sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants she packed. The total number of pairs of pants and shirts was 16

Answer:

Read carefully below

Step-by-step explanation:

We can use spherical coordinates to represent the points on the sphere. These coordinates are typically denoted as (r, θ, φ), where r is the radius of the sphere, θ is the polar angle, and φ is the azimuthal angle.

In order to find a parametric representation of the part of the sphere that lies inside the given cones, we can use the following approach:

First, we need to find the intersection of the sphere and the cone. This is the set of points that satisfy the equations of both the sphere and the cone.

Then, we can use spherical coordinates to represent these points on the sphere.

Finally, we can use these spherical coordinates as parameters in a parametric equation of the form x = x(r, θ, φ), y = y(r, θ, φ), z = z(r, θ, φ) to represent the points on the part of the sphere that lies inside the cone.

Let's use this approach to find a parametric representation of the part of the sphere that lies inside the cone z = 3(x^2 + y^2) in the first case.

To find the intersection of the sphere and the cone, we need to solve the following system of equations:

x^2 + y^2 + z^2 = 16 (equation of the sphere)

z = 3(x^2 + y^2) (equation of the cone)

Substituting the second equation into the first equation, we get:

x^2 + y^2 + 9(x^4 + y^4) = 16

This equation represents an ellipse in the xy-plane. We can use the parametric equations of an ellipse to represent the points on this ellipse:

x = a * cos(t)

y = b * sin(t)

where a and b are the semi-major and semi-minor axes of the ellipse, respectively, and t is a parameter that varies from 0 to 2π.

We can now use spherical coordinates to represent the points on the part of the sphere that lies inside the cone. We can let r be the radius of the sphere (r = 4), θ be the polar angle (0 ≤ θ ≤ π), and φ be the azimuthal angle (0 ≤ φ ≤ 2π).

The parametric equations of the sphere in spherical coordinates are:

x = r * sin(θ) * cos(φ)

y = r * sin(θ) * sin(φ)

z = r * cos(θ)

Substituting the equations for x and y from the ellipse into the equations for x and y from the sphere, we get:

x = 4 * sin(θ) * cos(φ) = a * cos(t)

y = 4 * sin(θ) * sin(φ) = b * sin(t)

z = 4 * cos(θ) = 3(x^2 + y^2) = 3(a^2 * cos^2(t) + b^2 * sin^2(t))

We can solve for a and b in terms of r and θ:

a = 4 * sin(θ)

b = 4 * sin(θ)

Therefore, the parametric equations for the part of the sphere that lies inside the cone z

x=19

According to question,

3x-12=2x+7    

Subtracting 7 from both sides

3x-12-7=2x+7-7

⇒3x-19=2x

Subtracting 3x from both sides

3x-19-3x=2x-3x

⇒-19=-x

⇒x=19

∴The value of x is 19.

For further information regarding linear equation in one variable

https://brainly.in/question/39414007

The complete question is Find the value of x in the equation 3x-12=2x+7 when 7 and 3x is subtracted from both sides.

Answer: To find the mean of the number of students who left school early, we must add all of the numbers together and then divide the sum by the number of days.

48 + 62 + 75 + 43 + 32 + 52 + 70 + 63 + 81 + 40 + 38 + 67 = 671

The mean of the number of students who left school early is 56.75 (671 / 12).

This mean represents the average number of students who left school early each day over the 12-day period. It tells us that on average, about 56.75 students left school early each day.  

Step-by-step explanation:  2. The mean of the group of teachers' ages is currently (25+32+33+35+41+43+45+48+52+55+60+62)/12=45.5. If another teacher with an age of 45 is added to the data, the mean will be (25+32+33+35+41+43+45+45+48+52+55+60+62)/13=44.5. The mean will be slightly lower, as the additional value of 45 is being added to the sum, but the number of values being averaged is also increasing by 1.

The following composition of two functions ( f o g ) ( 0 )  = 1 and ( g o f ) ( 1 ) = 1 .

Given :

The functions f and g are defined by the following tables:

Tables :

x       -2       -1      0       1

f ( x )   1        2     1        0

x          1       -3      0       -4

g ( x )   -2      0      1         5

( f o g ) ( 0 ) = ( f ( g ( 0 ) )

from the table g ( 0 ) = 1

= ( f ( 0 ) )

=  1

( g o f ) ( 1 ) = ( g ( f ( 1 ) )

= ( g ( 0 ) )

= 1

Learn more about the function here:

https://brainly.com/question/9046022

#SPJ4

Answer:

Your answer is A.

Step-by-step explanation:

The expression that represents the total number of customers held by all three companies is 5x + 10.

A mathematical expression is a combination of numbers, variables, and mathematical operands (multiplication, division, subtraction, and addition).

What differentiates a mathematical expression from an equation is the equal symbol because a mathematical expression does not have it.

In simple terms, a mathematical expression is like a phrase in the English language without the complete form of a sentence.

The number of customers held by Company B = x

The number of customers held by Company A = 3x

The number of customers held by Company C = x + 10

The total number of customer for all three companies = x + 3x + x + 10

= 5x + 10

Thus, mathematically, we can conclude that the three companies have 5x + 10 customers.

Learn more about mathematical expressions at https://brainly.com/question/1859113

#SPJ1

The expression that represents the total number of customers held by all three companies is; 5X + 10

An expression consists of one or more numbers or variables along with one more operation.

X + 1 is an example of an expression.

"X" is the variable, "+" is the operation and 1 is a number. Think of "X" as any number that is unknown.

Representing the variables;

X, Y and Z represents number of customers

Let Company A = Y

Let Company B = X

Let Company C = Z

But,

Company A = 3X

Company C = 10 + X

Therefore;

Total number of customers = Y + X +Z

Substituting;

Total number of customers = 3X + X + 10 + X

Total number of customers = 5X + 10

Learn more about expressions here:https://brainly.com/question/1859113

#SPJ1

The solution of the logarithmic equation:

ln(x - 7) = 3

Is x = 27.09

Here we have the following logarithmic function:

ln(x - 7) = 3

And we want to solve this for x.

Remember that the logarithmic function is the inverse of the exponential function, so now we can use the exponential function in both sides so we get:

exp( ln(x - 7) ) = exp(3)

x - 7 = exp(3)

Now we can add 7 in both sides so we isolate x, we will get:

x = exp(3) + 7

x = 27.09

That is the solution of the logarithmic equation.

Learn more about logarithmic equations by reading:

https://brainly.com/question/28041634

#SPJ1

The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]

The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].

The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]

As per the details share in the above question are as follow,

Poisson process with a rate λ per hour

While customer buys a book with probability p

First we have to find the distribution of the time until the first sale of a book.

Second  to find the probability that no books are sold during a particular hour.

Third to find the expected number of customers who buy a book during a particular hour.

Giving the duration till a book sells its first copy

Consider,

Following are some instances of waiting times,

[tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]

The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]

Now, to calculate the likelihood that no books will be sold at a specific time.

[tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex]

The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].

Consider the Poisson distribution to determine the anticipated number of book purchases during a specific hour.

[tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]

The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex].

For more such question on Poisson process.

https://brainly.com/question/9123296

#SPJ4

The number of hours taken by man to paint the whole garage alone is 31.5 hours.

Given that, one man can paint a garage in 28 hours.

The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.

Let x be number of hours taken by second man paint the whole garage.

Work done by first man be 1/28

So, work completed by first man =1/28 ×12

= 12/28

= 3/7

Remaining work is 1-3/7 =4/7

1/x ×18 =4/7

⇒ 18/x=4/7

⇒ 4x=126

⇒ x=126/4

⇒ x=31.5 hours

Therefore, the number of hours taken by man to paint the whole garage alone is 31.5 hours.

To learn more about the time and work visit:

https://brainly.com/question/3854047.

#SPJ1

The French character who is considered the father of sociology has been Auguste Comte.

This character was a Frenchman, he himself was a philosopher and is recognized mainly by:

Due to the above, Auguste Comte is considered the initiator of the social sciences, which are currently very important sciences for the study of various events.

¡Hope this helped!

Therefore the solution to the given matrix problem is  

a)det(B) = det(A) = 3  ,det(B) = 3*det(A) = 9  and c)det(B) = -det(A) = -3

A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity.

Here,

The following will be demonstrated using determinant properties:

A)Det(B) = 3

B) Det(B) = 9

C) det(B) = -3

Assuming A is a 4x4 matrix, we can see that:

det(A) = 3.

a) In this case, we are adding one row to another row by performing a transformation to the data in A. These operations don't alter the matrix's determinant, therefore in this instance:

det(B) = 3 = det(A)

b) If K is used to multiply a row of A to produce B, then:

B = det(K*det) (A).

In this situation, we have:

det(A) = 3*det(B) = 9

c) If we switch two rows around once (this is an odd permutation), the determinant's sign changes:

det(B) = -det(A) = -3

To know more about matrix, visit

https://brainly.com/question/29418562

#SPJ4

The complete question is "If the determinant of a 4 by 4 matrix A is det(A) = 6, and the matrix D is obtained from A by adding 9 times the third row to the first, then det(D) is equal to?"

NP finished. Only two jobs share resources with the reduction provided in section A.

to put in the same order or rank. : to bring into a common action, movement, or condition : harmonize. coordinate schedules. She'll be coordinating the relief effort.

The overall issue is NP-complete. From Independent Set, this is a decrease. We substitute jobs for the graph's vertex points. If there is an edge connecting vertices v and w, we establish a resource called r v,w that v and w can share.

If k = 2, we are simply checking to see if there are any jobs that are resource-exclusive. By checking every pair of jobs, we can accomplish this using sheer force.

NP finished. Only two jobs share resources with the reduction provided in section A.

To know more about coordinate visit:-

https://brainly.com/question/27749090

#SPJ4

The perimeter of the state of Wyoming, given the rectangle ABCD and the vertices, is 1, 282 miles

The perimeter is the distance around the shape so to find the perimeter of the shape, you need to find the distance between the sides of the rectangle and then add them up.

The distance between vertices can be found by the formula :

= ((x2 – x1)² + (y2 – y1)²)

The distance between AB is therefore 3.65 miles.

The distance between BC is 2.76 miles

The distance between CD is 3.65 miles.

The distance between AD is 2.76 miles

The perimeter of Wyoming is therefore :

= ( 3.65 x 2) + ( 2.76 x 2 )

= 12.82 miles x 100

= 1, 282 miles

Find out more on perimeter at https://brainly.com/question/21249260

#SPJ1

The general solutions for tanx−3cotx=0 is [tex]\frac{\pi}{3} \text { and } \frac{2 \pi}{3}[/tex]

[tex]\begin{aligned}& \tan x-\frac{3}{\tan x}=0 \\& \tan ^2 x-3=0 \text { (condition } \tan \times \text { not zero) } \\& \tan ^2 x=3 \rightarrow \tan x=\pm \sqrt{3}\end{aligned}[/tex][tex]a. $\tan x=\sqrt{3} \rightarrow x=\frac{\pi}{3}$b. $\tan x=-\sqrt{3} \rightarrow x=\frac{2 \pi}{3}$Extended answers:$$\begin{aligned}& x=\frac{\pi}{3}+k \pi \\& x=\left(2 \frac{\pi}{3}\right)+k \pi\end{aligned}[/tex]

What is the general equation for tan's solution?

Tan + Tan Equals Tan

n Z (i.e., n = 0, 1, 2, 3, etc.), so n = n + n. Therefore, n Z (i.e., n = 0, 1, 2, 3, etc.) is the value for which the general solution of tan = tan is given as = n +. Because cot = 1/tan and cot = 1/tan, the expression cot = cot is identical to tan = tant

To learn more about tan's solution visit:

https://brainly.com/question/24268805?

#SPJ4

Answer:

a = -3

Step-by-step explanation:

The explanation is in the image

Answer:

$120

Step-by-step explanation:

1) rewrite the mixed numbers into improper fractions. We do this by multiplying the denominator by the whole number, and then adding the numerator. The numerator stays the same:

[tex]3 \frac{3}{4} = \frac{(4 \times 3) + 3}{4} = \frac{15}{4} [/tex]

[tex]2 \ \frac{2}{7} = \frac{(7 \times 2) + 2}{7} = \frac{16}{7} [/tex]

So the length of the cloth = 15/4 meters

width of the cloth = 16/7 meters

2) Calculate the area of the cloth:

area = length × width

[tex]area \: = \: \frac{15}{4} \times \frac{16}{7} = \frac{240}{28} = \frac{60}{7} (simplest form)[/tex]

area = 60/7 m²

3) The cloth costs $14 per square meter, so the total cost of the cloth is:

the area of the cloth × cost of cloth per square meter

[tex]cost \: = \: \frac{60}{7} \times 14 = \frac{840}{7} = 120[/tex]

the cost is $120

Answer:

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

[tex]x=-2[/tex]

[tex]x=\dfrac{-1 + \sqrt{3}\:i}{2}[/tex]

[tex]x=\dfrac{-1- \sqrt{3}\:i}{2}[/tex]

Step-by-step explanation:

Given polynomial:

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

Rational Root Theorem

If P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

Possible p-values

Factors of the constant term:  ±1, ±2

Possible q-values

Factors of the leading coefficient:  ±1

Therefore, all the possible values of p/q:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 2}{\pm 1}=\pm1,\pm2[/tex]

Substitute each possible rational root into the function:

[tex]x=-1 \implies p(-1) =(-1)^3+3(-1)^2+3(-1)+2=1[/tex]

[tex]x=1 \implies p(1) =(1)^3+3(1)^2+3(1)+2=9[/tex]

[tex]x=-2 \implies p(-2) =(-2)^3+3(-2)^2+3(-2)+2=0[/tex]

[tex]x=2 \implies p(2) =(2)^3+3(2)^2+3(2)+2=28[/tex]

Therefore, x = -2 is a root of the polynomial since f(-2) = 0.

Divide the polynomial by the root using synthetic division:

[tex]\begin{array}{c|crrr}-2 & 1 & 3 & 3 & 2\\\cline{1-1} & \downarrow &-2&-2&-2\\ \cline{2-5} & 1&1&1&0\end{array}[/tex]

The bottom row (except the last number) gives the coefficients of the quotient.  Therefore, the quotient is:

[tex]x^2+x+1[/tex]

So the fully factored form of p(x) is:

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

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore, the solutions to the quadratic factor are:

[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3\cdot -1}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3} \sqrt{-1}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\:i}{2}[/tex]

The 3 solutions of p(x) are:

The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]

An item or particle that is projected in a gravitational field, such as from the surface of the Earth, and moves along a curved route while solely being affected by gravity is said to be in projectile motion.

According to the given information

Given, [tex]$\quad b_1=\left[\begin{array}{c}2 \\ 2 \\ -2\end{array}\right], \quad b_2=\left[\begin{array}{l}2 \\ 0 \\ 2\end{array}\right], \quad w=\left[\begin{array}{c}-2 \\ 1 \\ -1\end{array}\right]$[/tex]

We know,

[tex]Proj_{v}(w)[/tex] = [tex]Proj_{b1}(w) + Proj_{b2}[/tex]

[tex]& =\left(\frac{w \cdot b_1}{b_1 \cdot b_1}\right) b_1+\left(\frac{w \cdot b_2}{b_2 \cdot b_2}\right) b_2[/tex]

[tex]w \cdot b_1 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{c}2 \\2 \\-2\end{array}\right][/tex][tex]=-4+2+2=0 \\[/tex]

[tex]w \cdot b_2 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]-4+0-2=-6 \\[/tex]

[tex]b_2 \cdot b_2 &[/tex]  =[tex]\left[\begin{array}{c}2 \\0 \\2\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]4+0+4=8[/tex]

Therefore

[tex]Proj_{v}(w)[/tex] = [tex]\left(\frac{0}{b_1 \cdot b_1}\right) b_1+\left(\frac{-6}{8}\right)\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]

[tex]& =0+\frac{-3}{4}\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]

[tex]& =\left[\begin{array}{c}\frac{-3}{2} \\0 \\-3 \\2\end{array}\right] \\[/tex]

[tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]

The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]

To know more about Projectile Motion

https://brainly.com/question/11049671

#SPJ4

The slope of the zipline in the given diagram is; -1/3

The slope of a line is defined as the change in y values divided by change in corresponding x-values.

The formula to find slope here will be;

Slope = (y₂ - y₁)/(x₂ - x₁)

Let us pick two points along line BD namely points C and D.

Coordinate of point C is (7, 2)

Coordinate of point D is; (10, 1)

Thus;

Slope = (1 - 2)/(10 - 7)

slope = -1/3

Let us pick point B and point D now.

Coordinate of point B is; (1, 4)

Thus slope of BD = (4 - 1)/(1 - 10)

= -3/9 = -1/3

The slopes are equal and as such that is the slope of the zip line

Read more about slope of line at; https://brainly.com/question/16949303

#SPJ1

Answer:

The correct answer is the 3rd option

Answer: (i) 10% (ii) 60% (iii) 40%

Step-by-step explanation:

(i)  Newar language = 65%

  Gurung language = 45%

Total covers = 110 but to sum it up to base that is 100% then 110-100 is 10.

so, 10% of people speak both the language.

(ii) people who speak only Newari only would be 60% as 5% among them speak Gurung language.

(iii) people who speak only Gurung only would be 40% as 5% among them speak Newari language.

Answer:

Step-by-step explanation:

So, they want the equation of the 4 colored lines, not a coordinate.

a --> x=-4

b --> x=4

c --> y=4

d --> y=-2

bc they are horizontal and vertical lines so only one value is staying the same, depending on whether it's vertical or horizontal.

Check the picture below.

let's notice that the triangle is an equilateral triangle, meaning all its sides are congruent and likewise, all its angles are also congruent.

all can be the answer I guess

Answer: 806.25

Step-by-step explanation: First, we need to find how much the sales tax is worth in dollars. Recall the formula:

Worth = Wole number x part percent / 100

Now, plug in the numbers:

Worth = 750 x 7.5 / 100

So, 750 x 7.5 = 5625

So, 5625 / 10 = 56.25

But remember, $56.25 is the amount of the SALES TAX. To find the total, we need to add 56.25 to 750. So,

750 + 56.25 = 806.25

Therefore, $806.25 is the TOTAL AMOUNT she needs to pay.

Ratio is the relation between two amounts that shows the number of times one value contains within the other.

What is Ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of vegetables contains eight tomato and six carrots, the tomato-to-carrot ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of carrots to tomato is 6:8 (or 3:4), while the proportion of tomato to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive.

Ratio is the relation between two amounts that shows the number of times one value contains within the other.

To learn more about Ratio from the given link

brainly.com/question/2328454

#SPJ4

There are $85.50 will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees.

What is convertibility of rupee?

Convertibility is the simplicity with which a national currency can be changed into gold or another asset through international exchanges. The rupee is a partially convertible currency in India; while smaller amounts can be exchanged at market rates, larger ones require permission.

Given:

Your friend just returned to the United States from their trip to Nepal and wants to exchange their 9,576 Nepalese rupees for U.S. dollars.

Since,

1 U.S dollar = 112 Nepalese rupees

Suppose x be the U.S dollars for 9576 Nepalese rupees.

So,

x = 9576/112 = 85.5

Hence, there are $85.50 will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees.

To know more about convertibility of rupees, click on the link

https://brainly.com/question/16627643

#SPJ1

The probability that a randomly selected bike is green given that the bike has road bike tires is 0.66

Given :

Nellie is shopping for a new bicycle. She is most interested in color and type of tires.

Probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event .

From the table given :

Total number of 6 road bikes = 4

Total road bikes = 2 + 4 = 6

Probability = 4 / 6

= 2 / 3

= 0.66

Hence the  probability that a randomly selected bike is green given that the bike has road bike tires is 0.66 .

Learn more about the probability here:

https://brainly.com/question/14210034

#SPJ4

The design that involves repeated measurement of a variable before and after some event will be matched group factorial design. Hence, option C is correct.

In this kind of experimental design, the research's participants are divided into groups, and key factors are matched to each group. The variables that are used to match the respondents must have an impact on the original study conclusion (the dependent variable).

The benefit of using matched group factorial design is,

Fewer people are needed for this kind of investigation, which could also produce more accurate results and results that are based on more information.

To know more about Factorial design:

https://brainly.com/question/29668399

#SPJ1