At the beginning of July, Kim had a mass of 63 kg.
At the end of July, his mass was 61 kg.
Calculate the percentage loss in Kim's mass.​

The graph of the function y = -2x + 1/3 is added as an attachment

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

y = -2x + 1/3

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

X    |   y

---------------

-2   |   3

-1   |   0

0   |  -3

1   |  -6

Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

The tolerance to defects and fracture toughness of a material can be evaluated using its fracture toughness parameter, Kic. The higher the Kic value, the better the material's tolerance to defects and fracture toughness.

To compare the two materials, we can use the concept of critical stress intensity factor (Kic) and factor of safety (FoS). The critical stress intensity factor is the maximum value of stress intensity factor (K) that a material can withstand without fracturing. The factor of safety is the ratio of the maximum allowable stress to the design stress, and it is used to ensure a safety margin in the design.

Assuming that the two materials have the same defect to tolerance ratio, we can calculate the maximum allowable stress for each material using the following formula:

σmax = FoS * Kic / (π * a)

where σmax is the maximum allowable stress, FoS is the factor of safety (assumed to be 2), Kic is the fracture toughness parameter, and a is the size of the defect.

Let's assume a defect size of 1 mm for both materials. Using the values given in the question, we get:

For Maraging (18% Ni) steel:

σmax = 2 * 82 * 10^6 / (π * 1 * 10^-3) = 52.1 GPa

For Medium strength steel:

σmax = 2 * 50 * 10^6 / (π * 1 * 10^-3) = 31.8 GPa

Therefore, Maraging steel has a higher maximum allowable stress, which indicates that it has a better tolerance to defects compared to medium strength steel.

To compare the fracture toughness of the two materials, we can use their respective Kic values. The higher Kic value indicates a better tolerance to defects and fracture toughness.

Comparing the given values, we can see that Maraging (18% Ni) steel has a higher fracture toughness parameter (Kic= 82 MNm-3/2) compared to Medium strength steel (Kic= 50 MNm-3/2).

Therefore, Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

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The angular velocity in rpm of a point on its rim is equals to the 4224 rad/min.

We have, a cylinder with Radius , R = 6 inch. Spining velocity, S = 24 miles per hour

We have to calculate the the angular velocity in rpm of a point on its rim. To calculate Angular and Linear Speed from Linear velocity :

Step 1: Identify which speed we are asked to calculate and Identify the radius and the velocity. We already identified all this in above.

Step 2: To calculate the angular speed when the linear speed and the radius of the circular object use : angular velocity = linear velocity/radius

First, we need to reconcile the unit of the radius of the wheel/rim and the unit of the speed of the car. Also, we are asked to give the answer in radians per minute. So, let's convert the speed to inches per minutes. So, the linear velocity of spining = 24 miles per hour × 5280 ft. per miles× 12 inches per ft. × 1 hour / 60 minutes

= 25,344 inches per minute

Now, the angular velocity is written as

angular velocity = linear velocity /radius

= 25,344 inches per minute / 6 inches

= 4224 /min. Hence, the angular velocity of the rim is 4224 rad/min.

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If a cylinder with a 6 in. radius is spinning at 24 mph, The angular velocity of a point on the rim of the cylinder is 672.27 rpm.

Angular velocity is a measure of the speed at which an object is rotating around a central axis. It is measured in units of radians per second (rad/s) or revolutions per minute (rpm). To find the angular velocity of a point on the rim of the cylinder, we need to first convert the linear velocity (24 mph) to linear velocity in feet per second (ft/s). We can use the formula:

where v is the linear velocity, r is the radius of the cylinder, and ω is the angular velocity.

Due to the 6 in. = 0.5 feet,

ω = v χ 1 r = 24 miles hr 1 0.5 ft χ 5280 ft mile = 253,440 (rad) hr

Then, 672.27 rpm at 253,440 (rad) hr  1 2pi rev rad  1 60 hr min

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Answer

40.1

Area of a triangle using sine rule = 1/2 a b sinC

a and b are the two known sides, sinC is the angle opposite the unknown side

1/2 x 14 x 7 sin(125) = 40.1 to the nearest tenth

Hope this helps

Answer:

40.1

Step-by-step explanation:

Answer:

\(2(\frac{1}{2} *20*50)+2(\frac{1}{2} *20*10)\)

Step-by-step explanation:

The formula for the area of a triangle is \(\frac{1}{2} *b*h\)

The triangles that can be made is the triangle that has legs 20 and 50 and the triangle that has legs 20 and 10.

Since there are 2 of each triangles, we get:

\(2(\frac{1}{2} *20*50)+2(\frac{1}{2} *20*10)\)

The answer that fits is the first option.

The composite function of (f.g)(2) is 33.

In mathematics, function composition is an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function.

f(x) = x^2 - 3x + 5

g(x) = -2x

The composite function of (f.g)(x) can be calculated as

(f.g)(2) = 33

This done by finding or substituting the value of 2 in the parts of the equation represented by x.

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Answer:

B) y - 2 = (-1/4)(x - 2)

Step-by-step explanation:

Start with the equation of the given line: y = 4x + 7.

Determine the slope of the given line, which is 4.

Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.

Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).

Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.

Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.

Simplify further: y = (-1/4)x + 5/2.

The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.

The value of numbers are 71 and 35.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The difference between two numbers = 36

And, Five time the larger is 11 times the smaller.

Now,

Let the larger number = x

And, The smaller number = y

So, We can formulate;

The difference between two numbers = 36

⇒ x - y = 36  ..(i)

And,  Five time the larger is 11 times the smaller.

⇒ 5x = 11y

⇒ 5x - 11y = 0  ..(ii)

Multiply by 5 in (i), we get;

⇒ 5x - 5y = 210  ..(iii)

Subtract above equation from (ii), we get;

⇒ 6y = 210

⇒ y = 35

And, From (i);

⇒ x - y = 36

⇒ x - 35 = 36

⇒ x = 36 + 35

⇒ x = 71

Thus, Two numbers are 71 and 35.

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The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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Answer:

Base × Height ÷ 2

Answer:

Hope this helps! :)

Answer:

32$

Step-by-step explanation:

There's a 25% discount, so,

After cutting discount, the total will be 9.78 -(9.78×25%)

=7.335

Again, after adding tax, total amount will be : 7.335+ ( 9.78×7.75%)

=8.09

So, the total cost of 4 DVD is 4× 8.09 =32.36

Answer: 18 with a remainder of 17

Step-by-step explanation:

H.

1) In this problem, we have to check out which one of those trios the Pythagorean Theorem doesn't work for the given measures.

F ) a² =b² +c²

5² = 3²+4² True Classic Pythagorean Triple 3,4 ,5

G) 5, 12, 13

13² = 5² +12² Another classic Pythagorean Trio for right triangle 5,12,13

169 = 25 +144 True

H) We have the following measures: hypotenuse of that triangle to be 21, 9, and 12, since the area of the square is l²=144 then l =12, writing the measurements plugging into the Pythagorean Theorem and taking 21 as the larger side (possible hypotenuse):

a²=b² +c²

21² ≠ 9² +12 ²

441 ≠ 81 +144

441 ≠ 225 FALSE

So the junction of those three sides does not yield a right triangle.

I) 10² = 8² +6² True

Answer:

Step-by-step explanation:

266 divided by 7 is 38 laps a day

He can buy less οr equal tο 14 shirts with the mοney left and The inequality that represents this situatiοn is s (stands fοr shirts) ≤ 14.

In Mathematics, it is the relatiοnship between twο values that are nοt equal. Inequality means twο values that are nοt equal. When the situatiοn is  tο cοmpare the values, '≤' οr '≥' sign are used.

Hey team can spend nο mοre than $300 οn shirts the team has already spent $80.

300- 80 = 220

220/ 15 = 14.6

Let us say s be the number οf shirts.

Then the inequality will be s≤14

As the numbers οf shirts cant be a fractiοnal term sο we cοnvert the fractiοnal term tο the integer οne.

Hence, the inequality that represents the situatiοn is s≤14.

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Answer:

\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)

Step-by-step explanation:

This is a rationalizing denominator question.

\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)

Answer:

L = 10.64°

Step-by-step explanation:

From the given information:

In triangle JKL;

line k = 9.6 cm

line l = 2.7 cm; &

angle J = 43°

we are to find angle L = ???

We can use the sine rule to determine angle L:

i.e

\(\dfrac{j}{SIn \ J} = \dfrac{l}{ SIn \ L}\)

Using Pythagoras rule to find j

i,e

j² = k² + l²

j² = 9.6²+ 2.7²

j² = 92.16 + 7.29

j² = 99.45

\(j = \sqrt{99.45}\)

j = 9.97

∴

\(\dfrac{9.97}{Sin \ 43} = \dfrac{2.7}{ Sin \ L}\)

\({9.97 \times Sin (L ) = (2.7 \times Sin \ 43)\)

\(= Sin \ L = \dfrac{ (2.7 \times Sin \ 43)}{9.97 } \\ \\ = Sin \ L = \dfrac{ (2.7 \times 0.6819)}{9.97 } \\ \\ = Sin \ L = 0.18466 \\ \\ L = Sin^{-1} (0.18466) \\ \\ L = 10.64 ^0\)

Answer:

x = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

3(x - 2) = 2(x + 1)

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 18 does indeed equal 18.

∴ x = 8 is a solution to the equation.

Answer:

\( \sin(58°) = \frac{12}{y} \\ y = \frac{12}{ \sin(58°) } \\ y = \frac{12}{0.85} \\ \boxed{y = 14.15(approx)}\)

\( \tan(58°) = \frac{12}{x} \\ x = \frac{12}{ \tan(58°) } \\ x = \frac{12}{1.6} \\ \boxed{x = 7.5(approx)}\)

Option • 12 is the answer .The number of treatments in the experiment is 12.

The understudy is directing a trial to comprehend the connection between microwave power and time on the quantity of unpopped bits in a pack of popcorn. There are three degrees of microwave power: low, medium, and high. Each sack of popcorn can be popped for either 3 minutes or 4 minutes, which provides us with a sum of double cross variables. To cover every one of the potential mixes of time and power, the understudy runs 12 distinct medicines (3 degrees of force x 2 degrees of time). Every treatment addresses one sack of popcorn that is popped for a particular time frame and with a particular power setting. The quantity of unpopped parts is recorded for every treatment, and the outcomes are utilized to make determinations about the impacts of microwave power and time on the quantity of unpopped pieces.

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The approximate value of 63000 x 200 will be 12600000.

In mathematics, multiplication is defined as the sum of the numbers to the other number given. Like if 2 is multiplied by 3 then the multiplication will be the sum of the two-three times.

Given expression is 63000 x 200 so here we need to calculate the sum of the 63000 to 200 times.

E = 63000 x 200

E = 12600000

Therefore the approximate value of 63000 x 200 will be 12600000.

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One giga-meter can be written as \(10^9\) meters.

Affixes, οr mοrphemes added tο a base wοrd tο mοdify its meaning, include prefixes and suffixes amοng their types. Adding suffixes tο the end οf a wοrd is mοre cοmmοn than adding prefixes tο the beginning.

Althοugh sοme, like heter- and megal-, are three syllables lοng, the majοrity οf prefixes and suffixes in English are typically οne οr twο.

Nο matter what base wοrd a prefix is attached tο, its meaning is always the same. Fοr instance, the prefix are- always denοtes "tο dο sοmething again"; when it appears in the wοrd reread, it means "tο read again," and when it appears in the wοrd rebuild, it denοtes "tο build again."

The prefix giga represents 1,000,000,000, which can be written as \(10^9\) in terms οf pοwers οf ten.

Therefοre, οne giga-meter can be written as 10^9 meters.

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Answer: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). ... the line y = x is the point (y, x). The reflection of the point (x,y) across. the line y = -x is the point (-y, -x).

Step-by-step explanation: I hope this helped! Actually, I just hope that my answer is correct but whatevs lol :)

The magnitude of the speed of the particle is determined as √ (17), m/s.

option A.

The speed of a particle is defined as the rate of change of the particle's displacement with time.

Mathematically, the formula for the speed of the a particle is given as;

v = dx/dt

where;

The speed of the particle is calculated as;

v = u + at

where;

at time, t = 0, the equation for the speed of the particle becomes;

v = u

v = i + 4j

The magnitude of the speed is calculated as follows;

v = √ (1² + 4²)

v = √ (17), m/s

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Answer:

B) -2⅛

Step-by-step explanation:

All other options are irrational

Answer:

23x+250 and that would equal your total cost