Amy just put new tires on her car. If the wheels have a diameter of 8 inches, about how far does the wheel travel in 2 revolutions?

Answer:

-12

Step-by-step explanation:

Distribute

20y+20-y=16y-16

Combine like terms

19y+20=16y-16

subtract 16y from 19y and subtract 20 from -16

3y=-36

Divide by 3

y=-12

The fuel required for an airplane to travel 612 NM, with fuel consumption of 14.7 gallons per hour and groundspeed of 157 knots is 226.368 gallons.

First, we need to calculate the time taken to travel 612 NM. We can use the formula

Distance = Speed × Time

where Distance is 612 NM and Speed is 157 knots. Rearranging the formula to solve for time, we have Time = Distance / Speed. Substituting the given values, we get Time = 612 NM / 157 knots.

Next, we multiply the time by the fuel consumption rate to find the total fuel required. The fuel consumption rate is 14.7 gallons per hour. So the total fuel required can be calculated as

Total Fuel = Time × Fuel Consumption Rate.

Substituting the calculated time and the given fuel consumption rate, we have Total Fuel = (612 NM / 157 knots) × 14.7 gallons per hour.

Performing the calculation, we find:

Total Fuel = (612 NM / 157 knots) × 14.7 gallons per hour

Total Fuel ≈ 226.368 gallons

Therefore, approximately 226.368 gallons of fuel are required for the airplane to travel 612 NM.

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The measure of x for the right triangle is equal to 13.7 to the nearest tenth using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

so by Pythagoras rule we can write:

16.5² = x² + 9.2²

272.25 = x² + 84.64

x² = 272.25 - 84.64 {collect like terms}

x² = 187.61

x = √187.61 {take square root of both sides}

x = 13.6971

Therefore, the measure of x for the right triangle is equal to 13.7 to the nearest tenth using the Pythagoras rule.

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Answer:

D\

Step-by-step explanation:

Answer: The answer should be D

Step-by-step explanation:

The probability that the first question she gets right is question number 4, is 0.1054.

Number of options there are for a single query = 4

P(guessing correct answer for a single question) = 1/4

P(guessing correct answer for a single question) = 0.25

Probability of getting correct answer P(correct) = 0.25

Probability of getting wrong answer P(wrong) = 1 - Probability of getting correct answer

Probability of getting wrong answer P(wrong) = 1 - 0.25

Probability of getting wrong answer P(wrong) = 0.75

So, the probability that the first question she gets right is question number 4 = Probability of getting 1st question wrong × Probability of getting 2nd question wrong × Probability of getting 3rd question wrong × Probability of getting 4th question right

The probability that the first question she gets right is question number 4 = 0.75 × 0.75 × 0.75 × 0.25

The probability that the first question she gets right is question number 4 = 0.1055

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The complete question is:

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. (Round your answers to four decimal places.)

What is the probability that the first question she gets right is question number 4?

Answer: i think its A

Step-by-step explanation: hope this helped

To make a stem-and-leaf display, we will separate the trunk circumferences into stems based on the tens digit and leaves based on the ones digit.

Stem Leaf

0  3 5 6 8 9

6  9

7  5 8 9

8  3 4 5 9

9  2 3 5 6 9

1  0 1 2 3 4 6 8

2  0 2 4 6 9

3  0 1 4 8 9

4  2

Therefore, the stem-and-leaf display of the trunk circumference distribution is:

0 | 3 5 6 8 9

6 | 9

7 | 5 8 9

8 | 3 4 5 9

9 | 2 3 5 6 9

1 | 0 1 2 3 4 6 8

2 | 0 2 4 6 9

3 | 0 1 4 8 9

4 | 2

A stem-and-leaf display is a graphical representation of a set of data. It is a way to organize and display data in a way that allows for easy interpretation and comparison of the data.

In a stem-and-leaf display, the data is separated into two parts: the stem and the leaf. The stem represents the tens digit of each data point, and the leaf represents the ones digit. For example, the number 47 would be represented as a stem of 4 and a leaf of 7.

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Answer:

Step-by-step explanation:

Hola!

Las variables aleatorias pueden Cualitativas o cuantitativas.

Las variables aleatorias cualitativas son aquellas que se refieren a atributos o características de los individuos o unidades de interés que no son cuantificables. Dentro de estas variables se pueden identificar dos tipos:

Ordinales: estas variables representan cierto tipo de cualidad que tiene un orden natural, por ejemplo: Opinión de una persona sobre una película de estreno, calificada en "muy buena", "buena", "regular", "mala", "muy mala"

Estas calificaciones son claramente cualidades, pero tienen un orden, todo el mundo sabe que una calificación "regular" es mejor que una "muy mala" y a su vez peor que una calificación "buena"

Nominales: Son aquellas que indican atributos no cuantificables que no tienen un orden natural. Por ejemplo, color de cabello, raza, sexo.  

Las variables aleatorias cuantitativas son aquellas que registran valores numéricos, dicho de manera coloquial: "cuentan cosas". Estas variables siempre toman valores dentro de un rango o intervalo de definición, teniendo esto en cuenta podemos definir dos tipos de variables aleatorias cuantitativas:

Continuas: pueden tomar cualquier valor dentro del intervalo de definición de la variable, por ejemplo, la estatura, el peso, la temperatura, entre un valor y otro existen infinita cantidad de valores que la variable puede tomar. En muchos casos, esto está restringido a la precisión de los métodos utilizados para tomar las mediciones.  

Por ejemplo, una balanza puede tomar pesos de kilogramo a kilogramo, ej: 20kg, 21kg, 22kg mientras que una más precisa puede tomar pesos intermedios de los mismos objetos, ej: 20.1kg, 21.5kg, 22.9kg y otra más precisa puede indicar mediciones más exactas, ej: 20.142kg, 21.538kg, 22.973kg es decir que, cuanto más precisa la balanza que usemos para obtener las mediciones, mayor será la gama de valores que puede tomar la variable.

Discretas: solo pueden tomar ciertos valores dentro del intervalo de definición de la variable aleatoria, a diferencia de las variables continuas, entre los valores posibles que pueden tomar estas variables, no se encuentra nada, es decir que "saltan" de valor en valor. Por esto también se las llama variables discontinuas.

Uno de los ejemplos más comunes de variable discreta es hacer rodar un dado de 6 caras, la variable puede tomar valores 1, 2, 3, 4, 5, 6 pero no puede tomar valores entre esos valores, es decir, el dado nunca va a mostrar valores intermedios como "2.5" o "3.3".

Dicho esto pasemos a identificar el tipo de cada ejemplo:

a) y c) Calidad del producto

Esta es algo engañosa, porque todo depende de la escala determinada para medir la calidad.

Es decir, si la escala de medición de la calidad de un objeto es de 0 a 10, siendo cero lo peor y 10 lo mejor, entonces la variable es cuantitativa discreta.

Sin embargo, si la escala es nominal, por ejemplo: Alto, medio, bajo, entonces la variable es cualitativa y como las categorías tienen un orden natural, no solo es cualitativa, sino que también es ordinal.

b) y d) Tiempo de publicidad

Esta variable aleatoria "cuenta el tiempo", toma valores numéricos con lo cual es cuantitativa y, además, puede tomar cualquier valor dentro del intervalo de definición, todo depende de la precisión del reloj utilizado lo que la califica como variable continua.

Espero que tengas un buen días!

Answer:45/496

Step-by-step explanation:

Answer:

.82 or 80 degrees rounded

Step-by-step explanation:

you can use SOH-CAH-TOA meaning sin = opposite/hypotenuse, so 14/17 = .82.

Answer:

ur answer is -4

Step-by-step explanation:

2*-4=-8

hope it helps ya

Answer:

m<PQR = 18.7°

Step-by-step explanation:

Apply the Law of Sines,

\( \frac{Sin A}{a} = \frac{Sin B}{b} \)

Where,

Sin A = Sin 140

a = 100 m

Sin B = Sin R (<PRQ)

b = 50 m

Substitute

\( \frac{Sin 140}{100} = \frac{Sin R}{50} \)

Cross multiply

\( 100*Sin(R) = 50*Sin(140) \)

Divide both sides by 100

\( Sin(R) = \frac{50*Sin(140)}{100} \)

\( Sin(R) = 0.32139 \)

\( R = Sin^{-1}(0.32139) \)

R ≈ 18.7° (nearest tenth)

m<PQR = 18.7°

The angle PRO is 1.7 degrees.

Given that,

The diagram shows three points P, Q, and R on horizontal ground.

PQ = 50 m, PR = 100 m and angle PQR = 140°.

We have to determine,

The angle PRO.

According to the question,

The value of angle PRO is determined by using the sin rule-following all the steps given below.

\(\rm \dfrac{sina}{a} = \dfrac{sinb}{b}\)

Where,  Sin A = Sin 140 , a = 100 m , Sin B = Sin R (<PRQ) , b = 50 m

Substitute all the values in the formula,

\(\rm \dfrac{sin140}{100} = \dfrac{sinR}{50}\\\\ \dfrac{0.64}{100} = \dfrac{sinR}{50}\\\\0.0064 = \dfrac{sinR}{50}\\\\0.0064 \times 50 = sinR\\\\0.321 = sinR\\\\R = sin{-1}(0.321)\\\\R = 18.7 \ degree\)

Hence, The angle PRO is 1.7 degrees.

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Answer:

$0.39

Step-by-step explanation:

First find the unit rate for store B ( $8.84/13)

At store B Artuto spends $0.68 for one bottle of apple juice

At store A they spent $0.29

0.68-0.29= 0.39

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number can only be divided evenly by 1 and itself.

To find the multiples of a prime number, you can use the following steps:

For example, if the prime number is 5, the multiples of 5 are 5, 10, 15, 20, 25, and so on.

It's important to note that a prime number only has two divisors: 1 and itself. This means that a multiple of a prime number will never be a prime number.

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The midpoint of the line segment with endpoints (6,1) and (2,10) is (4, 5.5)

To find the midpoint of a line segment, we need to average the x-coordinates of the endpoints to find the x-coordinate of the midpoint, and average the y-coordinates of the endpoints to find the y-coordinate of the midpoint.

Let (x1, y1) = (6, 1) and (x2, y2) = (2, 10) be the endpoints of the line segment. Then, the midpoint (x, y) is:

x = (x1 + x2)/2

Substitute the values in the equation

= (6 + 2)/2

= 4

y = (y1 + y2)/2

Substitute the values in the equation

= (1 + 10)/2

= 5.5

Therefore, the midpoint is (4, 5.5)

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The width of the rectangle with a length of 42 inches is 70 inches.

To find the width of a rectangle that has a length of 42 inches, we can use the concept of proportions based on the given table.

First, we observe that the length and width of the rectangles are proportional. We can set up a proportion using the values from the table:

Length (in inches): 6, 9, 18, 24

Width (in inches): 10, 15, 30, 40

Using the proportion, we have:

Length / Width = Length / Width

We can select any corresponding pair of length and width values to set up the proportion. Let's choose the first pair: 6 and 10.

6 / 10 = 42 / x

To find the width (x) when the length is 42, we can solve the proportion:

6 / 10 = 42 / x

Cross-multiplying:

6x = 10 * 42

6x = 420

Dividing both sides by 6:

x = 420 / 6

x = 70

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The combined radical is: \(- 26\sqrt{3}\)

The radical is given as:

\(- 12\sqrt{12} - 2\sqrt{3}\)

We start by expressing 12 as 4 * 3

\(- 12\sqrt{12} - 2\sqrt{3} = - 12\sqrt{4* 3} - 2\sqrt{3}\)

Split the radical

\(- 12\sqrt{12} - 2\sqrt{3} = - 12\sqrt{4}* \sqrt{3} - 2\sqrt{3}\)

Take square root of 4

\(- 12\sqrt{12} - 2\sqrt{3} = - 12*2* \sqrt{3} - 2\sqrt{3}\)

\(- 12\sqrt{12} - 2\sqrt{3} = - 24* \sqrt{3} - 2\sqrt{3}\)

\(- 12\sqrt{12} - 2\sqrt{3} = - 24\sqrt{3} - 2\sqrt{3}\)

Combine like terms

\(- 12\sqrt{12} - 2\sqrt{3} = - 26\sqrt{3}\)

Hence, the combined radical is: \(- 26\sqrt{3}\)

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Given a function of two variables, n and k, denoted as h(n, k), the function describes a mathematical relationship or operation that depends on the values of both n and k. Further details about the specific function, its definition, or purpose are required to provide a more comprehensive explanation.

A function of two variables, h(n, k), typically represents a mathematical relationship or operation that involves two independent variables, n and k. The specific form and purpose of the function can vary widely depending on the context or problem at hand.

To understand the behavior and properties of the function h(n, k), additional information is needed. This may include the mathematical expression defining the function, any constraints or conditions on the variables, and the intended interpretation or application of the function.

The function h(n, k) could represent various scenarios, such as a cost function in economics, a probability distribution in statistics, or a mathematical model in a scientific context. Without more details, it is challenging to provide a specific explanation or analysis of the function and its implications.

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Answer:I think is am B

Step-by-step explanation:

Step-by-step explanation:

(5x)°+(3x+4)°=180°

5x+3x+4=180

8x=176

x=22

D=5x

D=110°

Answer:

answer is c

Step-by-step explanation:

Step-by-step explanation:

That symbol is sigma, which is the sum of that equation from k = 1 to n = 4

Equation is 2(3^n-1)

Since we're going 1 to 4, the sum would be as follows (replacing n with 1, 2, 3, and 4

\(2( {3}^{1 - 1}) + 2( {3}^{2 - 1}) + 2( {3}^{3 - 1}) + 2( {3}^{4 - 1}) = {?}\)

\(2(1) + 2(3) + 2(9) + 2(27) = \)

\(2 + 6 + 8 + 54 = 70\)

Answer:

25

Step-by-step explanation:

There is a right angle which is 90 degrees. 65+90=155.

A triangle has a total of 180 degrees angles

180-155=25.

The missing angle is 25 degrees

Answer:

Step-by-step explanation:

the points are not coplanar

lets use the first three points to find the equation of the plane:

we need to find two vectors. we can use vectors from (2,-1,2) to (0,0,1) and from (2,-1,2) to (0,5,-2)

vector 1= (-2,1,-1)

vector 2=(-2,6,-4)

now we can find the normal vector:

n= (-2,1,-1) x (-2,6,-4) = (2,6,8)

so the equation containing first three points is:

2x+6y+8z=0

now lets check if the fourth point, (-1,3,-1), lies on this plane:

2(-1) +6(3) +8(-1) =6

since 6 is not equal to 0, the fourth point does not lie on the plane containing the first three points.

therefore, the points are not coplanar.

The value of \(\alpha\) that makes \(f(x)\) continuous at \(x = 1\) is \(\alpha = 0\).

The function \(f(x) = x^{\alpha}\) is defined for \(0 < x < 1\).

We want to find the value of \(\alpha\) such that \(f(x)\) is continuous at \(x = 1\).
To check continuity at \(x = 1\), we need to ensure that the left-hand limit of \(f(x)\) at \(x = 1\) is equal to the right-hand limit of \(f(x)\) at \(x = 1\), and that these limits are equal to \(f(1)\).
First, let's find the left-hand limit of \(f(x)\) as \(x\) approaches 1:
\(\lim_{x \to 1^-} f(x) = \lim_{x \to 1^-} x^{\alpha}\)
Since \(0 < x < 1\), as \(x\) approaches 1 from the left, \(x^{\alpha}\) will approach 1.

Therefore, the left-hand limit of \(f(x)\) as \(x\) approaches 1 is 1.

Next, let's find the right-hand limit of \(f(x)\) as \(x\) approaches 1:
\(\lim_{x \to 1^+} f(x) = \lim_{x \to 1^+} x^{\alpha}\)
Since \(0 < x < 1\), as \(x\) approaches 1 from the right, \(x^{\alpha}\) will also approach 1.

Therefore, the right-hand limit of \(f(x)\) as \(x\) approaches 1 is 1.
For \(f(x)\) to be continuous at \(x = 1\), the left-hand limit, right-hand limit, and \(f(1)\) must all be equal.

In this case, that means: 1 = \(f(1) = 1^{\alpha}\)
Since any number raised to the power of 0 is equal to 1, we can conclude that \(\alpha = 0\) for \(f(x)\) to be continuous at \(x = 1\).

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A series is convergent when the sequence of partial sums, which are the sums of the first n terms in the series, approaches a finite limit as n approaches infinity. In other words, the series has a sum that can be found. On the other hand, a series is divergent if the sequence of partial sums does not approach a finite limit. This means the series does not have a sum. So, to determine if a series is convergent or divergent, analyze the behavior of its sequence of partial sums.

A series is a sum of the terms in a sequence. A convergent sequence is one that has a limit as n approaches infinity, meaning that the sequence approaches a specific value. Similarly, a sequence of partial sums is the sum of the first n terms of the series. If this sequence of partial sums converges to a specific value, then the series is convergent. However, if the sequence of partial sums diverges, meaning it does not approach a specific value, then the series is divergent. Understanding whether a series is convergent or divergent is important in various fields such as physics and engineering.
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The number of bacteria in 25g sample is 1.225*10^8

Data;

To find the number of bacteria in 25g, we just need to multiply the number of bacteria in 1g by 25. This implies that the bacteria increase in a multitude of 25.

\(1g = 4.9*10^6\\25g = x\)

Let's cross multiply both sides and solve for x

\(1g =4.9*10^6\\25g = x\\x = 25 * 4.9*10^6\\x = 122,500,000\\\\x = 1.225*10^8\)

The number of bacteria in 25g sample is 1.225*10^8

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The Null and Alternative hypothesis are

H₀ : µ= 68

Hₐ : µ not equal to 68

we get the result that P-Value< alpha

=> null hypothesis Rejected.

So, there is sufficient evidence at the α=0.10 level to conclude that the mean weight of the eggs in this batch is not equal to 68 g.

We have given that

Tala is in charge of a quality control test that involves weighing a sample of eggs to test.

let the null and alternative hypothesis :

H₀ : µ= 68

Hₐ : µ not equal to 68

Sample size, n = 12

Sample mean, X-bar = 68.5 g

Standard deviations, σ = 1 g

degree of freedom , df = 12 -1 = 11

Standard error,

S.E = Standard deviations /√n

=1/√12 = 0.288

t- test statistic:

t-value = (x-bar - µ)/ S.E

=> t = (68.5 - 68) /0.288 = 1.7361

the p-value for t =1.7361 using t-table is 0.0072 .

The confidence level , α= 0.10

We can see that p-value < α, which implies that reject the null hypothesis (H₀). Therefore, there is evidence to support the claim.

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I believe the answer is between 90-100.

Hopes this helps