What is the equation of the vertical asymptote of h(x)=6log4(x−3)−5 ? Enter your answer in the box.

If an average person listens to music for 1,000 hours in a year, the probability that the component lasts for more than 3 years is 2.3%.

In Mathematics and Statistics, the z-score of a given sample size or data set can be calculated by using the following formula:

Z-score, z = (x - μ)/σ

Where:

σ represents the standard deviation.

x represents the sample score.

μ represents the mean score.

Since an average person listens to music for 1,000 hours in a year, the total life span of the component for 3 years can be calculated as follows;

Total life span = 3 × 1000

Total life span = 3000 years.

By substituting the parameters into the z-score formula, we have the following:

Z-score, z = (3000 - 2400)/300

Z-score, z = 2.0

Based on the standardized normal distribution table, the required probability is given by:

P(X > 3000) = P(x > Z)

P(X > 3000) = 1 - P(Z < 2)

P(X > 3000) = 1 - 0.9773

Probability = 0.0227 × 100.

Probability = 2.27 ≈ 2.3%.

Answer:

Rose is 34.

Anne is 14.

Step-by-step explanation:

Let rose be x years age now and anne be y years old now. Then:

x + 6 = 2 (y + 6)

x - 4 = 3(y - 4)

Subtracting:

6 - -4 =  2y + 12 - (3y - 12)

10 = - y + 24

-y = -14

y = 14

Substituting for y:

x + 6 = 2(14+6)

x = 40 - 6 = 34.

Answer:

2a² - 2b - 1

Step-by-step explanation:

Given

- 5 + b + 2a² - 3b + 4 ← collect like terms

= 2a² + (b - 3b) + (- 5 + 4)

= 2a² + (- 2b) + (- 1)

= 2a² - 2b - 1

Answer:

x=-19/3

Step-by-step explanation:

(3x-1)/4=-5

3x-1=-5*4

3x-1=-20

3x=-20+1

3x=-19

x=-19/3

Answer:

Step-by-step explanation:

3x-1/4=-5

3x-0.25=-5

3x=-5.25

x=-1.75

Answer:

[tex]y=-4x+5[/tex]

Step-by-step explanation:

Step 1:  Find the slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{13-5}{-2-0}[/tex]

[tex]m=-\frac{8}{2}[/tex]

[tex]m=-4[/tex]

Step 2:  Use point slope form

[tex](y-5) = -4(x-0)[/tex]

[tex]y-5 + 5=-4x + 5[/tex]

[tex]y=-4x+5[/tex]

Answer:  [tex]y=-4x+5[/tex]

y=-4x+5

Step-by-step explanation:

Step 1:  Find the slope

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{13-5}{-2-0}

m=-\frac{8}{2}

m=-4

Step 2:  Use point slope form

(y-5) = -4(x-0)

y-5 + 5=-4x + 5

y=-4x+5

Answer:

56.3 in²

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

area ratio = a² : b²

Here linear ratio = 4 : 3, thus

area ratio = 4² : 3² = 16 : 9

Let x be the surface area of the smaller can then by proportion

[tex]\frac{16}{100}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )

16x = 900 ( divide both sides by 16 )

x ≈ 56.3 in² ( to the nearest tenth )

The surface area of the smaller can is approximately 56.3 square inches.

The student's question involves finding the surface area of a smaller can based on its similarity ratio to a larger can. Given that the ratio of the corresponding linear measures of two similar cans is 4:3 and the larger can has a surface area of 100 square inches, we can determine the surface area of the smaller can by using the square of the ratio between their sizes. Since the ratio of their surface areas is the square of their linear dimensions ratio, we can set up the calculation as follows:

[tex](3/4)^2 = x/100,[/tex]

where x represents the surface area of the smaller can. Solving for x:

[tex](3/4)^2 = (9/16) = x/100,[/tex]

x = (9/16) * 100,

x = 56.25.

Therefore, the surface area of the smaller can is approximately 56.3 square inches when rounded to the nearest tenth.

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

[tex]a_n=a+(n-1)d[/tex] , where

The third term means n = 3

∵ [tex]a_3=a+(3-1)d[/tex]

∴ [tex]a_3=a+2d[/tex]

∵ [tex]a_3[/tex] = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ [tex]a_5=a+(5-1)d[/tex]

∴ [tex]a_5=a+4d[/tex]

∵ [tex]a_5[/tex] = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ [tex]a_24=-9+(24-1)(7)[/tex]

∴ [tex]a_24=-9+(23)(7)[/tex]

∴ [tex]a_24=-9+161[/tex]

∴ [tex]a_24=152[/tex]

The 24th term is 152

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Answer:

42÷227=42/227

Step-by-step explanation:

Answer:

0.185

Step-by-step explanation:

Do the long division.

Answer:

3/2

Step-by-step explanation:

(3/4)/(1/2)=(3/4)(2/1)=6/4=3/2

Answer: in decimal form it is 0.375

Step-by-step explanation:

Exponential functions are something like y = 2^x where the variable is in the exponent (ie the exponent isnt a fixed number). What is given here, y = 3x^3, is a cubic function. You can also call this a power function. Power functions are of the form a*x^b, where a & b are constants.

Answer:

7/10

Step-by-step explanation:

3/10+2/5=3/10+4/10=7/10

Answer: 7/10

Step-by-step explanation: To add these two fractions together, we start by finding their common denominator.

The common denominator for 10 and 5 will be the least common multiple of 10 and 5 which is 10.

Since 10 already has a 10 in the denominator, it stays the same.

We multiply top and bottom of our second fraction by 2 and we get 4/10.

Now we are adding like fractions so we simply add across the numerators and keep the same denominator.

So, 3/10 + 4/10 = 7/10.

Therefore, 3/10 + 2/5 = 7/10.

Answer: 31

Step-by-step explanation: A coefficient is a number that appears in front of a variable. So in this case, since 31 appears in front of the variable y, 31 is the coefficient.

Now, you might think that 7 is a coefficient also but it's not. The reason it's not is because it doesn't have a variable attached to it so a coefficient needs to have a variable next to it.

Answer:

y+1=2(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=2(x-(-3))

y+1=2(x+3)

Answer: b= -3

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

(-1)^2=(-1)(-1)=1

2(1)(3)=2*3=6

2x*2y

Replace x with -1 and y with 3

2(-1) * 2(3)

2*-1 = -2

2*3=6

Now multiply -2 with 6 and it should be -12.

Answer:

13 trails

Step-by-step explanation:

The histogram shows following numbers of trails:

So, there are 5 trails with length less than 6 km and 4 + 1 + 3 = 8 trails that are at least 24 km long.

In total, 5 + 8 = 13 trails

Answer:

m = 0.75

Step-by-step explanation:

Since (m, 2m + 1 ) is a solution of the equation then substituting the values into the equation will make it true, that is

substitute x = m and y = 2m + 1 into the equation, thus

4m + 2(2m + 1) = 8 ← distribute and simplify left side

4m + 4m + 2 = 8

8m + 2 = 8 ( subtract 2 from both sides )

8m = 6 ( divide both sides by 8 )

m = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75

Answer:

13/20 of her money was spent.

Step-by-step explanation:

To find the answer you have to add these two fractions together, and to do that you must find a common denominator.

For this problem I chose to use 20 for the denominator since it is the smallest number that both 4 and 5 have in common.

Keep in mind that, whatever you do to the denominator, you must also do to the numerator, so if you multiply 5 by 4, you must also multiply 2 by 4.

5/20 + 8/20 = 13/20

Answer:

The lateral Area of a cube [tex]= 17.64in^{2}[/tex]

Step-by-step explanation:

In Mathematics Geometry, the lateral surface of a solid object like cube would be the face of the sold on its side, excluding base. Meaning, any surface, apart from base, would be included to determine the lateral surface of the solid.

A cube has six sides - also called faces.

A cube has a base i.e. the bottom side of the cube, and an ant-bottom base i.e. the top side of the cube.

So, lateral area of a cube would exclude both bottom side base and anti-bottom side base. In other words, it is the area of all the sides of the object, excluding the area of its base and top.

Hence, lateral area of a cube is the square of all the remaining four sides of the object, excluding the area of its base and top.

Hence, the lateral area of a cube can be calculated by the formula:

Lateral Area of a cube [tex]= 4s^{2}[/tex], where s is the length of one edge.

So,

As the given length of edge = s = 2.1

So,

lateral Area of a cube [tex]= 4s^{2}[/tex]

                                     [tex]= 4(2.1)^{2}[/tex]

                                     [tex]= 17.64in^{2}[/tex]

Keywords: cube, lateral area

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Answer:

The system has no solutions

Step-by-step explanation:

we have

[tex]4x-5y=5[/tex] -----> equation A

[tex]-0.08x+0.10y=0.10[/tex] ----> equation B

Isolate the variable y in the equation A

[tex]5y=4x-5[/tex]

[tex]y=\frac{4}{5}x-1[/tex]

[tex]y=0.8x-1[/tex] -----> equation A'

Isolate the variable y in equation B

[tex]0.10y=0.08x+0.10[/tex]

[tex]y=\frac{0.08}{0.10}x+1[/tex]

[tex]y=0.8x+1[/tex] ------> equation B'

Compare the equations A' and B'

The lines have the same slope but different y-intercept

Are parallel lines

therefore

The system has no solutions

Answer:

A. no solutions

Step-by-step explanation:

100% on edge

The value of x is 58°

Step-by-step explanation:

we can see in the figure that the triangle formed is a right-angled triangle

In a right-angled triangle, one angle is always 90 degrees and the other two angles are complementary i.e. their sum is 90 degrees

So,

Using the axiom

[tex]32 + x = 90\\x = 90-32\\x = 58[/tex]

Hence,

The value of x is 58°

Keywords: Triangles, angles

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Answer:

[tex]y-2=-5(x - 2)[/tex]

Step-by-step explanation:

Given:

The equations given are:

[tex]y-2=-5(x - 2)\\X+ 7 = -4(X + 8)\\y - 3 = y(x + 4)\\y + 9 = x(x - 1)[/tex]

Now, a linear function is of the form:

[tex]y=mx+b[/tex]

Where, 'm' and 'b' are real numbers and [tex]m\ne0[/tex]

Equation 1: [tex]y-2=-5(x - 2)[/tex]

Simplifying using distributive property, we get:

[tex]y-2=-5x+10\\y=-5x+10+2\\y=-5x+12[/tex]

The above equation is of the form [tex]y=mx+b[/tex]. So, it represents a linear function.

Equation 2: [tex]X+ 7 = -4(X + 8)[/tex]

Here, both sides of the equation has same variable 'X'. So, it will form an equation of 1 variable. So, it's not a linear function.

Equation 3: [tex]y - 3 = y(x + 4)[/tex]

Simplifying the above equation. This gives,

[tex]y-3=yx+4y\\y-4y-yx=3\\y(1-4-x)=3\\y(-3-x)=3\\y=\frac{3}{(-3-x)}[/tex]

This is not of the form of the linear function. So, it is also not a linear function.

Equation 4: [tex]y + 9 = x(x - 1)[/tex]

Simplifying the above equation. This gives,

[tex]y+9=x^2-x\\y=x^2-x-9[/tex]

This is not of the form of the linear function. So, it is also not a linear function.

Answer:

A

Step-by-step explanation:

on edge 2020

Answer: 34

Step-by-step explanation:

The average rate of change of f(x)= x³-9x in interval [1,6] is 34.

If f(x) is a function the [a,b] is interval then the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Given the function is f(x)= x³-9x and the interval is [1,6].

then first we have to find the value of f(1) and f(6).

So  

f(1) = (1)³-9(1)

    = 1-9

    = -8

and

f(6) = (6)³-9(6)

    = 216- 54

    = 162

therefore average rate of change of f is

[tex]\frac{f(6)-f(1)}{6-1}= \frac{162+8}{6-1}[/tex]

              = 170/5

              = 34

Hence the average rate of change of f is 34.

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Answer:

[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]

Step-by-step explanation:

We begin with the integral [tex]\int{sin^2(x)cos(3x)} \, dx[/tex]

First, we can apply the power reducing formula to [tex]sin^2(x)[/tex]

This formula states: [tex]sin^2(x)=\frac{1}{2} -\frac{1}{2} cos(2x)[/tex]

This gives us

[tex]\int{(\frac{1}{2} -\frac{1}{2} cos(2x))(cos(3x)} \, dx \\\\\int{(\frac{1}{2}cos(3x) -(\frac{1}{2} cos(2x)cos(3x)} \, dx \\\\\frac{1}{2} \int{cos(3x)} \, dx -\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]

Now, we can use integrate the first integral

[tex]\frac{1}{2} \int{cos(3x)} \, dx\\u=3x\\du=3dx\\\\\frac{1}{6} \int{3cos(u)} \, du\\\\\frac{1}{6} sin(u)+C\\\\\frac{1}{6} sin(3x)+C[/tex]

And now we can begin to integrate the second

[tex]-\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]

To integrate this, we need to use the Product-to-sum formula, which states

[tex]cos(\alpha )cos(\beta )=\frac{1}{2} [cos(\alpha +\beta )+cos(\alpha -\beta )[/tex] . For this formula, we will use [tex]\alpha =3x\\\beta =2x[/tex]

This gives us

[tex]-\frac{1}{2} \int{\frac{1}{2}[cos(5x)+cos(x)] } \, dx \\\\-\frac{1}{4} \int{[cos(5x)+cos(x)] } \, dx\\\\-\frac{1}{4}\int{cos(5x)} \, dx -\frac{1}{4}\int{cos(x)} \, dx[/tex]

We can then use the same process of u-substitution as the previous to get the answer of [tex]-\frac{1}{20} sin(5x)-\frac{1}{4} sin(x)+C[/tex]

Lastly, we can add the values of the two integrals together to give us the final solution of

[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]

Answer:

l-5l < l-6l

Step-by-step explanation:

the absolute will remove the negative of both numbers

Answer: |−5| < |−6|

Step-by-step explanation:

The function of the absolute symbol is to cancel out negative , considering the values one after the other.

/ - 6/ < 5  is the same as 6 < 5 ....... this is not true

(ii) /-6/ < /5/ is the same as 6 < 5 ..... this is not true

(iii) /-5/ < / -6/ is the same as 5 < 6 ...... this is true

(iv) /-5/ < -6 is the same as 5 < -6 ..... this is not true

Answer:

The are certain things that need to be carefully observed when you add or combine the polynomials. Here is the list of certain rules for adding/combining polynomials.

Step-by-step explanation:

The are certain things that need to be carefully observed when you add or combine the polynomials - especially the polynomials with more than one variable.

Here are some of the rules for adding polynomials:

Lets add and simplify the following polynomials.

(4x + 7y) + (5x – 3y)

4x + 7y + 5x – 3y

4x + 5x + 7y - 3y

9x + 4y

So, 9x + 4y is the answer.

Note: I can not further combine or add 9x + 4y as they are un-like. The reason is simple; un-like polynomials have different variables.

The polynomials can be add vertically too.

Here is the vertical method of adding (4x + 7y) and (5x – 3y) .

4x    +7y

5x     -3y

________

9x + 4y

________

Keywords: add, combine, polynomials

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Answer:

Step-by-step explanation:

If we are looking for the composition of f(g(7)), we will start at the innermost part of the problem, which is to evaluate g(7).  That means that we put 7 in for x in the g function and come up with a solution to that first.

If g(x) = x - 3, then g(7) = 7 - 3 which is 4.  Now take that 4 and put it in for x in the f function:

f(4) = [tex](4)^2+4[/tex] which is 16 + 4 which is 20

Therefore, f(g(7)) = 20

Answer:

If we are looking for the composition of f(g(7)), we will start at the innermost part of the problem, which is to evaluate g(7).  That means that we put 7 in for x in the g function and come up with a solution to that first.

If g(x) = x - 3, then g(7) = 7 - 3 which is 4.  Now take that 4 and put it in for x in the f function:

f(4) =  which is 16 + 4 which is 20

Therefore, f(g(7)) = 20

Step-by-step explanation:

Answer:

length = x + 5

Step-by-step explanation:

Given

area = x² + 8x + 15 and area = length × width

We require to factorise x² + 8x + 15

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are + 5 and + 3, since

5 × 3 = 15 and 5 + 3 = 8, thus

x² + 8x + 15 = (x + 5)(x + 3)

x + 3 is the width, thus x + 5 is the length

Answer:

perimeter of the shaded region = 88 +44+28 =160 cm

Step-by-step explanation:

perimeter of shaded region = length AO + arc OB + arc AB

length AO = radius of bigger circle

radius of bigger circle = OX + OB = 2×radius of smaller circle = 2×14 cm = 28 cm

therefore AO = 28 cm

length of arc oB= half of circumference of smaller circle = [tex]\pi[/tex]×14 = 44 cm

length of arc ab = half of circumference of bigger circle  = [tex]\pi[/tex]×28 =[tex]\frac{22}{7}[/tex]×28= 88

therefore perimeter of the shaded region = 88 +44+28 =160 cm

area of the shaded region = half of area of bigger circle - half of area of smaller circle

                                           =[tex]\frac{1}{2} \pi 28^{2} -\frac{1}{2} \pi 14^{2}[/tex]

                                           =[tex]\frac{\pi }{2} (28^{2} -14^{2} )[/tex]

  solving we gen area of shaded region = 924

Answer:

The speed of slower car is 55 miles per hour.

Step-by-step explanation:

Given as :

The speed of slower car = [tex]s_2[/tex] = s  mph

The speed of faster car = [tex]s_1[/tex] = ( s + 20 ) mph

The distance cover by slower car = [tex]d_2[/tex] = 165 miles

The distance cover by faster car = [tex]d_1[/tex] = 225 miles

The time taken by both cars for travelling = t hours

The speed of the cars remains constant

Now, According to question

∵ Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]

So, For slower car

t = [tex]\dfrac{d_2}{s_2}[/tex]

Or, t = [tex]\dfrac{165}{s}[/tex]           ............1

So, For faster car

t = [tex]\dfrac{d_1}{s_1}[/tex]

Or, t = [tex]\dfrac{225}{s+20}[/tex]           ............2

Now, equating both the equations

I.e  [tex]\dfrac{225}{s+20}[/tex] = [tex]\dfrac{165}{s}[/tex]  

By cross multiplying

Or, 225 × s = 165 × (s + 20)

Or, 225 s = 165 s + 3300

Or, 225 s - 165 s = 3300

Or, 60 s = 3300

∴  s = [tex]\dfrac{3300}{60}[/tex]

I.e s = 55 miles per hour

So , The speed of slower car = [tex]s_2[/tex] = s = 55 miles per hour

Hence , The speed of slower car is 55 miles per hour.  Answer