A magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the ​respondents, ​% chose chocolate​ pie, and the margin of error was given as percentage points. Describe what is meant by the statement that​ "the margin of error was given as percentage​ points."

It looks like the limit you want to compute is

[tex]\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}[/tex]

Since [tex]g(4)=4[/tex], this limit corresponds exactly to the derivative of [tex](f\circ g)(x) = f(g(x))[/tex] at [tex]x=4[/tex]. Recall that

[tex]f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}[/tex]

By the chain rule,

[tex](f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}[/tex]

Since [tex]g'(4)[/tex] exists, [tex]g[/tex] is differentiable at [tex]x=4[/tex] so it must be continuous.

By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Given the following system of inequalities:

y ≤ 1/3x  ⇒ y - 1/3x ≤ 0

y - 2x < 4

By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

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Complete Question:

Graph the following system of inequalities.

y ≤ 1/3x and y - 2x < 4

Answer:

8

Step-by-step explanation:

A cube is equal on all sides. Therefore the cubes must be 3cm x 3cm x 3cm. Therefore, each cube has an area of 27cm^3. The box that the cube has an area in is 3cm x 6cm x 12 cm which = 216cm^3. If you do [tex]216cm^3/27cm^3 = 8 cubes[/tex]

There are 17 hops in a hop, a skip, and a jump.

We have the relations:

How many hops are in a hop, a skip and a jump?

So we have:

1 hop + 1 skip + 1 jump.

First, using the second relation we rewrite:

1 hop + 1 skip + 3 skips = 1 hop + 4 skips.

Now, using the first relation:

1 hop + 4 skips = 1 hop + 4*(4 hops) = 1 hop + 16 hops = 17 hops.

There are 17 hops in a hop, a skip, and a jump.

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The center and radius of the circle is (b) center: (-5, 1) radius: 2

The circle equation is given as:

(x-5)^2 + (y+1)^2 = 4

The circle equation is represented as:

(x-a)^2 + (y-b)^2 = r^2

Where:

Center = (a,b)

Radius = 4

By comparison, we have:

(a, b) = (-5, 1)

r^2 = 4

This gives

(a, b) = (-5, 1)

r = 2

Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2

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Step-by-step explanation:

well there is a very simple point that you have mistaken tho:

484cm², 25cm²

Areas are defined in square cm but the radius is in cm

so:

[tex] \sqrt{ \frac{484 {cm}^{2} }{25 {cm}^{2} } } = \frac{7.92}{r} = = = > 4.4 = \frac{7.92cm}{x} = = > x = \frac{7.92cm}{4.4} = x = 1.8cm[/tex]

and there you go

The amount of material needed for the entire kite is 48 square inches

The given parameters:

KI =6 inches

ET = 8 inches

KT=10 inches

Area of ΔKIT = 17 square inches

Start by calculating the area of the bottom triangle using:

A = 0.5 * Base * Height

This gives

A = 0.5 * 10 * 6

Evaluate

A = 30

The amount of material is

A = 30 + 17

A = 47

Hence, 48 square inches of material is used for the entire kite,  quadrilateral KITE

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the probability that the sample mean will be smaller than m = 22 is 0.02275.

For the given question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Here sample size, n = 4

mean, μ = 30

standard deviation, σ = 8

The probability that the sample mean will be smaller than m = 22 is

z = [tex]\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

⇒ z =[tex]\frac{22-30}{\frac{8}{\sqrt{4} } }[/tex]

⇒ z = [tex]\frac{22-30}{\frac{8}{2} }[/tex]

⇒ z = [tex]-\frac{8}{4}[/tex]

⇒ z = -2

Refer the Z table for p value,

Thus for P(z < -2) is 0.02275.

Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.

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Step-by-step explanation:

[tex]12 {x}^{2} - 6( {a}^{2} + {b}^{2} )x + 3 {a}^{2} {b}^{2} = 0[/tex]

Using quadratic formula, we get

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( - 6) {}^{2}( {a}^{2} + {b}^{2}) {}^{2} - 4(12)(3 {a}^{2} {b}^{2} )} }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( {a}^{2} + {b}^{2} ) {}^{2} - 144 {a}^{2} {b}^{2} } }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( ({a}^{2} + {b}^{2}) {}^{2} - 4 {a}^{2} {b}^{2} }) }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{6 \sqrt{ ({a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{24} [/tex]

[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( {a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{4} [/tex]

Answer: x₁=6b²,  x₂=6a².

Step-by-step explanation:

[tex]12x^2-6*(a^2+b^2)+3a^2b^2=0\\D=(6*(a^2+b^2))^2-4*12*3a^2b^2\\D=6^2*(a^2+b^2)^2-144a^2b^2\\D=36*(a^4+2a^2b^2+b^4)-144a^2b^2\\D=36a^4+72a^2b^2+b^4-144a^2b^2\\D=36a^4-72a^2b^2+36b^4\\D=(6a^2)^2-2*6a^2*6b^2+(6b^2)^2\\D=(6a^2-6b^2)^2\\\sqrt{D}=\sqrt{(6a^2-6b^2)^2}=|6a^2-6b^2|=б(6a^2-6b^2).\\\displaystyle x_{1,2}=\frac{-(-6*(a^2+b^2))б(6a^2-6b^2)}{2} .\\x_1=\frac{6a^2+6b^2-6a^2+6b^2}{2} \\x_1=\frac{12b^2}{2} \\x_1=6b^2.\\x_2=\frac{6a^2+6b^2+6a^2-6b^2}{2} \\x_2=\frac{12a^2}{2} \\x_2=6a^2.[/tex]

The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]

[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]

[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]

[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]

[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]

l=4.2659

Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

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Answer: 22

Step-by-step explanation:

Using the proportionality theorem, the length of the missing segment is 25 units.

According to the proportionality theorem, the middle segment in the diagram given divides the two sides it intersects proportionally.

Therefore, we would have:

x = missing segment

36/21 = (35 + x)/35

Cross multiply

35(36) = 21(35 + x)

1,260 = 735 + 21x

1,260 - 735 = 21x

525 = 21x

525/21 = x

x = 25

The missing segment is: 25 units.

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Answer:

Breadth=8

Length=6

OR

breadth = 6

length=8

Step-by-step explanation:

Area of 4 walls = 2(l+b)h

112=2.4(l+b)

112/8=l+b

14=l+b

l=14-b

Area of base or ceiling=l x b

48=(14-b).b

48=14b-b²

b²-14b+48=0

factorize it and we get

(b-6)(b-8)=0

taking b-6=0

b=6

l=14-6

l=8

The system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, yolanda used is n + q = 28

n + q = 280.05n + 0.25q = 4

n + q = 28

0.05n + 0.25q = 4

n = 28 - q

0.05n + 0.25q = 4

0.05(28 - q) + 0.25q = 4

1.4 - 0.05q + 0.25q = 4

- 0.05q + 0.25q = 4 - 1.4

0.20q = 2.6

q = 2.6 / 0.20

q = 13

Substitute into

n + q = 28

n + 13 = 28

n = 28 - 13

n = 15

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Answer:

80

Step-by-step explanation:

The sum of the interior angles of a triangle is 180.  Subtract out the 2 angles that you know.

180 - 70 - 30 = 80

0.129 is the change in the growth rate of company.

According to statement

we have to find and compare the growth rate of the company weekly.

we use the growth rate formula is

GROWTH RATE = present - past / present

Substitute the values in this formula

1st week = 220-190 / 220

1st week = 0.136

2nd week = 252-220 / 252

2nd week = 32 / 252

2nd week = 0.126

3rd week = 290-252 / 290

3rd week = 0.131

4th week = 337 - 290 / 337

4th week = 0.139

5th week = 380 - 337 / 380

5th week = 0.113

6th week = 440 - 380 / 440

6th week = 0.136

7th week = 505 - 440 / 505

7th week = 0.128

Now we find the average value of growth rate

Average = 0.136 + 0.126+0.131+0.139+0.113+0.136+0.128 /7

Average = 0.909/7

Average = 0.129

So, 0.129 is the change in the growth rate of company.

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The value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]

The equation is given as:

x^yz = y^2

Rewrite the equation properly as follows

[tex]x^{yz} = y^2[/tex]

Take the yz root of both sides

[tex]\sqrt[yz]{x^{yz}} = \sqrt[yz]{y^2}[/tex]

Apply the law of indices

[tex]x^{\frac{yz}{yz}} = \sqrt[yz]{y^2}[/tex]

Divide yz by yz

[tex]x = \sqrt[yz]{y^2}[/tex]

Hence, the value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]

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Answer:

e

Step-by-step explanation:

Using euler's identity we can see that e^ipi=-1 and considering that i=y and  i^2=-1 we can conclude that x=e

The cross-section would be the same shape as the base. A cross-section cannot be a sphere because a cross-section must be two-dimensional, but a sphere is three-dimensional.

The statement that is true about the domain and range of each function is; A) Both the domain and range of the transformed function are the same as those of the parent function.

We are told that the graph of f(x) = |x| is reflected across the y-axis. Thus;

|-x| = x

Now, the function is translated to the left by 5 units and so the transformed function is; g(x) = |x + 5|

Thus, from the graph, we get;

Domain of both functions is the set of all real numbers.

Range of both functions is the set {y|y ≥ 0}

Thus, we conclude that Both the domain and range of the transformed function are the same as those of the parent function.

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Angles are formed when two or more lines intersect. Angles are majorly measured in degrees.

The required proof is as shown below:

Whenever a transversal passes through two parallel lines, angles are formed which have some similar properties.

             STATEMENTS                                           REASONS

1. AB ║DC                                                          Given.

2. < FDC ≅ < FBA                                              Alternate angle theorem.

3. <AFB  ≅ < DFC                                              Vertical opposite angle rule.

4. DF ≅ BF                                                         Given

5. ΔDFC  ≅ Δ BFA                                            Angle-Angle-Side property

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Step-by-step explanation:

The picture is the full explanation for this question answer.

18.19 is the solution for the given improper function.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

To add 8 11/12 and 9 5/18, we need to first find a common denominator. The smallest number that both 12 and 18 divide evenly is 36.

Converting 8 11/12 to an improper fraction:

8 11/12 = (8 × 12 + 11) / 12 = 107/12

Converting 9 5/18 to an improper fraction:

9 5/18 = (9 × 18 + 5) / 18 = 167/18

Now that we have a common denominator of 36, we can add the two fractions:

107/12 + 167/18 = (107 × 3) / (12 × 3) + (167 × 2) / (18 × 2)

= 321/36 + 334/36 = 655/36

So 8 11/12 + 9 5/18 = 655/36 or approximately 18.19.

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based on the number of marbles in the bag, the number of marble groups possible is 7,140 groups.

the probability of selecting 2 red and 1 yellow is 1/68.

first, find the number of marbles:

= 7 + 8 + 9 + 7 + 5

= 36

the number of marble groups are:

= 36 ! / (3 ! x 33 !)

= 7,140 groups

the probability of picking 2 red and 1 yellow is:

= (( (7! / (2! x 5!)) x ( ( 5! / (1! x 4!))) / 7,140

= 1 / 68

= 1.47%

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The unknown sides and angles of the triangle are 18 cm and 39 degrees respectively.

The side and angle of a triangle can be found as follows:

using sine law,

Angle A = 180 - 68 - 59 = 53 degrees

19.5 / sin 59 = a / sin 53

19.5 sin 53 = a sin 59

a = 19.5 sin 53 / sin 59

a = 15.5733924459 / 0.8571673007

a = 18.1680280047

a = 18 cm

15 / sin ∅ = 20 / sin 57

15 sin 57 = 20 sin ∅

sin ∅ = 12.5800585192 / 20

sin ∅= 0.62900292595

∅ = sin ⁻¹ 0.62900292595

∅ = 38.9763828249

∅ = 39 degrees.

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The business owner should be told to angle a spotlight mounted on the roof at the angle of =39°

The distance of the flagpole from the building = 55ft

The building has the height of = 45ft

The flagpole has the height of = 25ft

The angle can be calculated using the formula;

Tan θ = opposite/adjacent

Where opposite= 45ft

adjacent = 55ft

Tan θ = 45/55 = 0.82

θ = Tan–¹0.82

θ = 39°

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The graph of Lin's distance as a function of time cannot be a straight line graph because of decrease in speed.

Given that Lin walks half a mile at a constant rate i.e. Lin velocity is constant.

If the speed is low then the time will be high. If speed is high then the time will be low because of the following rule:

Speed=Distance/ time.

For the first five minutes the graph will be upward sloping because he was sprinting and his speed was high so he will cover much more distance.

But after five minutes the graph will be downward sloping as the speed becomes low and he willcover less distance.

Hence the graph of Line's distance will not look like linear curve.

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Answer:

[tex]\sf -3xy\left(2x^2-3xy+4y^2\right)[/tex]

Step-by-step explanation:

[tex]\sf -6x^3y+9x^2y^2-12xy^3[/tex]

To factor the GCF of 6x³y + 9x²y2 - 12xy³ let's apply the exponent rule:-

[tex]\boxed{\sf a^{b+c}=a^ba^c}[/tex]

[tex]\boxed{\sf x^3y=xx^2y,\:x^2y^2=xxyy,\:xy^3=xyy^2}[/tex]

[tex]\sf -6xx^2y+9xxyy-12xyy^2[/tex]

Rewrite,

[tex]\sf 2\cdot \:3xx^2y+3\cdot \:3xxyy+4\cdot \:3xyy^2[/tex]

Now, factor out the common term [tex]\sf -3xy[/tex]:-

__________________________

The item which yield the greatest level of accuracy to the true weight of rock with the least error is bricks.

A rock refers to a solid substance formed from the fusion of organic minerals.

Therefore, bricks is the item which yield the greatest level of accuracy to the true weight of rock with the least error.

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Answer:

The bars cost 1 each and the drinks cost 2 each.

Step-by-step explanation:

Let b = bars and d = drinks

4b + 3d = 10           6b + 2d = 10

There are a few ways to solve this.  If I want to eliminate the b's from both equations.  I would multiple the first equation all the way through by -6 and the second equation all the way through by 4.

4b+ 3d = 10

-6(4b + 3d) =(10)-6   Multiple all the way through by -6

-24b -18d = -60  A positive multiplies by a negative is a negative

6b + 2d = 10  

4(6b + 2d) = (10)4  Multiple all the way through by 4

24b + 8d = 40

Take the two bold equations from above and add them together

-24b - 18d = -60

24 b + 8d = 40  

          -10d = -20  Divide both sides by -10

d = 20 A negative divided by a positive is a negative.

Plug in 2o for d in either of the top two equations and get b = 1.