**PLEASE HELP 10 POINTS** what is the missing value in the equation y=5(?)^x that models the date from the data table?

X 0 1 2 3 4 5 6
Y 5 10 20 40 80 160 320


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The conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.

A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

Note: The exact value of cos(π/3) is equal to ½.

Substituting the given parameters into the formula, we have;

z = 2(½)

z = 2/2

z = 1.

In conclusion, we can logically deduce that the conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.

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Complete Question:

Convert z = 2(cos(π/3)) in rectangular form

The length of the arc CD is 14.13 centimeters.

Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:

L  = (a/360°)*2*pi*R

Where pi = 3.14

Here the angle is a = 45°

And R = 18cm, so we can replace that in the formula above to find the length.

L = (45°/360°)*2*3.14*18cm = 14.13cm

That is the length of the arc CD.

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Therefore, the quotient X is 3 and the remainder Y is 25.

So, X = 3 and Y = 25.

Expression division is a mathematical operation where one expression is divided by another. In mathematics, an expression is a combination of numbers, variables, and operators that represent a mathematical relationship or a value. Division is an arithmetic operation that involves splitting a quantity into equal parts or groups.

So, expression division refers to dividing one mathematical expression by another. For example, if we have two expressions "x + 5" and "3", we can perform expression division by dividing the first expression by the second expression, which would result in the expression "(x + 5) ÷ 3". The result of this expression would be another expression that represents the quotient of the two expressions.

To perform the division of 15h^2 + 10h + 25 by 5h, we need to follow the long division process as shown below:

    ________

\(5h | 15h^2 + 10h + 25\)

   \(15h^2\)      

    _______

      \(10h + 25\)

         \(10h\)

         _____

             25

Therefore, the quotient X is 3 and the remainder Y is 25.

So, X = 3 and Y = 25

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Answer:

slope of red line=6

Step-by-step explanation:

Hi there!

We're given a set of perpendicular lines and the slope of the green line being -1/6

Perpendicular lines have slopes that are negative and reciprocal; if they are multiplied together, the result is -1

So to find the slope of the red line, we can use this formula (m is the slope):

-1/6m=-1

Multiply both sides by -6 (clears the fraction to get 1m on the left)

m=6

So the slope of the red line is 6

Hope this helps!

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

name me brainleist and say thank you, and rate 5 stars.

Answer:

This identity holds as long as \(\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}\) for all integer \(k\).

For the proof, make use of the fact that:

\(\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\) (definition of tangents,) and

\(\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}\) (Pythagorean identity,) which is equivalent to \(1 - \cos^{2}(\theta) = \sin^{2}(\theta)\).

Step-by-step explanation:

Assume that \(\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}\) for all integer \(k\). This requirement ensures that the \(\tan(\theta)\) on the left-hand side takes a finite value. Doing so also ensures that the denominator \(\sqrt{1 - \sin^2(\theta)}\) on the right-hand side is non-zero.

Make use of the fact that \(\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\) to rewrite the left-hand side:

\(\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}\).

Apply the Pythagorean identity \(\sin^{2}(\theta) = 1 - \cos^{2}(\theta)\) and \(\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}\) to rewrite this fraction:

\(\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}\).

Hence, \(\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\).

Answer:

24 gallons per minute

Step-by-step explanation:

Hope this helped!

Answer:

24 gallons per minute :)

The simplified expressiοn is \(-3x^3y^2 - 4x^2y + 8y\).

Mathematical statements are called expressiοns when they cοntain at least twο terms that are cοnnected by an οperatοr and cοntain either numbers, variables, οr bοth. The mathematical οperatοrs can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn. Fοr instance, the expressiοn x + y is an expressiοn where x and y are terms with an additiοn οperatοr in between.

In mathematics, there are twο types οf expressiοns: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables.

Tο simplify \((2x^3y^2-8x^2y+4y) − (5x^3y^2-4x^2y - 4y)\), we need tο distribute the negative sign in frοnt οf the secοnd set οf parentheses, and then cοmbine like terms. This gives:

\(2x^3y^2 - 8x^2y + 4y -5x^3y^2 + 4x^2y + 4y\)

\(= (2x^3y^2 - 5x^3y^2) + (-8x^2y + 4x^2y) + (4y + 4y)\)

\(= -3x^3y^2 - 4x^2y + 8y\)

Therefοre, the simplified expressiοn is \(-3x^3y^2 - 4x^2y + 8y\).

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Answer:

its C −3x3y2 − 4x2y + 8y

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

10 subtract 1 is 9.

Given:

10 people ate pie

1 person ate cake

No of people who ate the pie than the cake

10-1 =9

Answer: 30%

Step-by-step explanation:
12/40 = 3/10 = 0.30

0.30*100 = 30%

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

B.

Step-by-step explanation:

If he makes 70% then 70% as a decimal would be 0.700 which is B

Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability that he makes at least two of the free throws is 0.0700.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head when a coin is tossed is 1/2

We have,

Each free throw is independent of the other.

Percentage of making free throws = 70%

The probability that he makes at least two of the free throws.

= 70%

= 70/100

= 0.07

This can be written as 0.0700.

Thus,

The probability that he makes at least two of the free throws is 0.0700.

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The value of \((f+g)(1)\) is 3.

In this question we must apply the definition of addition between functions, whose operation is described below:

\((f+g) (x) = f(x) + g(x)\) (1)

\((x, (f+g)(x)) = (x, f(x))+(x, g(x))\) (1b)

If we know that \((x, f(x) ) = (1,1)\) and \((x,g(x)) = (1,2)\), then the result of the operation is:

\((1, (f+g) (1)) = (1, 3)\)

The value of \((f+g)(1)\) is 3.

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An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

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Answer:

D

Step-by-step explanation:

C is the first quadrant (where both x and y are positive).

A is the y-axis.

B is the origin.

D is the x-axis

Answer: D

Step-by-step explanation: it wouldn't be B because that's the origin point and A is the y-axis and C is in the open, the Answer is D

The length AB of the triangle is 59 units.

A triangle is a polygon with three sides equal to each other. The sum of angles in a triangle is 180 degrees.

The line AC is a perpendicular bisector of the line BD. The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn.

Hence,

AD = AB

6x + 17  = 14x - 39

6x - 14x = -39 - 17

-8x = -56

x = -56 / -8

x = 7

Therefore, let's find AB

AB = 14(7) - 39

AB = 98 - 39

AB = 59 units

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The Total cost for 24 cents (pencils) + 8N cents (notebooks) + 12P cents (colored paper) = 170 cents.

The total for everything cannot be $1.70,  the individual costs and calculate the total cost separately.

the price of each notebook is N cents and the price of each sheet of colored paper is P cents.

The cost of the pencils can be calculated as follows:

For the 2 pencils at 2 cents each: 2 pencils * 2 cents/pencil = 4 cents

For the 5 pencils at 4 cents each: 5 pencils * 4 cents/pencil = 20 cents

So, the total cost of the pencils is 4 cents + 20 cents = 24 cents.

the cost of the notebooks and colored paper:

The cost of 8 notebooks is 8 notebooks * N cents/notebook = 8N cents.

The cost of 12 sheets of colored paper is 12 sheets * P cents/sheet = 12P cents.

the total cost of the notebooks and colored paper, we add these two amounts together: 8N cents + 12P cents.

the total cost for everything is $1.70, we can express it in cents as 170 cents.

Therefore, the total cost for everything can be written as:

24 cents (pencils) + 8N cents (notebooks) + 12P cents (colored paper) = 170 cents.

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Answer:

24%

Step-by-step explanation:

Room capacity = 150

Each table consists of 6 chairs

The number of people seated = 6 tables occupied = 6 * 6 = 36 people

The percentage of seats filled :

(Number of people seated / total capacity) * 100%

(36 / 150) * 100%

0.24 * 100%

= 24%

Hence, 24% of training room is occupied

Answer:

ILOVEMYCOUNTRY!!!

Step-by-step explanation:

F........U.......C.......K.....YOU.....BRO.......USE UR BRAINS !!!!

Answer:

yes

Step-by-step explanation:

All four sides of a rhombus are congruent. Its properties include that each pair of opposite sides is parallel, also making it a parallelogram. ... All rectangles are parallelograms, but not all parallelograms are rectangles. And all of these shapes are quadrilaterals.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

32%

Step-by-step explanation:

Let x be the mean of the values and σ their standard deviation.

Since the minimum value of the diameter of the washers is 1.53 mm, then

x - σ = 1.53 mm  (1)

Also, the maximum value of the diameter of the washers is 1.65 mm, then

x + σ = 1.65 mm  (2)

Adding (1) and (2), we have

x - σ = 1.53 mm

+

x + σ = 1.65 mm  

2x = 3.18

x = 3.18/2

x = 1.59 mm

Subtracting (1) and (2), we have

x - σ = 1.53 mm

-

x + σ = 1.65 mm  

-2σ = -0.12

σ = -0.12/-2

σ = 0.06 mm

Since the diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long, and x - σ = 1.53 mm to x + σ = 1.65 mm are the required values, 68% of the washers lie in this range. The other values lie outside this range. The amount that the factory would have to discard is 100% - 68% = 32%

This question is based on the percentage. Thus, 32%  of washers will the factory have to discard.

Given:

The diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long.

We need to determined the percentage of washers will the factory have to discard.

According to question,

Let x be the mean and σ be their standard deviation.

The minimum value of the diameter of the washers is 1.53 mm.

Then,

x - σ = 1.53 mm  (1)

Also, the maximum value of the diameter of the washers is 1.65 mm, then

x + σ = 1.65 mm  (2)

Adding (1) and (2), we have

   x - σ = 1.53 mm  

+  x + σ = 1.65 mm  

⇒ 2x = 3.18

We get,

x = 1.59 mm

Subtracting (1) and (2), we have

 x - σ = 1.53 mm

- x + σ = 1.65 mm  

⇒ -2σ = -0.12

We get,

σ = 0.06 mm

Therefore, the diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long, and x - σ = 1.53 mm to x + σ = 1.65 mm are the required values, 68% of the washers lie in this range.

And the other values lie outside this range. The amount that the factory would have to discard is 100% - 68% = 32%.

Thus, 32%  of washers will the factory have to discard.

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Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:

Course fees for continuing legal education: $1,400

Airfare and hotel room: $500

Meals provided by the hotel's restaurant: $300

Snacks from the newsstand: $10

To calculate the total amount that Bob can deduct, add up these expenses:

$1,400 + $500 + $300 + $10 = $2,210

Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

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Answer:

4. x = 23 degrees

5. m<A = 33 degrees

m<B = 66 degrees

m<C = 82 degrees

Step-by-step explanation:

4.

(2x + 21) + 90 degrees + x = 180 degrees

(2x + 21) + x = 90 degrees

3x + 21 = 90

3x = 69

x = 23 degrees

5.

2x + x + (2x + 15) = 180 degrees

5x + 15 = 180

5x = 165

x = 33

Answer:

x > -3

Step-by-step explanation:

Since you need to get a by itself as a variable divide both sides by -9 (but in inequality when you divide by - the sign flips)

x > -3

The initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The initial height of the rocket is given by the value of h when t = 0:

h(t)=-4t² + 16t + 24

h(0)=-4(0)² + 16(0) + 24

h(0)=24

So the initial height of the rocket is 24 metres.

The rocket will hit the ground when its height is 0 metres, so we can set h = 0 in the equation and solve for t:

0 = -4t²+ 16t + 24

-4t² + 16t + 24 = 0

t=-0.88 seconds

So the rocket will hit the ground after approximately 0.88 seconds.

The height of the rocket after 4 seconds is given by:

h(4)== -4(4)²+ 16(4) + 24

=-64+64+24

=24

So the height of the rocket after 4 seconds is 24 metres.

Hence, the initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

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The expression of the statement is x³ - 7

The statement is given as

7 is subtracted from the cube of a number.

Represent the number as x

So, we have the following representation

"7 is subtracted from the cube of a number" ⇒ 7 is subtracted from the cube of x

The cube of x can be represented as x^3

So, we have

"7 is subtracted from the cube of a number" ⇒ 7 is subtracted from x³

"7 is subtracted" means minus 7

So, we have

"7 is subtracted from the cube of a number" ⇒  x³ minus 7

Rewrite as

"7 is subtracted from the cube of a number" ⇒  x³ - 7

Hence, the expression is x³ - 7

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Answer:

$17.64

Step-by-step explanation:

7% of $252

=7/100 × 252

=0.07 × 252

=$17.64

In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5.  In algebra, an equation is a mathematical statement .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. An equation is a mathematical statement that proves the equality of two mathematical expressions, according to the definition of an equation in algebra. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable.

given

4x-1/ 3x + 7 = 6/5

20x - 5 = 18x + 42

x = 23.5

In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5.

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Answer:

B. 4d + 50 = 114

Step-by-step explanation:

Given parameters:

Hourly rate = $d/hr

Flat fee = $50

Charge for the 4hrs = $114

Number of hours = 4hrs

To find d;

    Total cost  = $114;

             $114  = Flat fee + (rate per hour x number of hours)

            $114 = $50 + 4d

The value of d can be calculate using;

           4d + 50 = 114

The value of d is 4d + 50 = 114