What is the value of x in this equation? Enter your answer in the box.

Mathematics

2 answers:

NikAS [45]3 years ago

8 0

Answer:

x = 6

Step-by-step explanation:

Using the rule of exponents

$a^{m}$ × $a^{n}$ ⇔ $a^{(m+n)}$

Consider

10³ × $10^{x}$ = $10^{9}$ , then

$10^{3+x}$ = $10^{9}$

Equating exponents

3 + x = 9 ( subtract 3 from both sides )

x = 6

Oduvanchick [21]3 years ago

7 0

Answer:

x=6

Step-by-step explanation:

Create equivalent expressions in the equation that all have equal bases, then solve for x.

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How to solve x^2>4x+3

Papessa [141]

Treat this as you would the quadratic equation x^2 - 4x - 3 + 0. Solve this by completing the square:

x^2 - 4x + 4 - 4 - 7 = 0

(x^2 - 4x + 4) = 11

(x-2)^2 = 11, and so x-2 = plus or minus sqrt(11).

Graph this, using a dashed curve (not a solid curve). Then shade the coordinate plane ABOVE the graph.

7 0

3 years ago

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

attashe74 [19]

Answer:

$0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286$

$0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562$

The 99% confidence interval would be given by (0.286;0.562)

Step-by-step explanation:

Information given:

$X= 36$ represent the families owned at least one DVD player

$n= 85$ represent the total number of families

$\hat p=\frac{36}{85}= 0.424$ represent the estimated proportion of families owned at least one DVD player

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.05$ . And the critical value would be given by: