using the following quantities, calculated from these data, estimate the correlation between the percentage of dopamine receptors blocked and subjects’ ratings of the cocaine high. provide a standard error with your estimate. sum of products: 957.5 sum of squares (receptors blocked): 8145.441 sum of squares (rating of high): 372.5

There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F=\(\frac{S^1_2}{S^2_2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

To learn more about the standard deviation, visit:

brainly.com/question/23907081

#SPJ4

There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F= \(\frac{S_2^1}{S_2^2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

To learn more about Standard deviation:

brainly.com/question/23907081

#SPJ4

Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

Step-by-step explanation:

Irrational numbers never stop.

Numbers that don't stop:

\(\pi\)

\( \frac{2}{3} \)

\( \frac{1}{9} \)

\( \frac{4}{7} \)

The Volume of the given composite shape is: 432 ft³

The formula for the volume of a triangular prism is:

Volume = base area * height

The volume of a cuboid is:

Volume = Length * Width * Height

Thus:

Volume of composite shape = (6 * 12 * 4) + (6 * 6 * 4)

= 432 ft³

Read more about Volume of composite figure at: https://brainly.com/question/12693294

#SPJ1

Answer:

30.2312

u should give the server $33

one $20 bill, one $10 bill, three $1 bills

Step-by-step explanation:

28.52*106/100=30.2312

u should give the server $33

    one $20 bill, one $10 bill, three $1 bills

    20+10+1+1+1=3

The amount of money needed to be given to the server is $30 and 23 cents.

Since tax is 6%, hence:

Total bill including tax = $28.52 + 6% of $28.52 = $30.23

The amount of money needed to be given to the server is $30 and 23 cents.

Therefore the denominations needed for this is one $20 bill, two $10 bills and 23 pennies.

Find out more at: https://brainly.com/question/14982475

Answer:

3y = 8x - 91

y = 8/3 * x - 30 1/3

Step-by-step explanation:

First we can find the slope of the second line.

Let's rewrite the equation as 8y=44-3x.

After dividing both sides of the equation by 8 we'll get an equivalent equation y = 5.5 - 3/8 * x. The coefficient of x is the slope -> the slope is -3/8. In order for the line to be perpendicular to this line the product of the slopes of two lines should be equal to -1 or in other words the slopes have to be opposite reciprocals of each other. The reciprocal of -3/8 is -8/3. Opposite to it is 8/3. Now we know the slop and the coordinates of a point on the line (given). Let's make the equation of the line in the form of y = mx+ b. We can plug in values for m, y and x. m = 8/3(slope), y=-9 (second coordinate of the point), x = 8 (first coordinate). We got

-9 = 8/3 * 8 +b

Now we need to solve the equation to find b

b =-91/3 or -30 1/3

Answer:

Slope = -0.750/2.000 = -0.375

Geometric figure: Straight Line

Slope = -0.750/2.000 = -0.375

x-intercept = 4/3 = 1.33333

y-intercept = 4/8 = 1/2 = 0.50000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3*x+8*y-(4)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve 3x+8y-4 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x+8y-4 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/2 so this line "cuts" the y axis at y= 0.50000

y-intercept = 4/8 = 1/2 = 0.50000

Calculate the X-Intercept :

When y = 0 the value of x is 4/3 Our line therefore "cuts" the x axis at x= 1.33333

x-intercept = 4/3 = 1.33333

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.500 and for x=2.000, the value of y is -0.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.250 - 0.500 = -0.750 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -0.750/2.000 = -0.375

Geometric figure: Straight Line

Slope = -0.750/2.000 = -0.375

x-intercept = 4/3 = 1.33333

y-intercept = 4/8 = 1/2 = 0.50000

Answer:

RECT and ANGL are similar triangles with a ratio of 9:16, and for TR, we have TR:24 in the ratio 9:16 so TR = 13.5

Hope this helps!

If you have a required return of 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, you would be willing to pay approximately $206,595.71 for this investment.

To determine the value you would be willing to pay for this investment, we can use the concept of present value. The present value of an investment is the current worth of the future cash flows it will generate. In this case, the investment will pay you $800 a month for 40 years.

To calculate the present value, we can use the formula:

\(PV = CF / (1 + r)^n\)

Where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods.

In this case, the cash flow is $800 per month, the required return is 6% per year (or 0.06/12 = 0.005 per month), and the number of periods is 40 years * 12 months = 480 months.

Plugging these values into the formula, we have:

PV = $800 / \((1 + 0.005)^(480)\)

Calculating this expression, we find that the present value is approximately $206,595.71. Therefore, you would be willing to pay approximately $206,595.71 for this investment to achieve your required return of 6% per year, compounded monthly.

Learn more about present value here:

https://brainly.com/question/30390056

#SPJ11

(a) the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

(b) the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

What is riemann sum?

A Riemann sum is a method used in calculus to approximate the area under a curve or the value of an integral. It involves dividing the region under the curve into smaller subintervals and approximating the area of each subinterval using a specific rule.

To find the Riemann sum using left endpoints and n equals 4, we need to divide the interval [2, 14] into four equal subintervals. The width of each subinterval, denoted as Δx, is calculated as (b - a) / n, where b is the upper limit (14) and a is the lower limit (2).

So, Δx = (14 - 2) / 4 = 12 / 4 = 3.

Now, we evaluate the function at the left endpoint of each subinterval and multiply it by the width (Δx).

The left endpoints for n = 4 are: x₀ = 2, x₁ = 5, x₂ = 8, x₃ = 11.

The Riemann sum using left endpoints is given by:

L₄ = f(x₀) Δx + f(x₁) Δx + f(x₂) Δx + f(x₃) Δx.

Now, let's substitute the given function f(x) = 2x² + 4x + 2 into the Riemann sum equation:

L₄ = (2x₀² + 4x₀ + 2) Δx + (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx.

L₄ = (2(2)² + 4(2) + 2) (3) + (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3).

L₄ = (8 + 8 + 2) (3) + (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3).

L₄ = (18)(3) + (72)(3) + (162)(3) + (288)(3).

L₄ = 54 + 216 + 486 + 864.

L₄ = 1620.

Therefore, the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

To find the Riemann sum using right endpoints and n equals 4, the process is similar. However, this time we evaluate the function at the right endpoint of each subinterval.

The right endpoints for n = 4 are: x₁ = 5, x₂ = 8, x₃ = 11, x₄ = 14.

The Riemann sum using right endpoints is given by:

R₄ = f(x₁) Δx + f(x₂) Δx + f(x₃) Δx + f(x₄) Δx.

Substituting the function into the Riemann sum equation:

R₄ = (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx + (2x₄² + 4x₄ + 2) Δx.

R₄ = (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3) + (2(14)² + 4(14) + 2) (3).

R₄ = (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3) + (392 + 56 + 2) (3).

R₄ = (72)(3) + (162)(3) + (288)(3) + (450)(3).

R₄ = 216 + 486 + 864 + 1350.

R₄ = 2916.

Therefore, the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

To learn more about riemann sum visit:

https://brainly.com/question/30241844

#SPJ4

There is no information displayed.

Here is how to do it.

How to calculate axis of symmetry:

Plug your numbers into the axis of symmetry formula. To calculate the axis of symmetry for a 2nd order polynomial in the form ax 2 + bx +c (a parabola), use the basic formula x = -b / 2a. In the example above, a = 2 b = 3, and c = -1. Insert these values into your formula, and you will get:

How to calculate vertex:

The vertex form of a quadratic is given by

y = a(x – h)2 + k, where (h, k) is the vertex.

The "a" in the vertex form is the same "a" as

in y = ax2 + bx + c (that is, both a's have exactly the same value). The sign on "a" tells you whether the quadratic opens up or opens down. Think of it this way: A positive "a" draws a smiley, and a negative "a" draws a frowny. (Yes, it's a silly picture to have in your head, but it makes is very easy to remember how the leading coefficient works.)

In the vertex form of the quadratic, the fact that (h, k) is the vertex makes sense if you think about it for a minute, and it's because the quantity "x – h" is squared, so its value is always zero or greater; being squared, it can never be negative.

Suppose that "a" is positive, so a(x – h)2 is zero or positive and, whatever x-value you choose, you're always taking k and adding a(x – h)2 to it. That is, the smallest value y can be is just k; otherwise y will equal k plus something positive. When does y equal only k? When x – h, the squared part, is zero; in other words, when x = h. So the lowest value that y can have, y = k, will only happen if x = h. And the lowest point on a positive quadratic is of course the vertex.

If, on the other hand, you suppose that "a" is negative, the exact same reasoning holds, except that you're always taking k and subtracting the squared part from it, so the highest value y can achieve is y = k at x = h. And the highest point on a negative quadratic is of course the vertex.

The equation sin^2(x) = 1/2 - 1/2cos(2x) is an identity that holds true for all values of x. It can be used to simplify expressions involving sine and cosine functions.

The equation sin^2(x) = 1/2 - 1/2cos(2x) is a trigonometric identity, which means it holds true for all values of x. To understand why this identity is true, we can use the double angle formula for cosine, which states that cos(2x) = cos^2(x) - sin^2(x). Rearranging this formula gives sin^2(x) = cos^2(x) - cos(2x).

Now, we can substitute the identity cos^2(x) + sin^2(x) = 1 into the above equation, which gives sin^2(x) = 1 - cos^2(x) - cos(2x). Rearranging further gives sin^2(x) = 1/2 - 1/2cos(2x), which is the desired identity.

This identity can be useful in simplifying expressions involving sine and cosine functions. For example, if we have an expression with both sin(x) and cos(x), we can use this identity to express everything in terms of sin(x) or cos(x) only.

To learn more about trigonometric click here: brainly.com/question/29156330

#SPJ11

Answer:

See below

Step-by-step explanation:

Rational

\( \frac{2}{3}, \: \: 0, \: \: \sqrt{1}, \: \: 7. \bar4, \: \: 15 \\ \\ irrational \\ 3.1415926535...., \: \: \sqrt{3} \\ \)

Answer:

35

Step-by-step explanation:

I hope this helps!

Answer:

35

Step-by-step explanation:

Simplify

(-7) X (-5)

Negatives cancel out so its going to be positive

That's how you get 35.

The probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events.

Let A be the event that the athlete has been using the prohibited drug, and let B be the event that the athlete tests positive.

We want to find the probability of A given B, which we can write as P(A | B).

Using Bayes' theorem, we have:

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

where P(B | A) is the probability of testing positive given that the athlete has been using the prohibited drug, P(A) is the prior probability of the athlete using the prohibited drug, and P(B) is the overall probability of testing positive, which can be calculated using the law of total probability:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

where P(B | not A) is the probability of testing positive given that the athlete has not been using the prohibited drug, and P(not A) is the complement of P(A), i.e., the probability that the athlete has not been using the prohibited drug.

Using the given information, we can plug in the values:

P(B | A) = 1 - 0.12 = 0.88 (probability of testing positive given the athlete is using the drug)

P(A) = 0.05 (prior probability of the athlete using the drug)

P(B | not A) = 0.04 (probability of testing positive given the athlete is not using the drug)

P(not A) = 1 - P(A) = 0.95 (probability that the athlete is not using the drug)

Then, we can calculate P(B) as:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

= 0.88 * 0.05 + 0.04 * 0.95

= 0.076

Finally, we can calculate P(A | B) as:

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

= 0.88 * \(\frac{0.05 }{ 0.076}\)

= 0.5789

Therefore, the probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

Learn more about Bayes' theorem and probability.

brainly.com/question/17010130

#SPJ11

Answer:

186-\

thank you

Answer:

A91=184

Step-by-step explanation:

a91=4+(91-1)•2

a91=4+180

a91=184

In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

Learn more about Boolean expressions

https://brainly.com/question/13265286

#SPJ4

In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

for such more question on logical operator

https://brainly.com/question/15079913

#SPJ11

The Normal distribution is symmetric and ranges from negative to positive infinity, while the Log-normal distribution is skewed and only takes positive values. To select the better fit for data, consider characteristics (positivity and skewness favor Log-normal, symmetry favors Normal), hypothesis testing, visualization, and statistical tests.

Let's analyze each section separately:
a) The major differences between the Normal and Log-normal distributions are:

Normal Distribution: The Normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution that is defined by its mean (μ) and standard deviation (σ). It follows a bell-shaped curve and is often used to model naturally occurring phenomena. The range of values extends from negative infinity to positive infinity.

Log-normal Distribution: The Log-normal distribution is a skewed probability distribution that arises when the logarithm of a random variable follows a normal distribution. It is characterized by its parameters mu (μ) and sigma (σ) of the underlying normal distribution. Unlike the Normal distribution, the Log-normal distribution only takes positive values.

b) Selecting which distribution fits the data better depends on the nature of the data and the research question at hand. Here are a few considerations:

1. Data Characteristics: If the data consists of positive values and the distribution appears to be skewed, the Log-normal distribution might be more appropriate. On the other hand, if the data is symmetric and unbounded, the Normal distribution may be a better fit.

2. Hypothesis Testing: If you have a specific hypothesis to test or a theoretical justification for choosing one distribution over the other, it is advisable to use that distribution.

3. Visualization: Plotting the data and comparing it to the shapes of the Normal and Log-normal distributions can provide visual insights into which distribution aligns better with the data.

4. Statistical Tests: Statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test can be used to assess the goodness-of-fit for each distribution and determine which one provides a better fit to the data.

In summary, selecting the appropriate distribution involves considering the characteristics of the data, the research question, and statistical tests. Visualization and hypothesis testing can further aid in determining the best fit distribution.

To know more about goodness-of-fit tests, refer here:

https://brainly.com/question/32668212#

#SPJ11

If the data shows that overweight children do not suffer from diabetes as predicted by your model, indicating a lower than 80% probability, it suggests that there may be a discrepancy between the model's predictions and the actual observations. In this case, your next step would be to reevaluate and potentially revise your model.

Here are some possible steps to consider:

1. Review the data: Double-check the accuracy and reliability of the data used to validate your model. Ensure that the data is representative, comprehensive, and properly collected.

2. Analyze potential errors: Look for potential errors or biases in the data collection, analysis, or interpretation process. Consider factors such as sample size, sampling method, data collection methods, or any confounding variables that may have affected the results.

3. Assess model assumptions: Review the assumptions made in developing the model and determine if any of them may have been invalid or inappropriate for the specific context or population under study. Adjust the model if necessary to better align with the observed data.

4. Consider additional variables: Examine if there are any other relevant variables that were not initially included in the model but may influence the relationship between child obesity and diabetes. Incorporating additional variables or adjusting the existing ones might lead to a more accurate model.

5. Seek expert opinions: Consult with experts or researchers in the field of child obesity and diabetes to gain insights and validate your findings. They may provide guidance on potential factors or mechanisms that could explain the discrepancy between the model and the observed data.

6. Further data collection: If necessary, consider collecting additional data to refine and improve the model. This could involve expanding the sample size, targeting specific subgroups, or collecting more detailed information on relevant variables.

7. Model refinement or reconstruction: Based on the findings from the above steps, refine or reconstruct the model to better capture the relationship between child obesity and diabetes. This may involve modifying the assumptions, incorporating new variables, or applying alternative modeling techniques.

8. Test and validate the revised model: After making revisions, test the updated model using independent data sets or conducting further studies to validate its accuracy and reliability.

Remember, the scientific process often involves iteration and continuous improvement. If the initial model does not align with the observed data, it is essential to critically evaluate the model and make necessary adjustments to improve its accuracy and usefulness.

#SPJ11

In order to prove the properties of the given space (X, T), we need to show the following: a) it is second countable, b) it is first countable without using Theorem 6.3, c) it is separable without using Theorem 6.3, and d) it is Lindelöf without using Theorem 6.3.

a) To prove that (X, T) is second countable, we need to show that there exists a countable basis for the topology T. Since X is a countably infinite set, we can construct a countable basis for T using the singleton sets {Xi} for each Xi in X. The collection of all such singleton sets forms a countable basis, satisfying the second countability property.

b) To establish that (X, T) is first countable without using Theorem 6.3, we need to demonstrate that every point in X has a countable local base. For each Xi in X, we can construct a countable local base consisting of the singleton sets {Xi}. Thus, every point in X has a countable local base, satisfying the first countability property.

c) To prove that (X, T) is separable without using Theorem 6.3, we need to show that there exists a countable dense subset of X. Since X is countably infinite, we can select a countable subset Y = {X1, X2, X3, ..., Xn, ...} of X. This subset is countable and every point in X is either an element of Y or a limit point of Y, making Y a dense subset of X.

d) To establish that (X, T) is Lindelöf without using Theorem 6.3, we need to demonstrate that every open cover of X has a countable subcover. Let C be an open cover of X. Since X is countably infinite, we can select a countable subcover by choosing a subset C' from C such that C' still covers all points in X. This countable subcover satisfies the Lindelöf property, making (X, T) a Lindelöf space.

By proving these properties individually, we have established that the given space (X, T) is second countable, first countable, separable, and Lindelöf without relying on Theorem 6.3.

Learn more about sets here: https://brainly.com/question/28860949

#SPJ11

Answer: 4 days

Step-by-step explanation:

Answer:

-3x+10=5x-8

so basically its like grouping.

so answer is

8x=18?

Step-by-step explanation:

sorry if incorrect

Answer:

x=2.25

Step-by-step explanation:

three -x make -3x and 10 +1s make +10 and 5 xs make 5x and 8 -1s make -8

which makes

-3x+10=5x-8

just solve

18=8x

2.25=x

Answer: the second one

Step-by-step explanation:

because \(-4^{4}\)= -256

Answer:

9.5 ft

Step-by-step explanation:

Since it is a rectangle. The lengths are the same and the widths are the same.

12.4 + 12.4 = 24.8

43.8 - 24.8 = 19

19/2 = 9.5

Answer:

a) 7085g

b) 6346g

c) 5342g

Step-by-step explanation:

1kg = 1000g

The result for the given data are-

Part A: A geometric sequence is being modelled by the data because they share a common ratio = 2.

Part B: The time in which she will complete station 5 calculated by recursive formula is 64 units.

Part C: The time in which she will complete the 9th station calculated by  explicit formula 512 units.

Any term of a series can be defined by its preceding term in a recursive formula (s).

We learn two things from recursive formulas: the first phrase in the series. The pattern rule states that any term can be derived from its preceding term.

Now, according to the question;

Part A: The data are modeling a geometric sequence since they have a common ratio of 2.

Part B: Use a recursive formula to determine the time she will complete station 5.

f(n)=f(n-1)×r

Where, r is the common difference

f(n)=f(5-1)×2

f(n)=f(4)×2

f(n)=(32)×2   {since, f(4) = 32)}

f(n)= 64

Part C: Use an explicit formula to find the time she will complete the 9th station.

f(n)=f(1)×r^(n-1)

f(n)=4×2^(8-1)

f(n)=4×(2^7)

f(n)=4×128

f(n)=512

To know more about the recursive formula, here

https://brainly.com/question/1275192

#SPJ4

The complete question is -

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 4), (2, 8), (3, 16), (4, 32)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence?

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Answer:

The result for the given data are-

Part A: A geometric sequence is being modelled by the data because they share a common ratio = 2.

Part B: The time in which she will complete station 5 calculated by recursive formula is 64 units.

Part C: The time in which she will complete the 9th station calculated by  explicit formula 512 units.

What is recursive formula?

Any term of a series can be defined by its preceding term in a recursive formula (s).

We learn two things from recursive formulas: the first phrase in the series. The pattern rule states that any term can be derived from its preceding term.

Now, according to the question;

Part A: The data are modeling a geometric sequence since they have a common ratio of 2.

Part B: Use a recursive formula to determine the time she will complete station 5.

f(n)=f(n-1)×r

Where, r is the common difference

f(n)=f(5-1)×2

f(n)=f(4)×2

f(n)=(32)×2   {since, f(4) = 32)}

f(n)= 64

Part C: Use an explicit formula to find the time she will complete the 9th station.

f(n)=f(1)×r^(n-1)

f(n)=4×2^(8-1)

f(n)=4×(2^7)

f(n)=4×128

f(n)=512

To know more about the recursive formula, here

brainly.com/question/1275192

#SPJ4

The complete question is -

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 4), (2, 8), (3, 16), (4, 32)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence?

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Explore all similar answers

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The rule is to add 3 so to find the next term, you add 3 to 9 which is 12.

Hope this helps!

Answer:

−3 - 3, 0 0, 3 3, 6 6, 9 9 This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 3 to the previous term in the sequence gives the next term. In other words, an = a1 +d(n−1) a n = a 1 + d (n - 1).

Step-by-step explanation:

Answer:

we have x = y +2

now we put that value in other eq.

2(y+2)-3y = 1

2y+4-3y = 1

2y-3y = 1-4

-y= -3 (cut the signs on both side)

y= 3

now we put y value in the other given equation

x = 3+2

x = 5

we have y as 3 and x as 5.

Answer:

X= -2

you draw a line down the equal sign and subtract 3 from each side of the equation then divide by -0.5 on both sides

-0.5x+3=4

-3 -3

-0.5x = 1

÷ -0.5 ÷ -0.5

x=-2

Answer:

Hello,

Answer 52/3

Step-by-step explanation:

using the theorem of the bissector :

\(\dfrac{x}{13} =\dfrac{20}{15 } \\\\x=\dfrac{20*13}{15} \\\\x=\dfrac{52}{3}\)

The value of x to the nearest tenth is 18.5

To get the value of x, we first need to get the height of the triangle.

\(h^2=20^2-15^2\\h^2=400-225\\h^2=175\\h=13.23\)

Next is to get the value of x

\(x^2=13^2+13.2^2\\x^2=343.24\\x=18.52\)

Hence the value of x to the nearest tenth is 18.5

Learn more on pythagoras theorem: https://brainly.com/question/343682