Complete the following statement.

Answer:

Option A i the right option.

First blank is 110-[tex]10\sqrt{61}[/tex] or 10(11-[tex]\sqrt{61}[/tex])

Second blank is 31.898

Let me know if anything didn't make sense.  

Step-by-step explanation:

So a diagonal through a rectangle makes two triangles.  The question wants to know how much walking is saved walking down the diagonal  vs walking along two sides that make the diagonal.  in this case the two non diagonal sides walked are 60 paces and 50 paces.

A diagonal through a rectangle specifically makes a right triangle, so to find the diagonal we can use the pythagorean theorem.  

c^2 = 60^2 + 50^2

c = [tex]\sqrt{60^2 + 50^2}[/tex]

c = [tex]\sqrt{6100} = 10\sqrt{61}[/tex]

if you don't get how to simplify a radical like that let me know.

Anyway, looking at the answers you can see right away the second option says no approximation is necessary.  Well, you need to approximate square root of 61, so we can say the second answer is not right.  So now we need to know what to fill in for option 1.

it wants the distance saved, well we know the distance of the diagonal is [tex]10\sqrt{61}[/tex]  Hopefully you can see the disctance walking the two other sides is just adding them up so 50+60=110.

Now, to find the difference, that is subtraction.  So subtract the smaller number from the larger number.  You do need to remember with a right triangle, the sum of the to non diagonal (hypotenuse) sides are always longer than said hypotenuse.  so that's 110-[tex]10\sqrt{61}[/tex].  That is the exact form.  Or you could use 10(11-[tex]\sqrt{61}[/tex])  They are the same.

Then just plug that into a calculator for a decimal approximation.

Solution :

Let [tex]p_1[/tex] and [tex]p_2[/tex]  represents the proportions of the seeds which germinate among the seeds planted in the soil containing [tex]3\%[/tex] and [tex]5\%[/tex] mushroom compost by weight respectively.

To test the null hypothesis [tex]H_0: p_1=p_2[/tex] against the alternate hypothesis  [tex]H_1:p_1 \neq p_2[/tex] .

Let [tex]\hat p_1, \hat p_2[/tex] denotes the respective sample proportions and the [tex]n_1, n_2[/tex] represents the sample size respectively.

[tex]$\hat p_1 = \frac{74}{155} = 0.477419[/tex]

[tex]n_1=155[/tex]

[tex]$p_2=\frac{86}{155}=0.554839[/tex]

[tex]n_2=155[/tex]

The test statistic can be written as :

[tex]$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}[/tex]

which under [tex]H_0[/tex]  follows the standard normal distribution.

We reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance, if the P-value [tex]<0.05[/tex] or if [tex]|z_{obs}|>Z_{0.025}[/tex]

Now, the value of the test statistics = -1.368928

The critical value = [tex]\pm 1.959964[/tex]

P-value = [tex]$P(|z|> z_{obs})= 2 \times P(z< -1.367928)$[/tex]

                                     [tex]$=2 \times 0.085667$[/tex]

                                     = 0.171335

Since the p-value > 0.05 and [tex]$|z_{obs}| \ngtr z_{critical} = 1.959964$[/tex], so we fail to reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance.

Hence we conclude that the two population proportion are not significantly different.

Conclusion :

There is not sufficient evidence to conclude that the [tex]\text{proportion}[/tex] of the seeds that [tex]\text{germinate differs}[/tex] with the percent of the [tex]\text{mushroom compost}[/tex] in the soil.

This is a relative frequency question. Applying the concept, we get that the relative frequency of gluten free breads sold at store A compared to those sold at all stores combined is 0.1667.

Relative frequency:

The relative frequency of a to b is given by a divided by b.

In this question:

a: Gluten free breads sold at store A

b: Gluten free breads sold at all stores combined.

2 + 7 + 3 = 12 gluten free breads sold.

2 sold at store A, so:

[tex]\frac{2}{12} = \frac{1}{6} = 0.1667[/tex]

Thus, the relative frequency of gluten free breads sold at store A compared to those sold at all stores combined is 0.1667.

Another example of a problem involving relative frequency you can check at https://brainly.com/question/20630951

Relative Frequency:

The relative frequency of gluten-free breads sold at Store A compared to those sold at all the stores combined is:

= 0.167

Data and Calculations:

Gluten-Free Breads at Different Stores

                           Gluten-Free         Not Gluten-

                               Breads            Free Breads

Store A                        2                          4

Store B                        7                         10

Store C                       3                         12

Since we are only considering Gluten-Free Breads at the three stores, we take the relevant data to calculate and compare their frequencies as follows:

                           Gluten-Free        Relative

                               Breads         Frequency

Store A                        2                0.167 (2/12) = 17%

Store B                        7                0.583 (7/12) = 58%

Store C                       3                0.250 (3/12) = 25%

Total Gluten-free     12                 1 = 100%

Thus, the relative frequency of gluten-free breads sold at Store A compared to those sold at all the stores combined is 0.167.

Answer:

74.80

Step-by-step explanation:

First find the discount

88 * 15%

88*.15

13.2

Subtract the discount from the original price

88-13.2

74.80

9514 1404 393

Answer:

  see below

Step-by-step explanation:

  [tex]\text{A. point: }X\\\\\text{B. ray through Y: }\overrightarrow{XY}\\\\\text{C. line through Z: }\overleftrightarrow{XZ}\\\\\text{D. plane: plane } XYZ[/tex]

__

Additional comment

When you don't have the benefit of typesetting, you can refer to the geometry by name: ray XY, line XZ,

ANSWER

8-2........3/4 but you have you ADD some people dont know that 8-2= 6

and so 6/1 + 3/4 is 24/4

Answer:

he has 48 dollars left to spend on clothes

Answer:

A) It’s the First graph

Step-by-step explanation: hope this helps!

The graph corresponds to the inequality -2x - 3y < 6 is option A.

To estimate the value of x and y, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Given: -2x - 3y < 6

then -2x - 3y = 6

Put the value of y = 0, then

[tex]$-2x-3*0=6[/tex]

-2x = 6

x = -6/2 = -3 and

-2x - 3y = 6

Put the value of x = 0, then

[tex]$-2*0-3y=6[/tex]

-3y = 6

y = -6/3 = -2

The value of x = -3 and y = -2.

Therefore, the correct answer is option A.

To learn more about inequality refer to:

https://brainly.com/question/12170562

#SPJ2

Answer:

1/4

Step-by-step explanation:

x^2 - x

Take the coefficient of x

-1

Divide by 2

-1/2

Square it

(-1/2)^2 = 1/4

Add it

x^2 -x +1/4

Answer:

[tex]\sqrt{280}[/tex] = 2[tex]\sqrt{70}[/tex]

37^2 = 1369

33^2 =1089

1369-1089 = 280

Step-by-step explanation:

C 89. What is the power of 5, so that 1 its value become ?

The power is 0. because if 0 is tge powwe of any variable or letters the value becomes 1.

Step-by-step explanation:

the answer is regular octagon

i think

Formula-

If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}

Symbol that can be used-

The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".

Hope it helps you... pls mark brainliest if it helped you.

z = 3i / (-1 - i )

z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )

z = (3i × (-1 + i )) / ((-1)² - i ²)

z = (-3i + 3i ²) / ((-1)² - i ²)

z = (-3 - 3i ) / (1 - (-1))

z = (-3 - 3i ) / 2

Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have

arg(z) = arctan((-3/2)/(-3/2)) - π

arg(z) = arctan(1) - π

arg(z) = π/4 - π

arg(z) = -3π/4

where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.

Step-by-step explanation:

f(x)=log(x)

     =d(log(x)/dx)

=>y=1/x

Step-by-step explanation:

Forty three thousand one hundred and six

Answer:

Forty three AND one hundred six thousandths

Step-by-step explanation:

If there is a comma ( , ) between the two numbers, you are correct.  

If there is a period / dot ( . ) between them, and you need to read the place values, you must read the numbers to the right of the . as decimals.  Those are the "th" numbers.  1 is in the tenths place, 0 in the hundredths place and the 6 in the thousandths place.  

If you are simply reading out the digit names, without assigning their value, you might say "forty three POINT one hundred six"  or "forty three DOT one hundred six" or "forty three DECIMAL one hundred six".

Answer:

Answer : 1/8.

Step-by-step explanation:

Hey there!

Please see the attached picture for your answer.

Hope it helps!

Answer:

Step-by-step explanation: Hello! Do

Answer:

answer is

In empty set, n(A) = { }.

Answer:

[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]

Step-by-step explanation:

Given

[tex](4x^3y^5)(3x^5y)^2[/tex]

Required

The equivalent expression

We have:

[tex](4x^3y^5)(3x^5y)^2[/tex]

Expand

[tex](4x^3y^5)(3x^5y)^2 = 4x^3y^5*9x^{10}y^2[/tex]

Further expand

[tex](4x^3y^5)(3x^5y)^2 = 4*9*x^3*x^{10}y^5*y^2[/tex]

Apply laws of indices

[tex](4x^3y^5)(3x^5y)^2 = 36*x^{13}y^7[/tex]

Answer:

x/8

Step-by-step explanation:

First, we are given "the quotient of...". This means that we are dividing something/something else. If two numbers are given in the phrase "something and something else", the first number given will be the something, and the second number will be the something else.

The first number listed is x. Therefore, we have

x/something else.

Next, we are given "and 8", so we have x/8 as our expression

Answer:

yes how can I help you???

Answer:

A∩B ={2;4}

Step-by-step explanation:

Chúc bạn học tốt

Answer:

Step-by-step explanation:

Assume the dish opens upwards. The cross-section through the vertex is a parabola. You know three points on the parabola: (0,0), (2,2), and (-2,2). Plug the points into y = ax² + bx + c to get a system of three equations where a=0.5, b=c=0.

Equation of parabola: y = 0.5x²

:::::

Vertex (0,0)

Focal length = 1/(4×0.5) = 0.5

Focus (0,0+0.5) = (0, 0.5)

Directrix y = 0-0.5 = -0.5

:::::

At endpoints of latus rectum, y = 0.5

x = ±√0.5 = ±√2/2

Focal width = 2×√2/2 = √2

:::::

Place antenna at focus, (9,2)

the function that connects the point (0;1) with the point (-1;0) is the graph

Answer:

It's option D. y = 1/2x - 4

Step-by-step explanation:

I used Desmos to find the answer, hope the graph helps!

Answer:

Expanded form: 4,000,000 + 500,000 + 80,000 + 7,000 + 900 + 2 + 0.4 + 0.05 + 0.003

Word form: Four million, five hundred eighty-seven thousand, nine hundred two and four hundred fifty-three thousandths.

Answer:

Answer:

a multiple of 3.

Step-by-step explanation:

1x3=3

3x3=9

9x3=27