The length of a rectangle is five times its width.
If the perimeter of the rectangle is 108 cm, find its length and width.

When 1,493,600 is divided by 8 the quotient is 186,700.

To divide 1,493,600 by 8, you can follow these steps:

We have to write down the dividend (1,493,600) and the divisor (8).

Now start with the largest place value in the dividend (the leftmost digit) and perform the division.

Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.

Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.

Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.

Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.

Divide 9 by 8. The quotient is 1, and the remainder is 1.

Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.

Divide 13 by 8. The quotient is 1, and the remainder is 5.

Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.

Divide 56 by 8. The quotient is 7, and there is no remainder.

Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.

Divide 70 by 8. The quotient is 8, and there is no remainder.

There are no more digits to bring down, and the division is complete.

The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.

Therefore, the result of 1,493,600 ÷ 8 is 186,700.

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The product of the expression 7 x 63 is 441.

We have,

To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:

7 x 63 = 7 x (60 + 3)

Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:

7 x (60 + 3) = 7 x 60 + 7 x 3

Simplifying further:

7 x 60 + 7 x 3 = 420 + 21

Therefore,

The product of 7 x 63 is 441.

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Answer:

\(y=5x^2-80x+324\)

Step-by-step explanation:

Answer:

There are 60 dvds.

Step-by-step explanation:

72 - 3 - 9 = 60

13.15 es un número decimal, si quieres convertirlo a una fracción se convierte en 1315/100.

El número decimal es un sistema numérico de base 10. En el aprendizaje de las matemáticas, además de ser un número de base 10, este número decimal también se puede interpretar como el número de décimas, centésimas, milésimas,…. pronto.

Los números decimales tienen muchas funciones en varios campos. Los números decimales también son los números más utilizados.

La conversión de números decimales al sistema binario será útil tanto en informática como en programación.

Las fracciones decimales son fracciones cuyos denominadores son diez, cien, mil, etc. Los siguientes son algunos ejemplos de fracciones en forma decimal, a saber:

0,2 = 2/10

0,03 = 3/2100

40/100 = 0,4

127/1000 = 0,127

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Answer:

you just need all your dimensions to equal 180

Step-by-step explanation:

180 = 20........

Answer:

\(E(x) = 4.500\) --- Expected value

\(SD(x) = 2.872\) --- Standard deviation

Step-by-step explanation:

Given

\(\begin{array}{ccccccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} & {7} & {8} & {9} \ \\ P(X=x) & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}}& {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} \ \end{array}\)

Solving (a): Expected value

This is calculated using:

\(E(x) = \sum\limits^{9}_{i=0} x_i * P(X = x_i)\)

Since they all have the same probability, the formula becomes:

\(E(x) = \frac{1}{10}\sum\limits^{9}_{i=0} x_i\)

\(E(x) = \frac{1}{10}(0+1+2+3+4+5+6+7+8+9)\)

\(E(x) = \frac{1}{10}*45\)

\(E(x) = \frac{45}{10}\)

\(E(x) = 4.500\)

Solving (b): Standard Deviation

First, we calculate the variance using

\(Var(x) = E(x^2) - (E(x))^2\)

In (a), we have:

\(E(x) = 4.500\)

\(E(x^2)\) is calculated as:

\(E(x^2) = \sum\limits^{9}_{i=0} x_i^2 * P(X = x_i)\)

Since they all have the same probability, the formula becomes:

\(E(x^2) = \frac{1}{10}\sum\limits^{9}_{i=0} x_i^2\)

So, we have:

\(E(x^2) = \frac{1}{10}(0^2+1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2)\)

Using a calculator

\(E(x^2) = \frac{1}{10}(285)\)

\(E(x^2) = 28.5\)

So:

\(Var(x) = E(x^2) - (E(x))^2\)

\(Var(x) = 28.5 - 4.5^2\)

\(Var(x) = 28.5 - 20.25\)

\(Var(x) = 8.25\)

The standard deviation is then calculated as:

\(SD(x) = \sqrt{Var(x)}\)

\(SD(x) = \sqrt{8.25}\)

\(SD(x) = 2.872\) ---- approximated

Answer:

We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:

A = Pe^(rt)

where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

A = $600.00e^(0.05*1)

Using a calculator, we get:

A ≈ $632.57

Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.

three shapes. three areas to find. three areas to add together to find the whole area. gotcha.

Step-by-step explanation:

length is 7 cm and width is 4 cm, so the area is 28 square cm

width is 4 cm and length is 10 cm, so the area is 40 square cm

Because the weird shape's bottom length was 13 cm. There are 3 cm and 7 cm on the top length(s) of the weird shape, next to each other. Looking at the dash lines, when adding 3 cm and 7 cm together, the larger rectangle's length is 10 cm.

base is 3 cm and height is 8 cm, so the area is (3x8)/2 = 24/2 = 12 square cm

With knowledge from figuring out the larger rectangle's length being 10 cm and the weird shape's bottom length being 13 cm, we know the right triangle's base is 3 cm. (13 cm - 10 cm = 3 cm for the base of the right triangle).

Due to adding 4 cm and 4 cm of weird shape's width, which is also a right triangle's height.

28 + 40 + 12

= 80 square cm (ANSWER)

Answer: Table D

Step-by-step explanation:

The coefficient of x^2 is -9, the coefficient of x is 7, and the constant is 0, so we know a = -9, b = 7, c = 0.

Thus, table D is the answer.

The correct answer is A) 3 feet.

A 15-foot statue casts the shadow of 20 food, then a 4-foot-long shadow will be cast by a 3-foot-tall person.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

From the data in the question,

15-foot statue = 20-foot shadow

x-foot man's height = 4-foot long shadow

20x = 60

x = 60/20

x = 3 foot.

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\(\textit{surface area of a sphere}\\\\ SA = 4\pi r^2~~ \begin{cases} r= radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies SA=4\pi (9)^2\implies SA=324\pi\)

Answer:

A and B

Step-by-step explanation:

The original equation simplifies down to -4m - 2

Answer A and B also simplify down to -4m -2, and therefor are equivalent

A: -2(4m + 1) + 4m

-8m - 2 + 4m

-4m - 2

B: 2(2m - 1) - 8m

4m - 2 - 8m

-4m - 2

If we consider  a pair of integers (a b) and the given operations, then the java program that depicts it is as written below.

The program that carries out the required operations on the pair of integers is;

static LinkedList<Pair<Integer,Integer>> pairs = new LinkedList<Pair<Integer, Integer>>();

   public static String isItPossible(Integer a, Integer b, Integer c, Integer d){

       pairs.addLast(new Pair<Integer, Integer>(a,b));

       while (!pairs.isEmpty()){

           Pair<Integer,Integer> pair = pairs.poll();

           Integer key = pair.getKey();

           Integer value = pair.getValue();

           if(key.equals(a) &&

                   value.equals(b)){

               return "YES";

           }

           int sum=key+value;

           if (sum<=c){

               pairs.addLast(new Pair<Integer, Integer>(sum,value));

           }

           if (sum<=d){

               pairs.addLast(new Pair<Integer, Integer>(key,sum));

           }

       }

       return "NO";

   }

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Complete question is;

Consider a pair of integers, (a, b). The following operations can be performed on (a, b) in any order, zero or more times:

• (a, b)(a + b, b)

• (a, b) → (a, a + b)

Return a string that denotes whether or not (a, b) can be converted to to (c,d) by by performing zero or more of the operations specified above. Example

(a, b) = (1, 1)

(c,d) = (5,2)

Perform the operation (1,1 + 1) to get (1, 2), perform the operation (1 + 2, 2) to get (3, 2), and perform the operation (3+2, 2) to get (5,2). Alternatively, the first operation could be (1+1, 1) to get (2, 1) and so on.

Complete the function is possible in the editor below. isPossible has the following parameter(s): int a: first value in (a, b) int b: second value in (a, b) int c: first value in (c,d) int d: second value in (c,d) Returns: str: Return 'Yes' if (a, b) can be converted to (c,d) by performing zero or more of the operations specified above, or 'No' if not Constraints • 1 sa,b,c,ds 1000

Answer:

(1, -1, 3)

Step-by-step explanation:

Given system of linear equations is,

2x + 3y - 2z = -7 ---------- (1)

x - 2y + 4z = 15 ------- (2)

2y + z = 1 ------------ (3)

Equation (2) multiplied by 2 then subtracted from equation (1),

(2x + 3y - 2z) - 2(x - 2y + 4z) = -7 - 30

(2x - 2x) + (3y + 4y) + (-2z - 8z) = -37

7y - 10z = -37 ------ (4)

Equation (3) multiplied by 10 then added to equation (4),

(20y + 10z) + (7y - 10z) = 10 - 37

27y = -27

y = -1

From equation (3),

2(-1) + z = 1

-2 + z = 1

z = 3

From equation (2),

x - 2(-1) + 4(3) = 15

x + 2 + 12 = 15

x + 14 = 15

x = 1

For this question we know that we have a point (-3,-2) and we want to find an equation perpendicular to the line

y=2/3x-2.

Since both lines are perpendicular we need to satisfy this:

With m1= 2/3. If we solve for m2 we got:

And then we can find the intercept for the new line using the point given with x=-3 and y=-2 and we got this:

And solving for b we got:

And then our final answer would be:

Based on the given conditions, the lock solution is 205.

To solve the lock, to calculate the total score based on the given conditions:

Crocus: + 20

Daffodil: + 25

Snowflake: - 50

Tulip: + 30

Bird-Red: + 25, else + 10

Calculating the scores for each input:

TULIP: +30

CROCUS: +20

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

CROCUS: +20

Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205

Therefore, the solution for the lock is 205.

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Image transcribed:

SPRING NOW LOADING.

<IF CROCUS, THEN +20>

<IF DAFFODIL, THEN +25>

<IF SNOWFLAKE, THEN -50>

<IF TULIP, THEN +30>

<IF BIRD-RED, THEN +25, ELSE + 10>

TULIP

CROCUS

DAFFODIL

TULIP

DAFFODIL

TULIP

DAFFODIL

CROCUS

Solve Lock

Answer:

0.0001815766

Step-by-step explanation:

The definition of negative exponent is  \(a^{-n}=\frac{1}{a^n}\).  For 5.6 to the negative 5 power, write the reciprocal of 5.6 to the 5th.

\(5.6^{-5}=\frac{1}{5.6^5}\)

A calculator can do the rest.  It can also find the decimal value directly.

Answer:

x=9

y=12

Step-by-step explanation:

. Substitute the given value of x into the equation so... -5(2y-15)+4y=3

. y=12

. Substitute the given value of y into the equation x=2y-15 so... x=2 x 12-5

. x=9

.The possible solution of the system is the ordered pair (x,y) so... (x,y)=(9,12)

Answer:

a = 6

Step-by-step explanation:

Given information:

Slope = 6

Coordinates: (-9, 0) and (-8, a)

Slope formula = y2 - y1 / x2 - x1

Substitute the given values into the formula.

6 = a - 0 / -8 - (-9)

6 = a - 0 / 1

6 = a - 0

a = 6

hope this helps!! p.s. i really need brainliest :)

To estimate \(\sf f'(1) \\\) using a positive difference quotient for the function \(\sf f(x) = 3\log(x) \\\), we can use the following formula:

\(\sf f'(1) \approx \frac{f(1+h) - f(1)}{h}\\\)

where \(\sf h \\\) is a small positive value. Let's choose \(\sf h = 0.001 \\\) for our estimation.

First, let's evaluate \(\sf f(1) \\\):

\(\sf f(1) = 3\log(1) = 3\cdot 0 = 0 \\\)

Next, let's evaluate \(\sf f(1+h) \\\):

\(\sf f(1+h) = 3\log(1+h) \\\)

Substituting \(\sf h = 0.001 \\\):

\(\sf f(1+0.001) = 3\log(1.001) \\\)

Now, we can calculate the positive difference quotient:

\(\sf f'(1) \approx \frac{f(1+h) - f(1)}{h} = \frac{3\log(1.001) - 0}{0.001} \\\)

Using a calculator, we find:

\(\sf f'(1) \approx 0.434 \\\)

Therefore, \(\sf f'(1) \approx 0.434 \\\) (rounded to three decimal places).

From the graph of \(\sf f(x) = 3\log(x) \\\), we would expect the estimate \(\sf f'(1) \\\) to be greater than \(\sf f'(1) \\\) since the graph of \(\sf f(x) \\\) is increasing at \(\sf x = 1 \\\).

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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I'm going to try my best to explain 90° rotation:

So, you know that if you rotate something 180°, it's completely flipped (think about spinning around half-way).

Or if you spin something 360°, you spin around the whole way and end up in the same spot that you did when you started.

Notice how 90 is actually 1/4 of 360.

So imagine spinning instead of 180, spinning half of that. so you barely rotate. That's exactly what you're doing to this shape here. and if you do it about the origin counterclockwise, the origin is (0,0) so I drew it in Quadrant III, as you can see in my attachment.

You can see that every point has been moved by 90°, I put all of the variables there so you could visualize it better!

I hope this helped, let me know if you have any questions! :)

Carina can assemble 10 products within the give time

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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The height of the largest photo is 16 inches.

Sydney's senior picture package includes several sizes of portraits. The smallest photo is a 1.5-inch wide and 2 inch tall rectangle.

The largest photo is 12 inches wide and is similar to the smallest photo.

Let's assume that the largest photo's height is h, then we can say the ratio of the largest photo to the smallest photo is given as:\[\frac{h}{2}=\frac{12}{1.5}\]

Simplify the ratio:\[\frac{h}{2}=8\]

Multiplying each side by 2:\[h = 16\]

Therefore, the height of the largest photo is 16 inches.

Hence, the answer is 16.

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