Compare the numbers using <, >, or =. 0. 78 ___ 0. 708 < > =

Answer:3 jeans and 11 shirts with 15 dollars leftover

Step-by-step explanation:

3x25=75

11x10=110

110+75=185

200-185=15

25x4 will make the leftover money higher, so 3 and 11

The Frobenius norm is a norm that satisfies the property ||CA||F = |C|||A||F for any scalar C and any matrix A in the set of complex matrices. This property demonstrates the linearity and scaling behavior of the Frobenius norm.

The Frobenius norm of a matrix A, denoted as ||A||F, is defined as the square root of the sum of the absolute squares of its elements. Mathematically, it can be expressed as:

||A||F = sqrt(Σ|aij|^2)

Now, let's consider a scalar C and a matrix A. We want to show that ||CA||F = |C|||A||F.

First, we calculate ||CA||F:

||CA||F = sqrt(Σ|cijaij|^2)

Using the properties of absolute values and squares, we can rewrite this as:

||CA||F = sqrt(Σ|cij|^2 * |aij|^2)

= sqrt(Σ|cij|^2) * sqrt(Σ|aij|^2)

= |C| * ||A||F

Thus, we have shown that ||CA||F = |C|||A||F, which demonstrates the linearity and scaling behavior of the Frobenius norm. This property makes the Frobenius norm a valid norm for matrices.

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Option (a) 1/50 The average of the 50 samples of x can be calculated as the sum of the values of x divided by the number of samples, which is 50 in this case.

Since x has a mean of 1, we know that the sum of the values of x is 50 times 1, which is 50. The variance of x is 4, which means that the standard deviation of x is 2. This means that the standard error of the mean of x, which is the standard deviation of the sample mean, is 2 divided by the square root of 50, which is approximately 0.283. Therefore, the 95% confidence interval for the mean of the 50 samples of x is [1 - 1.96(0.283), 1 + 1.96(0.283)] = [0.44, 1.56]. Since none of the answer choices fall within this interval, we cannot determine the correct answer without additional information.

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64.77% of a given amount remains after 900 years.

To determine the percentage of radioactive radium remaining after 900 years, we'll use the half-life formula:

Final Amount = Initial Amount * \(1/2^{(time elapsed / half-life)}\)

In this case, the half-life is 1599 years and the time elapsed is 900 years. We want to find the percentage remaining, so let's assume the initial amount is 100%.

Final Amount = 100 * \((1/2)^{(900 / 1599)}\)

Now, we'll calculate the exponent:

Exponent = 900 / 1599 ≈ 0.5635

Then, we'll compute the final amount:

Final Amount ≈ 100 * \((1/2)^{0.5635}\) ≈ 100 * 0.6477 ≈ 64.77%

After 900 years, approximately 64.77% of the initial radioactive radium remains. This percentage was found using the half-life formula, which accounts for the exponential decay of radioactive substances over time.

The formula shows how the remaining amount of a substance decreases as time progresses based on its half-life, which is the time it takes for half of the substance to decay. In this scenario, radium's half-life of 1599 years and the 900-year time frame were used to determine that roughly 64.77% of the initial radium remains.

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We have that, given the curve x = e5y, 0 ≤ y ≤ 2, it rotates around the y axis, we are going to obtain the following integrals

Part A: State, but do not evaluate, an integral for the surface area resulted by integrating with respect to x. Integrating with respect to x, the formula for finding the surface area of a curve rotated about the y axis is:

\(S=2\pi \int abxf(y)\sqrt{[1+({f(x))^2}']}dx\)

Since the curve revolves around the y-axis, the equation will have the form x = f(y). Therefore, x = e5yTaking the derivative of the equation, we have:

\({f(y)}' = 5e5y\)

multiplying by

\(f(y)2\pi \intabxf(y)\sqrt{[1+(f′(x))^2]}dx=2\pi \int 02e^5y(2\pi(5e5y)\sqrt{[1+(5e^5y)^2]}dx\)

Integrating and substituting the limits are obtained;

\(2\pi \int 02e^5y( 2\pi(5e^5y)\sqrt{[1+(5e5y)^2}]dx = 2 \pi \int 02e^5y \sqrt{(1+ 25e10y)}dy\)

Part B: Establish, but do not evaluate, an integral for the surface area resulted by integrating with respect to y. Integrating with respect to y, the formula for finding the surface area of a curve rotated about the y-axis is:

\(S=2\pi \int abxf(y)\sqrt{[1+(f′(x))^2}] dx\)

Since the equation is given as \(x = e^5y\), we will convert it to \(y = f(x)\) by taking the natural logarithm of both sides.

\(ln x = ln(e)^5y5 = 5y\)

So, the formula is \(y = 1/5 ln(x)\) using this formula as f(x) in the surface area formula;

\(S = 2\pi \int ab1/ 5ln(x) \sqrt{[1+((1 /5x)\\2}]dx.\)

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The cone is defined as the pyramid which has a circular cross section. So the cones are also called circular cones. Here the volume of cone is  83.56 cm³.

A cone has a three dimensional geometry which narrows smoothly from a flat base to a point called the apex or vertex. The formula used to calculate the curved surface area and total surface area is called the cone formula.

πr ( r+l) = 130.73

3.14 ×4 (4+l) =  130.73

4+l = 130.73 / 12.56

4+l = 10.40

l = 6.4 cm

r² + h² = l²

4²+ h² = 6.4 ²

h² = 24.96

h = 4.99 cm

Volume = 1 /3 Πr²h

1/3× 3.14 × 4×4× 4.99

V = 83.56 cm³

Thus the volume of cone is 83.56 cm³.

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Answer:

Step-by-step explanation:

Step one:

given data

we are told that weekly salary is $300

and a commission of 7% of the weekly sales

let the sales be s

7% of s = 0.07s

hence weekly commission = 0.07s

let the total earning be y

the linear model for Mr. Randall earnings is

y=300+0.07s

step two:

For the situation whereby he earned $426

the model is given as

426=300+0.07s

let us solve for s, the sales made

426-300=0.07s

126=0.07s

divide both sides by 0.07

s=126/0.07

s=1800

Hence he made sales of $1800 for that week

Answer:

7mn

Step-by-step explanation:

3 + 4 is 7

m + n is mn

7mn

Answer:

50 years

Step-by-step explanation:

Given data

Principal= $500

Rate= 6%

Amount = $2000

The simple interest expression is given as

A=P(1+rt)

Substitute

2000= 500(1+0.06*t)

open bracket

2000=500+ 30t

2000-500=30t

1500=30t

t= 1500/30

t= 50 years

Hence the time is 50 years

Answer:

50 years

Step-by-step explanation:

Formula for simple interest:

I = Prt

where

I = interest earned

P = principal amount deposited

r = annual interest rate

t = number of years

When the account reaches $2000, $500 is from the principal and

$2000 - $500 = $1500 is from the interest.

We use the simple interest formula to find the number of years needed to earn $1500 in interest from $500 principal at 6% interest rate.

1500 = 500 * 0.06 * t

t = 50

Answer: 50 years

The probability of finding such people will get closer to 0.61 as the sample gets bigger.

a) This means that if you were to take a large sample of US adults and inquire them about having breakfast, about 61%(i.e. 0.61) will say that they usually have breakfast.

b) It is, for sure, expected that if we take a sample of 100, around 61% of these americans will say that they usually eat breakfast. But if the number will be 61 exactly is not a certainty and it will vary from sample to sample.

The probability of finding such people will get closer to 0.61 as the sample gets bigger.

Explanation has been provided in the answers above due to their descriptive nature.

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The width of a rectangular rug is \(2\frac{1}{4} yards\)

From the question, we have

Length(l) = 4 yards

Area of a rectangular rug = 9 square yards.

We know that,

Area of a rectangular rug = length × width

⇒\(9 = 4*width\)

⇒\(width=\frac{9}{4} =2\frac{1}{4} yards=2.25 yards\)

Area of rectangle:

Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another. It should be noted that a parallelogram likewise has equal and parallel opposite sides, but the angles are not exactly 90 degrees.

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Answer:

C = 43.98 inches; A = 153.94 square inches

Step-by-step explanation:

2*pi*(7)=43.98

pi*(7)^2=153.94

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Answer:

The value of the length of the side C is 11.49.

Step-by-step explanation:

Cosine formula is applicable.

c² = a² + b² -2abcos(C)

substitute the values:

c² = (5)² + (12)² -2(5)(12)cos(72)

= 25 + 144 - 2 (60) (0.309)

= 169 - 37.08

c² = 131.92

square root both sides:

c = sqrt(131.92)

C = 11.49

The current date using the TODAY function, you can enter the formula "=TODAY()" in cell H5. This will display the current date in the cell.

Switch to the Cost Estimates worksheet. In cell A9, create a formula using the AVERAGE function that calculates the average of the values in the range A5:A7, then copy your formula to cell 09.

cell A10, create a formula using the MAX function that identifies the maximum value in the range A5:A7 and then copy your formula to cell D10. In cell A11, create a formula using the MIN function that identifies the minimum value in the range A5:A7 and then copy your formula to cell 011.

In cell B13, create a formula using the VLOOKUP function that looks up the value from cell A11 in the range A5:B7, returns the value in column 2, and specifies an exact match. Copy the formula to cell E13. Switch to the Profit Projections worksheet. In cell H5, use the TODAY function to insert the current date.

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Answer:

it can't be simplified.

Step-by-step explanation:

Answer:

Step-by-step explanation:perp. 3/2

y + 8 = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14

The reliability of the machine can be estimated to be 0.9833, calculated as (1000 - 1) / 1000 + (600 - 5) / 600.  we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

The reliability of a machine can be estimated by taking the ratio of machines that did not fail to the total number of machines operated in a given period. In this case, the reliability of the machine from Factory A can be estimated to be 0.99 (1000 - 1 / 1000). The reliability of the machine from Factory B can be estimated to be 0.9833 (600 - 5 / 600). To estimate the reliability of the machine based on both factories, we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

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Answer:

Step-by-step explanation:

The Smith family went out to dinner . The price of the meal was $ 29.85 .

The sales tax was 6 % of the price of the meal .

LEts find sales tax amount sales tax amount = price of meal *

sales tax 6 % ( 0.06 ) = 29.85 * 0.06 = 1.791 sales tax amount = 1.791

Price of the mean with sales tax = 29.85 + 1.791 = 31.641

The tip was 15 % of the meal and the sales tax now we find out tip amount for 31.641 15 % is 15 / 100 = 0.15

Tip amount = 31.641 * 0.15 = 4.74615

Now we add the top amount with 31.641 31.641+ 4.74615 = 36.38715

the Smith family pay for the meal = $ 36.39

Step-by-step explanation:

She has 1050

400 of that is the DB fee

Now she has 650 dollars

650/50 per person is 13

She can have 13 people

The missing angles ;

22.6°

53.1°

28.1°

A right triangle is a type of triangle that has one of its angles measuring 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti.

We have that;

\(Sin \alpha = 5/13\\ \alpha = Sin-1(5/13)\\ \alpha = 22.6\)

\(Tan  \alpha = 16/12\\\alpha = Tan-1 (16/12)\\= 53.1\)

\(Sin \alpha = 8/17\\\alpha = Sin-1(8/17)\\\alpha = 28.1\)

Right triangles have many practical applications, such as in trigonometry, engineering, and architecture.

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Graph f(x)=14.

Plot each graph on the same coordinate system.

f(x)=14x

image of graph

The amount of wrapping paper that is required is; c. 202 sq. in.

The formula for the surface area of a rectangular cuboid is given as:

SA = 2(lw + lh + hw)

where;

l = length

h = height

w = width

We are given;

Length; l = 3 in.

Width; w = 7 in.

Height; h = 8 in.

Thus, surface area is;

SA = 2((3*7) + (3*8) + (8*7))

SA = 2(21 + 24 + 56)

SA = 2(101)

SA = 202 sq. in

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Answer:

y=6

Step-by-step explanation:

Multiply both sides by 3y-8.

2y+3=9y/2-12

Add 12 to both sides.

2y+15=9y/2

Multiply both sides by 2.

Subtract both sides by 4y.

30=5y

Divide both sides by 5.

Therefore, y=6.

Answer:

2y+3/3y-8=3/2

multiply through by 3

3(2y+3-8)= (3/2)*3

6y-5= 9/2

6y =9/2+5

6y=19/2

y= 19*6/2

y= 57

Answer:

4

Step-by-step explanation:

\( \frac{2}{3} \times 6 = 4\)

I think she can make 4 throw pillows if she should use 6 yards of fabric

i hope this helped

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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Answer:

y = 3x - 5

Step-by-step explanation:

3x-y=5

-3x     -3x

-y= -3x + 5

divide each number by -1

-y/-1 = y

-3x/-1 = 3x

5/-1 = -5

The equation 3x - y = 5 can be converted to slope-intercept form as follows: y = 3x - 5

Given is an equation 3x - y = 5, we need to convert it in slope-intercept form.

To convert the equation 3x - y = 5 into slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate the variable "y" on one side of the equation.

Let's rearrange the given equation step by step:

Starting with 3x - y = 5, we can begin by moving the term involving "x" to the other side:

3x - y + y = 5 + y

Simplifying:

3x = y + 5

Now, let's isolate "y" by subtracting "y" from both sides:

3x - y = y + 5 - y

Simplifying:

3x - y = 5

To eliminate the "y" term on the left side, we can add "y" to both sides:

3x - y + y = 5 + y

Simplifying:

3x = 5 + y

Next, let's rearrange the equation to have "y" on the right side:

3x = y + 5

We can write this equation as:

y = 3x - 5

Now the equation is in slope-intercept form (y = mx + b), where the slope "m" is 3, and the y-intercept "b" is -5.

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Answer:

(59,93)

Step-by-step explanation:

Answer:

im pretty sure its -2x but i might be wrong

Step-by-step explanation: