1. Given f(x) = x2 - 4x + 5, find each value.
a. f(2)

Carly reads at a faster rate than Monica. The number of pages in Monica's novel is greater than the number of pages in Carly's novel.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Carly Equation:

y= - 35x + 220

and, Monica equation:

slope = (90- 240)/ 5-0

slope = -150/5

slope= -30

and, the equation is

y- 240 = -30 x

y= -30x + 240

From comparing both cases Carly start with 220 pages and Monica with 240 pages and Carly will complete in 7 hours whereas Monica will complete in 8 hours.

Hence, Carly reads at a faster rate than Monica.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ1

A scatterplot shows the number of miles driven versus the gallons of gasoline remaining in the gas tank of a car. Which correlation best describes the relationship shown on the scatterplot?

Answer:

Negative correlation

Step-by-step explanation:

The kind of relationship which exists between two variables can be obtained whwn plotted in a graph such that we can visually access the data and note its trend. Datasets with fit lines trending downward will always have a slope value which is negative. In the scenario above, gallon of gasoline falls as the number if miles driven increases. This is a very reasonable relationship. And thus correlation between Both variables will be negative

Z would ultimately have a value of 2, since 5 minus 7 equals 2.

x = 5; y = 7; z = x - y z = 5; y z = 7; z = 2;Consequently, z's final value is 2.

Given that x is 5 and y is 7, the final value of z would be 2. These two numbers are divided by two, giving the answer 2. Subtraction is the action of comparing two integers to determine their differences. In this instance, since x and y differ by 2, the ultimate value of z is also 2. The solution is 2, which can alternatively be written as 5 - 7 = 2. In this case, the ultimate value of z is 2, since the difference between x and y is 2, which can be found using the useful mathematical technique of subtraction.

Learn more about value here

https://brainly.com/question/18523098

#SPJ4

It implies that there is a significant relationship between the explanatory variable and the response variable. However, it is important to note that a small p-value does not necessarily imply a strong relationship between the variables, but rather suggests that the observed relationship is unlikely due to chance.

When conducting a regression analysis, the slope of the regression line represents the relationship between the explanatory variable and the response variable. If the null hypothesis is that the slope is zero, it suggests that there is no relationship between the two variables. On the other hand, if the alternative hypothesis is that the slope is different from zero, it implies that there is a significant relationship between the variables.
When examining the results of a regression analysis, a p-value is used to determine the statistical significance of the results. A p-value is a measure of the probability that the observed relationship between the explanatory variable and the response variable is due to chance. If the p-value is less than the significance level (usually set at 0.05), it suggests that there is a significant relationship between the two variables.
In the context of the question, if the p-value is very small (less than 0.0001), it indicates that there is strong evidence to reject the null hypothesis and support the alternative hypothesis. Therefore, it implies that there is a significant relationship between the explanatory variable and the response variable. However, it is important to note that a small p-value does not necessarily imply a strong relationship between the variables, but rather suggests that the observed relationship is unlikely due to chance. The strength of the relationship is better measured by the magnitude of the slope coefficient, rather than just reying on the p-value.

To know more about explanatory variable visit :

https://brainly.com/question/31991849

#SPJ11

Answer: 12 only

Step-by-step explanation:

The value of f(0) from the graph of f(x) is (a) 12 only

Functions are used to represent graphs, equations, ordered pairs and relations.

To interpret the value of the function, we start by reading the graph.

From the graph, the value of the function when x = 0 is 12

This means that:

\(f(0) = 12\)

Hence, the value of f(0) from the graph of f(x) is (a) 12 only

Read more about functions and graphs at:

https://brainly.com/question/13136492

The proportion of persons who are 38 years old or older is 0.25.

Proportion is defined as when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal. It is a mathematical comparison between two numbers.

Proportion = (number of persons 38 years old or older) / (total number of persons)

For example, if there are 100 persons and 25 of them are 38 years old or older, the proportion would be:
Proportion = 25 / 100 = 0.25

To round to 2 decimal places, we would round 0.25 to 0.25.

So the proportion of persons who are 38 years old or older is 0.25, or 25%.

Know more about proportion here:

https://brainly.com/question/1496357

#SPJ11

The probability that the number of calls will exceed the maximum design constraint of the station is approximately 0.038, or 3.8%

A telecommunication station is designed to receive a maximum of 10 calls per 1/2 second.

If the number of calls to the station is modeled as a Poisson random variable with a mean of 9 calls per 1/2 second, the probability that the number of calls will exceed the maximum design constraint of the station is approximately 0.038.

We can find this probability using the Poisson distribution formula and solving for the probability of having more than 10 calls in 0.5 seconds.

The Poisson distribution formula is:

P(X = k) = (e^-λ * λ^k) / k!

where X is the random variable (number of calls), λ is the mean of the distribution (9 calls per 0.5 seconds), k is the number of occurrences, e is Euler's number (approximately 2.71828), and k! is the factorial of k.

To find the probability of having more than 10 calls, we need to sum up the probabilities for

k = 11, 12, 13, and so on, up to infinity:

P(X > 10) = 1 - P(X ≤ 10)≈ 1 - 0.962≈ 0.038

Therefore, the probability that the number of calls will exceed the maximum design constraint of the station is approximately 0.038, or 3.8% (rounded to three decimal places).

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

.2 Cm

Step-by-step explanation:

The diagonals of a rectangle are congruent

The diagonal of a rectangle is calculated by the formula

From the Pythagoras Theorem , The hypotenuse² = base² + height² , and

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

Given data ,

Let the rectangle be represented as ABCD

Now , the diagonals of the rectangle are AC and BD

And , the diagonals are congruent by

The measure of side AD = measure of side BC ( property of rectangle )

And , the measure of side AB = measure of side CD ( property of rectangle)

And , The measure of ∠D = measure of ∠C ( for a rectangle , the angles are perpendicular )

Therefore , ΔADC ≅ ΔBCD

So , the diagonals of the rectangle are congruent by the ASA theorem

Hence , the diagonals of the rectangle are congruent

To learn more about diagonals of a rectangle click :

https://brainly.com/question/13583275

#SPJ1

Answer:

60 students are divided into equal groups of 5 student each.

Groups of 5 students per group totaled up to 60 students.

The quotient in both expression is 60:5 = 12 students per group.

Step-by-step explanation:

The ratio expression is a way of expressing the division of numerator by a denominator.

Here,

The total number of students is the numerator = 60

The denominator is the number of students per group = 5

Hence, the quotient is the value of the divison obtained which is (60/2) = 12

Therefore, there are 12 groups of 5 students.

Answer:

B. 24700

Step-by-step explanation:

Answer:

b. 24700 cm³

Step-by-step explanation:

\(\frac{lwh}{3} \\\\65*30*38/3 = 24700 cm^3\)

Hope this helps! :)

Answer:

5.99 • .25 = 1.50

4.99 • 1.5 = 7.48

6.99 • 1 = 6.99

3.99 • 0.75 = 2.99

The costumer will pay approximately $18.96 before taxes.

Step-by-step explanation:

Answer:

1,960,000 square feet

Step-by-step explanation:

First let's round 679 to the nearest hundred. To do this we look at the 10s digit. If it is 5 or greater, we round up to 700 (because it is past halfway between 600 and 700), and is not we round down back to 600.

The 10s digit of 679 is 7, which is greater than 5. Therefore 679 rounded to the nearest hundred is 700.

Now let's look at 2828. The 10s digit here is 2, which is smaller than 5, therefore we round back down to 2800, which is closer than 2900.

Now we have 700 and 2800. To find the area, (assuming the yard is a rectangle) we multiply the length by the width together (these two values). 700x2800 = 1,960,000 square feet.

Hope this helped!

The function is :\(y(x) = 10 + (7/8) e^8x + (97/72) e^9x + 3 e^x\)

To find y as a function of x, we need to solve the differential equation:

\(y′′′ − 17y′′ + 72y′ = 168e^x\)

Step 1: Find the characteristic equation

\(r^3 - 17r^2 + 72r = 0\)

Factor out r:

\(r(r^2 - 17r + 72) = 0\)

Factor the quadratic:

r(r - 8)(r - 9) = 0

So the roots are:

r₁ = 0, r₂ = 8, r₃ = 9

Step 2: Find the general solution

The general solution will be of the form:

\(y(x) = C1 + C2e^8x + C3e^9x + y_p(x)\)

where y_p(x) is a particular solution to the non-homogeneous equation.

Step 3: Find the particular solution

We can use the method of undetermined coefficients to find a particular solution. Since the right-hand side is an exponential function, we can guess that the particular solution is also an exponential function:

\(y_p(x) = A e^x\)

\(y_p′(x) = A e^x\)

\(y_p′′(x) = A e^x\)

\(y_p′′′(x) = A e^x\)

Substituting into the differential equation:

\(A e^x - 17A e^x + 72A e^x = 168 e^x\)

Simplifying:

\(56A e^x = 168 e^x\)

A = 3

So the particular solution is:

\(y_p(x) = 3 e^x\)

Step 4: Find the constants using initial conditions

y(0) = C₁ + C₂ + C₃ + 3 = 16

y′(0) = 8C₂ + 9C₃ + 3 = 23

\(y′′(0) = 8^2 C2 + 9^2 C3 = 24\)

Solving for the constants, we get:

C₁ = 10, C₂ = 7/8, C₃ = 97/72

Step 5: Write the final solution

Substituting the constants and the particular solution into the general solution, we get:

\(y(x) = 10 + (7/8) e^8x + (97/72) e^9x + 3 e^x\)

So the function y(x) is:

\(y(x) = 10 + (7/8) e^8x + (97/72) e^9x + 3 e^x\)

To learn more about the differential equation,

https://brainly.com/question/31583235

#SPJ4

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

the inverse of a number a is \(\frac{1}{a}\)

then

the inverse of 2 is \(\frac{1}{2}\)

Answer:

ur mom reminds me of my dad lol

Step-by-step explanation:

This is your perfect answer

Answer:

\(g(-3)=7\)

\(g(0)=7\)

\(g(5)=\dfrac15\)

Step-by-step explanation:

\(g(x) =\begin{cases}7 & \text{if } x \leq 0 \\ \\\dfrac{1}{x} & \text{if } x > 0\end{cases}\)

This means:

\(\implies g(-3)=7\)

\(\implies g(0)=7\)

\(\implies g(5)=\dfrac15\)

\(\sf\f(x)=\grey{\begin{cases}\rm 7\quad ,x\geqslant 0\\ \rm \dfrac{1}{x}\quad ,x>0\end{cases}}\)

So

Hence

z = 20°

Hope it helps! Please do comment if you have any query.

Thank you

Let the two consecutive odd numbers be (2n + 1) and (2n - 1)

There product is (2n - 1)(2n + 1)

4n² - 1

2(2n) - 1

let 2n² = x

2x - 1

Hence , we can say that product of two consecutive odd number is always odd.

To learn more about Arithmetic Progression: https://brainly.com/question/13484598

The actual distance between two cities is 70 miles when 1 inch is equal to 20 miles

Given that Daniel is planning to drive from City X to City Y.

The distance between two cities is \(3\frac{1}{2}\) inches

Given that 1 inch = 20 miles

We have to find the actual distance between two cities in miles

\(3\frac{1}{2}\)  = 3.5

Now multiply 3.5 with 20 to find distance in miles

3.5×20

70 miles

Hence, the actual distance between two cities is 70 miles when 1 inch is equal to 20 miles

To learn more on Distance click:

https://brainly.com/question/15172156

#SPJ1

Answer:15%

Step-by-step explanation:

(a) The probability that exactly two of the four components last longer than 1,000 hours is 0.3679

(b) The probability that the subsystem operates longer than 1,000 hours is 0.8130

(a) Let X be the number of components that last longer than 1,000 hours. Then X follows a binomial distribution with n = 4 and p = 0.55 (the probability that a component lasts longer than 1,000 hours is 1 - 0.45 = 0.55). The probability that exactly two of the four components last longer than 1,000 hours is

P(X = 2) = (4 choose 2) × 0.55^2 × 0.45^2 = 6 × 0.3025 × 0.2025 = 0.3679

So the probability that exactly two of the four components last longer than 1,000 hours is 0.3679 (rounded to four decimal places).

(b) The subsystem will operate if any two of the four components are operating. This means that the subsystem will fail if either none or only one component is operating. Let Y be the number of components that are operating. Then Y follows a binomial distribution with n = 4 and p = 0.45 (the probability that a component fails in less than 1,000 hours is 0.45). The probability that none of the four components are operating is

P(Y = 0) = 0.45^4 = 0.0081

The probability that exactly one of the four components is operating is

P(Y = 1) = (4 choose 1) × 0.55 × 0.45^3 = 0.1789

Therefore, the probability that the subsystem fails is

P(failure) = P(Y = 0) + P(Y = 1) = 0.0081 + 0.1789 = 0.1870

So the probability that the subsystem operates longer than 1,000 hours is

P(success) = 1 - P(failure) = 1 - 0.1870 = 0.8130 (rounded to four decimal places).

Learn more about probability here

brainly.com/question/29350029

#SPJ4

The calculated value of P(-2) for P(x) = x⁴ - 6x³ - 2x² + 7x + 10 is 52

The expression is given as

P(x) = x⁴ - 6x³ - 2x² + 7x + 10

We are to calculate

P(-2)

Using a synthetic method of quotient, we have the following set up

-2 |   1   -6   -2   7   10

    |__________

Bring down the first coefficient, which is 1:

-2 |   1   -6   -2   7   10

    |__________

         1

Multiply -2 by 1 to get -2, and write it below the next coefficient and repeat the process

-2 |   1   -6   -2   7   10

    |___-2_16_-28__42___

         1   -8  14    -21  52

This means that

P(-2) = 52

So, the value of P(-2) for P(x) = x⁴ - 6x³ - 2x² + 7x + 10 is 52

Read more about synthetic method at

brainly.com/question/13820891

#SPJ4

Answer:

when giving a rate you need to get a unit rate which is a fraction with a 1 on top then you would divide by the same number as the number if you have 6/6 then divide by 6

Step-by-step explanation:

Connection between normal probabilities and empirical rule links to an external site probability is 0.95 probability is 0.02.

The parts from a supplier in an average  have a mean value  of 31.8 inches and a standard deviation value  of 2.4 inches. Probability is 0.02, which is inconsistent with the.

Probability is basically the chances of something happening . The theoretical probability is the form of probability that is  based on the reasoning behind probability. For example, if a coin is tossed than the theoretical probability of the chance or outcome of getting a head will be ½.

Probability is the branch of mathematics that basically deal for outcome of something or the chances of getting the favorable outcome four main types of probability exist: classical, empirical, subjective and axiomatic.

Probabilities always range between 0 and 1. The formula to find the  probability can be expressed as: Probability =Favorable number of Outcomes / Total Number of Outcomes. or. P(A) = f / N.

Learn more about probability here:-

brainly.com/question/11234923

#SPJ4

Answer:

{x,y}={5,-3}

Step-by-step explanation:

Answer:

first one is 4.

and sorry, don't know about the second one. i'll try and figure it out tho

Step-by-step explanation:

Answer:

270

Step-by-step explanation:

18.9 / 0.07 and get 270

Answer:

(a^2+2)(a+2)

Step-by-step explanation:

Factor a^3+2a+2a^2+4.

Using Factoring by grouping

a^3+2a   +    2a^2+4

Factor out a from the first two terms and 2 from the last two terms.

a( a^2 +2) + 2 ( a^2+2)

Factoring out a^2+2.

(a^2+2)(a+2)