Solve This Question To The Answer And Show All Your Steps And Make Sure It Is Legible.
Find the equation of the line that is orthogonal to both u = 2i + 5j – 3k and the
z-axis.solve this question to the answer and show all your steps and make sure it is legible.

The correct answer is A. The standard error of the sample proportion will become larger as the sample size increases.

The standard error is a measure of the variability or uncertainty associated with an estimate. In the case of the sample proportion, it measures the spread or variability in the proportion of successes observed in the sample compared to the true population proportion.

As the sample size increases, the standard error decreases, indicating greater precision in estimating the true population proportion. This is because a larger sample provides more information and reduces the impact of sampling variability.

On the other hand, options B, C, and D are incorrect. The standard error is not affected by the population proportion itself but rather by the sample size. The population proportion approaching 0.50, 1.00, or 0 does not directly impact the standard error, although it may affect other measures such as the margin of error or confidence intervals. The primary factor influencing the standard error is the sample size, with larger samples leading to smaller standard errors.

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The margin of error used to construct this confidence interval is approximately 0.053, rounded to three decimal places.

To find the margin of error (E) used to construct the confidence interval, we can use the formula:

E = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, the upper limit of the confidence interval is 0.519, and the lower limit of the confidence interval is 0.413.

Plugging in these values, we get:

E = (0.519 - 0.413) / 2

= 0.106 / 2

≈ 0.053

Therefore, the margin of error used to construct this confidence interval is approximately 0.053, rounded to three decimal places.

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The direct materials quantity variance is \(\$89,600\) unfavorable.

To calculate the direct materials quantity variance, we need to compare the actual quantity of materials used to the standard quantity allowed for the production of \(5,500\)  units.

The standard quantity of materials for \(5,500\) units can be calculated as:

Standard quantity = \(7\) pounds/unit × \(5,500\) units = \(38,500\) pounds

The actual quantity of materials used was 37,100 pounds.

The direct materials quantity variance can be calculated as:

Quantity variance = (Standard quantity - Actual quantity) × Standard price per pound

\(Quantity variance = (38,500 pounds - 37,100 pounds) * $64/pound\)

\(Quantity variance = 1,400 pounds * \$64/pound\)

\(Quantity variance = \$89,600 unfavorable\)

Therefore, the direct materials quantity variance is \(\$89,600\) unfavorable.

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Answer:

22.2 years

Step-by-step explanation:

Doubling formula is given as:

P(t) = Po × (2)^t/k

Where

Po = Initial amount invested = $5600

P(t) = Amount after time t = $72500

k = Time it takes to double = 6 years

t = Time in years = ??

Hence:

72500 = 5600 × (2)^t/6

Divide both sides by 5600

72500/5600 =( 5600 × (2)^t/6)5600

12.946428571 = (2)^t/6

Take the In of both sides

In 12.946428571 = In (2)^t/6

In 12.946428571 = t/6 In (2)

Divide both sides by In 2

In 12.946428571/In 2 = t/6

3.6944822628 = t/6

Cross Multiply

t = 6 × 3.6944822628

t = 22.166893577 years

Approximately

t = 22.2 years

Therefore, it would take 22.2 years

The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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The probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok

To calculate this, we will use a standard normal distribution table and the Z-score formula.

First, we need to calculate the Z-score for the sample average of 8.47. This is done by using the Z-score formula:

Z-score = (x - mean)/standard deviation

where x is the sample average, mean is the average of all samples, and standard deviation is the standard deviation of all samples.


In this case, the Z-score is:

Z-score = (8.47 - 8.50)/0.22 = -0.14


Then, we need to look up the Z-score in a standard normal distribution table. The probability of the sample average being more than 8.47 is equal to 1 minus the Z-score probability. So, in this case, the probability of the sample average being more than 8.47 is equal to 1 - 0.5594 = 0.4406.

Therefore, the probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok.

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3 km 9 hm 9 dam 19 m + 7 km 2 dam=​

we know that

1 km-1,000 m

1 hm=100 m

1 dam=10 m

Convert the measures to meters

3 km=3*1,000=3,000 m

9 hm=9*100=900 m

9 dam=9*10=90 m

7 km=7*1,000=7,000 m

2 dam=2*10=20 m

substitute

3 km 9 hm 9 dam 19 m=3,000+900+90+19=4,009 m

7 km 2 dam=7,000+20=7,020 m

so

4,009+7,020=11,029 m

Convert to km hm dam m

11,029 m=11 km+0 hm+ 2 dam+9 m

therefore

Julian makes and sells wallets.

income could be equated as y=9x-178,

where is x the number of wallets he sells.

cost could be equated as y=3x+74

to break even , income =  equal to cost

so  9x-178=3x+74 , where x is the no of wallets

  9x-178 = 3x+ 74

9x-3x = 74+178 = 252

 6x = 252

x= 42

so, Julian need to make 42 wallets to break even

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Answer:

D) 5

Step-by-step explanation:

we see that every 4 hours 20 miles are traveled.

so, the rate of change of miles travels over hours is

20/4 = 5/1 = 5

in other words, the speed was 5 mph.

1.5·10⁸ kilometers

As a result, the Earth Sun distance is 150 million kilometers. To use scientific notation, pick a value between 1 and 10, then multiply it by 10ˣ.

So the number between 1 and 10 in 150,000,000 is 1.5, with 8 decimal points.

As a result, the solution is 1.5·10⁸

The benefits of Earth's prime placement in the solar system are numerous. We are just far enough away from the Sun for life to thrive.

Venus is excessively hot. Mars is quite chilly. Scientists refer to our region of space as the "Goldilocks Zone" because it looks to be ideal for life.

As previously stated, Earth's average distance from the Sun is around 93 million miles (150 million kilometers). That's one AU.

On this hypothetical scale, these so-called "linebackers" resemble minuscule specks rather than the massive linebackers of the NFL.

If all of the known asteroids in our solar system were combined, their total mass would be less than 10% that of Earth's moon.

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Option a) $213.34 is the correct answer.

Given that, Suppose that you are 34 years old now and that you would like to retire at the age of 75. Furthermore, you would like to have a retirement fund from which you can draw an income of $70,000 annually. You plan to reach this goal by making monthly deposits into an investment plan until you retire. The amount to be deposited each month needs to be calculated. It is assumed that the annual interest rate is 8% and compounded monthly.

The formula for the future value of the annuity is given by, \(FV = C * ((1+i)n -\frac{1}{i} )\)

Where, FV = Future value of annuity

            C = Regular deposit

            n = Number of time periods

            i = Interest rate per time period

In this case, n = (75 – 34) × 12 = 492 time periods and i = 8%/12 = 0.0067 per month.

As FV is unknown, we solve the equation for C.

C = FV * (i / ( (1 + i)n – 1) ) / (1 + i)

To get the value of FV, we use the formula,FV = A × ( (1 + i)n – 1 ) /i

where, A = Annual income after retirement

After substituting the values, we get the amount to be deposited as $213.34.

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Answer:The answer is 108 for sure.

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

[7^(-8)]^(-4) =

A power raised to a power: multiply the exponents.

= 7^[(-8)*(4)]

= 7^(32)

Answer: D.

Answer:

7^32, the fourth option

Step-by-step explanation:

For the power rule, if you have a number to a power, for example \(x^{a}\) and raise it to another power so it becomes, \((x^{a} )^{b}\), We simplify by multiplying the powers together. So the simplified answer would be \(x^{(a*b)}\).

Answer:

18%

Step-by-step explanation:

0.12 is 12 percent.

We also have the 0.06 percent which would just be 6 percent

We need to add up those percentages to get 18 percent, for the people surveyed that cannot swim would be 18 percent.  

Our final answer is D.

The length of each side of the sign will be 14.81-inch approx.

It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.

           \(s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1\)

Also, it is a square. So, the measurement of length from side to side

            \(2x+s=36....................Eq.2\)

solving Eq.1 we get,

\(s=\sqrt{2} x\)...putting this value in Eq.2,

            \(s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }\)

Putting this value of x in Eq.1,

          s = 14.8

Hence, The length of each side of the sign will be 14.81-inch approx.

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Answer:

as a mixed number it will be 1 13/15

but in exact form it will be 28/15

Step-by-step explanation:

hope this helped.. :)

\(1\frac{13}{15}\) is the solution for \(3\frac{10}{15}\) - \(1\frac{12}{15}\)

Fractions represent the parts of a whole or collection of objects.

The given expression is

\(3\frac{10}{15}\) - \(1\frac{12}{15}\)

Firstly we need to convert this mixed fraction to improper fraction.

Improper fractions are fractions whose numerator is greater than denominator.

((15×3)+10)/15 -  ((15×1)+12)/15

(45+10)/15 - (15+12)/15

55/15-27/15

15 is the LCM

(55-27)/15

28/15

Now we convert this to improper fraction

\(1\frac{13}{15}\)

Hence \(1\frac{13}{15}\) is the solution for \(3\frac{10}{15}\) - \(1\frac{12}{15}\).

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Usando proporciones, hay que se necessita 8.42 litros de pintura para pintar 1 metro cuadrado de pared.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

En este problema, se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados, por eso, la cantidad relativa a 1 metro cuadrado es dada por:

c = 9.01/1.7 = 8.42 litros.

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Answer:

x = 3

Step-by-step explanation:

since it's hitting 3 on the x axis and just goes up and down where 3 is, all the points have an x of 3 and nothing else. making the equation x = 3

Answer:

C .12 units I think so if wrong I am sorry

Answer:

it's a rational number and perfect square and decimal form is 8.77

The area of the circle is  12. 56 square units

The formula for calculating the area of a circle is expressed as;

A = πr²

This is so such that the parameters of the equation are;

From the information given, we have that;

Area = unknown

Radius = 2 units

Now, substitute the values into the formula, we have;

Area = 3.14 ×2²

Find the square

Area = 3.14 × 4

Multiply the values, we have;

Area = 12. 56 square units

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8. 1,1

9. 5,-5

10. 4, -3

11. 1536, 6144

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.

8. 1000, 100, 10,

In this sequence, each term is getting divided by 10,

So, next two terms are, 1, 1

9.  5, -5, 5, -5, ..

In this sequence, each term is alternating with a minus sign,

So, next two terms are 5, -5

10. 34, 27, 20, 13, ...

In this sequence, each term is i getting substracted by 7,

So, next two term  are 4, -3

11. 6, 24, 96, 384, ...

In this sequence each term is getting multiplied by 4,

So, next two terms are 1536 , 6144

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The expression in simplest radical form is 2√5

From the question, we have the following parameters that can be used in our computation:

sqrt{20}[tetx]

Express properly

So, we have the following representation

√20

Express 20 as 4 * 5

So, we have the following representation

√20 =√4 * √5

take the square root of 4

√20 =2 * √5

So, we have

√20 = 2√5

Hence, the expression is 2√5

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Note:

Ortho centre :a point of intersection of altitudes of a triangle meets the opposite angle.

Given:

For Orthocentre:.

A(1, 2), B(2, 6), C(3,-4). are vertices of a triangle:

Slope of AB[m1]=\( \frac{6-2}{2-1} \)=4

Since it is perpendicular to CX.

slope of CX=m2

we have for slope of perpendicular

m1m2=-1

m2=-¼

It passes through the point C(3,-4)

equation of line CX becomes;

(y-y1)=m(x-x1)

y+4=-¼(x-3)

4y+16=-x+3

x+4y+16-3=0

x+4y+13=0........[1]

again:

Slope of AC[m1]=\( \frac{-4-2}{3-1} \)=-3

Since it is perpendicular to BY

slope of BY=m2

we have for slope of perpendicular

m1m2=-1

m2=⅓

It passes through the point B(2,6)

equation of line BY becomes;

(y-y1)=m(x-x1)

y-6=⅓(x-2)

3y-18=x-2

x-3y+18-2=0

x-3y+16=0.........[2]

Subtracting equation 1&2.

x+4y+13=0

x-3y+16=0

-__________

7y-3=0

y=\( \frac{3}{7} \)

again

Substituting value of y in equation 1.

x+4*\( \frac{3}{7} \)+13=0

x=-13-\( \frac{12}{7} \)

x=\( \frac{-103}{7} \)=-14\( \frac{5}{7} \)

So

orthocenter is (-14\( \frac{5}{7} \),\( \frac{3}{7}\))

Circumcentre: a point of intersection of perpendicular bisector of the triangle.

Now

X,Y and Z are the midpoint of AB,AC and BC respectively.

X(a,b)=(\( \frac{2+1}{2} \),\( \frac{2+6}{2} \))=

(\( \frac{3}{2} \),4)

Slope of AB=4

Slope of OX=-¼

Equation of line OX passes through (\( \frac{3}{2} \),4)is

y-4=-¼(x-\( \frac{3}{2} \))

4y-16=-x+\( \frac{3}{2} \)

8y-16*2=-2x+3

2x+8y=3+32

2x+8y=35

x+4y=\( \frac{35}{2} \)........[1]

again

Y(c,d)=(\( \frac{3+1}{2} \),\( \frac{-4+2}{2} \)=(2,-1)

Slope of AC:-3

Slope of OY=⅓

Equation of line OY passes through (2,-1) is

y+1=⅓(x-2)

3y+3=x-2

x-3y=3+2

x-3y=5......[2]

Multiplying equation 2 by 3 and

Subtracting equation 1&2.

x+4y=35/2

x-3y=5

-_______

7y=\( \frac{25}{2} \)

y=\( \frac{25}{14} \)

Substituting value of y in equation 2.

x-3*\( \frac{25}{14} \)=5

x=5+\( \frac{75}{14} \)

x=\( \frac{145}{14} \)

x=10\( \frac{5}{14} \)

circumcenter of a triangle: (10\( \frac{5}{14} \),1\( \frac{11}{14} \))

324 is the maximum value of the product of these three numbers

What is maxima and minima?

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, and minima will be its lowest.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

Let the three nonnegative numbers are x,y,z

According to the question

x+y+z=36

and y=2x

therefore, 3x+z=36--------------------------------------------------(1)

z=36-3x

Let 3xz= u--------------------------------------------------------------(2)

differentiating equation 2

du/dx=3z + 3xdz/dx

or

du/dx= z + xdz/dx

differentiating equation 1

3 + dz/dx = 0

dz/dx = -3

du/dz = 36-3x + x(-3)

du/dx = 12 - 2x--------------------------------------------------------------(3)

for maxima put du/dx = 0

x=6-------------------------------------------------------------------------------(4)

again differentiating du/dx = 12 - 2x

d2u/dx2=-2

which means 3xz= u is maximum at x=6

from equation 1 and 4

we get 18+z=36

z=18

Therefore 3xz= 3(6)(18)=324

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Answer:

Step-by-step explanation:

No they do not, the first is -64 and the other is 64

Answer:

No

Step-by-step explanation:

-(2³)² = -(2^6) = -64

(-2³)² = (-8)² = 64

\(f(f^{-1}(x))=f \left(\frac{x+6}{5} \right)=5 \left(\frac{x+6}{5} \right)-6=x+6-6=x\\\\f^{-1}(f(x))=f^{-1}(5x-6)=\frac{5x-6+6}{5}=\frac{5x}{5}=x\)

Since \(f(f^{-1}(x))=f^{-1}(f(x))=x\), the functions are inverses of each other.

The composition of functions is x, f(x) and f⁻¹(x) are inverse functions.

Inverse function is represented by f⁻¹ with regards to the original function  and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

The given functions are f(x)=5x-6 and f⁻¹(x)=(x+6)/5.

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).

Now, h(x)=f(f⁻¹(x))

h(x)=5((x+6)/5 -6)

h(x)=x+6-6

h(x)=x

Since, the composition of functions is x, f(x) and f⁻¹(x) are inverse functions.

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Answer: Carrots cost(s) the most per pound

Step-by-step explanation: