Dena is going to construct a paper box. She will make the box x inches wide. The height of the box is 3 inches greater than the width, and the box is twice as deep as it is high. The volume of the box is 6464 in33. Which equation correctly describes the volume of the box?

Answer:

P=0.2613

Step-by-step explanation:

-Notice that this is a poison probability distribution problem.

-The Poisson probability function is expressed as:

[tex]P(X=x)=\frac{\lambda^x e^{-\lambda}}{x!}[/tex]

where:

Given that x= 2 and [tex]\lambda=2.4[/tex], the probability is calculated as:

[tex]P(X=2)=\frac{\lambda^xe^{-\lambda}}{x!}\\\\=\frac{2.4^2e^{-2.4}}{2!}\\\\\\=0.2613[/tex]

Hence, the  probability that in a randomly selected office hour, the number of student arrivals is 2 is 0.2613

Final answer:

To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4.

Explanation:

To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4, so the parameter λ for the Poisson distribution is 2.4.

The probability of getting exactly 2 student arrivals can be calculated using the formula:

P(X=k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of student arrivals, k is the desired value (2 in this case), and λ is the average number of student arrivals per office hour.

Calculate e^-λ: e is the base of the natural logarithm and λ is 2.4. e^-2.4 ≈ 0.0908.

Calculate λ^k: 2.4^2 ≈ 5.76.

Calculate k!: 2! = 2.

Plug in the calculated values into the formula: P(X=2) = (0.0908 * 5.76) / 2 ≈ 0.2613.

So, the probability that in a randomly selected office hour, the number of student arrivals is 2 is approximately 0.2613 or 26.13%.

The information given results in one triangle. By applying the law of sines and trigonometric relation, we find the angles A=107.52, B=30, C=42.48 degrees for a triangle with sides b=6, c=8.

The problem deals with the Law of Sines which can be used to determine if a triangle exists given two sides and a non-included angle. According to the law of sines, ratio of the length of a side to the sine of the opposite angle is the same for all  three sides of a triangle. Using this, we can determine whether the given conditions lead to a valid triangle.

Given: b = 6, c = 8, B = 30 degrees

1. Compute the value of sin(B) = sin(30) = 0.5 (using standard angle values).

2. Apply the law of sines to compute the missing angle. You get sin(C) = c*sin(B)/b = 8*0.5/6 = 0.67

3. Check sin(C): if sin(C) is greater than 1 or less than -1, no triangle exists. If sin(C) = 0.67, we get C = arcSin(0.67) = 42.48 degrees.

4. To find the third angle A, use the relationship 'Sum of angles in a triangle' equals 180. Hence, A = 180 - B - C = 180 - 30 - 42.48 = 107.52 degrees. We know that in a triangle, no angle can exceed 180 degrees, hence A=107.52 degrees confirms that the triangle is possible.

Hence given information results in one triangle with sides b=6, c=8 and angles A=107.52, B=30 and C=42.48

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The given information results in one triangle. To solve the triangle, we can use the Law of Sines.

The given information of b=6, c=8, and B=30 degrees results in one triangle.

To solve the triangle, we can use the Law of Sines.

By plugging in the values, we can find the length of side a using the formula: a = (b * sin(A)) / sin(B).

After substituting the values, we find that the length of side a is approximately 3.464 units.

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Answer:

Step-by-step explanation:

the length of the smallest side is 4 inches.

the length of the middle side is 8 inches.

the length of the longest side is 12 inches.

Step-by-step explanation:

Let x represent the length of the middle side of the triangle.

The longest side is 4 more than the middle side. It means that the length of the middle side is x + 4.

The smallest side is half the length of middle side. It means that the length of the smallest side is

x/2

The formula for determining the perimeter of a triangle is

Perimeter = a + b + c

Where a, b and c are the lengths of each side of the triangle. The perimeter of the triangle is 24 inches. It means that

x + 4 + x + x/2 = 24

Multiplying both sides of the equation by 2, it becomes

2x + 8 + 2x + x = 48

5x = 48 - 8

5x = 40

x = 40/5

x = 8 inches

The length of the longest side is

8 + 4 = 12 inches

The length of the smallest side is

8/2 = 4 inches

Answer:

c

Step-by-step explanation:

im not explaining im taking the test

Answer:

Lengths can't be negative

Step-by-step explanation:

Dimensions of the base are:

(8.5-2x) × (11 - 2x)

Since length cannot be negative:

x > 0

8.5 - 2x > 0

2x < 8.5

x < 4.25

11 - 2x > 0

x < 5.5

The set of values of x which satisfies all is:

0 < x < 4.24

Answer:

B) Translate the graph [tex] k [/tex] units to the left.

Answer:

C

Step-by-step explanation:

Answer:

C. 24 degrees

Step-by-step explanation:

The 3 angles inside ∠ABE: ∠ABC,∠DBC and∠EBD must add to 126 degrees

∠ABC+∠DBC+∠EBD =126

We already know that ∠DBC is 30 degrees, and ∠EBD is 72 degrees, so we can substitute them in

∠ABC+30+72=126

Combine like terms

∠ABC+102=126

Subtract 102 from both sides

∠ABC=24

So, ∠ABC equals 24 degrees, and C is the correct choice

Answer:1/2

Step-by-step explanation: i dont really have a explanation but its right

Step-by-step explanation:

uhhh link an image please?

Answer:

  $3.85 per ounce

Step-by-step explanation:

If we assume that all of the purchased ingredients are used in a mixture, their total cost is ...

  3(4.03) +2(3.42) +4(3.92) = 34.61

The total quantity of mix is ...

  3 + 2 + 4 = 9 . . . ounces

Then the cost per ounce is ...

  $34.61/(9 oz) ≈ $3.85 /oz

The cost per ounce of the perfume that Charlene and Gary made is $3.85. This is calculated by adding the total cost of each ingredient and dividing by the total quantity of all ingredients.

To find the cost per ounce of the perfume that Charlene and Gary wish to make, you need to determine the total cost of all the ingredients first, then divide by the total quantity of the perfume produced.

First, calculate the total cost of each ingredient:

Total cost is thus $12.09 + $6.84 + $15.68 = $34.61.

The total quantity of the perfume is 3 ounces (rose oil) + 2 ounces (ginger essence) + 4 ounces (black currant essence) = 9 ounces.

Therefore, the cost per ounce of the perfume is $34.61 / 9 ounces = $3.85 per ounce (rounded to the nearest cent).

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Answer:

12

Step-by-step explanation:

h = V / A

Height equals volume divided by (base) area.

144 / 12 = 12

The height of the cylinder is 12 cm.

To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by:

[tex]\[ V = B \times h \][/tex]

 where [tex]\( V \)[/tex] is the volume, [tex]\( B \)[/tex] is the base area, and [tex]\( h \)[/tex] is the height of the cylinder.

 Given that the base area [tex]\( B \)[/tex] is 12 cm² and the volume [tex]\( V \)[/tex] is 144 cm³, we can solve for the height [tex]\( h \)[/tex] by rearranging the formula:

[tex]\[ h = \frac{V}{B} \][/tex]

 Substituting the given values:

[tex]\[ h = \frac{144 \text{ cm}^3}{12 \text{ cm}^2} \][/tex]

[tex]\[ h = 12 \text{ cm} \][/tex]

 Therefore, the height of the cylinder is 12 cm.

Answer:d

Step-by-step explanation:

Clearly from observation option D is the exponential sequence

256,64,16,4 is decreasing exponential function

[tex]\Rightarrow \frac{256}{64}=\frac{4^4}{4^3}=4[/tex]

[tex]\Rightarrow \frac{64}{16}=4[/tex]

for other option they simply follow an AP

2,6,10,14,18

common difference d=4

So the first thing you would want to do is rewrite the equation like so.

−x+4y=−3;−5x−4y=−15

once you done that you'll have to think about what variable are you trying to get be itself which in this case it'll be x. So now you'll be solving this equation.

−x+4y=−3

next you'll add -4y to both sides

Once you done so you should have this written down

-x over -1 = 4y- 3 over -1

divide -1 to both sides and you should end up with x= 4y+3

Now you have to substitute 4y+3 for x in -5x-4y=-15

So it should look like this now

−5(4y+3)−4y=−15

The next step is to simplify both sides with the following equation

−24y−15=−15

After simplifying add 15 to both sides, It then should look like this

−24y=0

Divide -24 to both sides and your answer should be this

y=0

hope this helps :)

Answer:

D. Euler Circuit.

Step-by-step explanation:

An Euler Circuit goes through every edge exactly once; starts and stops at the same vertex.

According to the Euler's Theorem, A graph has an Euler path if there are two 2-degree vertices without odd degrees and all other vertices have even degrees.

Mathematically, it is given as;

V+F=2-E

where;

F is the number of faces

V the number of vertices

E the number of edges.

Final answer:

An Euler Path traverses every edge of a graph exactly once and can start and end at different vertices, fitting the student's question.

Explanation:

The student's question hints at two different types of paths in graph theory: the Euler Path and the Hamiltonian Path. An Euler Path goes through every edge exactly once and can start and stop at different vertices. This path doesn't have to cover all vertices, but it must include every edge.

Here's a breakdown of the terms:

Hamiltonian Path: A path that visits every vertex exactly once, but it may start and end at different vertices.

Hamiltonian Circuit: A path that visits every vertex exactly once and starts and ends at the same vertex (creating a cycle).

Euler Path: A path that uses every edge exactly once, but it may start and end at different vertices.

Euler Circuit: A path that uses every edge exactly once and starts and ends at the same vertex (creating a cycle).

On the other hand, a Hamiltonian Path also goes through every vertex exactly once, but it is not concerned with edges.

In this case, since the definition provided in the question states the requirement is about edges and not vertices, the correct answer is c. Euler Path.

Answer:

Answer: 3x + 3 = 2x + 1

Answer: 3x + 3 = 2x + 1 <=>3x - 2x = 1 - 3

Answer: 3x + 3 = 2x + 1 <=>3x - 2x = 1 - 3 <=> x = -2

Answer:

46.5

Step-by-step explanation:

Answer:

◽Angle 14 and Angle 12

◽Angle 10 and Angle 8

Step-by-step explanation:

Vertical angles are opposite to each other on a pair of intersecting lines.

◽Angle 1 and Angle 4

These angles are not on the same two intersecting lines.

◽Angle 14 and Angle 12

These angles are on the same two intersecting lines. They are also opposite to each other.

◽Angle 7 and Angle 8

These angles are on the same intersecting lines, but they are not opposite to each other.

◽Angle 10 and Angle 8

They are on the same pair on lines, and opposite to each other.

◽Angle 3 and Angle 5

They are not on the same pair of intersecting lines.

◽Angle 8 and Angle 12

These angles are not on the same pair on intersecting lines. (However, they are also equal because they are corresponding, on the insides of an "F" pattern).

Answer:

A and D

Step-by-step explanation:

Edge 2020

Answer:

Ethan

Step-by-step explanation:

In the scenario presented, Ethan is right to say that adjacent angles are not supplementary. This is as a result of the fact that no other condition was attached.

Adjacent angles are only supplementary "if they are all on a straight line" as in Mia's case.  This is a special case and an extra condition has been imposed.

Answer:

y= 12x + 5 for part A, part B is 89 thousand miles

Step-by-step explanation:

Just copy the answer you nerd.

Answer:

one angle is 150 degrees and the other is 30 degrees.

Step-by-step explanation:

please kindly check the attached file for explanation.

Answer:

I think, one angle is 150 and the other 30.

Step-by-step explanation:

First, you can make a table of 3 columns: Angle 1, Angle 2 and Total

Then, you will work with the ratio 5:1 and say

Angle 1    Angle 2     Total

5               1                 6

Then you do a little algebra process like this:

6a=180

6 x a /6= 180 / 2

a=30

6a=180

6 x a / 6=180/2    This means 6 times a divided by 6= 180 divided by 2. We insolate the variable, and we cross out the two six

a=30 And our answer is 30.

You can choose any variable. In this case I did with the variable a since we are talking about angles.

Returning to the table, the thing we need to do is this:

Angle 1    Angle 2     Total

5               1                 6

150          30               180

We need to multiply 5x30 and 1x30

Then we add 150 plus 30 is 180.

So one angle is 150 and the other 30.

Hope this helps.

Answer:

144=2x2x2x2x3x3

Step-by-step explanation:

Answer:

[tex]2^4\cdot3^2[/tex]

Step-by-step explanation:

The first step is to break this down. 144=12^2 or 12*12. Now you can break down 12. 12=4*3=2*2*3. This means that 144=2*2*3*2*2*3=[tex]2^4\cdot3^2[/tex]. Hope this helps!

Answer:

6/25

Step-by-step explanation:

Given two events A and B, the conditional probability of event A is the probability that event A occurs given that event B has occurred. It is calculated as

[tex]p(A|B)=\frac{p(A\cap B)}{p(B)}[/tex]

where

[tex]p(A\cap B)[/tex] is the probability that both A and B occur at the same time

[tex]p(B)[/tex] is the probability that B occurs

In this problem, we call:

A = the camera has a lens defect

B = the camera has a charging defect

Here we have:

a = 20 is the number of cameras with lens defects

b = 25 is the number of cameras with charging defects

c = 6 is the number of cameras having both defects

n = 800 is the total number of cameras

So we have:

[tex]p(A\cap B)=\frac{c}{n}=\frac{6}{800}[/tex] is the probability that the camera has both lens and charging defect

[tex]p(B)=\frac{b}{n}=\frac{25}{800}[/tex] is the probability that the camera has a charging defect

So the conditional probability is

[tex]p(A|B)=\frac{6/100}{25/100}=\frac{6}{25}[/tex]

To determine the minimum sample size needed to estimate the population proportion, and the minimum sample size needed, assuming no prior information is available, is approximately 6636.

To determine the minimum sample size needed to estimate the population proportion, we can use this formula: [tex]n = (Z^2 * p * (1-p)) / E^2.[/tex]

Where:

By plugging in the values into the formula, we get:

[tex]n = (2.58^2 * 0.5 * (1-0.5)) / 0.02^2[/tex]

= 6635.44

Similarly, a prior study found that 38% of the respondents think the president can control the price of gasoline, which is 9448.7 The sample size needed when using the prior estimate (9449) is larger than when assuming no prior information (6636). This is because having a prior estimate reduces the uncertainty, which allows for a smaller sample size to achieve the same level of confidence and margin of error.

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Final answer:

The minimum sample size needed for estimating the population proportion depends on the desired confidence level, margin of error, and estimated proportion. The formula used is n = (Z^2 * p * (1-p)) / E^2, and without prior estimate, p is taken as 0.5, whereas using a prior study, the actual estimate from the study is used.

Explanation:

To calculate the minimum sample size needed to estimate the population proportion with certain confidence and precision, we use the following formula for sample size calculation:

n = (Z^2 * p * (1-p)) / E^2

Where:

n is the sample size

Z is the Z-score corresponding to the desired confidence level

p is the estimated proportion of the population (p-hat)

E is the margin of error

(a) Without preliminary estimate: Assuming that no prior information is available, we use p = 0.5 for the most conservative sample size estimate. For a 99% confidence level, the Z-score is approximately 2.576. With a margin of error E of 0.02, the formula becomes:

n = (2.576^2 * 0.5 * (1-0.5)) / 0.02^2

(b) Using a prior study: If a prior study found p = 0.38, the calculation uses this value. The formula with Z = 2.576 and E = 0.02 becomes:

n = (2.576^2 * 0.38 * (1-0.38)) / 0.02^2

(c) Comparing results: Using p = 0.5 in (a) will result in a larger sample size than using p = 0.38 in (b) because the variance (p * (1-p)) is maximized when p = 0.5.

Answer:

A

Step-by-step explanation:

A trail would consist of three random digits.

The problem asks for the probability that it will take at least a sample of four to find one person with brown hair. This implies that the first three people do not have brown hair. Therefore, a trial would consist of three random digits. A success is none of the three digits are 0, 1, 2, or 3. For example, 675 would be a success and a failure would be 792.

Answer:

A

Step-by-step explanation:

USA testprep said...

A trail would consist of three random digits.

The problem asks for the probability that it will take at least a sample of four to find one person with brown hair. This implies that the first three people do not have brown hair. Therefore, a trial would consist of three random digits. A success is none of the three digits are 0, 1, 2, or 3. For example, 675 would be a success and a failure would be 792.

Answer: 11 1/3

Dhdgdhdhd

To find the rate at which the area of the rectangle decreases as its length changes, use the formula for the area of a rectangle and evaluate the area at the two lengths. Then, calculate the average rate of decrease by taking the change in an area divided by the change in length.

The problem involves understanding the properties of rectangles and how the changes in one dimension (length in this case) can affect another (area). Let's consider a rectangle with a perimeter of 35 cm. If 'L' is the length and 'W' is the width, the perimeter = 2*(L+W) which equals 35 cm.

Next, we figure out that W= 17.5 - L as we isolate W in the equation. The area of the rectangle is then given by A = L * W = L * (17.5 - L). If we plug in L = 13 cm and L = 16 cm, we get two area values. The decrease in area ΔA = A2 - A1.

Finally, the average rate of change, or the rate at which the area decreases, as the length goes from 13 cm to 16 cm is calculated by ΔA / ΔL.

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The store sold 7 red scarfs and 5 white Scarfs

5+5+5+5+5+5+5+3+3+3+3+3=50

This Maths question involves formation and solution of a system of equations, where equations are representing the number and total cost of scarves sold. The variables used are 'w' for white scarves and 'r' for red scarves, forming two equations: w + r = 12, and 3w + 5r = 50.

This question can be approached by using a system of equations. A system of equations is a set of two or more equations that have the same variables. You can think of this problem as having two equations:

Let's represent the number of white scarves sold as 'w' and the red scarves sold as 'r'. So, our first equation would become: w + r = 12

And knowing the cost of each scarf, the second equation would be: 3w + 5r = 50

Now with these two equations, one can solve for 'w' and 'r'. This type of problem is often seen in algebra and is an example of linear equations.

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Answer:

Ejemplos de funciones polinómicas son: , la cual es de grado 3, ya que el exponente mayor es 3. , que es una función polinómica de grado 2, o sea cuadrática, cuya gráfica es una parábola. ... Muchas veces a partir de la gráfica de un polinomio se puede deducir la ecuación de la función.

Step-by-step explanation:

Una función polinómica es una expresión matemática compuesta por términos de variables elevadas a exponentes no negativos con coeficientes.

Una función polinómica es una función matemática definida por una expresión polinómica, que es una combinación lineal de variables elevadas a exponentes no negativos, multiplicadas por coeficientes constantes. Formalmente, una función polinómica [tex]\( f(x) \)[/tex]se expresa como:

[tex]\[ f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0 \][/tex]

Donde:

[tex]- \( n \)[/tex] es un número entero no negativo (grado del polinomio).

[tex]- \( a_n, a_{n-1}[/tex], [tex]\ldots, a_1, a_0 \)[/tex] son coeficientes constantes.

[tex]- \( x \)[/tex] es la variable independiente.

Por ejemplo, [tex]\( f(x) = 2x^3 - 3x^2 + 5x - 7 \)[/tex] es una función polinómica de grado 3. Las funciones polinómicas son un tipo importante de funciones en matemáticas y se utilizan en una variedad de campos, incluyendo álgebra, cálculo, estadística y física.

Answer: She bought about 150 markers.

Step-by-step explanation:

Given : A teacher bought 15 boxes of markers.

i.e. Total boxes of markers = 15

Each box contained 8 markers.

That is , the estimated number of markers in each box = 10 [∵ 8≈10 [Round to the nearest tens]]

Now , the total number of markers in all 15 boxes of markers = (15) x (10)

= 150

Hence, she bought about 150 markers.

Step-by-step explanation:

compared with the rest of Europe northern Italy had many cities

When compared with the rest of Europe, one will notice that Northern Italy has a lot of cities.

The Northern part of Italy is much more developed than the South and is so developed that it has one of the highest rates of developments in all of Europe.

This is due to the high density of cities located there such as:

There are about 23 cities in Northern Italy alone which leads us to conclude that in Europe, Northern Italy has one of the highest number of cities.

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Answer:

A skeleton that has lost 50% of its carbon-14 is 5750 years old.

Step-by-step explanation:

The halflife on an element is the amount it takes to decrease to half it's original amount, that is, when the amount is 50% of the initial amount.

How old is a skeleton that has lost 50% of its carbon-14?

If the skeleton lost 50% of its carbon-14 it has the other 50%, that is, it is in it's half-life.

The radioactive element carbon-14 has a half-life of 5750 years.

This means that a skeleton that has lost 50% of its carbon-14 is 5750 years old.

A skeleton that has lost 50% of its carbon-14 is 5,730 years old, which corresponds to one half-life of carbon-14 (C-14).

The age of a skeleton that has lost 50% of its carbon-14 can be determined using carbon-14 dating. Since the half-life of carbon-14 (¹⁴C) is 5,730 years, if a skeleton has only 50% of the original carbon-14 remaining, it would mean that one half-life has passed. Therefore, the skeleton would be 5,730 years old. Carbon-14 dating measures the radioactive decay of ¹⁴C in formerly living matter to estimate its age. This method is effective for dating biological tissues up to about 50,000 to 60,000 years old.

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