Is (–5, 0.5) a solution of this system? x – 4y = –7, 0.2x + 2y = 0 Substitute (–5, 0.5) into x – 4y = –7 to get . Substitute (–5

Answer:

The anticipated number of tests required to identify 680 acceptable circuits is 907.

Step-by-step explanation:

For any circuit, there are two potential results: it either passes the test or it fails. The likelihood of passing is independent between circuits. Therefore, we apply the binomial probability distribution to address this scenario.

Binomial probability distribution

This distribution calculates the chance of obtaining exactly x successes across n trials, where x has only two possible outcomes.

To find the expected number of trials to achieve r successes with a probability p, the formula is given by:

Circuits from a specific factory pass a certain quality evaluation with a probability of 0.75.

Thus, to determine the expected number of tests needed for 680 acceptable circuits, let’s denote this as E where r = 680.

The expected number of tests necessary to find 680 acceptable circuits is 907.

The accurate statements are 0.75 (x,y) = (0.75x, 0.75y), LM is parallel to L'M', and "the vertices of the image are nearer to the origin relative to the pre-image".

Explanation:

It is stated that the triangle ABC underwent dilation as per the rule DO,0.75 (x,y)

DO, 0.75(x,y) signifies the dilation rule, where both x and y values are scaled by 0.75, indicating that the dilation, centered around the origin, has a scale factor of 0.75. The representation for this dilation would be,

Consequently, the first statement holds true.

Since both x and y coordinates are scaled down by 0.75, the sides of the image are parallel, but shorter, with a scale of 0.75 compared to the pre-image’s sides.

Thus, the second statement "LM is parallel to L'M'" is also accurate, while the third and fifth statements are incorrect.

The scale factor of 0.75, being less than 1, suggests that the vertices of the image are closer to the origin compared to those of the pre-image.

Hence, the fourth statement "The vertices of the image are nearer to the origin compared to the pre-image" is indeed correct.

Answer:

a.  0.68 or 68%

b. 0.08 or 8%

c. 0.32 or 32%

Step-by-step explanation:

The probability of contacting the client on the first call is 60%

The likelihood of reaching the client on the second call is 20%

a. The chance of the manager successfully connecting with her client within two calls is the sum of the chances for one or two calls:

b. The probability that the manager connects during the second call but not the first is:

c. The probability that the manager fails to connect in two consecutive calls (requiring more calls) is P(X>2):

Every confidence interval correlates with a specific z value. As the confidence interval expands, so does the corresponding z value.
You can compute the confidence interval using the formula:

Here represents the mean, z is the respective z value, s denotes the standard deviation, and n indicates the sample size.
Standard deviation is simply the square root of variance:

For a confidence interval of 95%, the z value is <span>1.960.
</span>Now, we can compute the confidence interval for our income: