An electronic company makes educational apps for 5 subjects including math. The app has 10 versions, with a different avatar in each version. One version has an avatar that looks similar to a lion. The company is randomly giving free apps to its customers. Find the probability of randomly receiving a math app with a lion avatar. How likely is the probability of receiving the app at random?

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

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: 6 and 6

Step-by-step explanation:6x6=36

6+6=12

Answer:

The correct option is;

(Choice B) Both the mean and median will increase, but the mean will increase by more than the median.

Step-by-step explanation:

Here, we are expected to show the differences (advantages/properties) of the mean and median

Note that the definition of the mean is the sum of the value of all data points divided by the number of data points

Assuming the four accountants each earn $ 55,000.00

Therefore, initial mean before getting rd of the part-time accountant is

(55+ 55+ 55 + 55 + 10)/5 = 46

Final mean after the part-time accountant is gone =(55+ 55+ 55 + 55 )/4 = 55

Therefore the mean increases

However, the median is given by the middle value when the list of values are arranged in increasing order as

55, 55, 55, 55, 10

Therefore the initial median is 55

Final median after the part-time accountant is gone is

55, 55, 55, 55

Therefore, final = (55 + 55)/2 = 55

That is the median remains the same that is little or increase.

Therefore, since the range of values for the full time accountants salaries weigh less than the difference between the average full time salary and a single part time, both the mean and the median will increase but the mean will increase more than the median

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

247.3 Ft

Step-by-step explanation:

c=3.14(78.75)

c=247.245 *rounded*

The question was about calculating the circumference of a circle using its diameter. The diameter was given, and the formula for circumference 'C = πd' was used, where 'd' was 78.75 feet and 'π' was approximated at 3.14. The circumference comes out to be approximately 247.35 feet when rounded to the nearest tenth.

The subject in this question is the measurement of the circumference of a cookie given its diameter, a basic concept in geometry in the field of Mathematics. Circumference which is the distance around a circle can be calculated using the formula 'C = πd', where 'C' is the circumference, 'd' is the diameter and 'π' is a constant approximately equal to 3.14.

In this case, the diameter 'd' of the cookie is 78.75 feet. So, by substituting the values into the formula, we get: C = 3.14 * 78.75.

After performing this calculation, you'll find that the approximate circumference of the cookie is 247.35 feet when rounded to the nearest tenth.

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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: 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:

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:

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:

Step-by-step explanation:

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

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

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

Answer:

1 out of 6 for green die and 1 out of 6 for red die

Step-by-step explanation:

As we know there are six numbers on both of the dices

so if we toss a die there is a 1 out of 6 outcomes that a 4 comes out for the green die and 1 out of 6 outcomes again for the red die

The probability that a 4 shows on the green die and a 5 shows on the red die is given by P ( C ) = 1/36

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that a 4 shows on the green die and a 5 shows on the red die be represented as P ( C )

Now , the number of outcomes in a roll of die = { 1 , 2 , 3 , 4 , 5 , 6 } = 6 outcomes

And , probability that a 4 shows on the green die P ( A ) = 1/6

The probability that a 5 shows on a red die P ( B ) = 1/6

Now , it is an independent experiment

So , the compound probability is P ( C ) = P ( A ) . P ( B )

And , the probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = ( 1/6 ) ( 1/6 )

The probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = 1/36

Hence , the probability is P ( C ) = 1/36

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Answer:

22?

Step-by-step explanation:

Just take 40 and subtract the 7 to get 33 and then 2 to get 31 and 9 to get 22.

Answer:

22 more rolls

Step-by-step explanation:

if she needs to sell 40 and she has sold 9+7+2=18 than you subtract 18 from 40 getting 22 more rolls

Answer:

the least common denominator is 4xy

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:

[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:

55/4

Step-by-step explanation:

13 3/4

(13×4 + 3)/4

55/4

Answer:

hope this helps!

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:

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: 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:

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:

4/5

Step-by-step explanation:

cos B = 3/5

cos Ф = adjacent/hypothesis

hypothesis ² = adjacent² + opposite²

5²= 3²+ o²

25 = 9+o²

25-9=o²

16 = o²

√16 = o = 4

Sin B = opposite/hypothesis = 4/5

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.