A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean isx⎯ ⎯ x¯ = 840 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student's t. (a) Construct an interval estimate of μ with 98% confidence. (Round your answers to 3 decimal places.) The 98% confidence interval is from to

=========================================================

Explanation:

We can prove this by contradiction.

Let's say

and

A+B = C

We'll show that a contradiction happens based on this.

If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.

If C is rational, then C = r/s for some other integers. We can't have s be zero.

Note the following

A+B = C

B = C - A

B = r/s - p/q

B = qr/qs - ps/qs

B = (qr - ps)/qs

B = (some integer)/(some other integer)

This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".

In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.

The template is

rational + rational = rational

Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.

Another template is

rational + irrational = irrational

Answer:

42 cm

Step-by-step explanation:

104/8 = 13

13 + 13 + 8 + 8 = 42 cm

The perimeter of △PQR is, 7.5/5x.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, Based on the given information, since △ABC∼△PQR,

we know that the corresponding sides are proportional.

Therefore, we can set up a proportion:

AB/PQ = BC/QR = AC/PR

Substituting the given values, we get:

2/5 = BC/QR = AC/PR

Since we know the perimeter of ΔABC is 3x, we can express its sides as:

AB + BC + AC = 3x

Substituting AB = 2, we get:

2 + BC + AC = 3x

Dividing both sides by 2, we get:

BC/2 + AC/2 = (3/2)x - 1

Substituting BC/QR = AC/PR = 2/5, we get:

(2/5)QR/2 + (2/5)PR/2 = (3/2)x - 1

Simplifying, we get:

QR + PR = (15/10)x - 2

Since the perimeter of ΔPQR is PQ + QR + PR, we can substitute PQ = 5, and get:

Perimeter of △PQR = 5 + QR + PR

Substituting QR + PR = (15/10)x - 2, we get:

Perimeter of △PQR = 5 + (15/10)x - 2

Simplifying, we get:

Perimeter of △PQR = (7.5/5)x - 2

Therefore, the answer is option B, 7.5/5x.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

Answer:

trueeeeeeeeeeeeeeeeeee

Answer:

it's 200

Step-by-step explanation:

it is rounded to 200 because the last two digit which are 62 should be 50 or above.

Answer:

13.3650978628

Step-by-step explanation:

Angle A=180-(Angle B+C)=180-117=63

Here,

b=BC, p=AC & AB=12

Using the relation of cos,

cosx=b/h

cos27=BC/15

15cos27=BC

Using a calculator,

BC=13.3650978628

Answer:

C

Step-by-step explanation:

degree 1 ( linear function

Answer:

1

Step-by-step explanation:

To do this, we can first look at each factor of each number.

For 5a²b², we can split this up into three parts: 5, a², and b². The factors of 5 are 1 and 5, the factors of a² are 1, a, and a² (because a*a = a² and a²*1 = a²), and the factors of b² are 1, b, and b²

For 9x³y³, the factors for 9 are 1, 3, and 9, the factors of x³ are 1, x, x², and x³ (because x * x² = x³ and x³ * 1 = x³), and the factors of y³ are 1, y, y², and y³.

The only number that is a factor of at least 1 item in each number is 1. Therefore, 1 is the HCF

Another way of looking at this is seeing that a, b, x, and y are all different variables with nothing to connect them, so as a result, they will have no common factors except for 1

Answer:

(x-3)^2 = 5

x = 3 ±sqrt(5)

Step-by-step explanation:

x ^2 −4x+4=2x

Subtract 2x from each side

x ^2 −4x-2x+4=2x-2x

x^2 -6x +4 = 0

Subtract 4 from each side

x^2 -6x+4-4 =0-4

x^2 -6x = -4

Take -6

Divide by 2

-6/2 = -3

Square it

(-3)^2 = 9

Add to each side

x^2 -6x+9 = -4+9

(x-3)^2 = 5

Take the square root

sqrt((x-3)^2) = ±sqrt(5)

x-3 =  ±sqrt(5)

Add 3 to each side

x = 3 ±sqrt(5)

Answer:

lusing completing square metjod

x

Step-by-step explanation:

x^2_6x+(_3)^2=_4+9

(x_3)^2=5

x_3=

[tex] \sqrt{5} [/tex]

[tex]x = 3 + or - \sqrt{5} [/tex]

Answer:

52.5

Step-by-step explanation:

Since ED ≈ AD, ∆AED is a isosceles triangle where <EAD and <AED has same angle measurement

Now, m<B = 105°, since ABCD is a parallelogram, <B = <D

so, m<ADC = 105° so, m<ADE = 180°-105° = 75°

Now, m<EAD+m<AED+m<ADE = 180°

or, m<AED+m<AED+m<ADE = 180°

or, x+x+75°=180°

or, 2x=180+75°

or, 2x=105°

or, x=52.5°

Answer:

I have explained the answer in detailed steps for you. If you do not understand any steps, please comment below, and I will help you out.

Answer:

V = 396 cubic inches

Step-by-step explanation:

width = w; length = l; height = h; volume = V; area of smallest face = a

base units are inches

w = 2 + l

h = l - 5

Height is smallest and length is second smallest (h = l -, l = l, w = l +), so a is for h and l.

a = h × l = (l - 5) × l

36 = l^2 - 5l ==> l^2 - 5l - 36 = 0

Factor ==> (l - 9) × (l + 4) = 0

l = 9 and l = -4

Since length cannot be negative, 9 is the only Real answer.

l = 9

h = l - 5 = 9 - 5 = 4

w = 2 + l = 2 + 9 = 11

Volume of rectangular prism/box is length times width times height.

V = l × w × h = 9 × 11 × 4 = 396

The volume of the box with the given dimensions is;

Volume = 396 in³

Let us denote the properties of the box as follows;

Length of box = l

Width of box = w

Height of box = h

Area of the smallest face of box = a  

We are told that the width is 2 inches more than the length. Thus;

w = 2 + l

We are told that the height is 5 inches less than its length. Thus;

h = l - 5

Since length is smaller than width but bigger than height, the height and length are the 2 smallest faces

Thus,

a = h × l

plugging in the relevant values gives;

a = (l - 5) × l

a = l² - 5l

We are told that the area of the two smallest faces is 36 in². Thus;

l² - 5l = 36

l² - 5l - 36 = 0

Using online quadratic equation solver, we have; l = 9 inches

Plugging in 9 for h in; h = l - 5  

h = 9 - 5

h = 4

Also, plugging in 9 for l into; w = 2 + l, we have;

w = 2 + 9

w = 11

Volume of box is given by;

Volume = length × width × height

Volume = 9 × 11 × 4

Volume = 396 in³

Read more at;https://brainly.com/question/13973603

Solution:-1

Number be 27

[tex]\\ \sf\longmapsto 27^2[/tex]

[tex]\\ \sf\longmapsto (30-3)^2[/tex]

[tex]\\ \sf\longmapsto 30^2-2(30)(3)+3^2[/tex]

[tex]\\ \sf\longmapsto 900-180+9[/tex]

[tex]\\ \sf\longmapsto 909-180[/tex]

[tex]\\ \sf\longmapsto 729[/tex]

[tex]\\ \sf\longmapsto 27^2[/tex]

Hence verified

Solution:-2

[tex]\\ \sf\longmapsto 10^3+9^3[/tex]

[tex]\\ \sf\longmapsto (10+9)(10^2-10\times 9+9^2)[/tex]

[tex]\\ \sf\longmapsto 19(100-90+81)[/tex]

[tex]\\ \sf\longmapsto 19\times 91[/tex]

[tex]\\ \sf\longmapsto 1729[/tex]

We know

[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

ATQ

[tex]\\ \sf\longmapsto \sqrt{(-1-2)^2+(x+2)^2}=5[/tex]

[tex]\\ \sf\longmapsto \sqrt{(-3)^2+x^2+4x+4}=5[/tex]

[tex]\\ \sf\longmapsto \sqrt{9+x^2+4x+4}=5[/tex]

[tex]\\ \sf\longmapsto \sqrt{x^2+4x+13}=5[/tex]

[tex]\\ \sf\longmapsto x^2+4x+13=5^2=25[/tex]

[tex]\\ \sf\longmapsto x^2+4x+13-25=0[/tex]

[tex]\\ \sf\longmapsto x^2+4x-12=0[/tex]

[tex]\\ \sf\longmapsto x^2+6x-2x-12=0[/tex]

[tex]\\ \sf\longmapsto x(x+6)-2(x+6)=0[/tex]

[tex]\\ \sf\longmapsto (x-2)(x+6)=0[/tex]

[tex]\\ \sf\longmapsto x=2\:or\:x=-6[/tex]

Answer: 7

Concept:

When encountering questions that ask for simplifying operation expressions, the order of operation would be following the PEMDAS method:

Solve:

Given expression

3 (2 - 5) + 4 (6 - 2)

Simplify values in the parentheses

=3 (-3) + 4 (4)

Simplify by multiplication

=-9 + 16

Simplify by addition

=[tex]\boxed{7}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

3(2 - 5) + 4(6 - 2)

By using the order of operations,

3(2 - 5) + 4(6 - 2)

3(-3)+4(4)

-9+16

7

I hope it helped U

stay safe stay happy

Answer:

under the condition of f(x)=x composite function is an identity one

Hi

two lines are parallel only if they have the same slope.

So :  3x+4y = 12

         4y = 12 -3x

           y =  12/4 - 3x/4

           y =   3 - 3/4 X

          y =   -3/4 X +3

Slope is   -3/4

and   6x+2y = 6

               2y = 6 -6x

                  y =  6/2 - 6x/2

                 y =   3 - 3X

                 y =  -3X +3

Slope is = -3

As  -3/4 ≠ -3  then   the two lines are not parallel.

Answer:

Answer is 3

Step-by-step explanation:

[tex] \frac{ \sqrt{144} }{ \sqrt[5]{243} } - 5 + 16 \div \sqrt[3]{64} \\ = \frac{12}{3} - 5 + (16 \div 4) \\ \\ = 4 - 5 + 4 \\ = 3[/tex]

Answer:

3

Step-by-step explanation:

step by step explaination is in picture

Send the question?

Must click thanks and mark brainliest

Answer:

a.

Step-by-step explanation:

f(x) has the highest or greatest maximum y value of 3

Answer:

0.19

Step-by-step explanation:

Total marbles=22

P(2 yellow marbles) = (10/22)(9/21)=0.19

Answer:

The angles that are congruent to 4 are: 3, 8, and 7.

3 and 4 are vertical angles, 8 and 3 are opposite interior angles, 8 and 7 are vertical angles.

Hope this helps!

Answer:

x = 147

Step-by-step explanation:

33 and x form a straight line which means they add to 180

x+33 =180

x = 180-33

x = 147

Answer:

[tex]x=147[/tex]

Step-by-step explanation:

we see that x and 33 are linear pairs so their sum is 180 degrees.

[tex]x+33=180[/tex]

Subtract :-

[tex]x=180-33[/tex]

[tex]x=147[/tex]

OAmalOHopeO

Answer:

1st option

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here g(x) = [tex]\sqrt{x}[/tex] - 19

The base graph f(x) has been shifted down 19 units

104 ft^2

Explanation:

The surface areaa of a rectangular prism is given by the formula:

2 (lw + hl + hw)

l = length

w = width

h = height

Substitute the formula with the givsn dimensions:

2 ([6 x 2] + [5 x 6] + [5 x 2])

= 2 (12 + 30 + 10)

2 (52)

= 104

So the SA is 104 square feet or ft^2

Hope this helps!

1. Open the GeoGebra link.

2. Select the triangle shape, or draw a triangle by combining line segments.

3. The application will also have a tool to measure the angles.

4. Measure all 3 angles.

5. Note them down in the assignment.

Click on the instructions hyperlink for detailed information.