in science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. if x represents a student's score, write an equation that represents the minimum and maximum scores. |x − 87|

The value of the expression [tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex] is [tex]cot(A)+\frac{A}{sin^{2}A}[/tex].

The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are also required to determine derivatives, continuity, and integrals.

Mathematical expressions consist of at least two variables or numbers, at least one arithmetic operation, and a statement. It's possible to divide, multiply, add, or subtract with this mathematical operation.

Consider the expression,

[tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex]

Adding and subtracting Acot(A) and A common in the numerator,

[tex]\lim_{x \to A} \frac{xcot(A)-Acot(A)+Acot(A)-Acot(x)}{x-A}[/tex]

Taking cot(A) common,

[tex]\lim_{x \to A} \frac{cot(A)(x-A)+A(cot(A)-cot(x))}{x-A}[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A(cot(A)-cot(x)}{x-A}[/tex]

Now, using the identity:

cot x = cos x / sin x

[tex]\lim_{x \to A} cot(A) + \frac{A(\frac{cos(A)}{sin(A)} -\frac{cos(x)}{sin(x)}) }{x-A}[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{cos(A)sin(x)-cos(x)sin(A) }{sin(A)sin(x)})[/tex]

By using the identity, sin ( a - b ) = sin(a)cos(b) - sin(b)cos(a)

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=\lim_{x \to A} cot(A) +\lim_{x \to A} \frac{sin(x-A)}{(x-A)}\frac{A}{sin^{2}A}[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=cot(A)+1 \cdot \frac{A}{sin^{2}A}[/tex]

Learn more about limits here:

https://brainly.com/question/27825021

#SPJ9

The value of function f(x) = 3x² + 8x-10 at f(2) is  18 .

We have given an function f(x) = 3x² + 8x-10

Putting x = 2 into this function , we get

 f(2) = 3(2)²+ 8x -10

        =3(4) + 8(2) -10

        = 12 + 16 -10

        = 18

Learn more about evaluation of function here :

https://brainly.com/question/1719822

#SPJ9

The value of the longest side of the triangle is 31 feet

The perimeter of the triangle is the sum of all its sides.

The formula for perimeter where a, b and c are the three sides of the triangle is given as:

Perimeter = a + b + c

It is given that the sides are consecutive integers and the perimeter is 90 feet, therefore

Let sides be x, x+1 and x+2

Perimeter = x + x+1 + x+2

90 = x + x+1 + x+2

90 = 3 + 3x

87 = 3x

x = 29 feet

The value of the longest side will be x+2, which will be 29+2 = 31 feet

Learn more about triangles:

https://brainly.com/question/2773823

#SPJ1

The probability would be zero that both the pirate and the captain hit each other's ships.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Captain Ashley has probability 1/2 of hitting the pirate ship.

Dread pirate Umaima has a 1/3 probability of attacking the Captain's ship if it hasn't already.

The captain must miss if the pirate hits, and the requirement that both hits are not satisfied. The requirement that both hits cannot be satisfied if the pirate misses.

Therefore, the probability would be zero that both the pirate and the Captain hit each other's ships.

Learn more about probability here:

brainly.com/question/11234923

#SPJ1

The circle graph/pie chart is made for the given bar graph.

A pie chart is a type of graph that displays data in a circular graph. The slices of pie represent the relative amount of information and are a type of pictorial data representation.

Now, as the data given in the bar graph.

The basketball is played the number of students is 4.

That is 40% of the total.

The football is played the number of students is 3.

That is 30% of the total.

The baseball is played the number of students is 2.

That is 20% of the total.

The soccer is played the number of students is 1.

That is 10% of the total.

Thus, the pi cart for the all data percentage is formed.

To know more about the pie chart, here

https://brainly.com/question/26851221

#SPJ9

Answer:

6 people took x amount of candy and 6 other people took 2 times that same amount how much candy did they all take... (I think that works)

Answer:

40billion for the tip question

Answer:

congruent

Step-by-step explanation:

Answer:

Step-by-step explanation:

Make the following operations:

and

The required value is:

Answer:

[tex]\dfrac{a+b}{a-b}=-\sqrt{2}[/tex]

Step-by-step explanation:

Given:

[tex]a^2+b^2=6ab[/tex]

[tex]0 < a < b[/tex]

Add 2ab to both sides of the given equation:

[tex]\implies a^2+b^2+2ab=6ab+2ab[/tex]

[tex]\implies a^2+2ab+b^2=8ab[/tex]

Factor the left side:

[tex]\implies (a+b)^2=8ab[/tex]

Subtract 2ab from both sides of the given equation:

[tex]\implies a^2+b^2-2ab=6ab-2ab[/tex]

[tex]\implies a^2-2ab+b^2=4ab[/tex]

Factor the left side:

[tex]\implies (a-b)^2=4ab[/tex]

Therefore:

[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=\dfrac{8ab}{4ab}[/tex]

[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=2[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:[/tex]

[tex]\implies \left(\dfrac{a+b}{a-b}\right)^2=2[/tex]

Square root both sides:

[tex]\implies \sqrt{\left(\dfrac{a+b}{a-b}\right)^2}=\sqrt{2}[/tex]

[tex]\implies \dfrac{a+b}{a-b}=\pm\sqrt{2}[/tex]

As 0 < a < b then:

Therefore:

[tex]\implies \dfrac{a+b}{a-b}=\dfrac{+}{-}=-[/tex]

So:

[tex]\implies \dfrac{a+b}{a-b}=-\sqrt{2}[/tex]

The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 )

critical value at 0.01 significance level with 17 df = 2.898

x = mean;

99% confidence interval for μ is

(x - t * S) /√n  <  μ <( x + t * S) /√n;

(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;

14.74<  μ< 48.89;

99% CI is ( 14.74, 48.89 ) ;

To learn more about this, visit: https://brainly.com/question/6350797

#SPJ4

Answer:

Step-by-step explanation:

9 is the answer

It is already in the simplest form.

The spam of the sets of vector of all linear combination is 0,

The span of the set {(2, 5, 3), (1, 1, 1)} is the subspace of R 3 consisting of all linear combinations of the vectors v 1 = (2, 5, 3) and,

v 2 = (1, 1, 1).

this defines a plane in R 3.

Since a normal vector to this plane in n = v 1 x v 2 = (2, 1, −3),

the equation of this plane has the form 2 x + y − 3 z = d for some constant d. the plane must contain the origin—it's a subspace— d must be 0.

No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line

to know more about linear equation;

visit : brainly.com/question/28449784:

#spj4

The locations of the vertices of the dilated figures are (48,16), (32,40), and (8,24).

This problem can be solved by using the concept of scale factor. Scale factor is useful in finding proportional measurements.

Proportion implies having the same ratio.

Scale factor can be defined as the ratio of the measurement of the model to the measurement of the actual form in the simplest form. In other words, the ratio of any two corresponding lengths in two similar geometric figures is called a scale factor.

If the scale factor is more than 1, that is, scale factor > 1,

then it is an enlargement,

If the scale factor is less than 1, that is, scale factor < 1,

then it is a reduction.

We can obtain the answer by multiplying the given coordinates, first by a scale factor of 4 and then by a scale factor of 2/3.

(18,6) => (18x4, 6x4) => (72,24) => (72x2/3, 24x2/3) => (48,16)

(12,15) => (12x4, 15x4) => (48,60) => (48x2/3, 60x2/3) => (32,40)

(3,9) => (3x4, 9x4) => (12,36) => (12x2/3, 36x2/3) => (8,24)

Therefore, using the concept of scale factor, we get the locations of the vertices of the dilated figures as (48,16), (32,40), and (8,24).

Learn more about Dilation of Triangles here:

https://brainly.com/question/13176891?referrer=searchResults

#SPJ9

The coordinates of A and B are-7 and 9. The coordinates of C and D are -4 and 12. AB and CD are not congruent

Congruent refers to objects that are precisely similar in size and shape. The forms stay equal no matter how they are rotated, flipped, or turned. For instance, create two circles with the same radius, cut them out, and stack them.

We'll see that they'll be placed entirely on top of one another and will superimpose one another. This demonstrates that the two circles are similar. Given that they have an equal radius and can be positioned exactly over one another, the circles below are considered to be congruent. "≅" is the sign used to represent the congruence of figures. Since circle A and circle B are similar, we may say the following: Circle B ≅ Circle A.

Lets assume AB and CD are congruent

Then according to Pythagoras theorem

Hypotenuse of AB of right-angled triangle AOB is equal to Hypotenuse of CD of right-angled triangle COD

Hypotenuse AB = Hypotenuse CD

Hypotenuse AB

a² + b² = c²

(-7)² + 9² = c²

49 + 81 = c²

130 = c²

Hypotenuse CD

a² + b² = c²

(-4)² + 12² = c²

16 + 144 = c²

160 = c²

Here, 130 ≠ 160

So, The coordinates of A and B are-7 and 9. The coordinates of C and D are -4 and 12. AB and CD are not congruent

Learn more about congruent

https://brainly.com/question/3999145

#SPJ9

32% of the same people spend their time listening.

The total number of mentioned  people will be 100% or 1. Now, in the total people, the remaining ones who are not stated in the question, must be the listeners. Thus, calculating the remaining percentage of people, we will get the percentage of listeners in same people.

So, number of people who spend time speaking = 26%

Number of people who spend time speaking = [tex]\frac{26}{100}[/tex]

Number of people who spend time speaking = 0.26

Number of people who spend time writing =  23%

Number of people who spend time writing = [tex]\frac{23}{100}[/tex]

Number of people who spend time writing = 0.23

Number of people who spend time reading =  19%

Number of people who spend time reading = [tex]\frac{19}{100}[/tex]

Number of people who spend time reading = 0.19

Total number of people involved in activities other than listening = 0.26 + 0.23 + 0.19

Total number of people involved in activities other than listening = 0.68

People who spend time listening = 1 - 0.68

People who spend time listening = 0.32

Percentage of people who spend time listening = 0.32 × 100

Percentage of people who spend time listening = 32%

Hence, 32% of the same people spend their time listening.

Learn more about percentage calculation -

https://brainly.com/question/24877689

#SPJ4

The mean waste recycled per person per day for the population of new- york is 1.9 < u < 2.3 .

Given that,

The mean waste recycled per person per day = 2.12

Standard Deviation = 0.250

c = 0.9 , So  [tex]\alpha[/tex] =1-c =0.10

n = 9<30 so we use t critical value.

From t table we get the critical value = 1.859

90% confidence interval for the mean u

So,

X = 2.1 , s = 0.25 , n= 9

2.1 - 1.86 (0.25/[tex]\sqrt{9}[/tex]) < u < 2.1 =1.86 (0.25/[tex]\sqrt{9}[/tex])

1.954  < u < 2.225

1.9 < u < 2.3 .

Therefore,

From 1.9 < u < 2.3 we get that the population is approximately normal.

To know more about " Confidence Interval"

Refer this link:

https://brainly.com/question/9386257

#SPJ4

The three ways that the problem that Ernie has written can  be solved are:

This is the term that is sued to refer to the topic in mathematics that has to do with the ways that numbers can be broken down into smaller units. The number that is being divided is often done with the aid of a divisor.

In this question, the number that is to be divided is 525 and the number that is to do the division is 1500. This can be written as 525 / 1500 for us to see clearly.

When written, we can write this out in the different ways that have been stated above. Hence we would have The three ways that the problem that Ernie has written can  be solved are:

The solution is 0.35

Read more on division here;

https://brainly.com/question/24662212

#SPJ1

Answer:

Step-by-step explanation: Hello! My name is Madison and I will being helping you how to go about doing these problems! First things first.

1) 50,000 divided by 12 would be 4166.6 repeating.

2)

Answer: b=7

Step-by-step explanation:

6b+7+7b-8=90

6b+7b+7-8=90

13b-1=90

13b=91

b=7

Answer: 10

Step-by-step explanation:

Distance formula = (x2-x1)^2 + (y2-y1)^2

In this circumstance, we have (0,0) and (6,8) as our two points.

(6-0)^2 + (8-0)^2

(6^2) + (8^2)

36 + 64 = 100

Square root the 100.

SQRT of 100 is 10 (perfect square) so your answer is, again, 10.

I hope I managed to help.

TX IS THE OVERALL MAGNITUDE OF THE LINE

TX IS THE OVERALL MAGNITUDE OF THE LINE WHICH IS MADE BY TW+WX

MATHEMATICALLY

TX=TW+WX

[tex](5x - 9) = (3x + 5) + 10 \\ 5x - 9 = 3x + 5 + 10 \\ 5x - 3x = 5 + 10 + 9 \\ 2x =24 \\ \frac{2x}{2} = \frac{24}{2} \\ x = 12[/tex]

HOPE THIS HELPS!!!

PLEASE DO NOT HATE MATHS I'M HERE FOR YOU TO MAKE SURE YOU ENJOY IT.

Answer:

Step-by-step explanation:

The length and width of the rectangular garden is estimated as-

A rectangle's perimeter is the total length and distance of its border across all sides. The perimeter of a rectangular box is a linear measurement that is expressed in meters, feet, cm, or yards. Let us first examine the two primary characteristics of a rectangle.

The perimeter of the rectangle is given as-

Perimeter = 2(length + width)

perimeter= 256

Let the width of the rectangle be x.

Length is 8 feet longer than width, Thus,

length = x+8

Substitute the values in the formula of perimeter;

256 = 2( x+ 8+ x)

256 = 2( 2x + 8)

128= 2x + 8

120= 2x

x=60

Thus, width = 60 ft.

Length = 60 + 8 = 68 ft.

Therefore, the length and width of the rectangular garden is estimated.

To know more about the area of the rectangle, here

https://brainly.com/question/2607596

#SPJ4

The complete question is -

A rectangular garden is fenced on all sides with 256 feet of fencing. The garden is 8feet longer than it is wide. Find the length and width of the garden.

Spherical geometry would be use in the real world practical applications to navigation. Professions that would need to make it use is astronomy.

These professions make use of spherical geometry for making Spherical conic, Spherical distance, Spherical polyhedron, Half-side formula.

Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2 dimensional surface and other terms like "ball" or "solid sphere" are used for the surface together with its 3-dimensional interior.

An important geometry related to that of the sphere is that of the real projective plane; it is obtained by identifying antipodal points (pairs of opposite points) on the sphere.

Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is non-orientable, or one-sided, and unlike the sphere it cannot be drawn as a surface in 3-dimensional space without intersecting itself.

Spherical geometry would be use in the real world practical applications to navigation. Professions that would need to make it use is astronomy.

These professions make use of spherical geometry for making Spherical conic, Spherical distance, Spherical polyhedron, Half-side formula.

To learn more about spherical geometry :

https://brainly.com/question/9980308

#SPJ1

Answer:

118 .........................

Answer:

-25+27k

Step-by-step explanation:

-5(1-5k)-4(2k+5)

= -5+35k-8k-20

=-5-20+35k-8k

= -25+27k

Answer:

Denominator, opposite of the numerator

Step-by-step explanation:

When divided by negative, it's the inverse (+/-) and changes signs.

2 parts to a fraction

Numerator

---------------

Denominator

Hope this helps! :)

The values of x will be 2 and -1.

Given that:-

[tex]14x+17=2(x+3)^2-5[/tex]

We have to find the value of x.

As it is a quadratic equation, there will be two values of x.

Opening the bracket and solving the equation further, we get,

[tex]14x+17=2(x^2+9+6x) -5\\14x+17 = 2x^2 +18+12x-5\\2x^2-2x-4 = 0\\2(x^2-x-2) =0\\x^2-x-2 = 0[/tex]

Using middle-term split theorem to solve the quadratic equation, we get,

[tex]x^2-x-2 = 0\\x^2+x-2x-2=0\\[/tex]

x(x + 1) - 2(x + 1) = 0

(x + 1)(x - 2) = 0

Hence, either x + 1 = 0 or x - 2 = 0 or both of them are 0.

x + 1 = 0

x = -1

and,

x - 2 = 0

x = 2

Hence, the values of x are 2 and -1.

To learn more about quadratic equation, here:-

https://brainly.com/question/17177510

#SPJ1