The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31
hours and the median is 27.2
hours. Twenty-four of the families in the sample turned on the television for 16
hours or less for the week. The 7th percentile of the data is 16
hours.

Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.

Evaluating when [tex]\( n = 1 \)[/tex], the value of S is: S = 1

Evaluate:

[tex]\[ S = 108(2)^{n-1} \][/tex]

When n = 1.

Remember: For a geometric series, the sum can be calculated using the formula:

[tex]\[ S = 108(2)^{n-1} \][/tex]

In this case, we have r = 2, since each term is multiplied by 2 to get the next term.

Substituting the values into the formula, we get:

[tex]\[ S = \frac{{(1 - 2^n)}}{{1 - 2}} \][/tex]

Simplifying further:

[tex]\[ S = \frac{{1 - 2^n}}{{-1}} \][/tex]

Since the denominator is -1, multiplying the numerator and denominator by -1, we get:

[tex]\[ S = 2^n - 1 \][/tex]

Therefore, when [tex]\( n = 1 \)[/tex], the value of S is:

S = [tex]2^1[/tex]- 1 = 2 - 1 = 1

Learn more about geometric series at https://brainly.com/question/1509142

#SPJ1

Answer:

0

Step-by-step explanation:

Certainly! Let's solve the equation step by step:

1. Write down the equation:

3x + 5 = 3x - 5

2. Attempt to isolate x by subtracting 3x from both sides:

3x - 3x + 5 = 3x - 3x - 5

3. Simplify the equation:

5 = -5

At this point, we see that the equation 5 = -5 is not true. This means there is no solution for x in the given equation, as the two sides of the equation cannot be equal.

Answer:

(A) -76

(B) 4/81

(C) -1/16

(D) 3

Step-by-step explanation:

It is given that u and v are functions of x and are differentiable at x=0 and that u(0) = -8, u'(0) = -4, v(0) = 9, and v'(0) = 5. We are asked to find the following derivatives at x=0.

(A) - [tex]\dfrac{d}{dx}[uv][/tex]

(B) - [tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big][/tex]

(C) - [tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big][/tex]

(D) - [tex]\dfrac{d}{dx} [-5v-7u][/tex]

[tex]\hrulefill[/tex]

Part (A) - Using the product rule.

[tex]\dfrac{d}{dx}[uv]=uv'+vu'[/tex]

Substituting in our values:

[tex](-8)(5)+(9)(-4)\\\\\\\therefore \boxed{=-76}[/tex]

Part (B) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big]=\dfrac{vu'-uv'}{v^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(9)(-4)-(-8)(5)}{(9)^2}\\\\\\\therefore \boxed{=\frac{4}{81} }[/tex]

Part (C) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big]=\dfrac{uv'-vu'}{u^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(-8)(5)-(9)(-4)}{(-8)^2}\\\\\\\therefore \boxed{=\frac{-1}{16} }[/tex]

Part (D) - Deriving the function.

[tex]\dfrac{d}{dx} [-5v-7u]=-5v'-7u'[/tex]

Substituting in our values:

[tex]-5(5)-7(-4)\\\\\\\therefore \boxed{=3}[/tex]

Thus, all parts have been solved.

Answer:

A) -5.44

Step-by-step explanation:

-7.94 + 2.5 = -5.44

 -7.94

+ 2.50

-------------

 -5.44

Hope this helps! :)

Answer:

-5.44

Step-by-step explanation:

Align the decimals.

since the greatest value (7.94) is having negative sign(-), your answer remains negative.

- 7.94

2.5

-5.44

a) The total number of days to finish by the builders is: 112 days

b) The speed per 1 hour is: 19 km/hr

An algebraic expression is the idea of ​​representing numbers in letters or alphabets without specifying the actual values. In Algebra Basics, we learned how to use letters such as x, y, and z to represent unknown values. These characters are called variables here. Algebraic expressions can use a combination of variables and constants. Any value that comes before the variable and is multiplied is a factor.

a) The builders complete 3/8 of a project in 42 days.

If the total number of days to finish is x, then we can say by proportion that:

(3/8)x = 42

x = (42 * 8)/3

x = 112 days

b) The rate of speed is 38 km per 2 hours.

Thus speed per hour = 38/2 = 19 km/hr

Read more about Algebraic Expressions at: https://brainly.com/question/4344214

#SPJ1

The point of intersection of line m and line n is: Line W

The intersection of two lines is defined as the point where the two lines intersect or intersects.

Line segments m and n are assumed to intersect. That is, they must eventually intersect.

In this question we need to find the intersection of lines l and m.

And suppose lines  A and B intersect.

From the given figure, we can see that in plane A, lines m and n intersect at point W. The point W is therefore the intersection of the two lines m and n.  

Read more about Point of Intersection at: https://brainly.com/question/30548599

#SPJ1

Answer:

-----------------------

Apply the intersecting chords theorem, which states that:

It gives us the following equation:

Solve it for x:

The matching choice is C.

Answer:

The list price would be $420.

The number of coffee shops per capita in the city is approximately 0.000124.

To calculate the number of coffee shops per capita in the given city, we divide the total number of coffee shops by the total population and round the result to six decimal places.

Number of coffee shops: 99

Population: 801,100

Coffee shops per capita = Number of coffee shops / Population

Coffee shops per capita = 99 / 801,100

Coffee shops per capita = 0.000123719

Rounding the result to six decimal places, the number of coffee shops per capita in the city is approximately 0.000124.

This means that for every person in the city, there are approximately 0.000124 coffee shops available. Another way to interpret this is that, on average, each person in the city can expect to have access to 0.000124 coffee shops.

Please note that this calculation assumes an equal distribution of coffee shops throughout the city and does not take into account factors such as location, density, or other variables that may affect coffee shop accessibility.

For more such questions on number

https://brainly.com/question/25734188

#SPJ8

Answer:

30

Step-by-step explanation:

ahora:

edad de Kevin = k

edad de Gabriela = g

k = 2g

hace 12 años:

edad de kevin = k - 12

edad de gabriela = g - 12

k - 12 = 6(g - 12)

k = 2g

k - 12 = 6(g - 12)

2g - 12 = 6(g - 12)

2g - 12 = 6g - 72

4g = 60

g = 15

k = 2g = 2 × 15 = 30

Answer:

probability that the claim will be accepted, assuming the actual probability of cure is 65%, is approximately 0.9631 or 96.31%.

Step-by-step explanation:

Apologies for the confusion earlier. Let's calculate the probabilities based on the given information:

1) Find the probability that the claim will be rejected, assuming that the manufacturer's claim is true:

Using the normal approximation, we can find the z-score corresponding to X = 139. We standardize the random variable as follows:

Z = (X - μ) / σ

Z = (139 - 150) / sqrt(37.5) ≈ -1.795

Now we can find the probability using the standard normal table or a calculator:

P(Z < -1.795) ≈ 0.0369

Therefore, the probability that the claim will be rejected, assuming the manufacturer's claim is true, is approximately 0.0369 or 3.69%.

2) Find the probability that the claim will be accepted, assuming that the actual probability that the drug cures the skin disease is 65%:

Using the normal approximation, we can find the z-score corresponding to X = 139:

Z = (139 - 150) / sqrt(37.5) ≈ -1.795

Now we can find the probability:

P(Z > -1.795) ≈ 1 - P(Z < -1.795) ≈ 1 - 0.0369 ≈ 0.9631

Therefore, the probability that the claim will be accepted, assuming the actual probability of cure is 65%, is approximately 0.9631 or 96.31%.

chatgpt

Therefore, the missing angle = (1080° - 947°) = 133°

Step-by-step explanation:

Given: Octagon

7 Interior Angles: 122°, 143°, 152°, 107°, 128°, 130° & 165°

Find: The measure of the missing angle:

Plan: Determine total sum of an octagons interior angles and subtract the total of the given angles

Sum of the Interior Angles of an Octagon:S = (n-2) 180°

S = (8 - 2)180° = 6 x 180° = 1080°

Sum of 7 Given Angles: S7IA = 947°

Answer:

2/3

Step-by-step explanation:

The effect on the graph of f(x) = x² when it is transformed to h(x) = 3x² - 7 is described by option B. The graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down.

For more such questions on graph, click on:

https://brainly.com/question/19040584

#SPJ8

Step-by-step explanation:

2). 5/2

3). 7/9

4). 12/5

5).5/6

Answer:

a) sum

b) shorter

c) longest

Step-by-step explanation:

a) sum

b) shorter

c) longest

The coordinate line such that it has a position s​=f(t)=t^2-6t+5 on the interval 0≤t≤8, body changes direction at `t=3s`.

Given that the position of the body is s = f(t) = [tex]t^2[/tex] − 6t + 5 on the interval 0≤t≤8 on a coordinate line.

Here, s is in meters and t is in seconds.

We need to find the following.

A) The body's displacement and average velocity for the given time interval.

B) The body's speed and acceleration at the endpoints of the interval.

C) The interval does the body change directionLet's solve each part.

A) Displacement is given by the formula:

[tex]$$\Delta s=f(t_2)-f(t_1)$$

$$\Delta s= f(8)-f(0)$$[/tex]

[tex]$$\Delta s=(8)^2-6(8)+5-[0^2-6(0)+5]$$

$$\Delta s=64-48$$

$$\Delta s=16m$$[/tex]

The average velocity is given by the formula:

[tex]$$\overline{v}=\frac{\Delta s}{\Delta t}$$[/tex]

where, [tex]$\Delta t$[/tex] is the time taken.

[tex]$$ \Delta t=8-0=8s$$

$$\overline{v}=\frac{16}{8}$$

$$\overline{v}=2m/s$$[/tex]

B) Speed is the magnitude of velocity.

The velocity is given by

The acceleration is given by [tex]v=\frac{ds}{dt}=f'(t)$$[/tex]

[tex]a=\frac{dv}{dt}=f''(t)$$[/tex]

Let's calculate the velocity at the endpoints of the interval.

[tex]$$v(0)=f'(0)=2(0)-6= -6m/s$$[/tex]

[tex]$$v(8)=f'(8)=2(8)-6= 10m/s$$[/tex]

Let's calculate the acceleration at the endpoints of the interval.

[tex]$$a(0)=f''(0)=2m/s^2$$[/tex]

[tex]$$a(8)=f''(8)=2m/s^2$$[/tex]

C) The body changes direction at the point where the velocity changes its sign.

Let's find the point where the velocity changes its sign.

[tex]$$v(t)=0$$

$$2t-6=0$$

$$2t=6$$

$$t=3s$$[/tex]

For more related questions on coordinate line :

https://brainly.com/question/14462788

#SPJ8

(a) The body's displacement and average velocity for the given time interval is 21 m and  2 m/s respectively.

(b) The​ body's speed and acceleration at the endpoints of the interval is 10 m/s and  2 m/s² respectively.

(c) The interval at which the body changes direction is 0 ≤ t ≤ 3 s.

(a) The body's displacement and average velocity for the given time interval is calculated as follows;

s = f(t) = t² - 6t + 5

0 ≤ t ≤ 8 s

f(0) = 0 - 0 + 5 = 5 m

f(8) = 8²  - 6(8) + 5 = 21 m

displacement = 21 m - 5 m = 16 m

average velocity = ( 16 m ) / (8 s - 0 s ) = 2 m/s

(b) The​ body's speed and acceleration at the endpoints of the interval is calculated as;

v = f'(t) = 2t - 6

v(8) = 2(8) - 6 = 10 m/s

a = dv/dt = 2 m/s²

(c) the time to reach maximum height is calculated as;

v = 2t - 6

0 = 2t - 6

2t = 6

t = 3 s

Interval = 0 ≤ t ≤ 3 s

the height when the direction is changed;

f(3) = (3²) - 6(3) + 5

f(3) = - 4m

Learn more about displacement here: https://brainly.com/question/28370322

#SPJ1

The property represented by the equation (8 x 5) x 6.75 = 8 x (5 x 6.75) is the associative property of multiplication.  The associative property of multiplication states that when three or more numbers are multiplied, the product is the same regardless of the grouping of the factors.

This means that if there are multiple numbers to multiply, it does not matter which numbers you multiply first.Here, both sides of the equation are equal: (8 x 5) x 6.75 = 340.5, and 8 x (5 x 6.75) = 340.5.

This shows that you can multiply the numbers in any order and still end up with the same product. Therefore, this equation represents the associative property of multiplication.

For more question on associative property of multiplication

https://brainly.com/question/21200887

#SPJ8

The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

The null hypothesis (H₀): The company's heaters have a mean lifespan of 5 years or more.

The alternative hypothesis (H₁): The company's heaters have a mean lifespan of less than 5 years.

In hypothesis testing, the null hypothesis represents the claim or assumption that is being tested. In this case, the null hypothesis assumes that the mean lifespan of the company's heaters is equal to or greater than 5 years. The alternative hypothesis, on the other hand, challenges this claim and suggests that the mean lifespan is less than 5 years.

To determine which hypothesis is supported by the evidence, statistical analysis would need to be conducted using appropriate data and methods. The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

To more on a hypothesis:

https://brainly.com/question/29576929
#SPJ8

Answer:

126000

Step-by-step explanation:

if from 2010 to 2012 there was an increase of 23000 that means every two years 23000 people are added then add 23000 to 80000 for four years and you will get 126000.In other words if you get 23000 divide it by two to get the amount for one year then multiply it by 8

The set A U U is:

A U U = {a, b, c, d, e, f, g, h}

A set is a collection or grouping of distinct objects, which are called elements or members of the set. These objects can be anything: numbers, letters, shapes, or even other sets.

We have:

A= {c, d, g, h}

U= {a, b, c, d, e, f, g, h}

A U U is the set of all elements (letters) that appear in both A and U. Thus, we can say:

A U U = {a, b, c, d, e, f, g, h}

Learn more about sets on:

brainly.com/question/13458417

#SPJ1

The value of the sum of 5 and the square of a number varies depending on the value of n. When n = 1, the result of the expression is 6, when n = 2, the result is 9, and when n = 3, the result is 14. The same applies when n is negative.

The sum of 5 and the square of a number is an expression that can be represented as (n² + 5), where n represents the number whose square is added to 5. The result of the expression varies depending on the value of n. In this answer, we will examine how to find the sum of 5 and the square of a number using various values of n.
If n = 1, then the square of n is equal to 1, and the sum of 5 and the square of n is equal to 6. Therefore, if n = 1, the result of the expression is 6.
If n = 2, then the square of n is equal to 4, and the sum of 5 and the square of n is equal to 9. Therefore, if n = 2, the result of the expression is 9.
If n = 3, then the square of n is equal to 9, and the sum of 5 and the square of n is equal to 14. Therefore, if n = 3, the result of the expression is 14.
If n = -1, then the square of n is equal to 1, and the sum of 5 and the square of n is equal to 6. Therefore, if n = -1, the result of the expression is 6.
If n = -2, then the square of n is equal to 4, and the sum of 5 and the square of n is equal to 9. Therefore, if n = -2, the result of the expression is 9.
If n = -3, then the square of n is equal to 9, and the sum of 5 and the square of n is equal to 14. Therefore, if n = -3, the result of the expression is 14.
In conclusion, the value of the sum of 5 and the square of a number varies depending on the value of n. When n = 1, the result of the expression is 6, when n = 2, the result is 9, and when n = 3, the result is 14. The same applies when n is negative.

For more questions on square.

https://brainly.com/question/428672

#SPJ8

It will take 14 days for 46 workers to build similar house.

When building a house, the number of days required to build is inversely proportional to the number of workers.

Therefore,

d α 1 / w

d = k / w

k = dw

where

Therefore,

k = 161 × 4

k = 644

Let's find the number of days to build similar house with 46 workers.

Therefore,

d = 644 / 46

d = 14 days

Therefore, it will take 14 days.

learn more on proportional relationships here: https://brainly.com/question/32623545

#SPJ1

The  12 feet of carpet is needed.

To round 11.5 feet to the nearest foot, we look at the decimal part, which is 0.5. According to the Rounding Rules, if the number being looked at is 5 or above, we round up by giving it a shove! Since 0.5 is exactly 5, we round up to the next whole number, which is 12 feet.

So, after rounding 11.5 feet to the nearest foot, we get 12 feet.

To determine how much carpet is needed, we use the rounded measurement, which is 12 feet.

For more question carpet

https://brainly.com/question/29150779

#SPJ8

Answer:

The slope of a line parallel to the equation y = (6/5)x - 2 is 6/5.

Step-by-step explanation:

In general, when two lines are parallel, they have the same slope. Therefore, any line that is parallel to the given equation will have a slope of 6/5.

If Store C sells 145,670 products then Store B sells 9,711 products. Option A is the correct answer.

To determine the number of products Store B sells, we need to calculate it based on the information given in relation to Store C.

Given that Store C sells 145,670 products, and Store A sells one-third as many as Store C, we can find the number of products Store A sells:

Store A = (1/3) * Store C = (1/3) * 145,670 = 48,557

Now that we know Store A sells 48,557 products, and it sells five times as many products as Store B, we can calculate the number of products Store B sells:

Store B = (1/5) * Store A = (1/5) * 48,557 = 9,711

Therefore, Store B sells 9,711 products. Option A is the correct answer.

For such more question on products:

https://brainly.com/question/29136043

#SPJ8

The value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

To determine the values that should be excluded in the equation x/(x - 3) + 1/3 = 1, we need to find the values of x that would make the equation undefined or result in a division by zero.

In this case, the expression x - 3 appears in the denominator, so we need to find the values of x that would make x - 3 equal to zero.

x - 3 = 0

x = 3

Therefore, the value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

Learn more about equation at https://brainly.com/question/14107099

#SPJ1

The calculated value of [-12] is (b) -12

From the question, we have the following parameters that can be used in our computation:

[-12]

Remove the square bracket

So, we have

-12

The above expression cannot be further simplified

So, we have

[-12] = -12

Hence, the calculated value of [-12] is (b) -12

Read more about expression at

https://brainly.com/question/31819389

#SPJ1

Answer:

-12

Step-by-step explanation:

took the quiz

The graph represents the system of inequalities: y ≤ −3x − 1 and y ≤ −x + 4.

The graph represents the system of inequalities: y ≤ −3x − 1 and y ≤ −x + 4.

Let's analyze the given information step by step:

Line f(x) goes through the points (0, 4) and (4, 0) and is shaded below the line.

This means that the region below line f(x) is labeled A.

Since line f(x) is solid, the inequality associated with it must be y ≤ −3x − 1.

Line g(x) goes through the points (0, -1) and (2, 5) and is shaded below the line.

This means that the region below line g(x) is labeled B.

Since line g(x) is also solid, the inequality associated with it must be y ≤ −x + 4.

The shaded area where f(x) and g(x) have shading in common is labeled AB.

This means that the overlapping region satisfies both inequalities.

Combining the information, we find that the system of inequalities represented by the graph is:

y ≤ −3x − 1 (corresponding to line f(x))

y ≤ −x + 4 (corresponding to line g(x))

For similar question on inequalities.

https://brainly.com/question/30681777  

#SPJ8