Which answers are examples of deductive reasoning? Select each correct answer.

Simplify the expression. Assume that all variables are positive. Exponents in simplified form should all be

Rainbow [258]

Given:

The given expression is $\frac{7^{\frac{1}{2}} \cdot 7^{\frac{3}{2}}}{7^{-3}}$

We need to determine the exponents in simplified form.

Exponents in simplified form:

Let us determine the exponent in simplified form.

Let us apply the exponent rule $\frac{x^{a}}{x^{b}}=x^{a-b}$

Thus, we have;

$7^{\frac{1}{2}+\frac{3}{2}-(-3)}$

Adding the fractions, we get;

$7^{\frac{4}{2}-(-3)}$

Cancelling the common terms, we have;

$7^{2-(-3)}$

Simplifying the exponent, we get;

$7^{2+3}$

Adding the exponent, we have;

$7^5$

Thus, the simplified form of the expression is $7^5$

8 0

3 years ago

34. A motorist started a journey at 10.25a.m. and ended at 6.15 p.m. Calculate the time

GenaCL600 [577]

Write the times for each hour from start time:

10:25 am

11:25 am

12:25 pm

1:25 pm

2:25 pm

3:25 pm

4:25 pm

5:25 pm

6:25 pm

There are 8 hours between 10:25 am and 6:25 pm.

they finished at 6:15 which is 10 minutes before 6:25 ( 25-15 = 10)

10 minutes less than a full hour is 50 minutes ( 60 - 10 = 50)

8 hours - 1 hour = 7 hours

7 hours + 50 minutes = 7 hours 50 minutes total time.

4 0

3 years ago

Read 2 more answers

Find the dimension of the subspace spanned by the given vectors. [Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column ne

vladimir1956 [14]

Answer:

4

Step-by-step explanation:

Given the following column vectors

(1, -2, 0), (-1, 3, 1), (2, 1, 5) and (-1, 1, 1)

Before we can get the dimension of the vector, the following steps must be followed;

Step 1:

We need to transform the vectors given into a matrix form and then reduce the resulting matrix.

Step 2:

Then we generated the basis of the matrix (new set of column vectors from the reduced matrix).

Step3:

The total number of column vectors generated will be equivalent to the dimension of the vectors.

The dimension spanned by the set of vectors is 4

Check the attachment for calculation

4 0

3 years ago

Yesterday your bus ride to school took 10 minutes. Today your bus ride took 12 minutes. What is the percent of change?

Readme [11.4K]

The percent of increase from 10 to 12 is 20 %. 10 x 1.2 = 12.

Hope This Helps You!
Good Luck Studying :)

5 0

3 years ago

Read 2 more answers

A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C is required to kill a destructive cro

VMariaS [17]

Answer:

From Commercial spray X: 4 liters from Chemical A, 8 liters from Chemical B and 8 liters from Chemical C.
From Commercial spray Y: 18 liters of Chemical C
From Commercial spray Z: 8 liters of Chemical A and 8 liters of Chemical B.

Step-by-step explanation:

Since we need a lot of chemical C, we are going to leave Commercial spray Y for last in case we lack in case we need more Chemical C, which is supplied by spray Y.

We need to cover the demand of both chemical A and B. For each liter of Chemical A we get 2 liters of Chemical B by using Commercial spray X. And for each liter of Chemical A we get 2 liters of Chemical B by using spray Z.

We will call X the number of units of Commercial spray X used, where each unit contains 1 liter of Chemical A, 2 liters of Chemical B and 2 iters of Chemical C. Y is the number of units of Commercial spray Y used, containing each of them 1 liter of Chemical C, and Z the number of units of commercial spray Z used, on units containing both 1 liter of Chemical A and Chemical B.

We can represent the amount of liters we have for each chemical on a vector of the form (a,b,c) where a reresents the amount of Chemical A, b the amount of chemical B, and c the amount of chemical C. We want (a,b,c) to be equal to (12,16,26), in other words, we want a to be 12, b to be 16 and c to b 26. Furthermore we can obtain (a,b,c) by using this equation

(a,b,c) = X * (1,2,2) + Y * (0,0,1) + Z * (1,1,0) = (1*X+0*Y+1*Z,2*X+0*Y+1*Z,2*X+1*Y+0*Z) = (X+Z,2*X+Z,2*X+Y)

Thus, we have

a = X+Z = 12
b = 2*X+Z = 16
c = 2*X+Y = 26

We can substract the second equation with the first one to obtain the value of X:

X = b-a = (2*X+Z)-(X+Z) = 16-12 = 4

Replacing X by 4, we obtain on the first expression that 4+Z = 12, hence, Z = 8. Since X is 4, 2*X+Y = 8+Y = 26. This gives us that Y must be 18.

We conclude that we need the following amount of Chemical A, B and C:

From Commercial spray X: 4, 4*2 = 8 and 4*2 = 8 liters respectively
From Commercial spray Y: 18 liters of Chemical C
From Commercial spray Z: 8 liters of Chemical A and 8 liters of Chemical B.

I hope i could help you!

6 0

3 years ago