what is it plz ????????????

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

To know more about notation visit:

https://brainly.com/question/29132451

#SPJ11

The length of the diagonal is 17.

Given that, In quadrilateral ABCD, sides AB and BC both have a length of 10, and sides CD and DA both have a length of 17.

The measure of ∠ADC = 60°

AD = CD ( according to the question)

So, Δ ABC is an isosceles triangle with ∠DAC = ∠DCA.

According to the image,

Angles in a triangle add up to 180°, and since ∠ADC = 60°, the other two angles are also 60°.

And Δ ADC is an equilateral triangle.

Therefore,  AC = DA = 17

S0, the diagonal of quadrilateral ABCD is 17.

Read more about quadrilateral:

https://brainly.com/question/27991573

#SPJ4

The rule for g(x) is:

g(x) =  6*(x + 3)^2 - 12

And the vertex of this function is at:

(-3, -12)

We know that the graph of g is a translation 1 unit left and 6 units down, followed by a vertical shrink by a factor of 1/2 of the graph of f(x).

First, the translation of 1 unit to the left is written as:

g(x) = f(x + 1)

Then we apply the translation of 6 units down, then we write this as:

g(x) = f(x + 1) - 6

Finally, a vertical shrink of scale factor k means that we need to divide the whole function by k, so a vertical shrink of scale factor 1/2 is written as:

g(x) = (f(x + 1) - 6)/(1/2)

g(x) = 2*(f(x + 1) - 6)

Now we know that f(x) = 3*(x + 2)^2

Replacing that in the above rule we get:

g(x) = 2*(3*(x + 1 + 2)^2 - 6) = 6*(x + 3)^2 - 12

Then the rule is:

g(x) =  6*(x + 3)^2 - 12

The vertex of this function is what we get when the squared part becomes zero, so we need to evaluate in x = -3

g(-3) = 6*(-3 + 3)^2 - 12

g(-3) = -12

The vertex is the point (-3, -12)

Learn more about translations:

https://brainly.com/question/24850937

#SPJ1

Step-by-step explanation:

CP=45

SP= 1.5 X 10,000/250

THEREFORE SP=60

PROFIT=15

PROFIT % =(PROFIT/CP) X 100

(15/45) X 100

=33.3%

Answer:The answer is the option C

Step-by-step explanation:we know that

In a right triangle the Pythagorean Theorem states that

where

c is the hypotenuse (the greater side)

a,b are the legs of the right triangle

in this problem we have

substitute the values

Answer:

15^2 + 16^2= x^2

Step-by-step explanation:

I took the usa test prep test and this is how you calculate it

Answer

So changing 1/4 by multiplying top and bottom by 9 gives 9/36 and changing 2/9 by multiplying top and bottom by 4/4 gives 8/36 and adding 9/36 to 8/36 gives 17/36 - a rational number.

Step-by-step explanation:

The weight of a randomly selected party size bag of tortilla chips coming off an assembly line is normally distributed with mean = 16.3 ounces and standard deviation = 0.2 ounces. Suppose we pick 4 bags at random and the sample mean = 16.26. The actual sampling error is 0.04 ounces and the typical sampling error is 0.05 ounces.

What is sampling error? The difference between a population parameter and its corresponding sample statistic is known as sampling error. It's also called estimation error. Sampling error can occur in any type of experiment or study when a sample of data is used to estimate a population's parameters or characteristics. The greater the sample size, the smaller the sampling error; the smaller the sample size, the greater the sampling error.

The sampling error formula is:

Sampling error = sample statistic - population parameter.

What is the actual sampling error?

To compute the actual sampling error, we use the formula:

Actual Sampling Error = Sample Mean - Population Mean.

Given the data we have, Sample Mean = 16.26Population Mean = 16.3

Actual Sampling Error = 16.26 - 16.3= -0.04.

Therefore, the actual sampling error is -0.04 ounces.

What is a typical sampling error? We use the formula below to compute the typical sampling error.

Typical Sampling Error = Standard Deviation / √(Sample Size)Standard deviation = 0.2 ounces

Sample size = 4 bags

Typical Sampling Error = 0.2/√4= 0.1/2= 0.05

Therefore, the typical sampling error is 0.05 ounces.

Learn more about sampling error at:

brainly.com/question/28008941

#SPJ11

If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

Learn more about y-intercept here:

https://brainly.com/question/14180189

#SPJ11

The probability that P(X1 < X2 < X3) is 1/8.

We can solve this problem using the fact that if X1, X2, X3 are independent exponential random variables with the same rate parameter λ, then the joint density function of the three variables is given by:

f(x1, x2, x3) = λ^3 e^(-λ(x1+x2+x3))

We want to find the probability that X1 < X2 < X3. We can express this event as the intersection of the following three events:

A: X1 < X2

B: X2 < X3

C: X1 < X3

Using the joint density function above, we can compute the probability of each of these events using integration. For example, the probability of A is:

P(X1 < X2) = ∫∫ f(x1, x2, x3) dx1 dx2 dx3

= ∫∫ λ^3 e^(-λ(x1+x2+x3)) dx1 dx2 dx3 (integration over the region where x1 < x2)

= ∫ 0^∞ ∫ x1^∞ λ^3 e^(-λ(x1+x2+x3)) dx2 dx3 dx1

= ∫ 0^∞ λ^2 e^(-2λx1) dx1 (integration by substitution)

= 1/2

Similarly, we can compute the probability of B and C as:

P(X2 < X3) = 1/2

P(X1 < X3) = 1/2

Note that these probabilities are equal because the three exponential random variables are identically distributed.

Now, to compute the probability of the intersection of these events, we can use the multiplication rule:

P(X1 < X2 < X3) = P(A ∩ B ∩ C) = P(A)P(B|A)P(C|A∩B)

Since A, B, and C are independent, we have:

P(B|A) = P(B) = 1/2

P(C|A∩B) = P(C) = 1/2

Therefore:

P(X1 < X2 < X3) = (1/2)(1/2)(1/2) = 1/8

Thus, the probability that X1 < X2 < X3 is 1/8.

To learn more about Probability

https://brainly.com/question/24870672

#SPJ11

A. The proportion we can set up is: c/a = d/b, and B. x = (c * b) / a. This gives us the value of x in terms of the lengths of the other segments.

A) The corresponding sides in similar triangles are proportional, so we can use this fact to set up a proportion between the sides of triangles BED and BCA. Let's call the length of segment BC "a", the length of segment AC "b", the length of segment BE "c", and the length of segment DE "d".
The proportion we can set up is:
c/a = d/b
This is because we know that triangle BED is similar to triangle BCA, so the ratio of the lengths of their corresponding sides must be the same.

B) We can now use the proportion to solve for x, which is the length of segment DE. We can start by cross-multiplying the proportion:
c * b = d * a
Then, we can isolate for x by dividing both sides by the coefficient of x:
x = (c * b) / a
This gives us the value of x in terms of the lengths of the other segments.

Learn more about segments: https://brainly.com/question/2437195

#SPJ11

So, based on the theoretical likelihood, we anticipate that 35 times out of 140 repeats, both spins will be odd numbers.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.

Here,

The theoretical probability of both spins being odd numbers is 9 over 36, which means that for every 36 times the experiment is repeated, we expect 9 of those times to result in both spins being odd numbers.

If the experiment is repeated 140 times, we can use the theoretical probability to estimate the number of times both spins will be odd numbers as follows:

140 * (9/36) = 35

So, based on the theoretical probability, we predict that both spins will be odd numbers 35 times out of 140 repetitions.

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

The equation of the tangent line to the curve y = (4ex)/(1 + x²) at the point (1, 2e) is y = 2e.

Here, we have,

To find the equation of the tangent line to the curve y = (4ex)/(1 + x²) at the point (1, 2e),

we need to determine the slope of the tangent line and then use the point-slope form of a linear equation.

Finding the slope of the tangent line:

To find the slope, we'll take the derivative of the given function y with respect to x.

y = (4ex)/(1 + x²)

Taking the derivative using the quotient rule, we have:

y' = [(4e)(1 + x²) - (4ex)(2x)] / (1 + x²)²

Simplifying this expression, we get:

y' = (4e + 4ex² - 8ex²) / (1 + x²)²

y' = (4e - 4ex²) / (1 + x²)²

Now, we can substitute x = 1 into the derivative to find the slope at the point (1, 2e):

m = y'(1) = (4e - 4e(1)²) / (1 + (1)²)²

= (4e - 4e) / 4

= 0

Therefore, the slope of the tangent line at the point (1, 2e) is 0.

Writing the equation of the tangent line:

The equation of a line with slope m and passing through the point (x₁, y₁) is given by the point-slope form:

y - y₁ = m(x - x₁)

Since the slope m is 0, the equation becomes:

y - 2e = 0(x - 1)

y - 2e = 0

y = 2e

Hence, the equation of the tangent line to the curve y = (4ex)/(1 + x²) at the point (1, 2e) is y = 2e.

learn more on tangent line :

https://brainly.com/question/32564880

#SPJ4

The value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths is 13.11.

In algebra, we often deal with equations with unknown values ​​represented by variables. To solve such an equation, we need to find the values ​​of the variables.

A one-step equation is an algebraic equation that can be solved in just one step. Solve it and you've found the values ​​of the variables that make the equation true. To solve a one-step equation, perform the inverse (reverse) of the operation performed on the variable to get the variable itself.

For the given case, the  equation can be written as follows:

\(\frac{x}{5\frac{7}{10} }\) = \(2\frac{3}{10}\)

x = \(5\frac{7}{10}\) × \(2\frac{3}{10}\)

x = 5.7 × 2.3

x = 13.11

To know more about algebraic equation visit:

https://brainly.com/question/24875240

#SPJ4

Answer: 4 :1 , 2

(The explanation is in the .pdf)

Approximately 17 students who took the optional class passed their driver's test.

Let's solve this problem step by step.

We are given the following information:

28 out of 75 students who took the optional class passed their driver's test.

8 out of 15 students overall passed their driver's test.

3 out of 5 students took the optional class.

To find the number of students who took the optional class and passed, we need to calculate the intersection of these two groups.

First, let's calculate the total number of students who took the optional class:

Total students who took the optional class = (3/5) \(\times\) Total number of students

Total students who took the optional class = (3/5) \(\times\) 75 = 45

Now, let's calculate the total number of students who passed their driver's test:

Total students who passed their driver's test = (8/15) \(\times\) Total number of students

Total students who passed their driver's test = (8/15) \(\times\) 75 = 40

Next, let's find the number of students who both took the optional class and passed their driver's test.

This can be found by taking the intersection of the two groups:

Number of students who took the optional class and passed = (28/75) \(\times\)Total students who took the optional class

Number of students who took the optional class and passed = (28/75) \(\times\)45 = 16.8 (approximated to the nearest whole number).

Therefore, approximately 17 students who took the optional class passed their driver's test.

It's important to note that since we're dealing with whole numbers, the approximated answer is 17, as we cannot have a fraction of a student.

For similar question on intersection.

https://brainly.com/question/30915785  

#SPJ8

Answer:

option 6b):) is correct

Question 2:

The low end cutoff is 52.

The high end cutoff is 90.

Question 3:

The low end value is 0.

The high end value is 45.5.

This dataset does have outliers.

The outlier is 95.

Question 4:

The low end is -1, the high end is 23, and there are no outliers in this dataset.

Question 2:

The low end cutoff is 52.

The high end cutoff is 90.

Question 3:

The low end value is 0.

The high end value is 45.5.

This dataset does have outliers.

The outlier is 95.

Question 4:

To check for outliers, we can use the following rule: An observation is considered an outlier if it falls below the low end or above the high end of the range defined by the following equation:

Low End = Q1 - 1.5 * IQR

High End = Q3 + 1.5 * IQR

Calculating the low end and high end using the given values:

Low End = 8 - 1.5 * 6 = -1

High End = 14 + 1.5 * 6 = 23

The outlier is NONE since there are no observations that fall below the low end or above the high end.

Therefore, the low end is -1, the high end is 23, and there are no outliers in this dataset.

For more such questions on outliers

https://brainly.com/question/24123584

#SPJ8

Answer:

24

Step-by-step explanation:

The numerator of the equivalent fraction of 3/8 is 9. From this, we can see that the common factor that is being multiplied is 3. So the denominator, 8, has to be multiplied by 3 as well which gives you 24. 9/24 is an equivalent fraction of 3/8

Answer:

Step-by-step explanation:

3/8 = 9/x

3x = 72

x = 24

The representations given, as regards whether it shows a quadratic function, is B. No.

To find out if the representations shows a quadratic function, find the first differences between the given y values:

10 - 5 = 5

15 - 10 = 5

20 - 15 = 5

Then, calculate the second differences, using the first differences :

5 - 5 = 0

5 - 5 = 0

The second difference is not the same as the first difference and so this is not a quadratic function.

Find out more on quadratic functions at https://brainly.com/question/29293854

#SPJ1

The sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.

The formula for sample mean is given by,

Sample Mean \((X)= (x1+x2+x3+...+xn) / n\)

Where x1, x2, x3,...,xn are individual observations and n is the number of observations.

In this case, the sample mean (X) is given as 20 and the number of observations (n) is 10.

Therefore, the formula can be written as:

\(X = (x1+x2+x3+...+x10) / 10\)

Since the population standard deviation (σ) is given as 5, the standard deviation of the sample (s) can be calculated using the formula:

s = σ/√n

Where n is the number of observations.

Therefore, in this case, the standard deviation of the sample (s) is calculated as:

s = 5/√10

s = 2.23

Thus, the sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.

Learn more about sample mean here:

https://brainly.com/question/31101410

#SPJ1

False. The complement of an event A, denoted by A', is the event consisting of all outcomes in the sample space S that are not in A.

In probability theory, a sample space S represents the set of all possible outcomes of an experiment or random phenomenon. An event A is a subset of the sample space S, representing a specific outcome or a combination of outcomes of interest.

The complement of event A, denoted by A', includes all the outcomes in the sample space S that are not part of event A. In other words, A' consists of all outcomes that do not satisfy the conditions for event A to occur.

For example, let's consider rolling a fair six-sided die. The sample space S consists of the numbers {1, 2, 3, 4, 5, 6}. Now, let event A be the event of rolling an odd number. In this case, A = {1, 3, 5}, and the complement of A, denoted by A', would be A' = {2, 4, 6}. A' includes all the outcomes that are not odd numbers.

It's important to note that the complement of an event A and the event itself together cover the entire sample space S. In other words, A and A' are mutually exclusive and exhaustive, meaning that any outcome must either be in A or in A'.

So, in summary, the complement of an event A is the set of all outcomes in the sample space S that do not belong to A.

To know more about probability theory refer here:

https://brainly.com/question/31469353

#SPJ11

the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

To determine the best estimate of the half-life by combining the two results, we can use the weighted average method. The weights assigned to each measurement are inversely proportional to the squares of their uncertainties. Here's how to calculate the combined result:

Step 1: Calculate the weights for each measurement.

  w1 = 1/σ1^2

  w2 = 1/σ2^2

  Where σ1 and σ2 are the uncertainties associated with each measurement.

Step 2: Calculate the weighted values.

  w1 * t1 = w1 * (15.5 days)

  w2 * t2 = w2 * (16.2 days)

Step 3: Calculate the sum of the weights.

  W = w1 + w2

Step 4: Calculate the weighted average.

  T = (w1 * t1 + w2 * t2) / W

Step 5: Calculate the combined uncertainty.

  σ = √(1 / W)

The best estimate of the half-life is given by the value of T, and the combined uncertainty is given by the value of σ.

Let's calculate the best estimate using the given values:

For the first measurement:

σ1 = 2.3 days

For the second measurement:

σ2 = 1.5 days

Step 1:

w1 = 1/σ1^2 = 1/(2.3^2) ≈ 0.1949

w2 = 1/σ2^2 = 1/(1.5^2) ≈ 0.4444

Step 2:

w1 * t1 ≈ 0.1949 * 15.5 ≈ 3.0195

w2 * t2 ≈ 0.4444 * 16.2 ≈ 7.1993

Step 3:

W = w1 + w2 ≈ 0.1949 + 0.4444 ≈ 0.6393

Step 4:

T = (w1 * t1 + w2 * t2) / W ≈ (3.0195 + 7.1993) / 0.6393 ≈ 13.7421 days

Step 5:

σ = √(1 / W) ≈ √(1 / 0.6393) ≈ 1.3772 days

Therefore, the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

To know more about half-life of a radioactive related question visit:

https://brainly.com/question/13979590

#SPJ11

Answer:

The 37th term of arithmetic sequence is 182.

Step-by-step explanation:

Here's the required formula to find the arithmetic sequence :

\(\longrightarrow\pmb{\sf{a_n = a_1 + (n - 1)d}}\)

Substituting all the given values in the formula to find the 37th term of arithmetic sequence :

\(\implies{\sf{a_n = a_1 + \Big(n - 1\Big)d}}\)

\(\implies{\sf{a_{37} = 2 + \Big(37 - 1\Big)5}}\)

\(\implies{\sf{a_{37} = 2 + \Big( \: 36 \: \Big)5}}\)

\(\implies{\sf{a_{37} = 2 + 36 \times 5}}\)

\(\implies{\sf{a_{37} = 2 + 180}}\)

\(\implies{\sf{a_{37} = 182}}\)

\({\star{\underline{\boxed{\sf{\red{a_{37} = 182}}}}}}\)

Hence, the 37th term of arithmetic sequence is 182.

\(\rule{300}{2.5}\)

Answer:

it is 1.7 hope it helps

Answer:

5x + 7

Step-by-step explanation:

\(2(x - 4) + 3(x + 5) = 2x - 8 + 3x + 15 = 5x + 7\)

The given statement is true.

If f and g are polynomials of degree n, then f + g is a polynomial of degree n as well.

Explanation:

Let the degree of polynomial f(x) be n, and let the degree of polynomial g(x) be m.Then we can express f(x) and g(x) as follows:f(x) = anxn + an-1xn-1 + ... + a1x + a0g(x) = bmxm + bm-1xm-1 + ... + b1x + b0When we add the two polynomials, we get:f(x) + g(x) = anxn + an-1xn-1 + ... + a1x + a0 + bmxm + bm-1xm-1 + ... + b1x + b0Since the degree of a polynomial is determined by the highest power of x that appears, the degree of f(x) + g(x) is max(n, m). Since f(x) and g(x) both have degree n, we can say that f(x) + g(x) has degree n as well.

To know more about Polynomial refer here:

https://brainly.com/question/11536910

#SPJ11

Answer:

8 Hours 15 Minutes

Step-by-step explanation:

12:00 p.m - 3:45 a.m = 8 Hours 15 Minutes

Answer:

114

Step-by-step explanation:

\(A= \frac{a + b}{2} h \\ = \frac{9 + 13}{2} 11 \\ = \frac{22}{2} 11 \\ = 11 \times 11 \\ = 121\)

the area of the trapezoid is 121 square feet

Answer:

A

Step-by-step explanation:

To find the percent of a number, write the percent as a decimal and multiply it by the number