change from rectangular to cylindrical coordinates. (let r ≥ 0 and 0 ≤ θ ≤ 2π.) A) (-1,1,1) B) (-7,7√3,7)

There are 10 dimes and 50 nickels.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Susan has a collection of 60 nickels and dimes.

And, The number of nickels is five times the number of​ dimes.

Now,

Let number of dimes = x

Then, The number of nickels = 5x

Since, Susan has a collection of 60 nickels and dimes.

Hence, We get;

⇒ x + 5x = 60

⇒ 6x = 60

⇒ x = 10

Thus, The number of dimes = x

                                           = 10

Then, The number of nickels = 5x

                                             = 5 × 10

                                             = 50

Therefore, There are 10 dimes and 50 nickels.

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the answer is -20 -15 -10 -5 -0

Answer:

y2= -15, y3=-10, y4=-5

Step-by-step explanation:

so basically, the answers have to decrease/increase by the same amount. idrk what else to say but those should be right.

One tenth of a number, something multiply it by 1/10 and then simplify or this is one tenth of that is just divide by 10.

We probably know that the number above the fraction bar is called the numerator and the number below it is called the denominator. To calculate the fraction of a number, we must first convert the whole number to a fraction as well, then multiply by 1/10. Alternatively, finding 1/10 of a number is the same as dividing it by 10.

Let's go through some examples to understand the concept.

a) What is 1/10 of 20?

20 can be put over 1 , since anything divided by

1 is itself. So do that and multiply:

1/10 × 20/ 1 → 20/10 → 2

b) What is 1/10th of 34 ?

=> 34 can be put over 1 and then multiply by 1/10

=> 34×1/10 = 34/10 = 3.4

So as we can see, all we have to do is divide the number by 10 and we've found one tenth of it.

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The simplified form of the expression [tex]\frac{2}{\frac{3}{11}}[/tex] is [tex]\frac{22}{3}[/tex].

To simplify the expression [tex]\frac{2}{\frac{3}{11}}[/tex], you can start by performing the division in the parentheses first:

[tex]\frac{2}{\frac{3}{11}}[/tex] = [tex]\frac{2}{\frac{3}{11}}[/tex] × [tex]\frac{11}{11}[/tex]

= 2 × [tex]\frac{11}{3}[/tex]

Then, you can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor:

2 × [tex]\frac{11}{3}[/tex] = [tex]\frac{(2 * 11)}{(3 * 1)}[/tex]

= [tex]\frac{22}{3}[/tex]

So the simplified form of the expression [tex]\frac{2}{\frac{3}{11}}[/tex] is [tex]\frac{22}{3}[/tex].

Simplification is a process of making something simpler or easier to understand by reducing the amount of complexity or detail. This can be done by removing or combining elements, or by reorganizing the structure. Simplification can be used in problem-solving, decision-making, or other tasks to make it easier to understand, interpret, or use the information.

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The odds that the chosen cookies being chocolate chip cookies is 1/7

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We are given that

A cookie jar contains six chocolate chip cookies, four peanut butter cookies and five oatmeal cookies

Hence the total number of cookies are 15

Two cookies are selected from the jar

This can be done in 15c2 ways that is 105

Now we have six Choco chip cookies in the same jar

Number of ways in which we can select 2 cookies is 6c2

That is 15

Hence the odds are 15/105

That is 1/7.

The odds that the chosen cookies being chocolate chip cookies is 1/7.

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Therefore the probability that all person are chosen at random for security screening is P=0.0315 Thus, the search was random and passengers should not be suspicious for the search

The likelihood of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these situations, we state that there is a likelihood that the event will occur or not.

Here,

The probability that all person are chosen at random for security screening is

Where four businessmen from the middle east= [tex]C^{4} _{2}[/tex]

and remaining 16 are not searched =[tex]{C^{16} _{0}[/tex]

Thus, for selection of 2 people at random from 4 businessman

P =   [tex]\frac{C^{16} _{0} * C^{4} _{2}}{ C^{20} _{2}}[/tex]

P=1*6/190

P=6/190

P=0.0315

Therefore the probability that all person are chosen at random for security screening is P=0.0315 Thus, the search was random and passengers should not be suspicious for the search.

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The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

Twenty-Five Decreased By One-Fifth Of A Number Is Eighteen.

Let the number be 'x'. Then the equation is given as,

25 - (1/5)x = 18

Simplify the equation, then the value of the variable 'x' is calculated as,

25 - (1/5)x = 18

(1/5)x = 25 - 18

(1/5)x = 7

x = 7 (5)

x = 35

The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.

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Yes, by definition, every NP problem can be reduced to an NP-complete problem in polynomial time.

All NP-complete problems can be reduced to each other in polynomial time since an NP-complete problem is itself an NP problem.

An NP-complete problem lies in NP, the set of all decision problems whose solutions can be verified in polynomial time. Similarly, NP can be defined as a set of decision problems that can be solved in polynomial time by a non-deterministic Turing machine. A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) to p in polynomial time.

Not sure if all NP issues can be resolved quickly. This is called the P-NP problem. However, if every NP-complete problem can be solved quickly, the definition of an NP-complete problem states that every problem in NP must be rapidly reducible to every NP-complete problem (i.e., it can be solved in polynomial time abbreviated by ). For this reason, NP-complete problems in general are often said to be harder or harder than NP problems.

A decision problem C is NP-complete if:

1. C is in NP and every problem in NP is reducible to C in polynomial time.

2. We can show that C is in NP by showing that the candidate solutions for C can be verified in polynomial time.

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The f(4) using is found using newton's interpolating polynomials of order 4.

function y=CL10_Exercise(part)

%% Input

% part: string for part a,b,c,d

%

%% Output

% y value of the underlying function at x=4

%

%% Write your code here

X=[1,2,3,5,6];

Y=[15,8,5.5,30,52];

x=4;

y=1;

switch part

case 'a'

%% Newton interpolation (Order 4)

a=X;

b=Y;

%x=input('Enter x: ');

[m,n]=size(a);

fx=0;

for i=1:n

%_____________Calculating Dividing Difference_____________________

s=0;

for j=1:i

p=1;

for k=1:i %Denominator part product

if(k~=j)

p=p*(a(j)-a(k));

end

end

s=s+b(j)/p; %summation f(x)/product

end

%_________________________________________________________________

p=1;

for j=1:i-1 %coefficient part of f[...]

p=p.*(x-a(j));

end

fx=fx+s.*p; %Polynomial!

end

y=fx;

case 'b'

%% not-a-knot spline

case 'c'

%% clamped spline

case 'd'

%% Hermite spline

end

end

Hence, the f(4) using is found using newton's interpolating polynomials of order 4.

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How you write it is...

m x 10n

Answer:

should be option 2, but im sorry if it isnt.

Step-by-step explanation:

The equation of line in point-slope form is y + 7  = -1/2(x - 6).

What is an equation of a line?

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

Given points are (2,-5) and (6,-7).

The  point-slope form of a line is y - y₁ = m(x - x₁).

The slope of the line that passes through the points (2,-5) and (6,-7) is

(-7 - (-5))/(6 - 2) = -2/4 = -1/2

Putting m =  -1/2 and x₁ = 6 ,  y₁ = -7 in y - y₁ = m(x - x₁):

y - (-7) = -1/2(x - 6)

y + 7  = -1/2(x - 6)

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Using the laws of inequality, the inequality x-36>4x can be solved as x>-12.

In mathematics, the term "inequality" refers to a relationship between two expressions or values that is not equal to each other. The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are deemed to be equal. The symbols >,,, or indicate that the two expressions in an inequality are not necessarily equal.

Here,

x-36>4x

3x<-36

-3x>36

x>-12

The solution for the inequality x-36>4x is x>-12 using properties of inequality.

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The possible formula for polynomial is P(x)=x⁵+3x⁴-9x³+5x²

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given,

The polynomial of degree 5.

P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−5

Each root corresponds to a linear factor, so we can write

P(x)=x²(x-1)²(x+5)

=x²(x²+1-2x)(x+5)

=(x⁴+x²-2x³)(x+5)

=x⁵+x³-2x⁴+5x⁴+5x²-10x³

=x⁵+3x⁴-9x³+5x²

Hence, the possible formula for polynomial is P(x)=x⁵+3x⁴-9x³+5x²

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The conventional form of the polynomial is f(x)=x 28x+17. If polynomial function f has rational coefficients and a leading factor of 1, then it has the lowest degree.

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses quasi integer powers or only positive integer coefficients of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.

As conjugate pairs make up complex zeros, we can infer that 4-i4-i is also a zero from the fact that 4+i4+i is also a zero.

A polynomial function's factor x-axa is one of the factors if aa is its zero. Consequently, the polynomial function is

f(x)=a[x-(4+i)] [x-(4-i)]

f(x)=a[x−(4+i)]

[x−(4−i)]

Expand:\sf(x)=a[x^2-(4-i)

x-(4+i)x+(4+i)(4-i)]

F(x) = a [x 2 (4i)x(4+i)x+(4+i)(4i)]

f(x)=a[x^2-4x+ix-4x-ix+

(16-i^2)]

F(x) = a [x 2 4x+ix4x+ix+(16i 2)]

f(x)=a[x^2-8x +(16-(-1))]

f(x)=a[x 2 −8x+(16−(−1))]

f(x)=a(x^2-8x +17)

f(x)=a(x 2 −8x+17)

Considering that a=1a=1 is the leading coefficient, this means:

color="#c34632" f(x)="x2-8x +17"

f(x)=x 2 −8x+17

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Answer:

d ≥ −11

Step-by-step explanation:

Step 1: Add 5 to both sides.

−2d−5+5 ≤ 17+5

−2d ≤ 22

Step 2: Divide both sides by -2.

−2d/−2 ≤ 22/−2

d ≥ −11

Answer:

1 + 17 = 18

2 + 16 = 18

3 + 15 = 18

4 + 14 = 18

5 + 13 = 18

6 + 12 = 18

7 + 11  =  18

8 + 10 = 18

9 + 9 = 18

Step-by-step explanation:

Answer:

0+18=18

1+17=18

2+16=18

3+15=18

4+14=18

5+13=18

6+12=18

7+11=18

8+10=18

9+9=18

10+8=18

11+7=18

12+6=18

13+5=18

14+4=18

15+3=18

16+2=18

17+1=18

18+0=18

Answer:

-

—4<x<8

Step-by-step explanation:

Given that,

x2−4x−32

⇒x2−(8−4)x−32

⇒x2−8x+4x−32

⇒x(x−8)+4(x−8)

⇒(x−8)(x+4)

Hence, −4<x<8

Answer:

6[tex]\sqrt{30}[/tex]i

Step-by-step explanation:

120 = 2x2x2x3x5  I can pull out a set of 's

3x2 = 6

6[tex]\sqrt{2x3x5}[/tex]

6[tex]\sqrt{30}[/tex]

[tex]\sqrt{-1}[/tex] = i

Therefore, the expression's 48th component is the cost per scarf.

A mathematical expression is a sentence that has at least two variables or integers and one mathematical action. In mathematics, it is possible to multiply, divide, add, or remove. An expression's structure is (Mathematical Operator, Number or Variable, Expression).

Here,

In the following expression, 483 denotes the total number of scarves, and 48 is the cost per scarf. For each scarf order, customers are charged a $4.75 delivery fee:

The 48 denotes the price per scarf, as can be seen from the supplied.

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Answer:

Around 3000 BC

Answer:

It is difficult to pinpoint a specific year or time period in which math was "invented," as math is a fundamental aspect of human thought and has likely been present in some form since ancient times.

The study of mathematics has a long and rich history, dating back to ancient civilizations in Mesopotamia, Egypt, Greece, and India. These early societies developed mathematical concepts and techniques to aid in practical tasks such as measuring land, calculating the volume of objects, and tracking the movement of celestial bodies.

As human civilizations developed and advanced, so too did the study of mathematics. Over time, new mathematical concepts and techniques were developed and refined, leading to the development of more advanced branches of mathematics such as algebra, geometry, trigonometry, and calculus.

In summary, math has a long and complex history, and it is difficult to pinpoint a specific year or time period in which it was "invented." It has likely been present in some form since ancient times and has evolved and developed over the course of human history.

Step-by-step explanation:

SELF EXPLANATORY

Answer: 59.9 m

Step-by-step explanation:

Area of rectangle = Length times Width

We already know the length is 18m

So take 215.1 divided by 18= 11.95m

To find the perimeter of the Rectangle we use the formula

p= 2(18+ 11.95) = 59.9 m

So the perimeter is 59.9 m

Answer:

The day before, Mike had 34 apples. Today, he had 24 times as much as the apples that he had the day before. How many apples did he have today?

Step-by-step explanation:

1st, gather information: The day before, Mike had 34 apples, Today, he had 24 times as much as the apples that he had the day before

2nd, plan to solve: I will do 34 x 24.

3rd, Solve: 34 x 24= 816.

4th, is it resonable? : Yes. 816/34=24.

Answer:

The answer is 60

Step-by-step explanation:

160 × 3/8 = 480/8 = 60

Thus, 60 new houses have been sold this year.

Answer:

5.4* 10^-2

Step-by-step explanation:

The value of the exponential equation is A = 5.4 x 10⁻²

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the number be represented as n

The value of n = 0.054

On simplifying the equation , we get

A = 5.4 x 10⁻²

On further simplification , we get

A = 0.054

Hence , the exponential equation is A = 5.4 x 10⁻²

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Using PEDMAS to simplify the expression, the result is -830t² + 164t + 5798.4

To solve this problem, we have to simplify the expression. This is a process of breaking it down from a complex form to the least possible form. In doing this, we often apply mathematical operations such as multiplication, addition, subtraction etc.

In the expression 362.4 * 16 - 2t + 83t * (2 - 10t)

Let's apply PEDMAS here

362.4 * 16 = 5798.4

83t (2 - 10t) = 166t - 830t²

We can bring them together now;

5798.4 - 2t + 166t - 830t²

Collecting like terms

-830t² + 164t + 5798.4

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Therefore, the probability that the mean number of lightning strikes per square kilometer is less than 5 is P([tex]X^{'}[/tex]<5)=0.0016

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

Here,

mu =6

α=2.4

n=50

Σxi=250

Formula used:

z=[tex]\frac{x-u}{\alpha }[/tex]

Step 2: Calculation

[tex]x^{'}[/tex] = Σ[tex]\frac{xi}{n}[/tex] = 250/50 = 5

z = [tex]\frac{x^{'} - u_{x} }{\alpha x^{'} }[/tex] = [tex]\frac{x^{'} - u_{x} }{ \frac{\alpha }{\sqrt{n} } }[/tex] = [tex]\frac{5- 6}{ \frac{2.4}{\sqrt{50} } }[/tex] ≈ -2.95

P([tex]X^{'}[/tex]<5)=P(Z<-2.95)

=0.0016

or 0.16%

Therefore, the probability  probability that the mean number of lightning strikes per square kilometer is less than 5 is P([tex]X^{'}[/tex]<5)=0.0016

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In the regression line y = a+ bx+ e, a is the slope of the regression line.

The above statement is False.

The correct Statement is :

The linear regression line has an equation of the form Y =a + bX

where, Y is called the dependent variable or response.

X means independent or predictor or explanatory variable.

a is the y-intercept and b is the slope of the line.

Regression Line:

A regression line is a statistical tool that shows the correlation between two variables. Specifically, it is used when the variation of one (the dependent variable) depends on changes in the value of the other (the independent variable).

Simple linear regression has two cases:

The formula for the least squares regression line (LSRL) from Y to X is:

                           Y=a + bX + ɛ

where,

Y is the dependent variable.

a is the Y intersection.

b is the slope of the regression line.

X is the independent variable.

ɛ is the residual (error).

and

b = (N∑XY-(∑X)(∑Y) / (N∑X2– (∑X)2) ;

and

a = (∑Y – b ∑X) / N

where, N is the total number of observations.

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