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ololo11 [35]
3 years ago
13

Estimate 10/12 − 3/8 using benchmark values. Your equation must show the estimate for each fraction and the final estimate for t

he expression.
Mathematics
1 answer:
Maksim231197 [3]3 years ago
8 0

Answer: \frac{11}{24}

Step-by-step explanation:

Give expression is,

\frac{10}{12}-\frac{3}{8}

Since L.C.M ( 12, 8 ) = 24

=\frac{10\times 2}{12\times 2}-\frac{3\times 3}{8\times 3}

=\frac{20}{24}-\frac{9}{24}

=\frac{20-9}{24}

=\frac{11}{24}

\text{Hence, }\frac{10}{12}-\frac{3}{8}=\frac{11}{24}

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10) A new car is available in a sedan model and
Dafna11 [192]

Answer:

Option (C) n = 256

Therefore, there are 256 ways to select a car with 2 car models, 8 different colors and any combinations of 4 optional features.

Step-by-step explanation:

A new car is available in a sedan model and a hatchback model.

So that means customers can select the model of the car in,

n₁ = 2 ways

It is available in eight  different colors.

After selecting the model, customers can select the color of the car in,

n₂ = 8 ways

Customers can choose to add any combination of four optional features.

After selecting the color, customers have the choice to add any combination of 4 optional features,

n₃ = 4² = 16 ways

Which means that there are 16 different ways to add 4 optional features e.g.

1. 0, 0, 0, 0

2. 0, 0, 0, 1

3. 0, 0, 1, 0

4. 0, 0, 1, 1

and the list goes on to 16 different ways.

Now the total ways to select a car is given by

n = n₁*n₂*n₃

n = 2*8*16

n = 256

Therefore, there are 256 ways to select a car with 2 car models, 8 different colors and any combinations of 4 optional features.

6 0
3 years ago
Identify the functions that are continuous on the set of real numbers and arrange them in ascending order of their limits as x t
Studentka2010 [4]

Answer:

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

Step-by-step explanation:

1.f(x)=\frac{x^2+x-20}{x^2+4}

The denominator of f is defined for all real values of x

Therefore, the function is continuous on the set of real numbers

\lim_{x\rightarrow 5}\frac{x^2+x-20}{x^2+4}=\frac{25+5-20}{25+4}=\frac{10}{29}=0.345

3.h(x)=\frac{3x-5}{x^2-5x+7}

x^2-5x+7=0

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function h is defined for all real values.

\lim_{x\rightarrow 5}\frac{3x-5}{x^2-5x+7}=\frac{15-5}{25-25+7}=\frac{10}{7}=1.43

2.g(x)=\frac{x-17}{x^2+75}

The denominator of g is defined for all real values of x.

Therefore, the function g is continuous on the set of real numbers

\lim_{x\rightarrow 5}\frac{x-17}{x^2+75}=\frac{5-17}{25+75}=\frac{-12}{100}=-0.12

4.i(x)=\frac{x^2-9}{x-9}

x-9=0

x=9

The function i is not defined for x=9

Therefore, the function i is  not continuous on the set of real numbers.

5.j(x)=\frac{4x^2-7x-65}{x^2+10}

The denominator of j is defined for all real values of x.

Therefore, the function j is continuous on the set of real numbers.

\lim_{x\rightarrow 5}\frac{4x^2-7x-65}{x^2+10}=\frac{100-35-65}{25+10}=0

6.k(x)=\frac{x+1}{x^2+x+29}

x^2+x+29=0

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function k is defined for all real values.

\lim_{x\rightarrow 5}\frac{x+1}{x^2+x+29}=\frac{5+1}{25+5+29}=\frac{6}{59}=0.102

7.l(x)=\frac{5x-1}{x^2-9x+8}

x^2-9x+8=0

x^2-8x-x+8=0

x(x-8)-1(x-8)=0

(x-8)(x-1)=0

x=8,1

The function is not defined for x=8 and x=1

Hence, function l is not  defined for all real values.

8.m(x)=\frac{x^2+5x-24}{x^2+11}

The denominator of m is defined for all real values of x.

Therefore, the function m is continuous on the set of real numbers.

\lim_{x\rightarrow 5}\frac{x^2+5x-24}{x^2+11}=\frac{25+25-24}{25+11}=\frac{26}{36}=\frac{13}{18}=0.722

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

6 0
3 years ago
3 to the -2nd power??
WARRIOR [948]

Answer:3^2=9

U are gonna times 3 two times

Example:3x3=9

7 0
3 years ago
Money that is collecting interest in a bank account doubles in value every 10 years.
MArishka [77]
C . 2 to the power of 9
6 0
3 years ago
A solid cylindrical steel rod has a base area of 100 cm2 and a length of 50 cm. What is the volume of the steel rod?
natulia [17]

Answer:

5000 cm3

Step-by-step explanation:

find radius

cal the volume

4 0
3 years ago
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