A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 15 hours, 55 mg of the substance remains.

How many milligrams will remain after 25 hours?

mg

Give your answer accurate to at least one decimal place.

Answer:

f(x) = - 2x + 4

Step-by-step explanation:

Since we are only trying to move the graph up 3 units, the slope does not change. So, it would be -2.

We also know that the 1 in f(x)= -2x + 1 is the y-intercept (y=mx+b). But again, we are moving the graph 3 units up, so we have to add 3. That makes it 4 (3+1=4).

So, the new equation would be f(x) = -2x + 4

Step-by-step explanation:

it simply means that g(x) is f(x) just shifted 3 units upwards.

that means nothing else changes, only whatever y result f(x) produces is increased by 3.

so,

g(x) = f(x) + 3 = -2x + 1 + 3 = -2x + 4

therefore, as domain and range were the whole set of real numbers, the addition of 3 does not make any difference in relation to infinity. so, they remain unchanged.

the slope stays the same (g(x) is simply a parallel line to f(x)).

the y-intercept (the y-value when x = 0) also increases by 3, and is 4.

the x-intercept (the x-value when y = 0) changes :

0 = -2x + 4

2x = 4

x = 2

the x-intercept is 2.

Answer:

both

Step-by-step explanation:

neither of those can be an answer. because x is less than or equal to -1

Answer: anita's age= 7 yrs

basilio age = 2.5 yrs

Step-by-step explanation:

Let age of anita and basilio be x

since anita is 4 1/2 years older than basilio

thereforce basilio age=x - 4.5

ATQ,

=>3x + 6(x-4.5) = 36

=>3x + 6x - 27=36

=>9x = 63

=>x=7

Answer:

n=8

Step-by-step explanation:

3n=−8+4n

Simplify both sides of the equation.

3n=4n−8   (there isn't so It stays the same.

Subtract 4n from both sides.

3n−4n=4n−8−4n

−n=−8

Divide both sides by -1.

−n/-1 =−8/-1

Answer:

n=8

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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ANSWER:

A.

STEP-BY-STEP EXPLANATION:

We have the following function:

To find the zeros of the function we must set the function equal to 0 in the following way:

We reorganize the equation in order to be able to factor and calculate the zeros of the function, like this:

Therefore, the zeros are:

And in its factored form the expression would be:

Answer:

I think its 4x^7y^7-2x^6y^6

Step-by-step explanation:

Answer:

I am doinnnnnmngggg gggg

Step-by-step explanation:

To hit the ball with the bumper, the ball needs to move towards the bumper.

The distance between the ball and the bumper is 8 - (-5) = 13 units.

Assuming the bumper is stationary, let's calculate the minimum force needed to move the ball towards the bumper.

We can use the formula:

force = mass x acceleration

The mass of the ball is not given, so let's assume it to be 1 unit.

The acceleration needed can be calculated using:

acceleration = (final velocity - initial velocity) / time

Let's assume that the time taken for the ball to reach the bumper is 1 second.

The initial velocity of the ball is 0 units (assuming it is stationary).

The final velocity needed to reach the bumper can be calculated using:

final velocity^2 = initial velocity^2 + 2 x acceleration x distance

final velocity^2 = 0 + 2 x acceleration x 13

final velocity^2 = 26 x acceleration

Since we want to hit the ball with the bumper and not destroy it, let's assume that the final velocity needed to reach the bumper is 1 unit per second.

Substituting this value in the equation above:

1^2 = 26 x acceleration

acceleration = 1 / 26 units per second^2

Substituting the values of mass and acceleration in the formula for force:

force = mass x acceleration

force = 1 x (1 / 26)

force = 1 / 26 units

Therefore, the minimum force needed to hit the ball with the bumper and collect the star is 1/26 units.

Answer:

1/3

Step-by-step explanation:

Slope is always represented by m in the equation y=mx+b. Therefore, the value that is attached to the x is always the slope.

Answer:

m=1/2

Step-by-step explanation:

The equation is in slope-intercept form, or

y=mx+b

where m is the slope and b is the y-intercept.

Essentially, the number that is multiplied by x is the slope, and the number that is added or subtracted from the term with an x is the y-intercept.

We are given the equation:

y=1/3x+22

1/3 is being multiplied by x (1/3*x=1/3x). Therefore, it must be the slope.

22 is being added to 1/3x (+22). Therefore, it must be the y-intercept.

m=1/3

b=22

The slope of the line is 1/3.

The fractional part of 70/28 is 35/14 i.e., 2.5

Percentage:

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100

28 of 70 can be written as:

=> \(\frac{28}{70}\)

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

\(\frac{28}{70}\) × \(\frac{100}{100}\)

=> (28 × 100) /70 ×\(\frac{1}{100}\)

=> 40/100

Therefore, the answer is 40%

The fractional part of 70/28 is 35/14 i.e., 2.5

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In order to calculate the probability of a student from this sample to be a seventh grader, we need to divide the number of seventh graders by the total number of students. This is done below:

A. The probability of a random selected student being a seventh grader is 1/5.

In order to calculate the probability of the selected student not being a seventh grader, we need to subtract the probability of them being a seven grader from one, because these two events are mutually exclusive. So we have:

B. The probability of a random selected student not being a seventh grader is 4/5.

Answer:

Step-by-step explanation:

If it takes 1 1/4 minutes to run 3 laps, then we can find how long it takes to run one lap by dividing the total time by the number of laps:

1 1/4 minutes = 1 minute + 1/4 minute = 60 seconds + 15 seconds = 75 seconds

So it takes 75 seconds to run 3 laps, and since each lap takes the same amount of time, we can divide by 3 to find the time for one lap:

75 seconds ÷ 3 laps = 25 seconds/lap

Therefore, it takes 25 seconds for the person to run one lap around his house.

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The number of seconds that it takes him to run each lap will be 25 seconds.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

It takes him 1 whole and 1/4 minutes to run 3 laps around his house. Then the number of total minutes is calculated as,

T = 1 + 1/4

T = 1 + 0.25

T = 1.25 minutes

Then the number of seconds to cover one lap is calculated as,

⇒ 1.25 / 3

⇒ 1.25 x 60 / 3

⇒ 25 seconds

The number of seconds that it takes him to run each lap will be 25 seconds.

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The values on the graph of the velocity of the body, indicates that we get;

a. t = 2 seconds and t = 7 seconds

b. 3 ≤ t ≤ 6

c. Please find attached the speed of the body in the interval 0 ≤ t ≤ 10 created with MS Excel

b. Please find attached the acceleration of the body in the interval 0 ≤ t ≤ 10

Velocity is the rate of change of the position of an object with respect to a specified reference frame and time.

The figure is a velocity time graph, and the velocity of an object is the rate of change of the displacement with time, such that when graph is above the horizontal axis, the velocity is positive, and when the velocity is below the horizontal axis, the velocity is negative, therefore, we get;

a. When the velocity of the changes sign, the direction of the body reverses. The points at which the velocity changes sign, which are the x-intercepts are at t = 2, and t = 7

b. The speed is constant when the velocity remains the same, which are locations on the graph, where the graph is an horizontal line. Therefore, the interval at which the body is moving at a constant velocity is; 3 ≤ t ≤≤6

c. The speed of a body is its absolute velocity, which can be found from the graph by taking the absolute value of the velocity at each point on the graph as follows;

The points on the resulting graph will therefore be; (0, 0), (1, 4), (3, 4), (6, 4), (8, 4) and (10, 0).

Please find attached the speed of the body in the interval 0 ≤ t ≤ 10

d. The acceleration is the rate of change of the velocity of the body with time. The acceleration of the body which has a velocity graph consisting of straight lines is a piecewise constant graph, such that we get;

From t = 0 to t = 1, a = (4 - 0)/(1 - 0) = 4

From t = 1 to t = 3, a = (4 - (-4))/(1 - 3) = -4

From t = 3 to t = 6 , a = (-4 - (-4))/(6 - 3) = 0
From t = 6 to t = 8, a = (4 - (-4))/(8 - 6) = 4

From t = 6 to t = 10, a = (0 - 4)/(10 - 8) = -2

Please find attached the graph of the acceleration of the body, created with MS Excel

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Answer:

B

Step-by-step explanation:

The value of x for the chord is:

x = 12

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

Recall that: If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords.

Using the above principle, we can say:

3 * x = 4 * 9

3x = 36

x = 36/3

x = 12

Thus, the value of x for the chord is 12.

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Answer:

52% of Ms. Green's class has a pet.

Step-by-step explanation:

So, I did this as simple as possible. First, I changed 25 to 100 to represent 100%. I multiplied 25 by 4 to get 100, so I then multiplied 13 by 4 to get 52.

25 → 100

13  →  52

So, this means that the answer is 52%.

A way to check, is by looking at the answer and seeing if it looks correct. Most of the time, you will be able to see if your answer is correct just by looking at it.

The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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Answer:

x² - 6x + 8 = 0

or, x² - (4+2)x + 8 = 0

or, x² - 4x - 2x + 8 = 0

or, x(x-4) -2(x -4)= 0

or , (x-4) (x-2) = 0

either,

x - 2 = 0

x = 2

OR,

x - 4 = 0

x = 4

next ,

x-p = 9

or, 2-p = 9

p= -7

either,

x-p = 9

or, 4 - p = 9

or, p= -5

hope this will help you

Answer:

1.) \(\left(x-3\right)\left(x+6\right)\)

2.) \(\left(a-3\right)^2\)

3.) \(=\left(t+8\right)\left(t-9\right)\)

4.) \(=\left(b+7\right)^2\)

Step-by-step explanation:

2.) \(=a^2-2a\cdot \:3+3^2\), \(\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2\).

\(a=a,\:b=3\)

\(=\left(a-3\right)^2\)

3.) \(=\left(t^2+8t\right)+\left(-9t-72\right)\)\(=t\left(t+8\right)-9\left(t+8\right)\), \(\mathrm{Factor\:out\:common\:term\:}t+8\).

\(=\left(t+8\right)\left(t-9\right)\)

The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.

Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.

The graph that represent this data using the points is added as an attachment

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

The x and y values

Where

x = stars

y = price

To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph

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Answer:

9.42

Explanation:

pi is approximately 3.14, So, 3 time pi is equal to:

3 x pi = 3 x (3.14) = 9.42

Therefore, 3 times pi is approximately 9.42

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

Its C

Step-by-step explanation:

To support her discussion, it would be best for Alex to use Graph A for her presentation. Alex should use this graph for her presentation because the number of faulty products appears to decrease less on this graph.

In Mathematics and Geometry, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In order to determine an equation with a declining line, we would have to determine the slope of each line graphically and then taking note of the line with a negative rate of change (slope) because it indicates a decreasing function.

In this context, we can reasonably infer and logically deduce that Graph A is more suited for Alex's presentation because the number of faulty products appears to decrease less on it.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

\(\cfrac{x}{4}-\cfrac{x+10}{2}=3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{x}{4}-\cfrac{x+10}{2} \right)=4(3)}\implies x-(2x+20)=12 \\\\\\ x-2x-20=12-x-20=12\implies -20=12+x\implies \boxed{-32=x} \\\\[-0.35em] ~\dotfill\)

\(\cfrac{2x+1}{5}-\cfrac{x-3}{7}=-2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{2x+1}{5}-\cfrac{x-3}{7} \right)}=35(-2) \\\\\\ 14x+7-(5x-15)=-70\implies 14x+7-5x+15=-70 \\\\\\ 9x+22=-70\implies 9x=-92\implies \boxed{x=-\cfrac{92}{9}}\)