Help Please! Solve this problem without the law of cosines.

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.

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:

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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Answer:

[tex]z = \frac{x}{y} [/tex]

Step-by-step explanation:

Let x be the price of carton of ice cream

Let y be the number of grams in carton

Let z be price per gram.

[tex]z = \frac{x}{y} [/tex]

Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.

Hope this helps ;) ❤❤❤

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:

-∞<x<∞

Step-by-step explanation:

volume of a cube=s^3

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

Answer:

Option A a right tailed hypothesis test

Step-by-step explanation:

A claim given symbolically is most of the time derived from the alternative hypothesis usually tested against the null hypothesis.

A symbolic claim with the option of a less than indicates a left tailed test, while one with the option of greatest than indicate a right tail test and one with the option of both (not equal to; either less or greater) indicates a two tailed test.

In this case study, the sample proportion for the claim was greater than 0.50 thus, the test is a right tailed hypothesis test

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:

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:

[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: 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:

Number of term N = 9

Value of Sum = 0.186

Step-by-step explanation:

From the given information:

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]

here;

m = 5

n = 9

r = 0.5

Then:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]

For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,

the responses are;

(1) The number of terms are 9

(2) The value of the sum is approximately 0.374

The given geometric series is presented as follows;

3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³

(1) The number of terms in the series = 13 - 4 = 9

Therefore;

(2) The value of the sum can be found as follows;

The common ratio, r = 0.5

The sum of the first n terms of a geometric progression is presented as follows;

[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]

The sum of the first 4 terms are therefore;

[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]

The sum of the first 13 terms is found as follows;

[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]

Which gives;

The sum of the 5th to the 13th term = S₁₃ - S₄

Therefore;

[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]

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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:

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:

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:

d)

Step-by-step explanation:

the general form is ax + by = c

Answer:

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Step-by-step explanation:

(i) probability with 16 success out of 24 = 16/24 = 2/3

(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3

Since the two experiments have the same probability, the observed probabilities are the same.

HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.

Using the binomial distribution,

(i)

p = 1/2

N = 24

x = 16 (number of successes)

P(16,24) = C(24,16) p^16* (1-p)^8

= 735471* (1/65536)*(1/256)

= 0.0438

(ii)

p = 1/2

N = 12

x = 8 (number of successes)

P(8,12) = C(12,8) p^8* (1-p)^4

= 495*1/256*1/16

= 0.1208

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Note: It would help to mention the topic you're on so answers will correspond to what is expected.  Here we cover probability and binomial distribution.

Answer:

8/5

Step-by-step explanation:

w = k / √x

4 = k / √4

k = 8

w = 8 / √x

w = 8 / √25

w = 8/5

Answer:

A: True

B, C and D: False

Step-by-step explanation:

We have a total sales tax for Alabama that is:

[tex]T_A=4.225+1.375+3=8.6[/tex]

The total sales tax for Florida is:

[tex]T_F=6.5+1+1.625=9.125[/tex]

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

The sales tax difference in this purchase can be calculated as:

[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).

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:-95 1/7 feet

Step-by-step explanation:

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

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]

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:

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:

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:

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:

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:

  [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:

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:

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: