If you walk for 1. 5 hours at 3mph how fast should you run the next 0. 5 hour to have an average speed of 4mph?

Answer:

11 in.²

Step-by-step explanation:

you can divide the shape into 2 rectangles and then you solve for the 2 rectangles and then you add them up.

Answer. The correct option is (E). 9.5 and 14.5

Explanation for step 1This is because 95% of the mean weights from samples of size 100 cats from this population will fall between 9.5 and 14.5 pounds. The other answers are incorrect because they do not fall within the range of 95% of the mean weights from samples of size 100 cats from this population

About 95% of the mean weights from samples of size 100 cats from this population would fall between approximately 11.51 pounds and 12.49 pounds.

To determine the range within which 95% of the mean weights from samples of size 100 cats would fall, we can use the concept of the confidence interval.

Given:

Population mean weight (μ) = 12 pounds

Population standard deviation (σ) = 2.5 pounds

Sample size (n) = 100 cats

Since the population distribution is assumed to be approximately normal, the sampling distribution of sample means will also be approximately normal. To calculate the range, we can use the formula for the confidence interval:

Confidence Interval = sample mean ± (z * standard error)

The standard error can be calculated using the formula:

Standard Error = σ / √n

Using a 95% confidence level, the corresponding z-value is approximately 1.96 (obtained from standard normal distribution table).

Plugging in the values:

Standard Error = 2.5 / √100 = 0.25

Confidence Interval = 12 ± (1.96 * 0.25)

Calculating the values:

Lower limit = 12 - (1.96 * 0.25) ≈ 11.51 pounds

Upper limit = 12 + (1.96 * 0.25) ≈ 12.49 pounds

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Answer:

25 dm²

Step-by-step explanation:

La superficie de nuestra pared tiene 12.5 m²

Si dividimos la superficie por la cantidad de paneles cuadrados, obtenemos la superficie de cada panel

12.5 m² /50 = 0.25 m²

Sabemos que la superficie de un cuadrado se calcula como l²

Convertimos los 0.25 m² a dm² → 0.25 m² . 100 dm² / 1m² = 25 dm²

Esa es la medida de cada papel.

Si calculamos la medida de cada lado será:

√ (25 dm²) = 5 dm

En conclusión un cuadrado con 5 dm de lado tiene 25dm² de superficie

Si convertimos a m² = 0.25 m²

0.25 m² es la medida que cubre 1 panel de papel

para cubrir 12.5 m² necesitariamos (12.5  . 1) /0.25 = 50 paneles.

Answer:

s+s+s and 3s

Step-by-step explanation:

imagine S as a number. lets say s is 1. they boyght 3 starts so it has to be 3. Option 1 and 3 has a sum of 3. Option 2 has the tital of 1 because 1³=1 and option 4 is 4.

The Non-real solutions for the equation \(x^{4} -x^{3}+10x^{2} -16x-96=0\) are (-4i, 4i).

Non-real solution:

An answer to a mathematical equation with the root of a negative number that cannot be determined using solely real numbers—i.e., numbers that can be described along a single axis—is referred to as a non-real solution.

If a quadratic has a negative discriminant, then the quadratic equation has a Non-real solution.

Given,

         \(x^{4} -x^{3}+10x^{2} -16x-96=0\)

On factorizing the above equation, we get

             \((x-3)(x-2)(x^{2} +16)=0\)

Applying Zero Product Property,

\(x^{2} +16 = 0\)      or     \(x-3=0\)     0r     \(x+2=0\)

Taking \(x^{2} +16 = 0\), we get

                \(x^{2} =-16\)

                x = ± \(\sqrt{-16}\)

                x = ± 4i              [∵ i = √-1]

Hence,

      The Non-real solutions for the equation \(x^{4} -x^{3}+10x^{2} -16x-96=0\) are (-4i, 4i).

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Answer:

C

Step-by-step explanation:

edge 2026

Answer:

The number is less than 4.

Explanation:

If we write the inequality out, we get this:

x<14(3x+4)

Now we just need to solve for x. Multiplying both sides by 4 yields:

4x<3x+4

Subtract 3x from both sides:

x<4

So any number less than 4 will work!

Answer: a rose bush is 10 dollars while a shrub is 3

Step-by-step explanation:

5x10 is 50

6x3 is 18

__________ +

68

10

11x3=33

________+

43

In the regression line y = a+ bx+ e, a is the slope of the regression line.

The above statement is False.

The correct Statement is :

The linear regression line has an equation of the form Y =a + bX

where, Y is called the dependent variable or response.

X means independent or predictor or explanatory variable.

a is the y-intercept and b is the slope of the line.

Regression Line:

A regression line is a statistical tool that shows the correlation between two variables. Specifically, it is used when the variation of one (the dependent variable) depends on changes in the value of the other (the independent variable).

Simple linear regression has two cases:

The formula for the least squares regression line (LSRL) from Y to X is:

                           Y=a + bX + ɛ

where,

Y is the dependent variable.

a is the Y intersection.

b is the slope of the regression line.

X is the independent variable.

ɛ is the residual (error).

and

b = (N∑XY-(∑X)(∑Y) / (N∑X2– (∑X)2) ;

and

a = (∑Y – b ∑X) / N

where, N is the total number of observations.

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The result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

What is long division method?

In mathematics, the long division method can be performed on the polynomial equations. Basically, in this big equation can be solved by making smaller group of equations to make the calculation simple. It divide the dividend with divisor.

According to the question, the given polynomial equation is 3x³ +19x² + 23x + 15. Using long division method, divide it by 25

Therefore, the expression can be written as:

Required expression: \(\frac{3x^{3} +19x^{2} + 23x + 15 }{25}\)

Dividing it by 25, we get:

(25/3x³) +(25/19x²) + (25/23x) + (25/15)

⇒ 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

Hence, the result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

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a) i)P(X > 18)= 0.65542

ii)P(7 < X < 15)=0.154

b)The value of a using the standard normal table or a calculator is 12.875

c)the value of b using the standard normal table or a calculator is 9.8

a) Let X be the normal random variable with mean μ = 20 and standard deviation σ = 5. We have to find P(X > 18) and P(7 < X < 15).

(i) P(X > 18)

This can be calculated using the standard normal table or a calculator as follows:

z = (18 - μ)/σ

= (18 - 20)/5

= -0.4

P(X > 18) = P(Z > -0.4)

= 1 - P(Z ≤ -0.4).

Using the standard normal table or a calculator, P(Z ≤ -0.4) = 0.34458

Therefore, P(X > 18) = 1 - 0.34458 = 0.65542

(ii) P(7 < X < 15). This can be calculated using the standard normal table or a calculator as follows:

z₁ = (7 - μ)/σ

(7 - 20)/5 = -2.6z₂

(15 - μ)/σ = (15 - 20)/5

= -1

P(7 < X < 15) = P(-2.6 < Z < -1)

= P(Z < -1) - P(Z < -2.6)

Using the standard normal table or a calculator,

P(Z < -1) = 0.15866P(Z < -2.6) = 0.00466

Therefore, P(7 < X < 15) = 0.15866 - 0.00466 = 0.154

b) We have to find the value of a such that

P(20 - a < X < 20 + a) = 0.99.

This can be calculated as follows:

z₁ = (20 - a - μ)/σ

= (20 - a - 20)/5

= -a/5z₂ = (20 + a - μ)/σ

= (20 + a - 20)/5 = a/5

We need to find a such that

P(z₁ < Z < z₂) = 0.99

Using the standard normal table or a calculator,

P(Z < z₂) - P(Z < z₁) = 0.99P(Z < a/5) - P(Z < -a/5) = 0.99

This can be rewritten as

P(Z < a/5) - [1 - P(Z < a/5)] = 0.99P(Z < a/5) - P(Z < -a/5) = 0.995

From the standard normal table or a calculator,

P(Z < 2.575) = 0.995P(Z < -2.575) = 0.005

Therefore,

2.575 = a/5 or -2.575 = -a/5a = 12.875

Therefore, the value of a is 12.875.

c) We have to find the value of b such that P(20 - b < X < 20 + b) = 0.95.

This can be calculated as follows:

z₁ = (20 - b - μ)/σ

= (20 - b - 20)/5

= -b/5z₂

= (20 + b - μ)/σ

= (20 + b - 20)/5 = b/5

We need to find b such that

P(z₁ < Z < z₂) = 0.95

Using the standard normal table or a calculator,

P(Z < z₂) - P(Z < z₁) = 0.95P(Z < b/5) - P(Z < -b/5) = 0.95

This can be rewritten as

P(Z < b/5) - [1 - P(Z < b/5)] = 0.95P(Z < b/5) - P(Z < -b/5) = 0.975

From the standard normal table or a calculator,

P(Z < 1.96) = 0.975P(Z < -1.96) = 0.025

Therefore,1.96 = b/5 or -1.96 = -b/5b = 9.8

Therefore, the value of b is 9.8.

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Answer:

80,000

Step-by-step explanation:

the 8 in 2,382,476 is in the ten thousands place (it's simple math once you understand it)

True. Any solution of Problem 1 (max f(x)) is also a solution of Problem 2 (max f(x) subject to g(x) = c).

True. If Problem 1 does not have a solution, then Problem 2 does not have a solution.

True. Problem 2 (max f(x) subject to g(x) = c) is equivalent to min -f(x) subject to g(x) = c.

False. In Problem 2, the quasi-convexity of f is not a sufficient condition for a point satisfying the first-order conditions to be a global minimum.

The function f(x,y) = 5x - 17y is quasi-concave.

Any solution that maximizes f(x) will also satisfy the constraint g(x) = c. Therefore, any solution of Problem 1 is also a solution of Problem 2.

If Problem 1 does not have a solution, it means that there is no maximum value for f(x). In such a case, Problem 2 cannot have a solution since there is no maximum value to subject to the constraint g(x) = c.

Problem 2 can be reformulated as finding the minimum of -f(x) subject to the constraint g(x) = c. This is because maximizing f(x) is equivalent to minimizing -f(x) since the maximum of a function is the same as the minimum of its negative.

False. Quasi-convexity of f is not a sufficient condition for a point satisfying the first-order conditions to be a global minimum in Problem 2. Quasi-convexity guarantees that local minima are also global minima, but it does not ensure that the point satisfying the first-order conditions is a global minimum.

The function f(x,y) = 5x - 17y is quasi-concave. A function is quasi-concave if the upper contour sets, which are defined by f(x,y) ≥ k for some constant k, are convex. In this case, the upper contour sets of f(x,y) = 5x - 17y are convex, satisfying the definition of quasi-concavity.

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After 10 days, the expected number of shoppers at the shopping mall is 163.

It is given that the number of shoppers increases daily by 5% from the number of shoppers the previous day.

As we can see that the increase in the number of shoppers is going to change every day, and the above case is compounded daily.

The formula of compound increase is

Amount = Base X (1 + r/n)ⁿˣ

where,

Base = original amount

r = rate of change

n = no. of times the change occurs in the time period

t = time

Here,

Base = 100

r = 5/100

n = 1, since it changes once every day

x = 10

Therefore we get

100 X (1 + 5/100)¹⁰

= 100 X 1.05¹⁰

162.88

Since the number of people cannot be in decimal,

the expected number of people is 163

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The sampling technique used in this scenario is a) random sampling. The researcher interviews all passengers on five randomly selected flights.

The sampling technique used in this scenario is random sampling. Random sampling involves selecting individuals from a population in such a way that each individual has an equal chance of being chosen. In this case, the researcher selects five flights at random, and then interviews all passengers on those selected flights.

Random sampling helps ensure that the sample is representative of the population and reduces the potential for bias. By randomly selecting flights, the researcher increases the likelihood of obtaining a diverse range of passengers, capturing a variety of opinions and experiences.

Other sampling techniques have different characteristics. Cluster sampling involves dividing the population into groups or clusters and randomly selecting entire clusters to be included in the sample. Stratified sampling involves dividing the population into subgroups or strata and then randomly selecting individuals from each stratum. Systematic sampling involves selecting every nth individual from a list. Convenience sampling involves selecting individuals based on their availability or accessibility, which may introduce bias into the sample.

In summary, the sampling technique used in this scenario is random sampling, as the researcher randomly selects five flights and interviews all passengers on those selected flights. This approach helps ensure a representative sample and reduces potential bias.

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As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

a=

Step-by-step explanation:

72+15=87

87/6= 14.5

a= 14.5

Answer: 14.5

Step-by-step explanation:

6a - 15 = 72

add 15 on both sides

6a = 87

divide by 6 on both sides

a = 14.5

The bowl of Kashi cereal has a total of 93 calories

Each gram of carbohydrates provides 4 calories, and each gram of fat provides 9 calories. To calculate the total calories in the bowl of Kashi cereal, we need to determine the calories from carbohydrates and fat separately and then add them together.

Calories from carbohydrates

Total carbohydrates = 25g

Fiber = 4g

Net carbohydrates = Total carbohydrates - Fiber = 25g - 4g = 21g

Calories from carbohydrates = Net carbohydrates x 4 calories/gram

Calories from carbohydrates = 21g x 4 calories/gram

Calories from carbohydrates = 84 calories

Calories from fat

Fat = 1g

Calories from fat = Fat x 9 calories/gram

Calories from fat = 1g x 9 calories/gram

Calories from fat = 9 calories

Total calories = Calories from carbohydrates + Calories from fat

Total calories = 84 calories + 9 calories

Total calories = 93 calories

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The value of x, which we get by using an exponent rule is x = 2.80259.

What is an exponent rule?

Exponent is defined as the method of expressing large numbers in terms of powers. That is, exponent refers to how many times a number is multiplied by itself. For example, 6 is multiplied by itself four times, resulting in 6 6 6 6. This can be written as 64. In this case, 4 is the exponent and 6 is the base.

We have,

               \(\frac{2}{3} ^{x} . \frac{3}{2} ^{2x} = \frac{81}{16}\)

By applying the exponent rule:

              \(\left(-1\cdot \:x+2x\right)\ln \left(\frac{3}{2}\right)=\ln \left(\frac{81}{26}\right)\)

By simplifying the equation:

               \(x=\frac{\ln \left(\frac{81}{26}\right)}{\ln \left(\frac{3}{2}\right)}\)

               x = 2.80259

Hence, the value of x = 2.80259

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Answer:

a=The sign of the correlation coefficient is the same as the sign of the slope for the best fit line.

b= When the y variable tends to increase as the x variable increases, we say there is a positive correlation between the variables.

Step-by-step explanation:

Answer:

Solution

a+148=180(Angles on a straight line equals180)

▪a=180-148=32

Now,

a+b=90(A right angle is equal to 90)

So,

▪b=90-a=90-32=58

Then,

b=b(base of iscoceles angles of traingle)

Now,

b+b+x=180(sum of angles of triangle equals 180)

or,58+58+x=180

or,x=180-116

▪x=64'

Answer.

All the options that apply for the Histograms and Bar graph are :

(b) in a histogram, the adjacent bars touch at real limits of intervals.

(d) the bars in a bar graph touch at the category boundaries.

The Option (a) and (c) are not correct because the bar graph can be drawn with either adjacent bars touching or leaving spaces between them, and shading is not a necessary feature of a bar graph.

The Option (e) is not correct because the histogram typically does not leave space between adjacent bars, but rather has the bars touching at the real limits of the intervals.

Therefore, options (b) and (d) are the correct options which describes  difference in appearance between a bar graph and a histogram.

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The given question is incomplete , the complete question is

Describe the difference in appearance between a bar graph and a histogram. Select all that apply.

(a) a bar graph leaves a space between adjacent bars.

(b) in a histogram, adjacent bars touch at the real limits of the intervals.

(c) in a bar graph, shading is used to give the bars a three-dimensional appearance.

(d) the bars in a bar graph touch at the category boundaries.

(e) a histogram leaves a space between adjacent bars.

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

The value of trigonometry function cot θ at θ = 690 degree is,

⇒ - √3

We have to given that,

A trigonometry function is,

⇒ cot θ

Where, θ = 690 degree

Now, We can simplify as;

⇒ cot θ

⇒ cot (690)

⇒ cot (2×360 - 30)

⇒ - cot 30°

⇒ - √3

Therefore, The value of trigonometry function cot θ at θ = 690 degree is,

⇒ - √3

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The appropriate test to examine the relationship between the number of steps taken and HR in a group of 1000 athletes depends on the type of data and the research question.

If the number of steps and HR are both measured on a continuous scale and the research question is to examine the strength and direction of the relationship between the two variables, then the appropriate test would be Pearson's correlation coefficient.

If either the number of steps or HR is measured on a continuous scale and the other variable is measured on an ordinal scale, then the appropriate test would be Spearman's correlation coefficient.

However, if the research question is to predict HR based on the number of steps taken, and there are other variables that may influence the relationship, then multiple regression analysis would be the appropriate test.

Chi-Square test is used to examine the association between two categorical variables. It is not appropriate for examining the relationship between a continuous and categorical variable.

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The surface area of a rectangular prism is found as 150 square inches.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.

Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.

Calculation for the surface area of rectangular prism-

Height of a rectangular prism => H = 4 inches

Width of a rectangular prism => B = 9 inches

Length of a rectangular prism => L = 3 inches

Surface area of a rectangular prism = 2(LB + BH + HL)

                                                           = 2(9×3 + 9×4 + 4×3)

                                                           = 150

Therefore, the surface area of a rectangular prism is found as  150 square inches.

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the corrected mean age and standard deviation are 32.32 and 13.76, respectively. Therefore, the required correct mean age and standard deviation are 32.32 and 13.76.

We are required to find the correct mean age and standard deviation. Concept Used: When a single observation in a data set is incorrectly recorded, we can make a new data set, substituting the correct value for the incorrect value, and then recalculating the statistics. The mean age is calculated as follows:

\($$\bar{x}=\frac{\sum_{i=1}^{n}x_i}{n}$$\)

where n is the total number of observations. The standard deviation is calculated as follows:

\($$s=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}$$\)

We are given the mean age and standard deviation to be 32.02 and 13.18, respectively.

Since one observation was misread as 27 instead of 57, we can substitute 57 for 27 and find the correct mean and standard deviation as follows:

\($$\bar{x}=\frac{\sum_{i=1}^{n}x_i}{n}$$\)

\($$\frac{\sum_{i=1}^{n}x_i}{n}=\frac{(32.02 \times 100)-27+57}{100}$$\)

\($$\bar{x}=32.32$$\)

Now, let's calculate the corrected standard deviation:

\($$s=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}$$\)

\($$s=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{99}}$$\)

Substituting the values of x_i and

$\bar{x}$, we have:

\($$s=\sqrt{\frac{(20-32.32)^2+(22-32.32)^2+...+(56-32.32)^2}{99}}$$\)

Substituting 57 for the misread observation of 27, we have:

\($$s=\sqrt{\frac{(20-32.32)^2+(22-32.32)^2+...+(56-32.32)^2+(57-32.32)^2}{99}}$$\)

$$s=13.76$$

Hence, the corrected mean age and standard deviation are 32.32 and 13.76, respectively.

Therefore, the required correct mean age and standard deviation are 32.32 and 13.76.

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Answer:

Step 3 is wrong because the subtraction property of equality was used incorrectly

Step-by-step explanation:

Henry showed all the steps he took to solve the equation.

The steps as show in the question is

4 (negative one-half x + 7) + 5 x = 15 Step 1

-Negative 2 x + 28 + 5 x = 15

Step 2

3 x + 28 = 15

Step 3

3 x = 15

Step 4

x = 5

Verifying the steps

The steps as show in the question is

4 (negative one-half x + 7) + 5 x = 15 Step 1

-Negative 2 x + 28 + 5 x = 15 (Distributive property of equality) This is correct

Step 2

3 x + 28 = 15(Addition property of equality this is correct)

Step 3

3 x = 15 (Subtraction property of equality) This is incorrect

The correct form is

3x +28 - 28 = 15 - 28

3x = -13

Step 4

x = -13/3

x = - 4.3333333333

Henry's solution is incorrect because Step 3 is wrong because the subtraction property of equality was used incorrectly.

x = -4.3

Answer:

c

Step-by-step explanation:

There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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