What is the equation of the line graphed below?

Answer:

18

Step-by-step explanation:

1. Try to create an equation. We can say that the first number is x and the following numbers are x+1 and x+2. That means that x*(x+1)*(x+2)=4896.

2. Solve and Simplify. x^3+3x^2+2x=4896.

3. Solve and Simplify (2) I'm assuming that you're not looking for the complex solutions, so x=16.

4. Find the 3rd number. 16+2=18

Answer: 18 is the largest number of the three

The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.

The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.

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p = -9.47

Step-by-step explanation:

-p + -8.1 = 1.37

-p = 1.37 + 8.1

-p = 9.47

p = -9.47

The cost per ounce of the premium walnut is $0. 23

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

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Answer:

1.80

Step-by-step explanation:

1%=0.01

10%=0.10

100%=1.00

Answer:

The range of the function is: -∞≤y≤∞.

Consider the provided function.

The range of the function is the set of all values which a function can produce or the set of y values which a function can produce after substitute the possible values of x.

The range of a cubic root function is all real numbers.

Now consider the provided function.

The above function can be written as:

Taking cube on both sides.

The graph of the function is shown in figure 1:

For any value of x we can find different value of y.

Here, the cube root function can process negative values. Since, the function can produce any values, the range of the given function is  -∞≤y≤∞ .

Therefore, the range of the function is: -∞≤y≤∞ (A).

The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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The blank spaces in the statements area. S, R, and Q  are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

(a.) S, R, and Q are on a straight line. Therefore S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

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9514 1404 393

Answer:

  {2.96, 12.66}

Step-by-step explanation:

A graph shows the rocket will be 600 feet up after 2.96 seconds, and again at 12.66 seconds.

__

You can solve the equation h = 600 to find the times.

  -16t^2 +250t = 600

  -16(t^2 -15.625t) = 600

  -16(t^2 -15.625t +7.8125²) = 600 -16(7.8125²)

  -16(t -7.8125)² = -376.5625

  t -7.8125 = √(376.5625/16) ≈ ±4.8513

  t = 7.8125 ± 4.8513 ≈ {2.9612, 12.6638}

The rocket will be 600 ft above the ground 2.96 and 12.66 seconds after launch.

By doing a change of units, we know that he will need 40 pint jars to hold the whole volume of sauce.

We know that Joe makes tomato sauce to sell at a craft fair, and we know that he did make that sauce in 5-gallon batches.

We want to see how many jars do he need to hold these 5 gallons, so we need to perform a change of units.

Remember the relation:

1 gallon  = 8 pints.

So, for each gallon, he will need 8 pint jars, then for the 5 gallons, he will need:

5*8 pint jars = 40 pint jars.

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The correct answer is 33 people went ice skating more than 2 times.

Frequency is a measure of how often a given event occurs. It is usually represented as a number, but can also be expressed as a percentage or a ratio. Frequency can be used to describe the number of times a certain event occurs in a given period, such as the number of times an event appears in a data set or the number of times an event occurs in a given time period.

The total number of people who went ice skating more than 2 times is 33, which is calculated by adding the frequencies of  people going for ice skating more than 2times, that is 3 and 4.

Thus, by adding the frequencies, 15 and 18 we get the value 33.

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Hey buddy I am here to help!

Red = 8

blue = 6

greem = 4

total = 18

probability of blue marble = 6/18 = 1/3

Answer:

I think it is 1/3

Step-by-step explanation:

you have 18 ways to pick one marble in the bag and have 6 ways to pick a blue marble so the probability that the marble will be blue is 6/18=1/3

The correct graph of the inequality -0.4x - 2 < - 1.2 is option 2.

Equation containing a relational operator and a linear expression is known as a linear inequality. In a coordinate plane or space, regions that satisfy a linear inequality are defined. A linear inequality defines a half-plane in two dimensions, which, depending on the inequality, can be either above or below a line. A linear inequality defines a half-space in three dimensions, which, depending on the inequality, is either above or below a plane. The goal of optimization problems is to determine the maximum or minimum value of a linear function under a set of constraints, which are typically represented by linear inequalities.

The given inequality is -0.4x - 2 < - 1.2.

-0.4x - 2 < - 1.2

Adding 2 on both sides of the equation we have:

-0.4x < -1.2 + 2

-0.4x < 0.8

-x < 2

x > -2

Hence, the correct graph of the inequality is option 2.

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Answer:

Step-by-step explanation:

The desired distribution can be found by factoring out the greatest common factor from two numbers.

  30 sweaters + 45 trousers = 15(2 sweaters + 3 trousers)

Each of 15 children got 2 sweaters and 3 trousers.

_____

Additional comment

The two numbers can be factored as ...

  30 = 2·3·5

  45 = 3·3·5

The factors these numbers have in common are 3·5 = 15

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

64.2 minutes

Step-by-step explanation:

We are given that

Shen set timer to run=93 minutes

He has finished his run=69%

We have to find total number of minutes have gone by.

69% of 93

=\(\frac{69}{100}\times 93\)

By using

a%\(=\frac{a}{100}\)

69% of 93=\(\frac{6417}{100}\)

69% of 93=64.17 min

69% of 93\(\approx 64.2min\)

Hence, 64.2 minutes have gone by.

The steps for bisecting a line segment are to place the reflective device, draw the line of reflection, place the reflective device on point B, move the reflective device around, place the reflective device on point A and repeat the process.

This process implies creating a new line that is perpendicular to the original line, which means the new line will cross the original one. The steps for this are:

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And , the Y's variance is \(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)To find the mode of Y, we need to find the value of y that maximizes the joint probability density function\(f_X, Y(x,y).\)

To do this, we can fix x to be a particular value and then find the value of y that maximizes \(f_X, Y(x,y).\)

For any fixed x between 0 and 2, the function\(f_X, Y(x,y)\) is maximized at y = 1, since this is the only value of y that depends on x and maximizes the function\(cx^2y.\) Therefore, the mode of Y is 1.

To find the value of c that makes this a valid probability density function, we need to ensure that the integral of \(f_X, Y(x,y)\)over the entire sky-plane is equal to 1. We can set up the integral as follows:

integral from 0 to 2 of (integral from 0 to 2 of cx^2y dy) dx

= integral from 0 to \(2 of [c*x^2/2 * y^2]\)evaluated from 0 to 2 dx

= integral from 0 to 2 of \(c*x^2 x2d\)

= [2c/3 * x^3] evaluated from 0 to 2

= (16c/3)

For this to equal 1, we must have c = 3/16. Therefore, the valid probability density function is:

f_X,Y(x,y) = { (3/16)x^2y, 0 <= x <= 2, 0 <= y <= 2; 0, otherwise }

To find the expected value of Y, we need to integrate Y times the joint probability density function f_X, Y(x,y) over the entire xy-plane:

E[Y] = integral from 0 to 2 of (integral from 0 to 2 of y*f_X, Y(x,y) dy) dx

= integral from 0 to 2 of \([(3/16)*x^2/2 * y^2]\) evaluated from 0 to 2 dx

= integral from 0 to 2 of (3/16)*x^2 dx

= [3/16 * x^3/3] evaluated from 0 to 2

= 1

Therefore, the expected value of Y is 1.

To find the variance of Y, we first need to find the second moment of Y by integrating Y^2 times the joint probability density function f_X, Y(x,y) over the entire xy-plane:

E[Y^2] = integral from 0 to 2 of (integral from 0 to 2 of y^2*f_X, Y(x, y) dy) dx

= integral from \(0 to 2 of [(3/16)*x^2/3 * y^3]\) evaluated from 0 to 2 dx

= integral from \(0 to 2 of (3/8)*x^2 dx\)

= \([3/8 * x^3/3]\) evaluated from 0 to 2

= 2

And , the Y's variance is

\(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)

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Answer:

its B. 636 to 1404

Step-by-step explanation:

Using the Empirical Rule, about 95% of the scores lie between values 636 to 1404. The correct option is c.

The standard deviation of a set of values is a measure of its variation or dispersion. The square root of the variance, which is the average of the squared differences from the mean, is used to calculate it.

According to the Empirical Rule, approximately 68% of the data for a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

In this case, the mean SAT score is 1020, with a standard deviation of 192. As a result, roughly 95% of the scores fall within two standard deviations of the mean, or between

(1020 - 2(192)) and (1020 + 2(192)).

Calculating, we get:

Lower bound: 1020 - 2(192) = 636

Upper bound: 1020 + 2(192) = 1404

Therefore, the answer is (b) 636 to 1404.

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Answer:

y = 4x + 10         x = 6

Step-by-step explanation:

a)  perimeter = 2x + 2x + 10 = 4x + 10

b)  perimeter = 34

⇒ 4x + 10 = 34

⇒ 4x = 34 - 10 = 24

⇒ x = 24 ÷ 4 = 6

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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Answer:    8.3 or C  

Eplanation: This is because a half life is 50 percent of a normal life so 50 percent divided by 6 is 8.3

\(8.3\)% is the approximate decay rate of the element after the first day.

What is Radioactive decay ?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles.

What is decay rate?

The rate of decay, or activity, of a sample of a radioactive substance is the decrease in the number of radioactive nuclei per unit time.

According to question, a radioactive element has a half-life of six days.

A half- life is \(50\)% of a normal life.

So, the approximate decay rate of the element after the first day

\(=\frac{50}{6}\)% \(=8.3\)%

Hence, we can conclude that \(8.3\)% is the approximate decay rate of the element after the first day.

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Answer:

#6:

Step-by-step explanation:

#6

So these two angles are actually the same. Since the lines l and m are parallels and those angles are opposite from each other, they are the same.

This means you can solve for x by saying:

3x-63 = 2x+2

x = 65

#7

Since the l and m are parallels, and the angles are NOT opposite, when you add the two angles together, you should get 180 degrees

So:

(2x + 20) + (6x + 24) = 180

x = 17

Based on the information, tere are 16224000 possible passwords.

There are 52 possible letters for the first two characters (26 uppercase and 26 lowercase).

There are 6 possible special characters for the third character.

There are 10 possible numbers for the last three characters.

We can use the Fundamental Counting Principle to calculate the number of possible passwords. The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another thing, then there are n×m ways to do both things.

In this case, there are 52×52=2704 ways to choose the first two characters, 6 ways to choose the third character, and 10×10×10=1000 ways to choose the last three characters.

Therefore, there are 2704×6×1000

=16224000 possible passwords.

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The sample variance and standard deviation are given as follows:

To obtain the variance and the standard deviation, first we must obtain the mean, which is given by the sum of all observations divided by the number of observations, hence:

Mean = (77.1 + 82.9 + 90 + 91.3 + 81.9 + 83.3 + 84.9 + 82.5 + 84.6)/10

Mean = 75.85.

Then we must obtain the sum of the differences squared between each observation and the mean, as follows:

(77.1 - 75.85)² + (82.9 - 75.85)² + (90 - 75.85)² + (91.3 - 75.85)² + (81.9 - 75.85)² + (83.3 - 75.85)² + (84.9 - 75.85)² + (82.5 - 75.85)² + (84.6 - 75.85)² = 784.9825

The sample variance is given by the above sum divided by one less than the sample size, hence:

Variance = 784.9825/9

Variance = 87.22 %².

The standard deviation is the square root of the variance, hence:

Standard deviation = sqrt(87.22)

Standard deviation = 9.34%.

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Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Answer:

We have the function g(x) = x^3 -15*x

First, to find extrema, we can find the zeros of the first derivative.

g'(x) = 3*x^2 -15

g'(x) = 0 = 3*x^2 - 15

x^2 = 15/3 = 5

x = √5

x = -√5

Now, watching at the second derivative we have:

g''(x) = 6*x

so when we have

g''(√5) = 6*√5 > 0 then x = √5 is a local minimum

g''(-√5) = -6*√5 < 0, then x = -√5 is a local maximum.

Answer:

4.

\(Daryll: \frac{8 miles}{40 minutes}\times \frac{60 min}{1 hr} = 12 miles per hr.\\Isabella: \frac{5 miles}{30 minutes} \times\frac{60 min}{1 hr} = 10 miles per hr.\\\)

Therefore Daryll will go 24 miles in 2 hours. Isabella will go 20 miles in 2  
hours.

     Final answer: Daryll goes further in two hours by 4 miles.

5.

\(\frac{2.00}{5} =\frac{x}{9} \\5x=18\\x= 3.60\) dollars

Final answer: 3.60 dollars

6.     8 oranges = 2(2.45) = 4.90 dollars

        12 oranges = 3(2.45) = 7.35 dollars

Step-by-step explanation:

Simple ratio problems. IF you still don't get it Khan Academy is helpful.

The probability is closer to one than zero.

Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.

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