Calculate r(-3) Please

Answer:

k - 2n = x

Step-by-step explanation:

4^n = 2 ^ 2n

2^k/2^2n = 2^(k-2n) = 2^x

k - 2n = x

Thanks

Answer:

x = k - 2n

Step-by-step explanation:

The main exponent properties

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex]         ........ (1)

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] ........ (2)

[tex](a^{m} )^{n}[/tex] = [tex]a^{m*n}[/tex] = [tex]a^{mn}[/tex]   ........ (3)

~~~~~~~~~~~~~~~~~~

[tex]\frac{2^{k} }{4^{n} }[/tex] = [tex]2^{x}[/tex]

Let apply (3) and (2) exponent properties

L.H. = [tex]\frac{2^{k} }{(2^2 )^{n} }[/tex] = [tex]\frac{2^{k} }{2^{2n} }[/tex] = [tex]2^{k-2n}[/tex]

[tex]2^{k-2n}[/tex] = [tex]2^{x}[/tex]  ⇒  x = k - 2n

Answer: The cosine of angle C is -0.0168.

Step-by-step explanation: To find the cosine of the angle opposite the side of length 2.92 meters, you can use the cosine law which states that:

c^2 = a^2 + b^2 - 2ab * cos(C)

where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides, and C is the angle opposite side c.

So in this case,

c = 8.82 m

a = 2.92 m

b = 7.67 m

then we can substitute the values into the equation and solve for cos(C):

(8.82)^2 = (2.92)^2 + (7.67)^2 - 2(2.92)(7.67) * cos(C)

cos(C) = (a^2 + b^2 - c^2) / (-2ab)

cos(C) = (2.92^2 + 7.67^2 - 8.82^2) / (-22.927.67)

cos(C) = -0.0168

Answer:

$1.44

Step-by-step explanation:

9kg costs $12.96

1kg costs ($12.96*1kg)÷9kg

=$1.44

The provided statement indicates that the differential equation's solution will be y = c₁ + c₂ e⁻ˣ - 1/2 cos x

Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variable x and y are related because y is an unidentified function of x. The component of y is also on the equation's left-hand side.

The analytical solution is, given that.

⇒ y'' + y = sin x

Now,

The system of equations as follows:

The difference between these two is,

⇒ y'' + y = sin x

Find its auxiliary equation as;

⇒ m² + m = 0

⇒ m (m + 1) = 0

⇒ m = 0 or m = - 1

Therefore, the auxiliary equation is c1 e0 + c2 ex.

                                     = c₁ + c₂ e⁻ˣ

And, Particular integral = 1/(D² + D) (sin x)

                                  = 1/2D (sin x)

                                  = 1/2 (- cos x)

                                  = - 1/2 cos x

Consequently, the differential equation's solution will be;

⇒ y = A.E + P.I

⇒ y = c1 + c2 e x - cos x / 2

As a result, the differential equation's solution is;

⇒ y = c1 + c2 e x - cos x / 2

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The complete question is-

Solve the differential equation by variation of parameters.

y'' + y = sin x

Answer: Keep it in the calculation

Step-by-step explanation:

The function c(x)  models the number of cookies sold each day by a bakery during a 10-day period between (c) days 02 and 03 did the number of cookies sold by the bakery increase.

Cox Proportional hazards Model:

Sir David Cox observed that if the proportional hazards assumption holds (or, is assumed to hold) then it is possible to estimate the effect parameter (s), denoted β₁  below, without any consideration of the full hazard function. This approach to survival data is called application of the Cox proportional hazards model, sometimes abbreviated to Cox model or to proportional hazards model. However, Cox also noted that biological interpretation of the proportional hazards assumption can be quite tricky.

Let Xi = ([tex]X_i1[/tex] , … , [tex]X_in[/tex]) be the realized values of the covariates for subject i. The hazard function for the Cox proportional hazards model has the form:

λ (t I [tex]X_i[/tex]) = λ₀(t) exp( β₁[tex]X_i1[/tex] +...... + βₙ[tex]X_in[/tex])

             = λ₀ (t) exp( [tex]X_i . \beta[/tex])

This expression gives the hazard function at time t for subject i with covariate vector (explanatory variables) Xi. Note : that between subjects, the baseline hazard is identical (has no dependency on i). The only difference between subjects' hazards comes from the baseline scaling factor exp [tex](X_i . \beta)[/tex].

⁡

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The volume of the pentagonal right pyramid with base area 30 square metres and height 5 metre is 50 m³.

Therefore the answer is 50 m³.

To find the volume of a pentagonal pyramid, we can use the formula:

V = (Bh)/3

where V is the volume, B is the area of the base and h is the height.

Area of the base is given, B = 30 m². From figure it is evident that the height of the pentagonal right pyramid is 5m. Therefore the volume of the figure is

V = 30 × 5/ 3

V = 50 m³

--The question is incomplete, answering to the question below--

"This pentagonal right pyramid has a base area of 30 m². What is the volume of the figure?"

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126 number of ways we can arrange the men, women in order to committee with 2 women and 2 men ,the combination is explained below as

We can use the combination formula to find  out the number of ways to choose 2 women and 2 men from a group of 4 women and 5 men.

as we know the  formula for combination as :

C(n ,k) = n! / (k!(n-k)!)

where n is the total number of people, k is the number of people we want to choose, and ! denotes factorial to find the number of combinations  (i.e. the product of all integers up to that number, e.g. 4! = 432*1 = 24).

In this case,  to choose the number of individuals as = 4 + 5 = 9 and k = 2 + 2 = 4. So, the number of ways to choose the committee is:

C(9,4) = 9! / (4!(9-4)!) = 126 ways

Hence the number of ways to choose committee is 126 ways.

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The slope of the curve at a point (x,y) is given as 3y. This means that the equation of the curve is in the form of y = mx + b, where m is the slope of the curve and b is the y-intercept.

Since the curve passes through the point (4,2), we can use this point to find the value of b:

y = mx + b

2 = 3(4) + b

b = -10

So the curve's equation is: y = 3x - 10

You can confirm this by plugging in the point (4,2) into the equation.

2 = 3(4) - 10

2 = 12 - 10

2 = 2

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Big boxes have 1/4 of 20 gigabytes of ram.

Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have

⇒ (1/4) x 20

⇒ 20 / 4

⇒ 5 gigabytes

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

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Answer:

We can start solving this problem by finding the two numbers that bound the range of integers we're looking for.

First, we can approximate $\sqrt{5}$ to the nearest integer by finding the square root of 5. We know that 2^2 = 4 and 3^2 = 9, so 2 < $\sqrt{5}$ < 3. Therefore, $\sqrt{5}$ is a little bit more than 2 and a little bit less than 3.

Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.

Step-by-step explanation:

Similarly, we can approximate $\sqrt{50}$ to the nearest integer by finding the square root of 50. We know that 7^2 = 49 and 8^2 = 64, so 7 < $\sqrt{50}$ < 8. Therefore, $\sqrt{50}$ is a little bit more than 7 and a little bit less than 8.

Now we know that the range of integers we are looking for is between 2 and 7, inclusive. There are 7-2+1 = 6 integers between 2 and 7: 2, 3, 4, 5, 6, 7.

Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.

The statement 2 is true i.e. He  is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be root multiplicities or complex.

Understanding the fundamental theorem of algebra, the number of roots of a polynomial equation must be equal to the degree of the equation. While been given any polynomial in factored form, we must expand the parentheses to find the highest-degree term.

For the equation  provided, simplified form could be x⁵ + 2x² = 0, and as looking at this polynomial and graphing it, it is evident that the total roots or solutions is equal to the highest exponent of the term x which is 5. Hence, Josh makes an incorrect statement.

The multiplicity of a root is the number of occurrences of the said root in the entire complete factorization of the polynomial, as by the means of the fundamental theorem of algebra. The root multiplicities are thus the repeated roots as involved in the full factorization process of a single equation of a polynomial.

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The correct question is:

Josh graphs a system of equations to determine the roots of the polynomial equation x⁵ = -2x²  . From the graph, he determines that there are two solutions to the equation. Which statement is true?

Step-by-step explanation:

(9-12)×5+13-2

=(-3)×5+13-2, (frist bracket )

=-15+13-2

=-4

Answer:

(9-12)x5+13-2= -4

Step-by-step explanation:

1. Solve the equation in parenthesis. 9-12 is -3. If you use a number line and add 9, then subtract twelve, you'll be three behind zero!

2. Then multiply -3 by five which is -15. -15+13 is -2, (since the thirteen is positive, it cancels out thirteen negative ones, and leaves us with two negative ones)

3. -2 -2=-4 (Negative two, subtracted by positive two, is negative four) subtracting a positive number, is the same as adding its opposite. Example. 8-5=3 (as we all know). And 8+-5=3. Numbers that have the same absolute value are opposites. AKA Numbers that are the same distance away from zero. -5 and 5 are both 5 spaces from zero!

The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.

What is the empirical rule?

If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.

It is given that the heights of a large population of ostriches are normally distributed. The percentage of these heights is within 3 standard deviations of the mean.

As we know from the empirical rule:

It is the rule of 68-95-99.7.

From the data given in the question: The height of a large population of ostriches is normally distributed.

X ~ (u, б²)

Normal distribution.

P{u - 3б < X < u + 3б}

From the distribution table:

P{u - 3б < X < u + 3б} = 99.7%

Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.

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The general form of a linear Equation in two variables is ax + by + c = 0.

32-y=1

0.x+y+32 = 0

Hence Proved.

Answer:

19

Step-by-step explanation:

Substitute x = -4/5 and solve for b.

5x² + bx + 12 = 0

5(-4/5)² + b(-4/5) + 12 = 0

16/5 − 4/5 b + 12 = 0

16 − 4b + 60 = 0

4b = 76

b = 19

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rounded answers In Your calculations to find missing measures is given below.

Given: a = 8.72, b = 11.1, c = 11.7

Using the Law of Cosines, we can calculate angle A:

A = arccos((b2 + c2 - a2)/2bc)
A = arccos((11.12 + 11.72 - 8.722)/(2*11.1*11.7))
A = arccos(2.61/265.57)
A = arccos(0.00984)
A = 89.8°

Using the Law of Sines, we can calculate angle B:


Using the Law of Cosines, we can calculate side c:

c2 = a2 + b2 - 2abcos(C)
c2 = 8.722 + 11.12

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A 1-factor graph is a graph that can be decomposed into one or more 1-factors. In other words, a 1-factor graph is a graph that can be partitioned into disjoint perfect matchings.

In graph theory, a 1-factor is a subgraph of a graph that forms a perfect matching, or 1-factorization. A perfect matching is a set of edges in a graph such that each vertex is incident to exactly one edge in the set. A 1-factorization of a graph is a collection of perfect matchings such that every vertex is included in exactly one perfect matching.

The study of 1-factors and 1-factorizations is an important area of graph theory because of its connections to other areas of mathematics such as algebra, combinatorics, and statistical physics. It has various applications including coding theory, scheduling, and transportation networks.

1-factor graph theory is the study of graphs that can be decomposed into 1-factors and the properties of such graphs. This field of study helps to understand the conditions under which a graph can be decomposed into 1-factors and the properties of such graphs.

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Answer:

3 cm

Step-by-step explanation:

The formula of a cylinder is given by:

[tex]\pi r^{2} h[/tex]

where r is the radius and h is the height of the cylinder.

Given information from the question:

Volume of cylinder = [tex]90cm^{3}[/tex]

Radius of cylinder = 3cm

We can derive an equation to find the height:

[tex]90=\pi 3^{2} h\\9\pi h=90\\h = \frac{90}{9\pi } \\h = 3.18cm[/tex]

Given the height is 3.18cm, we will choose the closest answer which is 3 cm.

The function that includes the data-set {(2,4), (6,6) (12,9)} is given as follows:

D. y = x/2 + 3.

The points of the data-set follow the format given as follows:

(x,y).

Hence the meaning of each point is given as follows:

Then the correct option is given by option D, that is:

y = x/2 + 3.

As we obtain the numeric values of y for the input x as follows:

Which are the three points that compose the data-set.

The options are given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

[tex] \: \: \: \: \: \: \: \: \: \huge \color{green}{ \fbox \colorbox{black}{ \fbox{ \green {Answer} \: }}}[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + 2 \cos(x) + 1} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + \cos(x) + \cos(x) + 1} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos {}^{} (x) ( \cos(x) + 1)+ 1(\cos(x) + 1} )= 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ ( \cos(x) + 1)(\cos(x) + 1} )= 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{2} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos(x) {}^{} }= - 1[/tex]

[tex]\longrightarrow \sf \color{teal}{ x{}^{} }= \cos {}^{ - 1}( - 1)[/tex]

[tex]\longrightarrow \sf \color{teal}{ x = (2n + 1) \pi \: \: \: \: rad}[/tex]

where, [tex]{ n \in \{whole \:\; number\}} [/tex]

Principle value -

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \cos {}^{ - 1} ( - 1) [/tex]

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2n + 1) \pi \: \: \: \: rad \: [/tex]

put n = 0

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2(0) + 1) \pi \: \: \: \: rad \: [/tex]

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (0 + 1) \pi \: \: \: \: rad \: [/tex]

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \pi \: \: \: \: rad \: = 180 \degree[/tex]

On solving the provided question, we can say that equation of cost of the roller blades is $ 89.66

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Let the total cost = A

initial cost = $ 129.50

he discount percentage = 40 %

So , the equation will be

= 129.50 - ( 40/100 ) x 129.50

= 129.50 - 51.8

= $ 77.7

sales tax percentage = 15 %

So , the equation will be

= 77.7 + ( 15/100 ) x 77.7

 = 77.7 + 11.655

= $ 89.655

final cost is A = $ 89.66

final cost of the roller blades is $ 89.66

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Therefore ,2.113 is the deemed appropriate of the greatest square that could be inscribed with in area between the square and the triangle.

A triangle is considered a polygon since it has four vertices or segments. It is a basic geometric form. Triangle ABC refers to a triangle the with ends A, B, and C. In Euclidean geometry, a singular plane plus square are produced when the sides are not collinear. A triangle is a polygon if it has three parts and three corners. The points where the three sides of the triangle meet are known as its corners. Three triangle angles add up to 180 degrees.

Here,

The midpoint of foot FE, G, is where we start by measuring the side length of the equilateral triangle.

Given that DE=GB and G is the midpoint, let GE equal x.

As a result, DGGB=x3 using fundamental trigonometry.

DB=2x3 follows.

We may then construct the equation 2x3=102 because DB is the orthogonal of ABCD and has length 102. Thus, the triangle's side length is

2x=(10√2)/√3.

Now, observe the diagonal AC. It is composed of the triangle's side length and the little square's diagonal multiplied by two. Let the little square's side length be y:

Let the little square's side length be y:

AC=y√2 + [(10√2)/√3]+y√2=10√2.

How to find y?

=>y√2+y√2 + (10√2√3)/3=10√2

=>y√2+y√2 + (10√6)/3=10√2

=> [3y√2+3y√2 + (10√6)] /3=10√2

=>6y√2+10√6=30√2

=>6y√2 = 30√2-10√6

=>y√2 = (30√2-10√6)/6

=>y = (30√2-10√6)/6√2

=>y = (60-20√3)/12

=>y= 5(3−√3)3  or 2.113

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The cost of credit, in dollars, for this loan is 299.6107 dollars.

Let's recall the total cost of the computer with tax C. Then,

C = 1999.99 + 0.07 × 1999.99 = 1999.99 + 139.9993 = 2139.9893.

Since the loan allows you to pay for the computer in 12 equal payments of $203.30, the total cost of the loan is 12 × 203.30 = 2439.60.

The cost of credit is then the difference between the total cost of the computer with tax and the total cost of the loan: 2439.60 - 2139.9893 = 299.6107.

So the cost of credit is 299.6103 dollars.

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Answer:

80

Step-by-step explanation:

96-16

Answer: C. [tex]2.8[/tex]

Step-by-step explanation:

Using the distance formula, [tex]\sqrt{(-1-1)^2 +(-1-1)^2} \approx 2.8[/tex].

On solving the provided question we cans ay that the upper bound for the integral is 1/(n+1).

In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.

The maximum value of the integrand on the interval [0, 1] is:

f(x) = 5x(1 + x)^(0.5)

At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.

Therefore, an upper bound for the integral is:

In ≤ 5√2∫x^n dx

Using integration by parts, we obtain:

In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1

= 5√2/ (n + 1)

Therefore, the upper bound for the integral is 1/(n+1).

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Answer: n = -16

Step-by-step explanation:

1) Distribute

—2(3n +6) = 3(-n + 12)

—6n - 12 =3(-n + 12)

2) Distribute

—6n - 12 = 3(-n + 12)

—6n — 12 = —3n +36

3) Add 12 to both sides

—6n — 12 = -3n +36

-6n = 12+ 12 = - 3n + 36 + 12

4) Simplify

----Add the numbers

—6n = -3n +48

5) Add 3n to both sides

—6n = -3n +48

—6n + 3n = —3n + 48 + 3n

6) Simplify

- Combine like terms

—3n = 48

7) Divide both sides by the same factor

—3n = 48

-3n ÷ -3 = 48 ÷ -3

8) Simplify

- Cancel terms that are in both the numerator and denominator

- Divide the numbers

n = —16

Please give brainliest

Answer:

24

Step-by-step explanation:

Let the number of members they visit last week be x.

Then, they visit x/4 + 10 this week

x/4 + 10 = 16

x = 4 x 6

x = 24

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