Consider a population that grows to the recursive rule Pn= Pn-1 + 50,
with initial population Po = 200
(a) Use the recursive formula to find: p1 and p2
(b) Find an explicit formula for the population.
(c) Use the explicit formula to find P60

Answer: 1. 3 • (x + 5) • (x - 5)

2. 2a*(2b+9)

Step-by-step explanation:

Answer:

1) 3(x+)(x-5)

2) 2a(2b+9)

Step-by-step explanation:

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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Al the nth term are,

1) a (n) = 6 + 4n

2) a (n) = 26 + 8n

3) a (n) = 23 - n

4) a (n) = 7n - 3

5) a (n) = 8n - 43

We have to given that;

All the sequence are,

1.10,14,18,22..

2.34,26,18,10,..

3.17;11;5;-1;-7;..

4.4;11;18;25;..

5.-35;-27;-19;-11;..​

Now, WE can find the nth term as;

1) 10,14,18,22..

Here, a = 10

Common difference = 14 - 10 = 4

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 10 + (n - 1)4

a (n) = 10 + 4n - 4

a (n) = 6 + 4n

2) 34,26,18,10,..

Here, a = 34

Common difference = 26 - 34 = 8

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 34 + (n - 1)8

a (n) = 34 + 8n - 8

a (n) = 26 + 8n

3) 17;11;5;-1;-7;..

Here, a = 17

Common difference = 11 - 17 = - 6

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 17 + (n - 1) (- 6)

a (n) = 17 - 6n + 6

a (n) = 23 - n

4) 4;11;18;25;..

Here, a = 4

Common difference = 11 - 4 = 7

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 4 + (n - 1) (7)

a (n) = 4 + 7n - 7

a (n) = 7n - 3

5) -35;-27;-19;-11;..​

Here, a = - 35

Common difference = - 27 + 35 = 8

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = - 35 + (n - 1) (8)

a (n) = - 35 + 8n - 8

a (n) = 8n - 43

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Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Another solution

The sum of angles in the shape AGBC = 360°

Answer:

2 minutes.

Step-by-step explanation:

Rate formula: Quantity / Time

24 / 8  = 3    -> Calculating rate

He can print out 3 photos per minute.

6 /  3 = 2    -> Calculating time it would take for 6 photos.

It will take him 2 minutes at that rate.

Answer:

72 1/2

Step-by-step explanation:

so, she ran 2 miles in 8 3/4 minutes each.

3 miles in 9 minutes each.

2 miles in 9 1/4 minutes each.

1 mile in 9 1/2 = 9 2/4 minutes.

in total that means

2×(8 3/4) + 3×9 + 2×(9 1/4) + 9 2/4 =

= 16 6/4 + 27 + 18 2/4 + 9 2/4 =

= 16 + 27 + 18 + 9 + 6/4 + 2/4 + 2/4 =

= 70 + 10/4 = 70 + 2 + 2/4 = 72 2/4 = 72 1/2 minutes

Answer:

wn work

Step-by-step explanation:

Answer:

B= left 6 up 7 C=left 2 up 6 D=left 3 up 2 E left 7 up 3

Step-by-step explanation:

I think this is how u do that. I'm not exactly sure but hope u get it right.

There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.

Let's solve the problem step by step:

Identify the given information:

The ratio of red pens to blue pens is 4 to 5.

There are a total of 342 pens in the drawer.

Set up the ratio equation:

Let's assume the number of red pens is 4x, and the number of blue pens is 5x.

Here, 'x' is a scaling factor that allows us to find the actual number of pens.

We can write the equation as: 4x + 5x = 342.

Simplify and solve the equation:

Combining like terms, we have 9x = 342.

Divide both sides of the equation by 9 to solve for 'x':

x = 342 / 9 = 38.

Calculate the number of red pens and blue pens:

Now that we have the value of 'x', we can find the number of red and blue pens:

Number of red pens: 4x = 4 × 38 = 152.

Number of blue pens: 5x = 5 × 38 = 190.

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Answer:

Step-by-step explanation:

Rounded to the underlined digit, 84.59 becomes 84.6.

Rounding a number means approximating it to a specified place value. In this case, we are rounding 84.59 to the nearest tenth, which is the first digit to the right of the decimal point.

1. Identify the Digit:

Underline the digit in the tenth's place, which is 5 in 84.59.

2. Look at the Next Digit:

The digit immediately to the right of 5 is 9. Since 9 is greater than or equal to 5, we round up the underlined digit.

3. Adjust the Digit: Add 1 to the underlined digit, which becomes

6 (5 + 1 = 6).

4. Replace Other Digits: Keep all the digits to the left of the underlined digit unchanged. Therefore, the 84 remains the same.

5. Final Result: The rounded number is 84.6.

So, when rounding 84.59 to the nearest tenth, we get 84.6. Rounding helps make numbers easier to work with when precision beyond a certain point is not necessary.

Remember that when the digit to the right of the one you're rounding to is 5 or greater, you round up, and when it's less than 5, you round down.

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We have that the length measuring 2 feet more than twice the width so this means

all in feet, now we know that the perimeter is 32 feet so we have

Using the first equation and replacing in the second one we get

this is

Replacing this in the first equation we get

The answer is: the length of the garden is 22 and the width is 10 feet.

Answer:

m < 3 ?

Step-by-step explanation:

Answer:

x≤20

Step-by-step explanation:

x+5≤25

 -5.  -5

x≤20

Hopes this helps please mark brainliest

Answer:

The answer is B

Step-by-step explanation:

20+5=25 and x can be greater than or equal to 25

\((a + c) ^{2} = t \\ c = \sqrt{t } - a \\ c = - \sqrt{t} - a\)

\(p = 3(y + 2x) ^{2} \\ x = \frac{ \sqrt{3p} }{6} - \frac{y}{2} \\ x = - \frac{ \sqrt{3p} }{6} - \frac{y}{2} \)

Answer:

a) 84th percentile.

b) The 25th percentile is of 67 inches.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The heights of the men age 18 and over in HANES5 averaged 69 inches; the SD was 3 inches.

This means that \(\mu = 69, \sigma = 3\)

Such a man that is 6 feet tall is at the percentile of this height distribution.

6 feet = 6*12 inches = 72 inches. So this percentile is the p-value of Z when X = 72. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{72 - 69}{3}\)

\(Z = 1\)

\(Z = 1\) has a p-value of 0.84, so 84th percentile.

What is the 25th percentile, to the nearest inch

X when Z has a p-value of 0.25, so X when Z = -0.675.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.675 = \frac{X - 69}{3}\)

\(X - 69 = -0.675*3\)

\(X = 67\)

The 25th percentile is of 67 inches.

1) To write in Scientific Notation we must keep a rational number multiplied by 10 raised to an exponent. In this case, we have

641,693,000,000,000,000,000,000kg

So this number can be rewritten as 6.41693 x 10^23 kg

To reach his goal by loosing weight of 2 lbs per week he needs 15 weeks.

A function is a from of an mathematical equation where the dependent variable determines the value of the independent variable.

According to the given question

His current weight is 215 lbs his plan is to loose 2 lbs of weight per week.

To reach his goal of 185 lbs.

The function will be

185 = 215 - 2v                                              (here v represents no. of weeks)

2v = 215 - 185

2v = 30

v = 15

∴ He need 15 weeks to reach his goal.

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The slope of line a = 3

The slope of line b = -1/3

Line a: -3x+y=1

Rewritting by making y the subject of formula:

y = 3x + 1

Using equation of line: y = mx + c

m = slope

c = y-intercept

compare both equations:

y = y

c = 1

3x = mx

m = 3

The slope of line a = 3

Line b: 2x+6y=12

Rewritting by making y the subject of formula:

6y = -2x + 12

divide both sides by 6 so y stands alone:

6y/6 = -2x/6 + 12/6

y = -1/3 x + 2

Comparing with equation of line: y = mx + c

y = y

c = 2

mx = -1/3 x

m = -1/3

The slope of line b = -1/3

The binomial distribution can be used to determine the likelihood that exactly two mice weigh between 80 and 100 grams and exactly one mouse weighs more than 100 grams.

a) The likelihood that a single mouse weighs between 80 and 100 grams is the same as the likelihood that it weighs between 80 and 100 grams and less than that. This is determined by the normal distribution's cumulative distribution function (CDF), which has a mean of 100 and a standard deviation of 20, and is assessed at 100 and 80, respectively. One less than the CDF of the normal distribution with a mean of 100 and a standard deviation of 20, evaluated at 100, yields the likelihood that a single mouse weighs more than 100 grams. The binomial probability mass function,

with parameters, n = 4

k = 2,

p = probability

that a single mouse weighs between 80 and 100 grams, then provides the likelihood that precisely two mice weigh between 80 and 100 grams and precisely one weighs more than 100 grams. The binomial probability mass function, with parameters, n = 4,

k = 4

p = probability

that a single mouse weighs more than 100 grams, provides the likelihood that all four mice weigh more than 100 grams.

b) We are unable to compute the probabilities precisely because we do not have the values of the CDF for the normal distribution. However, it is possible to state that the likelihood of all four mice weighing more than 100 grams is less likely than the likelihood that two mice exactly weigh between 80 and 100 grams and one mouse precisely weighs more than 100 grams. This is so because it is less likely that a single mouse will weigh more than 100 grams than it is that it will weigh between 80 and 100 grams.

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The function g(x) is translated down 2 units compared to f(x).

A vertical shift is a transformation of a parabolic function that moves the entire graph vertically either upwards or downwards.

If the parameter c in the equation of the parabola is increased or decreased by a constant k, the parabola will be shifted vertically by k units.

If k is positive, the parabola will be shifted upward, while if k is negative, the parabola will be shifted downward.

Here we have

Two fuctions f(x) = eˣ, and g(x) = eˣ - 2

Here the function is transformed by subtracting -2

Therefore,

The function g(x) is translated down 2 units compared to f(x).

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The value of the apartment in 6 years is $104,527.46.

The value of the apartment appreciates (increase in value) by 6% every year. The formula that can be used to determine the future value of the apartment is:

FV = P (1 + r)^n

Where:

$78,000(1.05)^6 = $104,527.46

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The worth of the apartment after 6 months is =$23,400

The original amount of the apartment(p) = $78,000

The rate of increase of the value of the apartment is(r)= 5%

Time(t) = 6years

But simple interest =

\(si = \: \frac{p \times t \times r}{100} \)

\(si = \frac{78000 \times 6 \times 5}{100} \)

\(si = \frac{2340000}{100} \)

si = $23,400

Therefore, the worth of the apartment after 6 months is =$23,400

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The boxplot required to answer the question has been attached below

Answer:

E

Step-by-step explanation:

The maximum value on a box plot can be obtained by taking the value at the end of the whisker positioned to the right of the box in the boxplot. From the boxplotvgiven above, the maximum value provided by the endpoint of the right hand side whisker is 48. The 48 point mark is labeled as E in the plot.

Hence, the letter depicting the maximum value position on the box plot is the letter E

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

Step-by-step explanation:

Sample standard deviation is found by steps below.

Find the mean:

Find deviations from the mean and their squares:

Sum the squares:

Divide by N - 1 (N - number of samples):

Square root is the sample standard deviation:

Type I error: Reject the null hypothesis H₀, when H₀ is true.

Failure to reject the null hypothesis H₀, when H₀  is untrue is a Type II mistake.

A hypothesis is a proposed explanation or prediction for a phenomenon or observed phenomenon. It is a statement that suggests an explanation for an observed fact or set of facts and provides a basis for further investigation or experimentation.

 Given Information

Determine the hypothesis:

Hₐ: p₁>p₂

Type I error: Reject the null hypothesis H₀, when H₀ is true.

Although being ineffectual, the adjustment gives the impression of being effective.

As a result, more vehicles than anticipated have brake problems, which might result in additional expenses for the company.

Failure to reject the null hypothesis H₀, when H₀  is untrue is a Type II mistake.

Interpretation: The adjustment is successful even though it appears to be ineffective.

As a consequence, fewer automobiles than anticipated have brake issues, which might result in financial savings for the corporation.

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Answer:

Use the Pythagorean therm

Step-by-step explanation:

A squared(one leg) + B square(one leg) = C(aka the hypotenuse)

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