What the answer fast

Answer:

  [tex]\boxed{2144}[/tex]

Step-by-step explanation:

The sum can be found by adding the parts:

  [tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]

__

The sum of numbers 1 to n is n(n+1)/2.

Answer:

1/2

Step-by-step explanation:

The probability of taking a yellow ball can be found by dividing the number of yellow balls over the total number of balls.

P(yellow ball)= yellow balls / total balls

There are 10 yellow balls. There are a total of 20 balls. There are 20 because there are 10 yellow, 5 orange, and 5 green. When 10, 5, and 5 are added, the result is 20.

yellow balls = 10

total balls= 20

P(yellow ball)= yellow balls / total balls

P(yellow ball)= 10/20

The fraction 10/20 can be simplified. Both the numerator( top number) and denominator (bottom number) can be evenly divided by 10.

P(yellow ball)= (10/10) / (20/10)

P(yellow ball)= 1/(20/10)

P(yellow ball)= 1/2

The probability of taking a yellow ball is 1/2.

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.

Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.

Answer:

A).   AC ≅ AE

Step-by-step explanation: took test on edge

Answer:

It is necessary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator.

Step-by-step explanation:

for example the denominator of the two addends are not the same. One has (x+2), the other (x-2).

Answer: She can select 7 workshops if more than 4 must be about anthropology in 1716 ways.

Step-by-step explanation:

Given, The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology.

If he select 7 workshops if more than 4 must be about anthropology, the possible combinations = (5 anthropology, 2 psychology), (  6 anthropology, 1 psychology), (7 anthropology, 0 psychology)

Number of possible combinations = [tex]^9C_5\times ^5C_2+^9C_6\times ^5C_1+^9C_7\times ^5C_0[/tex]

[tex]=\dfrac{9!}{5!4!}\times\dfrac{5!}{2!3!}+\dfrac{9!}{6!3!}\times(5)+\dfrac{9!}{7!2!}\times (1)\\\\=\dfrac{9\times8\times7\times6}{4\times3\times2\times1}\times\dfrac{5\times4}{2}+\dfrac{9\times8\times7}{3\times2\times1}\times5+\dfrac{9\times8}{2}\\\\=1260+420+36\\\\=1716[/tex]  [using formula for combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]

Hence, she can select 7 workshops if more than 4 must be about anthropology in 1716 ways.

Step-by-step explanation:

Hello there!!

no need to be panic we will help you, alright.

look solution in picture ok...

sorry for cutting in middle.

Hope it helps...

Answer:

Step-by-step explanation:

When the input is 4, the output of f(x) = x + 21 is f(4).

Substitute x = 4 to f(x):

f(4) = 4 + 21 = 25

Answer:

25

Step-by-step explanation:

We can find the output by plugging in 4 as x into the function:

f(x) = x + 21

f(4) = 4 + 21

f(4) = 25

Answer:

{ } or empty set.

Step-by-step explanation:

The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.

Hope this helps!

Answer:

{ } or empty set

Step-by-step explanation:

It's because these lines are parallel so they don't intersect to give you a coordinate.

Answer: 52%

Step-by-step explanation:

Let the original price be 100.

After 40% reduction, price will be 100 - 40% = 60

After further 20% reduction, price will be 60 - 20% = 48

%age = (cur val - orig. val ) / orig val x 100

= (48 - 100) / 100 x 100%

= -52

The actual percentage of reduction is 52%

The first reduction is given as:

[tex]r_1 = 40\%[/tex]

The second reduction is given as:

[tex]r_2 = 20\%[/tex]

Assume that the original price of the item is x.

After the first reduction of 40%, the new price would be:

[tex]New = x\times (1 -r_1)[/tex]

So, we have:

[tex]New = x\times (1 -40\%)[/tex]

[tex]New = x\times 0.6[/tex]

[tex]New = 0.6x[/tex]

After the second reduction of 20% on the reduced price, the new price would be:

[tex]New = 0.6x\times (1 -r_2)[/tex]

So, we have:

[tex]New = 0.6x\times (1 -20\%)[/tex]

[tex]New = 0.6x\times 0.8[/tex]

[tex]New = 0.48x[/tex]

Recall that the original price is x.

So, the actual reduction is:

[tex]Actual = \frac{x - 0.48x}{x}[/tex]

[tex]Actual = \frac{0.52x}{x}[/tex]

Divide

[tex]Actual = 0.52[/tex]

Express as percentage

[tex]Actual = 52\%[/tex]

Hence, the actual percentage of reduction is 52%

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Answer:

The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.

Step-by-step explanation:

The Newton's method is a numerical method by approximation that help find roots of a equation of the form [tex]f(x) = 0[/tex] with the help of the equation itself and its first derivative. The Newton's formula is:

[tex]x_{i+1} = x_{i} - \frac{f(x_{i})}{f'(x_{i})}[/tex]

Where:

[tex]x_{i}[/tex] - i-th approximation, dimensionless.

[tex]x_{i+1}[/tex] - (i+1)-th approximation, dimensionless.

[tex]f(x_{i})[/tex] - Function evaluated at the i-th approximation, dimensionless.

[tex]f'(x_{i})[/tex] - First derivative of the function evaluated at the i-th approximation, dimensionless.

The function and its first derivative are [tex]f(x) = x^{3}+x+8[/tex] and [tex]f'(x) = 3\cdot x^{2}+1[/tex], respectively. Now, the Newton's formula is expanded:

[tex]x_{i+1} = x_{i}-\frac{x_{i}^{3}+x_{i}+8}{3\cdot x_{i}^{2}+1}[/tex]

If [tex]x_{1} = -1[/tex], the value of [tex]x_{2}[/tex] is:

[tex]x_{2} = -1 - \frac{(-1)^{3}+(-1)+8}{3\cdot (-1)^{2}+1}[/tex]

[tex]x_{2} = -1.5000[/tex]

The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.

Answer:

-2.5000

Step-by-step explanation:

Answer:

[tex]\boxed{\sf A. \ 0.34}[/tex]

Step-by-step explanation:

The first triangle is a right triangle and it has one acute angle of 70 degrees.

We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.

The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.

The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.

[tex]\sf \frac{3.4}{10} =0.34[/tex]

Answer:

-∞<x<∞

Step-by-step explanation:

volume of a cube=s^3

the domain is (-∞,∞) the domain is all the real number of s

Work Shown:

[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\left(\frac{3}{10}\right)^2 + \cos^2 \theta = 1\\\\\frac{9}{100} + \cos^2 \theta = 1\\\\\cos^2 \theta = 1 - \frac{9}{100}\\\\\cos^2 \theta = \frac{100}{100}-\frac{9}{100}\\\\\cos^2 \theta = \frac{91}{100}\\\\\cos \theta = \sqrt{\frac{91}{100}} \ \text{ cosine positive in Q1}\\\\\cos \theta = \frac{\sqrt{91}}{\sqrt{100}}\\\\\cos \theta = \frac{\sqrt{91}}{10}\\\\[/tex]

Answer:

√91/10

Step-by-step explanation:

sin 0.3 is equal to 18(approximate value)

cos18°=0.951

which is √91/10

Answer:

r=$14,400

The hotel should charge $120

Step-by-step explanation:

Revenue (r)= p * n

where,

p = price per item

n = number of items sold

A change in price leads to a change in number sold

A variable to measure the change in p and n needs to be introduced

Let the variable=x

Such that

p + x means a one dollar price increase

p - x means a one dollar price decrease

n + x means a one item number-sold increase

n - x means a one item number-sold decrease

for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)

know that at $60 per room, the hotel rents 210 rooms

r = (60 + 2x) * (210 - 3x)

=12,600-180x+420x-6x^2

=12,600+240x-6x^2

r=2100+40x-x^2

= -x^2 +40x+2100=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a= -1

b=40

c=2100

x= -b +or- √b^2-4ac / 2a

= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)

= -40 +or- √1600-(-8400) / -2

= -40 +or- √ 1600+8400 / -2

= -40 +or- √10,000 / -2

= -40 +or- 100 / -2

x= -40+100/-2 OR -40-100/-2

=60/-2 OR -140/-2

= -30 OR 70

x=70

The quadratic equation has a maximum at x=70

p+2x

=60+2(30)

=60+60

=$120

r= (60 + 2x) * (210 - 3x)

={60+2(30)}*{(210-3(30)}

r=(60+60)*(210-90)

=120*120

=$14,400

Answer:

5

Step-by-step explanation:

We know that we have to add all numbers then divide it by how many numbers there are. So, 10 + 6 + 9 + 2 + 0 + 3 = 30.  30/6 = 5.  

Answer:-95 1/7 feet

Step-by-step explanation:

-120 4/7+25 3/7=-95 1/7 feet

Answer:

x

Step-by-step explanation:

f(x)=2x+5

Input: x

Output: f(x)

For i.e:

Input: 1

Output: f(1) = 2(1) + 5 = 2 + 5 = 7

Answer:

speed=3.33m/s

Step-by-step explanation:

speed= distance÷time

3.33 m/s

length = ?

Answer:

Length  : 50m

Speed   : 5 m  /  s

im sorry if im too late :'(

Answer:

27 in²

Step-by-step explanation:

area of triangle (whole) = 1/2 x base x height

                                       = 1/2 x 10 x 6

                                       = 30 in²

area of small triangle = 1/2 x base x height

                                   = 1/2 x 3 x 2

                                   = 3 in²

area of shaded region = 30 in² - 3 in²

                                     = 27 in²

Answer:

B. 3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Step-by-step explanation:

A B

Bread $3.19 $3.49

Milk $4.59 $4.39

Sue paid $137.24 in supermarket A

Sue paid $140.04 in supermarket B

Let

Price of bread A=$3.19

Price of bread B=$3.49

Price of milk A=$4.59

Price of milk B=$4.39

Quantity of Bread=b

Quantity of Milk=m

Pb=price of bread

Pm=price of milk

Qb=Quantity of bread

Qm=Quantity of milk

For each supermarket

Supermarket A Equation

PbQb + PmQm =$137.24

3.19b+ 4.59m = 137.24

Supermarket B Equation

PbQb + PmQm=$140.04

3.49b + 4.39m = $140.04

Combining both equations

3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Answer:

700✖️0.08=56 people is late

700✖️0.12=84 people bought the shirt.

Step-by-step explanation:

8%=0.08

12%=0.12

700✖️0.08=56 people is late

700✖️0.12=84 people bought the shirt.

HOPE THIS HELPS!

Answer:

18.4°

Step-by-step explanation:

Use law of cosine.

a² = b² + c² − 2bc cos A

11² = 20² + 28² − 2(20)(28) cos A

121 = 1184 − 1120 cos A

cos A = 0.949

A = 18.4°

Answer:

8/5

Step-by-step explanation:

w = k / √x

4 = k / √4

k = 8

w = 8 / √x

w = 8 / √25

w = 8/5

An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent.

Answer:

The person above me is correct ( :

Step-by-step explanation:

B

Answer:

Step-by-step explanation:

Given that :

A web page is accessed at an average of 20 times an hour.

Therefore:

a. he rate parameter λ of the distribution of the time until the first hit = 20

b.  What is the expected time between hits?

Let consider E(Y) to be the expected time between the hits; Then :

E(Y) = 1/λ

E(Y) = 1/20

E(Y) = 0.05 hours

E(Y) = 3 minutes

(c.)  What is the probability that there will be less than 5 hits in the first hour?

Let consider X which follows Poisson Distribution; Then,

P(X<5) [tex]\sim[/tex] G(∝=5,  λ = 20)

For 5 hits ; the expected time will be :

Let 5 hits be X

E(X) = ∝/λ

E(X) = 5/20

E(X) =1/4

E(X) = 0.25 hour

E(X) = 15 minutes

From above ; we will see that  it took 15 minutes to get 5 hits; then

[tex]P(\tau \geq 0.25) = \int\limits^{\alpha}_{0.25} \dfrac{\lambda^{\alpha}}{\ulcorner^{\alpha}} t^{a\pha-1} \ e^{-\lambda t} \, dt[/tex]

[tex]P(\tau \geq 0.25) = \int\limits^{5}_{0.25} \dfrac{20^{5}}{\ulcorner^{5}} t^{5-1} \ e^{-20 t} \, dt[/tex]

[tex]\mathbf{P(\tau \geq 0.25) =0.4405}[/tex]

Answer:

AC2  =  AB2 + BC2     --->     AC2  =  122 + 52     --->   AC  =  13

AD / AB  =  AB / AC     --->     AD / 12  =  12 / 13     --->     AD  =  144/13

DC  =  AC - AD     --->   DC  =  13 - 144/13     --->     DC  =  25/13

AD / DB  =  DB / DC     --->   DB2  =  AD · DC     --->     DB2  =  (144/13) · (25/13)  --->     DB  =  60/13

DB is the geometric mean of AD and DC.

Step-by-step explanation:

Answer:

[tex]x \geq -91/2[/tex]

Step-by-step explanation:

[tex]6(x+8) \geq -43 + 4x[/tex]

Resolving Parenthesis

[tex]6x+48 \geq -43 + 4x[/tex]

Collecting like terms

[tex]6x - 4 x \geq -43-48[/tex]

[tex]2x \geq -91[/tex]

Dividing both sides by 2

[tex]x \geq -91/2[/tex]

Answer:

x ≥ - 91 / 2

Step-by-step explanation:

In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.

Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]

[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,

[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,

[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,

[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.

Answer:

11

Step-by-step explanation:

To do this you would just multiply 9 by 3 so you get 27 and subtract 6+10 which is 16 from it and then you will get 11 and that is what you will need for your third score

The third score which must be added is 11.

The average can be calculated by dividing the sum of observations by the number of observations.

Average = Sum of observations/the number of observations

Given; count = 3 (there are three trials)

average = 9

9 = sum / 3

The sum = first score + second score + third score

The sum   =  6 + 10 + third score

9 = (6+10+third score)/3

Then multiply both sides by 3 to remove the denominator

27 = 6 + 10 + third score

27 = 16 + third score

Now, subtract 16 from both sides to isolate the third score

11 = third score

Hence, the third score which must be added is 11.

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Your integrand is missing some symbols. My best interpretation is the following integral:

[tex]I=\displaystyle\int\frac{x^4+18x^2+4}{x^5+30x^3+20x}\,\mathrm dx[/tex]

Decompose into partial fractions; we're looking for an expansion of the form

[tex]\dfrac{x^4+18x^2+4}{x^5+30x^3+20x}=\dfrac ax+\dfrac{bx^3+cx^2+dx+e}{x^4+30x^2+20}[/tex]

Now:

[tex]x^4+18x^2+4=a(x^4+30x^2+20)+(bx^3+cx^2+dx+e)x[/tex]

[tex]=(a+b)x^4+cx^3+(30a+d)x^2+ex+20a[/tex]

Matching up coefficients tells us that

[tex]\begin{cases}a+b=1\\c=0\\30a+d=18\\e=0\\20a=4\end{cases}\implies a=\dfrac15,b=\dfrac45,d=12[/tex]

so that

[tex]I=\displaystyle\frac15\int\frac{\mathrm dx}x+\frac45\int\frac{x^3+15x}{x^4+30x^2+20}\,\mathrm dx[/tex]

The integral is trivial:

[tex]\displaystyle\frac15\int\frac{\mathrm dx}x=\frac15\ln|x|+C[/tex]

For the second integral, notice that

[tex]\mathrm d(x^4+30x^2+20)=(4x^3+60x)\,\mathrm dx[/tex]

Distribute the 4 over the numerator, then substitute [tex]u=x^4+30x^2+20[/tex] and [tex]\mathrm du=(4x^3+60x)\,\mathrm dx[/tex]:

[tex]\displaystyle\frac15\int\frac{4x^3+60x}{x^4+30x^2+20}\,\mathrm dx=\frac15\int\frac{\mathrm du}u=\frac15\ln|u|+C=\frac15\ln(x^4+30x^2+20)+C[/tex]

So we have

[tex]I=\dfrac15\ln|x|+\dfrac15\ln(x^4+30x^2+20)+C[/tex]

and with some simplification,

[tex]I=\boxed{\ln\sqrt[5]{|x^5+30x^3+20x|}+C}[/tex]

Answer:

d)

Step-by-step explanation:

the general form is ax + by = c