Write a recursive formula for the sequence: 25, 5, 1,...
O a (1)=25 and a (n) = a(n − 1)
O a (1)=25 and a (n) = 5 a(n-1)
O a (1)=25 and a (n) = a(n-1) +5
O a (1) = 25 and a (n) = a(n-1) - 20

The scores on the math portion of the SAT are roughly normally distributed, with a mean of 500 and a standard deviation of 100. Approximately 95% of scores lie within two standard deviations of the mean, which is between 300 and 700.

To calculate this, we need to know that 68% of scores lie within one standard deviation of the mean, and 95% of scores lie within two standard deviations of the mean. To calculate the two standard deviations from the mean, we must use the equation (x + 2σ) and (x - 2σ). The 'x' in this equation is the mean, and the 'σ' is the standard deviation. Plugging in the values, we get: (500 + 2(100)) = 700 and (500 - 2(100)) = 300. Therefore, approximately 95% of scores on the math portion of the SAT lie between 300 and 700.

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Therefore, the 95% confidence interval for the population standard deviation is approximately (2.6, 12.3).

To construct a 95% confidence interval for the population standard deviation, we will use the chi-square distribution. Here are the steps:

Step 1: Identify the given values.
n = 5 (sample size)
s = 4.4 (sample standard deviation)
c = 0.95 (confidence level)

Step 2: Find the degrees of freedom.
df = n - 1 = 5 - 1 = 4

Step 3: Find the chi-square values.
For a 95% confidence interval, we will use the values corresponding to 2.5% and 97.5% in the chi-square distribution table. For df = 4:
Chi-square (0.025) = 11.143
Chi-square (0.975) = 0.485

Step 4: Calculate the confidence interval for the population variance.
Lower limit:[tex] (n - 1) * s^2 / Chi-square (0.025) = 4 * (4.4)^2 / 11.143 = 6.960[/tex]
Upper limit:[tex] (n - 1) * s^2 / Chi-square (0.975) = 4 * (4.4)^2 / 0.485 = 151.977[/tex]

Step 5: Calculate the confidence interval for the population standard deviation by taking the square root of the variance limits.
Lower limit: [tex]√6.960 = 2.6[/tex]
Upper limit:[tex] √151.977 = 12.3[/tex]

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The probability that outdoor equipment will meet all of their demand is 0.0478.

We are given that Outdoor equipment purchased 215 hydra insulated water bottles. The demand for the hydra water bottle is normally distributed with a mean of 150 and a standard deviation of 77.The formula for calculating the probability of demand can be given by: P(X ≤ 215)P(X ≤ 215) is the probability of selling all 215 water bottles.

It means that they will sell a maximum of 215 bottles. The probability of selling less than or equal to 215 bottles is calculated as: P(X ≤ 215)=P(Z ≤ (215 - 150)/77)=P(Z ≤ 0.844).

Therefore, P(X ≤ 215) = 0.8023P(X ≤ 215) = 0.8023P(X = 215) is calculated as: P(X = 215) = P(X ≤ 215) - P(X ≤ 214). Therefore, P(X = 215) = 0.8023 - P(Z ≤ (214.5 - 150)/77)= 0.8023 - 0.7545 = 0.0478.

Therefore, the probability that outdoor equipment will meet all of their demand is 0.0478.

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When Will ran around the track 12 times, he ran a total distance of 12 x 0.25 = 3 miles. The answer is 3 miles.

The lap is the total distance a runner has to cover to complete one full circuit of the track. Depending on the size of the track, the lap distance can vary.

In the case of Will, he ran a total of 12 laps of a track that was 1/4 of a mile long.

This means that he ran a total distance of 12 x 0.25 = 3 miles.

This is because 1/4 of a mile is equal to 0.25 miles.

The equation used to calculate the total distance run by Will is: Distance = Number of laps x Length of each lap.

This equation can be used to calculate the total distance run by any runner on any track of any length.

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The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.

Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as function of time(days) is given by [tex]D(t)= (t-10)^2[/tex]; 0. We will solve this problem by finding the answer step by step. FunctionThe function of the lesion's size over time is provided by the equation D(t)= (t-10)2, where t is the time in days and D(t) is the diameter of the lesion at the time t.

The origin of this equation is given by D(t) = f(t), where the variable t represents the independent variable, and the variable D(t) represents the dependent variable. To calculate the diameter of the lesion over time, substitute values of t into the equation D(t) = (t-10)2. When t = 0, for instance, D(0) = (0-10)2 = 100. This means that the lesion's diameter at time zero is 100cm.

The model's interpretation The mathematical model that describes the diameter of a lesion as a function of time was created by a medical researcher. The equation D(t) = (t-10)2 represents this model. The researcher's model indicates that the diameter of the lesion is equal to the square of the difference between the time and ten. The difference between the time and ten is squared, which means that the model represents a parabolic curve.

The question is, "Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as a function of time (days) is given by D(t)= (t-10)^2; answer in 200 words."
The given equation is a quadratic function, which is expressed as[tex]D(t)= (t-10)^2.[/tex]This means that the diameter (D) of the lesion is dependent upon the time (t) that has passed since the lesion's onset. Specifically, the diameter of the lesion will increase as the time since onset increases.
The graph of this equation will be a parabola with its vertex at (10, 0). This is because, when t=10, the diameter of the lesion (D) will be zero. As t increases, the graph will move up and to the right, forming a parabola with a positive slope.
In addition to describing the diameter of the lesion as a function of time, the equation also allows us to calculate the diameter of the lesion for any given time. To do this, we can plug in the desired time value for t, and calculate the resulting diameter.
For example, if the medical researcher wants to determine the diameter of the lesion when t=15 days, they can plug in 15 for t, and calculate that the diameter of the lesion at that time is 25 cm. This can be found by plugging in 15 for t and calculating [tex]D(15)=(15-10)^2[/tex]=25 cm.
In conclusion, the equation[tex]D(t)= (t-10)^2.[/tex]is a quadratic function that describes the diameter of a lesion in cm as a function of time (days). The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.

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Answer:

The television tower is 132 feet high.

Step-by-step explanation:

Let h be the height of the television tower. Set up and solve this proportion.

[tex] \frac{3}{5} = \frac{h}{220} [/tex]

[tex]5h = 660[/tex]

[tex]h = 132[/tex]

In 1996, the cooperative expects approximately 40% of cranberries processed to be water-harvested.

This is a decrease of 18% from 1995. This decrease is likely due to the fact that water-harvested cranberries cost more to process than traditional dry-harvested cranberries.

Additionally, the cooperative may not be able to find enough cranberry farmers willing to switch to the water-harvesting method, which is a labor-intensive process.

Thus, the cooperative is likely to experience a decrease in the percentage of water-harvested cranberries processed in 1996.

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The probability that a specific fire engine is not available when needed is 0.04 (since the probability of it being available is 0.96).

The question asks for two probabilities related to the availability of fire engines in a town. The first part asks for the probability that neither engine is available when needed, and the second part asks for the probability that a fire engine is available when needed.

To calculate the probability that neither engine is available when needed, we need to use the multiplication rule for independent events. We know that the probability that one specific engine is not available when needed is 0.04 (1 - 0.96). Since the two engines operate independently, the probability that both are not available when needed is the product of their individual probabilities:

P(neither available) = P(engine 1 not available) * P(engine 2 not available)

P(neither available) = 0.04 * 0.04

P(neither available) = 0.0016

Therefore, the probability that neither fire engine is available when needed is 0.0016.

To calculate the probability that a fire engine is available when needed, we can simply use the given probability of 0.96:

P(available) = 0.96

Therefore, the probability that a fire engine is available when needed is 0.96.

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The value of the angle x is 30 degrees

Trigonometric identities are identified as those equalities of a function holding that all of the values in the given function, equation or expression are true.

There are distinct trigonometric identities. They are enumerated thus;

Note that the sine identity is represented as;

sin θ = opposite/ hypotenuse

Opposite of angle x = 48cm

Hypotenuse = 96cm

Substitute the values

sinx =48/96

sin x = 0. 5000

Take sine inverse

x = 30 degrees

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Answer:

C is the correct function.

Answer:

Step-by-step explanation:

Credits : sqdancefan (Brainly.com)

I changed some of it myself  :)

Answer:

A) intercept: 0 profit : Maximum(max) : max profit. increasing x <4 ; decreasing x > 4

B) average slope: ≈50, about $50 increasing profit for each $1 increasing in price.

Step-by-step explanation:

A) The vertical axis of the graph represents profit, so the x-intercepts represent prices in the produce 0 profit. The maximum value of the graph is the maximum profit that can be obtained for anyprice

The higher or largest number of the chart is the maximum reach

B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about ...

(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50

The average rate of the change from x = 1 to x = 4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in what interval.

______

* if we take the peak profit to be $270 we can write f(x) as ...

f(x) 16.875x(x-8)

Then f(1) = 118.15 ad average rate if changed is 50.625. For the purpose here, we judge the extra precision to be pointless

the inequality that describes the problem is x ≤ 210, meaning that Simon can drive at most 210 more miles before his electric car runs out of battery.

If Simon has driven 140 miles since fully charging his car, then the amount of charge remaining in the battery can power the car for x miles. We can set up the following inequality to represent this situation:

x ≤ 350 - 140

The amount of charge left in the battery is shown on the right-hand side of the inequality and is equal to the maximum amount of charge the battery can store (350 miles) minus the amount of charge that has already been utilised (140 miles). The left-hand side of the inequality displays the number of miles Simon can travel until his battery runs out, which is either less than or equal to the battery's remaining charge.

Simplifying the inequality, we get:

x ≤ 210

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The family-sized box requires 130 more square inches of cardboard than the regular-sized box, has an additional 228 cubic inches of cereal capacity, and costs less per cubic inch of cereal.

To calculate the additional square inches of cardboard needed for the family-sized box, we need to find the difference in surface area between the regular-sized box and the family-sized box.

The regular-sized box has a surface area of 2 x 6 + 2 x 11 + 6 x 11 = 104 square inches.

The family-sized box has a surface area of 2 x 8 + 2 x 15 + 3 x 15 + 3 x 8 + 3 x 15 = 234 square inches.

Therefore, the additional square inches of cardboard needed for the family-sized box is 234 - 104 = 130 square inches.

B. To find how many more cubic inches of cereal fit in the family-sized box than the regular-sized box, we need to calculate the difference in volume between the two boxes.

The regular-sized box has a volume of 2 x 6 x 11 = 132 cubic inches.

The family-sized box has a volume of 3 x 8 x 15 = 360 cubic inches.

Therefore, the additional cubic inches of cereal that fit in the family-sized box is 360 - 132 = 228 cubic inches.

C. To determine which cereal costs less per cubic inch of cereal, we need to divide the cost of each box by its respective volume.

The regular-sized box costs $3.99 for 132 cubic inches of cereal, which gives us a cost of $0.03 per cubic inch.

The family-sized box costs $5.69 for 360 cubic inches of cereal, which gives us a cost of $0.02 per cubic inch.

Therefore, the family-sized box costs less per cubic inch of cereal.

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The most likely number of marbles in Aileen's bag is given as follows:

The most likely number of marbles is obtained applying the proportions in the context of the problem.

Out of 10 marbles, from the sample, the results are given as follows:

Aileen has 40 colored marbles inside a bag, which is four times the size of the sample, hence the most likely number of marbles in Aileen's bag is obtained as follows:

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Answer:

Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.

Step-by-step explanation:

please

give brianliest

Answer: Area = 0

Step-by-step explanation:

((2*2)*3.14)-(4*3.14) = 0

The need for capital by the Sport Bat Corporation will spread through the financial system as it interacts with banks, investors, and the broader financial markets.

When the Sport Bat Corporation needs to borrow $2 million to upgrade their equipment, they will likely seek a loan from a financial institution, such as a bank. The bank will evaluate the creditworthiness of the company and may require collateral or a personal guarantee before approving the loan.

Once the loan is approved, the bank will add the Sport Bat Corporation's loan to their portfolio of assets. The bank may choose to sell the loan to other investors, such as insurance companies or pension funds, to diversify their portfolio and manage risk.

These investors will then receive the interest payments on the loan as a source of income. The loan may be bundled together with other loans and sold as a package, called a securitization, to other investors in the financial markets, thus representing the spread of the loan throughout the financial system.

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Answer:Hence, Nathan rode 2 miles

Step-by-step explanation:ask if you need any questions

Answer:  72

Step-by-step explanation:

b + 108 = 180

        b = 180 - 108

        b = 72 = c

Answer:

[tex]26a - 10 = 2(13a - 5)[/tex]

The correlation coefficient between heights from the ground of two people on the opposite ends of a seesaw would depend on the weight of the people and their distance apart.

When the seesaw is in equilibrium, the height of the people will be related inversely proportional to their weight. If the weight of one person increases, the height of the other person would decrease and vice versa.

The correlation coefficient will be negative and can range from -1 to 0, with -1 being the highest correlation. The closer the correlation coefficient is to -1, the more closely related the heights of the two people will be. The correlation coefficient will be zero when the people are not in equilibrium.

This is because the height of the people is not related in any way when the seesaw is not in equilibrium. Therefore, the correlation coefficient between heights from the ground of two people on the opposite ends of a seesaw is negative and ranges from -1 to 0.

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The probability that a student chosen at random likes science given that he or she likes art is 41.4%

In our case, we want to find P(Science|Art), which is the probability of a student liking science given that he or she likes art. Using Bayes' theorem, we have:

P(Science|Art) = P(Art|Science) x P(Science) / P(Art)

We know that P(Art) = 0.35 and P(Science|Art) = 0.22. To find P(Art|Science), we can use the formula:

P(Art|Science) = P(Science|Art) x P(Art) / P(Science)

We don't know P(Science) yet, but we can calculate it using the fact that:

P(Science) = P(Science|Art) x P(Art) + P(Science|Not Art) x P(Not Art)

where P(Not Art) is the probability that a student does not like art, which is 1 - P(Art) = 0.65. We are given that P(Science|Not Art) = 0.15, which is the probability that a student who does not like art likes science. Substituting these values, we get:

P(Science) = 0.22 x 0.35 + 0.15 x 0.65 = 0.1855

Now we can substitute all the values into Bayes' theorem:

P(Science|Art) = 0.22 x 0.35 / 0.1855 = 0.414 or 41.4%

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In linear equation, The actual height of the statue is 300 feet.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.  

                                  Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

A scale factor of a famous statue uses a scale factor of 250:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?

= 1.2 x 250

The actual height of the statue is 300 feet.

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Answer:(D) 300

Step-by-step explanation: the scale factor is 250:1 and the Hight of the drawing is 1.2 feet you need to multiply 1.2 by 250

1.2 x 250 = 300

Answer:

15 Full orbits per day

Step-by-step explanation:

To work out the number of full orbits the ISS does in 1 day, we need to know how long it takes for the ISS to complete one orbit around the Earth.

We can use the information given to us to calculate the time it takes for the ISS to complete one orbit:

Distance traveled in one orbit = 42,600 kilometers

Speed of the ISS = 27,576 kilometers per hour

To calculate the time taken for one orbit:

Time taken = Distance traveled / Speed

Time taken = 42,600 kilometers / 27,576 kilometers per hour

Time taken = 1.54 hours (rounded to 2 decimal places)

So, the ISS takes approximately 1.54 hours to complete one orbit around the Earth.

Now, we can calculate the number of orbits the ISS does in one day:

Number of orbits per day = 24 hours / Time taken for one orbit

Number of orbits per day = 24 hours / 1.54 hours

Number of orbits per day = 15.58 (rounded to 2 decimal places)

Therefore, the ISS completes approximately 15 full orbits around the Earth in one day.

The provided assertion states that is the answer to a inequality 4x - 5 ≥ 7 is x ≥ 3.

In mathematics, "inequality" refers to a connection between two formulas or numbers that is not identical to each other. As a result, disparity results from a lack of balance.

To solve 4x - 5 ≥ 7, we can isolate the variable x by adding 5 to both sides of the inequality:

4x - 5 + 5 ≥ 7 + 5

Simplifying:

4x ≥ 12

Next, we can isolate x by dividing both sides by 4:

4x/4 ≥ 12/4

Simplifying:

x ≥ 3

Therefore, the solution to the inequality 4x - 5 ≥ 7 is x ≥ 3.

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The probability of a family having two boy children is 0.25, or 25%. This probability is determined by a simple calculation. If there are two children in the family, the probability of each child being a boy is 0.5 (50%), and the probability of both children being boys is 0.5 x 0.5, or 0.25 (25%).

When it comes to probability, the likelihood of an event is determined by the number of possible outcomes. In the case of this question, there are four possible outcomes: two boys, two girls, one boy and one girl, and one girl and one boy. Since each outcome is equally likely, each has a probability of 0.25 (25%).

It is important to note that the probability of a family having two boy children is the same as the probability of a family having two girls. In each case, the probability is 0.25 (25%). This is because the gender of a child is independent of the gender of their sibling.

In conclusion, the probability of a family having two boy children is 0.25 (25%). This probability is determined by the number of possible outcomes, each of which is equally likely. It is also important to note that this probability is the same for a family having two girls.

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The degrees of freedom associated with the t-test is [tex]n_1 + n_2[/tex] - 2. The t-distribution is used to calculate the p-value of the t-test. There is no significant difference between the mean number of lesions per leaf produced by the two strains.

The appropriate t-test for testing to see if there is a difference between the mean number of lesions per leaf produced by the two strains has [tex]n_1 + n_2[/tex] - 2 degrees of freedom.

Here, [tex]n_1[/tex]  is the sample size of the first group and [tex]n_2[/tex]  is the sample size of the second group. This t-test is a two-sample t-test where the samples are independent and normally distributed with equal variances.
The formula for the t-test is:
[tex]t = (x_1 - x_2) / (s \times \sqrt{(1/n_1 + 1/n_2))}[/tex]
Where [tex]x_1[/tex] and [tex]x_2[/tex]  are the sample means of the two groups, s is the pooled standard deviation, and [tex]n_1[/tex] and [tex]n_2[/tex] are the sample sizes of the two groups.
The pooled standard deviation is calculated as:
s = [tex]\sqrt{((n_1 - 1) \times s_1^2 + (n_2 - 1) \times s_2^2)}  / (n_1 + n_2 - 2)[/tex]
Where [tex]s_1[/tex] and [tex]s_2[/tex] are the sample standard deviations of the two groups.
The p-value is the probability of getting a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true. If the p-value is less than the significance level (usually 0.05), then the null hypothesis is rejected and it is concluded that there is a significant difference between the mean number of lesions per leaf produced by the two strains. Otherwise, the null hypothesis is not rejected.

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{x | x ∈ R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.

In interval notation, the set {x | x R, x < 5} can be written as (-∞, 5). The symbol (-∞) represents negative infinity, which means all numbers less than any finite number.

So, the interval (-∞, 5) includes all real numbers less than 5, but does not include 5 itself.

To graph this set on a number line, we would draw an open circle at the point 5, because 5 is not included in the set. Then, we would draw a ray pointing to the left, because the set includes all numbers less than 5.

The ray extends indefinitely to the left, because there is no greatest number that is less than 5.

Therefore, the graph of the set {x | x R, x < 5} on a number line would have an open circle at 5 and a ray pointing to the left.

What does an open circle on a number line indicate?

An open circle on a number line indicates that the number is not included in the set.

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The total number of cups of dried fruit Lucas need for his one dozen snacks are 3 cups of dried cherries and 6 cups of dried apricots

Cups used of dried cherries = 1/4

Cups used of dried apricots = 2/4

An element of a number or any number of equal pieces is represented by a fraction. A fraction with a numerator and denominator exists.

Lucas is making one dozen snacks, which means the total number of snacks made is = 12.

Calculating the total amount of dried cherries -

= 1/4 cup/serving x 12 servings

= 3 cups of dried cherries

Similarly,

Calculating the total amount of dried apricots -

1/2 cup/serving x 12 servings

= 6 cups of dried apricots

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Step-by-step explanation:

The side opposite to the 4 degree angle is 18 m

The side adjacent the 4 degree angle is x

tan(4) = opposite / adjacent

adjacent = opposite / (tan(4))

adjacent = 18 / tan(4)

adjacent = 257.41