Why did the scientist make an exact duplicate of himself

Answer:

Option D.

Step-by-step explanation:

We have to find the equation of the parabola which has vertex at ( 0,3 )

If we write the equation of a parabola in the vertex from then we will write

y = ( x - h )² + (k)²

In this equation ( h, k) will be the vertex.

(a) y = (x-3)² + 0

    so ( 3,0) will be the vertex

(b) y = ( x+3)² + 0

   or y = [x - (-3)]² + 0

   then ( -3,0) will be the vertex

(c) y = (x² - 3)

   y = ( x-0 )² + (-3)

  then ( 0, -3) is the vertex.

(d) y = x² + 3

    y = ( x-0 )² + 3

Then ( 0, 3 ) will be the vertex of this parabola.

Option D. is the answer.

0.30 as a fraction is 30/100 = 3/10

0.30 as a percent = 0.30 * 100 = 30%

 answer is D. 3/10 and 30%

.30 is .3

do .30 divided by 1 and you get 3/10

Percentage= move the decimal 2 places to the right and you get 30%

So your answer is D.

B is the correct answer                                            

Answer:

The cost of the new top $924.

Step-by-step explanation:

You want to replace the counter-tops in a kitchen.

The dimensions of the first counter is 24 inches by 6 feet.

i.e [tex]24 \text{ inch} \times 6 \text{ feet}[/tex]

or [tex]2\text{ feet} \times 6 \text{ feet}[/tex]

As 1 feet =12 inches

Hence the area of the counter is [tex]2\times 6=12\text{ feet}^2[/tex]

The dimensions of the second counter is 30 inches by 4 feet.

i.e [tex]30 \text{ inch} \times 4 \text{ feet}[/tex]

or [tex]2.5\text{ feet} \times 4 \text{ feet}[/tex]

Hence the area of the counter is [tex]2.5\times 4=10\text{ feet}^2[/tex]

Hence, the total area will be [tex]12+10=22 \text{ feet}^2[/tex]

The unit cost of the counter-top is [tex]\$42.00\text{ feet}^2[/tex]

So the net cost will be,

[tex]=42\times 22=\$924[/tex]

Answer:  The correct option is (C) [tex]\dfrac{256}{3}.[/tex]

Step-by-step explanation:  The given function is

[tex]f(x)=\dfrac{1}{3}\times 4^x.[/tex]

We are to find the value of f(4).

To find the value of f(4), we need to substitute the value of x as 4 in the given definition of function f(x).

Substituting x = 4 in f(x), we have

[tex]f(4)=\dfrac{1}{3}\times 4^4=\dfrac{1}{3}\times 256=\dfrac{256}{3}.[/tex]

Therefore, the value of f(4) is [tex]\dfrac{256}{3}.[/tex]

Option (C) is correct.

Answer:

1.8444444....=1.8+1/10*0.44444....

=1.8+1/10*4/9

=1.8+4/90

=162/90+4/90

=166/90

=83/45

2.126262626...=2.1+1/10*0.262626...

=2.1+1/10*26/99

=2.1+26/990

=2079/990+26/990

=2105/990

=421/198

The height of the frame is 1.5 meters.

The Width of the frame is 1 meter.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

Given that,

P = 5 meters

w = 2/3h = 0.67h

We have to determine the height of the frame.

The perimeter of the frame = 2h + 2W

We know all the other values So we can plug in values to solve for h:

5 = 2h + 2(.67h)

5 = 2h+ 1.33h

5 = 3.33h

5/3.33 = h

h = 1.5

So the height of the frame is 1.5 meters

We need to find the width and we know that W = 0.67h

W = 0.67(1.5)

W = 1

So the Width of the frame is 1 meter.

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The standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]

In order to write  4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones in standard form, let us write each of the expressions in figures

4 hundred-thousand   =  400,000

13 thousand = 13,000

11 hundreds = 11 x 100

11 hundreds = 1100

4 ones = 4 x 1

4 ones = 4

The next step is to sum up all the figures together

400000 + 13000 + 1100 + 4  =  414,104

Convert 414104 to standard form

[tex]414104 = 4.14104 \times10^5[/tex]

Therefore, the standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]

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2/10

There is one tenth in a mile. I have the same question. But I am just guessing.

The interquartile range (IQR) is 5 minutes. Any values below 19.5 minutes or above 39.5 minutes would be considered outliers. In this data set, both the minimum time of 15 minutes and the maximum time of 50 minutes are outliers.

The question is whether there are any outliers in the finish times of a group of runners based on the IQR definition. To determine this, we first calculate the interquartile range (IQR), which is the range of the middle 50 percent of the data. Q1 = 32 min - 2 For this data set, we calculate the IQR by subtracting the first quartile (Q1) from the third quartile (Q3). Here, IQR = Q3 - 7 min = 5 min.

Next, we multiply the IQR by 1.5, which is our test for outliers. This gives 1.5 * IQR = 1.5 * 5 min = 7.5 min.

An outlier is defined as a data point that is below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. So, any time less than 27 min - 7.5 min = 19.5 min or greater than 32 min + 7.5 min = 39.5 min would be considered an outlier.

Given the five-number summary: min=15 min, Q1=27 min, median=31 min, Q3=32 min, max=50 min, we can clearly see that the minimum time of 15 min is an outlier because it's less than 19.5 min. Also, the maximum time of 50 min is an outlier because it's greater than 39.5 min.

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The minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the given data set.

To determine if there are any outliers using the 1.5 * IQR (interquartile range) definition, we need to calculate the IQR first. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

Given:

- Q1 = 27 minutes

- Q3 = 32 minutes

We can calculate the IQR as follows:

[tex]\[ IQR = Q3 - Q1 = 32 - 27 = 5 \text{ minutes} \][/tex]

Now, we can use the 1.5 * IQR rule to find the lower and upper bounds for potential outliers:

Lower Bound: Q1 - 1.5 * IQR

Upper Bound: Q3 + 1.5 * IQR

[tex]\[ \text{Lower Bound} = 27 - 1.5 \times 5 = 27 - 7.5 = 19.5 \text{ minutes} \]\[ \text{Upper Bound} = 32 + 1.5 \times 5 = 32 + 7.5 = 39.5 \text{ minutes} \][/tex]

Any finish times below 19.5 minutes or above 39.5 minutes would be considered potential outliers according to the 1.5 * IQR rule.

Since the minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the data set.

1st number = x

2nd number = x-5

x*(x-5) = 36

x^2-5x =36

x^2 -5x-36 = 0

factor the polynomial:

(x-9) (x+4)

9-9 = 0, -4 +4 = 0

 so x = 9 or -4

 the question states a positive number

 so x = 9

 the 2 numbers are 9 and 4

By dividing the total number of bows (110) by the number of bows that fit in one bag (10), we find that Kate can fill 11 bags with her bows.

To find out how many bags Kate can fill with her bows, we need to divide the total number of bows by the number of bows that fit in one bag. In this case, Kate has 110 bows and 10 bows fit in one bag.

So, we divide 110 by 10: 110 / 10 = 11

Therefore, Kate can fill 11 bags with her 110 bows.

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Kate can fill 11 bags with her 110 bows.

Given:

Kate has 110 bows

No. of bows fit in the bag = 10

No. of bags she can fill:

110 bows ÷ 10 bows per bag

= [tex]\frac{110}{10}[/tex]

= 11 bags.

So, Kate can fill 11 bags with her 110 bows.

The point of intersection between the given line and plane is (1/6, -5/3, 5/2). This is determined by substituting the parametric line equations into the plane equation, simplifying to find the value of the parameter t, and substituting that value back into the line equations.

The given line and plane equations are, x = 1 + t, y = 2t, z = -3t and x + y - z = -4 respectively. To find where the line intersects the plane, we need to substitute the parametric line equations into the plane equation.

Step by Step Solution

Step 1: Substitute x, y, and z from the line equation into the plane equation, giving you (1+t) + 2t - (-3t) = -4.
Step 2: Simplify the equation to find the value of t. You get 6t + 1 = -4, so t = -5/6.
Step 3: Substitute t = -5/6 into the line equations to find x = 1/6, y = -5/3, and z = 5/2.

So, the point P where the line intersects the plane is (1/6, -5/3, 5/2).

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The fraction of an hour is 4 minutes in lowest terms is 1/15.

To find the fraction of an hour that 4 minutes represents, we need to compare the number of minutes to the total number of minutes in an hour, which is 60.

We can set up a fraction where the numerator represents the number of minutes we want to find the fraction for (4 minutes) and the denominator represents the total number of minutes in an hour (60 minutes).

So, the fraction can be written as 4/60.

To simplify the fraction to its lowest terms, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 60 is 4.

Dividing both the numerator and denominator by 4, we get:

4/60 = (4 ÷ 4) / (60 ÷ 4) = 1/15.

Therefore, 4 minutes in lowest terms is equal to 1/15th of an hour.

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Answer:

B. [tex]2x^2+\frac{3x}{2}-5[/tex]

Step-by-step explanation:

Given functions,

[tex]f(x)=\frac{x}{2}-2[/tex]

[tex]g(x)=2x^2+x-3[/tex]

Since, (f+g)(x) = f(x) + g(x)

[tex]=\frac{x}{2}-2+2x^2+x-3[/tex]

[tex]=2x^2+\frac{x+2x}{2}-5[/tex]    ( combine like terms )

[tex]=2x^2+\frac{3x}{2}-5[/tex]

Option 'B' is correct.

To find the six sixth roots of 64, you can use polar form and De Moivre's Theorem to calculate the complex numbers. The roots are 2, 1+i√3, -1+i√3, -2, -1-i√3, and 1-i√3.

[tex]X^6 = 64[/tex]

The sixth roots of 64 are complex numbers and can be found by writing 64 in polar form and applying De Moivre's Theorem. Let's find the six roots:

First root: 2(cos(0) + i sin(0)) = 2

Second root: 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + i√3

Third root: 2(cos(2π/3) + i sin(2π/3)) = 2(-1/2 + i√3/2) = -1 + i√3

Fourth root: -2

Fifth root: -2(cos(-π/3) + i sin(-π/3)) = -2(1/2 - i√3/2) = -1 - i√3

Sixth root: -2(cos(-2π/3) + i sin(-2π/3)) = -2(-1/2 - i√3/2) = 1 - i√3

0.2x+4-3>-7-6.2x

0.2x+1>-7-6.2x

0.2x+0.6x>-8

0.8x>-8

the correct answer is: x>-1.25