f(t) = 4t2; t = 3, t = 3 +
h
(a) Determine the net change between the given values of the
variable.
(b) Determine the average rate of change between the given values
of the variable.

Answer:

D) n=13

Step-by-step explanation:

n+n+7+2n-12+3n+4=90

7n-1=90

7n=90+1

7n=91

n=91/7

n=13

Answer:

Step-by-step explanation:

The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2/3x + 5/2y = 15

4x + 15y = 12

Multiply the first equation by 6, to eliminate the fractions.

6 * (2/3x + 5/2y = 15)

This gives

4x + 15y = 90

Subtract the equation 4x + 15y = 90 from 4x + 15y = 12

4x - 4x + 15y - 15y = 12 - 90

Evaluate the difference

0 + 0 = -78

Evaluate the sum

0 = -78

The above equation is the same equation as option (b) 0 = 26

This is so because they both represent that the system of equations have no solution

Hence, the equation that could represent a linear combination of the system is 0 = 26

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Complete question

The system of equations below has no solution.

2/3x + 5/2y = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

As the total number of weekly reservations remains the same. The average number of booked rooms is likely to decrease.

By offering a discount on three-bed rooms, some customers who would have originally booked a different type of room now book a three-bed room instead. This means that the number of three-bed rooms booked will increase, while the number of other room types booked will decrease.

Since the total number of weekly reservations remains the same, the increase in three-bed room bookings must be offset by a decrease in bookings for other room types. This means that the average number of booked rooms will likely decrease.

For example, suppose there were originally 50 room bookings, consisting of 20 three-bed rooms and 30 other room types. If the discount on three-bed rooms leads to 25 bookings for three-bed rooms and 25 bookings for other room types, then the average number of booked rooms would be (25 x 3 + 25 x 1) / 50 = 2, which is lower than the original average of (20 x 3 + 30 x 1) / 50 = 1.8.

Therefore, the average number of booked rooms is likely to decrease when a discount is offered on three-bed rooms, even if the total number of weekly reservations remains the same.

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Answer:

58g

Step-by-step explanation:

I'm assuming the mass of the Bottle is 8g for this answer.

1mL = 1g

So 50mL = 50g

8g + 50g = 58g

Therefore, the mass of the bottle + water inside of it is 58g

Answer:

89.004

Have a good day :)

Answer:

Step-by-step explanation:

sin of angle x is the trig ratio sine of x.

sin-1 x is the angle whose sine is x.

sin-1 x can also be written as arcsin x.

Answer:

x ^2 y √ 3 y

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

The change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

We have,

Length of coasts along the hill = 62.2 meters,

And,

The angle car make with the ground = 28.3°,

And,

The mass of the car = 1234 kg,

Now,

We know,

From the Work Energy Theorem that,

The change in Potential energy = The work done on the mass.

And,

Work done i.e. W = F × s × CosΘ

Here,

F = Force,

s = Distance car cover,

And,

Θ = Angle car make with the ground,

And,

We know that,

Force i.e. F = mass × acceleration due to gravity = m × g

And,

g= Acceleration of gravity = 9.8 m/s²

So,

Now,

Putting values,

i.e.

F = 1234 × 9.8 = 12093.2 Newton

Now,

Using the Formula of Work done,

i.e.

W = F × s × CosΘ,

Putting values,

i.e.

W = 12093.2 × 62.2 × Cos(28.3°)

On solving we get,

W = 662,292.459 Joule

So,

Chane in potential energy = 662,292.459 Joule

Hence we can say that the change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

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Answer:

240 students

Step-by-step explanation:

     To find the minimum number of students, we have to find the LCM of 10, 12, 16

10 = 2 * 5

12 = 2 * 2 * 3

16 = 2 * 2 * 2 * 2

LCM = 2 * 2 *  2 * 2 * 3 * 5

       = 240

The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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To return true if both x and y are positive, you can use a simple if statement in Python that checks if both variables are greater than 0. If they are, the statement will return true.

Here is an example in Python:

```python
def check_positive(x, y):
 if x > 0 and y > 0:
   return True
 else:
   return False
```
In this example, the function `check_positive` takes in two variables, `x` and `y`, and checks if they are both greater than 0. If they are, the function returns `True`. If either `x` or `y` is less than or equal to 0, the function returns `False`.

You can also write this function more concisely using a single return statement:

```python
def check_positive(x, y):
 return x > 0 and y > 0
```
This function will return `True` if both `x` and `y` are greater than 0, and `False` otherwise.

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A straight line that approaches the graph without touching; is referred to as an asymptote.

The graph of \(y = \frac{x - 1}{x}\) has \(y = 1\) as an asymptote

To solve this question, I have attached the graphs of:

\(y = \ln(x)\), \(y = \frac{x - 1}{x}\), \(y =e^x\) and \(y = \sin(x)\)

From the attached graphs, we have the following observations

Hence, the solution to the question is option (b).

See attachment for the graphs of the four functions

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2025.8 = x  the cost of tuition as a function of x, the number of

years since 1990.

Linear function C(x) would be,

C(x) = 96 + 5(x - 1990)

(x is the year)

Now for x = 2002

C(2002) = 96..+ 5( 2002 - 1990)

C(2002) = 96 + 5(12)

C(2002) = 96 + 60

C(2002) =156

In year 2002 tution fee will be $238 per credit hour.

Now cost C(x) = 156

So,

456 = 98 + 10(x - 1990)

456- 98 = 10 (x - 1990)

358 = 10(x - 1990)

358/10 = x - 1990

35.8 + 1990 = x

2025.8 = x

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not possible, the hypotenuse must be the longest side of a right triangle

The graph of the exponential function is on the image at the end.

Here we want to graph the function:

f(x) = 0.5*(4)ˣ

To graph this (or any function) we can find some points on the function, and to do so, we need to evaluate it.

when x = 0:

f(0) =   0.5*(4)⁰ = 0.5

Then the point is (0, 0.5)

when x = 1

f(1) =   0.5*(4)¹ = 2

So we have the point (1, 2)

if x = 2

f(2) =   0.5*(4)² = 8

So we have the point (2, 8)

Now we can graph these points and connect them with a general exponential curve.

The graph of the exponential function is shown below.

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Answer:

Parte 1

a) {0, 1, 2, 3, 4}

b) {11, 13, 17, 19}

c) {12, 24, 36, 48, 60}

d) Conjunto A = {4, 5, 6, 7, 8, 9, 10, 11}

Conjunto B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Parte 2

a) {x ∈ Z / x > 10}

{11, 12, 13, 14, 15, ....}

b) {x ∈ Z / 2x}

{2, 4, 6, 8, 10, 12, ....}

c) {x ∈ Z / 1 ≤ x ≤ 5}

{1, 2, 3, 4, 5}

d) {x ∈ N / x < 10}

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9} o {1, 2, 3, 4, 5, 6, 7, 8, 9}

e) {x ∈ Z / 2x < 15}

{2, 4, 6, 8, 10, 12, 14}

Step-by-step explanation:

Parte 1

a.) El conjunto de enteros no negativos menos de cinco.

Los enteros son números enteros. Los enteros no negativos son enteros positivos y 0 (0 es un entero neutral ya que es un número entero)

{0, 1, 2, 3, 4}

b.) El conjunto de números primos entre 10 y 20.

Los números primos son números divisibles por solo 1 y ellos mismos.

{11, 13, 17, 19}

c.) El conjunto de múltiplos de 12 que son menores de 65.

Los múltiplos de 12 son números que surgen cuando 12 se multiplica por números enteros.

{12, 24, 36, 48, 60}

d.) A = {x ∈ Z / 3 < x < 12}. y. B = {x / x es un número de un dígito}.

El conjunto A se refiere a todos los números enteros entre 3 y 12 (no incluido)

Conjunto A = {4, 5, 6, 7, 8, 9, 10, 11}

El conjunto B es un conjunto de todos los números de un dígito.

Conjunto B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Parte 2

a. El conjunto de enteros mayores que diez.

El conjunto variará de 11 a infinito.

Se escribirá como {x ∈ Z / x> 10}

{11, 12, 13, 14, 15, ....}

b.) El conjunto de enteros pares.

El conjunto de enteros pares comenzará desde 2 e incluirá todos los números pares hasta el infinito.

Se escribirá como {x ∈ Z / 2x}

{2, 4, 6, 8, 10, 12, ....}

c.) El conjunto {1, 2, 3, 4, 5}.

Este es un conjunto de enteros entre 1 y 5 (inclusive)

Se escribirá como {x ∈ Z / 1 ≤ x ≤ 5}

{1, 2, 3, 4, 5}

d.) El conjunto de números naturales menores de 10.

Los números naturales son números de conteo.

Se escribirá como {x ∈ N / x < 10}

Algunos casos incluyen 0 como número natural y otros no.

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9} o {1, 2, 3, 4, 5, 6, 7, 8, 9}

e.) El conjunto de múltiplos de 2 que son menores que 15.

Se puede escribir como {x ∈ Z / 2x <15}

{2, 4, 6, 8, 10, 12, 14}

¡¡¡Espero que esto ayude!!!

In English

Part 1

a. The set of nonnegative integers less than five.

Integers are whole numbers. Non-negative integers are positive integers and 0 (0 is a neutral integer as it is a whole number)

{0, 1, 2, 3, 4}

b. The set of prime numbers between 10 and 20.

Prime numbers are numbers divisible by only 1 and themselves.

{11, 13, 17, 19}

c. The set of multiples of 12 that are less than 65.

Multiples of 12 are numbers that arise when 12 is multiplied by whole numbers.

{12, 24, 36, 48, 60}

d. A = {x ∈ Z / 3 < x < 12}. and. B = {x / x is a one-digit number}.

Set A refers to all integer numbers between 3 and 12 (non-inclusive)

Set A = {4, 5, 6, 7, 8, 9, 10, 11}

Set B is a set of all the one digit numbers.

Set B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Part 2

a. The set of integers greater than ten.

The set will range from 11 to infinity.

It'll be written as {x ∈ Z / x > 10}

{11, 12, 13, 14, 15, ....}

b. The set of even integers.

The set of even integers will start from 2, and include all the even numbers till infinity.

It'll be written as {x ∈ Z / 2x}

{2, 4, 6, 8, 10, 12, ....}

c. The set {1, 2, 3, 4, 5}.

This is a set of integers between 1 and 5 (inclusive)

It'll be written as {x ∈ Z / 1 ≤ x ≤ 5}

{1, 2, 3, 4, 5}

d. The set of natural numbers less than 10.

Natural numbers are counting numbers.

It'll be written as {x ∈ N / x < 10}

Some cases include 0 as a natural number and some others do not.

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9} or {1, 2, 3, 4, 5, 6, 7, 8, 9}

e. The set of multiples of 2 that are less than 15.

It can written as {x ∈ Z / 2x < 15}

{2, 4, 6, 8, 10, 12, 14}

Hope this Helps!!!

Answer:

Pilar did not include the   14.

The mean is 20.

The median is 15.5.

Step-by-step explanation:

The mean: \(\frac{12+15+15+16+18+44}{6} =20\)

The median: 12, 15, 15, 16, 18, 44

The median is \(\frac{15+16}{2} =15.5\)

Hope this helps

Answer: (6, -6)

Step-by-step explanation:

so midpoint =(\(\frac{X1+X2}{2}\),\(\frac{Y1+Y2}{2}\))

for x co ordinate

\(\frac{-2+X2}{2}\)=2

-2+X=4            (X2=x co ordinate point for b, can be written as just x now)

X=6

x co ordinate of B= 6

y co ordinates of y

\(\frac{-8+Y2}{2}\)=-7

-8+Y=-14

Y=-6

co ordinates B (6,-6)

for proof/extra explanation (NOT necessary for working):

\(\frac{Y1+Y2}{2}\)

=\(\frac{(-2)+6, (-8)+(-6)}{2}\)

=\(\frac{4, -14}{2}\)

=(2,-7)

which is the midpoint M

Using the z-distribution, as we are working with a proportion, it is found that the margin of error for a 95% confidence interval would be of 0.0008.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

Considering the 99% confidence interval, which has z = 2.575, the estimate and the sample size are given by:

\(\pi = \frac{0.67 + 0.74}{2} = 0.705\)

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.74 - 0.705 = 2.575\sqrt{\frac{0.705(0.295)}{n}}\)

\(0.035 = 2.575\sqrt{\frac{0.705(0.295)}{n}}\)

\(0.035\sqrt{n} = 2.575\sqrt{0.705(0.295)}\)

\(\sqrt{n} = \frac{2.575\sqrt{0.705(0.295)}}{0.035}\)

\((\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.705(0.295)}}{0.035}\right)^2\)

\(n = 1126\)

Hence, the margin of error is given by:

\(M = 1.96\sqrt{\frac{0.705(0.295)}{1126}} = 0.0008\)

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The terms are as follows:

t₃ = -62

t₇ = -29.6

tₙ = 10.8n - 105.2

t₁₄ = 46

t₁₉ = 100

Therefore,

tₙ = a + (n - 1)d

where

Hence,

46 = a + 13d

100 = a + 18d

5d = 54

d = 10.8

46 - 13(10.8) = a

a = 46 - 140.4

a = - 94.4

t₃ = a + 3d = - 94.4 + 3(10.8) = -62

t₇ = a + 6d = - 94.4 + 6(10.8) = -29.6

tₙ = -94.4 + 10.8n - 10.8 = 10.8n - 105.2

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Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

288 ft squared.

Answer:

Step-by-step explanation:

T3 = S(a, 1) = {x ∈ M : d(x,a) < 1} = {a} U (M{a}), using the same argument as for S3 in part (a).

In a discrete metric space, any subset of the space is an open set, since every point has a neighborhood of radius 1 that contains only that point. Therefore, for any point a in the discrete metric space, we have:

(a) Si = B(a, j) = {x ∈ M : d(x,a) < j} = {a}, since the only point within a distance of j from a is a itself.

S2 = B(a, g) = {x ∈ M : d(x,a) < g} = {a}, since the only point within a distance of g from a is a itself.

S3 = B(a, 1) = {x ∈ M : d(x,a) < 1} = {a} U (M{a}), since every point in M except a is within a distance of 1 from a, so the open ball of radius 1 centered at a contains all points in M except a, as well as a itself.

(b) Ti = S(0,7) = {x ∈ M : d(x,0) < 7} = M, since every point in the discrete metric space is within a distance of 7 from 0.

T2 = S(a, 1) = {x ∈ M : d(x,a) < 1} = {a} U (M{a}), using the same argument as for S3 in part (a).

T3 = S(a, 1) = {x ∈ M : d(x,a) < 1} = {a} U (M{a}), using the same argument as for S3 in part (a).

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The statistical technique used to predict the outcome of a variable of interest based on the value of a categorical variable is called logistic regression.

Logistic regression is a commonly used method when the dependent variable is binary or categorical. It allows us to estimate the probability of an event occurring based on one or more independent variables. The dependent variable, also known as the outcome or response variable, typically takes on two values (e.g., success/failure, yes/no).

To perform logistic regression, we use a mathematical function called the logistic function or sigmoid function, which maps any real-valued number to a value between 0 and 1. The logistic function is defined as:

P(Y=1) = 1 / (1 + e^-(β₀ + β₁X₁ + β₂X₂ + ... + βₖXₖ))

Where:

- P(Y=1) represents the probability of the event occurring.

- β₀, β₁, β₂, ..., βₖ are the coefficients to be estimated.

- X₁, X₂, ..., Xₖ are the independent variables.

To estimate the coefficients, various techniques such as maximum likelihood estimation or gradient descent can be used.

Logistic regression is a powerful statistical technique used to predict the outcome of a variable of interest based on the value of a categorical variable. By estimating the probabilities using the logistic function, we can assess the relationship between the independent variables and the likelihood of an event occurring. Logistic regression provides insights into the impact and significance of the categorical variable on the outcome, enabling prediction and inference in a wide range of fields such as medicine, marketing, and social sciences.

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Distance 1 = 1662 km

Time T= 3 hours

Distance 2= 2142 km

Time T=3 hours

Also

V1 = Plane velocity

V2= Air velocity

Then

Distance1/T = V1 - V2

and

Distance2/T= V1 + V2

1662/3= 554 = V1 - V2

2142/3= 706= V1 + V2

Now solve this 2x2 system, by substitution

then

V1= (554+ 706)/2= 1260/2= 630

V2= 706 - 630= 76

Then answer is

Velocity of plane= 630 km/h

Velocity of air= 76 km/h

Answer:

68 degrees fahrenheit.

Step-by-step explanation:

Formula:

(20°C × 9/5) + 32 = 68°F

Answer:

Its around 68F

Step-by-step explanation:

Hope this helped

Answer:

\(\displaystyle 9\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

\(\displaystyle 8 + (7 + 1)^2 \div 4 \cdot (\frac{1}{2})^4\)

Step 2: Evaluate