pls help me with this

[tex]1+\frac{1}{6}+\frac{1}{11}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-4} \\ \\ \frac{1}{4}+\frac{1}{9}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-1} \\ \\ S=\sum^{\infty}_{n=1} \left(\frac{1}{5n-4} -\frac{1}{5n-1} \right) \\ \\ =\frac{\pi}{5} \sqrt{\frac{1}{5} (5+2\sqrt{5})}[/tex]

The quarterly annuity payment is $582.46.

What is an ordinary annuity?

An ordinary annuity in case of investment is the one that pays its end-of-the period cash flows rather than at the beginning as it is case of annuity due.

The applicable formula in this case is the present value formula of an ordinary annuity as shown below:

PV=quarterly payment*(1-(1+r)^-N/r

PV=initial investment=$10,000

quarterly payment=unknown(assume it is X)

r=quarterly interest rate=1.5%

N=number of quarterly payments in 5 years=5*4=20(there are 4 quarterly payments in a year)

$10,000=X*(1-(1+1.5%)^-20/1.5%

$10,000=X*(1-(1.015)^-20/0.015

$10,000=X*(1-0.742470418223773)/0.015

$10,000=X*0.257529581776227/0.015

X=$10,000/(0.257529581776227/0.015)

X=quarterly payment=$582.46

Note that the unknown in this case is the annuity payment, the present value can also be the unknown as well.

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Answer:

91.5 - 5.2 = 86.3

Step-by-step explanation:

The initial weight was 91.5 pounds.

The dog lost 5.2 pounds which means subtraction.

91.5 pounds subtracted by 5.2 pounds that the dog lost equals 86.3 pounds.

Test statistic is 0.42.

Given

Testing:

h0 : p = 0.74

h1 : p < 0.74

Successes x = 33

Subject n = 43

A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.

It measures the accuracy of the predicted data distribution relating to the null hypothesis you use when analyzing data samples.

Test statistics z = [tex]\frac{p_{hat} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

Where [tex]p_{hat}[/tex] = Sample proportion = [tex]\frac{x}{n}[/tex]

p = population proportion

n = sample size

z = [tex]\frac{(\frac{33}{43})-0.74 }{\sqrt{\frac{0.74(1-0.74)}{43} } }[/tex]

z = 0.42

Hence,

Test statistics is 0.42..

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Using it's concept, the domain of the function is given as follows:

{x| –2 ≤ x <= 5}

The domain of a function is the set that contains all possible input values for the function.

The function described is defined for x between -2 and 5, hence the domain is given by the following interval:

{x| –2 ≤ x <= 5}

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Answer:

{x| –2 ≤ x < 5}

Step-by-step explanation:

The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.

Note that this is simple probability.

Hence probability of the 75% football starts selected randomly where the chance is 93% =

75% x 93%

= 69.75%

The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:

Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.

Recall that the total population is 100%.

From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.

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The terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.

In this case, we have to expand a power binomial by means of the Pascal's triangle, which offers a useful and quick resource to expand expressions of this kind, now we proceed to present the result of this approach:

(3 · a + 4 · b)⁸ = 6 561 · a⁸ + 69 984 · a⁷ · b + 326 592 · a⁶ · b² + 870 912 · a⁵ · b³ + 1 451 520 · a⁴ · b⁴ + 1 548 288 · a³ · b⁵ + 1 032 192 · a² · b⁶ + 393 216 · a · b⁷ + 65 536 · b⁸

Such combinations of products between variables a and b are also supported by the theorem of the binomial. Finally, the terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.

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The domain of the function y = √(x + 6) - 7 is x > -6

The equation of the function is given as

y = √(x + 6) - 7

Set the radical greater than 0

x + 6 > 0

Subtract 6 from both sides of the equation

x > -6

Hence, the domain of the function y = √(x + 6) - 7 is x > -6

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The domain of the function in discuss described as; y = √x+6 -7 is; x >= -6.

According to the task content, it follows that the domain of.the function can be evaluated by means of the characteristics associated with the square root.

The function given is; y = √x+6 -7

Since, the square root of a negative number renders a complex number as it's results, it follows that; x+6 >= 0.

Hence, x >= -6.

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Answer:

4x +6

Step-by-step explanation:

No explanation

Straight answer

Answer:

1. <1 ~= <4 (Given)

2. <2 is supplementary to <1; <3 is supplementary to <4 (Because <1 & <2, <3 and <4 form linear pairs, they are supplementary by the linear pair postulate.)

3. <2 ~= <3 (By the definition of supplementary angles, m<1 + m<2 = 180 and  m<3 + m<4 = 180. By definition of congruent angles, m<1 = m<4, therefore m<2 = m<3 by substitution property of equality.)

4. AB ~= BC (Converse of Isosceles Triangles Theorem)

5. Triangle ABC is isosceles (Definition of Isosceles Triangles)

Answer:

1.187991

Step-by-step explanation:

sin^2(225)−(cos(330))(cos(240))

=(−0.930095)2−(cos(330))(cos(240))

=0.865076−(cos(330))(cos(240))

=0.865076−−0.991199(cos(240))

=0.865076−(−0.991199)(0.325781)

=0.865076−(−0.322914)

=1.187991

percentage of students say they have witnessed hazing and did not report it are  = 95%

No matter how voluntarily a person is to take part, hazing, initiation or deposition are all actions that are demanded of someone when they join or participate in a group and which humiliate, degrade, abuse, or imperil them.

involves humiliating a person or group. involves making fun of someone or something. involves or includes the deliberate destruction of or removal of private or public property for the purpose of affiliation with, initiation into, or as a requirement for continuing membership in an organization.

Paddling, beating, or other types of attack. Branding. consumption of disgusting substances or mixtures under duress or force.

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The computation shows that the maximum number of pants per employee that can be washed each week is 6.

The maximum number of pants per employee that can be washed each week will be:

7 + 4.5x + 12 <= 46

4.5x <= 27

x <= 6

The maximum number is 6.

The maximum number of chef coats per employee that can be washed each week will be:

= 6 + 8

= 14

The maximum total number of items per employee that can be washed in a week will be:

= 6 + 14 = 20

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Answer:

5/6

Step-by-step explanation:

we add all the marbles together to get 6

then we seperate the marbles according to the question which would be yellow and red. that would make the probability of getting one of those to 5/6. Hope this helps :)

The side lengths of the isosceles triangle are:

AO = 16 units

AB = 16 units

OB = 6 units.

An isosceles triangle is a type of triangles that has two sides that are congruent to each other, and two base angles that are opposite these two sides that are also congruent to each other.

Referring to the isosceles triangle in the image attached below, we have the following:

One of the congruent sides = AO = 3x + 4 units

The other congruent side = AB = x + 12 units

The third side = OB = 4x - 10 units

Applying the definition of an isosceles triangle, we can create an equation as shown below to find x:

AO = AB [congruent sides]

Substitute

3x + 4 = x + 12

3x - x = - 4 + 12

2x = 8

2x/2 = 8/2

x = 4

Find the side lengths of the isosceles triangle by plugging in the value of x:

One of the congruent sides = AO = 3x + 4 = 3(4) + 4 = 16 units

The other congruent side = AB = x + 12 = 4 + 12 = 16 units

The third side = OB = 4x - 10 = 4(4) - 10 = 6 units.

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The value of the given trigonometry function is 2√15/15

Half angles are trigonometric identities used to express sine, cosine and tangent of half angles.

For instance the value of cos theta is expressed as shown below;

cosФ = cos(Ф/2+Ф/2)

cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ  = 1 - 2cos²Ф/2

Given the following parameters

cosФ = -7/15

Substitute

cosФ  = 1 - 2cos²Ф/2

-7/15  = 1 - 2cos²Ф/2

-2cos²Ф/2 = -7/15 - 1

-2cos²Ф/2 = -8/15

cos²Ф/2 = 4/15
cosФ/2 = 2/√15

Rationalize

2/√15 * √15/√15

2√15/15

Hence the value of the given trigonometry function is 2√15/15

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Answer:

Step-by-step explanation:

A function is even when f(-x) = f(x) for all x in the domain of f. We can say that the function is simetrical over x axis.

That's all i know, Hope it helps!

Answer: [tex]\Large\boxed{-30x^2+40x}[/tex]

Step-by-step explanation:

Given expression

10x (4 - 3x)

Expand the parenthesis by distributive property

= 10x · 4 - 10x · 3x

= (10 × 4)x - (10 × 3) (x × x)

[tex]\Large\boxed{=-30x^2+40x}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Hi :)

We'll use distributive property to solve this

[tex]\LARGE\boldsymbol{10x(\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}4-\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}{3x)}}}[/tex]

Thus

[tex]\large\boldsymbol{10x\cdot4-3x\cdot10x}[/tex]

Simplify

[tex]\Large\boldsymbol{40x-30x^2}[/tex]

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

The correct description that cab made of these graphs is that  They have the same x- and y-intercepts.

This is the term that is used to describe the behaviors of these functions as they approach infinity.

the y-intercept of a function

This is what is used to tell us the y value when we put x to be = 0

The y-intercept of f(x) is y = -2

The y-intercept of g(x) is y = -2

the x-intercept of a function

It is the value of x when y = 0.

The x-intercept = 2

The x-intercept = 2

Hence statement B is correct. They have the same x- and y-intercepts.

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Answer:

[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}[/tex]

Step-by-step explanation:

To find y-intercept of a graph, we have to substitute x = 0 to find it - consider each functions:

First Choice

[tex]\displaystyle{f(x) = 2x(x+14)-64}\\\\\displaystyle{f(0) = 2\cdot 0(0+14)-64}\\\\\displaystyle{f(0) = 0\cdot 14-64}\\\\\displaystyle{f(0) = -64}[/tex]

Second Choice

[tex]\displaystyle{f(x) = (x+4)^2+2x}\\\\\displaystyle{f(0) = (0+4)^2 + 2(0)}\\\\\displaystyle{f(0) = 4^2}\\\\\displaystyle{f(0) = 16}[/tex]

Third Choice

[tex]\displaystyle{f(x) = (x-16)^2 + 4}\\\\\displaystyle{f(0) = (0-16)^2 + 4}\\\\\displaystyle{f(0) = (-16)^2 + 4}\\\\\displaystyle{f(0) = 256 + 4}\\\\\displaystyle{f(0) = 260}[/tex]

Fourth Choice

[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}\\\\\displaystyle{f(0) = -2(0-3)^2 + 2}\\\\\displaystyle{f(0) = -2(-3)^2 + 2}\\\\\displaystyle{f(0) = -2\cdot 9 + 2}\\\\\displaystyle{f(0) = -18+2}\\\\\displaystyle{f(0) = -16}\\[/tex]

Therefore, fourth choice is correct.

Answer:

Step-by-step explanation:

Refer to attached diagram with added details.

Circle O with:

Since r = OC + CD, the radius is 4 cm.

Consider right triangles OAC or OBC:

Recall the property of 30°x60°x90° triangle:

It means OC: OA = 1 : 2, so angles AOC and BOC are both 60° as adjacent to short legs.

In order to find the shaded area we need to find the area of sector OADB and subtract the area of triangle OAB.

Area of sector:

Area of triangle AOB:

The shaded area is:

Use of identity for sum of cubes:

Change it as:

It is easy to notice that:

So the sum of cubes for the given expression will be:

Now substitute the values and calculate each of these:

(a) 4a + 5b = 5, ab = -1.

(b) 4a + 5b = -2, ab = 1/15.

(c) 4a + 5b = 1/3, ab = -1/9.

(d)  4a + 5b = -1, ab = 1.

The athlete that has the shortest training ride is athlete A.

The athlete that has the shorter range is Athlete B.

The athlete that has the greater median is Athlete B.

The athlete that has the greater IQR is  athlete A.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.

Range of Athlete A = 36 - 13 = 13

Range of Athlete B = 30 - 19 = 11

Training ride of  Athlete A = 16

Training ride of  Athlete B = 21

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median of  Athlete A = 20

Median of  Athlete B = 25

IQR of  Athlete A = 30 - 16 = 14

IQR of  Athlete B = 28 - 21 = 7

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In order to solve this IVP using Laplace transforms, we must first write f(t) in terms of the Heaviside function.

f(t)=0*(u(t)-u(t-Pi))+1*(u(t-Pi)-u(t-2Pi))+0*(u(t-2Pi))

f(t)=u(t-π)-u(t-2π)

So, the rewritten IVP is

y'' +y = u(t-π)-u(t-2π)y(0)=0, y'(0)=1

Taking the Laplace transform of both sides of the equation, we get:

s2L{y}-sy(0)-y'(0)+L{y}=(1/s)*e-πs-(1/s)*e-2πs

s2L{y}-1+L{y}=(1/s)*e-πs-(1/s)*e-2πs

(s2+1)L{y}=1+(1/s)*e-πs-(1/s)*e-2πs

L{y}=1/(s2+1)+(1/s(s2+1))e-πs-(1/s(s2+1))*e-2πs

Now, we must take the inverse transform of both sides to solve for y.

The first inverse transform is easy enough. By definition, it is sin(t).

The second two inverse transforms will be a little tougher, we will have to use partial fraction decomposition to break them down into terms that are easier to compute.

A/s+(Bs+C)/(s^2+1)=1/(s(s^2+1))

A(s^2+1)+(Bs+C)(s)=1

As^2+A+Bs^2+Cs=1

Rewriting this system in matrix form, we get:

1  1  0    A     0

0  0  1  * B  = 0

1  0  0    C     1

Using row-reduction we find that A=1, B=-1, and C=0. So, our reduced inverse transforms are:

L-1{(e-πs)(1/s-s/(s2+1))}

and

L-1{(e-2πs)(1/s-s/(s2+1))}

Using the first and second shifting properties, these inverse transforms can be computed as.

L-1{(e-πs)(1/s-s/(s2+1))}=u(t-π)-cos(t-π)u(t-π)

L-1{(e-2πs)(1/s-s/(s2+1))}=u(t-2π)-cos(t-2π)u(t-2π)

Combining all of our inverses transforms, we get the solution the IVP as:

y=sin(t)+u(t-π)-cos(t-π)u(t-π)+u(t-2π)-cos(t-2π)u(t-2π)

In mathematics, the Laplace transform, named after its discoverer Pierre Simon Laplace (/ləˈplɑːs/), transforms a function of real variables (usually in the time domain) into a function of complex variables (in the time domain). is the integral transform that Complex frequency domain, also called S-area or S-plane).

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The equation of the directrix is x = -3

A mirror-symmetrical, roughly U-shaped plane curve known as a parabola. It corresponds to a number of mathematical models that appear to be superficially dissimilar but yet all define the exact same curves. A point and a line are one way to describe a parabola.

Given the general equation of a parabola expressed as

(y-y0)² = 4a(x-x0) ... 1

Equation of the directrix will be expressed as x = x0 - a

From the equation given;

y² = 12x ... 2

Comparing 1 and 2;

x - x0 = x

-x0 = x - x

-x0 = 0

x0 = 0

Similarly;

y-y0 = y

-y0 = y - y

-y0 = 0

y0 = 0

Also;

4a = 12

a = 12/4

a = 3

Substituting x0 =0, y0 = 0 and a = 3 into the equation of the directrix above, we will have;

x = x0 - a

x = 0 - 3

x = -3

Hence,

the equation of the directrix is x = -3

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Answer: 177

Step-by-step explanation:

1. 4x4=16

(3-16)^2+8

2. 3-16=-13

(-13)^2+8

3. -13x-13=169

169+8

4.169+8=177

177

Answer:

177

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

Given expression:

[tex](3-4^2)^2+8[/tex]

Parentheses

Begin by calculating the part inside the parentheses.

Following PEMDAS, calculate the exponent first:

[tex]\implies (3-4^2)^2+8=(3-16)^2+8[/tex]

Then carry out the subtraction:

[tex]\implies (3-16)^2+8=(-13)^2+8[/tex]

Exponents

[tex]\textsf{Apply the exponent rule}: \quad (-a)^n=a^n, \quad \textsf{if }n \textsf{ is even}[/tex]

[tex]\implies (-13)^2+8=169+8[/tex]

Addition

[tex]\implies 169+8=177[/tex]

Therefore:

[tex]\implies (3-4^2)^2+8=177[/tex]

Answer:2.36

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

5x - 625[tex]x^{4}[/tex] ← factor out 5x from each term

= 5x(1 - 125x³) ← this factor is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

1 - 125x³

= 1³ - (5x)³

= (1 - 5x) (1² + 5x(1) + (5x)² )

= (1 - 5x) (1 + 5x + 25x²)

Then

5x - 625[tex]x^{4}[/tex] = 5x(1 + 5x + 25x²)

The tessellated plane has translational symmetry option (A) translational symmetry is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

A geometric figure is given:

As we know, from geometric transformation, geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, etc.

Without any further changes, the tessellated plane is moved a few units to the right. If the translated plane is again moved left by the same amount of units, we will once more obtain the original plane. Translational symmetry is present as a result.

Thus, the tessellated plane has translational symmetry option (A) translational symmetry is correct.

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