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3 years ago

8

The access code for a car's security system consists of six digits. the first digit cannot be zero and the last digit must be e

ven . how many different codes are available?

1 answer:

Scrat [10]3 years ago

3 0

The first digit can only range from 1-9, resulting in 9 possible options. The last digit can only be 2, 4, 6, and 8, resulting in 4 possible options. The other four digits can range from 0-9, resulting in ten options for each. Using the fundamental counting principle, we can use the following equation to solve for the different amount of codes possible.
$9 \times 10 \times 10 \times 10 \times 10 \times 4 \\ 360000$

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Given that events A and B are independent with P(A)=0.24P(A)=0.24 and P(B|A)=0.85P(B∣A)=0.85, determine the value of P(B)P(B), r

NemiM [27]

Answer:

P(B) = 0.85

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

$P(A) = 0.24, P(B|A) = 0.85$

These events are independent.

This means that $P(A \cap B) = P(A)*P(B)$ . So

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(B|A) = \frac{P(A)*P(B)}{P(A)}$

$P(B|A) = P(B)$

So

$P(B) = 0.85$

5 0

3 years ago

A goat is grazing outside of a rectangular barn that has dimensions 20 ft by 30 ft.

MariettaO [177]

Answer:

108π ft² or 339.29 ft²

Step-by-step explanation:

<em>Refer to attached picture.</em>

<u>The grazing area of the goat is 3/4 of area of circle with 12 ft radius:</u>

A = 3/4(πr²) = 3/4(π*12²) = 108π or 339.29 ft²

5 0

3 years ago

Can someone please help me on this?

pychu [463]

A jump discontinuity occurs when the limits as x approaches a number from the left and right are not equal. Basically, the graph "jumps" from one number to another at that x value.

A point discontinuity occurs when limits as x approaches a number from the left and right are equal, but the actual value of f(x) at x is not equal to the limit. Basically, a point is missing and there is a "hole" in the graph at that x value.

Looking at your graph, you can see that at x=0, the graph "jumps" from a value of 2 as the graph approaches x=0 from the left to a value of 1 as the graph approaches x=0 from the right. That means there is a jump discontinuity at x=0.

You can also see that there is a "hole" in the graph at x=-2 and x=8 as seen by the open circle. There is no hole at x=3 because the circle is filled in. That means there is a point discontinuity at x=-2 and x=8.

Your answer is B) jump discontinuity at x=0; point discontinuities at x=-2 and x=8.

6 0

4 years ago

Find the slope of the line that passes through the points (9, -2) and (4, 3)

vovikov84 [41]

Answer:

-1

Step-by-step explanation:

Formula: $y=mx+b$

<u>Using two points:</u>

Since we are given the $y$ and $x$ value, what is left is the $m$ and $b$ in the formula, which represent slope and the y-intercept.

<u>Slope</u>

$m$ is slope

Formula: $\frac{y_2-y_1}{x_2-x_1}$

Plug points: $\frac{3-(-2)}{4-9}$

Solve: $\frac{5}{-5}$

Simplify: $\bold{m=-1}$

Therefore, the slope is -1

Learn more:

<u>y-intercept</u>

$b$ is the y-intercept

Plug one of the points and the slope into the formula, solve for b: (4, 3)

$3=-1(4)+b$

$3=-4+b$

$3+4=-4+b+4$

$\bold{b=7}$

6 0

3 years ago

A country's education department reported that in 2015, 70.8% of students enrolled in college or a trade school within 12 months

Gennadij [26K]

Answer:

The confidence interval has a lower limit of 0.546 and an upper limit of 0.675.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

In 2017, a random sample of 154 individuals who graduated from high school 12 months prior was selected. From this sample, 94 students were found to be enrolled in college or a trade school.

This means that $n = 154, \pi = \frac{94}{154} = 0.6104$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6104 - 1.645\sqrt{\frac{0.6104*0.3896}{154}} = 0.546$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6104 + 1.645\sqrt{\frac{0.6104*0.3896}{154}} = 0.675$

The confidence interval has a lower limit of 0.546 and an upper limit of 0.675.

6 0

3 years ago