5. Find all the solutions to the equation x²e^x– 2xe^x – 3e^x =0.

√5 km/h fast is the distance between the ships changing at 4:00 PM .

What is the Pythagorean theorem ?

The Pythagorean theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

                      This is represented by the equation a2 + b2 = c2 in common algebraic notation.

Ship A is sailing 25 km/h east and Ship B is sailing 15 km north. They are giving us the time frame, which is 4 hours ( t = 4). Recall that Distance = Rate * time. Let us find the distance for each ship after 4 hours

Ship A Ship B

d=25*4 = 100 km d=15*4= 60 km

the Pythagorean theorem.

a2+b2=c2

(30)2+(60)2=c2

c=30√(5)

From the question, "How fast" is asking us for a rate. The rate on the hypotenuse side. We have to take the derivative of the pythagorean theorem with respect to time.

2a(da/dt) + 2b(db/dt) = 2c(dc/dt)

Solve for dc/dt

dc/dt = [a(da/dt) + b(db/dt)] / c

dc/dt = [30(-25) + 60(15)] / 30√5 ****Note: we have -25 as time increases, the distance is smaller

dc/dt = √5 km/h

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The measure of angle B is (d)  114 degrees

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

B = 13x - 16

Exterior of B = 8x - 14

As a general rule, the sum of an angle and its exterior is 180 degrees

This means that

13x - 16 + 8x - 14 = 180

Evaluate the like terms

So, we have

21x = 210

Divide both sides

x = 10

Recall that

B = 13x - 16

So, we have

B = 13 x 10 - 16

Evaluate

B = 114

Hence, the measure is 114 degrees

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Answer:

The measure of angle B is (d)  114 degrees

Step-by-step explanation:

a) The probability that both are girls is of: 21/150.

b) The probability that both are from the same school is of: 0.7333 = 73.33%.

How to obtain the probabilities?

The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

One girl from school A -> 7/15 probability.

One girl from school B -> 3/10 probability.

Hence the probability that both are girls is of:

p = 7/15 x 3/10 = 21/150.

The probability that the two boys are from the same school can be given by these two cases:

School A: 8/15 x 7/14.

School B: 7/10 x 6/9.

Then the probability is of:

p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.

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Answer: (fog)(x) = f(g(x)) = f(6x) = 5(6x) = 30x

So (fog)(x) = 30x, which is a polynomial in simplest form

The number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, M Attend to Precision Ricardo has 325 tiles to make 4 mosaics.

Here, the number of tiles need for each mosaic is 325/4

4|325|81

  324

______

    1

Therefore, the number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.

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A true proportion of the figure based on the triangle proportionality theorem is: A) i/j = h/k.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

The triangle proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

Since side TU is parallel to side QR, side TU will divide both sides QS and RS proportionally in accordance with the triangle proportionality theorem as follows;

RU/QT = SU/ST ≡ i/j = h/k

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There are solutions when k = -1 and when k = -3

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

|x + 3| - 2 = k

Removing the modulus sign

x + 3 - 2 = k -----(i) = x + 1 = k

-x - 3 - 2 = k -----(ii) -x - 5 = k

Putting k = -1

(i) x = -2 and (ii) x = -4

Putting k = -3

(i) x = -4 and (ii) x = -2

Since, x has solution on both the values of k

We can say that,

There are solutions when k = -1 and when k = -3

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To develop an equation to predict the surface area of a person as a function of their height and weight using numerical methods and MATLAB, you can follow these steps:

The required details for MATLAB in given paragraph

Begin by organizing the given data into two separate arrays: one for height (H) and one for weight (W). For example, you might create the following arrays:

H = [182 180 179 187 189 194 195 193 200];

W = [74 88 94 78 84 98 76 86 96];

A = [1.92 2.11 2.15 2.02 2.09 2.31 2.02 2.16 2.31];

Use the MATLAB function "polyfit" to fit a polynomial function to the data. You can specify the degree of the polynomial function based on the number of variables you want to include in the model. For example, to fit a second-degree polynomial function, you can use the following command:

p = polyfit(H,A,2);

This will fit a polynomial function of the form A = p(1) * H^2 + p(2) * H + p(3) to the data, where p(1), p(2), and p(3) are the coefficients of the polynomial.

Use the MATLAB function "polyval" to evaluate the fitted polynomial function at a specific value of H. For example, to estimate the surface area for a person with a height of 187 cm, you can use the following command:

A_estimated = polyval(p,187);

This will return the estimated surface area for a person with a height of 187 cm. You can use similar commands to estimate the surface area for different values of H

what do you mean by MATLAB?

MATLAB (short for "Matrix Laboratory") is a programming language and software environment for numerical computation, visualization, and programming. It is commonly used in scientific, engineering, and mathematical fields to analyze and visualize data, develop algorithms, and build mathematical models.

A function in MATLAB is a self-contained block of code that performs a specific task or computation. Functions are useful because they allow you to reuse code and make your programs more modular and easier to understand. In MATLAB, you can define your own functions or use built-in functions that are provided with the software.

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Answer:

Infinitely many

Step-by-step explanation:

2x+y=1

4x+2y=2

Divide both sides of the second equation by 2.

2x + y = 1

This is the same as the first equations. Both equations are the same equation. Since you have only one equation and two variables, there is an infinite number of solutions.

Answer: Infinitely many

The area of the shaded region is given as follows:

0.879.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the percentile, the area in this problem is given by one subtracted by the p-value of z = -1.17, which is of 0.121.

Hence:

1 - 0.121 = 0.879.

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Using the Leading Coefficient Test the end behavior of the given function f(x) = −x⁴ − 2x³ + 2x² − 5 is

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = −x⁴ − 2x³ + 2x² − 5

The end behavior is determined by the leading Coefficient =  −x⁴  and it is described as

x ⇒ ∞ f(x) ⇒ ∞

x ⇒ -∞ f(x) ⇒ -∞

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =\frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }\cdot 6^2 ~~}{2}\implies A=12\pi \implies A\approx 37.68[/tex]

Only the transitive relation is true for the provided relation for (x, y) R if x y defined on the set of positive integers.

Assuming (x, y), R

To determine whether or not a relation is transitive, symmetric, antisymmetric, reflexive, or a partial order:

If (x, x)R for all x R x x for all x R, which is false.

b. Symmetric: For all (x, y) R, if "x" and "y" are related, then "y" is also related to "x."

In this case, x y y x for all (x, y) R, which is false.

c. Antisymmetric: If "x" and "y" are related, then "x" equals "y" for all (x, y) R.

In this case, x y and y x x = y are false.

not in opposition.

c. Transitive: If "x" and "y" are related, then

For all values of x, y, and z R, 'x' is connected to 'z'.

For any x, y, and z R, x y, y z x z.

True.

Therefore, only the transitive relation for the given relation for (x, y) R if x y defined on the set of positive integers is true.

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Because both of its x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5 according to symmetry, the vertex's x-coordinates are 5/2.

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

Here,

The parabola is symmetric around its vertex. This means that the roots are the same horizontal distance away from the vertex. Furthermore, we can apply the midpoint formula on the given roots to find the x coordinate of the vertex.

Find the midpoint of 2 and 3 to get

(2+3)/2 = 5/2

The x-coordinates of its vertex is 5/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5.

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Answer: 128 square centimeters

Step-by-step explanation:

If the perimeter is 48 cm, then the sum of the lengths of any two adjacent sides must be 24 cm.

Since the length of one of these sides is given to be 8 cm, it follows the length of the corresponding adjacent side is 16 cm.

Thus, using the formula for the area of a rectangle, the area is 128 square centimeters.

tile will it take to cover the pedestal, including the bottom is 288 square feet

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Answer:

Part A is 100

Part B is 50

Part C is 25

all of it goes down by 15 so just keep subtracting

Step-by-step explanation:

I used common since and a sheet of paper

Answer:

x^2-2x-48

Step-by-step explanation:

FOIL

Firsts = x*x = x^2

outside = x*-6 = -6x

inside = 8*x = 8x

lasts = 8*-6 = -48

add all together x^2-6x+8x-48 = x^2-2x-48

Answer:

x² + 2x - 48

Step-by-step explanation:

( x + 8 ) ( x - 6 )

=  x ( x - 6 ) + 8 ( x - 6 )

= x*x - 6*x + 8*x + 8*( - 6 )

= x² - 6x + 8x  - 48

= x² + 2x - 48

Answer:

minimum value = 10

Step-by-step explanation:

the minimum value is at the left side of the whisker in the box plot, then

minimum value = 10

Answer:75%

Step-by-step explanation:

Answer:

36.96 calories

The area of the cylinder's base is 1÷4π.x² is the correct option

What is a cylinder?

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.

The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centres of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centres.

The cylinder seems to be a rectangle from the side perspective and a circle from the top view.

Since a cylinder has a curved form and no straight lines, it lacks vertices in contrast to cones, cubes, and cuboid shapes. Two of its faces are round.

According to the question volume of the cylinder is

1. πr^2h = πr^3

h=r=x/2

2.

The radius of cylinder is

= x/2

3.

The area of the cylinder's base is

= πr^2

= (π x^2)/4

4.

The height of the cylinder is =

radius= height =x/2

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Using the Central Limit Theorem, it is found that these conditions are required to avoid the high variability associated with small samples.

[tex]s=\sqrt{p(1-p)/n}[/tex]

[tex]p v=2*p(z < -0.531)=0.595[/tex]

1) Data given and notation

n=500 represent the random sample taken

X=380 represent the number of people with some characteristic

estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

3) Calculate the statistic  

[tex]z=\frac{0.76 - 0.77}{\sqrt{\frac{0.77(1-77)}{500} } =0.531}[/tex]

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha =0.05[/tex]The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]pv=2*p(z < -0.0531)=0.595[/tex]

If we compare the p value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.  

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Answer:

the football team sells 805,000 tickets each season

Step-by-step explanation:

average number of tickets sold per match=23,000

the average number of games played each session=35

the number of tickets sold on average each session = 23,000 x 35 which equals 805,000

so the average football club sells 805,000 tickets each season

a) The linear functions each cell phone provider are given as follows:

The graph with these functions is given by the image shown at the end of the answer.

b) The cheaper companies are given as follows:

The linear functions in this problem are defined in slope-intercept format as follows:

y = mx + b.

In which the coefficients and their meaning are given as follows:

Hence the cost functions for this problem are given as follows:

The functions intersect at x = 6.67, hence the cheaper plans are given as follows:

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Area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.

As given in the question,

Given values to find area under the standard normal curve = 0.97 to 1.26

From the table of area under the given standard normal curve

z - score of 0.97 is equal to 0.33398

z-score of 1.26 is equal to 0.39617

Area under given standard normal curve between z-scores 0.97 and 1.26

= P ( 0.97 < z < 1.26 )

= 0.39617 - 0.33398

= 0.06219

Therefore, the area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.

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Answer:

f(x)=x/2-4

-f(x)=a

a=x/2-4

x=a/2-4

a/2-4=x /×2

a-8=2x

a=8+2x -> f^-1(x)=8+2x