Misha’s hamster weighed 0.845 kilograms. About how much does it weigh, rounded to the nearest hundredth?
0.85 kilograms
0.8 kilograms
1 kilograms
0.84 kilograms

The length of the diagonal for this rectangle is 13 cm.

To find the length of the diagonal for a rectangle with measurements of 5 cm by 12 cm, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides (length and width).

In this case, the length is 5 cm and the width is 12 cm. Using the Pythagorean theorem:

Diagonal² = Length² + Width²
Diagonal² = 5² + 12²
Diagonal² = 25 + 144
Diagonal² = 169

Now, take the square root of 169 to find the length of the diagonal:

Diagonal = √169
Diagonal = 13 cm

To learn more about  Pythagorean theorem : brainly.com/question/14930619

#SPJ11

The statement for the congruency of the triangles and the corresponding sides are as follows:

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal .

In other words, triangles that have exactly the same size and shape are called congruent triangles.

Let's write a congruency statement for the triangles and identify the pair of congruent corresponding side.

Therefore,

ΔPQR ≅ ΔCBA

Hence,

∠Q = ∠B

∠R = ∠A

∠P = ∠C

PQ = BC

QR = AB

learn more on congruent triangles here: brainly.com/question/15485747

#SPJ1

Answer:

Step-by-step explanation:

A=4πr2=4·π·1002≈1.25664×105

Let's denote the ages of the two remaining men as x and x + 3 (since one is 3 years older than the other).

We know that the average age of 6 men is 35 years. So, the sum of their ages is 6 * 35 = 210 years.

We also know that the average age of four of them is 32 years. So, the sum of their ages is 4 * 32 = 128 years.

To find the sum of the ages of the two remaining men, we subtract the sum of the ages of the four men from the sum of the ages of all six men:

210 - 128 = 82 years.

Now, we can set up an equation to solve for the ages of the remaining two men:

x + (x + 3) = 82.

Combining like terms, we get:

2x + 3 = 82.

Subtracting 3 from both sides:

2x = 79.

Dividing both sides by 2:

x = 39.5.

So, one of the remaining men is 39.5 years old, and the other is 39.5 + 3 = 42.5 years old.

Answer:

y - 9x - 82 = 0

Step-by-step explanation:

Given expression;

y - 10 = 9(x + 8)

Find:

Write into standard form

Computation:

Given expression;

⇒ y - 10 = 9(x + 8)

Using BODMAS role

Multiply 9 into (x - 8)

⇒ y - 10 = 9(x) + 9(8)

⇒ y - 10 = 9x + 72

⇒ y - 9x - 10 = 72

⇒ y - 9x = 72 + 10

⇒ y - 9x = 82

⇒ y - 9x - 82 = 0

Standard form of given expression

y - 9x - 82 = 0

To evaluate the given integral using Green's theorem, we need to express it in the flux form.  The result of the integral is -r/6.

Green's theorem states that for a region R bounded by a simple closed curve C, the flux of the vector field F = (P, Q) across C is equal to the double integral of the curl of F over R.

In this case, we have the vector field F = (r^2xy, 1/2y^3), where r is the position vector (x, y).

The flux form of Green's theorem is:

\(∫∫R (curl F) · dA = ∫∫R (∂Q/∂x - ∂P/∂y) dA\)

Let's calculate the curl of F:

∂Q/∂x = 0

∂P/∂y = 2rxy

So, the curl of F is given by\((∂Q/∂x - ∂P/∂y) = 0 - 2rxy = -2rxy.\)

Now, let's evaluate the integral using the flux form of Green's theorem:

∫∫R (-2rxy) dA

Since the region R is a triangle with vertices (0,0), (1,0), and (0,1), we can express it as:

\(R = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}\)

Now, we can rewrite the integral:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Let's evaluate the inner integral first:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Now, evaluate the outer integral:

\(∫₀¹ -r(x-x²) dx = -r(x²/2 - x³/3) ∣₀¹ = -r(1/2 - 1/3) = -r(3/6 - 2/6) = -r(1/6) = -r/6\)

Therefore, the result of the integral is -r/6.

Learn more about Green's theorem

https://brainly.com/question/27549150

#SPJ11

Answer:

here you go

Step-by-step explanation:

(a) Y(s) = 1 / (5)(s^2 + 4) + s / (s^2 + 9) ,(b) Y(s) = [1 / s − 1 / s exp(-10s) + 0.5] / (s^2 + 3s + 2) , (c) Y(s) = [1 / (s^2 + 1)(s^2 + 49)] − 1 / (s^2 + 1) and (d) Y(s) = (8 / s^2 + 0.1) / (s^2 + 6) .

(a) For the first initial value problem, we need to solve for y. The Laplace transform is denoted as L{y(t)} or F(s), where s is the complex frequency variable that transforms the time function into the frequency domain. The formula for the Laplace transform is as follows:

L{y"(t)}=s^2Y(s)−sY(0)−Y'(0)L{y(t)}=Y(s)

Thus, the equation y" + 9y = cos(2t) in Laplace domain is:

s^2Y(s) − s + 9Y(s) = 1 / (s^2 + 4)

To solve for Y(s), we need to find a common denominator. That is,

(s^2 + 9)Y(s) = 1 / (s^2 + 4) + s

Y(s) = [1 / (s^2 + 4) + s] / (s^2 + 9)

Y(s) = (1 / (s^2 + 4)) / (s^2 + 9) + s / (s^2 + 9)

Y(s) = 1 / (5)(s^2 + 4) + s / (s^2 + 9)

Now, we can use the inverse Laplace transform to find y(t).

(b) For the second initial value problem, we need to solve for y again. In Laplace domain, the equation y" + 3y' + 2y = 1 – U10(t) becomes:

s^2Y(s) − sy(0) − y'(0) + 3(sY(s) − y(0)) + 2Y(s) = 1 / s − 1 / s exp(-10s)

Now, we can substitute the initial conditions:

s^2Y(s) − s(0) − 0.5 + 3(sY(s) − 0) + 2Y(s) = 1 / s − 1 / s exp(-10s)

s^2Y(s) + 3sY(s) + 2Y(s) = 1 / s − 1 / s exp(-10s) + 0.5

Factor the left side:

(s^2 + 3s + 2)Y(s) = 1 / s − 1 / s exp(-10s) + 0.5

Y(s) = [1 / s − 1 / s exp(-10s) + 0.5] / (s^2 + 3s + 2)

(c) For the third initial value problem, we can use the same method as in (a) and (b) to solve for Y(s). The Laplace domain equation for y" + y = (1 – w7 (t)) sin(t) is:

s^2Y(s) − y(0) − y'(0) + Y(s) = (1 / (s^2 + 1)) − (1 / (s^2 + 49))

Substitute the initial conditions:

s^2Y(s) − 0 − 0 + Y(s) = (1 / (s^2 + 1)) − (1 / (s^2 + 49))

(s^2 + 1)Y(s) = (1 / (s^2 + 1)) − (1 / (s^2 + 49))

Y(s) = [1 / (s^2 + 1)(s^2 + 49)] − 1 / (s^2 + 1)

(d) For the fourth initial value problem, we again use the Laplace transform. The Laplace domain equation for y" + 5y + y = 8(t – 1) is:

s^2Y(s) − s(0) − 0.1 + 5Y(s) + Y(s) = 8 / s^2

(s^2 + 6)Y(s) = 8 / s^2 + 0.1

Y(s) = (8 / s^2 + 0.1) / (s^2 + 6)

Inverse Laplace transform will give us y(t).

To know more about Inverse Laplace transform visit:

https://brainly.in/question/20093732

#SPJ11

Answer:

The method of substitution involves three steps:

Solve one equation for one of the variables.

Substitute (plug-in) this expression into the other equation and solve.

Resubstitute the value into the original equation to find the corresponding variable.

Step-by-step explanation:

Answer:

The equation is non-linear.

Step-by-step explanation:

If x has an exponent of to it becomes a non-linear equation.

Answer:

the 3rd on

Step-by-step explanation:

Answer:

m∠BNP=90∘ and m∠ANP=90∘

Step-by-step explanation:

Looking at the diagram these are perpindicular which means they have 90 degree angles.

Answer:

C

Step-by-step explanation:

Answer:

y = -x/3 + 1/3

Step-by-step explanation:

If a line is perpendicular to another line, then the gradient would be the negative reciprocal of the equation.

The line perpendicular to y = 3x + 5 would be y = -x/3 + c

To find c, you sub in the given point (4, -1)

-1 = -4/3 + c

-3/3 + 4/3 = c

c = 1/3

Hence the equation of the perpendicular line would be:

y = -x/3 + 1/3

The domain choice that is a possibility is A. A. Real numbers greater than 0.

A continuous function in mathematics is one in which a continuous variation of the argument causes a continuous variation of the function's value. This means that there are no abrupt changes in value, which are referred to as discontinuities.

Option A: Real numbers greater than zero:

Because real numbers are continuous functions, the greater than zero part of them can be used to represent the balance sheet.

Option B: Use only whole numbers: It is not possible.

Whole numbers are discrete, not continuous, and thus cannot represent decimal points.

Option C: Integers: Invalid

Because integers are discrete rather than continuous, they cannot represent decimal points.

Natural numbers are not an option.

Natural numbers, like whole numbers, are discrete rather than continuous and cannot represent decimal points.

In conclusion, the correct option is A.

Learn more about real number on:

https://brainly.com/question/155227

#SPJ1

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

r = \(\frac{5}{8}\) t - 9 ← is in slope- intercept form

with y- intercept c = - 9

Function 2 has the ordered pair (0, - 9 )

This indicates that when t = 0 , r = - 9

This is the y- intercept at - 9

Thus both functions have the same y- intercept

39 subjects were tested in this simple one-way ANOVA.

We are given that:

F(7 , 31) = 4.78

Step 1: Find the total degrees of freedom.

The treatment df = 7

The error df = 31

\(df_{treatment} &\ +df_{error} &\ = df_{total}\)

Hence, the total df = 7+31 = 38.

Step 2: Find the number of subjects tested.

We know that in a one-way ANOVA test:

df = n-1

⇒ 38 = n-1

⇒ n = 39.

Hence, 39 subjects were tested in this simple one-way ANOVA.

For similar questions on the one-way ANOVA test, visit:

https://brainly.com/question/28206544

#SPJ4

The flow rate to produce the balls is 12.5in/s and 1.25in/s

The number of toys = 100

The increase in radius = 1inch/sec

5 toys are going to increase by 0.5 radius

The rate flow to produce the balls

5x100 = 500

Rate flow = 500 x 0.5³ / 5

= 12.5inch/s

Time = 10 seconds x 5 = 50 seconds

radius = 0.5 inches

Flow rate = 50 * 0.5³/5*10

= 1.25 inches/s

Read m ore on flow rate here:

https://brainly.com/question/1154328

#SPJ1

Answer:

She would receive $10.05 cents back

Step-by-step explanation:

Add 6.75, 1.45, and 1.75. You would get 9.95. Then, you would subtract $20.00 by $9.95, getting 10.05 as change.

Hope this helps!

Answer:

children = $6 ; adults = $13

Step-by-step explanation:

6c + 8a = 140

12c + 9a = 189

3c + 4a = 70

4c + 3a = 63

3c = 70 - 4a

c = 70/3 - 4/3 a

4(70/3 - 4/3 a) + 3a = 63

280/3 - 16/3 a + 3a = 63

(-16a + 9a)/3 = 63 - 280/3

-7/3 a = (189 -280)/3

-7/3 a = -91/3

a = - 91/3 · -3/7

a = 91/7

a = $13

c = 70/3 - 4/3 · 13

c = 70/3 - 52/3

c = (70-52)/3

c = 18/3

c = $6

a) To find out how much L is needed to produce 400 toys per hour when K is equal to 20, we can use the production function formula provided, which is Q = 4K + 5L.

To solve for L, we can rearrange the formula as follows: Q - 4K = 5L 400 - 4(20) = 5L 320 = 5L L = 64

Therefore, to produce 400 toys per hour with K = 20, the manufacturer would need 64 units of labor input per hour.

b) Similarly, to find out how much K is needed to produce 500 toys per hour when L is equal to 40, we can use the production function formula: Q = 4K + 5L

Substituting the given values, we get: 500 = 4K + 5(40) 500 = 4K + 200 4K = 300 K = 75

Therefore, to produce 500 toys per hour with L = 40, the manufacturer would need 75 units of capital input per hour.

In conclusion, the production function formula provides a useful tool for toy manufacturers to produce a desired level of output. By manipulating the formula, the manufacturer can also calculate the maximum output possible given a certain combination of inputs.

For similar question on production function formula  

https://brainly.com/question/24136783

#SPJ11

Answer:

let the number be a

product of a number and six = 6 times a=6a

three less than the product of a number= 6a-3

then the full equation will be 6a-3=27

Answer:

Statistical inference

Step-by-step explanation:

Answer: 2.16 x 10^2

Step-by-step explanation:

6^3 = 216
2.16 x 10^2

Answer:

180 RS discount

Step-by-step explanation:

because 940-760 is 180

Answer:

True

hope this helps

have a good day :)

Step-by-step explanation:

The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

Find out more on dilation at https://brainly.com/question/11662153

#SPJ1

18 ft is equal to 6 yards. A yard is one linear yards. "Yd" is the yard symbol. It is equivalent to three feet or 36 inches.

The majority of cloth is now sold by the linear yard. A linear yard is 36" long, with a width that varies depending on the cloth roll. Only the length of the material is considered when measuring in linear yards. To calculate square yards, multiply the length and width in yards. In a yard, there are 36 inches. The length of a yard of fabric is 36 inches. Calculating the amount of fabric required for a sewing job is a little more difficult than that, though. A yard of fabric is always one yard long, however the breadth varies depending on where you get it. Between 33 and 44 inches are the typical widths.

Add the conversion factor "0.33333333333278" to the number in feet.

So, 18 feet

= 18 × 0.33333333333278

= 5.99999999999 yards.

Learn more about linear yards here

https://brainly.com/question/9644327

#SPJ4

Answer:

3. <BAC = <BCA

so,

x+x+36° = 180°

=>2x + 36 = 180

=>2x = 180–36

=>2x = 144

=>x = 144/2

=>x = 72°