Identify the initial amount (a) and the decay factor (b) in the exponential function
y = 5 * 0.5^x

Answer:

To increase R245 in the ratio 5:6, you can add an amount proportional to the ratio 5:6 to R245.

Let's say you want to increase R245 by x.

The new value for 5 parts will be 5x + 245, and the new value for 6 parts will be 6x + 245.

So, the new ratio would be (5x + 245) : (6x + 245), which is still 5:6.

Therefore, to increase R245 in the ratio 5:6, you would add x to R245.

Answer: 35/4

Step-by-step explanation:

8x4=32

32+3=35

The original amount of the bill was $7000 and the GST paid to the State Government by the CA is $1260.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

The bill services including the GST = 8260

and, Rate of GST= 18%

So, let the original amount was x

x+ 18% of x= 8260

x + 0.18x = 8260

1.18x= 8260

x= $7000

and, the GST paid to Govt. = 8260 -7000 = $1260.

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The polynomial function is f(x) = (x - 3)((x - 2)² + 9)

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

Zeros: x=3, 2 +-3i

The polynomial can be repesented as

f(x) = product of (x - zeros)

using the above as a guide, we have the following:

f(x) = (x - 3)(x - (2 - 3i))(x - (2 + 3i))

This can be expressed as

f(x) = (x - 3)((x - 2)² + 9)

hence, the polynomial is f(x) = (x - 3)((x - 2)² + 9)

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To make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

From the given table, we have

Boxes          Gelatin Powder (oz)        Water (cups)

    3                             9                                6

Here,

Gelatin Powder = 3 × Boxes

Water  = 2 × Boxes

The equations for 8 boxes is

Gelatin Powder = 3 × 8

= 24 oz

Water  = 2 × 8

= 16 cups

Hence, to make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.

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Answer:

[tex]5x - 6 = 44 \\ \longrightarrow \: 5x = 44 + 6 \\ \longrightarrow \: 5x = 50 \\ dividing \: both \: sides \: by \: 5 \: \\ \\ \longrightarrow \: \cancel\frac{5x}{5} = \cancel\frac{50}{5} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]

hope helpful! :)

Answer:

Step-by-step explanation:

5x - 6 = 44

5x = 50

x = 10

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

check

5 x 10 - 6 = 44     (remember pemdas)

44 = 44

the answer is good

Coin tossing has a simple event of heads or tails, a joint event of multiple coin combinations, the complement of heads is tails, and sample space is {heads, tails}.

a. A simple event in coin tossing is getting either heads or tails on a single coin flip.

b. A joint event in coin tossing is getting heads on one coin and tails on another coin, for example.

c. The complement of getting heads on a coin flip is getting tails. The complement of getting tails is getting heads.

d. The sample space in coin tossing consists of all the possible outcomes of a single coin flip. This can be represented as a set, such as {heads, tails}. The sample space is the set of all possible outcomes of the experiment.

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Area of square B is 729.

Now, According to the question:

A square is a two-dimensional figure with four sides. It is also known as a quadrilateral. The area of a square is defined as the total number of unit squares in the shape of a square. In other words, it is defined as the space occupied by the square.

"Information available from the question"

We have been given that the ratio of the side length of square a to the side length of square b is 4:9. The side length of square a is 12 yards.

First of all, we will find the side length of square b using proportions as:

[tex]\frac{a}{b} = \frac{4}{9}[/tex]

[tex]\frac{12}{b}=\frac{4}{9}[/tex]

Cross multiplying the equation:

4b = 108

b = 108/4

b = 27

We know that area of a square is [tex]side^2[/tex]

=> b = 27

Area of square = [tex]27^2[/tex]

Area of square = 729

Hence, Area of square B is 729.

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Answer:

y = 6x

Step-by-step explanation:

Each value of x is multiplied by 6 to get the corresponding y value

Answer:

1050

Step-by-step explanation:

Answer:

the answer is: 1050

Step-by-step explanation:

hope it helped you mark brainliest

Answer:

see below

Step-by-step explanation:

z+66+z+69+43z=180

so 45z=180-66-69 = 45

so z=1

so angle U= 43 its opposite side length ST is the smallest

same logic for the other 2.

66+1=67

69+1=70

so ST<US <TU

Yes -20 degrees and 340 degrees are co-terminal angles

are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330°.

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. All of these angles are coterminal angles.

co-terminal angles are found by adding or subtracting 360° to the angles.

for example the co-terminal angles of -10° = -10° + 360 = 350°

Similarly The co-terminal angles of -20 = -20+360 = 340°

therefore the -20 and 340 are co-terminal angles

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Answer:8/

Step-by-step explanation: It is because any number after decimal point contains zero at it's end then the number is considered as it is. For example here 0.800 so after decimal point is 8, and after 8 there are zero's. So numerically, it is 0.8 or 0.800 both are same . Hence it's fraction form would be 8/ 10.

Answer:

4/5

Step-by-step explanation:

0.800 = 800/1000 = 8/10 = 4/5

The  [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.

The radius of earth is 6371 km.

Let's say the length of the piece of wood is L.

The diameter of the Earth is 2 times its radius

The radius of our planet, The Earth, is the distance from the center of the Earth to a point on or near its surface, and it ranges from nearly 6,378 km to nearly 6,357 km.

The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle. It is usually denoted by ‘d’ or ‘D’.

The diameter of the Earth is 2 times its radius, or 2 x 6371 km = 12742 km.

The diameter of the Earth is 12742 km / L times longer than the length of the piece of wood.

In scientific notation, we can express this as:

12742 km / L = [tex]1.2742*10^4 km / L[/tex]

The  [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.

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The solutions are decreasing when y is in the set (1,3).

(A) Equilibrium solutions, also known as constant solutions, fulfill dy/dx=0.

When the right-hand side of the equation is taken into account, we have

dy/dx equals y2(y-1) (y-3). We get the constant solutions y=0, y=1, and y=3 by setting the right side to zero.

(b) Solutions rise when dy/dx exceeds 0. For the set of y values (-,0) (0,1) (3,) see that dy/dx > 0. Therefore, when y in is the set (-,0) (0,1) (3,), solutions are growing.

(c) When dy/dx 0, solutions are decreasing, and dy/dx 0 when 1 y 3. That is, while y is in the set, solutions are decreasing (1,3).

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Answer: 11.2

Step-by-step explanation:

a) d= k/r

=> 7= k/8

=> k= 7x8

therefore, k=56

b) d=k/r

=> d=56/ 5

so, d= 11.2

The value of d is 7 when r = 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

d is inversely proportional to r.

This can be written as,

d ∝ 1/r

d = k/r

Now,

d = 7 when r = = 8

This means.

7 = k/8

k = 56

Now,

Substituting r = 8.

d = 56/8

d = 7

Thus,

d = 7.

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The exact own price elasticity of demand is (A) -0.67.

The own price elasticity of demand measures the responsiveness of the quantity demanded to changes in price. It can be calculated using the formula:

epsilon = (dQ/dP) * (P/Q)

where dQ/dP is the derivative of the demand curve with respect to price and P/Q is the price elasticity of demand.

In this case, the demand curve is QD = 200 - 4P, so dQ/dP = -4. When P=$30, Q = 200 - 4 * 30 = 140. So,

epsilon = (-4) * (30/140) = -0.67

Hence, the exact own price elasticity of demand at P=$30 is -0.67, so the answer is A. -0.67.

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Let's call the number of hours Jamie works "J" and the number of hours Taylor works "T".

We know from the problem that T = 2 * J, because Taylor works twice as many hours as Jamie.

We also know that J + T = 4 * (3 + 2), because they are working together to complete 4 lawns and it takes 3 hours for Taylor and 2 hours for Jamie to complete one lawn.

So we can substitute the first equation into the second equation:

2J + J = 4 * (3 + 2)

3J = 4 * 5

J = 4

So Jamie works 4 hours and Taylor works 2 * 4 = 8 hours.

The observed data indicates that the null hypothesis should be rejected at a rejection criterion of 0.05. This means that the data supports the researcher's hypothesis that ants show handedness, and that they are more likely to turn into the right or left arms of a T-maze.

The researcher is interested in determining if ants show handedness.

The researcher is hypothesizing that if ants show handedness, they will be more likely to turn into the right or left arms of a T-maze.The researcher placed 20 ants into the maze and observed that 16 of the ants walked into the right arm and 3 into the left arm (one ant managed to crawl over the edge of the maze before it went down either of the arms). The probability that exactly 16 of the ants enter the right arm when the null hypothesis is true is 0.368. This is calculated using the binomial formula, P(x=16) = (20 choose 16) * (0.5)^16 * (0.5)^4, where 0.5 is the probability of each ant turning into either arm.Outcomes that are equally extraordinary or more extraordinary than the outcome observed under conditions in which the null hypothesis is true include: 17R, 3L; 18R, 2L; 19R, 1L; and 19R, OL.The probabilities associated with the outcomes identified in Problem 5 under conditions in which the null hypothesis is true are: 0.246 for 17R, 3L; 0.127 for 18R, 2L; 0.052 for 19R, 1L; and 0.026 for 19R, OL.The probability that an outcome as extraordinary or more extraordinary than the outcome observed would occur when the null hypothesis is true is 0.451. This is calculated by adding up the probabilities associated with each of the outcomes identified in Problem 5 (0.368 for 16R, 4L, 0.246 for 17R, 3L, 0.127 for 18R, 2L, 0.052 for 19R, 1L, and 0.026 for 19R, OL).

The observed outcome does not indicate that the null hypothesis should be rejected at a rejection criterion of 0.05 since the P value for the binomial test (0.451) is greater than 0.05. Therefore, we cannot reject the null hypothesis and conclude that ants do not show handedness.

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If distinct vertices of an octagon are chosen at random , then the probability that they are adjacent is 2/7 .

An Octagon has 8 vertices, so there are 8 possible vertices to choose from. To find the probability that two chosen vertices are adjacent, we need to determine the number of ways in which two adjacent vertices can be chosen,

Since there are 8 vertices and each vertex has 2 adjacent vertices,

The total number of pairs of vertices in octagon is = ⁸C₂  =  28;

the possible Adjacent pairs are : {(1,8),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8)} ;

So , probability of vertices being adjacent is = 8/28 ;

Simplifying further , we get ;

Probability ⇒ 2/7 .

Therefore , the probability that vertices are adjacent is 2/7 .

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7) The factors of the expression (x² + 17x + 60) is, (x + 5) (x + 12)

8) The factors of the expression (x² - 6x - 27) is, (x + 3) (x - 9)

9) The factors of the expression (2x² - 18x + 28) is, 2 (x - 2) (x - 7)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We can factor as;

7) The factors of the expression (x² + 17x + 60) is,

⇒ x² + 17x + 60

By using quadratic formula as;

⇒ x = - 17 ± √(17² - 4×1×60 / 2

⇒ x = - 17 ± √289 - 240 / 2

⇒ x = - 17 ± √49 / 2

⇒ x = - 17 ± 7 / 2

⇒ x = - 17 + 7 / 2

⇒ x = - 10/2

⇒ x = - 5

And, x = - 17 - 7 / 2

⇒ x = - 24/2

⇒ x = - 12

Thus, The factors of the expression (x² + 17x + 60) is,

⇒ (x + 5) (x + 12)

8) The factors of the expression (x² - 6x - 27) is,

⇒ x² - 6x - 27

⇒ x² - 9x + 3x - 27

⇒ x (x - 9) + 3 (x - 9)

⇒ (x + 3) (x - 9)

Thus, The factors of the expression (x² - 6x - 27) is,

⇒ (x + 3) (x - 9)

9) The factors of the expression (2x² - 18x + 28) is,

⇒ 2x² - 18x + 28

⇒ 2 (x² - 9x + 14)

⇒ 2 (x² - 7x - 2x + 14)

⇒ 2 (x (x - 7) - 2 (x - 7))

⇒ 2 (x - 2) (x - 7)

Thus, The factors of the expression (2x² - 18x + 28) is,

⇒ 2 (x - 2) (x - 7)

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Answer: The equation y = 5 * 2^x represents an exponential function where the base is 2 and the y-intercept is 5.

The graph that best fits this equation is:

d. On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 5) through quadrant 1.

y-intercept = 5

So, the correct answer is d.

Step-by-step explanation:

The express in the form of a + bi would be 0 + 5i.

Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to  (√-1). A pair of real and imaginary numbers combined in the form a + bi.

When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.

Let the given expression be [tex]$\sqrt{-25}$$[/tex].

We have to evaluate the expression.

[tex]$$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$[/tex]

The express in the form of a + bi = 0 + 5i.

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Answer: it’s b

Step-by-step explanation:

your welcome

Answer:

8.5

Step-by-step explanation:

this is a right triangle so we could use the formula, which is Pythagorean theorem

so it is [tex]13.5^{2} -10.5^{2} =72\\\sqrt{72} =8.5[/tex]

The model that is most likely rule out on the basis of this simulation is 40%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

First set of trials:  ththththht ( where T = Tails ; H = Heads)

Number of heads = 5

Number of outcomes = 10

Second set of trials: ttthtthtth

Number of heads = 3

Number of outcomes = 10

Total number of heads = 5 + 3 = 8

Total number of outcomes = 10 + 10 = 20

Probably of heads = 8/20 * 100%

Probably of heads = 0.4*100%

Probably of heads = 40%

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Answer:

  see attached

Step-by-step explanation:

You want to draw a triangle with angle measures 30° and 75° at vertices Y and Z, and the length of YZ as 8.5 cm.

The third angle of the triangle will be 180° -30° -75° = 75°. This means the triangle is isosceles, and the two congruent sides are both 8.5 cm.

Once you measure the length YZ as 8.5 cm, you can draw angles at 30° and 75° from points Y and Z, respectively. A protractor is a suitable tool for the purpose. The point of intersection of these rays is X, giving you the desired triangle XYZ.

A right triangle with hypotenuse 8.5 cm will have the leg opposite the 30° angle as 4.25 cm, half the hypotenuse. This offers opportunities to construct the triangle several ways.

Here's one. Draw an arc (or circle) of radius 8.5 cm centered at point Y. Mark a point Z on the arc. Using the same radius, draw an arc that intersects the first one at point A. Angle ZYA is 60°, as is angle YZA. Now, you can bisect angle ZYA, or segment ZA, or you can simply measure off 4.25 cm on segment ZA. The point halfway between Z and A can be marked point B. Where ray YB intersects the original arc (or circle) centered at Y, is point X of your triangle XYZ.

__

Additional comment

We used a geometry program to draw the triangle in the attachment. It conveniently provided angles with the necessary measures. In terms of the construction described above, the vertex of the right angle is point B.

Another way to start is by identifying right angle lines BZ and BY on grid paper. Once you locate point Z 4.25 cm from B, you can draw an arc centered at Z with radius 8.5 cm that intersects line BY at Y. Then an arc with the same radius centered at Y will identify the location of point X.

The conclusions with regards to the similar right triangles, Yvonne needs to prove the Pythagorean Theorem are;

PQ/PR = PS/PQ and QR/PR = RS/QR

Pythagorean Theorem outlines the relationship between the length of the hypotenuse side and the lengths of the legs of a right triangle. The theorem states that the sum of the squares of the lengths of the legs of a right triangle, is equivalent to the square of the length of the hypotenuse side.

The specified similar triangles are;

ΔPQR ~ ΔQSR ~ ΔPSQ

PQ/PS = PR/PQ...(1)

(PQ)² = PS·PR

QR/RS = PR/QR...(2)

(QR)² = RS·PR

(PQ)² + (QR)² = PS·PR + PR/RS = PR·(PS + RS) = PR×PR = (PR)²

(PQ)² + (QR)² = (PR)²

Equations (1) and (2), can be expressed as follows;

PQ/PS = PR/PQ...(1)

Multiply both sides by PS/PR

PQ/PS × (PS/PR) = PR/PQ × (PS/PR)

PQ/PS × (PS/PR) = PQ/PR

PR/PQ × (PS/PR) = PS/PQ

Therefore;

QR/RS = PR/QR...(2)

Multiplying both sides by (SR/PR). we get;

QR/SR × (RS/PR) = QR/PR

PR/QR × (RS/PR) = RS/QR

Therefore, the conclusions about the triangles, Yvonne can use in her proof of the Pythagorean Theorem are;

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For the orthogonal matrices, the product of two invertible matrices is also invertible.

Orthogonal matrices are matrices that have a special property: the dot product of each of their rows or columns is equal to 0.

The dot product of two vectors is equal to 0 when the vectors are orthogonal to each other, meaning they are perpendicular.

Since U and V are orthogonal matrices, each is invertible by the definition of orthogonal matrices.

The inverse of an orthogonal matrix is its transpose.

This is because the dot product of each row (or column) with itself is equal to 1, so the transpose of an orthogonal matrix is its inverse.

The product of two invertible matrices is also invertible, so UV is invertible.

Answer C is correct.

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