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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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Answer:5 gallons

Step-by-step explanation:

20 quarts/4=5

Answer:

\(\{8,-8\}\)

Step-by-step explanation:

\(~~~-|x| = -8\\\\\implies |x| = \dfrac{-8}{-1}\\\\\implies |x| = 8\\\\\implies x = \pm 8\\\\\text{Hence, the solution set is}~ \{8,-8\}\)

In order to fill each missing statement and reason, let's check for the corresponding part of the missing statement or reason.

For example, reason 5 is missing. The statement 5 is reflexive property of congruency.

In the same way, statement 6 is missing, and the reason is AA Similarity Postulate.

Therefore the statement is Triangles CDB and CDA are similar.

Reason 7 comes from the proportion written in statement 7. So the reason is the proportion between corresponding sides in similar triangles is the same.

(or we can write "corresponding sides of similar triangles are proportional)

Reason 8 comes from the cross product in a fraction equation.

Reason 9 is that all right angles are congruent.

Reason 10 is the reflexive property of congruency.

Statement 11 is that triangles BCA and CDA are similar.

Reason 12 is that the proportion between corresponding sides in similar triangles are the same.

Reason 13 is the cross product in a fraction equation.

Reason 14 is the addition of the equations from statements 8 and 13.

Statement 15 is a² + b² = c(x + y)

Reason 16 is point D is on segment AB (therefore AD + DB = AB)

Reason 17 is the substitution from the equation of statement 16 in the equation of statement 15.

Probability of requiring repair by the four cars in the first six months is equal to 0.009235.

As given in the question,

Probability of having repair requirement in the first six months = 31%

Success rate 'p' = 31%

                          = 0.31

1 - p = 1 - 0.31

       = 0.69

Total number of cars 'n' = 4

Number of cars need to repair 'x' = 4

Probability for all the four cars require repairment in the first six months

= ⁿCₓ pˣ ( 1 - p)ⁿ⁻ˣ

= ⁴C₄ ( 0.31)⁴ ( 0.69)⁴⁻⁴

=( 4!/ (4-4)!4!) × ( 0.31)⁴ × 1

= ( 0.31)⁴

= 0.009235

Therefore, the probability of all the four cars require repairing in the first six months is equal to 0.009235.

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The coordinates of the image of the point (-9, 3) under the same translation is (-8, 1).

Given,

The points whose image is there = (0, 9)

The points under translation = (1, 7)

We have to find the image of the point (-9, 3) under the same translation:

Now, we have to find the transformation of given points:

Point: (0, 9)

Translation: (1, 7)

x coordinate:

1 - 0 = 1

x coordinate is increased by 1.

y coordinate:

7 - 9 = -2

y coordinate is increased by -2

Apply the same transformation to the point given:

Point : (-9, 3)

x coordinate:

1 + (-9) = 1 - 9 = -8

y coordinate:

-2 + 3 = 3 - 2 = 1

Therefore, the coordinates of the image of the point (-9, 3) under the same translation is (-8, 1).

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Answer:

t = 4 + 6n

Step-by-step explanation:

a = 10

d = 6

in general

tn = a + (n-1)*d

tn = 10 + (n-1)*6

tn = 10 + 6n - 6

tn = 4 + 6n

So if n = 5 then

t5 = 4 + 6*5

t5 = 4 + 30

t5 = 34 which agrees with your givens.

Answer:

5

Step-by-step explanation:

The value of the fraction 2 1/6 + 7 3/6 is B. 9 2/3

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

The fraction is given as:

2 1/6 + 7 3/6

= 9 4 / 6

Reduce to lowest term

= 9 2/3

The correct option is B.

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Answer:

-8/9.

Step-by-step explanation:

The slope = difference in y-values / corresponding difference in x values

Slope = (-8-0)/(5 - (-4))

= -8/9.

Answer:

250 minutes.

Step-by-step explanation:

1/5=50/x

cross product

5*50=1*x

250=x

The initial value problem. y'(t) = 1 + e^t, y(0) = 20 The specific solution is y(t)= t + e^t + 19.

Let's go step-by-step:
1. Identify the problem: We are given a differential equation y'(t) = 1 + e^t and an initial value y(0) = 20.

2. Integrate the differential equation: To find y(t), we need to integrate the given equation with respect to t.
  ∫(y'(t) dt) = ∫(1 + e^t dt)

3. Perform the integration: After integrating, we obtain the general solution of the problem:
  y(t) = t + e^t + C, where C is the constant of integration.

4. Apply the initial value: We are given y(0) = 20, so we can plug this into the general solution to find the specific solution.
  20 = 0 + e^0 + C
  20 = 1 + C

5. Solve for the constant of integration C: From the above equation, we find the value of C.
  C = 19

6. Write the specific solution: Now that we have the value of C, we can write the specific solution for y(t).
  y(t) = t + e^t + 19

So, the specific solution for this initial value problem is y(t) = t + e^t + 19.

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Answer:

(f*g)(x) = 3x^2 + 25x - 18

Step-by-step explanation:

(f*g)(x) represents the product of the two functions f and g:

(f*g)(x) = 27x - 18 + 3x^2 - 2x, or, after simplification,

(f*g)(x) = 25x - 18 + 3x^2, or

(f*g)(x) = 3x^2 + 25x - 18

Answer:

the answer is 2

Step-by-step explanation:

add -4x and -6x and the answer is -10x bc they are both negative x. then divide both -10x and -20 by -10 so that it is x by itself on one side and 2 on the other so its 2=x :)

Mathematics is a broad subject that covers a wide range of topics, one of which is probability. Probability is a branch of mathematics that deals with the study of random events or situations. It involves the calculation of the likelihood of an event occurring, which is often expressed as a fraction or a percentage.

A common probability question is the "dice problem." Suppose you roll a fair six-sided dice. What is the probability of rolling a number less than or equal to 3? The answer to this question can be found by counting the number of favorable outcomes and dividing by the total number of possible outcomes. In this case, there are three favorable outcomes (rolling a 1, 2, or 3) and six possible outcomes (rolling any number from 1 to 6).

Therefore, the probability of rolling a number less than or equal to 3 is 3/6, which can be simplified to 1/2 or 50%.

Probability is an important concept that is used in many real-life situations, such as weather forecasting, sports betting, and financial investment.

By understanding the principles of probability, we can make informed decisions and make sense of the uncertain world around us.

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There is no polynomials such that \(P(z)e^{\frac{1}{z} }\) is entire.

Sums of elements of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the equation 3x+2x-5. a description of polynomials.

By the Taylor expansion, \(e^{\frac{1}{z} }\) = ∑∞n= 0.

Let P(z)= (ad)zd+.......+a0.

For n>0, the coefficient of z-n in the expansion of \(P(z)e^{\frac{1}{z} }\) is :-

\(tn= n^{a0} 1 + (n+1)!+.......+(n+d)!\)

So the Laurent expansion of \(P(z)e^{\frac{1}{z} } = 0\)will have terms of the form tn2-n where an is not equal to zero.

if r is the smallest non negative integer such that ar is not equal to zero, then we see that we can rewrite:-

\(tn= (n^{1} +r)![ar+n^{ar+1} +1+.....+(n+r+d)....(n+d)]\)

as we know that \(\lim_{n \to \infty} (n+r+1+....+(n+r+d).....(n+d)=0\)

so there exists an N∈N, such that:-

\(/ar/ > n+r+1+....+(n+r+d)....(n+d)=0\)

HenHence tn is non zero for all n>N. In other words, expansion contains terms of negative powers.

So, apart from P(z)=0, there is no polynomials such that \(P(z)e^{\frac{1}{z} } .\)

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The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Answer:

She made 67 shots

She missed 23 shots

Step-by-step explanation:

Margot missed 90(0.25) = 22.5, or about 23 shots

Margot made 90-23 = 67

Answer:

b=4 and a does not equal 3

Step-by-step explanation:

For the system to have no solutions

The x terms have to have the same coefficient and the constants have to be unequal

b=4 and a does not equal 3

Answer:

explain aLOLaolop:o

Step-by-step explanation:

Domain of the function is \(0\leq b\leq 10\) and range of the function is \(0\leq W\leq 120\).

The range of values that we are permitted to enter into our function is known as the domain of a function.

A function's range is the collection of values it can take as input.

Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.

The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.

Therefore, the domain of the function is  \(0\leq b\leq 10\) and the range of the function is \(0\leq W\leq 120\).

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Answer:

Multiply 5 to both sides to get

(x+3)^2 = 100

Step-by-step explanation:

Please refer to the picture above.

Simplify the equation by aiming to eliminate the fraction in the right hand side of the equation by multiplying the denominator to both sides of the equation in step 2

Answer:

\((x + 3)^{2}\) = 100

Step-by-step explanation:

Answer: x > -7

Step-by-step explanation:

so first, we move the constant to the right.

-3x < 15 + 6

the, we calculate that.

-3x < 21

then, we divide both sides.

solution: x > -7

Answer:

14.2 units

Step-by-step explanation:

use the distance formula -  take the square root of the following:

(\(y_{2}\)-\(y_{1}\))^2 +(\(x_{2}\)-\(x_{1}\))^2

should be sq rt of 202, or approx 14.2 units

Answer:

Step-by-step explanation:

25.12 inches around means diameter. So radius = 12.56 inches

   volume  \(= \pi r^2 \times h =\pi \times 12.56^2 \times 66 = 32709.44 \ in^3\)

Answer:

The volume of the drained pipe is 32692.11 in ³.

Step-by-step explanation:

Diameter of drainage pipe = 25.12 in

So, radius , r = 25.12 in = 12.56 in

Height of drainage pipe, h = 66 in.

Volume of the drainage pipe

We know that,

Volume of cylinder = π × r ² × h

substitute the values

Volume of pipe = 3.14 × (12.56 in)² × 66 in

simplify

Volume of pipe =3.14 ×157.7536 in² × 66in

multiplying ✖ the values

Volume of the pipe = 32,692.11 in ³

Therefore, the volume of the drained pipe is 32692.11 in ³.

The statement with the inequalities are:

a. In △HEY, m∠1 is > m∠4.

b. In △HEY, m∠1 is = m∠4 + m∠6.

c. In △HEY, m∠3 is > m∠5.

d. In △HEY, m∠2 is > m∠6.

e. In △HEY, m∠4 is < m∠3​.

We have,

From the figure,

m∠1, m∠3 and m∠2 are exterior angles.

So,

m∠1 = m∠4 + m∠6

m∠3 = m∠5 + m∠4

m∠2 = m∠5 + m∠6

Now,

a.

In △HEY,

m∠1 is  > m∠4.

b.

In △HEY,

m∠1 is = m∠4 + m∠6.

c.

In △HEY,

m∠3 is > m∠5.

d.

In △HEY,

m∠2 is > m∠6.

e.

In △HEY,

m∠3 = m∠5 + m∠4

m∠4 = m∠3 - m∠5

The angles can not be negative.

So,

m∠4 is < m∠3​.

Thus,

a. In △HEY, m∠1 is > m∠4.

b. In △HEY, m∠1 is = m∠4 + m∠6.

c. In △HEY, m∠3 is > m∠5.

d. In △HEY, m∠2 is > m∠6.

e. In △HEY, m∠4 is < m∠3​.

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