(06.05 MC)

Dylan surveyed the students at his sports camp to find out if they like diving and/or boxing. The table below shows the results of the survey:









Like Diving




Do Not Like Diving




Total





Like Boxing


28

12

40



Do Not Like Boxing


20

5

25



Total


48

17

65



If a student likes diving, what is the probability that student also likes boxing?

43.1%
58.3%
70.0%
73.8%

sqrt(32) = 5.66

 so it is in section B

Answer:

section B.

YOUR WELCOME

After setting up a system of equations based on the given age relationships and solving for both Grace and Joseph, we deduce that Grace is 20 years old and Joseph is 40 years old currently.

Let's denote Grace's current age as G and Joseph's current age as J. According to the problem, Grace is half of Joseph's age, so we have the first equation:

G = 0.5 * J

In 10 years, Grace will be three-fifths of Joseph's age, giving us the second equation:

G + 10 = (3/5) * (J + 10)

Ten years ago, Grace was one-third of Joseph's age, which gives us the third equation:

G - 10 = (1/3) * (J - 10)

We now have a system of three equations with two variables. We can solve this system to find the current ages of Grace and Joseph. After solving for G and J, we find that Grace is 20 years old and Joseph is 40 years old.

I believe the problem ask for s which is the standard deviation. We must recall that the formula for z statistic is stated as:

z = (x – x over bar) / s

Where,

z = z statistic = 2.5

x = sample value or sample score = 102

x over bar = the sample mean or sample average  = 100

s = standard deviation = unknown

Rewriting the equation in terms of s:

s = (x – x over bar) / z

Substituting the given values into the equation:

s = (102 – 100) / 2.5

s = 0.8  

Therefore the standard deviation s is 0.8

Answer:

u didn't provide a chart but the dependent variable is the y axis, or the vertical line

Step-by-step explanation:

It's always the y axis (the vertical line)

The probability of independent events Q and R both occurring is calculated by multiplying the individual probabilities of each event. Thus in this case, P(Q and R) = (1/8) * (2/5) = 1/20.

The question posed asks for the probability of events Q and R both occurring. Given that Q and R are independent events, the likelihood of both happening is calculated by multiplying the probabilities of each event.

That is, P(Q and R) = P(Q)P(R). From the question, we know that P(Q) is 1/8 and P(R) is 2/5.

Therefore, the probability of both Q and R occurring would be (1/8) * (2/5) = 1/20.

https://brainly.com/question/32917010

#SPJ2

Answer:

The explicit formula of the geometric sequence is:

                   [tex]a_n=4\times 5^{n-1}[/tex]

Step-by-step explanation:

The explicit formula is the expression where the nth term is given in terms of the first term of the sequence.

We know that the explicit formula for a geometric sequence is given by:

       [tex]a_n=(a_1)^{r-1}[/tex]

Here we are given:

The second and fifth terms as: 20 and 2500 respectively.

i.e.

[tex]a_2=20[/tex] and  [tex]a_5=2500[/tex]

i.e.

[tex]ar=20\ and\ ar^4=2500[/tex]

Hence,

[tex]\dfrac{ar}{ar^4}=\dfrac{20}{2500}\\\\\\\dfrac{1}{r^3}=\dfrac{1}{125}\\\\\\(\dfrac{1}{r})^3=(\dfrac{1}{5})^3\\\\\\\dfrac{1}{r}=\dfrac{1}{5}\\\\\\r=5[/tex]

Also,

we have:

[tex]ar=20\\\\i.e.\\\\a\times 5=20\\\\i.e.\ a=4[/tex]

Hence, the explicit formula is given by:

         [tex]a_n=4\times 5^{n-1}[/tex]

Final answer:

There can be 900,000 unique 6-digit numbers formed using the digits 0-9 with repetitions allowed, considering the first digit cannot be 0.

Explanation:

Calculating 6-Digit Numbers with Repetitions

The question pertains to the number of unique 6-digit combinations that can be made from the digits 0-9 when repetitions are allowed. Since the first digit of a 6-digit number cannot be 0 (as it would make the number a 5-digit number), there are 9 possibilities for the first digit (1-9). For each of the five remaining positions, all 10 digits (0-9) are possibilities because we are allowing repetitions. Therefore, the total number of combinations is calculated by multiplying the possibilities for each digit place.

The solution is as follows: 9 possibilities for the first digit times 10 possibilities for each of the second, third, fourth, fifth, and sixth digits.

9 (first digit) * 10 (second digit) * 10 (third digit) * 10 (fourth digit) * 10 (fifth digit) * 10 (sixth digit) = 900,000 unique 6-digit numbers that can be formed.

Segment AB has slope 0. Segment DE, with midpoints of AC and BC, also has slope 0. Thus, DE is parallel to AB.

To prove that segment DE is parallel to segment AB, we need to show that the slopes of both segments are equal.

The slope of segment AB, denoted as [tex]\( m_{AB} \)[/tex], can be calculated using the coordinates of points A and B:

[tex]\[ m_{AB} = \frac{{y_B - y_A}}{{x_B - x_A}} \][/tex]

Given that point A is at (0, 0) and point B is at [tex]\((x_2, 0)\)[/tex], the slope [tex]\( m_{AB} \)[/tex] is:

[tex]\[ m_{AB} = \frac{{0 - 0}}{{x_2 - 0}} = 0 \][/tex]

Now, let's find the coordinates of points D and E.

Point D lies on segment AC, so it is at the midpoint of segment AC. Therefore, the coordinates of point D, denoted as [tex]\((x_{D}, y_{D})\)[/tex], are the average of the coordinates of points A and C:

[tex]\[ x_{D} = \frac{{x_1 + 0}}{2} = \frac{{x_1}}{2} \][/tex]

[tex]\[ y_{D} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]

Similarly, point E lies on segment BC, so it is at the midpoint of segment BC. Therefore, the coordinates of point E, denoted as [tex]\((x_{E}, y_{E})\)[/tex], are the average of the coordinates of points B and C:

[tex]\[ x_{E} = \frac{{x_1 + x_2}}{2} \][/tex]

[tex]\[ y_{E} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]

Now, let's calculate the slope of segment DE, denoted as [tex]\( m_{DE} \)[/tex]:

[tex]\[ m_{DE} = \frac{{y_{E} - y_{D}}}{{x_{E} - x_{D}}} \][/tex]

Substituting the coordinates of points D and E:

[tex]\[ m_{DE} = \frac{{\frac{{y_1}}{2} - \frac{{y_1}}{2}}}{{\frac{{x_1 + x_2}}{2} - \frac{{x_1}}{2}}} \][/tex]

[tex]\[ m_{DE} = \frac{0}{{\frac{{x_1 + x_2 - x_1}}{2}}} \][/tex]

[tex]\[ m_{DE} = 0 \][/tex]

Since the slopes of segments AB and DE are both equal to 0, we can conclude that segment DE is parallel to segment AB.

Part A

months = m

 since birds decrease by 7%, there will be 93% left. 93% = 0.93
birds: 975 x 0.93^m
trees: 350 - 7m

Part B
birds: 975 x 0.93^12 = 408
trees: 350-7(12) = 266

Part C

350 - 7m = 0.93^m(975)

We have intersection points at approximately 22.21 and 44.4781. round off to whole numbers, we have 22 and 44 months.

The correct option is a. 625.

The total number of outcomes in 4 spins of the spinner can be found by multiplying the number of outcomes in one spin by itself 4 times, resulting in 625 outcomes.

The sample space for 4 spins of the spinner can be calculated by raising the number of outcomes in one spin to the power of the number of spins.

In this case, as there are 5 outcomes on the spinner, the total number of outcomes in 4 spins would be 5^4 = 625.

Therefore, the correct option is a. 625.