a) The sum of the three dimensions of a cuboid is 48 cm and the ratio among the lengths of its dimensions is 5: 4:3, Find its area.​ (grade 6)

Step-by-step explanation:

A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point.

Answer: 9/16 as a decimal is 0.5625

9-16-as-a-decimal-is-0.5625

Let's look into the two methods to write 9/16 as a decimal.

Explanation:

Method 1: Writing 9/16 as a decimal using the division method

To convert any fraction to decimal form, we just need to divide its numerator by denominator.

Here, the fraction is 9/16 which means we need to perform 9 ÷ 16

This gives the answer as 0.5625. So, 9/16 as a decimal is 0.5625

Method 2: Writing 9/16 as a decimal by converting the denominator to powers of 10

Step 1: Find a number such that we can multiply by the denominator of the fraction to make it 10 or 100 or 1000 and so on.

Step 2: Multiply both numerator and denominator by that number to convert it into it's an equivalent fraction.

Step 3: Then write down just the numerator, putting the decimal point in the correct place, that is, one space from the right-hand side for every zero in the denominator.

9/16 = (9 × 625) / (16 × 625) = 5625/10000 = 0.5625

Irrespective of the methods used, the answer to 9/16 as a decimal will always remain the same.

You can also verify your answer using Cuemath's Fraction to Decimal Calculator.

Thus, 9/16 as a decimal is 0.5625

Step 1

State the compound interest formula

where;

Step 2

Find the amount after 22 years

Answer;

The 10th figure will have 19 blocks.

An arithmetic progression (AP) is a sequence in which the differences between each successive term are the same. The formula Tₙ = a+(n-1)d finds the general term (or) nth term of an AP whose first term is 'a' and the common difference is 'd'.

In the given figures,

Figure 1 has 1 block.

Figure 2 has 3 blocks.

Figure 3 has 5 blocks.

We have to find the number of blocks in the 10th figure.

The number of blocks in the figures are forming an arithmetic progression of 1,3,5.....with a common difference of 2.

So the 10th term of AP can be calculated as,

[tex]T_{10} = 1 + (10 -1)2[/tex]

[tex]T_{10} = 1 + 9*2[/tex]

[tex]T_{10} = 19[/tex]

Therefore, the 10th figure will have 19 blocks.

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The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

What is rectangle short answer?

the points (-1 , 2) and (3 , 2 ) form one the of the rectangle w =     [tex]\sqrt{( 3 + 1 )^{2} + ( 2 - 2 )^{2} }[/tex]

= [tex]\sqrt{4^{2} + 0 }[/tex]

= √ 16

= 4

The length can be obtained by finding distance between the points (-1,2) and ( -1, - 5)  = [tex]\sqrt{( -1 -2 )^{2} + ( -5 + 1)^{2} }[/tex]

                 = [tex]\sqrt{(-3)^{2} + ( -6)^{2} }[/tex]

                 = √9 + 36

                  = √45 = 3√5

The perimeter of the rectangle is: P = 2( w + L) = 2( 4 + 3√5) ⇒ 8 + 6√5 unit

The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

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The length and breadth should be 2 feet each and height should be 3 feet to minimize the cost of the materials.

Let consider the length of the box =x

considering a square bottom ,

length = breadth = x

and let the height  =h

The surface area of the box is

SA = x² + 4xh      ( box is open from top )

cost of 1sq feet material for bottom =$3    

cost of 1sq feet material for sides =$1    

The cost functions can be written as

C =  3x² + 1(4xh)

C =   3x² + 4xh

Also the volume equation is

x²h = 12

h = 12/x²

substituting the value of h into the cost function.

C =  3x² + 4x (12/x²)

C =  3x² + 48/x

C = (3x³ + 48)/ x

Take the derivative of C and set it equal to zero. So we get

6x³ - 48 = 0

x³ = 48/6 = 8

x = 2

∴ h = 12/x²

h = 12/4

h = 3

This is the value of x and h that minimizes the cost.

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Answer:

To decrease it by 13% we will multiple (100-13 = 87) .

Step-by-step explanation:

Multiply the decimal form of the number (in this case 13) to the number.

For example: 13% of 50

13% can also be said as 0.13 in decimal form.

50*0.13=6.5

13% of 50 is 6.5.

The radius of the hole to the nearest hundredth of a foot is 2.88 feet.

What is radius?

The volume of the cylinder, V = 4200 cubic feet

Height, H = 2.1 miles = 11088 feet

The volume of the cylinder is given by the formula, V =πr²H

Putting values in the formula to find out radius,

4200=πr²(11088)

r²=[(11088)π]/4200

r²=8.2938

r=2.879~2.88 feet

The radius of the hole to the nearest hundredth of a foot is 2.88 feet.

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For 1 xylobar and 2 yackities Dado would pay $0.61   .

In the question ,

it is given that

Zimak paid $1.75 for 3 xylobars and 5 yackities .

let the price of 1 xylobar = x

and let the price of 1 yackities = y

According to the question

3x+5y=1.75    ...(i)

Jeejunu paid $1.88 for 4 xylobars and 1 yackity .

So , equation becomes

4x+y=1.88    ...(ii)

y = 1.88-4x

substituting it in equation (i), we get

3x + 5(1.88 - 4x) = 1.75

3x + 9.4 - 20x = 1.75

20x-3x = 9.4 - 1.75

17x = 7.65

x = 7.65/17

x = 0.45

So, the price of 1 xylobar = $0.45

put x = 0.45 in y= 1.88-4x , we get

y = 1.88 - 4(0.45)

y = 1.88 - 1.8

y = 0.08

So , the price of 1 yackity is $0.08   .

So, For 1 xylobar and 2 yackities , Dado would pay

= x+2y

= 0.45 + 2(0.08)

= 0.45+0.16

= 0.61

Therefore , for 1 xylobar and 2 yackities Dado would pay $0.61   .

The given question is incomplete , the complete question is

Zimak bought 3 xylobars and 5 yackities from the intergalactic candy store for $1.75 . Jeejunu paid  $1.88 and got 4 xylobars and 1 yackity . How much would dado pay for 1 xylobar and 2 yackities ?

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Answer in the attachment

Answer:

319

Step-by-step explanation:

hope this helps

The expected number of unaffected kittens should be 84

Find the below calculation of chi square:

Category   Affected Unaffected Total

Observed values   44                 84                 128

Expected Ratio         1                  3                   4

Expected Values, E  32             96

Deviation, D              12              -12

Deviation Squared     14            144

D^2/E                           4.5      1.5                  6

X^2                               6  

Degrees of freedom                       -                  1

Unaffected number of kittens:

Observed values for Affected=44

Total=128

25% of the 128 are affected.

The unaffected proportion is,

Total-Observed values for Affected kittens

=128-44

=84

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By evaluating f(x) in x = 3, we will get that:

f(3) = 4

Thus the correct option is D:

Here we have the following function:

[tex]f(x) = x + \frac{\sqrt{x + 1} }{x - 1}[/tex]

We want to get f(3), and to get that, we just need to replace all the "x" in the equation by the number 3, we will get:

f(3) = 3 + (3 + 1)/(3 - 1)

f(3) = 3 + √4/2 = 4

With this, we can conclude that the correct option is D:

f(3) = 4.

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Answer: 7921   123569 5410

Step-by-step explanation:

1. 7912

2. 123569

3. 5210

The scalar factor is of 6.

What is the scalar factor?

A scale factor is the ratio between corresponding measurements of an object and a representation of that object. in simple words how big or small is one object compared to another.

We are given two triangle and the measurements of the corresponding sides of the triangle.

side of one triangle is 4 and side of another triangle is 24.

To find the scalar factor we divide the two

We get the answers as 6

Hence the scalar factor is of 6

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If a value that is is greater than 100% of the original value will always be larger than original value.

If a value is less than 1% of the original value will always be less than the original value.

Given,

A value that is greater than 100% of the original value.

And it is 1% less than the original value.

We have to compare these values with the original value;

That is,

A value that is greater than 100% of the original value,

eg;

130% of 20 = 20 × 130/100 = 26

26 is greater than 20.

That is,

If a value that is is greater than 100% of the original value will always be larger than original value.

Next,

It is 1% less than the original value.

eg;

1% of 20 = 1/100 × 20 = 0.2

0.2 is less than 20

That is,

If a value is less than 1% of the original value will always be less than the original value.

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Answer: Hello Love I believe the answer is the LAST one

Step-by-step explanation:

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities. Equivalent inequality refers to linear inequalities with the same solution. Both equality and inequality are subject to laws. For inequality involving smaller than or equal to () and greater than or equal to (), all the principles listed below apply. Let's look at some of the key inequality rules for all these operations before learning how to solve linear inequalities.

As with multi-step linear equations, start by separating the variable from the constants when resolving multi-step linear inequalities with one variable. According to the laws of inequality, it is crucial that we remember to flip the inequality sign when multiplying or dividing with negative values while resolving multi-step linear inequalities.

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The composite functions of  (f o g)(x), (g o f)(x) and their domains in the function f( x ) = x² + x and  g( x ) = 1/(x+1) are (x+2) / (x+1)², Domain: {x|x ≠ -1 } and 1/(x² + x + 1 ), Domain: {x|x ∈ R } respectively.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, set up the composite result function (f o g)(x).

(f o g)(x) = f( g(x) )

f( x ) = x² + x

f( g(x) ) = f( 1/(x+1) )  = ( 1/(x+1) )² + 1/(x+1)

Apply product rule to simply

f( g(x) ) = 1² /(x+1)² + 1/(x+1)

f( g(x) ) = (1 + x + 1 )/ (x+1)²

f( g(x) ) = (x+2) / (x+1)²

Next, find the domain by equating the denominator to 0 and solve for x.

x + 1 = 0

x = -1

Domain: {x|x ≠ -1 }

For (g o f)(x), set up the composite result function (g o f)(x).

(g o f)(x) = g( f(x) )

g( x ) = 1/(x+1)

g( f(x) ) = g( x² + x ) = 1/( (x² + x) + 1 )

g( f(x) ) = 1/( (x² + x) + 1 )

g( f(x) ) = 1/(x² + x + 1 )

Next, find the domain by equating the denominator to 0 and solve for x.

x² + x + 1 = 0

x = ( -1±√(1² - 4 ×(1×1) ) / (2 × 1 )

x = (-1±i√3)/2

x = (-1+i√3)/2, (-1-i√3)/2

Hence,

Domain is set of all real numbers.

Domain: {x|x ∈ R }

Therefore the composite functions and their domain are (x+2) / (x+1)², Domain: {x|x ≠ -1 } and 1/(x² + x + 1 ), Domain: {x|x ∈ R }.

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Notice that:

Which means that, for large values of x:

Since the function:

is a 4th degree monomial, with positive coefficient, then it keeps growing as x grows. Then, we know that:

Which means that the end behavior is such that f(x) approaches infinity as x approaches infinity.

On the other hand, for large negative values of x, the function is also positive. Then:

The value of x in the angles is equal t0 15

To solve this problem, we can simply apply the theorem that states the sum of angles in a straight line is equal to 180 degrees.

This implies that;

[tex]AOF + FOG + GOB = 180^0[/tex]

substituting the values into the equation;

[tex]AOF + FOG + GOB = 180^0\\(5x -15) + 90 + 2x = 180[/tex]

Let's solve for x

[tex]5x - 15 + 90 + 2x = 180\\7x + 75 = 180\\7x = 105\\x = 15[/tex]

The value of x that makes the angles equal to 180 degrees is 15.

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The area of a regular polygon is 84.87 in²

A polygon with congruent sides and equal angles is referred to as a regular polygon. Equilateral triangles, squares, regular pentagons, and more are examples of regular polygons.

In this case Formula of the area of the equilateral triangle is (  [tex]\sqrt{3\\}[/tex]×a²)/4

where a is the length of the side of triangle.

Here the length of the side of the polygon(triangle) is 14in.

So the area of the equilateral triangle is (√3xa²)/4.

And a=14 in the above equation.

So the area of the regular polygon is: (√3x14x14)/4 =84.87 in²

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Let:

A = students who passed the test = 14

B = students who completed the assignment = 13

N = Total students = 22

(A⁺ ∩ B⁺) = 6

P(A ∪ B) = 1 - 6/22 = 8/11

P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 14/22 + 13/22 - 8/11 = 1/2

P(A|B) = P(A ∩ B)/P(B) = (1/2)/(13/22) = 11/13 ≈ 0.85 ≈ 85%

There are two questions to be solved, therefore, I'll solve the buckets one first and then I'll solve the other one. To solve both we need to apply LCM (least common multiple).

There are three buckets with differente capacities, one with 15 litres, one with 18 litres and one with 24 litres. Since they can fill a drum in an exact number of times, this means that the capacity of the drum is a multiple of the capacity of each bucket, therefore we should break each number into their multiples and find the common ones as shown below.

We now need to multiply all the common multiples:

For the second problem we have three items a book, a pen and a box. They cost respectively 36, 45 and 54. We need to then find the smallest sum of money that could buy a exact number o each item. We need to apply LCM once again as shown below:

We now need to multiply all the common multiples:

Answer: [tex]x=20, m\angle 1=109^{\circ}, m\angle 2=71^{\circ}[/tex]

Step-by-step explanation:

Angles that form a linear pair add to 180 degrees, so:

[tex]5x+9+3x+11=180\\\\8x+20=180\\\\8x=160\\\\x=20\\\\\implies m\angle 1=5(20)+9=109^{\circ}\\\\\implies m\angle 2=180^{\circ}-109^{\circ}=71^{\circ}[/tex]

Answer:

The answer is 3 or 3/1

Step-by-step explanation:

The equation you use is m=y2-y1/x2-x1

Answer:

Slope = 3

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define two points on the line from the given table:

Substitute the defined points into the formula:

[tex]\implies \textsf{Slope}=\dfrac{13-7}{4-2}=\dfrac{6}{2}=3[/tex]

Note:

Therefore, the question may require you to enter 6/2 into the answer boxes.  However, the slope of the line is 3.

The final point where -(-7)−(−7) number after simplification lie is 14

In the above question it is given,

-(-7)−(−7)

We need to find the position of this number on the number line.

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can be infinitely expanded in any direction.

To do that, we will first simplify the given numbers by using the sign rules of the real numbers

According to the sign rule of real numbers,

(i) (-) x (-) = +

(ii) (-) x (+) = -

(iii) (-) +(-) = -

(iv) (+) + (+) = +

Now using the above sign rules, we will simplify the given number

-(-7)−(−7)

-(-7)+ [-(−7)]

7 + 7

Now, on the number line, we'll move 7 steps in the positive direction of 0, we'll be on 7. Again from 7 we'll take next 7 steps in the same direction and we'll reach the point 14.

Hence, 14 is the final point where -(-7)−(−7) number after simplification lie.

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Answer:

y > 15

Step-by-step explanation:

y + 7 > 22 ( subtract 7 from both sides )

y > 15

Answer:

23

110

Step-by-step explanation:

We have a + 1/a = 5

(a + 1/a)² = a² + (1/a²) + 2.a.1/a =  a² + (1/a²)  + 2

But (a + 1/a)² = 5² = 25

So a² + (1/a²) = 25 - 2 = 23

(a + 1/a)³ = a³ + 3a²(1/a) + 3a(1/a)² + (1/a)2

= a³ + 1/a³ + 3a + 3/a

= a³ + 1/a³ + 3(a + 1/a)

= a³ + 1/a³ + 3(5)

=  a³ + 1/a³ + 15

But (a + 1/a)³ = 5³ = 125

So

a³ + 1/a³ + 15 = 125

a³ + 1/a³  = 110

Answer:

23 and 110

Step-by-step explanation:

using the expansion

(a + b)² = a² + 2ab + b² , then

a + [tex]\frac{1}{a}[/tex] = 5 ( square both sides )

(a + [tex]\frac{1}{a}[/tex] )² = 5²

a² + 2(a × [tex]\frac{1}{a}[/tex] ) + [tex]\frac{1}{a^2}[/tex] = 25

a² + 2(1) + [tex]\frac{1}{a^2}[/tex] = 25

a² + 2 + [tex]\frac{1}{a^2}[/tex] = 25 ( subtract 2 from both sides )

a² + [tex]\frac{1}{a^2}[/tex] = 23

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

using the expansion

(a + b)³ = a³ + b³ + 3ab(a + b) , then

a + [tex]\frac{1}{a}[/tex] = 5 ( cube both sides )

(a + [tex]\frac{1}{a}[/tex] )³ = 5³

a³ + [tex]\frac{1}{a^3}[/tex] + 3(a × [tex]\frac{1}{a}[/tex] )(a + [tex]\frac{1}{a}[/tex] ) = 125

a³ + [tex]\frac{1}{a^3}[/tex] + 3(1)(5) = 125

a³ + [tex]\frac{1}{a^3}[/tex] + (3 × 5) = 125

a³ + [tex]\frac{1}{a^3}[/tex] + 15 = 125 ( subtract 15 from both sides )

a³ + [tex]\frac{1}{a^3}[/tex] = 110

(f + d)/c.

First get rid of -d on the left side by adding d to both sides

cx - d = f  -->   cx = f + d

Then remove c from the left side by dividing both sides by c.

cx = f + d  -->  x = (f + d)/c

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