Which is the graph of the function f(x) = x3 + x2 + x + 1?

Answer:

15.2

Step-by-step explanation:

The explanation is in the photo.. but basically this question is about similar triangles and you need to find the scale factor to find the height.

Hope it helps

the height of the tree is approximately 15.2 meters.

To find the height of the tree, we can set up a proportion between Andrew's height and the height of the tree based on their respective shadow lengths.

Let's denote the height of the tree as "h" meters.

The proportion between the height and shadow lengths can be written as:

h / 28.0 = 1.9 / 3.5

Now, we can solve for "h":

h = (1.9 / 3.5) * 28.0

h ≈ 15.2 meters

To the nearest tenth of a meter, the height of the tree is approximately 15.2 meters.

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The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%. Computed using conditional probability.

The probability of any event A given that event B has already taken place is found using the formula P(A|B) = P(A ∩ B)/P(B). This is known as conditional probability, where P(A ∩ B) is the probability of events A and B, and P(B) is the probability of event B.

In the question, we are given that 70% of kids who visit a doctor have a fever and 21% of kids have a fever and sore throats.

We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever.

We suppose the event of going to the doctor while having a fever to be B, and going to a doctor while having a sore throat to be A.

We are given that 70% of kids who visit a doctor have a fever, that is, the probability of event B, P(B) = 70% = 0.7.

We are given that 21% of kids who visit a doctor have a fever and sore throats, that is, the probability of event A and event B, P(A ∩ B) = 21% = 0.21.

We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever, that is, we are asked to find the conditional probability of event A, when event B has already taken place, that is, P(A|B).

By formula, we know that:

P(A|B) = P(A ∩ B)/P(B) = 0.21/0.70 = 0.30.

Thus, the probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%.

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The graphed function, F(x), has a value greater than 0 over the intervals (-0.7, 0.76) and (0.76,  ∞) . F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞) is the correct statement [Fourth choice].

About a Graphed Function

The function graph of an object F stands for the set of all points in the plane that are (x, f(x)). The graph of f is also known as the graph of y = f. (x). The graph of an equation is thus a specific example of the graph of a function. A graphed function is a function that has been drawn out on a graph.

It is evident from the attached graph that the supplied function exceeds 0 for the following range:

-0.7 < F(x) < 0.76

And, 0.76 < F(x) < ∞

As a result, the intervals for which the given graphed function, F(x) is greater than 0 are as follows,

(-0.7, 0.76) and (0.76, ∞)

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The probability that olga will select a red pair of socks and a red hairband is 14/47

Probability defines the likelihood of an event occurring. There are many situations in real life where we may need to predict the outcome of an event. We may or may not be certain of the outcome of the event. In such cases, we say that there is a probability that the event will or will not occur. Probability in general has great applications in games, in business for probabilistic predictions, and also probability has extensive applications in this new field of artificial intelligence.

The probability of an event can be calculated using the probability formula simply by dividing the number of favorable outcomes by the total number of possible outcomes. The value of the probability of an event occurring can lie between 0 and 1 because the number of favorable outcomes can never exceed the total number of outcomes. Also, a favorable number of results cannot be negative

For an experiment that has "n" number of outcomes, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is as follows.

Probability (event) = favorable outcomes/total outcomes = x/n

Olga has a drawer of socks with four red pears, two gray pears, and a black hairs. she also has a bag of hair bands with 10 red, six gray, and 24 black hair bands

Therefore total number of items are = 4 + 2 + 1 + 10 + 6 + 24 = 47

Probability that olga will select a red pair of socks and a red hairband is 4/47 + 10/47

= 14/47

Hence the probability that olga will select a red pair of socks and a red hairband is 14/47

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The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

VAT = 13% = 0.13 * 8000 = 1040

Selling price - VAT = 11300 - 1040 = 10260

Profit = [(10260 - 8000)/8000] * 100% = 28.25%

The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

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Using the relation between velocity, distance and time, it is found that his jogging rate was of 4.5 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Jogging, his velocity was of v, while the time was of t + 2, for a distance of 10 miles, hence:

[tex]v = \frac{10}{t + 2}[/tex]

Riding, his velocity was of 16, while the time was of t, also for a distance of 10 miles, hence:

[tex]v + 16 = \frac{10}{t}[/tex]

Then, considering the first equation and replacing in the second:

[tex]\frac{10}{t + 2} + 16 = \frac{10}{t}[/tex]

[tex]\frac{10}{t} - \frac{10}{t + 2} = 16[/tex]

[tex]\frac{10t + 20 - 10t}{t(t + 2)} = 16[/tex]

16t² + 32t - 20 = 0 -> t = 0.5.

Then his jogging rate in mph was:

[tex]v = \frac{10}{0.5 + 2} = 4.5[/tex]

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Answer:

If f(-x) = f(x), f is even and is symmetric about y

If f(-x) = -f(x), f is odd and is symmetric about the origin

If [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], f is neither even nor odd and does not have symmetry

Step-by-step explanation:

As we discussed in one of the previous questions, if f(-x) = f(x), we have an even function. One basic example of an even function is x^2 since (-x)^2 = x^2. On the other hand, if f(-x) = -f(x), we have an odd function. One common example is x^3 since (-x)^3 = -x^3. What we have not been over yet is the symmetry of the functions. In order to do this, let's examine x^2 and x^3. x^2, which is an even function, is symmetric to the y-axis. The graph is a parabola that looks exactly the same on the left and the right of the y-axis.

On the other hand, x^3, which is an odd function, is not symmetric to the y-axis. On the other hand, it is symmetric to the origin. You can imagine that if you flipped y = x^3 across the origin, you would end up getting a graph that looks exactly the same.

A function that is neither even nor odd, meaning [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], one that is not odd or even, has no symmetry. It is not symmetric about the y-axis or the origin.

Answer:

Below in bold.

Step-by-step explanation:

Total number of marbles = 3+4+5 = 12

P(white, red) = 4/12 * 3/11

                      = 12/132

                      = 1/11,

P(blue, white, red)  = 5/12 * 4/11* 3/10

                                 = 60/1320

                                 = 6/132

                                 = 1/22.

The other fraction is [tex]1\frac{1}{55}[/tex].

Provided that ,

One fraction = [tex]9\frac{3}{7}[/tex] = [tex]\frac{66}{7}[/tex]

The product of their fraction = [tex]9\frac{3}{5}[/tex] = [tex]\frac{48}{5}[/tex]

We have to find out the other fraction.

When one fraction and their product are given, the formula to find out another fraction = product / one fraction

So, the other fraction = [tex]\frac{48}{5}[/tex] / [tex]\frac{66}{7}[/tex]

= [tex]\frac{48}{5} * \frac{7}{66}[/tex]

= 336/330

= 56/55 [divided both the numerator & denominator by 6]

= [tex]1\frac{1}{55}[/tex]

Therefore it is concluded that the other fraction is [tex]1\frac{1}{55}[/tex] .

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Using translation concepts, the graph of g(x) = -|x - 4| is shown at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The graph of g(x) = -|x - 4| is the graph of f(x) = |x| with these following changes:

At the end of the answer, the graph shows functions f(x) in red and g(x) in blue.

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Answer:

3n+1

Step-by-step explanation:

Subtract one from all the values, you get multiples of 3 in the equation 3n=nth term

So when you add one back, your equation is 3n+1=nth term

Answer:

600ft

Step-by-step explanation:

The balloon falls 200 feet in one minute and we need the amount it fell in 3 minutes: 200feet*3minutes = 600 ft

Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

In this problem, the parameters are:

a = 800, b = 900, C = 70º.

Hence the distance across the lake is c, found as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

c² = 800² + 900² - 2(800)(900)cos(70º)

c² = 957491

[tex]c = \sqrt{957491}[/tex]

c = 978.5.

The distance across the lake is of 978.5 feet.

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The equation which represent the interpretation of the scenario is 5 + 2x

Total laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)

= 5 + (2 × x)

= 5 + 2x

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The cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. By generalizing this in form of a principle which we would use to prove any mathematical statement is 'Principle of Mathematical Induction'.

The question says that between any two cities X and Y, either there’s an

one-way road from X to Y or from Y to X, but not both. Then show that

there is a path from some city A which visits all the cities exactly once.

This problem is very similar to the Football league problem #7 in Homework 1. This problem can be modeled as a directed graph in which cities

are represented as vertices and there’s an edge from vertices X to Y if

there’s a road from cities X to Y. And then, our goal is to find a path

in this graph which visits every vertex in the graph.

The rest of the solution is very similar to the argument in Problem 7 of

homework 1. We use induction of number of cities, say n.

As a base case, if n = 2, there are only two cities X and Y and the path

is simply the edge between X and Y.

For induction hypothesis, assume that the statement is true for any set

of n cities. That is’ for any set of n cities, we can find a path which visits

all the cities exactly once.

Let’s prove the statement for n + 1 cities. Leave out n + 1 th city (say,

[tex]c_{n}+1[/tex]) and for the remaining n cities, by induction hypothesis, we can find a path which visits all these n cities exactly once. Let us label the cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

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Answer:

7 hot dogs

Step-by-step explanation:

Set up an equation:

2.5x + 1.25 = 21

2.5x = 19.75

x = 7.9

You cannot buy .9 of a hot dog, so the answer is 7

The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.

Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]

Lets simplify the equation:

[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]

Expression:

An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.

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Answer:

y = 7.25 + 0.65x

Step-by-step explanation:

y = total cost

x = each mile

it starts at 7.25

any mile after that is an extra $0.65

y = 7.25 + 0.65x

The equations of the corresponding circles can be any equation only have to satisfy the  general equation for circle .

The question seems incomplete and complete question given in the image !!!!

A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)

We know that the general equation for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where ( h, k ) is the center and r is the radius.

According to the question

The equation of circle given is [tex]x^2+y^2=1[/tex]

Center at origin

i.e

(h,k) = (0,0)

and radius = 1 unit

Now ,

By changing changing center (h,k) and radius of equation it will give following equations

h                      k                       r                            equation of circle

0                       1                       3                      [tex](x-0)^2+(y-0)^2=3^2[/tex]  

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

1                        1                        1                     [tex](x-1)^2+(y-1)^2=1^2[/tex]  

-2                      -1                       2                      [tex](x+2)^2+(y+1)^2=2^2[/tex]

3                       2                       1                        [tex](x-3)^2+(y-2)^2=1^2[/tex]      

-5                      1                        3                       [tex](x+5)^2+(y-1)^2=3^2[/tex]

Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .

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The distance from Jim's home to the gym is 12 km.

Speed is defined as the rate at which the position of object is changed.

Speed = Distance / Time

Here, there are two different speeds given for the same distance.

Average speed is the total distance travelled by the total time taken.

If distance is a constant,

Average speed = 2xy / (x + y), where x and y are two different speeds for the same distance.

Average speed = (2 × 15 × 10) / (15 + 10)

                          = 12 km/hr

So, Total distance travelled = Average speed × total time taken

                                              = 12 × 2

                                              = 24

Distance = 24 / 2 = 12

Hence, the distance from Jim's home to the gym is 12 km when average speed is taken.

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Total number of teams are 10

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is one that includes a variable, such as x.

As given in the problem,

total number of students in class=30

now professor want to create study teams .

one team consist of 3 members,

lets suppose professor will form n teams

So,

3×n=30

solve this equation to get value of n

n=30÷3

n=10 teams

hence total number of teams are 10 .

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Answer:

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

Step-by-step explanation:

Use the formula f(t)=P(1+b)^t

Plug in the information.

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

The only thing I did in the second equation is I subtract 0.12 from 1.

Hope this helps!

Answer:

a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm

b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)

= 4√10 cm

c) Simplifying √72: √36 x √2 = 6√2

   Simplifying √18: √9 x √2 = 3√2

   Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm

Answer:

Incorrect

Step-by-step explanation:

Formula:

the Diagonal of a square with side square of lengths a

is equal to a√2.

=============

Then

Diagonal of LMNO : 7√2

Then

OM = 7√2

…………………………………………

Using the Pythagorean theorem:

The diagonal of the rectangle PQRS is equal to :

√(14²+7²) = √245 = 7√5

Then

SQ = 7√5

………………

Conclusion:

7√5 ≠ 2×(7√2)

Therefore

Anna is not correct.

The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.

The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x

where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.

It is given that the triangle is a right triangle with angles 30°-60°-90°

For such a triangle, the ratio of side lengths is x: x[tex]\sqrt{3}[/tex]:2x

we have the length of the hypotenuse is [tex]2\sqrt{6}[/tex]

So, 2x = [tex]2\sqrt{6}[/tex]

⇒ x = [tex]\sqrt{6}[/tex]

So,

the other length of the other leg is x√3 = √6 × √3 = 3 √2

Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.

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The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

According to the statement

we have a given that the Among the 1000 respondents,

12​% chose chocolate​ pie, and the margin of error was given as

±5 percentage points.

and we have to explain the statement that the margin of error was given as ±5 percentage​ points.

We know that the interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

And this statements also indicates the interval between the like and unlike respondents of chocolate pie.

So, this statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

So, The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

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The circumference of the circle of diameter 35cm is 109.9 cm.

Given the diameter of the circle is 35 cm.

We are required  to find the circumference of the circle.

The circumference is the arc length of the circle, The perimeter is the curve length around any closed figure. It is equat to the length of the outer ring of a circle.

Formula of circumference=2πr where r is the radius of the circle.

Diameter=35 cm

Radius=35/2 cm (Radius is half of diameter)

Circumference=2π*35/2

=35π

Put the value of π =3.14 (it can be 22/7 as well.)

=35*3.14

=109.9 cm

Hence the circumference of the circle  is 109.9 cm.

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Answer:

3x - 4/2

Step-by-step explanation:

2 result(s) for "f(x) = 4x³ - 10 g(x)