A scientist observes the bacteria’s growth. In the first observation, there were 12 bacteria, 24 in the second observation, 48 in the third and so on. How many bacteria will be there in the 8th observation? Use the explicit formula.

1,536
28
126
27

Answer:

[tex]\dfrac{2}{3}[/tex]

Step-by-step explanation:

To find the scale factor of the dilation of a figure, simply divide the x-value (or y-value) of a vertex of the dilated image Q'R'S'T' by the x-value (or y-value) of the corresponding vertex of the pre-image QRST.

[tex]\implies \sf Scale\;factor=\dfrac{x_{Q'}}{x_{Q}}=\dfrac{-2}{-3}=\dfrac{2}{3}[/tex]

[tex]\implies \sf Scale\;factor=\dfrac{y_{T'}}{y_{T}}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

Therefore, the scale factor is 2/3.

To find the scale factor of the dilation of a figure, first find the lengths of corresponding sides using the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

From inspection of the given diagram:

[tex]\implies QR=\sqrt{(x_R-x_Q)^2+(y_R-y_Q)^2}[/tex]

[tex]\implies QR=\sqrt{(3-(-3))^2+(6-9)^2}[/tex]

[tex]\implies QR=\sqrt{(6)^2+(-3)^2}[/tex]

[tex]\implies QR=\sqrt{36+9}[/tex]

[tex]\implies QR=\sqrt{45}[/tex]

[tex]\implies QR=3\sqrt{5}[/tex]

From inspection of the given diagram:

[tex]\implies Q'R'=\sqrt{(x_{R'}-x_{Q'})^2+(y_{R'}-y_{Q'})^2}[/tex]

[tex]\implies Q'R'=\sqrt{(2-(-2))^2+(4-6)^2}[/tex]

[tex]\implies Q'R'=\sqrt{(4)^2+(-2)^2}[/tex]

[tex]\implies Q'R'=\sqrt{16+4}[/tex]

[tex]\implies Q'R'=\sqrt{20}[/tex]

[tex]\implies Q'R'=2\sqrt{5}[/tex]

To find the scale factor of dilation that maps QRST onto Q'R'S'T', divide the length of Q'R' by the length of QR:

[tex]\implies \dfrac{Q'R'}{QR}=\dfrac{2\sqrt{5}}{3\sqrt{5}}=\dfrac{2}{3}[/tex]

Therefore, the scale factor is 2/3.

In Class 12, to find the domain and range of a function, you can use the following steps:

For example, if the function is f(x) = 1/x, the domain of the function is all real numbers except 0, because dividing by 0 is undefined. In this case, the domain of the function is (-∞,0) U (0,+∞)

For example, if the function is f(x) = √x, the domain of the function is all non-negative real numbers, because √x is only defined for non-negative values of x. In this case, the range of the function is [0,+∞)

Note that some functions may have more complex expressions, in such cases, you may have to use algebraic methods to find the domain and range.

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Answer:

[tex]2(3p - 2) - (p + 4) = 3p \\ \\ \dashrightarrow \: 6p - 4 - p - 4 = 3p \\ \\ \dashrightarrow \: 5p - 8 = 3p \\ \\ \dashrightarrow \: 5p - 3p = 8 \\ \\ \dashrightarrow \: 2p = 8 \\ \\ \dashrightarrow \: p = 4[/tex]

hope helpful :-;

Answer:

2

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

10 = 2 × 5

15 = 3 × 5

LCD = 2 × 3 × 5 = 30

Answer:

  in ℤ, successive values alternate signs

Step-by-step explanation:

You want to know what happens when the base of an exponential function is negative.

Consider the exponential function ...

  y = a·b^x

For b < 0 and integer values of x, the signs of the corresponding values of y will alternate.

Example

  y = 2·(-1)^x

A table of values will be ...

  [tex]\begin{array}{ccccccc}x&-1&0&1&2&3\\y&-2&2&-2&2&-2\end{array}[/tex]

For non-integer values of x, the values of y become more complicated. For fractional values of x, where x has an even denominator, the equation does not produce a real value. Instead, you get a complex number.

For fractional values of x where x has an odd denominator, the power is defined, and the sign will depend on whether the numerator is even or odd.

For irrational values of x, the function value in general is complex.

Of course, there are an infinite number of rational numbers between any pair of numbers on the number line, so the graph will have both positive and negative values, but will not be continuous. The attached graph can give you the idea. It is not in any way a complete graph of the function, but plots selected values.

__

Additional comment

The second attachment shows one of the uses of an exponential factor with a negative base. It creates the alternate signs of the series expansion of the sine function. Only whole number exponents are used in this case.

The actual area of the rectangular desk is 264 feet²

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Scaling is used to increase or decrease the size of a figure by a scale factor.

The drawing is at a scale of 1 inch = 2 feet.

11 inches = 11 inches * 2 feet per 1 inch = 22 feet

6 inches = 6 inches * 2 feet per 1 inch = 12 feet

Area of the desk = length * width = 22 feet * 12 feet = 264 feet²

The actual area is 264 feet²

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Answer:1558

Step-by-step explanation:

Answer:1558

Step-by-step explanation:

[tex]82\\19[/tex]

put a line under it multiply the 9x2 and then 9x8 make sure to carry

put a zero under the 8 and multiply 1x2 and 1x8

now add the the numbers together

you get 1558

1. The sequence is 2, 8, 16, 32.

2. The sequence is 4, 16, 64, 256.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

For example, 3, 7, 11, 15, ... is a sequence as there is a pattern where each term is obtained by adding 4 to its previous term.

Given:

The first term of a sequence is 4.

1. let the common ratio 2.

Then, second term= 4 x 2= 8

third term = 8 x2 =16

fourth term = 16 x 2= 32

So, the sequence is 2, 8, 16, 32..

2. let the common ratio 4.

Then, second term= 4 x 4 = 16

third term = 16 x 4 = 64

fourth term = 64 x 4 = 256

So, the sequence is 4, 16, 64, 256.

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Value of X is 8.

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Given,

Figure OUTD is a rectangle.

Each angle in a rectangle measures 90 degrees.

Therefore,

(7X + 2) + 4X = 90

7X + 2 + 4X = 90

11X + 2 = 90

Subtract 2 from both sides of the equation

11X = 88

Divide both sides of the equation by 11

X = 8.

Hence, 8 is the value of x.

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Taking the given ride lengths for 3 consecutive days and adding them the total number of miles ridden by the rider is 14.67 miles.

On Tuesday, the distance traveled is 1 and 1/2 times further than Monday's distance. This means that the distance traveled on Tuesday is 1.5 times the distance traveled on Monday.

To find the total distance traveled over a period of multiple days, we can add up the distances traveled on each day. This can be done by summing up all the individual distances traveled on each day. This can be done either in fraction or decimal. If the distances are in mixed numbers, it is good to convert them into fractions before adding them. This will give the total distance traveled over the period of multiple days.

On Tuesday, you ride 1 and 1/2 times further than on Monday, which is 3 and 2/3 miles * 1 and 1/2 = 5 and 1/2 miles.

On Wednesday, you ride 1 and 1/4 miles less than on Tuesday, which is 5 and 1/2 miles - 1 and 1/4 miles = 4 and 1/4 miles.

The total number of miles you rode on Monday, Tuesday, and Wednesday is:

3 and 2/3 miles + 5 and 1/2 miles + 4 and 1/4 miles = 13 and 5/6 miles

You can convert the mixed numbers to fraction to find the total miles.

3 and 2/3 miles = (33 + 2)/3 = 11/3 miles

5 and 1/2 miles = (52 + 1)/2 = 11/2 miles

4 and 1/4 miles = (4*4 + 1)/4 = 17/4 miles

So, the total number of miles you rode on Monday, Tuesday, and Wednesday is :

11/3 + 11/2 + 17/4 = (114 + 113 + 172)/12 = 11/3 + 33/4 = (114 + 11*3 + 34)/12 = 44/3 = 14.67 miles

You rode 14.67 miles in total for 3 days.

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According to angle symmetry, the value of x=125°

The two parallel lines intersected by a transversal form alternate angles. Consider the following figure, where EF and GH are two parallel lines. The transversal line RS intersects EF at L and GH at M. If a transversal cuts two parallel lines, the alternate angles are equal.

Since, AK and BL are parallel lines.

Hence,

∠ADC=∠BED=72°

∠EIH=∠DHG=55°

∠DHG+∠GHK=180°

∠GHK=180°-55°

∠GHK=125°=x

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solution for the two equation is x = 1, and y = - 2

It is a mathematical term that acts as the substitute of variables present in one or more equations. It is the value of unknown numbers that makes an equation true.

equation given, y = - 4x + 2

                    y = 6x - 8

if we use addition method then y = - 4x +2

                                                    y = 6x -8

                                                 -        -    +

                                          0       = - 10x + 10

                                         10 x = 10

                                          x = 1

                      putting the value of x in one of the above equations we get the y value.

                                  y = 6×1 -8

                                y = -2

the solution is the x = 1 and y = - 2

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The angle x in a right-angled triangle is 12.8°.

What is a right-angled triangle?

A triangle is said to have a right angle if one of the angles is 90 degrees. Right triangles are those with angles at 90 degrees, which are referred to as right angles.

The diagram shows a right-angled triangle with opposite = 12 units and hypotenuse as 54 units.

To find the angle x, apply the formula -

sin(x) = opposite/hypotenuse

sin(x) = 12/54

x = sin^-1(12/54)

x = sin^-1(2/9)

x = 12.84°

Rounding it to nearest tenth gives x = 12.8°.

Therefore, the value of x is 12.8°.

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The solutions to the different sides and values of square are given below. The length of the side of the square is 6.71m.

Square is a polygon which four equal sides and all angles are right- angles.

Given area of square = 45 m²

     Area = side²

     Side = √Area = √45 = 6.71 m

Therefore side of the square is 6.71m.

41) Negative numbers do not have square roots.

Therefore √-4 is undefined.

42) Option D is correct as it is not a fraction.

43) Any number multiplied by zero is zero.

Therefore (a) is the correct option.

44) When y = 15, x = 3

   For direct variation, y =kx

so k = y/x =15/3 = 5

When x=5, y = kx =5*5 = 25

Therefore (a) is correct.

45) For inverse variation

   MN = k

  Given 5*3 = k

k=15

When M = 10 , N = k/M = 15 /10 = 3/2

Therefore option a is correct.

48) Let the amount of work be W

     For 3 men,

          8 days = W

             1 day = W/8

Now work done by 1 man in one day = (W/8) /3 =W/24

In six days, work done by one man = W/24 * 6 = W/4

Therefore for the work to be completed, the number of men required is 4 (W/4 *4 = W).

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From the explicit rule the first three terms of sequence is 16, 16.5, 17.

Here given,

F(n) = 16+(1/2)(n-1)

We have to find first three terms.

F(1) = 16 + (1/2)(1-1)

      = 16 + 1/2 x 0

      = 16

F(2) = 16 + (1/2) (2-1)

       = 16 + 1/2

       = 16 + 0.5

       = 16.5

F(3) = 16 + (1/2) (3-1)

      = 16 + 1/2 x 2

      = 16 + 1

      = 17

So the first three terms in the sequence is 16, 16.5, 17 with common difference of .05.

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Displacement is the change in the position of an object relative to a reference point over a period of time.

It is usually represented by a vector quantity and is measured in meters (m). The formula for displacement is displacement = final position - initial position. Mathematically, displacement is denoted by s and is equal to the final position (x2) minus the initial position (x1), or s = x2 - x1. As an example, if a person walks a path of length 10 meters, starting at the origin (x1 = 0) and ending at x2 = 10, then their displacement would be s = 10 - 0 = 10 meters. To calculate displacement, we need to know the initial and final positions of the object, and the direction in which it moves.For example, if an object moves from position 5 m to position 10 m, the displacement is 5 m. This can be calculated by subtracting the initial position (5 m) from the final position (10 m). The result is 5 m, which is the displacement of the object.

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Therefore , the solution of congruency problem is its two congruent halves are LJ and LI. The sections' sizes and forms must be consistent to be considered congruent.

Using the Side-Angle-Side Congruity Theorem (SAS), two triangles are believed to be compatible with one another if their corresponding two sides and included angle are the same. A defined angle is found to be present on 2 sections that are being taken into account. Therefore, it is insufficient to use the SAS Congruity Theorem to establish the congruence of two triangles based just on the presence of two pairs of reciprocals and one set of points of intersection.

Here,

Given: The illustration shows a congruent link between

the two portions LI and LJ.

The segments will be identical in terms of size and shape if they are congruent.

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Answer: 0

Step-by-step explanation: if the 5 doesn't change at all, it doesn't change at all. Common sense.

Answer:

the answer is 1 I just know cause ima genius and smart also I'm like 6'7 how could i.be wrong

Step-by-step explanation:

look

For this kind of issue, you can select any option and the procedure will remain the same. Let's choose coffee as the beverage to analyse for the purposes of this response.

When a correlation coefficient's magnitude is between 0.5 and 0.7, it means that the variables are moderately correlated. Low correlation between the variables is indicated by correlation coefficients with magnitudes between 0.3 and 0.5.

In this equation, x stands for price, and y for sales.

-22.7x+130.3

The slope indicates the number of units that the sales would change by if we raised the price by one unit. Since our slope is -22.7, this indicates that a 1 unit price increase would result in a 22.7 decrease in sales.

The scatterplot's points are all intersected by the line of best fit, as can be seen. We can also calculate the Pearson correlation coefficient, which gives us -0.998, to add to the evidence. This suggests a very adverse relationship.

For this item we will just need the equation for the line of best fit and the data that has been given in the problem. For the actual sales, we will just refer to the given while we will compute for the predicted sales using the line of best fit.

PRICE            ACTUAL SALES              PREDICTED SALES

1.5                              96                                       96

1.6                              94                                       94

1.8                              91                                       89

2.0                              85                                       85

2.1                              83                                       83

2.2                              79                                       80

2.5                              73                                       74

2.7                              70                                       69

2.9                              64                                       64

3.0                              63                                       62

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In order to make the stream of water from a garden hose approximate a sine curve, the nozzle of the hose should be moved in an up-and-down motion.

The reason is because a sine curve is a smooth wave-like pattern that oscillates between positive and negative values. If the nozzle is moved up and down, it will cause the water to be released in a similar wave-like pattern, creating a stream that approximates a sine curve. This is due to the nozzle moving in a sinusoidal motion, which causes the water to be released in the same motion. This kind of motion is known as a harmonic motion, and it's the same motion that causes a wave to have a sinusoidal shape.

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The value of X that satisfies both -9X + 4Y = 8 and -3X - Y = 4 given the same value of Y is X = -8/7.

An equation is a mathematical statement that shows that two mathematical algebraic expressions are equal. For example, x + 7 = 10 is an equation, in which x + 7 and 10 are two expressions separated by an 'equal to' sign.

An equation also has two sides, the let hand side and the right hand side.

Solving the two equations simultaneously we have:

-9x + 4y = 8 --- (1)

-3x - y = 4 --- (2)

Multiply 2 by 3 and subtract from (1) as shown below

-9x + 4y = 8

-9x - 3y = 12

------------------

0 + 7y = - 4

7y = -4

y = -4/7

Substituting the value of y in equation 2 we get the value of x.

-3x - (- 4/7) = 4

-3x + 4/7 = 4

-3x = 4 - 4/7

-3x = 24/7

x = -8/7

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Answer:

3/10(3x+1)

Step-by-step explanation:

Answer: Here is my question

Step-by-step explanation:

a) Vertical plane not passing through the cone's topmost point - hyperbola.

b) Horizontal plane - circle.

c) Diagonal plane - ellipse or parabola

What is a cone?

A cone is a three-dimensional geometric shape that narrows smoothly from a flat base (typically circular base) to a point called the apex or vertex (which creates an axis to the center of the base).

Cross section of a cone:

A cross section is a representation of a shape's axis of symmetry intersected by a plane. When a plane cuts a solid, such as a cone, cylinder, or sphere, it creates a shape known as a cross-section. Depending on how the plane cuts the cone, the cross-section of a solid, such as a cone, can be a circle, a parabola, or a triangle.

When a cone's cross-section is split horizontally, it is circular.

When a cone is cut vertically, its cross-section is an isosceles triangle, and this plane slices through the center of the cone.

When a cone is cut vertically, the cross-section is parabolic except for the plane running through the center.

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On solving the provided question, we can say that We can use the trigonometry sine to solve for the other side: sin 65 = y/20 => y = 18.126

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study.

We can arrange a right triangle with 20 feet as the hypotenuse and 65 degrees as the angle between the hypotenuse and adjacent side assuming that the ground and wall meet at a 90 degree angle. The side across from the angle would be the amount of feet the ladder extends up the wall

We can use the trigonometric function sine to solve for the other side:

sin 65 = y/20

y = sin(65) . 20

y = 18.126

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With the help of cosine function, the amount fan rotates each minute is 1000 times.

We can use the cosine function:

Y = a cos ( b c - x ) + d

Y = equals 6 cosine (2000 pi x) + 11

Where x is time in minutes.

To find the period (p):

P = 2 pi/b

P = 2 pi/ 2000 pi

P = 1/1,000

P = 0.001

To find the rotation per minute we can use:

Rpm = 1/p

Rpm = 1/0.001

Rpm = 1,000

As the result, the amount of rotation is 1,000 times per minute

Your question is incomplete, but most probably your full question was:

A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y = Equals 6 cosine (2,000 pi x) + 11, where x is time in minutes.

How many times does the fan rotate each minute?

A 1,000

B 2,000

C 4,000

D 6,000

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Answer: 9

Step-by-step explanation:

Given equation is

3v-12 = 15

Now let's add 12 to both sides of the equation.

You'll get

3v = 27

Divide 3 from both sides, and you get

v = 9

Let's check.

Substitute 9 for v in the equation and you get

27 - 12 = 15

Which is true.

Final Answer: v=9

The solution to the given equation 3v - 12 = 15 is x = 9.

What is the solution to the equation?

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

The equation is given in the question, as follows:

3v - 12 = 15

We have to determine the solution to the given equation.

As per the question, we have

3v - 12 = 15

Rearrange the terms in the above equation, and solve for v:

3v = 15 + 12

3v = 27

Divided by 3 into the above equation, we get

v = 27/3

v = 9

Thus, the solution to the given equation is x = 9.

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Answer:

below

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

to make it easier try 8-5 and then add a negative sign