Which is the most precise description of quadrilateral ABCD?

Answer:

Step-by-step explanation:

The standard deviation of the sampling distribution of sample means is given by the formula:

standard deviation = population standard deviation / sqrt(sample size)

Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:

standard deviation = 0.8 / sqrt(38)

standard deviation ≈ 0.13

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.

Answer:

D

Step-by-step explanation:

f(x) = 3x - 12

f(2) = 3(2) - 12

= 6 - 12

= -6

Answer:

The answer is -6

Step-by-step explanation:

f(x) = 3x - 12; f(2)

f(2) = 3x - 12

f(2) = 3(2) - 12

f(2) = 6 - 12

f(2) = -6

Thus, The answer is -6

-TheUnknownScientist

Answer:

I don't know the answer it is to hard.

Answer:

440 in ^2 in the surface area

Step-by-step explanation:

Hope this helps

Answer:

13.245 rounded to the nearest tenth is 13.2 seconds

Step-by-step explanation:

Ro round a number to the nearest 10, look at the units digit. If the units digit is 5 or more, round up. If the units digit is 4 or less, round down.

Answer:

13.250

Step-by-step explanation:

befause number five is near ten

The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer:

Company A's cost would be $530

Company B's cost would be $610

difference is $80

Step-by-step explanation:

Answer:

\(P(11.5<X<15.5)=P(\frac{11.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{13.5-\mu}{\sigma})=P(\frac{11.5-13.5}{2}<Z<\frac{15.5-13.5}{2})=P(-1<z<1)\)

And we can find the probability with this difference

\(P(-1<z<1)=P(z<1)-P(z<-1)\)

And we can use the normal standard distribution or excel and we got:

\(P(-1<z<1)=P(z<1)-P(z<-1)=0.841-0.159=0.682\)

So then we expect a proportion of 0.682 between 11.5 and 13.5

Step-by-step explanation:

Let X the random variable that represent the price earning ratios of a population, and for this case we know the distribution for X is given by:

\(X \sim N(13.5,2)\)  

Where \(\mu=13.5\) and \(\sigma=2\)

We want to find the following probability

\(P(11.5<X<15.5)\)

And we can use the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

Using this formula we got:

\(P(11.5<X<15.5)=P(\frac{11.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{13.5-\mu}{\sigma})=P(\frac{11.5-13.5}{2}<Z<\frac{15.5-13.5}{2})=P(-1<z<1)\)

And we can find the probability with this difference

\(P(-1<z<1)=P(z<1)-P(z<-1)\)

And we can use the normal standard distribution or excel and we got:

\(P(-1<z<1)=P(z<1)-P(z<-1)=0.841-0.159=0.682\)

So then we expect a proportion of 0.682 between 11.5 and 13.5

The requried, there are 240 possible ways the race can finish with a mouse placing first, second, and third.

To find the number of ways the race can finish with a mouse placing first, second, and third, we can use the concept of permutations.

Since the mouse is guaranteed to finish first, there are 5 mice to choose from for the first position.

Once the first place is determined, there are 4 mice left for the second position.

After the first two positions are filled, there are 3 mice left for the third position.

Now, we need to determine the order of the cats. There are 4 cats to choose from for the fourth position.

The total number of ways the race can finish with a mouse placing first, second, and third is given by the product of these choices:

Number of ways = 5 (for first place) * 4 (for second place) * 3 (for third place) * 4 (for fourth place)

Number of ways = 5 * 4 * 3 * 4

Number of ways = 240

There are 240 possible ways the race can finish with a mouse placing first, second, and third.

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Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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Answer:
132

Step-by-step explanation:

582 - 450 = 132
They already give you the ground seats and the total.

All the ordered pairs that represent points on the graph of this equation include the following:

A. (-4, 4).

C. (-2, 1)

E. (2, -5)

F. (0, -2)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the solutions are include following;

Ordered pair = (-4, 4).

Ordered pair = (-2, 1).

Ordered pair = (2, -5).

Ordered pair = (0, -2).

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Complete Question:

Which ordered pairs represent points on the graph of this equation? Select all that apply.

2y= –3x–4

(-4, 4)

(7, 6)

(-2, 1)

(0, 7)

(2, -5)

(0, -2)

Answer:4^6

Step-by-step explanation:

Properties of exponents dictates that when a power is raised to a power, you multiply the exponents so 3*2 =6 meaning that the expression is equal to 4^6

Answer:

127.1

Step-by-step explanation:

This is easy, if you see the hundredth 0.07, that is above 5 so it rounds up to become 0.1 tenth, normally we check for things like 0.003 in the thousandth, but here it is less than 5 so it does nothing, not to mention it wouldnt change the outcome

Answer:

60 contain 6 tens

then

60+10

contain

7 tens

the

correct answer

is

7 tens

Answer:

6 tens + 1 ten = 7 tens

Step-by-step explanation:

6 tens = 60

1 ten = 10

7 tens = 70

Answer:

Given that:

Volume of the storage shed = 833 cubic feet

Cost of the concrete for the base per square foot = $8

Cost of concrete for the root per square foot = $9

Cost of the material for the sides per square foot = $3.50

Let x be the length of the side of the square and h be height of the shed.

The formula to calculate the volume is

V = Bh

where B is the base area.

Since the base is a square with side 'x',

Substitute the given values into the formula of V.

The base will have the same area with the roof.

Area of the roof = Base area

Cost to construct base

Cost to construct the roof

Area of one side = xh

Cost to construct one side = 3.5xh

Cost to construct 4 sides of the box

The total cost is the sum of these three costs. So, the objective function is

The dimension for the most economical cost will occur when dC/dx = 0. Then

The length of side of the base is 7 feet.

Substitute the value of x into the equation of h.

The height of the storage shed is 17 feet.

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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Answer:

The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.

Step-by-step explanation:

Geometrically speaking, the volume of the rectangular box (\(V\)), in cubic feet, is represented by this formula:

\(V = l^{2}\cdot h\) (1)

Where:

\(l\) - Side length of the box, in feet.

\(h\) - Height of the box, in feet.

In addition, the total cost of the box (\(C\)), in monetary units, is defined by this formula:

\(C = (c_{b}+c_{t})\cdot l^{2} + 4\cdot c_{s}\cdot l\cdot h\) (2)

Where:

\(c_{b}\) - Unit cost of the base of the box, in monetary units per square foot.

\(c_{t}\) - Unit cost of the top of the box, in monetary units per square foot.

\(c_{s}\) - Unit cost of the side of the box, in monetary units per square foot.

By (1), we clear \(h\) into the expression:

\(h = \frac{V}{l^{2}}\)

And we expand (2) and simplify the resulting expression:

\(C = (c_{b}+c_{t})\cdot l^{2}+4\cdot c_{s}\cdot \left(\frac{V}{l} \right)\) (3)

If we know that \(c_{b} = 0.34\,\frac{m.u.}{ft^{2}}\), \(c_{s} = 0.05\,\frac{m.u.}{ft^{2}}\), \(c_{t} = 0.16\,\frac{m.u.}{ft^{2}}\) and \(V = 40\,ft^{3}\), then we have the resulting expression and find the critical values associated with the side length of the base:

\(C = 0.5\cdot l^{2} + \frac{8}{l}\)

The first and second derivatives of this expression are, respectively:

\(C' = l -\frac{8}{l^{2}}\) (4)

\(C'' = 1 + \frac{16}{l^{3}}\) (5)

After equalizing (4) to zero, we solve for \(l\): (First Derivative Test)

\(l-\frac{8}{l^{2}} = 0\)

\(l^{3}-8 = 0\)

\(l = 2\,ft\)

Then, we evaluate (5) at the value calculated above: (Second Derivative Test)

\(C'' = 3\)

Which means that critical value is associated with minimum possible total costs. By (1) we have the height of the box:

\(h = 5\,ft\)

The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.

Answer:

\(c = \frac{A}{12h} - b\)

Step-by-step explanation:

Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with \(\frac{A}{12h} = b+c\). Now, we can subtract both sides by b, and we will be left with \(\frac{A}{12h} - b = c\). Yay! We've now isolated c and that is our final answer!

Hope this helped! :)

First make a guest check

My Guest check #9

1 donut = $1.29

Donut holes = $4.89

Dozen Donuts = $12

Donut Holes = $4.89

$1.29 + $4.89 + $12 + $4.89 = $23.07

$23.07 * 8% = $24.92 is the 9th check list

My Guest check #10

1 donut = $1.29

1 donut = $1.29

Dozen Donuts = $12

Donut Holes = $4.89

$1.29 + $1.29 + $12 + $4.89 = $19.47

$19.47 * 8% = $21.03 is the 10th check list

78

1) Since we have a Combination, we can write out the following formula:

Note that we canceled 11! on the numerator by the factorial of 11! on the denominator. And notice this is only possible when the order does not matter.

2) Hence, the answer is 78 because there are 78 combinations of 13 choosing 11.

Answer:

58.8 in²

Step-by-step explanation:

you have no calculator ?

since you clearly have a computer or smart phone - there are calculator apps on all of them.

you really just need to use the given numbers and multiply and add them following the formula. so, what is your problem ?

anyway,

2pi×r×h + 2pi×r²

h = 5.9

r = 1.3

2pi × 1.3 × 5.9 + 2pi × 1.3² = 2pi × 7.67 + 2pi × 1.69 =

= 58.8 in²

Answer:

C

Step-by-step explanation:

An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is

The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

f(x) = a(b)^x

Where:

Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 13 = 87% = 0.87.

By substituting the parameters into the exponential equation, we have the following;

\(f(x) = 95(0.87)^x\)

When x = 12, we have;

\(f(12) = 95(0.87)^{12}\)

f(12) = 17.86 ≈ 18 milligrams.

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Answer:

Amount after 4 years = $3274.125

Step-by-step explanation:

Time t= 4 years

Principal amount p= $2500

Interest rate R= 6.75%

Number of times compounded n= 4*12

Number of times compounded n= 48

Amount A = p(1+r/n)^(nt)

A= 2500(1+0.0675/48)^(48*4)

A= 2500(1+0.001406)^(192)

A= 2500(1.001406)^192

A= 2500(1.30965)

A= 3274.125

Amount after 4 years = $3274.125