Find all relative extrema in the function h(x)=cos((2π/3)x) on the interval [0, 2]

Find all ABSOLUTE extrema in the function h(x)=cos((2π/3)x) on the interval [0, 2]


HELP!!!

Answer:

Step-by-step explanation:

the answer is y= -4x/3 + 13

Answer:

x= 56/3

y= 14/3

Step-by-step explanation:

for process look at provided image

The required simplified solution of the expression is given as,
1. -2√15      2.3c      4. -5
3. √6         5. 2a

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
1.
[tex]=\sqrt{(3 -\sqrt{15} )^2} - \sqrt{(3 +\sqrt{15} )^2} \\=3 -\sqrt{15} - (3 +\sqrt{15})\\=3 -\sqrt{15} -3 -\sqrt{15}\\= -2\sqrt{15}[/tex]

Similarly, the solution of the various expression can be determined.
2.3c
3. √6
4. -5
5. 2a

Thus, the solution of the expression are given above

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The value of x, the distance from the base of the roof to the top of the roof is 8 feet

The length of the base of the triangle = 30 feet

The side of the triangle = 17 feet

The triangle is the combination of two right triangles

Consider one right triangle

The base length = 30 / 2 = 15 feet

The side of the triangle = 17 feet

The length of the third side = x

Here we have to apply Pythagorean theorem

Then

17^2 = 15^2 + x^2

x^2 = 17^2 - 15^2

x^2 = 289 - 225

x^2 = 64

x = 8 feet

Therefore, the height of the roof is 8 feet

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Answer:

x = 25

Step-by-step explanation:

the angle in a semicircle is 90°

given the legs of the triangle are congruent then the triangle is isosceles with the 2 base angles congruent.

the sum of the 3 angles in the triangle = 180°

base angle = (180 - 90)° ÷ 2 = 90° ÷ 2 = 45° , then

2x - 5 = 45 ( add 5 to both sides )

2x = 50 ( divide both sides by 2 )

x = 25

Answer:

140 pennies

Step-by-step explanation:

Information:

Define the variables:

If the piggy bank contains 350 pennies and nickels:

[tex]\implies x+y=350[/tex]

If the piggy bank contains pennies and nickels worth $11.90:

[tex]\implies 0.01x+0.05y=11.90[/tex]

Rearrange the first equation to make y the subject:

[tex]\implies y=350-x[/tex]

Substitute the expression for y into the second equation and solve for x:

[tex]\implies 0.01x+0.05(350-x)=11.90[/tex]

[tex]\implies 0.01x+17.5-0.05x=11.90[/tex]

[tex]\implies -0.04x=-5.6[/tex]

[tex]\implies x=140[/tex]

Therefore, there are 140 pennies in the piggy bank.

Answer:

$40,601.92

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 1.5/100

r = 0.015 per year,

Then, solve the equation for P

P = I / ((1 + r/n)nt - 1)

P = 3150 / ((1 + 0.015/2)(2)(5) - 1)

P = 3150 / ((1 + 0.0075)(10) - 1)

P = $40,601.92

Summary:

The principal investment required to get a total interest of $3150 from compound interest at a rate of 1.5% per year compounded 2 times per year over 5 years is $40,601.92.

Answer:

Drink: $5

Candy : $3.75

Step-by-step explanation:

Let d = the cost of a drink

Let c = the cost of a candy

9d + 4c = 60

10d + 2c = 57.50 ⇒ Mult. by -2 ⇒ -20d -4c = -115  Add this to the first equation

-20d  - 4c = -115

9d + 4c = 60

-11d = -55  Divide both sides by -11

d = 5

A drink costs $5.00.

Plug in 5 for d in either of the two equations to solve for c

9d + 4c = 60

9(5) + 4x = 60

45 + 4c = 60  Subtract 45 from both sides

4c = 15  Divide both sides by 4

x = 3.75

A candy costs $3.75

Answer/Step-by-step explanation:

Since the axes are labelled and there are nice points marked on the line, you can practically SEE the slope here without any calculating, just by counting. Start with a point and find the directions to the next point. To get from one point to the next, go UP2 and OVER3.

"UP2 and OVER3" is the slope 2/3.  Double check that you get a slope that is positive because the line is going up to the right, it should have positive slope.

If the teacher is insisting that you use the slope formula, then name two of the points, such as (0, 4) and (3, 6). First subtract the y's, 6 - 4 is 2, put that on top of a fraction. Then subtract the x's, 3 - 0 is 3, put that on the bottom of a fraction. You get 2/3 again. Doesn't matter what points you use, since they are all on the same line it will come out the same.

The moment generating function of a Bern(p) random variable x is given by: M(t) = pe^(pt) + (1 - p).The moment generating function of a Bin(n, p) random variable y is given by:M(t) = (pe^(pt))^n + (1 - p)^n

To find the moment generating function of a Bern(p) random variable x, we first need to calculate the probability mass function of x.

p(x) = p^x (1-p)^(1-x).

The moment generating function of x is then given by the formula:

M(t) = pe^(pt) + (1-p).

To use the moment generating function of x to find the moment generating function of a Bin(n, p) random variable y, we first need to calculate the probability mass function of y.

p(y) = (n choose y)p^y(1-p)^(n-y).

The moment generating function of y is then given by the formula:

M(t) = (pe^(pt))^n + (1-p)^n.

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(a) The System of equations that representing this situation is

x= y+14; x+y = 64

(b) There are 39 students in the film-making club and 25 students in the yearbook club.

In the given question, there are a total of 64 students in a film-making club and a yearbook club.

The film-making club has 14 more students than the yearbook club.

a. We have to write a system of linear equations that represents this situation.

Let x represent the number of students in the film-making club

Let y represent the number of students in the yearbook club.

As given that the film-making club has 14 more students than the yearbook club.

So x = y+14

Total students are 64.

So x+y = 64

System of equations:

x= y+14

x+y = 64

b. Now we have to find how many students are in the film-making club and the yearbook club.

The system of equations are;

x= y+14...................(1)

x+y = 64...................(2)

Now putting the value of x in equation 2.

y+14+y = 64

2y+14 = 64

Subtract 14 on both side, we get;

2y = 50

Divide by 2 on both side, we get;

y = 25

Now putting the value of y in equation 1.

x = 25+14

x = 39

There are 39 students in the film-making club and 25 students in the yearbook club.

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1. Number  of generators of  Z*4969 = 1584

2. Probability of a randomly chosen element a Z*_969 being a generator      = [tex]\frac{1584}{4968}[/tex]

3. 1001 is the smallest generator

4. Number of generators

      ∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]

1. Every relative prime of 4968 offers a generation if a is the generation of Z.

4968 = 4 × 1242

         = 4 × 3 × 414

         = 4 × 3 × 2 ×207

         = 4 × 3 × 2× 3× 69

         = 4 × 3 × 2 × 3 × 3 ×23

         [tex]= 2^{3} * 3^{3} * 23[/tex]

Number of generators ∅ (4968) = 4968[tex](1 - \frac{1}{2} )(1 - \frac{1}{3} )(1 - \frac{1}{23} )[/tex]

Number  of generators of  Z*4969 = 1584

2. When a Z*4969 value is set, it becomes a generation and belongs to one of the 1584 elements.

The probability that a element is selected from Z*4968 becomes a generation is

=  favorable elememt / total element

= [tex]\frac{1584}{4968}[/tex]

= 0.3188

3. To find the smallest generator a Z*_969 with a > 1000.

      a > 1000

Every relative prime of 4968 gives a generation of Z*4969

G C D (1001   4968) = 1

Hence, 1001 is the smallest generator

4. Number of generators

      ∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]

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Answer:

The statement that the mean attendance is higher than 523 does not have enough facts to stand up.

What is null hypothesis?

A null hypothesis is an educated guess or a prediction of the expected outcome of a particular experiment. It is a statement that assumes there is no difference between two groups or no association between two variables. The null hypothesis is often the opposite of the alternative hypothesis, which is the prediction that the researcher is hoping to prove.

Example 1: In a study of the effectiveness of a new drug for treating depression, the null hypothesis would be that the drug has no effect on depression levels.

Example 2: In a study of the association between smoking and lung cancer, the null hypothesis would be that there is no association between the two variables.

Example 3: In a study of the effect of a new educational program on student performance, the null hypothesis would be that the program has no effect on student performance.

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The eligible amount of work-related daycare expenses will be $2600

Married filing jointly is a filing status for married couples, allowing them to file joint tax returns. When filing taxes under married filing jointly status, a married couple can record their respective incomes, deductions, credits, and exemptions on the same tax return.

Given here wages of the cliff are $16,228 and if the deb is  $2,600

now the mfj is 35% hence cliffs credit is 35% ×  $16,228 = $5679.8

and daycare yearly expenses are = $250×12

                                                        = $3000

but deb's income is $2600 and thus credit cannot exceed deb's wages therefore the revised credit would be $2600

Hence, the eligible amount of work-related daycare expenses will be  $2600

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Answer:

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

We know supplementary angles sum to 180 deg:

And we are given:

Substitute the second equation into the first one and solve for m∠B:

Find m∠A:

Correct choice is C.

James received total scholarships of $30,000 to pursue his accounting degree at State University. He spent $15,000 of the money on tuition, $1,000 on books, and $14,000 on rent for his off-campus apartment. James must include 14000 in gross income on his tax return.

Your wages, dividends, capital gains, business income, and retirement distributions are all included in your gross income. Acclimations to Pay incorporate such things as Instructor costs, Understudy loan revenue, Provision installments or commitments to a retirement account.

The total amount of your earnings and income for the tax year minus certain income adjustments is your adjusted gross income (AGI). Your AGI is listed on Line 11 of Forms 1040, 1040-SR, and 1040NR for the tax year 2022.

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Answer:

25456

Step-by-step explanation:

None of the options are valid because the specified functions are both parabolic.

Functions represent the connection between two groups of values. For instance, if y=f(x), each value of x has a corresponding value in the set of y. The dependent variable is Y, and the independent variable is x.

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x. In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Given functions in this case are

f(x)=-15x2+32

g(x)=-17x2+5x+32.

The functions' zeros are

x = 1.461, -1.233, and 1.527.

When g(x) has a higher maximum than f(x), f(x)intercept exceeds g. (x).

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Answer:

u = 8 ; v = 7

Step-by-step explanation:

5u = u + 32

5u - u = 32

4u = 32

4/4 u = 32/4

u = 8

v + 7 = 2v

2v - v = 7

v = 7

The domain is {2, -1, 4, 5} and the relation is not a function

From the question, we have the following parameters that can be used in our computation:

{(2,4), (-1,8), (4,-2), (5,6), (2,-2)}

The domain is the set of the x values

So, we have the following representation

x = {2, -1, 4, 5, 2}

Remove repeated entries

x = {2, -1, 4, 5}

So, the domain is {2, -1, 4, 5}

Also, the relation is not a function

This is because the x value 2 has several y values

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The possible equation of the parabola is f(x) = (x - 1)² - 5

From the question, we have the following parameters that can be used in our computation:

Vertex = (1, -5)

Rewrite the vertex as follows

So, we have the following representation

(h, k) = (1, -5)

A quadratic function can be represented as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

Substitute the known values in the above equation, so, we have the following representation

f(x) = a(x - 1)² - 5

Set a = 1

f(x) = (x - 1)² - 5

Hence, the function is (d) f(x) = (x - 1)² - 5

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The value of x, in degrees, is given as follows:

A. 48.

Similar triangles are triangles that share these two features given as follows:

The similar triangles in this problem are listed as follows:

WUV and WUT.

In triangle UWV, the length of the side adjacent to the angle of 48º has a length of 13.5 cm.

In triangle WUT, the length of the side adjacent to the angle of x has a length of 13.5 cm.

Reminding the two features of similar triangles, namely congruent angle measures and proportional side lengths, the measure of angle x is given as follows:

x = 48º.

(as the equivalent side length is the same, hence the angle measure is also the same).

This means that option A is correct.

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The model of the function is  y = -13.75x + 27853.75 and the estimated population in 2010 is 216.25

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

In this problem, we can take the two points to find the slope and y-intercept of the function.

using a linear function model;

y = mx + c

slope (m) = y₂ - y₁ / x₂ - x₁

m = 285 - 340 / 2005 - 2001

m = -13.75

Using the slope, we can find the y-intercept

y = mx + c

Taking one point;

285 = -13.75(2005) + c

c = 27853.75

The model of the function is y = -13.75x + 27853.75

b) The population in 2010 will be

y = -13.75(2010) + 27853.75

y = 216.25

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Answer:

21 quarts of soup

Step-by-step explanation: I take . as a mutiply

This is easy you just need to take [tex]3 : \frac{1}{7} = \frac{3}{1} : \frac{1}{7} = \frac{3}{1} . \frac{7}{1} = \frac{3 . 7 }{1 . 1} = \frac{21}{1} = 21[/tex] quarts of soup

W =∫ lower power (-r) to higher power (r + h) (h + r - x) 2pgl [tex]\sqrt{r^2+x^2}[/tex] dx is the integral for the effort needed to pump water out of a spout that is 2 m above the tank.

Integral: In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

r = 2m

l= 5m

sinθ=x/r

[tex]dv=2l\sqrt{r^2+x^2} dx[/tex]

Let g be the acceleration brought on by gravity, and let p be the density of water.

dm = p dv

dw = dmg (h + r - x)

dw = pg (h + r - x) dx

dw = 2lpg  (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx

w = ∫dw

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x)  [tex]\sqrt{r^2+x^2}[/tex] dx

Therefore, the integral for the work required to pump the water out of a

spout that rises 2 m above the tank is

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx

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the number of members using the values in the animal field. then the value is 63

1. Application layer: this is the interface that connects a user to a network, the files or data are generated and seek from this layer. Protocols in this layer are FTP, TFTP, DNS, SMTP, SNMP etc.

2. Presentation layer: it is the sixth layer in the OSI model. It is used to present data in a well organized syntax and format to and application and also for document format encryption. Protocols in this layer are XDR, TLS, SSL and MIME.

3. Session layer: this layer is used to create and terminate sessions between the destination and source node, in a network. Protocols in this layer are PPTP, SAP, L2TP and NETBIOS.

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1. There are two performance obligations in a contract to buy a pair of SunBoots from Clarks Inc: Delivery of Sunboots and Discount Coupon.

2. The journal entry to record the revenue for the sale of 1,000 pairs of SunBoots when Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon is as follows:

Debit Cash $70,000

Credit Sales Revenue $65,800

Credit Deferred Revenue from Discount Coupon $4,200

(To record the sale of 1,000 pairs of SunBoots, including the discount coupon.)

Performance obligations refer to distinct goods and services agreed to be provided in a contract between the two parties.

Performance obligations arise because each separate goods or services benefit the customer distinctly from others.

In accounting for the revenue or costs, efforts should be geared toward recognizing the activity as soon as they bestow or transfer economic benefits to the buyer.

Selling price per pair = $70

Discount coupon = 30%

Estimated percentage of customers who will utilize the coupon = 20%

The number of SunBoots sold = 1,000

Cash $70,000 Sales Revenue $65,800 Deferred Revenue from Discount Coupon $4,200 ($70,000 x 30% x 20%)

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If two cities on map are [tex]5\frac{3}{4}[/tex] inches apart, then the actual distance between the cities is 345 miles .

In the question ,

it is given that ,

the scale on the map is 1/2 inches is = 30 miles .

So , 1 inches on the map is = 60 miles.

So , the scale factor is 1 inch = 60 miles .

also given that the distance between the two cities on the map is = [tex]5\frac{3}{4}[/tex] inches ,

means , 23/4 inches .

So , the actual distance is = 23/4 × 60

Simplifying further ,

we get ,

= 345 miles .

Therefore , the actual distance is 345 miles , the correct option is (d) .

The given question is incomplete , the complete question is

The scale on a map reads 1/2 inch = 30 miles. If two cities on the map are [tex]5\frac{3}{4}[/tex] inches apart, find the actual distance between the cities.

A. 300 miles

B. 315 miles

C. 327 miles

D. 345 miles

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(ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected

the best is always to look for points on the line that are exactly corner points of grid squares.

the true utilities of the four individuals for the five alternatives

(0.3, 0.4) and (0.6, 0.8)

so, the linear equation is

y = ax + b

0.4 = a×0.3 + b

0.8 = a×0.6 + b

let's subtract the second from the first equation :

-0.4 = a×-0.3 + 0

a = -0.4/-0.3 = 0.4/0.3 = 4/3

so, the equation is

y = (4/3)x

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