An apartment building has 11 floors in it. Each floor has 9 rooms on it. If each room has two people living there, how many people live in this apartment building?**

Answer:

probably not, but if you were to post the questions without it saying on it that its an exam (because those get deleted all the time) people could help you through it. :)

Step-by-step explanation:

Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

Answer:

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  43 out of a random sample of 100 people said they pick their noses at red lights.

sample proportion

                           \(p^{-} = \frac{x}{n} = \frac{43}{100} = 0.43\)

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

95% of confidence interval of the proportion of all people who pick their noses at red lights

\((p^{-} -Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } ,p^{-} +Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })\)

\((0.43 -1.96 \sqrt{\frac{0.43(1-0.43)}{100} } ,0.43 +1.96 \sqrt{\frac{0.43(1-0.43)}{100} })\)

( 0.43 -  0.0958 , 0.43 + 0.0958)

(0.3342 , 0.5258)

Conclusion:-

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)

The fourth term a₄ of the sequence is 29933

From the question, we have the following definition of the function that can be used in our computation:

a₁= 3

aₙ = (aₙ₋₁)² + 4

The above definitions imply that we simply square the previous term and then add 4 to the squared result to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = (3)² + 4

a₂ = 13

Also, we have

a₃ = (13)² + 4

a₃ = 173

Lastly, we have

a₄ = (173)² + 4

Evaluate the equation

a₄ = 29933

Hence, the value of a₄ is 29933

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Step-by-step explanation

Then you count how many numbers are after the decimal point(6,0,0,5) making 4. So the decimal point will be inserted by counting 4 spaces from the back.

Answer:

A) W = 28 + H

B) W * H = 52

A) Height = W -28

B) W * (W -28) = 52

B) W^2 -28W = 52

W^2 - 28W - 52 = 0

Width = 29.748

Height = 1.748

Step-by-step explanation:

Answer: 225

Step-by-step explanation:

Create a ratio part/whole for radians = part/whole for degrees

\(\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}\)      Keep change flip because you are dividing fractions for left side

\(\frac{5\pi }{4} (\frac{1}{2\pi }\)) = \(\frac{x}{360}\)

\(\frac{5}{8} (\frac{360}{1} ) =x\)

x = 225

The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate.

The Pythagorean Theorem states that the sum of the squares of the lengths of the two sides of a right triangle are equal to the square of the length of the hypotenuse. The theorem is written as a^2 + b^2 = c^2. The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate.  To prove this postulate, we can start with an arbitrary triangle ABC. If we extend the side AC to D, then we can create a line parallel to BC, creating two similar triangles, ABC and ADC. Since similar triangles have corresponding angles that are congruent, then  angle A = angle D. Since side AC is congruent to side AD, then angle A is also congruent to angle B. This proves the Corresponding Angles Postulate.

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Answer:

2nd graph from the top

Step-by-step explanation:

We can rewrite the inequality as n < -3

Answer:

66-26 = 40

Step-by-step explanation:

u = 40 degrees

Answer: A

Step-by-step explanation: Pic is attached. Hope this helps.

Answer: 29,000.00

Step-by-step explanation:

Let the income=x.  22%=0.22.

So 6380/x=0.22

x=6380/0.22=29,000.00

Answer:

d

Step-by-step explanation:

The as the value of x increases, f and g both approach positive infinity.

Functions describe relationship between set of variables.

g(x) = 2ˣ - 5

As the values of x increases, the value of g increases to positive infinite.

From the given table of function f, as the value of x increases, f approaches positive infinity.

Thus, the as the value of x increases, f and g both approach positive infinity.

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Answer: the answer is A.

The equation is expanding Pascal's triangle and the Binomial theorem

(x + 0.5)³ = x³/8 + 3x²/4 + 3x/2 + 1/8

(s + 4t)⁶ = s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶

(3a - 3b)⁴ = 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴

(3m - 2n)⁵  = 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵

(a-4)⁵ = a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024

The binomial theorem formula for any positive integer n.

(x + y)n = nC0 xn + nC1 xn-1 by+ nC2 xn-2 y2 + … + nCn-1 x yn-1 + nCn x.

11) Using the Binomial Theorem, we have:

(x + 0.5)³ = C(3,0) x³(0.5)⁰ + C(3,1) x²(0.5)¹ + C(3,2) x¹(0.5)² + C(3,3) x⁰(0.5)³

= x³/2³ + 3x²/2² + 3x/2 + 1/2³

= x³/8 + 3x²/4 + 3x/2 + 1/8

12) Using Pascal's Triangle, we have:

(s + 4t)⁶ = C(6,0) s⁶(4t)⁰ + C(6,1) s⁵(4t)¹ + C(6,2) s⁴(4t)² + C(6,3) s³(4t)³ + C(6,4) s²(4t)⁴ + C(6,5) s(4t)⁵ + C(6,6) (4t)⁶

= s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶

13) Using Pascal's Triangle, we have:

(3a - 3b)⁴ = C(4,0) (3a)⁴(-3b)⁰ + C(4,1) (3a)³(-3b)¹ + C(4,2) (3a)²(-3b)² + C(4,3) (3a)(-3b)³ + C(4,4) (-3b)⁴

= 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴

14)Using Pascal's Triangle, we have:

(3m - 2n)⁵ = C(5,0) (3m)⁵(-2n)⁰ + C(5,1) (3m)⁴(-2n)¹ + C(5,2) (3m)³(-2n)² + C(5,3) (3m)²(-2n)³ + C(5,4) (3m)(-2n)⁴ + C(5,5) (-2n)⁵

= 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵

15) Using Pascal's Triangle, we have:

(a-4)⁵ =  C(5,0) a⁵(-4)⁰ + C(5,1) a⁴(-4)¹ + C(5,2) a³(-4)² + C(5,3) a²(-4)³ + C(5,4) a(-4)⁴ + C(5,5) (-4)⁵

= a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024

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The equation is expanding Pascal's triangle and the Binomial theorem ,

\((x + 0.5)^3= x^3/8 + 3x^2/4 + 3x/2 + 1/8\)

\((s + 4t)^6 = s^6+ 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4+ 6s(4t)^5 + 4t^6\)

\((3a - 3b)^4 = 81a^4 - 324a^3b + 486a^2b^2- 324ab^3 + 81b^4\)

\((3m - 2n)^5 = 243m^5 - 810m^4n + 1080m^3n^2- 720m^2n^3 + 240mn^4- 32n^5\)

\((a-4)^5= a^5 - 20a^4 + 160a^3 - 640a^2+ 1280a - 1024\)

What is the binomial theorem formula?

The binomial theorem formula for any positive integer n.

\((x + y)^n = nC_0 x^n + nC_1x^{n-1} y+ nC_2 x^{n-2} y_2 + … + nC_{n-1} x y^{n-1} + nC_n x.\)

11) Using the Binomial Theorem, we have:

\((x + 0.5)^3 = C(3,0) x^3(0.5)^0 + C(3,1) x^2(0.5)^1 + C(3,2) x^1(0.5)^2 + C(3,3) x^0(0.5)^3\)

=\(x^3/2^3 + 3x^2/2^2 + 3x/2 + 1/2^3\)

= \(x^3/8 + 3x^2/4 + 3x/2 + 1/8\)

12) Using Pascal's Triangle, we have:

\((s + 4t)^6 = C(6,0) s^6(4t)^0+ C(6,1) s^5(4t)^1+ C(6,2) s^4(4t)^2 + C(6,3) s^3(4t)^3 + C(6,4) s^2(4t)^4+ C(6,5) s(4t)^5 + C(6,6) (4t)^6\)

= \(s^6 + 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4 + 6s(4t)^5 + 4t^6\)

13) Using Pascal's Triangle, we have:

\((3a - 3b)^4 = C(4,0) (3a)^4(-3b)^0 + C(4,1) (3a)^3(-3b)^1 + C(4,2) (3a)^2(-3b)^2 + C(4,3) (3a)(-3b)^3 + C(4,4) (-3b)^4\)

= \(81a^4 - 324a^3b + 486a^2b^2 - 324ab^3 + 81b^4\)

14)Using Pascal's Triangle, we have:

\((3m - 2n)^5= C(5,0) (3m)^5(-2n)^0 + C(5,1) (3m)^4(-2n)^1 + C(5,2) (3m)^3(-2n)^2+ C(5,3) (3m)^2(-2n)^3 + C(5,4) (3m)(-2n)^4 + C(5,5) (-2n)^5\)

= \(243m^5- 810m^4n + 1080m^3n^2 - 720m^2n^3 + 240mn^4 - 32n^5\)

15) Using Pascal's Triangle, we have:

\((a-4)^5= C(5,0) a^5(-4)^0+ C(5,1) a^4(-4)^1 + C(5,2) a^3(-4)^2 + C(5,3) a^2(-4)^3 +C(5,4) a(-4)^4 + C(5,5) (-4)^5\)

= \(a^5 - 20a^4 + 160a^3 - 640a^2 + 1280a - 1024\)

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The sentence which show correct verb tense usage is The overall outlook is favorable.

Verbs are a necessary component of communication in every language, including English, without which it would be difficult to convey what the subject is doing. All acts, including those motivated by sentiments and emotions, are included.

Verbs exist in a variety of forms and kinds so they can function in many ways to convey the whole meaning. Let's have a look at how different dictionaries define the word "verb" before we examine the many kinds of verbs and their forms.

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Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

Answer:

A. 232 in²

B. 216 in²

Step-by-step explanation:

A. Box A is a cuboid/rectangular prism.

Surface area of box A = 2(LW + LH + WH)

L = 10 in

W = 2 in

H = 8 in

Surface area = 2(10*2 + 10*8 + 2*8)

= 2(20 + 80 + 16) = 2(116)

Surface area = 232 in²

B. Surface area of B = surface area of cube

Surface area of cube = 6s²

s = 6 in

Surface area = 6(6²)

= 6(36)

= 216 in²

Answer:

~

Step-by-step explanation:

To make it easier to graph using a translation, we can rewrite the given equation as:

y - 5 = √√4x + 16

This is obtained by subtracting 5 from both sides of the equation.

The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.

Answer:

1900

Step-by-step explanation:

1000+900=1900

The division of 10y³ - 9y² + 6y - 10 by 2y + 3 will give 5y² - 12y + 21 - (73/2y + 3)

Long division is a method of dividing two numbers using repeated subtraction and multiplication. It is called "long" division because the process involves writing out a long sequence of steps to perform the division. Long division is typically used for dividing two large numbers, such as when doing polynomial division in algebra, or when dividing money or measurements.

Using long division, the dividend 10y³ - 9y² + 6y - 10 is divided by the divisor 2y + 3

The result is 5y² - 12y + 21 - (73/2y + 3)

where the remainder is -73

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Answer:

\(l = \boxed{167.}\\w=\boxed{40.}\)

Step-by-step explanation:

Since the perimeter is 414 meters, half of the perimeter is 207 meters. We can write the following equation and solve for h.

\(w + l = 207\\w + (4w + 7) = 207\\5w +7 = 207\\5w = 200\\w = \boxed{40.}\)

Here, we substituted 4w + 7 in place of l as the problem tells us that the length of the pool is 7 meters more than 4 times the width. Solving for the width gave us 40 meters.

Using this information, we can determine that the length of the swimming pool is:

\(4(40) + 7 = 160 + 7 = 167.\)

To double-check that this is correct, we can add twice the length and twice the width to see if it equals the given perimeter:

\(167 + 167 + 40 + 40 = 414.\)

Therefore, your length and width of this swimming pool are:

\(l = \boxed{167.}\\w=\boxed{40.}\)

The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.

The distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.

The circumference of a circle is given by the formula:

C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.

The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.

The circumference of the circle traced by the tip of the minute hand is:

\(\text{C} = 2\pi \text{r}\)

\(= 2\pi (8)\)

\(= 16\pi \ \text{centimeters}\)

Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.

The distance traveled by the tip of the minute hand in 15 minutes is:

\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)

\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)

\(= 4\pi \ \text{centimeters}\)

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Answer:

4π cm ≈ 12.6 cm

Step-by-step explanation:

The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand:  r = 8 cm.

A clock face is divided into 12 equal sectors (numbered 1 to 12).

It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.

This means that 15 minutes equals 3 sectors, which is a quarter of the circle.

To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.

The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:

\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)

Simplifying, we get:

\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)

\(\sf Distance=4 \pi\)

Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.

Answer:

2/5 or 0.4

Step-by-step explanation:

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

A. 3

Step-by-step explanation:

\( - x + 5y \\ - 12 + 5(3) \\ - 12 + 15 \\ = 3 \\ \)

Answer:

24 females with unlisted phone numbers

Step-by-step explanation:

20% of the staff at this hospital have unlisted telephone numbers

40% of the staff at the hospital that have unlisted telephone numbers are females

This means that 40% of the 20% of the 300 names in the phone book will be females with unlisted phone numbers.

1/5 (20%) of 300 is 60, and 40% of these 60 people is 24.

There are 24 females in this 300 with unlisted phone numbers.

I'm not entirely sure if this is what you were asking, since you had some errors in your question.

We'll first need to determine what the composite function f(g(x)) is equal to.

Start with the outer function f(x). Then replace every copy of x with g(x). Afterward, plug in g(x) = 3x-2

So we get the following:

\(f(x) = \sqrt{x^2-4}\\\\f(g(x)) = \sqrt{(g(x))^2-4}\\\\f(g(x)) = \sqrt{(3x-2)^2-4}\\\\f(g(x)) = \sqrt{9x^2-12x+4-4}\\\\f(g(x)) = \sqrt{9x^2-12x}\\\\\)

Next, we apply the derivative

\(f(g(x)) = \sqrt{9x^2-12x}\\\\f(g(x)) = (9x^2-12x)^{1/2}\\\\f'(g(x)) = \frac{1}{2}(9x^2-12x)^{-1/2}*\frac{d}{dx}(9x^2-12x)\\\\f'(g(x)) = \frac{1}{2}(9x^2-12x)^{-1/2}*(18x-12)\\\\f'(g(x)) = \frac{9x-6}{\sqrt{9x^2-12x}}\\\\\)

Don't forget about the chain rule. The chain rule is applied in step 3 of that block of steps shown above.

The last thing we do is plug in x = 3 and simplify.

\(f'(g(x)) = \frac{9x-6}{\sqrt{9x^2-12x}}\\\\f'(g(3)) = \frac{9*3-6}{\sqrt{9*3^2-12*3}}\\\\f'(g(3)) = \frac{21}{\sqrt{45}}\\\\f'(g(3)) = \frac{21}{\sqrt{9*5}}\\\\f'(g(3)) = \frac{21}{\sqrt{9}*\sqrt{5}}\\\\f'(g(3)) = \frac{21}{3*\sqrt{5}}\\\\f'(g(3)) = \frac{7}{\sqrt{5}}\\\\\)

Side note: if you choose to rationalize the denominator, then you'll multiply both top and bottom by sqrt(5) to end up with \(f'(g(3)) = \frac{7\sqrt{5}}{5}\\\\\); however, your teacher has chosen not to rationalize the denominator.

Answer: 39.96 people

Step-by-step explanation:

If 55.6% quit, that means 44.4% still go to the gym.

44.4%*90 = 39.96 people