Find the slope m of the tangent to the curve y = 5/√x at the point where x = a > 0.m = ?

A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.

In light of the conditions stated, come up with: [tex]$\frac{8 \frac{3}{4}}{2 \frac{1}{7}}$[/tex] To improper fractions, change the mixed numbers to: [tex]$\frac{\frac{35}{4}}{\frac{15}{7}}$[/tex] Multiply the reciprocal of a fraction to get its division: [tex]$\frac{35}{4} \times \frac{7}{15}$[/tex]

Mark this common element as a no-go: Multiplying [tex]$\frac{7}{4} \times \frac{7}{3}$[/tex] Mark the common element as absent: Multiplying [tex]$\frac{7 \times 7}{4 \times 3}$[/tex] . Put the following in one fraction : [tex]$\frac{49}{12}$[/tex] . The product or quotient should be

calculated.Find the biggest number that is greater than [tex]$\frac{49}{12}$[/tex] and less than or equal to it . A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.Otherwise, you or a device will need to count 127 turns (the irreducible repeat, independent of thread pitch), after which the half nut must be closed.

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If Sₙ denotes the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive , then the smallest positive integer n for which Sₙ is an integer is 63 .

The "Sₙ" be the sum of reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive ;

We Let [tex]K= \sum_{i=1} ^{9} \frac{1}{i}[/tex] ,

On further examination , we get that , [tex]S_{1} =K+1[/tex] ;

Since each digit "n" appears once and the number 1 appears for an extra time.

Now , we write  S₂ .

So ,Each term of K will appear 10 times in the units place and 10 times in the tens place ,

So , we get [tex]S_{2} = (n10^{n-1})K+1[/tex] ; and there are total "n" places ;

The denominator of K is written as [tex]D=2^{3} .3^{2} .5.7[/tex] .

For Sₙ to be an integer, [tex]n10^{n-1}[/tex] must be divisible by D , we must select "n" to be divisible by [tex]3^{2} .7[/tex]   .

And since need to find the smallest integer "n" , So , the n is [tex]3^{2} .7 = 63[/tex] .

Therefore , For Sₙ to be an integer , the smallest positive integer n is 63 .

The given question is incomplete , the complete question is

Let Sₙ be the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive. find the smallest positive integer n for which Sₙ is an integer .

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Answer:

5:4

Step-by-step explanation:

girls = 4

boys = 5

ratio = boys:girls = 5:4

HOPE THIS HELPED

Answer:

add up variables and divide by 2

Answer: [tex]303^{\circ}[/tex]

Step-by-step explanation:

The point [tex]P[/tex] lies in the fourth quadrant, so the angle is given by [tex]360^{\circ}-\alpha[/tex], where [tex]\alpha[/tex] is the reference angle.

The reference angle is given by [tex]\arctan \left(\frac{\frac{\sqrt{7}}{4}}{\frac{\sqrt{3}}{4}} \right)=\arctan \left(\sqrt{\frac{7}{3}} \right)[/tex].

This means [tex]\theta=360^{\circ}-\arctan \left(\sqrt{\frac{7}{3}}} \right) \approx 303^{\circ}[/tex].

Answer:

8x + 2y = 10  ==>  y = -4x + 5

12x - 3y = -25​  ==>  y = 4x + 25/3

Step-by-step explanation:

8x + 2y = 10  ==> solve for y

2y = 10 - 8x  ==> subtract 8x on both sides

(2y = 10 - 8x) / 2 ==> divide the equation by 2 to make 2y into y

y = 5 - 4x  ==> simplify

y = -4x + 5  ==> put the equation in y=mx+b form

12x - 3y = -25​  ==> solve for y

12x = -25 + 3y  ==> make y positive by adding 3y on both sides

12x + 25 = 3y ==> add 25 on both sides to isolate y

(3y = 12x + 25) / 3  ==> divide the equation by 3 to make 3y into y

y = 4x + 25/3 ==> simplify

The ordered set pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),

is not a function. Because one x value corresponds to two different y values.

Given a set of ordered pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),

Function is special relations that pair each member of set A (domain) with exactly one member of set B (codomain).

Discuss the options provided.

a. yes, because there are two x values that are the same that is 3. Then the statement is false, the value of x cannot be the same.

b yes, because every x value corresponds to exactly one y-value. Then the statement is false.

c. no, because two of the y-values are the same. Then the statement is false.

d. no, because one xvalue corresponds to two different y-values. Then the statement is true.

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Algebra test because the correlation is higher.

What does a statistical correlation mean?

A statistical metric known as correlation, which is given as a number, describes the strength and direction of a relationship between two or more variables.

                         Although there may be a correlation between two variables, this does not necessarily imply that the change in one variable is what led to the change in the values of the other variable.

Why correlation, you ask?

In common conversation, we use the word correlation to describe situations where two or more items seem to be connected.

                       In the field of analytics, correlations are certain numbers that are computed to express how closely related variables are to one another.

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The solution to the simultaneous equation is x = -1/2 and y = √71 / 2

What is a Linear Expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, t² is a variable raised to the second power, but t is a variable raised to the first power.

x² + y² = 18 ----- 1

x + 2 = - 3x ---- 2

From equation 2

x + 2 = - 3x

x + 3x = -2

4x = -2

x = -2/4

x = -1/2

Substitute x in equation 1

(-1/2)² + y² = 18

1/4 + y² = 18

y² = 18 - 1/4

y² = (72 - 1)/4

y² = 71/4

y = √71 / 2

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Step-by-step explanation:

let addicts be x and Nike be x+6

so ,

x+x+6=12

or,2x=6

or x=-3

now x+6=3+6=9

therefore he had 9 Nike and 3 Adidas

Determine appropriate formula to model scenarios.

Sometimes, different formulas can generate similar results. The key is to choose the formula that is most appropriate for the scenario, and it's also important to consider the complexity of the formula and its interpretability.

Based on the problem or question, the available data, and the literature review, determine the appropriate mathematical model to use. The model should be able to capture the key features of the problem or question and provide an accurate representation of the data.

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A circle chart, often known as a pie chart, is a means to summarize a set of nominal data or a visual depiction of the many values of a particular variable (e.g. percentage distribution).

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about center at every angle. Every pair of vertices in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric the about center at every angle.

Here,

The pie chart is divided into sectors and segments, and each sector and segment corresponds to a specific amount of the overall (percentage).

The data is a representation of 360°. The pie is always valued at 100% overall.

A pie chart is useful for organising and displaying data by percentage of the total.

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The exact value of cos  is cos([tex]\frac{\pi }{12}[/tex])  = ([tex]\sqrt{2}[/tex] + [tex]\sqrt{6}[/tex]) /4

given that

Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.

Trigonometry has been used historically in fields like geodesy, surveying, celestial mechanics, and navigation.

Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

now , we need to find the value of cos

[tex]\pi[/tex]/12 can be written as [tex]\pi[/tex]/3 and [tex]\pi[/tex]/4

using cos(-) we need to find

cos(A - B) = cos(A)cos(B)+sin(A)sin(B)

cos([tex]\frac{\pi }{3}[/tex] - [tex]\frac{\pi }{4}[/tex]) = cos([tex]\frac{\pi }{3}[/tex])cos([tex]\frac{\pi }{4}[/tex]) + sin([tex]\frac{\pi }{3}[/tex])sin([tex]\frac{\pi }{4}[/tex])

cos([tex]\frac{\pi }{12}[/tex]) = (1/2)(1/[tex]\sqrt{2}[/tex]) +([tex]\sqrt{3}[/tex]/2)(1/[tex]\sqrt{2}[/tex])

          = (1/2)([tex]\sqrt{2}[/tex]/2) + ([tex]\sqrt{3}[/tex]/2)([tex]\sqrt{2}[/tex]/2)

          = ([tex]\sqrt{2}[/tex]/4) + ([tex]\sqrt{6}[/tex]/4)

cos([tex]\frac{\pi }{12}[/tex])  = ([tex]\sqrt{2}[/tex] + [tex]\sqrt{6}[/tex]) /4

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The slope intercept form of the equation is B) y=2x-6.

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here According to the table using two points [tex](x_1,y_1) =(0,-6)[/tex] and [tex](x_2,y_2)=(3,0)[/tex] .

Now using slope formula m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> m = [tex]\frac{0-(-6)}{3-0}[/tex]

=> m = [tex]\frac{6}{3} = 2[/tex]

Now using equation formula then

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-(-6)=2(x-0)

=> y+6 = 2x

=> y = 2x-6

Hence the slope intercept form of the equation is B) y=2x-6.

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The value of x in the simplest radical form is 3.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: Let the triangle be ΔABC

The triangle ABC is a right-angled triangle and the angles inside the triangles are 45°, 45° and 90°

tan θ = x / 3

Now , θ = 45°

So, tan 45° = x / 3

The value of x is 3.

Hence, the value of x is 3.

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The result of.tge evaluation of the given expression as required is; 11 / 4.

It follows from the task content that the value of the expression given be determined upon evaluation.

Since the given expression is; 5 - 3/2 to the second power

5 - (3/2)²

= 5 - 3²/2²

= 5 - 9/4

= 20 / 4 - 9 /4

On this note, the resulting expression is; ( 20 - 9 ) / 4 = 11/4.

Ultimately, the result of the expression evaluation as required to be determined is; 11 / 4.

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Answer:

2 1/5

Step-by-step explanation:

Answer:

Let x be the number of sweets that Ryan has.

Since the ratio of the number of sweets Mary has to the number Ryan has is 3:2, we can say that Mary has 3/2*x sweets.

We know that if Mary gave 5 sweets to Ryan they would have the same number of sweets, so we can write the following equation:

3/2*x -5 = x

By solving this equation, we can find that x = 10. So, Ryan has 10 sweets

Therefore, Mary has 3/2*10 = 15 sweets.

Altogether, Mary and Ryan have 15+10 = 25 sweets.

Answer: 25

Step-by-step explanation:

3x - 5 = 2x, so

x = 5.

And 5x = 5*5 = 25

Three minutes equal 180 beats on the double number line. three minutes of 270 beats 2:180=90 , 3:270=90

In music, a beat is a pulse that occurs repeatedly. Simple meters are those in which the beat first breaks into two, and subsequently into four. There are two beat groups in double meters, three beat groups in triple meters, and four beat groups in quadruple meters.

For double, triple, and quadruple meters, there are several conducting patterns. One group of beats equals one measure (duple, triple, or quadruple). Bar lines divide the measures. Simple meters' time signatures specify two things: the beat unit, or note value that represents the beat, and the number of beats in each measure (the top number). Notes are graphically grouped by beat and connected by a beam.

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Answer:

53

Step-by-step explanation:

This implied that they were unable to rule themselves and establish their own rules. The king demanded that they pay enormous taxes.

They believed they were contributing taxes to an unrepresentative administration. They were also upset that the colonists had to allow the British soldiers to eat and sleep in their residences.

The colonists of America formed a protest in response to the actions of Parliament. A network of covert organizations called the Sons of Liberty was established throughout the colonies with the intention of scaring the tax collectors for Parliament. migrated to America because they wanted political liberty. They desired both economic opportunity and religious freedom. Self-government and individual liberties are valued in the United States.

Because the colonists opposed the British,

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No, the conditions for inference have not been met. The two samples must be independent, meaning that the individuals in the college sample should not also be in the high school sample. Without independent samples, it is not possible to construct a 95% confidence interval for the true mean difference.

1. Collect data from the two samples of seniors in high school and college.

2. Calculate the mean difference in the number of hours of sleep for the two samples.

3. Calculate the standard deviation of the differences in hours of sleep for the two samples.

4. Calculate the standard error of the mean difference.

5. Calculate the critical value for a 95% confidence interval.

6. Calculate the lower and upper bounds of the confidence interval by

adding and subtracting the critical value from the mean difference.

7. Interpret the confidence interval to determine the true mean difference in the number of hours of sleep for seniors in high school and colleg

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i) Joint density distribution function  is given as

f(x,y) =  1/2Πσ1σ2  exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]

ii) E(aX + bY + c) = aµx + bµy + c iii) E(X^2) = σx^2 + µx^2

We have been given that, X ~ N(µx , σx^2) and Y~ N(µy , σy^2)

and X and Y are independent that is

                                ρ = 0

Note that the joint density function of two normal distribution is known as bivariate normal distribution which is given as

   (X , Y) ~ BVN(µ1 , µ2 , σ1^2 , σ2^2 , ρ)

And whose joint density function is          

f(x,y)  =   1/(2Πσ1σ2√(1-ρ^2))  exp[(-1)/(2(1-ρ^2)) {((x-µ1)^2)/(σ1^2)-2ρ (x-µ1)(y-µ2)/σ1σ2+ ((y-µ2))/(σ2^2)}]

 Where ρ = correlation coefficient of (x,y)

i) Joint density function of given X and Y which follows

(X , Y) ~ BVN(µx , µy , σx^2 , σy^2 , 0) is given as

f(x,y) =  1/2Πσ1σ2  exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]

ii) E(aX + bY + c) = aE(X) + bE(Y) + c

                       = aµx + bµy + c

iii) E(X^2) = V(X) + [E(X)]^2      {V(X) = E(X^2) - [E(X)]^2}

           = σx^2 + µx^2

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Answer:

$27,400.

Step-by-step explanation:

We know that the salesman makes $25,000 annually plus 6% commission on his total sales.

We also know that he sold $40,000 worth of trampolines this year.

So we can find out his commission by multiplying the value of sales with 6% commission rate.

Commission = 0.06 * $40,000 = $2400

To find out his total earnings we need to add his annual salary with commission earned.

Total earnings = $25,000 + $2400 = $27,400

So the salesman's total earnings for this year is $27,400.

In graph theory, a 2-factor is a subgraph of a given graph that includes every vertex of the original graph and has the property that every vertex has even degree (i.e. degree is a multiple of 2).

The term "2-factor" is used because it is a factor of the original graph that is made up of edges and every vertex has degree 2.

A 2-factor can also be defined as a set of cycles that cover all vertices of the graph. In other words, it is a collection of cycles such that every vertex belongs to exactly one cycle. A 2-factor can also be thought of as a cycle cover of a graph.

A graph that has a 2-factor is called a 2-factorizable graph. Not all graphs are 2-factorizable, for example a graph with an odd number of vertices can't have a 2-factor.

2-factors have many applications in various fields such as scheduling, coding theory, and computer science. They are also used to study the connectivity and robustness of graphs.

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Answer:

8.25

Step-by-step explanation:

trapezoid area =

(a+b)/2 times h =

if its 1.5

(4+7)/2 times 1.5 =

11/2 times 1.5 =

5.5 times 1.5 =

8.25

if its 15

5.5 times 15 =

82.5

its probably 1.5

wikipedia

Answer:

yes

Step-by-step explanation:

The absolute value is only greater than or equal to zero.

The ratio in simplest form in the three cases is 5 : 6, 36 : 29 and 1 : 5.

30 treadmills to 36 elliptical machines can be simplified to 5 treadmills to 6 elliptical machines. To simplify, you can divide both numbers by their greatest common factor, which in this case is 6.

30/6 = 5 and 36/6 = 6

So 30 : 36 = 5 : 6

180 red marbles to 145 blue marbles can be simplified to 12 red marbles to 11 blue marbles. To simplify, you can divide both numbers by their greatest common factor, which in this case is 5.

180/5 = 36 and 145/5 = 29

180 : 145 = 36 : 29

In the word "flashlight", the ratio of vowels to total letters is 2:8. The word "flashlight" has 2 vowels (a,i) and 10 total letters. To simplify divide by 2.

2 : 10 = 1 : 5

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The probability that all three Escher prints will be placed consecutively is 3/5 or 0.6

The probability that all three pieces by Escher will be placed consecutively when hanging the 10 pieces of art in a random order is the probability that the 3 Escher prints will be in a row among the other 7 pieces.

There are 10!/(3! × 7!) = 120 ways to order the 10 pieces of art, and 3! = 6 ways to order the 3 Escher prints among themselves.

So the total number of ways to order the art such that the Escher prints are consecutive is 120 × 6 = 720.

Now to find the probability that all three Escher prints will be placed consecutively, we divide the number of ways that this can happen (720) by the total number of ways the art can be arranged (120) to get 720/120 = 6/10 = 3/5.

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The total number of different collections of pets your roommate can take is 10 + 10 = 20.

In this scenario, your roommate has two options for which pets to take with him: either the dog or the cat. If he takes the dog, he can take any two of the remaining five pets (fish, turtle, rock, pony). There are 5 choose 2 = 10 ways for him to do this. If he takes the cat, he can take any two of the remaining five pets (fish, turtle, rock, pony, dog). There are 5 choose 2 = 10 ways for him to do this.

Therefore, the total number of different collections of pets your roommate can take is 10 + 10 = 20.

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