An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 13 inches, and the length of the base is 8 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Discrete-data is a category of quantitative information that has countable or finite values.

This indicates that there are no intermediate values between the precise numerical values that can be used to convey the data; only those values can be used. The number of siblings a person has, the number of pets a home has, and the number of individuals in a room are all examples of discrete data.

Numerous statistical methods, such as measures of central tendency like the mean, median, and mode, as well as measures of dispersion like range and standard deviation, can be used to analyse discrete data. Additionally, discrete data can be displayed graphically using tools like bar charts and frequency histograms.

A discrete data set is the number of stories in a skyscraper in Manhattan. A continuous data set, on the other hand, can be divided into ever-smaller pieces and can take on any value within a range. Therefore (b), "A discrete data set because the possible values can be counted."

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By using the concept of probability, it can be calculated that

a)  P(X \(\leq\) 1) = 0.25

b) P(0.5 \(\leq\) X \(\leq\) 1)  = 0.1875

c) P(X > 1.5) = 0.4375

d) Median = 1.414

e) F'(X) = 0.5x , 0 \(\leq\) x \(\leq\) 2

           0, otherwise

f) E(X) = 1.33

g) V(X) = 0.2311, SD(X) = 0.4807

h)  E(h(X)) = 2

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

The cdf is

f(x) = \(\left \{ {\frac{x^2}{4}},{ 0 \leq x \leq 2} \atop {1, x=2}} \right.\)

Now,

a) P(X \(\leq\) 1) = \(\frac{1^2}{4} = 0.25\)

b) P(0.5 \(\leq\) X \(\leq\) 1)

= \(\frac{1^2}{4} - \frac{0.5^2}{4}\\\\\frac{3}{16}\\\\0.1875\)

c) P(X > 1.5) = 1 - P(X \(\leq\) 1.5)

                      \(1 - \frac{1.5^2}{4}\)

                       0.4375

d) Let \(\mu\) be the median

P(x \(\leq \mu\)) = 0.5

\(\frac{\mu^2}{4} = 0.5\)

\(\mu^2 = 0.5 \times 4 =2\\\mu = \sqrt{2}\\\mu = 1.414\)

e) F'(x) =

\(\frac{2x}{4}, 0 \leq x \leq 2\\0, otherwise\)

F'(X) = 0.5x , 0 \(\leq\) x \(\leq\) 2

           0, otherwise

f) E(x) =

\(\int_0^2 x \times 0.5 xdx\\=0.5 \times \frac{x^3}{3} |_0^2 \\=0.5 \times \frac{2^3}{3}\\=\frac{4}{3}\\=1.33\)

g) V(X) = E(\(X^2\)) -\((E(X))^2\)

    E(X^2) =

                   \(\int_0^2x^2(0.5x)dx \\0.5 \times \frac{x^4}{4}|_0^2\\2\)

\(V(X) = 2 - (1.33)^2\)

V(X) = 0.2311

SD(X) = \(\sqrt{0.2311} = 0.4807\)

h) h(X) = \(X^2\)

   E(h(X)) = \(\int_0^2X^2({0.5X)dx\)

               = \(0.5 \frac{x^4}{4}|_0^2\)

               = \(0.5 \times \frac{2^4}{4}\)

               = 2

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Explanation:

The angles marked with a single arc are one pair of congruent angles forming one "A" of "ASA".

The other "A" is the angles marked with double arcs.

The "S" refers to the sides between those said angles. These sides overlap perfectly so we have a shared side, meaning they must be the same length (refer to the reflexive property).

This is why the triangles are congruent by the ASA (angle side angle) congruence theorem. One triangle is a reflected version of the other. The mirror line being that shared overlapping side. Congruent triangles are like twin identical copies.

Option 4, where most people keep the original item, aligns with psychological tendencies such as loss aversion and the endowment effect.

Among the given options, the most likely scenario is option 4: most people will keep the original item since people tend to value what they have more than a product they do not possess. This behavior can be attributed to the concept of loss aversion and the endowment effect.

Loss aversion refers to the tendency of individuals to strongly prefer avoiding losses rather than acquiring equivalent gains. In the context of the scenario, people may perceive the act of exchanging their original item as a potential loss because they already possess and value it. As a result, they may be reluctant to give up their original item, even if the alternative item is of equal value.

The endowment effect further strengthens this inclination to keep the original item. The endowment effect suggests that people assign a higher value to items they already possess compared to identical items that they do not own. This valuation bias stems from the psychological attachment and sense of ownership associated with the original item.

Given these behavioral biases, it is reasonable to expect that most individuals will choose to keep their original item rather than exchange it for an alternative item. This preference is driven by the aversion to perceived losses and the elevated value placed on the possession of the original item.

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Answer:

7

Step-by-step explanation:

49(waterballoons) divided by 7=7groups

The required final answer is option a) Incentre

The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".

It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.

The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.

The incentre is always within the triangle and is equidistant from all three sides of the triangle, making

it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.

Thus, required answer is "Incentre".

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Answer:

principal is the correct answer

Step-by-step explanation:

principal is the correct answer

Answer:

Its b

Step-by-step explanation:

I took the test on edge 2020

Answer:

The correct option is A,3875  passengers

Step-by-step explanation:

The curve of best fit for the date y=-5x^2+60x+3715

For April which month 4  which means that x is 4

By substituting 4 for x in the equation we can determine y, the number of passengers that arrived on flights at the airport  is determined thus.

y=-5*4^2+(60*4)+3715

y=-5*16+240+3715

y=-80+240+3715=3875

The number of passengers that arrived by flights in April, month 4 is 3875

the end behavior of the polynomial function f(x) = \(2x^3 + 5x^2 - 2x - 3\) is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

To describe the end behavior of a polynomial function, we need to examine the degree and leading coefficient of the function. In the polynomial function f(x) =\(2x^3 + 5x^2 - 2x - 3\), the degree is 3 and the leading coefficient is 2.

The end behavior of the polynomial function f(x) is determined by the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the leading term dominates the behavior of the function. Since the leading coefficient is positive and the degree is odd, the function will increase without bound, or approach positive infinity. In other words, as x becomes very large and positive, the function will also become very large and positive.

As x approaches negative infinity, the leading term also dominates the behavior of the function. However, since the degree is odd, the function will decrease without bound, or approach negative infinity. In other words, as x becomes very large and negative, the function will also become very large and negative.

Therefore, the end behavior of the polynomial function f(x) = \(2x^3 + 5x^2 - 2x - 3\) is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

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In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.

Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.

An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.

Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.

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Answer:

1.98 is your tax rate of the lipstick

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:

I think B ... not sure though

Step-by-step explanation:

tell me if I'm wrong.. TwT

The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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When it says the "x - 1 " is the factor of that function means when you find the root of the phrase x - 1 which is x = 1 , put it in the function then you have to get zero for the answer :

thus :

\(f(1) = 0\)

Thus :

\(2 \times {1}^{3} + k(1) - 9 = 0\)

So :

\(2 + k - 9 = 0\)

\(k - 7 = 0\)

Add both sides 7

\(k - 7 + 7 = 0 + 7\)

\(k = 7\)

There you go...

Have a great day ❤

After 3 months memberships will cost the same.

We have,

Cost of Membership of 1st gym = $ 10  per month

And, the Cost of the sign-up fee for 1st gym = $ 45

And,

Cost of Membership of  2nd gym =  $ 25 per month

And, the Cost of the sign-up fee of the 2nd gym = $ 0

Now,

Let the number of months = m

So,

According to the question;

45 + 10m = 25m

⇒

25m - 10m = 45

15m = 45

m=3

So, After 3 months memberships will cost the same.

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Answer:

i don't understand the question sorry

Answer:

Step-by-step explanation:

20.70/90= 0.23 per foot

30*.23= 6.90

It'll cost $6.90 for 30 more feet.

Answer:

To find Anna's rate of pay, we need to divide her earnings by the number of hours worked.

Earnings for 13 hours = $235.30

Earnings for 19 hours = $343.90

Earnings for 23 hours = $416.30

To find the rate of pay, we can choose any set of earnings and hours and divide them. Let's choose the first set:

Rate of pay = Earnings / Hours worked

Rate of pay = $235.30 / 13 hours

Using a calculator, we get:

Rate of pay = $18.10/hour

Therefore, Anna's rate of pay is $18.10 per hour.

Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

As given in the question,

Macro earns commission rate of 6% for the first $6500

And 9% on sales over $6500

Out of $10,500

For first $6500 Commission =(6500 × 6)/ 100

                                            = $390

For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100

                                                                   = $360

Total graduated commission on sales of $10,500 = $( 390 + 360)

                                                                             = $750

Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

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The different ways in which she can jump up a set of five steps is: 4 + 3 + 1 = 8 ways.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

Here, the differences between permutation and combination are described in detail.

The given steps are 5.

Thus, we have the following possibilities:

For 1 double step and 3 single steps:

4! / 3! = 4

For 2 double steps and 1 single step:

3! / 2! (1!) = 3

For 5 single steps: 1 way

Thus, the different ways in which she can jump up a set of five steps is:

4 + 3 + 1 = 8 ways.

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Answer:

2 TB of oil every TB of vinegar

Step-by-step explanation:

8/16=0.5

0.5 is equal to 1/2

therefore, since you need a 1/2 TB of vinegar, it would take two 1/2 TB to make 1 TB of vinegar, meaning you would need 2 TB of oil per tablespoon of vinegar.

greatly appriecated if you give me brainliest!

(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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Answer: X = 4

Step-by-step explanation: Move all the terms besides X to the right side, from there you will divide each term by 3 then simplify.

Based on the given data, a 95% confidence interval estimate of the mean number falls between 12.22 and 16.78.

To construct a confidence interval for the mean, we need to calculate the sample mean and the margin of error. The formula for the margin of error is:

Margin of Error = Z * \(\frac{standard deviation}{\sqrt{n} }\)

where Z is the critical value corresponding to the desired confidence level (for 95% confidence level, Z ≈ 1.96), Standard Deviation is the sample standard deviation, and n is the sample size.

From the given data, we calculate the sample mean to be 14.33 and the sample standard deviation to be 1.91. Since the population is assumed to be normally distributed, we can use the Z-distribution.

Using the formula for the margin of error, we find:

Margin of Error = 1.96 * (1.91 / √9) ≈ 1.39

The confidence interval is calculated by subtracting and adding the margin of error to the sample mean:

Confidence Interval = (14.33 - 1.39, 14.33 + 1.39) = (12.94, 15.72)

Rounded to at least two decimal places, the 95% confidence interval estimate of the mean number is approximately (12.22, 16.78). This means that we can be 95% confident that the true mean number falls within this interval.

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Answer:

D: 19 should have been subtracted from, not added to, both sides of the equation.

Step-by-step explanation:

Because if we subtract 19 from both sides, we directly get the value of x.

Equation:-

x + 19 = 34

Subtracting 19 from both sides,

=> x + 19 - 19 = 34 - 19

=> x = 15

9. Expression matches with option C: log3 12.
10. Expression matches with option D: log3 36.
11. Expression matches with option A: log3 64.
12. Expression matches with option C: log3 12.

To match the expression with the logarithm that has the same value, we need to simplify each expression and rewrite it

in the form of log3 x.

9. log3 6 + log3 2 = log3 (6 × 2) = log3 12.

Therefore, the expression matches with option C: log3 12.

10. \(2 log36 = log36^2 = log3 (6^2)^2 = log3 36.\)

Therefore, the expression matches with option D: log3 36.

11. \(6 log32 = log32^6 = log3 (2^5)^6 = log3 2^30.\)

Therefore, the expression matches with option A: log3 64.

12. log3 6 + log3 2 = log3 (6 × 2) = log3 12.

Therefore, the expression matches with option C: log3 12.
In summary:
9. Expression matches with option C: log3 12.

10. Expression matches with option D: log3 36.

11. Expression matches with option A: log3 64.

12. Expression matches with option C: log3 12.

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Answer:

4 miles

Step-by-step explanation:

4 miles because if if if 58 of mile which is just a half mile basically and she does 7 laps

7 x 0.58=4.06 which is 4 miles

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