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The correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'

In this question, we have been given a statement 'the distribution of sample means approaches a normal curve as _________  increases to infinity'

We need to complete the statement.

The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

This means, the distribution of sample means approaches a normal curve as the sample size i.e., n increases to infinity.

Therefore, the correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'

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Answer:

Step-by-step explanation:

find the gradient of given equation:

3y+4x=12

3y= -4x+12

y= -4/3x+4

gradient= -4/3

perpendicular gradient:

m1xm2=-1

-4/3m2=-1

-4m2=-3

m2= 3/4

find y-intercept by inputting coordinates in y=mx+c

5=3/4(3)+c

5=9/4+c

5-9/4=c

c= - 11/4

equation:

y=3/4x-11/4

They must sample 385 subscribers to obtained this interval.

What do you mean by sample?

An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values.

According to the given question,

We have:

95% confidence interval for z-score is  1.96

Using this formula to find the number of  subscribers  they must sample to obtain this interval

n≥ (zσ/2 ÷ 2ME)²

Where:

n= Sample

zσ = Z-score

ME = margin of error

Let put in the formula,

n≥ [1.96 / 2(0.05)]²

n≥ [1.96 / 0.1]²

= (19.6)²

= 384.16

=385 (Rounded)

Therefore, they must sample 385 subscribers to obtained this interval.

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Answer: 6

Step-by-step explanation: the mean is the average. 5+3+10 = 18 and then you divide by the people (3) to get 6.

The length of  CF is 51 inches.

Complete question:

( In triangle ABC in which AD,BE and CF are the medians ),

In △ABC, ​ GF=17 in. ​ What is the length of CF¯¯¯¯¯? Enter your answer in the box.

What is the median in a triangle?

A line segment that joins a vertex to the mid-point of the side that is opposite to that vertex

The centroid G divides each median into the ratio 2:1, so GF is 1/3 of CF. That is, ...

CF = 3(GF) = 3(17 in)

CF = 51 in

So, the length of  CF is 51 inches.

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option (a) and (C).

The height of the parallelogram is 2 units and 2/3 units.

The sides of parallelogram are 6 units and 18 units .

Area of parallelogram (A) =12 square units.

Base of parallelogram (B) = 6 units.

formula used:

A = B*H

12 = 6*H

H = 12/6

H = 2 units.

if, base of parallelogram (B) = 18 units

A = B*H

12= 18*H

H = 12/18

H = 2/3 units.

the height of parallelogram are 2 and 2/3 units.

#123

For more information:

The parallelogram has a height of 2/3 units.

Given that,

A parallelogram has a surface area of 12 square units. The parallelogram has a side that is 18 units long. There are 6 units on the other side.

For a parallelogram to find the height;

Let,

Area of the parallelogram = Base * Height

12 = 18 * H

H = 12/18

H = 2/3

Therefore, the height of the parallelogram is 2/3 units.

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Answer: 25% of 12 is 3

Step-by-step explanation:

Since there 25% is 1/4 of 100%, you'd need to divide.

There are 12 pints of berries.

If 1/2 of 25% is 6 since [tex]2 \sqrt{12}=6[/tex], you can say that the percentage would be 2/4.

Now, divide 12 by 4: [tex]4\sqrt{12}=3[/tex]

3 in this case would be the 1/4 and the 1/4 is substituting 25%

So there are 3 pints of blueberries.

The spread of the sampling distribution of x is smaller than the spread of the corresponding population distribution sampling distribution.

In the given question,

We have to find the spread of the sampling distribution of x is............... the spread of the corresponding population distribution sampling distribution.

As we know that,

The size of the sample as well as its dispersion affect the sampling distribution's spread. We calculate the sampling distribution's spread as the population's standard deviation divided by the sample size's square root.

So, the spread of the sampling distribution of x is smaller than the spread of the corresponding population distribution sampling distribution.

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The right question is

The spread of the sampling distribution of x is .......... the spread of the corresponding population distribution sampling distribution.

larger than

smaller than

the same as

exactly 1/2

The ΔSVR ≅ ΔSUT by side angle side property of triangle.

The size of the sides and angles determines whether two or more triangles are congruent. The three sides and three angles of a triangle define its size and shape, accordingly. Two triangles are said to be congruent if their respective side and angle pairs are the same.

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In triangle SVR and triangle SUT

SR = ST (given)

∠RSV = ∠TSU ( Common)

SV = SU (given)

So, the ΔSVR ≅ ΔSUT by SAS property.

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According to the solving the co-ordinate mid-point D is (-4,0).

A point on a line which bisects the same line is a mid point. It divides the line in two equal halves.

The mid-point is equidistant from both the ends of the given line.

Middle point formula in coordinate geometry

M={(x1+x2)/2,(y1+y2)/2}

We need to find the coordinates of mid-point D of line AB, where

A is (-6x,4y)

B is (-2x,-4y)

By using Mid-point formula for coordinate D, we get

   x=-6+(-2)/2

⇒ x=-6-2/2

⇒x=-8/2

⇒x=-4

And y coordinate

y=4+(-4)/2

⇒y=4-4/2

⇒y=0/2

⇒y=0

The coordinates of mid-point D of line AB is (-4,0)

Hence, D is (-4,0)

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Answer:

length = 32.5, Width = 25.5

Step-by-step explanation:

Let x rep the width. Let x plus 7 rep the length.

x + x + 7 = 58

2x=58-7

2x=51

2x/2 = 51/2

x= 25.5

x plus 7 =

= 25.5 + 7

=32.5

✨️Hope that helps✨️

Both areas are equal, 4 cm²

Answer:

Area of triangle = 4 cm²

Area of square = 4 cm²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

From inspection of the given diagram:

Substitute the values into the formula to find the area of the triangle:

[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \times 2 \times 4\\A&=1 \times 4\\A&=4\;\sf cm^2\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]

From inspection of the given diagram:

Substitute the value into the formula to find the area of the square:

[tex]\begin{aligned}\implies A&=2^2\\A&=2 \times 2\\A&=4\;\sf cm^2\end{aligned}[/tex]

The area of the triangle is 4 cm², and the area of the square is 4 cm², thus proving that the triangle and the square have the same area.

Answer:

$594

Step-by-step explanation:

450x1.32=$594

450+32%=$594

Answer:

[tex] \huge{ \bold{f(g(x)) = 4x + 4}} \\ \\ \huge{ \bold{g(f(x)) = 4x - 5}}[/tex]

Step-by-step explanation:

f(x) = 4x-8

g(x)=x+3

In order to find f(g(x)) you substitute g(x) into f(x) that's where ever you find x in f(x) you replace it with g(x) and solve

We have

[tex]f(g(x)) = 4(x + 3) - 8 \\ = 4x + 12 - 8 \\ = 4x + 4[/tex]

In order to find g(f(x)) you substitute f(x) into g(x) that's where ever you find x in g(x) you replace it with f(x) and solve

We have

[tex]g(f(x)) = (4x -8) + 3 \\ = 4x - 8 + 3 \\ = 4x - 5[/tex]

Hope this helps you

If a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter

The total distance that tram moved downwards = 35 meters

Total time taken = 7 seconds

Here we have to use the unitary method

The change in the tram's elevation for each second = The total distance that tram moved downwards / Total time taken

Substitute the values in the equation

The change in the tram's elevation for each second = 35 /7

Divide the terms

= 5 meters

Hence, if a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter

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Answer:

30 lb

Step-by-step explanation:

75% of trash is recyclable.

40 lb trash.

75% of 40 lb = = 40/100 × 75 lb = 0.40 × 75 lb = 30 lb

Answer: 30 lb

Answer:

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

Answer:

32.3x + 136.85y

Step-by-step explanation:

Let's take it as,

→ z = 100%

Forming the equation,

→ z + 15% = 38x + 161y

Now the value of z will be,

→ z + 15% = 38x + 161y

→ z = 38x + 161y - (1 - (15/100))

→ z = (38x + 161y) × (1 - 0.15)

→ z = (38x + 161y) × (0.85)

→ [ z = 32.3x + 136.85y ]

Hence, the answer is above.

Ximena need to invest $2384 so that account value reach $5,100 in

6 years.

As given in the question,

We have to find Principal ' P'

Given interest rate R = 2.2%

Amount = $5100

time t  = 6 years

Formula used

Amount = P + P( 1 + R%)^t

Putting values in the formula

5100 = P + P (1 + 2.2%)^6

5100 = P ( 1 + (1 + 2.2%)^6)

5100 = P (1 + (1.022)^6)

5100 = P (1 + 1.139)

5100 = P (2.139)

P = 5100/2.139

P = 2384.291 ≈ 2384

Therefore,  Ximena need to invest $ 2384 to reach $5,100 in 6 years with interest rate 2.2%.

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Answer:

P=4470

Step-by-step explanation:

i did it

The value of x=5 if given quadrilateral is parallelogram.

What is parallelogram?

A parallelogram is a flat shape with four straight, connected sides so that opposite sides are congruent and parallel. This means a parallelogram is a plane figure, a closed shape, and a quadrilateral.

We know, the opposite sides of parallelogram are equal

therefore, 5x-8 = 2x+7

5x -2x = 7+8

3x = 15

x =5

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Answer:

4.47 seconds.

Step-by-step explanation:

Given function:

[tex]h(t)=-10t^2+200[/tex]

where:

The rock will hit the ground when h(t) = 0.  

Therefore, set the function to zero and solve for t:

[tex]\begin{aligned}h(t)&=0\\\implies -10t^2+200&=0\\10t^2&=200\\t^2&=20\\t&=\pm\sqrt{20}\\t&=-4.47, 4.47\;\; \sf (2\;d.p.)\end{aligned}[/tex]

As time is positive, t = 4.47 s only.

Answer :

Step-by-step

Answer:

18%,1/8,18%, 8/20 0.8

Step-by-step explanation:

0.8 8/100 18/100 1/8 8/20

0.8 , 0.08 0.18 0.12 0.4

0.08 0.12 0.18 0.4 0.8

Answer:

8%, 1/8, 18%, 8/20

Step-by-step explanation:

Lets make all of these into decimals (its easier that way).
8% = 0.08
18% = 0.18
1/8 = 0.125

8/20 = 0.4

Now, put them into least to greatest! :)

The equation that represents the line  that is perpendicular to the graph of 4x + 3y = 9 and passes through (-2,3) is

[tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]

Let us revise some rules

1.   The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]

2.  The slope of a line whose equation is ax + by = c is [tex]m = \frac{-a}{b}[/tex], where a is the coefficient of x and b is the coefficient of y

The equation of the given line is 4x + 3y = 9

[tex]m = \frac{-a}{b}[/tex]

whereas a is the coefficient of x and b is the coefficient of y

Therefore the coefficient of x = 4 and the coefficient of y = 3

a = 4 and b = 3

[tex]m = \frac{-a}{b}[/tex]

The slope of the perpendicular line to the given line is [tex]\frac{-1}{m}[/tex]

That means reciprocal the fraction and change its sign

The slope of the perpendicular line = [tex]\frac{3}{4}[/tex]

The form of the equation is y = mx + b

- Substitute m by [tex]\frac{3}{4}[/tex]

y = [tex]\frac{3}{4}[/tex] x + b

To find b substitute x and y in the equation by the coordinates

of a point on the line

The perpendicular line passes through point (-2 , 3)

x = -2 and y = 3

3 = [tex]\frac{3}{4}[/tex](-2) + b

3 = [tex]\frac{-3}{2}[/tex]+ b

Add to both sides

[tex]\frac{9}{2}[/tex] = b

y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]

The equation that represents the line  that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]

Hence the answer is perpendicular to graph of 4x+3y=9 and passes through (-2,3) is [tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]

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Answer:

3x -4 >5 = x > 3.

1 -2x>7 = x ≥ -3

Step-by-step explanation:

The population in the next 20 years would be 2653 people. The result is obtained by the equation of estimating the future population.

The future population can be estimated by the following equation:

P = P₀ × (1 + i)ⁿ

Where

If the recent population is 1000 people and the growth rate is 5% per year, what would the population be in the next 20 years?

The population in the next 20 years would be

P = P₀ × (1 + i)ⁿ

P = 1000 × (1 + 0.05)²⁰

P = 1000 × (1.05)²⁰

P = 1000 × 2.6533

P = 2653 people

Hence, the population in the next 20 years would be 2653 people.

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Answer:

(5x5) + (5x2)

Step-by-step explanation:

is that helpful i dont really get what youre asking

Answer:

1+2*3*5+4

Step-by-step explanation:

Step-by-step explanation:

false.

QR and ES are line segments.

a ratio between them is about their lengths, not about their position.

so, no, the given ratio has nothing to do with the coordinate itself.