20 points please help!!

Answer: 8cxs^c= -3 csc (x) +1

Step-by-step explanation:

To solve for c you need to simplify both sides of the equation, then isolating the variable

Answer:

x = - π/2   or x = - π/2 + 2nπ       n = integer

Step-by-step explanation:

4csc²x+3cscx-1=0

(csc x + 1) (4csc x - 1) = 0

csc x = - 1 or csc x = 1/4

1/ sin x = - 1      or 1 / sin x = 1/4

sin x = - 1      or sin x = 4  (x no solution when sin x = 4)

sin x = - 1

x = - π/2   or x = - π/2 + 2nπ       n = integer

Answer:

Probability of selecting a ball from the first ball if it is a blue ball =  = 0.75

Step-by-step explanation:

Number of blue balls in the first box = 3

Number of blue balls in the second box = 1

Total number of blue balls = 3 + 1

Total number of blue balls = 4

Probability = (Number of possible outcomes)/(Number of total outcomes)

Probability of selecting a ball from the first ball if it is a blue ball = 3/4

Probability of selecting a ball from the first ball if it is a blue ball =  = 0.75

There are 3 even numbers out of A total of 8 numbers.

Each spin would have a 3/8 chance of landing in an even number.

Multiply the chance of landing on even by number of spins:

120 x 3/8 = 360/8 = 45

The answer would be 45 times.

Answer:

The amount made in a month with 9 sales people = 334,734.53

Step-by-step explanation:

The amount, Y, made by a sales company in dollars is related to the number of sales people, x, at the company through the relation,

Y = 60,209.47x - 207,150.70

where Y = amount made in dollars

x = number of sales people

when x = 9, what is Y.

Y = 60,209.47x - 207,150.70

Y = (60,209.47×9) - 207,150.70

Y = 541,885.23 - 207,150.70

Y = 334,734.53

Hope this Helps!!!

Answer: I think it's 50.2 but I might be wrong

Answer:

We can use the sample about 42 days.

Step-by-step explanation:

Decay Equation:

[tex]\frac{dN}{dt}\propto -N[/tex]

[tex]\Rightarrow \frac{dN}{dt} =-\lambda N[/tex]

[tex]\Rightarrow \frac{dN}{N} =-\lambda dt[/tex]

Integrating both sides

[tex]\int \frac{dN}{N} =\int\lambda dt[/tex]

[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]

When t=0, N=[tex]N_0[/tex] = initial amount

[tex]\Rightarrow ln|N_0|=-\lambda .0+c[/tex]

[tex]\Rightarrow c= ln|N_0|[/tex]

[tex]\therefore ln|N|=-\lambda t+ln|N_0|[/tex]

[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex].......(1)

                            [tex]\frac{N}{N_0}=e^{-\lambda t}[/tex].........(2)

Logarithm:

130 days is the half-life of the given radioactive element.

For half life,

[tex]N=\frac12 N_0[/tex],  [tex]t=t_\frac12=130[/tex] days.

we plug all values in equation (1)

[tex]ln|\frac{\frac12N_0}{N_0}|=-\lambda \times 130[/tex]

[tex]\rightarrow ln|\frac{\frac12}{1}|=-\lambda \times 130[/tex]

[tex]\rightarrow ln|1|-ln|2|-ln|1|=-\lambda \times 130[/tex]

[tex]\rightarrow -ln|2|=-\lambda \times 130[/tex]

[tex]\rightarrow \lambda= \frac{-ln|2|}{-130}[/tex]

[tex]\rightarrow \lambda= \frac{ln|2|}{130}[/tex]

We need to find the time when the sample remains 80% of its original.

[tex]N=\frac{80}{100}N_0[/tex]

[tex]\therefore ln|{\frac{\frac {80}{100}N_0}{N_0}|=-\frac{ln2}{130}t[/tex]

[tex]\Rightarrow ln|{{\frac {80}{100}|=-\frac{ln2}{130}t[/tex]

[tex]\Rightarrow ln|{{ {80}|-ln|{100}|=-\frac{ln2}{130}t[/tex]

[tex]\Rightarrow t=\frac{ln|80|-ln|100|}{-\frac{ln|2|}{130}}[/tex]

[tex]\Rightarrow t=\frac{(ln|80|-ln|100|)\times 130}{-{ln|2|}}[/tex]

[tex]\Rightarrow t\approx 42[/tex]

We can use the sample about 42 days.

Final answer:

The radioactive sample can be used for approximately 390 days.

Explanation:

The half-life of a radioactive element is the time it takes for half of the radioactive nuclei to decay. In this case, the half-life is 130 days. The sample is considered no longer useful when 80% of the nuclei have decayed. To determine how many days the sample can be used, we need to find the number of half-lives it takes for 80% of the nuclei to decay.

80% is the same as 0.8, which means 20% (or 0.2) of the nuclei remain. Each half-life reduces the amount of nuclei by half, so we can set up an equation:

0.2 = (1/2)^n

where n is the number of half-lives.

To solve for n, we can take the logarithm of both sides:

n = log_base(1/2)(0.2)

Using a calculator, we find n ≈ 2.737.

Since we can't have a fraction of a half-life, we round up to the nearest whole number, which gives us n = 3.

Now, we can find the number of days by multiplying the half-life by the number of half-lives:

Number of days = 130 days * 3 = 390 days.

Therefore, the sample can be used for approximately 390 days.

Answer:

Step-by-step explanation:

sin(-295°)=-sin (295)=-sin (360-65)=-(-sin 65°)=sin (65°)

Answer: the third answer. Explanation below.

Step-by-step explanation:

The first passage shows Antigone as a rebel because she chooses to defy the State. The second passage shows Boadicea as a warrior because she "herself led the soldiers, encouraging them with her brave words."

Antigone and Boadicea are presented with different archetypal roles across the passages; Antigone as a warrior, tragic heroine, rebel, and villain; and Boadicea as a tragic heroine, sage, warrior, and sage again.

The archetypes presented in these passages are different in the roles and characteristics assigned to Antigone and Boadicea. In the first set of passages, Antigone is depicted as a warrior, then as a tragic heroine, next as a rebel, and lastly as a villain. Conversely, Boadicea is presented as a tragic heroine, followed by a sage, then as a warrior, and finally as a sage once again. These variations represent unique depictions of these mythical figures, giving us different lenses to interpret their actions and significance within their respective narratives.

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Answer:

third graph

Step-by-step explanation:

Answer:

the least common denominator is 4xy

Answer: The answer is B. 1.0

Step-by-step explanation:

That’s the closest mean

Answer:

A is 15.27 and B is 12.05

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

1 box is 5 x 5 which=25 x 6 boxes=150

150 squared is your answer

Answer: 150

Step-by-step explanation:

The side of one cube is 5. 5 * 5 = 25 So 25 is the surface area of one cube side. A cube a 6 sides, and 25 * 6 = 150. Therefore, 150 is the surface area of the cube.

Answer:

The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.

The radius of the right circular cone when constructed this way is [tex]\sqrt6[/tex] cm.

The volume of the right circular cone when constructed this way is [tex]6\sqrt3 \pi[/tex] cm³.

Step-by-step explanation:

Given that,

A right triangle whose hypotenuse is 3 cm long is revolved .

Then other two legs of the triangle will be radius and height of the cone.

Assume the height and radius of the cone be h and r respectively.

From Pythagorean Theorem :

h²+r²=3²

⇒ r²= 9 - h²

Then the volume of the cone is

V= π r²h

⇒ V= π(9-h²)h                [ ∵ r²= 9 - h²]

⇒V= π(9h - h³)

Differentiating with respect to h

V'=π(9 - 3h²)

Again differentiating with respect to h

V''= π(-6h)

⇒V''= (-6πh)

To maximum or minimum ,we set V'=0

π(9 - 3h²)=0

⇒3h²=9

⇒h²=3

[tex]\Rightarrow h=\sqrt3[/tex]

Now, [tex]V''|_{h=\sqrt3}=-6\pi (\sqrt3)<0[/tex].

Since at [tex]h=\sqrt3[/tex],V''<0.

The volume of cone is maximum at [tex]h=\sqrt3[/tex] cm when constructed this way.

The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.

The radius of the right circular cone when constructed this way  [tex]r=\sqrt{9-(\sqrt3)^2[/tex]

   =  [tex]\sqrt{9-3}[/tex]

   [tex]=\sqrt6[/tex] cm.

The volume of the  right circular cone when constructed this way is

=π r²h

[tex]=\pi (\sqrt6)^2\sqrt3[/tex]

[tex]=6\sqrt3 \pi[/tex] cm³

Answer:

orthogonal

Step-by-step explanation:

If the dot product of the two vectors is 0, then they must be orthogonal.

[tex]u*v=9(0)-9(0) = 0[/tex]

Answer: c

Step-by-step explanation: edge 2021

Answer:

1/6 chance

Step-by-step explanation:

10+5+3+3+3+6=30 draws

out of 30 draws 5 blue

5/30 reduced is 1/6.

Final answer:

The given system of equations has one unique solution because the lines represented by the equations have different slopes, hence they intersect at exactly one point.

Explanation:

To answer how many solutions there are for the given system of equations:

6y=12x+36
15y=45x+60 (Assuming the '+60' was meant instead of '60', as '+60' makes it a linear equation)

We first simplify both equations to determine if they are identical, parallel, or intersecting.

For the first equation, we divide by 6:

y = 2x + 6

For the second equation, assuming a typo and it should be '+60', we divide by 15:

y = 3x + 4

Since the slopes (2 and 3) are different, the lines are not parallel and will intersect at exactly one point. Therefore, there is one unique solution to this system.

Answer:

22.9 miles

Step-by-step explanation:

We are given that

Acceleration=Deceleration=a=[tex]4ft/s^2[/tex]

Maximum cruising speed,v=[tex]90mi/h=90\times \frac{5280}{3600}=132ft/s[/tex]

1 hour=3600 s

1 mile=5280 feet

Time,t=15 minutes=[tex]15\times 60=900 s[/tex]

1 min=60 s

Initial speed,u=0

[tex]v=u+at[/tex]

Substitute the values

[tex]132=0+4t[/tex]

[tex]t=\frac{132}{4}=33 s[/tex]

[tex]s=u+\frac{1}{2}at^2=0+\frac{1}{2}(4)(33)^2=2178 ft[/tex]

Distance,d=[tex]speed\times time=vt=132\times 900=118800ft[/tex]

Total distance=s+d=2178+118800=120978ft

Total distance=[tex]\frac{120978}{5280}=22.9miles[/tex]

Hence, the maximum distance traveled by train =22.9 miles

Answer:

[tex]F(t) = 18000(0.6666)^{t}[/tex]

Step-by-step explanation:

The fish population after t years can be modeled by the following equation:

[tex]F(t) = F(0)(1-r)^{t}[/tex]

In which F(0) is the initial population and r is the constant rate of decay.

Year one the fish population was 18000

This means that [tex]F(0) = 18000[/tex]

In year three the fish population was 8000 fish.

Two years later, so [tex]F(2) = 8000[/tex]

[tex]F(t) = F(0)(1-r)^{t}[/tex]

[tex]8000 = 18000(1-r)^{2}[/tex]

[tex](1-r)^{2} = 0.4444[/tex]

[tex]\sqrt{(1-r)^{2}} = \sqrt{0.4444}[/tex]

[tex]1 - r = 0.6666[/tex]

[tex]r = 0.3334[/tex]

So

[tex]F(t) = 18000(0.6666)^{t}[/tex]

Answer:

The height of the cross section if 2 feet

Step-by-step explanation:

To solve this problem recall the formula for the area of a trapezoid of bases B (larger base) and b (smaller base) and height H:

[tex]Area = \frac{(B+b)\,H}{2}[/tex]

Therefore, for our case we have:

[tex]Area = \frac{(B+b)\,H}{2}\\34 \,ft^2 = \frac{(28\,ft+6\,ft)\,H}{2}\\34 \,ft^2 = \frac{(34 \,ft)\,H}{2}[/tex]

So, now we can solve for the height H:

[tex]34 \,ft^2 = \frac{(34 \,ft)\,H}{2}\\2\,*\,34 \,ft^2 =34\,ft\,* H\\H=\frac{2\,*\,34 \,ft^2}{34\,ft}\\ H=2\,ft[/tex]

Answer:

The answer to your question is     (3, -6)

Step-by-step explanation:

Data

           x  -  2y  =  15                  Equation l

         2x +  4y  = -18                  Equation ll

Solve the system of equations by elimination

-Multiply equation l by 2

         2x  -  4y  =  30

         2x  + 4y  = -18

         4x   + 0    = 12

                    4x = 12

                      x = 12/4

                      x = 3

-Substitute x in equation l

          3  -  2y = 15

-Solve for y

               -2y = 15 - 3

               - 2y = 12

                   y = 12/-2

                   y = -6

-Solution

              (3, -6)

Answer:

C.  x = 3, y = -6

Step-by-step explanation

Answer is correct from Plato

Answer:

a) The antibiotic is made with a greater initial amount of active ingredient

b) The two medications will have the same amount of active ingredients in the blood stream at exactly 8 hours after first taking the medication.

Step-by-step explanation

Active ingredient of Nasal spray left in the bloodstream is modelled as

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

Active ingredient of Antibiotic left in the bloodstream is modelled as

a(t) = 9/(t+3)

with t in hours.

a) At the instance of usage, the active ingredient for both drugs are at their initial concentration as they appear in the drugs.

So, we find the amount of active ingredient for each drug in the bloodstream at t=0 and compare.

For nasal spray,

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

At t = 0

n(0) = (1/5) + (18/15) = 1.4

For antibiotics,

a(t) = 9/(t+3)

At t=0

a(0) = (9/3) = 3

3 > 1.4

Hence, the antibiotic is made with a greater initial amount of active ingredient.

b) when both medications will have the same amount of active ingredients in the bloodstream, n(t) = a(t)

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

a(t) = 9/(t+3)

Note that (t² + 8t + 15) = (t + 3)(t + 5)

When n(t) = a(t)

((t + 1)/(t + 5)) + (18/(t² + 8t + 15)) = 9/(t+3)

Multiplying through by (t² + 8t + 15) or more properly written as (t + 3)(t + 5)

(t+1)(t+3) + 18 = 9(t+5)

t² + 4t + 3 + 18 = 9t + 45

t² - 5t - 24 = 0

Solving the quadratic equation

t = 8 or t = -3

Time can't be negative, hence, t = 8 hours.

Hope this Helps!!!

Answer: 6 and 6

Step-by-step explanation:6x6=36

6+6=12

Answer:

Step-by-step explanation:

Answer:15

Step-by-step explanation:

I’m on USA test prep

In a triangle, the midsegment is always half the length of the base. Given that the length of AC is 30, the midsegment DE will be half of this which is 15. Thus, the answer is B) 15.

In geometry, a midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle. For every triangle, the length of the midsegment is always half the length of the base of the triangle.

From your question, the length of AC (which is the base of the triangle) is 30. Therefore, the length of the midsegment DE would be half of 30, which is 15.

So the answer to your question is: B) 15.

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Answer:

22/100 or 0.22 or 22%

Step-by-step explanation:

Out of the 50 times you drew a marble, you got 11 blue ones.

11/50

We can divide 11/50 and get 0.22, which is the same as 22/100 or 22%.

Hope this helps! ;-)

The required probability is,

[tex]P(B)=\frac{11}{50} [/tex]

The total number f marbles are 50

Now, the formula for finding the experimental probability is,

P(B)=Possible outcomes/ Number of outcomes

[tex]P(B)=\frac{11}{50} [/tex]

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After simplifying [tex]\(\frac{{21^x}}{{7^x}}\)[/tex], we find it equivalent to [tex]\(3^x\)[/tex], confirming options a, b, and f as correct.

To simplify the expression [tex]\(\frac{{21^x}}{{7^x}}\)[/tex], we can use the property of exponents which states that [tex]\(a^m/a^n = a^{m-n}\)[/tex]. Applying this property, we get:

[tex]\[\frac{{21^x}}{{7^x}} = \frac{{(7 \cdot 3)^x}}{{7^x}} = \frac{{7^x \cdot 3^x}}{{7^x}} = 3^x\][/tex]

So, the simplified expression is [tex]\(3^x\).[/tex]

Now, let's check each option:

a. [tex]\(\frac{{7^x \cdot 3^x}}{{7^x}} = 3^x\)[/tex]. This expression is equivalent to the simplified form.

b. [tex]\((\frac{{21}}{{7}})^x = 3^x\)[/tex]. This expression is equivalent to the simplified form.

c. [tex]\(3\)[/tex]. This expression is not equivalent to the simplified form.

d. [tex]\((21 - 7)^x = 14^x\)[/tex]. This expression is not equivalent to the simplified form.

e. [tex]\(3^{x-7}\)[/tex]. This expression is not equivalent to the simplified form.

f. [tex]\(3^x\)[/tex]. This expression is equivalent to the simplified form.

Therefore, the expressions equivalent to [tex]\(\frac{{21^x}}{{7^x}}\)[/tex] are options a, b, and f.

The question probable maybe:

Given in the attachment