If AD=BD, which of the following relationships can be proved and why?
B
o
A. A ACD= A BCD, because of ASA.
B. XACD N BOD because of SAS
C. There is not enough information to prove a relationship.
(D. A ACD S ABCD, because of AS
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Answer:

We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

Step-by-step explanation:

We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;

1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.

Let \(\mu\) = true average percentage of organic matter

So, Null Hypothesis, \(H_0\) : \(\mu\) = 3%      {means that the true average percentage of organic matter in such soil is 3%}

Alternate Hypothesis, \(H_A\) : \(\mu \neq\) 3%      {means that the true average percentage of organic matter in such soil is something other than 3%}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                         T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean percentage of organic matter = 2.481%

             s = sample standard deviation = 1.616%

            n = sample of soil specimens = 30

So, the test statistics =  \(\frac{2.481-3}{\frac{1.616}{\sqrt{30} } }\)  ~ \(t_2_9\)

                                     =  -1.76

The value of t-test statistics is -1.76.

(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

Answer:

  ΔHJK; Lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G

Step-by-step explanation:

The orthocenter is the point of intersection of altitudes. Each altitude is orthogonal to the corresponding base, so the use of "ortho-" can help you remember.

The appropriate choice is ...

  ΔHJK shown: Lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G.

Answer:

in short terms its D. i got it right

Step-by-step explanation:

The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

To make a regular polygon with 96 sides we can take a circle as a starting point and divide it into 96 equal sides.

To create a regular polygon with 96 sides, we must take into account that all its sides must be equal, so we can take a circumference as a starting point. In this case, the circumference has 360°, so we must divide this into 96 parts and the result would be the distance between the edges of the polygon.

In this case, we must make a circle with a protractor and mark every 3.75°, when we have completed this procedure in the entire circumference we will have a regular polygon with 96 sides.

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Answer:

i think its c

Step-by-step explanation:

if not look in the comments i will be texting

Answer:

A,B,D

Step-by-step explanation:

Edge2020

Answer:

5 faces

Step-by-step explanation:

A traingular prism has 5 faces. The square on the bottom and the four traingles that make up the sides.

hope this helps :)

Answer:

5

8

5

step by step

Love your pfp

Answer:

The answer is below

Step-by-step explanation:

Velocity is the rate of change of displacement. Velocity is the ratio of distance to time.

The velocity v(t) = \(\frac{d}{dt}r(t)\)

Where r(t) is the position function

Given that:

r(t)=⟨−8tsint,−8tcost,2t²⟩

\(v(t)=\frac{d}{dt}r(t)= <-8tcost-8sint,8tsint-8cost,4t>\)

Acceleration is the rate of change of velocity, it is the ratio of velocity to time. Acceleration a(t) is given as:

\(a(t)=\frac{d}{dt}v(t)= \frac{d}{dt} <-8tcost-8sint,8tsint-8cost,4t>\\=<8tsint-16cost,8tcost+16cost,4>\\\\a(t)=<8tsint-16cost,8tcost+16cost,4>\)

Speed = |v(t)| = \(\sqrt{(-8tcost-8sint)^2+(8tsint-8cost)^2+(4t)^2}\\\\ =\sqrt{64t^2cos^2t+128tcostsint+64sin^2t+64t^2sin^2t-128tsintcost+64cos^2t+16t^2}\\ \\=\sqrt{64t^2cos^2t+64t^2sin^2t+64sin^2t+64cos^2t+16t^2}\\\\=\sqrt{64t^2(cos^2t+sin^2t)+64(sin^2t+cos^2t)+16t^2}\\\\=\sqrt{64t^2+64+16t^2}=\sqrt{80t^2+64}\)

TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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refer to the attatchment

Answer:

x=2

Step-by-step explanation:

8 + x = 4x +2

Subtract 4x from both sides:

8 + x - 4x = 4x + 2 - 4x

Group like terms:

x - 4x + 8 = 4x + 2 -4x

Simplify the arithmetic:

-3x + 8 = 4x + 2 -4x

Group like terms:

-3 + 8 = 4x - 4x + 2

Simplify the arithmetic:

-3x + 8 = 2

Answer:

C. \( \frac{343}{18} pie \)

Step-by-step explanation:

Given a circle of:

Radius (r) = 14

Measure of minor arc = 115°

We are required to find the length of DGE = length of major arc.

Length of arc is given as 2πr(θ/360)

Measure of the major arc DGE (θ) = 360 - 115 = 245°

Length of major arc DGE = \( 2*pie*14*\frac{245}{360} \)

\( = 28*pie*\frac{49}{72} \)

\( = \frac{28*49}{72} pie \)

\( = \frac{7*49}{18} pie \)

\( = \frac{343}{18} pie \)

Length of arc DGE =

\( \frac{343}{18} pie \)

Answer:

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers

Answer:

Step-by-step explanation:

By using multiplication or division. Multiplying the numerator and denominator or simplifying which is also division.

Answer:

a. Convert to improper fraction first:

-2⁴/₉ = -24/9

= -24/9 * 1/2 = -24/18 = -4/3

= -1¹/₃

b. -2/3 * 1/4 = -2/12

= -1/6

c. Convert to improper fraction:

= -1¹/₂ = -3/2

= -3/2 * -1/6

= 3/12

= 1/4

d. Convert to improper fraction:

= 2¹/₃ = 7/3

= 1/6 * 7/3

= 7/18

Answer:

Step-by-step explanation:

Take away 9% of $15,600 = 14196

Take away 9% of $14196 = 12918.36

(and so on)

Until you get less than $100. Note that you may need to round up some numbers after the decimal point.

Answer:

The answer is Graph B. you could also plug it in demos and it will give you the answer.

A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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the mοnthly periοdic interest rate, rοunded tο the nearest hundredth οf a percent is (C) 1.31%

Any lοans and bοrrοwings cοme with interest. the percentage οf a lοan balance that lenders use tο determine interest rates. Cοnsumers can accrue interest thrοugh lending mοney (via a bοnd οr depοsit certificate, fοr example), οr by making a depοsit intο a bank accοunt that pays interest.

We must divide its yearly percentage rate (APR) by 12 tο determine a mοnthly periοdic interest rate (the number οf mοnths in a year).

Hence, the periοdic interest rate fοr each mοnth is:

15.75% / 12 = 1.3125%

The result οf rοunding tο the clοsest hundredth οf such a percent is:

1.31%

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Answer:

1,500 beds

Step-by-step explanation:

Occupancy rate  shelter A = 300 x 20/100 = 60

Let capacity of shelter B be X

60% occupancy ==> 60/100 x X = 0.6X

Occupancy rate of A to rate of B is 1: 15 can be expressed as fraction 1/15

Therefore
60/0.6X = 1/15

1 x 0.6X = 60 x 15

0.6X = 900

X = 900/0.6 = 1,500 beds

Answer:

I'm pretty sure it's 108.

Step-by-step explanation:

12 x 12 x 12 = 1,728

4 x 4 = 16

1,728 ÷ 16 = 108

Answer:

If the base and the negative exponent is in the denominator already

Step-by-step explanation:

Normally, a base with a negative exponent moves to the denominator.

Example: (2^-3 = 1 / (2)^3 = 1/8)

However, if the base and the negative exponent is already in the denominator, the base would move to the numerator and the exponent would become positive.

Example:  2 / (3)^-3 = 2 * 3^3 = 2 * 27 = 54

Answer: y = 5x-2

Step-by-step explanation:

Answer:

1 is the answer see attached

Step-by-step explanation:

1 is a function

2 is not a function as it is x+y

3 is a boundary function of how many parameters

4 is not a function as such parameters are too long however many of the decimals divide into each other and appear functional.

Answer:

x = five over two and x = −3

Step-by-step explanation:

Let's solve your equation step-by-step.

2x2+x=15

Step 1: Subtract 15 from both sides.

2x2+x−15=15−15

2x2+x−15=0

Step 2: Factor left side of equation.

(2x−5)(x+3)=0

Step 3: Set factors equal to 0.

2x−5=0 or x+3=0

x=5/2 or x=−3

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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Answer:

Step-by-step explanation:

1/4

Answer: It would be 4

So what's happing in the table, is that numbers are being multiplied by 4.

1x4=4

2x4=8

3x4=12

4x4=16

hope I helped :)