A car moving at a constant speed passed a timing device at t=0. After 6 ​seconds, the car has traveled 684 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.

The linear function rule is d = ?

This indicates that there is an about 0.1587 chance that a particular student will like Eminem tracks between 5.5 and 8.5.

The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.

There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

To find:

P(X < 5.5)

Z = -1.0

However;

P(X< 5.5) = P(Z < -1.0)

P(X< 5.5) = 0.1587

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The Probability P(Green and odd) for given Sample Space is 1/5.

The likelihood of an event is expressed by probability. A random event's occurrence is the subject of this mathematical field of study. From zero to one, the value is available. In mathematics, probability is used to forecast the likelihood that events will take place.

The likelihood of something happening is referred to as a probability. The probability distribution also makes use of this basic concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood of a specific event occurring.

Event's likelihood of occurring P(E) = The number of positive outcomes divided by the total number of outcomes

Now,

Total number of outcomes=10

No. of Box that are green and marked odd=2

Hence, the probability

           P(Green and odd)=2/10=1/5

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The price of each pair of skates is given as follows:

$8.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

A skating rink charges a rate of $4, hence the intercept b is given as follows:

b = 4.

Hence:

y = mx + 4.

A family rents 2 pairs of skates and pays a total of $20, meaning that when x = 2, y = 20, then the slope m, representing the cost of each pair, is obtained as follows:

20 = 2m + 4

2m = 16

m = 16/2

m = 8.

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The new coordinates of the point (-7, -6) are (-6, 7).

From the question, we have the following parameters that can be used in our computation:

(x, y) = (-7, -6)

The rule is given as

A rotation of 90° clockwise around the origin.

Mathematically, this can be represented as

(x, y) = (y, -x)

So, we have

Image = (-6, 7)

Hence, the image is (-6, 7)

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Answer:

Yes.

Step-by-step explanation:

They will be either side of the 2 circles.

(a) Kenton is running 2.5 miles per day.

(b) An equation that illustrates the relationship between the day number and the total number of miles since Kenton began training is t = 2.5d

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The table describes Kenton’s running progress during his training.

In the table, d represents the day number, and t represents the total number of miles he ran since he began training.

From the table,

In a day Kenton ran = 5/2 = 2.5 miles.

2.5 is a common difference.

(a) Kenton is running 2.5 miles per day.

(b) An equation that illustrates the relationship between the day number and the total number of miles since Kenton began training is t = 2.5d

Therefore, the equation is t = 2.5d

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The image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.

Given that the image of (8,12) after dilation by a scale factor of 1/4 centered at the origin.

The image of the dilated point will be:-

x : - 8 ⇒ 8 / 4 = 2

y : - 12 ⇒ 12 / 4 = 3

Therefore, the image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.

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An expansion within a population that happens at the same pace across time is represented by the function of exponential growth.

Examples :

The analyst can determine the possible returns after three, five, and ten years if the customer deposits an initial starting capital of $5,000 into their compound savings account. The analyst decides: Using a 5% interest rate

Upon completion of three years: ($5,000)(1 + 0.05)(3) = $5,788

Upon completion of five years: ($5,000)(1 + 0.05)(5) = $6,381

A decade later, ($5,000)(1 + 0.05)(10) = $8,144

The Complete Question is exponential growth.

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The required multiplicative rate in the given function is 3 / 4.

Option B is correct.

The function which is in format f(x) =a^x  where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,

From the table of the exponential functions,

The multiplicative factor is given as,

K = y₂/y₁

K =  [9 / 8] / [3/2]

K = 3 / 4

Thus, the required multiplicative rate in the given function is 3 / 4. Option B is correct.

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The nearest whole number is 814. The value of 338/698 < 0.5

What is whole number?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

Given mixed number is [tex]814\frac{338}{698}[/tex].

The fraction part of the mixed number is 338/698.

2 times of 338 is 676 < 698.

Thus the value of 338/698< 0.5.

It is necessary to look at the first digit following the decimal point in order to round a number to the nearest whole number. We don't need to do anything if this digit is less than 5 (1, 2, 3, 4), but we must round up if it is 5 or higher (5, 6, 7, 8, 9).

This means the decimal value of the given number is less than 814.5.

Since the digit in the tenth place is less than 5, thus the nearest whole number of the given mixed number is 814.

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Answer: -6x + 21y = -42Now we can solve for y:21y = -42 + 42

y = 0Substitute y = 0 back into one of the original equations:-3x + 14(0) = -28

-3x = -28

x = 9/1So the solution to the system of equations is (x, y) = (9, 0).

Step-by-step explanation:

The length of the arc of the circle formed by the central angle of 90° is approximately 12.57 units

The length of an arc in a circle can be found using the formula:

Arc Length = (Central Angle / 360) * (2 * π * Radius)

Given a central angle of 90° and a radius of 8, the arc length can be found as follows:

Arc Length = (90 / 360) * (2 * π * 8)

Arc Length = (1/4) * (16π)

Arc Length = 4π

So, we have

Arc length = 12.57

So, the length of the arc of the circle is 12.57 (rounded to two decimal places).

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Percentage multiplier calculates the percentage of an amount. It is also used to increase or decrease an amount by a percentage.

In order to find the percentage multiplier of 26% of an amount we can multiply the number by a multiplier.

26% = [tex]\frac{26}{100}[/tex] = 0.26

Hence, 0.26 is the multiplier.

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The second order differential equation:-

[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].

Now, According to the question:

A differential equation is an equation that consists of a function and its derivative. A differential equation that consists of a function and its second-order derivative is called a second order differential equation. Mathematically, it is written as y'' + p(x)y' + q(x)y = f(x), which is a non-homogeneous second order differential equation if f(x) is not equal to the zero function and p(x), q(x) are functions of x. It can also be written as F(x, y, y', y'') = 0. Further, let us explore the definitions of the different types of the second order differential equation.

Hence, The second order differential equation.

[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].

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Answer:

P = (-6, 4)

Step-by-step explanation:

A = (x1,y1) = (-7,5)

B = (x2,y2) = (-2,0)

m:n = 1:4

P = (x, y)  

= (    mx2 + nx1/ m + n       ,       my2 + ny1/ m + n     )

= (        1(-2) + 4(-7)/1+4       ,         1(0) + 4(5)/ 1+4       )

= (       -2 - 28 / 5                ,             20 / 5                )

= (         - 30 / 5                   ,                 4                   )

= ( -6 , 4)

P = (-6, 4)

The actual length of the swing set area is 0.5 * 20 feet = 10 feet.

Since the scale drawing represents the actual dimensions of the park,

We can use the ratio of the scale drawing dimensions to the actual dimensions to find the actual length of the swing set area.

Let's call the actual length of the swing set area L.

Then, on the scale drawing, the length of the swing set area is 0.5 inches.

The ratio of the actual length to the scale drawing length is 20 inches : L feet.

We can set up an equation to find L:

L * (20 inches / L feet) = 0.5 inches

Solving for L, we find:

L = (0.5 inches * L feet) / (20 inches / L feet)

= (0.5 * L feet) / (20 / L feet)

= (0.5 * L feet) / (20 / L feet)

= 0.5 * (L feet / 12 inches/foot)

= 0.5 * 20 feet

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Answer:

The answer is 100 feet. I took the quiz and it was 100 feet.

Step-by-step explanation:

Answer: x =13

Step-by-step explanation:

subtract 7 from both sides

7-7= 0

-7+20=13

x=13

Answer:

[tex] \sf \: x = 13[/tex]

Step-by-step explanation:

Given equation,

→ x + 7 = 20

Now the value of x will be,

→ x + 7 = 20

→ x = 20 - 7

→ [ x = 13 ]

Hence, the value of x is 13.

Answer:  40 divided  by 2 (half) = 20+16 = 36

Step-by-step explanation:

relational algebra is a sufficient tool for manipulating data in a distributed system because it provides a uniform and consistent way to access and manipulate data.

Regardless of where it is stored in the system, and because it is a declarative language that abstracts away implementation details, making it easier to maintain and evolve the system.

Relational algebra is a powerful mathematical tool used to manipulate data in a relational database. It provides a way to perform operations on data in a structured and organized manner.

In a distributed system, where multiple nodes store and process data, relational algebra is still sufficient because it provides a uniform and consistent way to access and manipulate data across the entire system.

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The recursive rule for the given sequence 1, 3, 4, 7, 11 ... is aₙ₊₁ = aₙ + aₙ₋₁.

The next two term of the sequence 1, 3, 4, 7, 11, is equal to 18 , 29.

Recursive rule for the sequence 1, 3, 4, 7, 11, ...... is represented by :

Let us consider before 1 it is 0.

Next term is sum of previous two terms :

0 + 1 = 1

1 + 3 = 4

3 + 4 = 7

4 + 7 = 11

Recursive rule for the given sequence is equal to :

3rd = 2nd + 1st term

4th term = 3rd term + 2nd term .....

aₙ₊₁ = aₙ + aₙ₋₁

Next two terms for the above sequence is equal to:

7 + 11 = 18

11 + 18 = 29

Therefore, the recursive formula to represents the sequence 1, 3, 4, 7, 11 is equal to aₙ₊₁ = aₙ + aₙ₋₁ and next two terms are 18, and 29.

The above question is incomplete, the complete question is:

Write a recursive rule for the sequence. Then write the next two term of the sequence. For 1,3,4,7,11

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Answer:

See below

Step-by-step explanation:

This is very easy once you understand what to do kiddo. They give you a x term, in this case -2, all you have to do is plug in this value into the equation y = x² -2x -3 which will give you your y value in this case +5 not - 5.

Heres the extra work

[tex]y = x^2 - 2x -3\\y = (-2)^2 -2(-2) -3\\y = 4 + 4 -3\\y = 5[/tex]

Answer:

Ответ:

Пошаговое объяснение:

Ответ : Пошаговое объяснение : - 1

Answer: 3 rose bushes

Step-by-step explanation:

1. First we must identify the unknown. We do not know how many rose bushes he can get, we will use "x" to represent this number.

2. We must set up an equation with the given information. We know the delivery fee will remain constant.

3. 15+18.75(x)=80

4. Subtract 15 from both sides and it leaves you with 18.75x=65

5. Then you must divide both sides by 18.75, which leaves you with x=3.46

6. We cannot buy .46 of a plant so we must round down to 3

7. Jim can buy 3 rose bushes

Answer:

isosceles, equilateral, scalene, obtuse, acute, and right triangles.

Step-by-step explanation:

isosceles, equilateral, scalene, obtuse, acute, and right triangles.

Triangles can be classified into six different shapes: right, obtuse, acute, equilateral, scalene, and isosceles. A triangle is said to be isosceles if two of its sides are congruent and one of its sides and angle is distinct.

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[tex]~~~~~~ \stackrel{\textit{\LARGE Quarterly}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]A = 7000\left(1+\frac{0.09}{4}\right)^{4\cdot 12} \implies A=7000(1.0225)^{48}\implies \boxed{A \approx 20367.48} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Annually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]A = 7000\left(1+\frac{0.09}{1}\right)^{1\cdot 12}\implies A=7000(1.09)^{12} \implies \boxed{A \approx 19688.65} \\\\[-0.35em] ~\dotfill\\\\ 20367.48~~ - ~~19688.65 ~~ \approx ~~ \text{\LARGE 678.83}[/tex]

In a repeated measures design with 20 subjects, each subjected to 2 measurements (before and after stimulus presentation), the degrees of freedom in the test would be 19.

The problem is about an experiment in which a measurement is taken before and after a stimulus is presented to 20 subjects. The aim is to determine the number of degrees of freedom in the data analysis of the experiment.

Degrees of freedom (df) are a measure of the amount of variability in a set of data that is free to vary in the calculation of a statistical test. In a repeated measures design, the degrees of freedom are calculated as the number of subjects minus 1. In this case, with 20 subjects, the degrees of freedom would be 19.

The concept of degrees of freedom is used in both mathematics and physics, but the specific context of a t-test for dependent samples is commonly used in statistical analysis, particularly in the social sciences, psychology, and education research. So, it is more related to mathematics.

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The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.

Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:

F_B = m_p * g

Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.

To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).

m_b = V * ρ

Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).

m_p = n * m

Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.

n = (F_B) / (m * g)

Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

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Answer:

See below

Step-by-step explanation:

The graph is of f(x) is shifted 1 unit to the LEFT to get g(x)

          so  4^x     is now  4^(x+1)

                                   then    4^(x+1) = 4^(x-h)

                                         would mean h = - 1

The equation has one solution at (0, -2) for the system of linear equations represented in the graph.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.

Given the graph,

and the line passes from (0, -2) and (4, 0)

since the line passes from  (0, -2) and (4, 0),

so one of the solutions is at (0, -2),

and another solution is at (4, 0).

according to the options equation has  (0, -2) as one of the solutions.

Hence option B is correct.

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The only one carton of pear is not enough because the sum of both Jo and Max requirement is max than the one.

There is only one carton of pear.

Jo want to buy 3/4 of it, and Max to buy 1/3 of it.

To check whether one carton of pear is enough for both Jo and Max we firstly add the part of Jo and Max to find the total pear they want. Then we check the one pear is enough y subtracting.

Now finding the total pear that Jo and Max want:

Total Pear they want = Jo want + Max want

Total Pear they want = 3/4 + 1/3

To add we equal the denominator.

Multiply and divide by 12 on both number

Total Pear they want = 3/4 × 12/12 + 1/3 × 12/12

Total Pear they want = 9/12 + 4/12

Total Pear they want = (9 + 4)/12

Total Pear they want = 13/12

Total Pear they want = 1 1/12

As we can see that the sum of both Jo and Max requirement is max than the one pear. So the only one carton of pear is not enough.

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