Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.

We assume that the population standard deviation are known, the samples from each population are independent, the population is normally distributed if we use t test of two samples.

Given T test of significance has been used.

T test is a statistical test that is like z test. Z test is used when n>30 and t test is used when n<30. It is used in hypothesis testing.

We know that there are many test which can be used to test a hypothesis.

The requirements to perform a two sample t procedure are as follows:

1)The two samples have equal variance. Hence the variance should be known.

2) The samples for which the two sample t procedure is performed must be independent.

3) The data are in alignment with the normal distribution probability.

4) The sample are random samples taken from different respective population.

Hence when two sample t procedure is performed we have to assume population standard deviation is known and population is normally distributed.

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Answer: 0.200 g

Given: Half life of Sm-146 = t1/2 = 103.5 million years

Time period, t = 1.035 billion years = 1035 million years

The original mass of the sample, [A]₀ = 205 g

To determine:

Amount of sample after t = 1035 million years

Explanation:

The rate of radioactive decay is given as:

Answer:

A: 0.200 g.

Step-by-step explanation:

An unusual event is an occurrence that has a low probability of happening. The cutoff for identifying unusual events not always be​ 0.05, because it is not always a good idea to utilize the same cutoff to spot unexpected occurrences.

An unusual event is an occurrence that has a low probability of happening.

If an event is improbable, its likelihood is zero. If an occurrence is unavoidable, its probability is one.

The probability of an event happening increases as it gets closer to 1. An occurrence that has a probability of 0.375, for instance, is more likely to happen than one with a probability of 0.125.

The less likely an event is to occur, the closer the probability is to 0. An unusual event is what this kind of event falls under. A probability of 5%, or 0.05, is typically regarded as unusual event.

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Answer:

answer is A - incenter just did it

Step-by-step explanation:

The area of the composite solid in the image given is: 399.6 m².

The surface are of the composite solid = area of the 3 triangular face of the top solid + area of the triangular base of the bottom solid + 3(area of rectangular face of the bottom solid).

Area of the 3 triangular face of the top solid = 3(1/2bh) = 3(1/2 × 8 × 7) = 84 m²

Area of the triangular base of the bottom solid = 1/2bh = 1/2 × 8 × 6.9 = 27.6 m²

3(area of rectangular face of the bottom solid) = 3(length × width) = 3(12 × 8) = 288 m²

Surface area of the solid = 84 + 27.6 + 288 = 399.6 m²

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Answer:

[tex]1[/tex]

Step-by-step explanation:

The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.

In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]

Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].

Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then:  [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.

Properties:

1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].

2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].

3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].

4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].

[tex]2001 * 2002 * 2003 + 2004^3 = 2002 * (2001 * 2003) + 2004^3 \equiv_{7} 0 * (2001 * 2003) + 2^3 \equiv_{7} 0 + 8 \equiv_{7} 8 \equiv_{7} 1[/tex]

Notice that [tex]2002 \vdots 7[/tex] already. There is no need to consider the rest multipliers because the product is [tex]0[/tex] anyways, we can cut corners in this regard.

We used property 4.

Recapitulating this: our remainder is [tex]1[/tex].

The probability that a person wins the game is 32.1%

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴ = 1/1296

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i know its the frist or second one i did the test i am also in flvs :)

Step-by-step explanation:

∠ACB=90∘

[∠ from diameter]

In ΔACB

∠A+∠ACB+∠CBA=180∘

∠CBA=180∘

−(90+30)

∠CBA=60∘ (1)

In △OCB

OC=OB

So, ∠OCB=∠OBC        

[The sides are equal]

∠OCB=60∘

∠OCD=90∘

∠OCB+∠BCD=90°

∠BCD=30∘ (2)

∠CBO=∠BCO+∠CDB    

[external ∠ bisectors]

60=30+∠CDB

∠CDB=30° (3)

from (2) & (3)

BC=BD    

[The ∠.S are equal]

Answer:

18+[tex]6\sqrt{5}[/tex]

Step-by-step explanation:

Since the helicopter flies east for six miles and north for 12 miles, it flies 18 miles. Then on the way back, it flies an unknown amount of miles. the path the helicopter takes is in the form of a triangle, and the path back is the hypotenuse of the triangle. To find the hypotenuse, we can do [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse. We do

[tex]6^2+12^2=c^2\\36+144=c^2\\180=c^2\\\sqrt{180}=c\\ 6\sqrt{5}=c[/tex]Therefore, the total distance flown by the helicopter is 18+[tex]6\sqrt{5}[/tex].  

Answer:

2/3

Step-by-step explanation:

expected over total

14/14+7 = 14/21 = 2/3

[tex]bad \: eggies = 7 \\ good \: eggies = 14 \\ total \: number \: of \: eggs = 21[/tex]

[tex]let \: event \: a = getting \: a \: good \: egg[/tex]

[tex]p(a) = \frac{number \: of \: good \: eggs}{total \: number \: of \: eggs} = \frac{14}{21} = \frac{2}{3} [/tex]

The volume of the cylinder given the radius and the height is 562.2 cubic units

Volume of a cylinder = πr²h

= 3.14 × 2² × 5

= 3.14 × 4 × 5

= 562.2 cubic units

Therefore, the volume of the cylinder is 562.2 cubic units.

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Answer:62.8

Step-by-step explanation:

just took the test

4/3 of the area of the larger hexagon to the area of the smaller hexagon

Let the sides of the interior hexagon be 2 cm long, then this hexagon is made up of 6 equilateral triangles of side = 2.

The area of this hexagon = 6 * 1 * sqrt3 = 6 sqrt3 ( as the triangle is made up of 2 60-30-90 triangles)

The exterior hexagon is made up of 6 equilateral triangles with altitude 2 and the area = 6 * 2 * (2 / sqrt3 ) = 24 / sqrt3

area exterior hex / interior hex = 24 / sqrt3 * 1 / 6sqrt3 = 24/18

= 4/3

Required ratio = 4/3 answer

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The congruency statement which is true among the answer choices is;

According to the task content, the initial transformation is; Triangle GHI is rotated 90Degrees clockwise and then reflected over the y-axis.

On this note, the congruency which are true regarding the transformation are;

This follows from the fact that the transformation.does not involved dilation by means of a scale factor and hence, size remains equal and all angle measures remain the same.

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Step-by-step explanation:

2k=3×4

2k=12

2k/2=12/2

k=6

Answer:

k = 6

Step-by-step explanation:

In Ratio Questions , The Denominator takes the same Ratio as the Numerator and vice versa

so for Question , 4 is double 2

Then k must be double of 3

Then k=2*3 = 6

Answer:

yes

_____________________________

you can look at 3:3 as 3/3 which is 1

and 1:1 = 1/1 which is also 1

the ratio sign also means divide.

_____________________________

hope this helps :)

The probability of randomly selecting a cream filled

Chocolate is 1/4

Let E be the event of selecting cream filled chocolate.

Number of favourable outcome = 6

Total number of possible outcome = 24

Probability if selecting a cream filled chocolate = 6/24

= 1 / 4

Hence, the probability of randomly selecting a cream filled chocolate is 1/4

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Answer:

y = x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m = [tex]\frac{2-0}{0-(-2)}[/tex] = [tex]\frac{2}{0+2}[/tex] = [tex]\frac{2}{2}[/tex] = 1

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = x + 2 ← equation of line

The value of x from the diagram is 42. 5

Since we have that △TUS∼△CBS

Line BS = 8. 5

Line CS = 7. 5

Line US =  42. 5

TS = x

To find TS, we can see that line US is equivalent in length to line TS

If line US = 42. 5, then line TS = 42. 5
TS = x = 42. 5

Thus, the value of x from the diagram is 42. 5

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Answer:

$150

Step-by-step explanation:

→ Find 3/5 of 1500

( 1500 ÷ 5 ) × 3 = 900

→ Find 6/20 of 1500

( 1500 ÷ 20 ) × 6 = 450

→ Find the sum of the 2 numbers

900 + 450 = 1350

→ Minus it from the original 1500

1500 - 1350 = $150

Completely factored form of Wen's polynomial is (6x² + 7) (x-2).

What is a polynomial?

An algebraic expression called a polynomial includes coefficients and variables. Indeterminates are another name for variables. For a polynomial expression, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents, but division by variable is not possible. Although a polynomial can have multiple number of terms, it can't be infinite.

Factorizing the polynomial

Complete factorization of a polynomial results in products-of-sums

Given polynomial is,

6x³ - 12x² + 7x - 14

This polynomial can be factorized as follows,

6x² (x - 2) + 7(x - 2)

Now, we can factor out the common term (x-2) form each term on either side of the plus operator. thus, we get the following factors,

(6x² + 7) (x-2)

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Answer:

Answer  is A   :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is thirty six times thirty eight divided by three

36 * 38 : 3 =

1368 : 3 =

456

Answer:

x=33ft

height of tower=33+6=39ft

Answer: 33/100, 33%

Step-by-step explanation:

I can't choose two answers if you don't give me the possible answers

67 days of homework = 100-67 or 33 days without homework.

33/100 or 33%

Step-by-step explanation:

100% = 100 days

1% = 100%/100 = 100/100 = 1 day

the student does NOT have homework on 100-67 = 33 days.

that is 33 out of 100 days or on 33/100 of days.

33 days are 33×1% = 33%

Answer:

B.

Step-by-step explanation:

an arithmetic sequence is B

Answer:0c

Step-by-step explanation:

30 lemon candies he give his friend.

It is given that a boy had 320 candies. There were 2 flavors. 7/16 were orange flavor and the rest were lemon. He gave his friend 30 orange candies and some lemon ones.

320 (7/16)  =   140  were orange

320 - 140  =  180  were lemon

Let x be the number of lemon ones he gave  away

So,

[ 140 - 30 ]  / [ 180 - x ] =  11/15

110  =  (11/15) ( 180 - x )

(15/11) (110)  = 180 - x

150  = 180  - x

x = 180  - 150  =   30

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The manufacturer should advertise 13811 pages for each cartridge if it wants to be correct 99% of the time

z-score is the number of standard deviations from the mean value of the reference population

99%=0.99

The z-value associate with 0.99 is 2.33:

2.33 = (X - 12425) / 595:

X - 12425 = 2.33 * 595

X = (2.33 * 595) + 12425

X = 138111

Therefore, The manufacturer should advertise 13811 pages for each cartridge if it wants to be correct 99% of the time

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The rigid transformations used for each figure:

In this question we must determine what kind of rigid transformations generates each image. Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. Now we proceed to determine the transformation rule for each case:

Figure 5 - Reflection around the x-axis followed by reflection around the y-axis.

(x, y) → (- x, - y)

Figure 6 - Translation one unit in the +x direction and two units in the -y direction.

(x, y) → (x + 1, y - 2)

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Answer:7m^5 - 3m^3 + 9

Step-by-step explanation: You’d have to remove the brackets, but remember that the second has to have everything multiplied by -1, because there’s a minus sign in front of the second bracket. Then you’d group like terms, then add or subtract. Here’s the step by step

6m^5 + 3 - m^3 - 4m + m^5 - 2m^3 + 4m + 6

2. 6m^5 + m^5 - 2m^3 - m^3 + 4m - 4m + 6 + 3

Subtract or add what’s needed, which would be figures with the same variable and coefficient.

3. 7m^5 - 3m^3 + 9

After this, there’s nothing you can add, since the remaining figures don’t have the same variable.
Hope it’s clear and this wasn’t that long

The bottom triangle is a 30°-60°-90° triangle that has the special property that its hypotenuse is twice the length of the shortest leg, 20√3.

The upper triangle is a 45°-45°-90° triangle, in which the hypotenuse is longer than one of its legs by a factor of √2.

All this to say x = √2 × 20√3 = 20√6 (A).