In the following diagrams calculate the
sides marked with letters x and y.
All dimensions are in cm.

The exponent is greater than 1 so it is exponential growth, 500 in the equation represents the initial value, and the growth rate in the second equation is 6%.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an exponential function:

[tex]\rm b_1(t) = 500(1.6)^t[/tex]

a) As the base of the exponent is greater than 1 so it is exponential growth.

b) 500 in the equation represents the initial value.

c) We have another exponential equation:

[tex]\rm b_2(t) = 800(1.6)^t[/tex]

For exponentikal gropwth:

1 + r = 1.6

r = 0.6 or

r = 6%

In the equation:

[tex]\rm b_1(t) = 500(1.6)^t[/tex]

The number of bacteria initially was 500 and from the second the number of bacteria initially was 800.

Thus, the exponent is greater than 1 so it is exponential growth, 500 in the equation represents the initial value, and the growth rate in the second equation is 6%.

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The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)

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Answer:

The 17th term of the given Arithmetic progression -6,-1,-4 will be 74.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

As per the given Arithmetic progression,

-6, -1, -4.

First term a = -6

Common difference d = -1 - (-6) = 5

The nth term of AP is given as a + (n - 1)d.

This 17th term will be as, -6 + (17 - 1)5

⇒ -6 + 16 × 5 = 74

Hence "The 17th term of the given Arithmetic progression -6,-1,-4 will be 74".

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The probability that he will be rejected to at least one of the colleges is 0.51.

Given probability that he will admit in A is 0.7, probability that he will not be admit in B is 0.5, probability that atleast one of his applications got rejected is 0.6.

We have to find the probability that he will be rejected to at least one of the colleges.

Probability that he will admit in A =0.7

Probability that he will not admit in A=1-0.7=0.3

Probability that he will not admit in B =0.5

Probability that he will admit in B=1-0.5=0.5

Probability  that he will be rejected to at least one of the colleges=probability that he will admit in A* probability that he will not admit in B+ probability that he will admit in B* probability that he will not admit in A+ probability that he will not admit in A* probability that he will not admit in B

=0.7*0.5+0.5*0.3+0.5*0.3

=0.35+0.15+0.15

=0.51

Hence the probability that he will be rejected to at least one of the colleges is 0.51.

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Answer:

98

Step-by-step explanation:

From the statement of similarity, we can write this proportion.

TV/MV = UV/LV

28/x = 16/56

16x = 28 × 56

x = 7 × 14

x = 98

Answer:

Please see attachment.

Step-by-step explanation:

Since there are no answer choices, I will just show you the graphs for each one.

Remember the dashed lines means it is either greater than, or less than.

The solid lines are either greater than or equal to, or less than or equal to.

Hope this helps!

If not, I am sorry.

The solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

to determine the solutions of the equation:

The equation is given as:

|2/3x + 2| − 8 = 0

Start by adding 8 to both sides of the equation.

So, we have

|2/3x + 2| = 8

Next, we remove the absolute value expression

So, we have;

2/3x + 2 = 8 and 2/3x + 2 = -8

Subtract 2 from both sides of the equation

2/3x = 6 and 2/3x = -10

Multiply the equation by 3/2

x = 9 and x = -15

Hence, the solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15

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Complete question:

Determine the solutions of the equation:

|2/3x+2−8=0

Ox= -9 and x = 9

Ox= -15 and x = 4

Ox= -15 and x = 9

Ox= -15 and x = 15

Using relations in a right triangle, the trigonometric function that should be used is given by:

b) tan.

The relations in a right triangle are given as follows:

Hence, if the opposite and adjacent side are know, the tangent function should be used, and option b is correct.

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You can purchase 10 gallons of Gasoline.

We have only $20 to spend on gasoline each week. If the price of gasoline is $2 a gallon

Here, we have $20

Cost per gallon $2

Number of gallons: 20/2 =10 gallons

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The correct equation for this transformation is given as (x, y) ⇒ (x - 9, -(y + 2))

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

The graph of √(5x - x²) was translated 9 units left and 2 units up, then reflected over the x axis to get the new graph.

The correct equation for this transformation is given as (x, y) ⇒ (x - 9, -(y + 2))

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Answer:

6h² + 3h + 5

Step-by-step explanation:

7h² + 2h + 5 - h² + h

= 7h² - h² + 2h + h + 5

= 6h² + 3h + 5

Answer:

B. 11.4

Step-by-step explanation:

By using the line segment formula

AC = √(9-(-2)^2+(2-5)^2

AC = √130

AC = 11.4

Answer: [tex]60cm^2[/tex]

Step-by-step explanation:

Looking at the figure, you can see that the length is 5cm + 3cm = 8cm and the width is 2cm + 5cm + 2cm = 9cm.

The formula for area is length x width, therefore you do 8x9 which is 72.

Next, we solve for the two "dips" in the rectangle. We can do that by subtracting the area of the "mini-rectangles" from the whole figure:

72-2(2x3) = 60

Thus, 60cm^2 is your answer.

Answer:

$25.00

Step-by-step explanation:

20% of $125 = $25

Graph C depicts the relation between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements )

Graph is the statistical representation of data , It helps to observe large data systematically.

It is given that

Sale of one sweater gives $3

The relation between the amount raised for funding , M and the number of shirts sold , n is given by

M = 3n

It has to be found that which graph exactly depicts the relation and the condition as given

Graph C depicts the relation given as , The graph is between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements ) , and for every 100 sweater , $300 is earned .

Therefore Graph C is the answer.

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Intelligent failure occur when you experiment in order to learn under conditions of high uncertainty

It's always possible to move forward from failure stronger and wiser. To do this, we must

a) descry and accept our failures snappily,

b)Dissect what happed and how it happed effectively to maximize what we can learn,  

c)Apply our literacy to change our mindsets, behaviours, and the way we do our work, and

d)Continue to take smart pitfalls and introduce, icing we make better miscalculations on our coming bold attempt.

Unfortunately, our instinct tends to be to exit the circle at every step.

That’s why the skill of Intelligent Failure takes practice.

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Answer:

2

Step-by-step explanation:

Let the missing length be " x ".

( 3 + 1 ) / 6 = x / 3

4 / 6 = x / 3

Cross multiply,

x * 6 = 4 * 3

6 = 2 * 3

4 = 2 * 2

x * 2 * 3 = 2 * 2 * 3

Divide 2 * 3 on both sides,

x = 2

Answer:

y-intercept = -12

Step-by-step explanation:

The y-intercept is the "y" value when x = 0. You can find the y-intercept by plugging 0 into the equation and simplifying.

y = 4x - 12                                      <----- Original equation

y = 4(0) - 12                                    <----- Plug 0 in "x"

y = 0 - 12                                        <----- Multiply 4 and 0

y = -12                                           <----- Subtract 12 from 0

Sally to get to the next town in 2/3 hour.

According to the statement

The distance covered by sally to get next town is 20 miles

Speed at which sally drive is 30 miles per hour

We know that the

TIME = DISTANCE / SPEED

Substitute the values in it and

TIME = 20 / 30

TIME = 2/3 hour

So, Sally to get to the next town in 2/3 hour.

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Answer:

012

Step-by-step explanation:

please mark brainliest if correct

The correct options, in order, are:

[tex]f(n) = 3*(2)^{n-1}[/tex]

[tex]f(n) = 2*(6)^{n - 1}[/tex]

[tex]f(n) = 2*(4)^{n - 1}[/tex]

The first table is:

n   f(n)

1     3

2    6

3    12

Notice that when n = 1, all the exponents are 0, then the initial value is 3.

When n = 2, all the exponents are 1. Then we need to find the exponential equation with a base equal to 2.

So the exponential equation is:

[tex]f(n) = 3*(2)^{n-1}[/tex]

The second table is:

n   f(n)

1     2

2    12

3    72

By looking at the first pair, we conclude that the initial value is 2, and by looking at the second pair, we conclude that:

2*b = 12

b = 12/2 = 6

The base is 6.

So the exponential equation now is:

[tex]f(n) = 2*(6)^{n - 1}[/tex]

The last table is:

n   f(n)

1     2

2    8

3    32

Here we again have an initial value of 2, and the base is:

2*b = 8

b = 8/2 = 4

Then the correct option now is:

[tex]f(n) = 2*(4)^{n - 1}[/tex]

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Hello

6x² - 2x + 6 - (6x² - 7x - 2)

= 6x² - 2x + 6 - 6x² + 7x + 2

= 5x + 8

The area of the triangle, trapezoid, rectangle and total area are 7. 5 ft², 10. 5 ft², 0.8 ft² and 18. 8 ft² respectively.

1. Area of a triangle = 1/2 base × height

Area = 1/2 × 5 × 3

Area = 1/2 × 15

Area = 7. 5 ft²

2. Area of trapezoid = [tex]\frac{a + b}{2} h[/tex]

a = 4ft

b = 0. 2ft

h = 5ft

Area = [tex]\frac{4 + 0.2}{2}* 5[/tex]

Area = [tex]\frac{4.2}{2} * 5[/tex]

Area = 2.1 × 5

Area = 10. 5 ft²

3. Area of rectangle = length × width

Area of rectangle = 0. 2 × 4

Area of rectangle = 0. 8 ft²

4. Total area of tree = area of triangle + area of trapezoid + area of rectangle

Total area of tree = 7. 5 + 10. 5 + 0. 8

Total area of tree = 18. 8 ft²

Thus, the area of the triangle, trapezoid, rectangle and total area are 7. 5 ft², 10. 5 ft², 0.8 ft² and 18. 8 ft² respectively.

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Answer:

12

Step-by-step explanation:

B x H x 1/2 = area of a triangle

we can break this figure into 4 different triangles and since we have the length of the chords (dotted lines) in the diamond we can easily solve it.

half of QS is 2 and half of PR is 3

2 x 3 = 6

6 / 2 = 3

since there are four triangles multiply 3 by 4 (3 x 4)

and you get 12.

Answer:

f(g(x) = 1x² + 4x + 3

Explanation:

Question: f(g(x))

Given following:

While solving such function questions, solve from right to left.

⇒ f(x + 2)

⇒ (x + 2)² - 1

⇒ x² + 4x + 4 - 1

⇒ x² + 4x + 3

The correct option regarding whether the table represents a proportional relationship is:

The relationship is proportional because the ratio of m to k is constant.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the ratio of m to km is given as follows:

k = 11/17.699 = 26/41.834 = 34/54.706 = 0.6215.

Since the values are equal, the correct option is:

The relationship is proportional because the ratio of m to k is constant.

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Flo should walk 60 extra minutes of time per day to accomplish her goal of walking 12,000 total steps per day.

Calculating the Time for Which Flo Walks Each Day

Flo walks 6,000 steps per day.

She walks 100 steps per minute.

⇒ Time taken by Flo to cover 6,000 steps = [tex]\frac{6000}{100}[/tex] minutes

⇒ Time taken by Flo to cover 6,000 steps, m₁ = 60 minutes

Hence, Flo walks for 60 minutes or 1 hour per day.

Calculating the Extra Hours of Walking

Steps to be covered by Flo each day = 12,000

Time required to walk 12,000 steps per day, m₂ = [tex]\frac{12000}{100}[/tex] minutes

⇒ m₂ = 120 minutes

Extra hours of walk per day = (m₂-m₁) minutes

= (120 - 60) minutes

= 60 minutes

Thus, Flow should walk 1 hour extra to be able to accomplish a goal of walking 12,00 steps per day.

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The next Answers are x > 0, and all real numbers

The correct function shown in graph is,

⇒ f (x) = log₁₀ x

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of the function is shown in figure.

Now, Points on the graph are (1, 0) , (5, 1) and (0.2, -1)

Hence, From the option 4;

⇒ f (x) = log₁₀ x

Put x = 1;

⇒ f (x) = log₁₀ 1

⇒ f (x) = 0

Thus, The correct function shown in graph is,

⇒ f (x) = log₁₀ x

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Using the normal distribution, it is found that there is a 0.3156 = 31.56% probability that the sample proportion will be less than 14%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion and the sample size are given, respectively, by:

p = 0.15, n = 294

Hence the mean and the standard error are given, respectively, by:

The probability is the p-value of Z when X = 0.14, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.14 - 0.15}{0.0208}[/tex]

Z = -0.48

Z = -0.48 has a p-value of 0.3156.

0.3156 = 31.56% probability that the sample proportion will be less than 14%.

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Answer:

Oy= -(x+4)^2 -2

potentially Oy= -x^2 -2

Answer:

See below

Step-by-step explanation:

285714 / 1000 000    which simplifies to 142,857 / 500,000