Myron got his paycheck of $40 this weck. He had $11 left after he spent m dollars on new video

Solve for x using technology 2 log 3(x-1)=log(4 x 2-25)

bagirrra123 [75]

2 log 3(x-1)=log(4 x 2-25)
1. Determine the domain. Since the input to the log function cannot be zero or negative, 4x^2-25 must be ≥ 0. Thus, x^2 must be >0, or x>0. Same domain applies to log (3(x-1); x must be > 0.
2. Rewrite 2 log 3(x-1) as log 3(x-1)^2.
3. Then we have log 3(x-1)^2 = log(4 x 2-25). We can discard the operator "log" from both sides: 3(x-1)^2 = 4 x 2-25. There are various ways in which to solve this. Since you're supposed to "use technology,"
graph y = 3(x-1)^2 and y = 4x^2 - 25 on the same set of axes. Determine, using visual estimation or your calculator's tools, the value or values of x that satisfy this equation. My result was x=3, y =11.

3 0

3 years ago

"6. A brand name has a 40% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small s

statuscvo [17]

Answer:

(a) The probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b) The probability that all of the selected consumers recognize the brand name is 0.0041.

(c) The probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d) The events of 5 customers recognizing the brand name is unusual.

Step-by-step explanation:

Let X = number of consumer's who recognize the brand.

The probability of the random variable X is, P (X) = p = 0.40.

A random sample of size, n = 6 consumers are selected.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...$

(a)

Compute the value of P (X = 5) as follows:

$P(X=5)={6\choose 5}0.40^{5}(1-0.40)^{6-5}\\=6\times0.01024\times0.60\\=0.036864\\\approx0.0369$

Thus, the probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b)

Compute the value of P (X = 6) as follows:

$P(X=6)={6\choose 6}0.40^{6}(1-0.40)^{6-6}\\=1\times 0.004096\times1\\=0.004096\\\approx0.0041$

Thus, the probability that all of the selected consumers recognize the brand name is 0.0041.

(c)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = P (X = 5) + P (X = 6)

= 0.0369 + 0.0041

= 0.041

Thus, the probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d)

An event is considered unusual if the probability of its occurrence is less than 0.05.

The probability of 5 customers recognizing the brand name is 0.0369.

This probability value is less than 0.05.

Thus, the events of 5 customers recognizing the brand name is unusual.

8 0

4 years ago

What is the product?

Alexxandr [17]

The correct answer is a)

3 0

3 years ago

nick has to build a brick wall. Each row of the wall requires 6/2 bricks. There are 10 rows in the wall. How many bricks will ni

alex41 [277]

Answer:

D. 10 x 6/2

Step-by-step explanation:

each row = 6/2

10 rows all together

so you do 10 x 6/2

5 0

3 years ago

Syyedah throws a baseball with an initial velocity of 30 meters per second from a roof at an initial height of 75 meters. Write

Yuliya22 [10]

Initial velocity: v o = 30 m/s
h = 75 m
h = v o * t + g * t² / 2
75 = 30 · t + 9.8 · t² / 2
75 = 30 t + 4.9 t²
An equation is: y = 4.9 t² + 30 t - 75
4.9 t² + 30 t - 75 = 0
$t_{12}= \frac{-30+/- \sqrt{900+1470} }{9.8}= \\ =\frac{-30+48.68}{9.8}$
t = 1.9 s

4 0

3 years ago