draw a rectangle give the length and the width to show that it has an area of 12cm make sure one side is longer than the other to show length and width

Answers

Answer 1
To find area, you multiply length * width. There are 4 sides on a number, so we need to have a equation like this. x * x * y * y = 12cm. If we do 4 * 4, we get 8. We could also use 2 * 2 = 4. 8 + 4 = 12. So, width = 8, and length = 4.

Hope this helps! ☺♥

Related Questions

help pleeeaaase this............... ..... .... .

Answers

check the picture below.

Determine if the given x value is a zero of f(x)=x^4+3x^3-6x^2+3; x=-2

Answers

Plug in -2 for x and evaluate.

f(-2) = (-2)^4 + 3(-2)^3 - 6(-2)^2 + 3

f(-2) = 16 - 24 - 24 + 3

f(-2) = -29

-2 is not a zero of the polynomial.

Estimate how many times larger 7 x 10^10 is than 13 x 10^8. A.50 B.100 c.200 d.400

Answers

7 x 10^10 = 70,000,000,000
13 x 10^8 = 1,200,000,000

70,000,000,000/1,200,000,000 = 58.3333333

I would go with A :)

What is the difference between –4 and 6?

Answers

The difference between -4 and 6 would be 2.
Hope this helps!

Answer:

2

Step-by-step explanation:

Took the test ;)

(This is very confusing)Tania planted five seeds in her garden nadia planted times as many seeds as Tania how many seeds did nadia plant

Answers

There's a number missing from the question. It's supposed to be right before the word "times".
If it were there, the answer would be (5 times that number).
The way the question is written, without that number, there's no answer.

Answer:

there isn't a number to multiply

Step-by-step explanation:

how would i write y= -7x+25 In Standard form?

please help:)

Answers

7x+y=25

nohpihot7 ggyfffffff
y = -7x + 25

Isolate the constant to write is in standard form.

You want it in the form

Ax + By = C

7x + y = 25

Done!

Where is the hole for the following function located? mc005-1.jpg

Answers

The holes of the graph are located at (5, 3) and (-1, 11)

How to determine the hole of the graph

From the question, we have the following parameters that can be used in our computation:

The graph

The holes of the graph are at (5, 3) and (-1, 11)

This is so because the function is not defined at this value

Also, we can see that

The function has it vertical asymptotes are x = 2 and x = -2

a pet store has 30 animals. some are cats the rest are dogs. the cats cost $50 each. the dogs cost $100 each. if the total for all 30 animals is $1900, how many cats are there?

Answers

Dogs= X
Cats= Y

X + Y = 30

100x + 50y= 1900

Easiest way is to solve by substitution.

[Looking for Y]

x+y=30

[subtract Y]

X= 30- Y

—————

Next, plug that into the next equation.

100 (30-y) + 50y= 1900

[Distribute]

300- 100y + 50y= 1900

[Combine Like Terms]

300- 50y= 1900

[subtract 300]

-50y= 1600

[divide by -50]

Y= ANSWER

This is Systems of Equations.

Answer:

There are 22 cats and 8 dogs.

Step-by-step explanation:

Let the cats be represented by = c

Let the dogs be represented by = d

Given, that the pet store has 30 pets.

First equation forms :

[tex]c+d=30[/tex]            ........(1)

Also given, the cats cost $50 each and dogs cost $100 each and the total for all is $1900. Now second equation forms:

[tex]50c+100d=1900[/tex]     .........(2)

From equation (1) we get [tex]c=30-d[/tex]

Putting this value of c in equation 2:

[tex]50(30-d)+100d=1900[/tex]

[tex]1500-50d+100d=1900[/tex]

=> [tex]50d=400[/tex]

=> [tex]d=8[/tex]

Now,[tex]c+d=30[/tex]

So, [tex]c=30-8[/tex]

[tex]c=22[/tex]

Hence, there are 22 cats and 8 dogs.

6% sales tax, hotel charges $265 find cost before tax?

Answers

265 x 0.06 = 15.9

265 - 15.9 = 249.1

249.1 is your answer

hope this helps
I think he is right maybe

Will the standard form 3.2 × 10^–4 be more or less than 1? Explain what effect the negative exponent has.

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ 3.2\cdot 10^{-4}\implies 3.2\cdot \cfrac{1}{10^4}\implies \cfrac{3.2}{10^4}\implies \cfrac{3.2}{10000}\implies 0.00032~\ \textless \ ~1[/tex]

A box contains 3 blue and 2 red marbles while another box contains 2 blue and 5 red marbles. a marble drawn at random from one of the boxes turns out to be blue. what is the probability that it came from the first box?

Answers

First add all the numbers together to get the total number of marbles which would be 12 then make a fraction 3/12. Which can be simplified to 1/4 which if needed can be changed to a percentage of 25%. So your answer is either 1/4 or 25% depending on how your teacher would like it written.

Final answer:

The probability that a randomly selected blue marble came from the first box is 7/31, which is approximately 0.2258 when rounded to four decimal places.

Explanation:

The probability that the blue marble came from the first box can be found using Bayes' theorem and the concept of conditional probability. First, we need to determine the probability of drawing a blue marble from either box (P(Blue)). Then, we calculate the probability of drawing a blue marble from the first box (P(Blue|First box)). Finally, we apply Bayes' theorem to find the probability that the blue marble came from the first box (P(First box|Blue)).

Here are the relevant probabilities:

P(First box) = 1/2 (since there are only two boxes)

P(Second box) = 1/2

P(Blue|First box) = 3/5 (3 blue out of 5 total marbles)

P(Blue|Second box) = 2/7 (2 blue out of 7 total marbles)

Using these probabilities, we calculate P(Blue):

P(Blue) = P(Blue|First box) * P(First box) + P(Blue|Second box) * P(Second box) = (3/5) * (1/2) + (2/7) * (1/2) = 3/10 + 1/7 = 21/70 + 10/70 = 31/70

Now, we apply Bayes' theorem to get P(First box|Blue):

P(First box|Blue) = [P(Blue|First box) * P(First box)] / P(Blue) = [(3/5) * (1/2)] / (31/70) = (3/10) / (31/70) = (3/10) * (70/31) = 21/310 = 7/31 or approximately 0.2258 (rounded to four decimal places)

Therefore, the probability that the marble came from the first box is 7/31.

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,7) and perpendicular to 3x+7y=1

Answers

Slope intercept form & in standard form , passes through (1, 7) , perpendicular to 3x + 7y = 1

Turn 3x + 7y = 1 into slope-intercept form.

Remember, slope-intercept form is : y=mx+b where m=slope & b=y-intercept.

To turn out given equation into slope-intercept form, we must get x & y onto different sides.

So, subtract 3x from both sides.

7y = -3x + 1

Then, divide both sides by 7.

y = -3/7x + 1/7

Remember, when an equation is perpendicular to another equation, both equations have negative reciprocals. 

m₁=-3/7 & m₂=7/3

Our new equation has these things in it :

A slope of 7/3 & it passes through (1, 7)

So, simply plug these into the slope-intercept equation.

y=mx+b

y = 7/3x + 7 → (a)Slope-intercept form 

Now we must put this into (b)standard form.

Standard form is :  Ax+Bx=C

So, we just use our slope-intercept form, but rearrange it :)

y = 7/3x + 7

In standard form, x & y are on the same side, so we simply subtract 7/3x from both sides.

-7/3x + y = 7 → (b)Standard Form

~Hope I helped!~

three times the quantity five less than x, divided by the product of six and x

Answers

3• 5-x
———- that would be it
6•x

The simplified expression is (x - 5) / (2x).

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The expression given is 3 (x - 5) / (6x)

We can simplify this expression by following the order of operations, which is a set of rules that tells us which operations to perform first in a mathematical expression.

The order of operations.

Perform any calculations inside parentheses first.

Exponents (ie: powers and square roots, etc.)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using the order of operations, we can simplify the expression as follows:

We start by simplifying the expression inside the parentheses.

x - 5 represents five less than x.

Next, we multiply the result of step 1 by 3.

= 3 (x - 5)

= 3x - 15

Finally, we divide the result of step 2 by the product of 6 and x.

= (3x - 15) / (6x)

= (3(x - 5)) / (6x)

= (x - 5) / (2x)

Therefore,

The simplified expression is (x - 5) / (2x).

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Which are the solutions of the quadratic equation?
x2 = 7x + 4

Answers

The solutions to the quadratic equation x² = 7x + 4 are found by using the quadratic formula, which results in two solutions: [tex](\frac{7 + \sqrt{65}}{2 },\frac{7 - \sqrt{65}}{2 })[/tex]

The solutions to the quadratic equation x² = 7x + 4 can be found by first rewriting the equation in standard form as x² - 7x - 4 = 0. To solve this quadratic equation, we can factor it, complete the square, or use the quadratic formula. In this case, let's factor the equation if possible. Unfortunately, this quadratic does not factor neatly. Therefore, we apply the quadratic formula which is [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex] , where a = 1, b = -7, and c = -4.

After substitution, we get [tex]x = \frac{7 \pm \sqrt{49 + 16}}{2}[/tex]. This simplifies to x = [tex]\frac{7 \pm \sqrt{65}}{2}[/tex], resulting in two solutions: [tex]x = \frac{7 + \sqrt{65}}{2 }[/tex]and [tex]x = \frac{7 - \sqrt{65}}{2 }[/tex]. Therefore, the solution set is [tex](\frac{7 + \sqrt{65}}{2 },\frac{7 - \sqrt{65}}{2 })[/tex]

Write an equation of a line that does not have a y intercept

Answers

Any equation that is simply x = [number] will never intersect the y-axis, and therefore has no y-intercept. An example of this would be x = 3. It would be a vertical line, going through 3 on the x-axis, but since it is perfectly vertical, it would never intersect the y-axis.

Which of the following functions are homomorphisms?

Answers

Part A:

Given [tex]f:Z \rightarrow Z, [/tex] defined by [tex]f(x)=-x[/tex]

[tex]f(x+y)=-(x+y)=-x-y \\ \\ f(x)+f(y)=-x+(-y)=-x-y[/tex]

but

[tex]f(xy)=-xy \\ \\ f(x)\cdot f(y)=-x\cdot-y=xy[/tex]

Since, f(xy) ≠ f(x)f(y)

Therefore, the function is not a homomorphism.



Part B:

Given [tex]f:Z_2 \rightarrow Z_2, [/tex] defined by [tex]f(x)=-x[/tex]

Note that in [tex]Z_2[/tex], -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular [tex]f(x)=x[/tex]

[tex]f(x+y)=x+y \\ \\ f(x)+f(y)=x+y[/tex]

and

[tex]f(xy)=xy \\ \\ f(x)\cdot f(y)=xy[/tex]

Therefore, the function is a homomorphism.



Part C:

Given [tex]g:Q\rightarrow Q[/tex], defined by [tex]g(x)= \frac{1}{x^2+1} [/tex]

[tex]g(x+y)= \frac{1}{(x+y)^2+1} = \frac{1}{x^2+2xy+y^2+1} \\ \\ g(x)+g(y)= \frac{1}{x^2+1} + \frac{1}{y^2+1} = \frac{y^2+1+x^2+1}{(x^2+1)(y^2+1)} = \frac{x^2+y^2+2}{x^2y^2+x^2+y^2+1} [/tex]

Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.



Part D:

Given [tex]h:R\rightarrow M(R)[/tex], defined by [tex]h(a)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right) [/tex]

[tex]h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\ \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)[/tex]

but

[tex]h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\ \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)[/tex]

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.



Part E:

Given [tex]f:Z_{12}\rightarrow Z_4[/tex], defined by [tex]\left([x_{12}]\right)=[x_4][/tex], where [tex][u_n][/tex] denotes the lass of the integer [tex]u[/tex] in [tex]Z_n[/tex].

Then, for any [tex][a_{12}],[b_{12}]\in Z_{12}[/tex], we have

[tex]f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\ \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)[/tex]

and

[tex]f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)[/tex]

Therefore, the function is a homomorphism.

A running cheetah begins to slow down. For each meter the cheetah travels, its speed changes by −3.4 kilometers per hour. The cheetah travels a total of 21.5 meters.

What is the total change in the cheetah's speed during this time?

Drag and drop the correct answer into the box.

73.1.
71.9.
-71.9.
-73.1.

Answers

Δv = -3.4 km/h/m * 21.5 m = -73.1 km/h

Using a table show an estimate of the solution of the equation 6n+3=2

Answers

6n+3=2
Regroup
6n=2-3
6n=-1
Divide by 6n
6n/6n=-1/6n
=-0.16666

Using disk washers, find the volume of the solid obtained by rotating the region bounded by the curves y=sec(x), y=1, x=−1, and x=1 about the x-axis.

Answers

General integral for volume using washer method:
[tex]V = \pi \int_a^b (R^2 - r^2) dx[/tex]

First determine limits along x-axis.
region is bounded by x=1 and x=-1, so the limits are also -1 and 1.

Next determine R(x) and r(x)
R is the long radius, which is distance from x-axis to upper bound.
The upper bound of region is y = sec(x).
R = sec(x)

r is the short radius, which is distance from x-axis to lower bound.
The lower bound is y = 1.
r = 1

Sub into integral:
[tex]V = \pi \int_{-1}^1 (sec^2 x - 1) dx[/tex]

Integrate
[tex]V = \pi |_{-1}^1 (tan x - x)[/tex]

Evaluate
[tex]V = \pi[(tan(1) -1) - (tan(-1) +1)] \\ \\ V = 2\pi(tan(1) -1) \\ \\ V = 3.502[/tex]

Final answer:

We are finding the volume of a solid obtained by rotating a region bounded by specific curves about the x-axis. This involves the method of disk washers and the calculation of an integral. However, the calculation is impossible with this exact set of curves due to the undefined values at x = π/2 and x = -π/2.

Explanation:

To answer your question, let's first understand what is happening. We are taking the region between the curves y=sec(x), y=1, x=-1, and x=1 and rotating it about the x-axis. This creates a type of solid shape called a solid of revolution. We can find the volume of such a shape using the method of cylindrical shells or disk washers.

The volume V of the solid obtained by rotating about the x-axis the region confined by the given curves is given by the formula:

V = ∫ (from a to b) π [R(x)² - r(x)²] dx

where R(x) is the distance from the x-axis to the outer curve (y=sec(x)), and r(x) is the distance from the x-axis to the inner curve (y=1).

However, calculating the integral ∫ (from -1 to 1) π [sec(x)² - 1] dx directly can be difficult because the function sec(x) is undefined at x = π/2 and x = -π/2.

A typical way around such difficulties is to use a suitable trigonometric substitution, but in this case, the function sec(x) is periodic with a period of 2π, so we can't avoid these points, both of which lie in the interval from -1 to 1. Hence, it is impossible to find the volume of the solid as stated by rotating about the x-axis the region between the curves y = sec(x), y = 1, x = -1, and x = 1.

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Translate the following into a mathematical equation:
The density D of a material is directly proportional to the mass of the object M and inversely proportional to its volume V.

Answers

Final answer:

The density of a material is equal to its mass divided by its volume.

Explanation:

The equation that represents the relationship between density (D), mass (M), and volume (V) is: D = M/V.

This equation shows that the density of a material is equal to its mass divided by its volume.

For example, if you have an object with a mass of 10 grams and a volume of 2 cubic centimeters, you can calculate its density by dividing the mass by the volume: D = 10g / 2cm³ = 5g/cm³.

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Final answer:

The density (D) of a material is directly proportional to the mass (M) and inversely proportional to its volume (V). The mathematical equation for this relationship is D = k * (M / V).

Explanation:

The density (D) of a material is directly proportional to the mass (M) and inversely proportional to its volume (V). To translate this into a mathematical equation, we can write:



D = k * (M / V)



Where D represents the density, M represents the mass, V represents the volume, and k represents the proportionality constant.



This equation demonstrates that as the mass of the object increases, the density also increases, while as the volume increases, the density decreases.

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14x25x4=

Using the common core showing your work.

Answers

The answer would be 1400

Simplify (4.5)(5)(−2).

Answers

-45 is ur answer for this
4.5(5)(-2) = 4.5(-10) = -45

Calculate the expected return in a game where sam wins $1 with the probability of 1 3 , $5 with the probability of 1 6 , and $0 with the probability of 1 2
a. $0.
b. $1 1 6 .
c. $ 2 1 6 .
d. $3

Answers

The expected value of events [tex]x_i[/tex] with probabilities [tex]p(x_i)[/tex] is given by

[tex]E(x)=\Sigma x_ip(x_i)[/tex]

Given that in a game, Sam wins $1 with the probability of [tex]\frac{1}{3}[/tex] , $5 with the probability of [tex]\frac{1}{6}[/tex] , and $0 with the probability of [tex]\frac{1}{2}[/tex]

Sam's expected winnings is given by:

[tex]E(x)=1\left( \frac{1}{3} \right)+5\left( \frac{1}{6} \right)+0\left( \frac{1}{2} \right) \\ \\ =\frac{1}{3}+\frac{5}{6}= \frac{7}{6} =1.17[/tex]

Therefore, Sam's expected winnings is $1.17
Final answer:

To calculate the expected return, multiply each amount that can be won by its corresponding probability, and sum these values. The expected return of the game is $1 1/6, which corresponds to answer choice (b).

Explanation:

The student is asking how to calculate the expected return in a game with different probabilities of winning different amounts. To find the expected return, you multiply each outcome by its probability and then sum these products. The possible wins are $1, $5, and $0, with probabilities of 1/3, 1/6, and 1/2, respectively.

To calculate the expected return:

For winning $1 with probability of 1/3: (1/3) × $1 = $1/3For winning $5 with probability of 1/6: (1/6) × $5 = $5/6For winning $0 with probability of 1/2: (1/2) × $0 = $0

Add up these expected values to get the total expected return:

$1/3 + $5/6 + $0 = $2/6 + $5/6 = $7/6

The expected return is $7/6, which simplifies to $1 1/6. Therefore, the correct answer is (b).

7.38 is 7.5% of what number

Answers

7.38 is 7.5% of 98.4 

(7.5 /100 ) x=7.38

so x= 738/7.5= 98.4

hope this helps

The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. 8. Time (days) Cost ($) 3 75 4 100 5 125 6 150

Answers

 $25/ 1 day or $25 a day

Answer:

The rate of change is 25. It means the cost increased by $25 per day.

Step-by-step explanation:

The given table is

Time (days)       Cost ($)

       3                   75

       4                  100

       5                  125

       6                  150

It means the graph of this constant function passing through the points (3,75) and (4,100).

If a line passing through two points, then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{100-75}{4-3}[/tex]

[tex]m=\frac{25}{1}[/tex]

[tex]m=25[/tex]

Therefore the rate of change is 25. It means the cost increased by $25 per day.

Higher order thinking if 1/2 is multiplied by 1/2 will the product be greater than half explain

Answers

Since we multiply both the numerator and denominator with fractions, 1/2*1/2 would be equal to (1*1)/(2*2)=1/4, which is 0.25 and less than 1/2=0.5

Find an equation for the line perpendicular to the line −7x−9y=−6 having the same y-intercept as 2x−6y=6

Answers

-7x - 9y = -6
-9y = 7x - 6
y = -7/9x + 2/3...slope here is -7/9....a perpendicular line will have a negative reciprocal slope. So the perpendicular line will have a slope of 9/7

2x - 6y = 6
-6y = -2x + 6
y = 1/3x - 1....the y int here is -1

so ur equation is : y = 9/7x - 1 <==

What is 4 - ( -h ) = 68?

Answers

4 + h = 68

h = 68 - 4

h = 64

hope this helps
First reduce brackets

Next subtract 4 from both sides

And lastly subtract 68 - 4 and u have your answer which is 64.

The assembly line that produces an electronic component of a missile system has historically resulted in a 2% defectiverate. a random sample of 800 components is drawn. what is the probability that the defective rate is greater than 4%? suppose that in the random sample the defective rate is 4%. what does that suggest about the defective rate on the assembly line

Answers

Defective rate can be expected to keep an eye on a Poisson distribution. Mean is equal to 800(0.02) = 16, Variance is 16, and so standard deviation is 4.
X = 800(0.04) = 32, Using normal approximation of the Poisson distribution Z1 = (32-16)/4 = 4.
P(greater than 4%) = P(Z>4) = 1 – 0.999968 = 0.000032, which implies that having such a defective rate is extremely unlikely.

If the defective rate in the random sample is 4 percent then it is very likely that the assembly line produces more than 2% defective rate now.

The probability that the defective rate exceeds 4% in the sample is approximately 0.0006, indicating a significant deviation from the expected 2%.

To solve this problem, we need to use the concept of binomial distribution and the normal approximation to the binomial distribution due to the large sample size.

Step 1: Understanding the problem

- The assembly line historically has a defective rate of 2%.

- A random sample of 800 components is drawn.

- We are interested in the probability that the defective rate is greater than 4%.

Step 2: Calculate the parameters

- Population defective rate (historical rate): [tex]\( p = 0.02 \)[/tex]

- Sample size: [tex]\( n = 800 \)[/tex]

- Sample defective rate (given): [tex]\( \hat{p} = 0.04 \)[/tex]

Step 3: Probability that defective rate is greater than 4%

- We need to find [tex]\( P(\hat{p} > 0.04) \).[/tex]

Since [tex]\( \hat{p} \)[/tex] is approximately normally distributed (by the Central Limit Theorem because [tex]\( n \)[/tex] is large), we can use the normal approximation to the binomial distribution.

Step 4: Calculate standard error of sample proportion

The standard error of the sample proportion [tex]\( \hat{p} \)[/tex] is given by:

[tex]\[ SE(\hat{p}) = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \][/tex]

Substitute the values:

[tex]\[ SE(\hat{p}) = \sqrt{\frac{0.04 \cdot 0.96}{800}} \][/tex]

[tex]\[ SE(\hat{p}) = \sqrt{\frac{0.0384}{800}} \][/tex]

[tex]\[ SE(\hat{p}) \approx 0.0062 \][/tex]

Step 5: Z-score calculation

To find the Z-score for [tex]\( \hat{p} = 0.04 \)[/tex]:

[tex]\[ Z = \frac{\hat{p} - p}{SE(\hat{p})} \][/tex]

[tex]\[ Z = \frac{0.04 - 0.02}{0.0062} \][/tex]

[tex]\[ Z \approx 3.23 \][/tex]

Step 6: Find the probability

Now, find the probability that [tex]\( \hat{p} > 0.04 \)[/tex]:

[tex]\[ P(\hat{p} > 0.04) = P(Z > 3.23) \][/tex]

Using the standard normal distribution table or a calculator:

[tex]\[ P(Z > 3.23) \approx 0.0006 \][/tex]

Conclusion:

The probability that the defective rate in the sample is greater than 4% is approximately [tex]\( 0.0006 \)[/tex], or [tex]\( 0.06\% \)[/tex].

Interpretation:

Since the probability is very low, it suggests that a defective rate of 4% in the sample is highly unlikely to occur if the true defective rate on the assembly line is 2%. This could indicate a potential issue or change in the process affecting the defective rate, warranting further investigation or quality control measures.

If $20,000 is invested in a savings account offering 3.5% per year, compounded continuously, how fast is the balance growing after 6 years? (round your answer to the nearest cent.)

Answers

The balance would have grown by $3,500

By using the continuous compound interest the balance is growing $4,673.56 after 6 years.

What is continuous compound interest?

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.

Formula of continuous compound interest rate;

[tex]P(t) = P_0e^{rt}[/tex] , where P₀ is the principal amount, r is the interest rate and t is the time period.

Given that the principal amount is $20000 and and interest rate 3.5% in a year.

And here we use formula of continuous compound interest rate;

[tex]P(t) = P_0e^{rt}[/tex]

Here, we have the value P₀ = $20000 , r = 3.5 % / 100 = 0.035% in a year and t = 6 years

Substitute these above values in the formula;

p(t) = $20000 × [tex]e^{0.035}[/tex] ×[tex]e^{6}[/tex]

P{t} = $24673.56

P{t} = $24673.56 nearest one cent

The final balance is $24673.56.

Therefore, the total continuous compound interest is $4,673.56.

To learn more about the continuous compound interest;

https://brainly.com/question/18722165

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