can somebody help me with this question please​

Answer:

The 68% confidence interval is (6.3, 6.7).

The 95% confidence interval is (6.1, 6.9).

The 99.7% confidence interval is (5.9, 7.1).

Step-by-step explanation:

The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\bar x[/tex]

And the standard deviation of the sample means (also known as the standard error)is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]

As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.

(a)

Compute the 68% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]

The 68% confidence interval is (6.3, 6.7).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]

(b)

Compute the 95% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]

The 95% confidence interval is (6.1, 6.9).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]

(c)

Compute the 99.7% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]

The 99.7% confidence interval is (5.9, 7.1).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]

Answer:

The value of the radius is 4.46cm.

Step-by-step explanation:

Given the perimeter is 28 cm. So, if we want to find the radius then we should consider this perimeter as the circumference of the circle. Thus, we have to equate this value with the circumference (perimeter of the circle).

The perimeter of the circle or circumference = 2π r  

Here, π = 22/7

r = radius

Now, 2π r = 28

r = 28 / 2π

r = 4.46 cm

Answer:

For the function [tex]f(x)=\frac{1}{x} +3[/tex]. The domain is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex] and the range is  [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

For the function [tex]g(x) =\sqrt{x+6}[/tex]. The domain is [tex]\left[-6, \infty\right)[/tex] and the range is [tex]\left[0, \infty\right)[/tex].

Step-by-step explanation:

The domain of a function is the set of input or argument values for which the function is real and defined.

The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.

[tex]f(x)=\frac{1}{x} +3[/tex] is a rational function.  A rational function is a function that is expressed as the quotient of two polynomials.

Rational functions are defined for all real numbers except those which result in a denominator that is equal to zero (i.e., division by zero).

The domain of the function is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex].

The range of the function is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

[tex]g(x) =\sqrt{x+6}[/tex] is a square root function.

Square root functions are defined for all real numbers except those which result in a negative expression below the square root.

The expression below the square root in [tex]g(x) =\sqrt{x+6}[/tex] is [tex]x+6[/tex]. We want that to be greater than or equal to zero.

[tex]x+6\geq 0\\x\ge \:-6[/tex]

The domain of the function is [tex]\left[-6, \infty\right)[/tex].

The range of the function is [tex]\left[0, \infty\right)[/tex].

Answer:

21

Step-by-step explanation:

Multiply 3 quarts to 7 hours

Which is 21

Mark me as brainliest

Step-by-step explanation:

Edith picks 3

Rupert picks 3

3 + 3 = 6 quarts of blueberries in 1 hour

6 blueberries = 1 hour

x. =. 7 hours

x = 7 hours ÷ 1 hour × 6 blueberries

x =. 42 quarts of blueberries

Answer:

Lateral surface area would be (13*4)*2 + (4*4)*2 = (52*2) + (16*2) = 104 + 32 = 136 units^2.

Surface area would be 136 + 104 = 240 units^2.

Step-by-step explanation:

I hope this helps you!

Answer:

1. Vertex (-3,2)

A) (x+3)² + 5

B) (x-3)² + 2

C) (x-1)² -5

I hope these are all correct

Step-by-step explanation:

Answer:

[tex]approx. = 85.28 {ft}^{2} [/tex]

Step-by-step explanation:

You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.

(l×w)+(πr^2)/2

(10×7)+((π2^2)/2

79+2π

[tex]approx. = 85.28 {ft}^{2} [/tex]

Answer:

  33 units²

Step-by-step explanation:

A (graphing) calculator shows you that f(4) ≈ 8, and f(8) ≈ 8.5. The curve is almost a straight line between, so the area is approximately ...

  A = (1/2)(8 + 8.5)(4) = 33

__

If you do the integration, it gets a bit messy.

  [tex]\displaystyle\dfrac{5}{7}\int_4^8{x^{2/7}}\,dx+\dfrac{1}{2}\int_4^8{x^{4/9}}\,dx+\int_4^8{6}\,dx\\\\=\left.\left(\dfrac{5}{9}x^{9/7}+\dfrac{9}{26}x^{13/9}+6x\right)\right|_4^8\approx 33.16[/tex]

The appropriate answer choice is 33 square units.

Answer:

Rate of change of function 1: ZERO

Rate of change of function 2: TWO

The rate of change of function 2 is 2 more than the rate of change of function 1.

Step-by-step explanation:

Hope this helps and please mark as brainiest!

Answer:

The answer is 2.

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

p^2 -6p +6

Let p=-1

(-1)^2 -6(-1) +6

1 +6+6

13

Answer: k = 12

Step-by-step explanation:

x² + kx + 36 = 0

In order for x to have exactly one solution, it must be a perfect square.

(x + √36)² = 0

(x + 6)² = 0

(x + 6)(x + 6) = 0

x² + 6x + 6x + 36 = 0

x² + 12x + 36 = 0

 k = 12

Answer:

y - 2 = (3/2)(x + 1)

Step-by-step explanation:

Start with the point-slope formula y - k = m(x - h).  With m = 3/2, h = -1 and k = 2, we get:

y - 2 = (3/2)(x + 1)

Answer:

A

Step-by-step explanation:

For point-slope form, you need a point and the slope.

y - y₁ = m(x - x₁)

Looking at the graph, the points you have are (4, 0) and (-4, -4).  You can use these points to find the slope.  Divide the difference of the y's by the difference of the x's/

-4 - 0 = -4

-4 - 4 = -8

-4/-8 = 1/2

The slope is 1/2.  This cancels out choices C and D.

With the point (-4, -4), A is the answer.

the equation of the line in slope-intercept form is:

y = (1/2)x - 2

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

From the graph, two points on the line are (-4, -4) and (4,0),

The formula for the slope of a line is:

m = (y₂ - y₁) / (x₁ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the given points (-4, -4) and (4, 0), we can calculate the slope:

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

m = 4 / 8

m = 1/2

Now that we know the slope, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

To find the y-intercept, we can use one of the given points on the line. Let's use the point (-4, -4):

y = mx + b

-4 = (1/2)(-4) + b

-4 = -2 + b

b = -2

Therefore, the slope-intercept form of the line is y = (1/2)x - 2.

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ7

Answer:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

Step-by-step explanation:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.

Answer:

B. No solution.

Step-by-step example

I will try to solve your system of equations.

3x−y=4;6x−2y=7

Step: Solve3x−y=4for y:

3x−y+−3x=4+−3x(Add -3x to both sides)

−y=−3x+4

−y

−1

=

−3x+4

−1

(Divide both sides by -1)

y=3x−4

Step: Substitute3x−4foryin6x−2y=7:

6x−2y=7

6x−2(3x−4)=7

8=7(Simplify both sides of the equation)

8+−8=7+−8(Add -8 to both sides)

0=−1

Therefore, there is no solution, and the lines are parallel.

Answer:

For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:

[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]

Where x represent the net price. And if we solve for the value of x we got:

[tex] x= 100 *\frac{156}{88}= 177.273[/tex]

So then the net price for this case would be $ 177.273

Step-by-step explanation:

For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:

[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]

Where x represent the net price. And if we solve for the value of x we got:

[tex] x= 100 *\frac{156}{88}= 177.273[/tex]

So then the net price for this case would be $ 177.273

Answer:

The percent of increase is 25%

Step-by-step explanation:

Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%

Answer:

14.45 = 14.5 = 15     8.05=8

Step-by-step explanation:

When rounding use the rule "5 or more raise the score, 4 or less let it rest." We round 14.45 to 14.5 because .45 will round to .50. We are left with 14.50. The .50 rounds the 14 to 15. For 8.05 because there is a 0 before the 5 we leave the number at 8.

Answer:

Step-by-step explanation:

Given:

AB║DC and BC║AE

To prove:

[tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex]

                Statements                  Reasons

1). ∠ABE ≅ ∠CDB                    1). Alternate interior angles

2). ∠AEB ≅ ∠CBD                  2). Alternate interior angles

3). ΔCBD ~ ΔAEB                   3). AA property of similarity

4). [tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex]                             4). Property of similarity [Corresponding sides                                                          of two similar triangles are proportional]

Answer:

The general term for the given sequence is:

[tex]a_n=(-1)^{n+1}\dfrac{n}{(n+1)^2}[/tex]

Step-by-step explanation:

The given series is:

[tex]\dfrac{1}4, - \dfrac{2}9, \dfrac{3}{16}, - \dfrac{4}{25}, ......[/tex]

First of all, let us have a look at the positive and negative sign of the sequence.

2nd, 4th, 6th ..... terms have a negative sign.

For this we can use the following

[tex](-1)^{n+1}[/tex]

i.e. Whenever 'n' is odd, power of (-1) will become even resulting in a positive term for odd terms i.e. (1st, 3rd, 5th ........ terms)

Whenever 'n' is even, power of (-1) will become odd resulting in a negative term for even terms i.e. (2nd, 4th, 6th ..... terms)

Now, let us have a look at the numerator part:

1, 2, 3, 4.....

It is simply [tex]n[/tex].

Now, finally let us have a look at the denominator:

4, 9, 16, 25 ......

There are squares of the (n+1).

i.e. 1st term has a square of 2.

2nd term has a square of 3.

and so on

So, it can be represented as:

[tex](n+1)^2[/tex]

[tex]\therefore[/tex] nth term of the sequence is:

[tex]a_n=(-1)^{n+1}\dfrac{n}{(n+1)^2}[/tex]

Answer:

7

Step-by-step explanation:

Answer:

a. 0.67

b. 1.31

Step-by-step explanation:

We have the following information n = 20, mean (m) = 10 and standard deviation (sd) = 3

a.

SE (m) = sd / n ^ (1/2)

replacing we have:

SE (m) = 3/20 ^ (1/2) = 0.67

Therefore the standard error of the mean is 0.67

b.

the critical value is obtained as shown below:

the level of sifnificance is alfa = 1 - 0.95 = 0.05

the critical value with level of significance alfa / 2 = 0.05 / 2 = 0.025

and to this value corresponds z = 1.96 (z table)

The margin of error with 95 confidence is calculated as follows:

E = z * SE

E = 1.96 * 0.67

E = 1.31

Therefore the margin of error is 1.31

(a) The standard error will be "0.67".

(b) The margin of error will be "1.31".

According to the question,

Standard deviation,

Sample size,

(a)

As we know,

→ The Standard error,

= [tex]\frac{sd}{\sqrt{n} }[/tex]

= [tex]\frac{3}{\sqrt{20} }[/tex]

= [tex]0.67[/tex]

(b)

As we know,

→ The margin of error,

= [tex]Z_{a/2}\times \frac{sd}{\sqrt{n} }[/tex]

By substituting the values, we get

= [tex]Z_{a/2}\times \frac{3}{\sqrt{20} }[/tex]

= [tex]1.96\times 0.67[/tex]

= [tex]1.31[/tex]

Thus the above response is right.

Learn more:

https://brainly.com/question/10501147

Answer:

Step-by-step explanation:

g(x) = |x-3| is neither even nor odd; the graph is not symmetric about the y-axis (as characterizes even functions), and is not symmetric about the origin either.

g(x) = x + x is actually g(x) = 2x, which is an odd function.  The graph is symmetric about the origin.

Answer:

a)

The object slowing down  S = -72 centimetres after t = 4 seconds

b)

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres

Step-by-step explanation:

Step(i):-

Given  S = t³ - 3 t² - 24 t + 8 ...(i)

   Differentiating equation (i) with respective to 'x'

       [tex]\frac{dS}{dt} = 3 t^{2} - 3 (2 t) - 24[/tex]

     Equating Zero

      3 t ² - 6 t - 24 = 0

 ⇒   t² - 2 t - 8   = 0

 ⇒  t² - 4 t + 2 t - 8 = 0

⇒ t (t-4) + 2 (t -4) =0

⇒  ( t + 2) ( t -4) =0

⇒ t = -2 and t = 4

 Again differentiating with respective to 'x'

   [tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6[/tex]

Step(ii):-

Case(i):-

Put t= -2

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( -2) -6 = -12 -6 = -18 <0[/tex]

The  maximum object

S = t³ - 3 t² - 24 t + 8

S = ( -2)³ - 3 (-2)² -24(-2) +8

S = -8-3(4) +48 +8

S = - 8 - 12 + 56

S = - 20 +56

S = 36

Case(ii):-

   put  t = 4

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( 4) -6 = 24 -6 = 18 >0[/tex]

The object slowing down at t =4 seconds

The minimum objective function

S = t³ - 3 t² - 24 t + 8

S = ( 4)³ - 3 (4)² -24(4) +8

S =  64 -48 - 96 +8

S = - 72

The object slowing down  S = -72 centimetres after t = 4 seconds

Final answer:-

The object slowing down  S = -72 centimetres after t = 4 seconds

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres

Answer:

Step-by-step explanation:

Area of a rectangle = l × w

where

l is the length

w is the width

The length is seven times the width is written as

l = 7w

Area of the rectangle = 175 cm²

7w × w = 175

7w² = 175

Divide both sides by 7

w² = 25

Find the square root of both sides

w = √25

w = 5cm

But l = 7w

l = 7(5)

l = 35cm

The length is 35cm

The width is 5cm

Hope this helps you.

Answer:

69.9 mg

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is time,

and T is the half life.

A = 400 (½)^(4000 / 1590)

A = 69.9 mg

Answer:

Step-by-step explanation:

x-4 greater or equal 0

x greater or equal 4

Answer:

The actual answer is x is greater than or equal to 6 (i used the answer that was on here and got it wrong so here is the correct answer!!)

just did the test on edg 2021

Answer:

H0: p = 3.5

H1: p < 3.5

Step-by-step explanation:

We are told that past studies have indicated that the percentage of smokers is estimated to be about 35%, but with the new smoking cessation programs that have been implemented, it is believed that the percentage of smokers has been reduced, we must propose our null and alternative hypotheses, which would be the following:

Null hypothesis: H0: p = 3.5

Alternative hypothesis: H1: p < 3.5

Answer:

4

Step-by-step explanation:

25% of 25

0.25 × 25 = 6.25

15% of 15​

0.15 × 15 = 2.25

Find the difference.

6.25 - 2.25

= 4

Answer:

y=-1/3x-1

Step-by-step explanation:

We have the information y=3x-5, the lines are perpendicular, and the new line passes through (6,-3). The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 3, so flip it to 1/3 and multiply by -1, we get the slope of the new line as -1/3. So far we have the equation y=-1/3x+b. We are given a point on the line, (6,-3), so we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as -3=-1/3(6)+b. First you multiply to get -3=-2+b, then you add 2 to both sides to isolate the variable and you get b=-1. Then you can use b to complete your equation with y=-1/3x-1.