The function f(x)=90e−0.3x+10 describes the percentage of​ information, f(x), that a particular person remembers x weeks after learning the information.
a.
Substitute 0 for x​ and, without using a​ calculator, find the percentage of information remembered at the moment it is first learned.
b.
Substitute 1 for x and find the percentage of information that is remembered after 1 week.
c.
Find the percentage of information that is remembered after 12 weeks.
d.
Find the percentage of information that is remembered after one year​ (52 weeks).

The measure that best describes the change in the location of the drone is D. -26 1/10m

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the underwater drone is located 9 3/5 meters below sea level and the drone is moved to a location that is 15 1/2 meters below sea level

The change will be:

= - 9 3/5 - 15 1/2

= - 9 6/10 - 15 5/10

= - 25 1/10

The change is - 25 1/10m.

The options are incorrect.

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Solving the system of linear inequalities, we get

-4x+3y<15 = (0,5),(-15/4,0)

-6x-4y<12 = (0,-3),(-2,0)

What is a system of linear inequalities?

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Here, we have

Given inequalities

-4x+3y<15 and -6x-4y<12

Now we solve  the system of linear inequalities

For, -4x+3y<15

When we put x= 0, we get

y = 5

and if we put y = 0 , we get

x = -15/4

For, -6x-4y<12

When we put x= 0, we get

y = -3

and if we put y = 0 , we get

x = -2

Hence,  Solving the system of linear inequalities, we get

-4x+3y<15 = (0,5),(-15/4,0)

-6x-4y<12 = (0,-3),(-2,0)

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Vertex of the given parabola : (1,-9), Axis of Symmetry: x = 1, Y-intercept : (0, -8), x-intercept(s) :  (-2,0) and (4,0), and Concavity: opens up.

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

The graph of the parabola is given in the question.

According to the given graph, the required solution would be as:

Vertex of the given parabola : (1,-9)

Axis of Symmetry : x = 1

Y-intercept : (0, -8)

x-intercept(s) :  (-2,0) and (4,0)

Concavity: opens up

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Answer: x = 45 degrees

Step-by-step explanation:

We can see that there is a straight line. A straight line is 180 degrees.

We also see a 90-degree angle. There are 2 angles that equal the same amount.

This gives the equation below:

90 + 2x = 180.

Now, we subtract 90 from both sides.

2x = 90.

Now, we divide both sides by 2.

x = 45.

This means that our final answer is 45 degrees.

The correct answer to this question is A.

A statement which could be a representation of the events for the simulation is: Assign the numbers 1-7 to represent a made goal and the numbers 8-10 to represent a missed goal.

A simulation can be defined as a model which is designed and developed to imitate the operation of an existing (proposed) real-life system or natural phenomenon, in order to enhance the ability to study, analyze, and make informed decisions about it.

Since this soccer player made 67% of her goal attempts last season, the number of goals the player will make out of 10 attempts in a game is given by:

Number of goals = 67/100 × 10

Number of goals = 0.67 × 10

Number of goals = 6.7 ≈ 7 goals.

Therefore, this soccer player would score seven (7) goals while missing three (3) goals. Also, the 7 goals would be represented by 1 - 7 while the missed goals would be represented by 8 - 10.

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Answer: 18

Step-by-step explanation:

Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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The table of values for the total cost is:

# of Rides, x    Total cost, y

0                             $8

1                              $11

2                               $14

3                               $17

4                                $20

5                                $23

The table of values create a linear function. This is because the table of value increases by a constant value.

The total cost is the sum of the amount the carnival charges, the number of rides and the cost per ride.

Total cost = cost to enter + (cost per ride x number of rides)

Total cost for 0 ride = $8 + ($3 x 0) = $8

Total cost for 1 ride = $8 + ($3 x 1) = $11

Total cost for 2 rides = $8 + ($3 x 2) = $14

Total cost for 3 rides = $8 + ($3 x 3) = $17

Total cost for 4 rides = $8 + ($3 x 4 ) = $20

Total cost for 5 rides = $8 + ($3 x 5) = $23

The table of values creates a linear function. This is because the total cost increases by a constant amount.

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The function g(t)=100(t-4)/84.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

g(0) = 4

g(1)= 4 + .84x

g(2)= 5.85

g(t) = mt+c

c = 4

g(t) = t-c/m = t-4/0.84 = 100(t-4)/84

Hence, the g(t)=100(t-4)/84.

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Answer:

12000 is the correct answer.

Step-by-step explanation:

Hope this helps you :)

Mark has brainiest please

Answer:

25.749504 kilometers

Step-by-step explanation:

16miles  x 1.609(constant) = 25.749504

Answer:

7

Step-by-step explanation:

First, we need to get rid of the square root. To do this, square both sides.

(x - 5)^2 = √((x - 3)^2)

x^2 - 10x + 25 = x - 3

Next, continue simplifying

x^2 - 10x + 25 - x + 3 = 0

x^2 - 11x + 28 = 0

(x - 7)(x - 4) = 0

x - 7 = 0         and        x - 4 = 0

x = 7              and        x = 4

Next, plug in these values into the equation

x = 7 ---> 7 - 5 = √(7 - 3)

              2 = √4

              2 = 2

x = 7 is a possible value

x = 4 ---> 4 - 5 = √(4 - 3)

               -1 = √1

x = 4 is an extraneous solution and not a possible value.              

Answer:

7 is the only solution

Step-by-step explanation:

x-5=square root x-3

7-5=square root 7-3

2=square root of 4

2=2

7 is a solution

4-5=square root 4-3

-1= square root of 1

-1=1

hopes this helps please mark brainliest

The ratio of the vertical lenght to the horizontal length of both triangles   from the graph is the same which is numerical equal to 1/2 and the slope of the line is 1./2.

A triangle is a plane shape that has three sides.

For triangle PRQ,

Ratio of the vertical lenght to the horizontal length of triangle PRQ(r) = Vertical length(v)/Horizontal length (h)

From the graph,

Given:

Substitute into equation 1

Similarly, for triangle SUT,

From the graph,

Given:

Substitute into equation 2

The slope the line is the same as the ratio of the vertical lenght to the horizontal length of both triangles

Therefore,

Slope of the line = 1/2

Hence, the ratio of the vertical lenght to the horizontal length of both triangles  is 1/2 and the slope is 1./2.

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By the concept of function, the value of g(x) obtained is

g(x) = 3f(x) is the required function

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, from the graph, it can be seen that

g(1) = 3 and g(-1) = 3

Let g(x) = [tex]kx^2[/tex]

g(1) = 3

[tex]k(1)^2 = 3\\k = 3[/tex]

So g(x) = [tex]3x^2[/tex] = 3f(x) is the required function

Option B is correct

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Complete Question

If f(x) = x², which equation represents function g?

A. g(x)=1/3f(x)

B. g(x)=3f(x)

C. g(x)=f(1/3x)

D. g(x)=f(3x)

The diagram has been attached here

Answer:

x^(9/7)

Step-by-step explanation:

inverse function f(x) = (x^(1/9))^7 = x^(9/7)

The equation for temperature 67, gives the time as 4.8 hours.

What is amplitude?

A sound is a type of energy that is created when objects vibrate. For it to spread, a medium is needed. As a result, sound cannot travel in a vacuum because there is nothing for the sound waves to travel through. The object's back-and-forth movement creates the sound. Sound vibration is the name for this. Additionally called oscillatory motion. Oscillation describes the regular rhythmic back-and-forth movement.

We know that the general equation of a sine wave is:

[tex]$$y(t)=A \{Sin}(W(t-C))+D$$[/tex]

where,

A- Amplitude

D = Average of Max(y) and Min(y);

[tex]W=\frac{2 \pi}{\text { Period }}[/tex]

C - Phase shift on y(axis)

Part a)

Given Max T= 94 and Min T = 66

Hence,

D = (Max+Min)/2 = 80

A = Max - D = 94-80= 14

Since period is 24 hours, so W = 2\pi/24 = \pi/12

Thus the function till now is:

[tex]T(t)=14Sin(\frac{\pi}{12}(t-C))+80[/tex]

Given low temperature occurs at 3 AM so,

T(3)=66

Solving this we get C = 9

Hence,

[tex]T(t)=14Sin(\frac{\pi}{12}(t-9))+80[/tex]

Part b)

Given Max T= 58 and Average = 45

Hence,

D = 45

A = Max - D = 58-45= 13

Since the period is 24 hours, so W = [tex]2\pi/24 = \pi/12[/tex]

Thus the function till now is:

[tex]T(t)=13Sin(\frac{\pi}{12}(t-C))+45[/tex]

Given high temperature occurs at 5 PM so,

T(17)=58

Solving this we get C = 11

Hence,

[tex]T(t)=13Sin(\frac{\pi}{12}(t-11))+45[/tex]

The temperature at 4 AM is:

[tex]T(4)=13Sin(\frac{\pi}{12}(4-11))+45 = 32.44[/tex]

Part c)

Given Max T= 86 and Min T = 64

Hence,

D = (Max+Min)/2 = 75

A = Max - D = 86-75= 11

Since period is 24 hours, so W = 2\pi/24 = \pi/12

Thus the function till now is:

[tex]T(t)=11Sin(\frac{\pi}{12}(t-C))+75[/tex]

Given average temperature occurs at 8 AM so,

T(8)=75

Solving this we get C = 8

Hence,

[tex]T(t)=11Sin(\frac{\pi}{12}(t-8))+75[/tex]

Now,

We need to find t such that T(t) = 67.

[tex]67=11Sin(\frac{\pi}{12}(t-8))+75[/tex]

[tex]\Rightarrow t=4.88945 \approx 4.89 hours[/tex]

Hence, The equation for temperature 67, gives the time as 4.8 hours.

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On solving the equations y = (-1/2)x + [tex]4\frac{1}{2}[/tex] and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

In the question ,

it is given that

the equations are y = (-1/2)x + [tex]4\frac{1}{2}[/tex]  and 3x - 4y = 12

which can be written as y = (-1/2)x + 9/2  and 3x - 4y = 12

to plot the graph of the given equations , we need intercept .

For the equation y = (-1/2)x + 9/2

when x= 0  , y = (-1/2)(0) + 9/2 = 9/2

when y = 0 ,

0 = (-1/2)x + 9/2

(1/2)x = 9/2

x = 9

the points are (0 , 9/2) and (9 , 0)

For the equation 3x - 4y = 12

when x = 0 , 3(0) - 4y = 12

-4y = 12

y = -3

when y = 0 , 3x -4(0) = 12

3x = 12

x = 4

the points are (0,-3) and (4,0) .

after plotting the lines on the graph , we can see that the both the lines intersect at the point (6 , 3/2) ,

Therefore , On solving the equations y = (-1/2)x + [tex]4\frac{1}{2}[/tex] and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

The given question is incomplete , the complete question is

Consider this equation y = (-1/2)x +  [tex]4\frac{1}{2}[/tex]  and 3x - 4y = 12 .

Solve the system by graphing. label each graph.

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The nth term of the given Quadratic Sequence is n² + 2n.

Given, a sequence of numbers i.e. 3, 8, 15, 24, 35

Now, we have to find the nth term of this quadratic sequence

Let, the quadratic sequence be defined as,

f(x) = ax² + bx + c

Now, as we have f(1) = 3

So, a + b + c = 3 ... (1)

also, we have f(2) = 8

So, 4a + 2b + c = 8 ... (2)

also, we have f(3) = 15

So, 9a + 3b + c = 15 ... (3)

On solving Eq (1) & (2), we get

3a + b = 5 ... (4)

also, On solving Eq (3) & (2), we get

5a + b = 7 ... (5)

Now, on solving Eq (4) & (5), we get

2a = 2

a = 1

On substituting the value of 'a' in Eq. (5), we get

b = 2

So, the quadratic sequence be f(x) = x² + 2x.

Hence, the Quadratic Sequence f(x) = x² + 2x and the nth term be

n² + 2n.

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value of the slope is 22.3 % per Kg

Charging a single, fixed price for a given service is known as flat rate pricing.

The U.S. Postal Service charges a $21.90 flat rate.

additional $4.90 per kilogram.

slope rate =[tex]\frac{4.90}{21.90} X 100 = 22.3 %[/tex] %

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Answer:

complement of acute angle = 2x - 46

Step-by-step explanation:

supplementary angles sum to 180° , that is

acute angle + supplement = 180

acute angle + (2x + 44) = 180 ( subtract 2x + 44 from both sides )

acute angle = 180 - (2x + 44) = 180 - 2x - 44 = 136 - 2x

complementary angles sum to 90° , that is

acute angle + complement = 90

136 - 2x + complement = 90 ( subtract 136 - 2x from both sides )

complement = 90 - (136 - 2x) = 90 - 136 + 2x = 2x - 46

Answer:

x = 16

y = 10

Step-by-step explanation:

x+5y =46 [1]

x-y =-14 [2]

x=-14+y [3]

put [3] into [1],

x+5y =46

-14+y+5y=46

6y = 60

y = 10

put y=10 into [1]

x+5(10)=46

x = 16

The point (0, 1) and (-2.5, 6) is the solution to y = 2x² + 3x + 1 and y = -2x + 1

From the information, we want to solve the system by graphing. y = 2x² + 3 x + 1 and y = - 2 x + 1.

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Given the quadratic and linear equation, y = 2x² + 3x + 1 and y = -2x + 1, the solution is at the intersection of both equations. Here, the intersection point of the equations is the solution of the system i.e. (-2.5,6) and (0,1). Therefore, the point (0, 1) and (-2.5, 6) satisfies this equation.

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Answer:

6261

Step-by-step explanation:

it was 6261 because I have to do a i test at

Answer:

part A=3x-23=28

part B=17

Step-by-step explanation:

3x-23=28

3x=23+28

3x=51

x=17

Answer:

$151.50 deducted

Step-by-step explanation:

Walter used his bank's ATM to withdraw $150. This was the sixth time he used the ATM in June. His bank does not charge for the first five ATM uses each month. After that, the fee is $1.50 for each use. What is the total he should subtract from his balance including fees?

1 charge of $1.50 + withdrawal of $150

= $151.50 deducted

Answer:

Step-by-step explanation:

$427,011.92

The probability that the customer would come in that time is  0.0007

The question puts the mean u = 7.3

We are required to get the probability of less than 1 customer in one hour. The poisson probability formula is what would be used to solve this problem

the formula is given as

[tex]P(X=x) = e^-^u*^u^x[/tex]/X!

where x = 1

p(X=x) = P(X = 0)

P(X < 1) = P(X = 0)

e⁻⁷.³ x 7.30 / 0!

=  0.0007

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