Rewrite 2 ^ x = 128as a logarithmic equation !???

Solve for x <img src="https://tex.z-dn.net/?f=x%20%2B%2015%20%3D%208" id="TexFormula1" title="x + 15 = 8" alt="x + 15 = 8" al

Makovka662 [10]

Answer:

x = -7

Step-by-step explanation:

Subtract 15 from both sides of the equation.

x = 8 -15 = -7

8 0

4 years ago

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans an

Y_Kistochka [10]

Answer: a) 15, b) 1.

Step-by-step explanation:

A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?

(a) 10% of all adult Americans support the changes

Here, $np>5\ and\ n(1-p)>5$

And , $p=0.10$

So, consider the equality, to find the value of 'n'.

$np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50$

So, there are $50-35=15$ more adult Americans needed.

(b) 15% of all adult Americans supports the changes

Here, $p=0.15$

So, again we get that

$np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34$

So, there are $35-34=1$ more adult Americans needed.

Hence, a) 15, b) 1.

5 0

3 years ago

EVALUATE THE WORD PROBLEMS

andrezito [222]

Another effective strategy for helping students improve their mathematics performance is related to solving word problems. More specifically, it involves teaching students how to identify word problem types based on a given problem’s underlying structure, or schema. Before learning about this strategy, however, it is helpful to understand why many students struggle with word problems in the first place.

Difficulty with Word Problems

Most students, especially those with mathematics difficulties and disabilities, have trouble solving word problems. This is in large part because word problems require students to:

7 0

3 years ago

The perimeter of a rectangular carton is 60 inches. If the width of the carton is 11 inches, calculate its length

Thepotemich [5.8K]

Answer:

19 inche

Step-by-step explanation:

Perimerer of rectangle = 2(length + breadth)

60 = 2(length + 11)

60/2 = (length + 11)

30 - 11 = length

19 = length

6 0

3 years ago

Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

x = 2
y = -1

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

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

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

4 0

3 years ago