If a rectangle has a length of 10 cm and a width of 12 cm, what is it's perimeter () and area

Answer:

The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{2.7}{\sqrt{400}} = 0.35[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 8.84 - 0.35 = 8.49 miles.

The upper end of the interval is the sample mean added to M. So it is 8.84 + 0.35 = 9.19 miles.

The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.

Answer:

The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:

[tex]a[/tex] is an arbitrary prime number. (1)

[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)

[tex]c[/tex] is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if [tex](x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]. From statement, we must fulfill the following identity:

[tex]a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]

By Associative and Commutative properties, we can reorganize the expression as follows:

[tex]a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}[/tex] (1)

Then, we have the following system of equations:

[tex]x = a[/tex] (2)

[tex](b^{2}-1) = 2\cdot x\cdot y[/tex] (3)

[tex]y = c[/tex] (4)

By (2) and (4) in (3), we have the following expression:

[tex](b^{2} - 1) = 2\cdot a \cdot c[/tex]

[tex]b^{2} = 1 + 2\cdot a \cdot c[/tex]

[tex]b = \sqrt{1 + 2\cdot a\cdot c}[/tex]

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, [tex]a, b, c > 1[/tex]. If [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are prime numbers, then  [tex]2\cdot a\cdot c[/tex] must be an even composite number, which means that [tex]a[/tex] and [tex]c[/tex] can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, [tex]b[/tex] must be a natural number, which means that:

[tex]1 + 2\cdot a\cdot c \ge 4[/tex]

[tex]2\cdot a \cdot c \ge 3[/tex]

[tex]a\cdot c \ge \frac{3}{2}[/tex]

But the lowest possible product made by two prime numbers is [tex]2^{2} = 4[/tex]. Hence, [tex]a\cdot c \ge 4[/tex].

The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:

[tex]a[/tex] is an arbitrary prime number. (1)

[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)

[tex]c[/tex] is another arbitrary prime number. (3)

Example: [tex]a = 2[/tex], [tex]c = 2[/tex]

[tex]b = \sqrt{1 + 2\cdot (2)\cdot (2)}[/tex]

[tex]b = 3[/tex]

Answer:

[tex]\sigma_x= 1.75\%[/tex]

Step-by-step explanation:

Given

[tex]n = 64[/tex]

[tex]\mu = 78\%[/tex]

[tex]\sigma = 14\%[/tex]

Required

The sample standard deviation

This is calculated as:

[tex]\sigma_x= \frac{\sigma}{\sqrt n}[/tex]

This gives:

[tex]\sigma_x= \frac{14\%}{\sqrt {64}}[/tex]

[tex]\sigma_x= \frac{14\%}{8}[/tex]

[tex]\sigma_x= 1.75\%[/tex]

Answer:

The appropriate set of hypothesis for his significance test is null hypothesis [tex]H_0: p = 0.06[/tex] and alternate hypothesis [tex]H_1: p \neq 0.06[/tex]

Step-by-step explanation:

Elliot read a report from a previous year saying that 6%, percent of adults in his city biked to work. He wants to test whether this proportion has changed.

At the null hypothesis we test if the proportion is still the same, that is, of 6%. So

[tex]H_0: p = 0.06[/tex]

At the alternate hypothesis, we test if the proportion has changed, that is, it is different of 6%. So

[tex]H_1: p \neq 0.06[/tex]

What is an appropriate set of hypotheses for his significance test?

The appropriate set of hypothesis for his significance test is null hypothesis [tex]H_0: p = 0.06[/tex] and alternate hypothesis [tex]H_1: p \neq 0.06[/tex]

CORRECT (SELECTED)

z=\dfrac{0.1-0.06}{\sqrt{\dfrac{0.06(0.94)}{240}}}z=

240

0.06(0.94)

​

​

0.1−0.06

​

Answer:

1x 2x 3x

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

18 boys

Answer:

i think 18 msy be

Step-by-step explanation:

Answer:

-86

Step-by-step explanation:

3x10=30

22-3=19-3=16-3=13

so if its tthe 37th term, lets do 30x3=90

now 13-90=-77

-77=34th term

now just -3 until 37

-80

-83

-86

the 37th term is -86

•ω• Hewo fren!

☆☆●◉✿Answer:✿◉●☆☆

The letters of hippopotamus is H-I-P-P-O-P-O-T-A-M-U-S

☆☆●◉✿Step-by-step explanation:✿◉●☆☆

I’m sowy, I didn’t really understand your question... did you want to learn about a hippopotamus? If so, please tell me in the comments I would answer there too!

HOPE I HELPED!  ∧∧

→⇒brainliest please? ∑(OΔO )♥♥︎

230FT

Regular tetrahedron

Solve for volume

V≈1.15×107

Use the formula for the volume of a triangular pyramid: V=13Ah , where A = area of the triangular base, and H = height of the pyramid.

Answer: 4.09

Step-by-step explanation:

4.09142857 rounded to the nearest hundredth is: 4.09

Answer:

Manuel owns 5 DVDS

Step-by-step explanation:

3/5 = 12/20

12 - 7 = 5

you watch seven deadly sins?

Step-by-step explanation:

a) A=π302=900π CM2 =2,827 CM 2

b) V=Ah=900=72000 π cm 3 = 226,195 cm3

Answer:

D. x²

Step-by-step explanation:

I calculated it logically

Answer:

[tex]\frac{x^6-yx-y^5}{x}[/tex]

Step-by-step explanation:

x^5-y^5 divided x-y

[tex]\frac{(x^5-y)x}{x} -\frac{y^5}{x}[/tex]

[tex]\frac{(x^5-y)x-y^5}{x}[/tex]

=> [tex]\frac{x^6-yx-y^5}{x}[/tex]

Answer:

An acute triangle

Step-by-step explanation:

[tex]\huge\mathfrak\blue{AnSwEr} [/tex]

[tex] \sf{54 \: km \: = 54000 \: meters}[/tex]

Answer:

Step-by-step explanation:

You would get the probability of double sixes as:

Correct choice is A

The Robin because there are 36 outcomes and only one is (6, 6) is the correct option.

We have given that,

Robin, Steven, and John are comparing tree diagrams for rolling double sixes on two six-sided number cubes (6, 6).

Robin thinks the probability is 136 based on the tree diagram they created.

Steven disagrees and argues that the probability of rolling double sixes is 16.

John counts twelve outcomes and claims the probability is 112.

The formula to calculate the probability of an event is as follows. Probability(Event) = Favorable Outcomes/Total Outcomes

You would get the probability of double sixes as:

P(6, 6) = 1/6*1/6 = 1/36

Correct choice is A.

Therefore the Robin, because there are 36 outcomes and only one is (6, 6).

To learn more about the probability visit:

https://brainly.com/question/25870256

#SPJ2

Answer:

12

Step-by-step explanation:

The range is the difference from the greatest data point and the least data point. By looking at the box plot, the lowest value would be 0 while the highest would be 12. You use the definition of range to find it:

12 - 0 = 12

Answer:

the height is 20 cm.

tsa is 940 cm square

Step-by-step explanation:

volume of cuboid = l*b*h

1800 = 9*10*h

h= 20 cm

TSA = 2(L*B+ B*H + L*H)

= 2(9*10 + 10*20 + 9*20)

=940 cm square

The height of the cuboid will be 20 cm

The total surface area of cuboid will be 940 cm²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The length of cuboid = 9 cm

The breadth of cuboid = 10 cm

And, The volume of cuboid = 1800 cm³

Now,

We know that;

Volume of cuboid = Length × Breadth × Height

⇒ 1800 = 9 × 10 × h

⇒ 1800 / 90 = h

⇒ h = 20 cm

And, The total surface area of cuboid = 2lw + 2lh + 2hw

Substitute all the values, we get;

⇒ The total surface area of cuboid = 2 (9 × 10 + 9 × 20 + 20 × 10)

                                                      = 2 (90 + 180 + 200)

                                                      = 2 × 470

                                                      = 940 cm²

Learn more about the multiply visit:

brainly.com/question/14176303

#SPJ2

Answer:

13.0833 ft²

Step-by-step explanation:

From the question given above, the following data were obtained:

Radius (r) = 5 ft

Angle sustained by the sector (θ) = 360 – 300

= 60°

Pi (π) = 3.14

Area of sector (A) =?

The area of the sector can be obtained as follow:

A = θ/360 × πr²

A = 60/360 × 3.14 × 5²

A = 1/6 × 3.14 × 25

A = 1/6 × 78.5

A = 78.5/6

A = 13.0833 ft²

Thus, the area of the sector is 13.0833 ft²

Step-by-step explanation:

The angle of the minor sector will be ,

> 360 - 300 = 60° .

Area of sector :-

> Area = ∅ / 360 × πr²

> A = 60/360 × 3.14 × 5ft²

> A = 13.09 ft²

Answer:

.; i don't know the constant but i know that the  degree is 3 Step-by-step explanation:

Answer:

(A) There should have been 5 outcomes of HT

(B) The experimental probability is greater than the theoretical probability of HT.

Step-by-step explanation:

Given

[tex]S = \{HH,HT,TH,TT\}[/tex] -- Sample Space

[tex]n(S) = 4[/tex] --- Sample Size

Solving (a); theoretical outcome of HT in 20 tosses

First, calculate the theoretical probability of HT

[tex]P(HT) = \frac{n(HT)}{n(S)}[/tex]

[tex]P(HT) = \frac{1}{4}[/tex]

Multiply this by the number of tosses

[tex]P(HT) * n= \frac{1}{4} * 20[/tex]

[tex]P(HT) * n= 5[/tex]

Solving (b); experimental probability of HT

Here, we make use of the table

[tex]P(HT) = \frac{n(HT)}{n(S)}[/tex]

[tex]P(HT) = \frac{6}{20}[/tex]

[tex]P(HT) = 0.30[/tex] ---- Experimental Probability

In (a), the theoretical probability is:

[tex]P(HT) = \frac{1}{4}[/tex]

[tex]P(HT) = 0.25[/tex] ---- Experimental Probability

By comparison;

[tex]0.30 > 0.25[/tex]

Answer:

5.26 hours or 315.6 minutes

Step-by-step explanation:

If he travels 0.19 miles in 1 hour

Then 1 mile is traveled (1x1)/0.19

5.26 approx. hours or 5.26 x 60 mins = 315.6.

Answer:

1.375 ft

Step-by-step explanation:

10/2.5 = 4

5.5 / 4 = 1 1.5/4 = 1 3/8 = 1.375 ft

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: 36 ft^2

Step-by-step explanation: 4x3/2=6. 6x2=12. 3x2=6. 4x2=8. 5x2=10. 12+8+6+10=36

Answer:

Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], you can use a normal distribution to approximate the binomial distribution.

The mean is of 11.1 and the standard deviation is of 2.64.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Using the normal distribution to approximate the binomial distribution.

This is possible if:

[tex]np \geq 10, n(1-p) \geq 10[/tex]

A survey of U.S. adults found that 37% have been to court. You randomly select 30 U.S.

This means that [tex]p = 0.37, n = 30[/tex]

Test if it is possible:

[tex]np = 30*0.37 = 11.1[/tex]

[tex]n(1-p) = 30*0.63 = 18.9[/tex]

Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], you can use a normal distribution to approximate the binomial distribution.

Mean and standard deviation:

[tex]E(X) = np = 30*0.37 = 11.1[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.37*0.63} = 2.64[/tex]

The mean is of 11.1 and the standard deviation is of 2.64.

Answer:

2/4

Step-by-step explanation: