factor of 2) = 1/3

P(Number less than 4) = 3/3 = 1

The required probability is

P = 1/3 * 1

Evaluate

P  = 1/3

Hence, the probability is 1/3

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NEED HELP ASAP!!!! WILL GIVE POINTS!!!!!

Answers

The decimal value for the current ratio is 1.3.

How to calculate the current ratio

Cash = $10,000

Inventory = $61,000

Total current assets = $10,000 + $61,000 = $71,000

The current liabilities are:

Notes = $45,000

Wages = $10,000

Total current liabilities = $45,000 + $10,000 = $55,000

The current ratio is:

Current ratio = Current assets / Current liabilities

Current ratio = $71,000 / $55,000

Current ratio = 1.3

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11
David made a class banner out of a large rectangular piece of paper. He cut a
triangular piece out of one side, as pictured below.
14 in.
5 in.
3 in.
-11 in.-
14 in.
What is the area, in square inches, of the banner?

Answers

Answer:

Okay, let's think through this step-by-step:

The original rectangular piece of paper is 14 inches wide and 5 inches tall.

So the area of the original rectangle = 14 * 5 = 70 square inches

David cut out a triangular piece from one side.

We are given:

** The triangle height = 3 inches

** The triangle base = 5 inches

** The triangle extends 11 inches from the edge

To find the area of the triangle:

** Triangle area = (base * height) / 2

** = (5 * 3) / 2 = 7.5 square inches

To find the area of the remaining rectangle shape:

** Length after triangle cut = 14 - 11 = 3 inches

** Remaining rectangle area = 3 * 5 = 15 square inches

Total area of banner = Area of original rectangle - Area of triangle + Area of remaining rectangle

= 70 - 7.5 + 15 = 77.5 square inches

So in summary, the area of the banner in square inches is 77.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

77.5

You have a ten by ten by ten inche cube that is mad up of little One by one by one cubes. You paint the outside of the big red cube. How many little cubes have paint on at least or of it side

Answers

There are 100 little cubes that have paint on at least one side.

To find the number of little cubes that have paint on at least one side, we need to calculate the surface area of the large cube, which is 6 times the area of one face. Since each face is a 10x10 square, the area of one face is 10x10 = 100 square inches. So, the total surface area of the cube is 6 x 100 = 600 square inches.

Each little cube has a surface area of 1x6 = 6 square inches, since it has 6 faces. Therefore, the number of little cubes with paint on at least one side is the surface area of the big cube divided by the surface area of one little cube.

600 square inches (surface area of big cube) divided by 6 square inches (surface area of one little cube) = 100 little cubes.

Therefore, there are 100 little cubes that have paint on at least one side.

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Use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx

Answers

The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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find the diagonal distance across a square of size 6

Answers

The diagonal distance across a square of size 6 is approximately 8.49 units.

To find the diagonal distance across a square of size 6, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the diagonal distance across the square, and the other two sides are the sides of the square, each of length 6.

So, we can set up the equation as follows:

c^2 = a^2 + b^2

where c is the length of the diagonal, and a and b are the lengths of the sides of the square. Substituting in the values we have:

c^2 = 6^2 + 6^2
c^2 = 36 + 36
c^2 = 72

To solve for c, we take the square root of both sides:

c = sqrt(72)
c ≈ 8.49

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The Excel function __________ generates integer values between lower and upper bounds.
a. RAND
b. RANDBETWEEN
c. LOWER
d. UPPER

Answers

RANDBETWEEN to generate random integer values between specified lower and upper bounds in Excel.

The Excel function that generates integer values between lower and upper bounds is RANDBETWEEN.

This function allows you to create random whole numbers within a specified range, making it useful for various applications, such as generating random sample data or assigning random values for simulation purposes.

To use RANDBETWEEN, simply input the desired lower and upper bounds as arguments in the following format: RANDBETWEEN(lower, upper).

Excel will then generate a random integer within the specified range.
For example, if you want to generate a random integer between 10 and 50, you would use the formula: =RANDBETWEEN(10, 50).

This would produce a whole number between 10 and 50, inclusive.
It's important to note that RANDBETWEEN is a volatile function, meaning it will recalculate and generate a new random number every time the worksheet is changed or recalculated.
In contrast,

RAND generates a random decimal number between 0 and 1, and the LOWER and UPPER functions are used for converting text to lowercase and uppercase respectively, rather than generating random numbers.
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Write A=[ 1 1 0 3 ] as XꓥX −1. Multiply Xe ꓥtX −1 to find the matrix exponential e At. Check e At and the derivative of e At when t = 0

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We need to identify a matrix X such that X1AX is in diagonal form in order to write A=[1 1 0 3] as XX1. One option is:

X = [1 1 1 0; 1 1 -1 0; 0 0 0 1; 1 -1 0 0]

Then, X⁻¹ = (1/4)[-1 1 -1 3; 1 1 1 -1; 0 0 0 4; -1 1 1 1]

X⁻¹AX = [5 0 0 0; 0 -1 0 0; 0 0 0 0; 0 0 0 -2]

A = X[5 0 0 0; 0 -1 0 0; 0 0 0; 0 0 0 -2] so.X⁻¹.

We must exponentiate each block of the diagonal matrix in order to determine eAt, so:

X[e5t 0 0 0; 0 e-t 0 0; 0 0 1 0; 0] = eAt

eA0 = X[e0 0 0 0; 0 e0 0 0; 0 0 1 0; 0 0 0 e0]X⁻¹

= X[I]X⁻¹

= AA⁻¹

= I

To find the derivative of eAt at t=0, we can use the formula:

d/dt(eAt)|t=0 = AXe0X⁻¹

= AXIX⁻¹

= A

Therefore, we have eA0 = I and d/dt(eAt)|t=0 = A.

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Help with state testing prep!!

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The requreid function has two intervals of decreasing values, one between -1 and 1, and the other between 3 and 5. Options C and E are correct.

The function is decreasing in the interval -1 < x < 1,
which means that as x increases from -1 to 1, the corresponding values of the function decrease.

Similarly, the function is decreasing in the interval 3 < x < 5, which means that as x increases from 3 to 5, the corresponding values of the function decrease.

Therefore, the function has two intervals of decreasing values, one between -1 and 1, and the other between 3 and 5.

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The data collected on the number of points scored in a basketball season are represented in the box plot.

A box plot uses a number line from 13 to 33 with tick marks every one-half unit. The box extends from 15 to 30.5 on the number line. A line in the box is at 21.5. The lines outside the box end at 14 and 32. The graph is titled Number of Points, and the line is labeled Points Scored in Basketball.

What value does 75% of the data lie above? Find the value.

Lower quartile (Q1) = 14
Lower quartile (Q1) = 15
Upper quartile (Q3) = 30.5
Upper quartile (Q3) = 32

Answers

Answer: a might be the answer

Step-by-step explanation: i do not know the answer

Answer: C

Step-by-step explanation:

The 75% mark is 30.5

So A, B, D is wrong WHICH MAKE C CORRECT Mark me as brainiest :)

a swimming pool is 4 yards long. How long is the pool in feet? And in inches

Answers

It would be 12 feet 144 inches

Windy bought widget stock at 14. 125 and sold it for 18 what was the percent increase

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Windy's widget stock increased in value by approximately 27.44%.

To find the percent increase in the value of the widget stock, we can use the following formula:

percent increase = [(new value - old value) / old value] x 100%

We are given that Windy bought the widget stock at 14.125 and sold it for 18, so the old value (the purchase price) is 14.125 and the new value (the selling price) is 18. Substituting these values into the formula, we get:

percent increase = [(18 - 14.125) / 14.125] x 100%

percent increase = 3.875 / 14.125 x 100%

percent increase = 0.2744 x 100%

percent increase = 27.44%

Therefore, Windy's widget stock increased in value by approximately 27.44%.

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