What is the length of the arc of a circle with a radius of 4 by a central angle of 7pi/4?

Answer:

[tex]f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{5 + x}[/tex]

Required

The power series centered at [tex]x = 0[/tex]

We have:

[tex]f(x) = \frac{1}{5 + x}[/tex]

Factor out 5 from the denominator

[tex]f(x) = \frac{1}{5(1 + \frac{x}{5})}[/tex]

Rewrite as:

[tex]f(x) = \frac{\frac{1}{5}}{(1 + \frac{x}{5})}[/tex]

Further, rewrite as:

[tex]f(x) = \frac{1}{5}(1 + \frac{x}{5})^{-1}[/tex]

Expand the bracket

[tex]f(x) = \frac{1}{5}(1 - \frac{x}{5} + (\frac{x}{5})^2 - (\frac{x}{5})^3+..........)[/tex]

Evaluate all exponents

[tex]f(x) = \frac{1}{5}(1 - \frac{x}{5} + \frac{x^2}{25} - \frac{x^3}{125}+......)[/tex]

Open brackets

[tex]f(x) = \frac{1}{5} - \frac{x}{5^2} + \frac{x^2}{5^3} - \frac{x^3}{5^4}+......[/tex]

Notice the pattern as:

[tex]f(x) = \frac{1}{5} - \frac{x}{5^2} + \frac{x^2}{5^3} - \frac{x^3}{5^4}+......\± \frac{x^n}{5^{n+1}}[/tex]

So, the power series is:

[tex]f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}[/tex]

Answer:

"The coefficient with the largest absolute value is the most narrow graph."

y = ⅓x² → widest

y = -½x²

y = -9x² → narrowest

Answer:

c. infinitely many solutions

General Formulas and Concepts:

Pre-Algebra

Distributive Properties

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

2(h - 8) - h = h - 16

Step 2: Solve for h

Hello from  MrBillDoesMath!

Answer:    c  (infinitely many solutions)

Steps:

1) Simplify  the original  equation

       2(h-8)- h= h - 16

2.As 2 (h-8) = 2h- 16,  the equation in 1) is equivalent to  

      (2h-16) -h  = h - 16

 or

      (2h-h) - 16 = h - 16

or

      h - 16 = h -16

which is true for all values of h.

Regards,  MrB

Answer:

I think

c. 164

Step-by-step explanation:

m<BAC=m<FAE = 25

m< CAD=m< DAE= 57

m<BAF= 25+25+57+57=164

Answer:

12000 bacteria

Step-by-step explanation:

Recall that

60 minutes = 1 hour

Given that the rate of growth of the bacterial population is proportional to the number present.

If there were 3000 bacteria in the initial population and the number doubled after the first 60 minutes

Then after 60 minutes, the number of bacteria present would be

= 3000 * 2

= 6000

In another 60 minutes, the number would have doubled again, thus the number present then would be

= 6000 * 2

= 12000

Hence after 120 minutes, the number of bacteria present is 12000. 120 minutes is same as 2 hours

Answer:

[tex]\angle P[/tex]

Step-by-step explanation:

Given

[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]

[tex]PQ = 20[/tex]     [tex]QR = 16[/tex]    [tex]PR = 12[/tex]

[tex]ST = 30[/tex]       [tex]TU = 34[/tex]    [tex]SU = 16[/tex]

See attachment

Required

Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]

Considering [tex]\triangle PQR[/tex]

We have:

[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse

So, we have:

[tex]\sin(P) = \frac{16}{20}[/tex]

Divide by 4

[tex]\sin(P) = \frac{4}{5}[/tex]

Hence:

[tex]\angle P[/tex] is correct

Answer:

A or <P

Step-by-step explanation:

on edge 2021

Answer:

just ignore this whole thing

Answer: There is a pattern if you look closely :)

So yhe required answer would be 7^-1

Step-by-step explanation:

g tau .......................

Answer:

Answer:

Option B 8.54\ units8.54 units

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Let

[tex]\begin{gathered}A(5,7)\\E(-3.4)\end{gathered} [/tex]

substitute the values

[tex]dAB=\sqrt{(4-7)^{2}+(-3-5)^{2}}[/tex]

[tex]dAB=\sqrt{(-3^{2}+(-8)^{2}}[/tex]

[tex]dAB=\sqrt{73}=8.54\ units[/tex]

Answer:

No

Step-by-step explanation:

Each "x" should have a corresponding "y" value. In this case, however, an x has two different y values which would not make this a function. You can check this through the vertical line test.

Answer:

[tex]H_0: \mu = 8[/tex]

[tex]H_1: \mu \neq 8[/tex]

Step-by-step explanation:

A company claims that its soup vending machines deliver exactly 8 ounces of soup to every customer.

This means that the null hypothesis is that the mean is exactly 8, that is:

[tex]H_0: \mu = 8[/tex]

You do not want the vending machines to deliver too much or too little soup.

We don't want the mean to be different from 8, which means that the alternative hypothesis is given by:

[tex]H_1: \mu \neq 8[/tex]

Answer:

5.7

Step-by-step explanation:

sine cosine tangent

soh cah toa

sine = opposite/hypotenuse

so sin(35)= x/10

you can multiply 10 to both sides to get rid of the 10 denominator on the right leaving you with 10sin(35)=x

be sure your calculator is in degrees.

put that into a calculator leaving you with 5.7

Let a be the first term in the arithmetic progression. Then each successive term differs from a by a fixed number c, so that

• first term = a

• second term = a + c

• third term = (a + c) + c = a + 2c

• fourth term = (a + 2c) + c = a + 3c

and so on. In general, the n-th term in the AP is a + (n - 1) c.

The sum of the 3rd and 7th terms is 38, so that

(a + 2c) + (a + 6c) = 38

==>   2a + 8c = 38

==>   a + 4c = 19 … … … [1]

The 9th term is 37, so

a + 8c = 37 … … … [2]

Subtracting [1] from [2] eliminates a and lets you solve for c :

(a + 8c) - (a + 4c) = 37 - 19

4c = 18

c = 18/4 = 9/2

Solve for a using either equations [1] or [2] :

a + 8 (9/2) = 37

a + 36 = 37

a = 1

Then the n-th term in the AP is 1 + 9/2 (n - 1) or 9/2 n - 7/2, where n ≥ 1.

Answer:

20'×15 in 54 inches

Step-by-step explanation:

The Best as a pool should be rectangular in shape and 54inches deep for safety of life's

The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi r^{2}[/tex]h

The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;

=  [tex]\pi r^{2}[/tex]h

[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]

The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;

V = 20 x 15 x 54

V = 16,200 cubic meter.

The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.

Learn more about volume;

https://brainly.com/question/1578538

#SPJ2

Answer:

Hence the distribution will be between 600 hours and 900 hours is 74.9%.

Step-by-step explanation:

Answer:

251.5 cm

Step-by-step explanation:

1 m = 100 cm

1 cm = 10 mm

2 m + 50 cm + 15 mm =

= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)

= 200 cm + 50 cm + 1.5 cm

= 251.5 cm

Answer:

a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

This means that [tex]\mu = 128, \sigma = 23[/tex]

a.) State the random variable.

Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the p-value of Z when X = 135, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{135 - 128}{23}[/tex]

[tex]Z = 0.3[/tex]

[tex]Z = 0.3[/tex] has a p-value of 0.6179.

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the p-value of Z when X = 141, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{141 - 128}{23}[/tex]

[tex]Z = 0.565[/tex]

[tex]Z = 0.565[/tex] has a p-value of 0.7140.

0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:

X = 125

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{125 - 128}{23}[/tex]

[tex]Z = -0.13[/tex]

[tex]Z = -0.13[/tex] has a p-value of 0.4483.

X = 120

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{120 - 128}{23}[/tex]

[tex]Z = -0.35[/tex]

[tex]Z = -0.35[/tex] has a p-value of 0.3632.

0.4483 - 0.3632 = 0.0851

0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From item b, when X = 135, Z = 0.3.

Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 128}{23}[/tex]

[tex]X - 128 = 1.28*23[/tex]

[tex]X = 157.44[/tex]

90% of all people in China have a blood pressure of less than 157.44 mmHg.

Answer:

a.

Step-by-step explanation:

The p-value is a measurement of the likelihood that a difference observed is due to a random chance or a sampling error. In an alternative way, the p-value of a study represents the probability or area under distribution for obtaining more radical outcomes whenever the null hypothesis is true.

Any observable change is deemed to be addressed by sampling variability if the P-value is greater than the selected alpha level. A statistical test will nearly always show a substantial difference with a suitably big sample unless there is no impact at all when the effect size is exactly zero.

As a result, simply reporting the P-value alone for a study is insufficient to fully validate the results and findings of scientific publications.

I also need help anyone can help

Given:

The expression is:

[tex]-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)[/tex]

To find:

The expression that is equivalent to the given expression.

Solution:

We have,

[tex]-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)[/tex]

Using the distributive property, we get

[tex]=-\dfrac{1}{4}-\dfrac{2}{5}-\dfrac{3}{7}[/tex]

Taking LCM, we get

[tex]=\dfrac{-35-56-60}{140}[/tex]

[tex]=\dfrac{-151}{140}[/tex]

Therefore, the expression [tex]-\dfrac{151}{140}[/tex] is equivalent to the given expression expression.

Note: There are more than one equivalent expressions.

More information pleaseeeeeeee

Answer:

0.31311311131111....

Step-by-step explanation:

We need to tell a number which when adds to 0.4 makes it a Irrational Number . We know that ,

Rational number :- The number in the form of p/q where p and q are integers and q is not equal to zero is called a Rational number .

Irrational number :- Non terminating and non repeating decimals are called irrational number .

Recall the property that :-

Property :- Sum of a Rational Number and a Irrational number is Irrational .

So basically here we can add any Irrational number to 0.4 to make it Irrational . One Irrational number is ,

[tex] \rm\implies Irrational\ Number = 0.31311311131111... [/tex]

So when we add this to 0.4 , the result will be Irrational . That is ,

[tex] \rm\implies 0.4 + 0.31311311131111 ... = 0.731311311131111 .. [/tex]

Answer:

Step-by-step explanation:

the arrows from the picture tells us that TV is parallel to RS

since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x

(alternate interior angles)

sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°

2x = 45*2 = 90°

Answer: 0.5747

Step-by-step explanation:

Given: Average time to serve a customer[tex](\mu)=4.35[/tex] minutes

standard deviation of the service time [tex](\sigma)=[/tex] 2.5 minutes

coefficient of variation = [tex]\frac{\sigma}{\mu}[/tex]

[tex]=\dfrac{2.5}{4.35}\\\\=\dfrac{250}{435}\\\\=0.5747[/tex]

Hence, the required coefficient of variation= 0.5747

[tex]\huge❥︎\underbrace\mathfrak\red {SoLuTiOn}✈︎[/tex]

1)

[tex] £7 \: of \: £20 \\ \\ \fbox{considering as x} \\ \\ x\%of \: 20 = 7 \\ \\ x\% = \frac{7}{20} \times 100 \\ \\ x\% = \frac{7}{ \cancel{20}} \times \cancel{ 100} \\ \\ x\% = 7 \times 5 \\ \\ x\% = 35\%[/tex]

2)

[tex]28 \: kg \: of \: 40 \: kg \\ \\ \fbox{considering as x} \\ \\ x\% 40 = 28 \\ \\ x\% = \frac{28}{40} \times 100 \\ \\ x\% = \cancel \frac{28}{4 \cancel0} \times 10 \cancel0 \\ \\ x\% = 7 \times 10 \\ \\ x\% = 70\%[/tex]

Answer:

If we have a given number N, and we increase it by x%, then the new number is:

N + (x%/100%)*N

While if we decrease it by x%, the new number will be:

N - (x%/100%)*N

Now, we know that:

"A number increased by a% and decreased by 80% is 400. What is the number?"

First, we can not solve the problem, because we have two unknown values, the original number and the "a%", which I guess is a typo.

So, to be general with my answer, let's assume that the actual question is:

"A number increased by 50% and decreased by 80% is 400. What is the number?"

Then, if our original number is N and we increase it by 50%, the new number will be:

N + N*(50%/100%)

N + N*0.5

N*(1 + 0.5)

N*(1.5)

Now we decrease it by 80%, and that will be equal to 400, then:

N*1.5 - N*(1.5)*(80%/100%) = 400

N*1.5 - N*1.5*0.8 = 400

N*(1.5 - 1.5*0.8) = 400

N*(0.3) = 400

N = 400/0.3 = 1,333.33...

Remember that this is a kinda general solution, so you can understand how to solve this type of problem.

Answer:

D

The missing piece (triangle) is facing right side up but the red triangle has its point facing left

TO get it facing up, turn it by 90 degrees clockwise

Answer:

TU ≅ CB

Step-by-step explanation:

HL Postulates that when a leg and the hypotenuse of a right triangle are congruent to a corresponding leg and hypotenuse of another, then both right triangles are congruent.

Both right triangles shown in the diagram above is indicated to possess corresponding lengths of a leg, that is side UV ≅ side BA

We need an additional information that shows that the hypotenuse, TU, of ∆TUV is congruent to the hypotenuse, CB of ∆CBA.

Therefore, additional information needed is TU ≅ CB

Answer:

128 square feet

Step-by-step explanation:

length of the bottom edge of the wall (a) = 22.5 feet

length of the top edge of the wall (b) = 9.5 feet

height of the wall (h) = 8 feet

then

area of the wall = [(a + b)/2] * h

                         = [ (22.5 + 9.5)/2] * 8 square feet

                          = (32/2) * 8 square feet

                          = 16 * 8 square feet

                          = 128 square feet