the results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year. what is the polls margin of error?

Answer:

Step-by-step explanation:

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

Answer:

endpoint or straight lines

Step-by-step explanation:

same

Explanation:

There are 7 ways to pick the first place position, then 6 ways for second place, 5 for third, and so on. We count down until we get to 1

7,6,5,4,3,2,1

Multiply out those values to get the final answer. On many calculators this can be done using the factorial button, indicated as an exclamation mark

7! = 7*6*5*4*3*2*1 = 5040

Hello,

    3y + 4 < 16

⇔ 3y < 16 - 4

⇔ 3y < 12

⇔ y < 12/3

⇔ y < 4

⇒ S = ] - ∞ ; 4 [

Answer:

d) -8 × 3 = -24

Step-by-step explanation:

a) -18 ÷ 6 = -3

b) 30 ÷ 3 = 10

c) -7 × -7 = 49

d) -8 × 3 = -24

Above from all, option d is done correctly.

Note: when negatives are multiplied together or divided they cancel out to being positive. For example: -1 × -1 = 1

Hello!

Let's solve to verify whether the equations are true.

⇒ -18 ÷ 6 = -3

⇒ Given answer : 3

⇒ Incorrect

⇒ 30 ÷ 3 = 10

⇒ Given answer : -10

⇒ Incorrect

⇒ -7 × -7 = 49

⇒ Given answer = -49

⇒ Incorrect

⇒ -8 × 3 = -24

⇒ Given answer = 24

⇒ Correct

∴ The equation which is correctly calculated is -8 × 3 = -24.

Answer: no they are not similar

Step-by-step explanation: if you find the ratio of sides 85:17, it is 5

The ratio of sides 30 to 6 is also 5

However, the ratio of sides 54 to 9 is 6 so it is not similar

The ratio has to be the same for all sides to be similar

I assume you meant [tex]g(x)=4^x -1[/tex].

The graph is shown in the attached image.

The two points on the graph are (0,0) and (1, 3).

The asymptote is y = -1.

The domain is (-∞,∞)

The range is (-1,∞)

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be written as 2 2 2 2=25 for the number 32. This phrase should be understood as "two to the fifth power."

The two points on the graph are (0,0) and (1, 3).

The asymptote is y = -1.

The domain is (-∞,∞)

The range is (-1,∞)

The graph of the function is attached with the answer.

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The product (a+b)(a-2b) is a^2 - ab - 2b^2

The product expression is given as:

(a+b)(a-2b)

Expand the bracket

a * a - a * 2b + b * a - b * 2b

Evaluate the product

a^2 - 2ab + ab - 2b^2

Evaluate the like terms

a^2 - ab - 2b^2

Hence, the product (a+b)(a-2b) is a^2 - ab - 2b^2

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Answer:

6^4 * 6^3

Step-by-step explanation:

Answer:

0.25 or 1/4

Step-by-step explanation:

P(coin is flipped as head) = 0.5 or 1/2 (one of 2 sides)

P(coin is flipped as head twice) = P(coin is flipped as head) x P(coin is flipped as head)

= 0.5 x 0.5

= 0.25 or 1/4

Answer:

1. Colouring Pencil 2. Notebook 3. Pencil Case

Step-by-step explanation:

The weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles was 3:4

Let 3x and 4x are the seeds from the smaller and bigger pile.

= 4x + 2  (greedy hamster placed another 2 pounds of seeds in the bigger pile)

= 3x - 1/4 (ate 1/4 pound from the smaller pile)

4x + 2 = 5x

Because the quantities of seeds in those piles is in the ratio of 5:16

After solving:

x = 2

Smaller pile weight = 3x = 3(2) = 6

Bigger pile wieght = 4x = 4(2) = 8

Thus, the weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4

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Answer:

$4.48

Step-by-step explanation:

It takes $1.12 to feed one kid, to find the cost of all four kids we multiply 1.12 by 4

1.12*4 = $4.48

Answer:

if we plus 12 and 10the answer is 22 feet

Answer:

6(q + 9)

Step-by-step explanation:

Answer:

$33.915 for the cd

Step-by-step explanation:

70% of 19.95 = 13.965

19.95 + 13.965= 33.91

Answer:

D

Step-by-step explanation:

Answer:

1/16

Step-by-step explanation:

To evaluate the function f(-4), we let x =4 in f(x) = [tex]2^{x}[/tex]

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

     = 1/[tex]2^{4}[/tex]

     =1/16

Answer:

Step-by-step explanation:

|√2-y|=|y-√2|

√2-y=±(y-√2)

when √2-y=y-√2

y+y=√2+√2

2y=2√2

y=√2

when √2-y=-(y-√2)

√2-y=-y+√2

or 0=0

it gives no value of y.

so only possible value is y=√2

Answer:x=4

Step-by-step explanation:

tendrías que poner términos similares juntos, asegurándote de cambiar el signo de cualquier figura que cruce el igual al signo. luego restarías o sumarías, resolverías las ecuaciones de cada lado, ya que ahora están agrupadas. luego dividirás tu respuesta por el coeficiente que es 2 (2x). esto te dejaría con 4

4x - 2x = 1+7

4x-2x= 8

2x =8

divisir

x=8

a. The exact value of cosθ = -5/√74

b. The exact value of secθ = -√74/5

c. The exact value of cotθ = 5/7

Since the terminal side of the θ is the point, (-5, -7), we need to find the length of the terminal side.

So, r = √(x² + y²) where

So, r = √(x² + y²)

r = √((-5)² + (-7)²)

r = √(25 + 49)

r = √74

Since the trigonometric ratio cosθ = x/r

Substituting the values of x and r into the equation, we have

cosθ = x/r

cosθ = -5/√74

So, the exact value of cosθ = -5/√74

Since the trigonometric ratio, secθ = r/x

Substituting the values of x and r into the equation, we have

secθ = r/x

secθ = √74/-5

secθ = -√74/5

So,  the exact value of secθ = -√74/5

Since the trigonometric ratio cotθ = x/y

Substituting the values of x and y into the equation, we have

cotθ = x/y

cotθ = -5/-7

cotθ = 5/7

So,  the exact value of cotθ = 5/7

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Two or more triangles are said to be congruent if their length of sides and measure of angles are equal. Thus, the required proof expected in the question is option D. <R ≅ <U

When the length of sides or measure of angles of two or more figures is equal, then we say the figures are congruent.

From the given question, the following can be deduced:

RT ≅ US (given: opposite sides are equal)

and TS is a common side for the two triangles.

<TRS  ≅  <RSU (alternate angle property)

<RTS  ≅ <UST (right angle property)

<RTU  ≅  <SUT (alternate angle property)

Therefore it can be observed that the necessary condition to prove that ΔRST ≅ ΔUTS is option D. <R  ≅ <U.

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Answer:

Step-by-step explanation:

The compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We know the formula for continuous compounding:

[tex]\rm A = P(e)^{rt}[/tex]

[tex]\rm A = 11000(e)^{0.023\times8}[/tex]

A = $13,222.17

I = A - P = 13,222.17 - 11000

I  = $2,222.17

Thus, the compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.

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Answer:

0

Step-by-step explanation:

same numerator for that it is zero

Answer: A

Step-by-step explanation:

The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Let x be the number.

According to the problem.

50% of x = 10

x = 10 ÷ 50%

= 10×(50/100)

= (50÷5)/(100÷5) = 10/20

Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

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Matching each equation of the plecewise function represented in the graph will be:

It should be noted that a domain simply means the set of inputs that are accepted by the function.

In this case, the equation of the piecewise function represented is given.

The graph is attached.

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The probability that a randomly selected x-value from the distribution will be in the interval:

The probability of a normal distribution can be determined from the symmetrical curve between 1 to 100%.

From the information given:

To determine the probability that a randomly selected x-value is in the given interval:

[tex]P(35 < x < 45) = P(\dfrac{35-40}{5} < Z < \dfrac{45-40}{5})[/tex]

[tex]P(35 < x < 45) = P(\dfrac{-5}{5} < Z < \dfrac{5}{5})[/tex]

[tex]P(35 < x < 45) = P(-1 < Z < 1)[/tex]

[tex]\mathbf{P(35 < x < 45) = P[Z\le 1] -P[Z\le -1]}[/tex]

Using normal distribution table:

P(35 < x < 45) = 0.8414 - 0.1587

P(35 < x < 45) = 0.6827

[tex]P(30 < x < 40) = P(\dfrac{30-40}{5} < Z < \dfrac{40-40}{5})[/tex]

[tex]P(30 < x < 40) = P(\dfrac{-10}{5} < Z < \dfrac{0}{5})[/tex]

[tex]P(30 < x < 40) = P(-2 < Z < 0)[/tex]

[tex]\mathbf{P(30 < x < 40) = P[Z\le0]-P[Z\le -2]}[/tex]

Using normal distribution table:

P(30 < x < 40) = 0.5 - 0.02275

P(30 < x < 40) = 0.47725

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The magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.

Ax = A cosθ

Ay = A sinθ

Ax = 7.7 x cos(27.8)

Ax = 6.81 m

Ay = 7.7 x sin(27.8)

Ay = 3.59 m

Bx = B cosθ

By = B sinθ

θ with respect to x - axis = 90 - 20 = 70⁰

Bx = 16.3 m x cos(70)

Bx = 5.575 m

By = 16.3 m x sin(70)

By = 15.32 m

Vx = Ax + Bx

Vx = 6.81 m + 5.575 m = 12.385 m

Vy = Ay + By

Vy = 3.59 m + 15.32 m = 18.91 m

V = √(Vy² + Vx²)

V = √(18.91² + 12.385²)

V = 22.6 m

tan θ = Vy/Vx

tan θ = (18.91)/(12.385)

tan θ = 1.527

θ = arc tan (1.527)

θ = 56.8⁰

Thus, the magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.

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Answer:

294pi

Step-by-step explanation:

1/3*pi*r^2*h=V

1/3*pi*49*18=V

V=294pi

Using a trigonometric identity, it is found that the sine of the angle is given as follows:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

Considering an angle [tex]\theta[/tex], the identity is given as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem, the cosine is given as follows:

[tex]\cos{\theta} = \frac{3}{5}[/tex]

Hence the sine is found as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]

[tex]\sin^2{\theta} = \frac{16}{25}[/tex]

[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]

In quadrant IV, the sine is negative, hence:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

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