The amount y (in grams) of the radioactive isotope phosphorus-32 remaining after t days is y=a(0. 5)t/14, where a is the initial amount (in grams). What percent of the phosphorus-32 decays each day? Round your answer to the nearest hundredth of a percent

Step-by-step explanation:

LET THE Point 1 A and point 2 is B

(AB) ^2=(-9-(-3))^2+ (5-(-6))^2+(-4-7)^2=278

AB=16.67 length unit

Midpoint

X=-9-3/2 =-6

Y=5-6/2=-0.5

Z=-4+7/2=-1.5

The distance between points (−3,−6,7) and (−9,5,−4) is 16.6 units, and midpoints are (-6, -0.5, -1.5).

Distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is determined by the following as D² = (x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²

The midpoint of the line joining  (x₁, y₁, z₁) and (x₂, y₂, z₂)  is given by :

{(x₂+x₁)/2 , (y₂+y₁)/2 , (z₂+z₁)/2}

To determine the distance between points (−3,−6,7) and (−9,5,−4)

Let mid points X, Y, and Z

The given points :  (−3,−6,7) and (−9,5,−4)

Distance between points  (−3,−6,7) and (−9,5,−4) :

D² = (x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²

D² =(-9-(-3))²+ (5-(-6))²+(-4-7)² = 278

D = √278

D = 16.6 units

The midpoint of the line joining (−3,−6,7) and (−9,5,−4) :

X = (-9-3)/2 = -6

Y =(5-6)/2 = -0.5

Z =(-4+7)/2 = -1.5

Hence, the distance between points (−3,−6,7) and (−9,5,−4) is 16.6 units, and midpoints are (-6, -0.5, -1.5).

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Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

The correlation between the time spent waiting at traffic lights and total cycling time was 0.50.

This means that there is a moderate positive correlation between the two variables.

This indicates that as the time spent waiting at traffic lights increases, so does the total cycling time.

Similarly, as the time spent waiting at traffic lights decreases, the total cycling time decreases as well.

The correlation coefficient measures the degree of association between two variables.

The value of the correlation coefficient ranges from -1 to +1.

A correlation coefficient of +1 indicates a perfect positive correlation between the variables.

A correlation coefficient of -1 indicates a perfect negative correlation between the variables.

A correlation coefficient of 0 indicates no correlation between the variables.

In this case, a correlation coefficient of 0.50 indicates a moderate positive correlation between the time spent waiting at traffic lights and total cycling time.

The strength of the correlation indicates that the two variables are related, but not perfectly related.

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Answer:

Step-by-step explanation:

Given function:

a)  g(2)

b)  g(t - 2)

c)  g(t) - g(2)

4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.

Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.

Here,

The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.

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Step-by-step explanation:

integral from 0 to 2pi of cos3x

(sin3x)/3 from 0 to 2 pi

sin 6pi /3 - sin 0 /3 = 0

Answer:

A

A would be the best answer since it asking how much did it change.

Answer:

  x ≠ -3

Step-by-step explanation:

Adding 4x-72 to the first inequality gives ...

  -12 < 4x

  -3 < x . . . . . divide by 4

Adding -11 to the second inequality gives ...

  14x < -42

  x < -3 . . . . divide by 14

Now we have ...

  x < -3 or x > -3

The solution is x ≠ -3.

_____

The graph of the solution set is the entire number line with a "hole" at -3. The number -3 is the only value not part of the solution set.

Step-by-step explanation:

Similar figures have different side lengths but corresponding angles are congruent.

The figure you sketch will have side length:

When k > 1, you sketch a larger figure, when 0 < k < 1, you sketch a smaller figure than pictured.

See attached, the two figures, one has side of 18 when k = 1.5, another one has side of 6, when k = 0.5

Answer: p = \(\frac{-n}{500} +68\)

Step-by-step explanation:

Let n represent the number of shirts and p represent the price, the there is a linear relationship between n and p, then the model equation is given as:

p = mn + b, where

m = slope and b is the intercept

From the question, when n = 1000, p = $66

And, when n = 10,000 , p = $48

The formula for finding slope is given as:

m = \(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)

\(y_{1} = 66\)

\(y_{2} = 48\)

\(x_{1} = 1000\)

\(x_{2} = 10000\)

substituting the values,

m = \(\frac{48-66}{10000-1000}\)

m = \(\frac{-18}{9000}\)

m = \(\frac{-2}{1000}\)

m = \(\frac{-1}{500}\)

The linear equation thus becomes

p = \(\frac{-n}{500}+b\)

To find the value of b, substitute  p = 66 and n =1000 into the equation

That is,

66 = \(\frac{-1000}{500}+b\)

66 = -2 + b

68 = b

Therefore b = 68

The linear equation is therefore

p = \(\frac{-n}{500} +68\)

Answer:

Hello,

Step-by-step explanation:

The volume of the tank is V, p is number of pipes, t the time, k as constant.

V=k*p*t

V=k*10*16 ==> k=V/160

V=k*8*t

V=V/160*8*t ==>1=8/160*t ==> t=160/8=20

Time to use: 20 min.

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

There are 34 integers in the given sequence. The formula for the nth term of an arithmetic sequence is: a_n = a_1 + (n - 1) d. We can use the formula for the number of terms of an arithmetic sequence: n = (a_n - a_1 + d)/d

The formula for the nth term of an arithmetic sequence is: a_n = a_1 + (n - 1) d. Where: a_1 = first term n = number of terms d = common difference a_n = nth term. The formula for the number of terms of an arithmetic sequence is: n = (a_n - a_1 + d)/d. We can use these two formulas to solve the given problem.

The given sequence is in arithmetic progression with common difference d = 6:17, 23, 29, 35, ..., 221Using the formula for the nth term of an arithmetic sequence: a n = a 1 + (n - 1)d Where: a 1 = first term n = number of terms d = common difference a n = 221We need to find n.

Here's the formula for the number of terms of an arithmetic sequence: n = (a n - a 1 + d)/d. Putting the values: n = (221 - 17 + 6)/6n = 204/6n = 34Thus, there are 34 integers in the given sequence.

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Answer:

\( \sqrt{ {1}^{2} + {2}^{2} + {( - 2)}^{2} } = \sqrt{1 + 4 + 4} = \sqrt{9} = 3\)

(1, 2, -2) is 3 units away from the origin.

(0, 0, 5) is 5 units away from the origin.

So (0, 0, 5) is farther away from the origin.

Answer:

£686.27 (nearest penny)

Step-by-step explanation:

100%+2% --- £700

102% --- £700

100% --- \(\frac{100}{102}\) × £700 = £686.27 (nearest penny)

Answer:

1) 8

2) 11

3) 15

Step-by-step explanation:

1) x - 3

2) x

3) x + 4

x-3+x+x+4 = 34

3x + 1 = 34

3x = 34-1

x = 33/3

x = 11

The required numbers are 8, 11, and 15.

Given that,
The sum of the three numbers is 34. The first is 3 less than the second, while the third is 4 more than the second. Find the numbers is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Let the three numbers be x, y and z
The Sum of the number is 34,
x + y + z = 34   - - - - -(1)

The first is 3 less than the second,
y = x + 3

The third is 4 more than the second.
z = y + 4
z = x + 7

Put y and z in equation 1
x + x +3 +x +4 = 34
3x = 24
x = 8

Now
Second number =
y = x + 3
y = 8 + 3 = 11

Third number
z = x + 7
z = 8 + 7
z = 15

Thus, the required number are 8, 11, and 15.

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The Kalman filter is a common algorithm used to filter out statistical noise on a GPS.

Statistical noise in the demand of a process is defined as the amount of demand that is purely a result of randomness and could not have been forecasted with the best forecasting method.

Kalman filter is an optimal estimator that makes predictions about the state of a linear dynamic system from a series of measurements that contain statistical noise.

The Kalman filter works by first making a prediction about the current state of the system based on the previous state and the control input. Then, it updates this prediction with the new measurement to obtain an updated estimate of the state. This process is repeated for each new measurement, resulting in a more accurate estimate of the system's state.

In the case of GPS noise, the Kalman filter can be used to reduce the effect of measurement noise on the estimated position of the vehicle. The filter uses the previous position estimate and the control input (e.g., acceleration, steering angle) to predict the current position. This prediction is then updated with the new GPS measurement to obtain an updated position estimate. By repeating this process for each new measurement, the Kalman filter can reduce the effect of GPS noise on the estimated position.

In conclusion, the Kalman filter is a commonly used algorithm for filtering out GPS noise. It works by making predictions about the state of a system based on previous measurements and control inputs and then updating these predictions with new measurements. This results in a more accurate estimate of the system's state, which can be used to reduce the effect of GPS noise on the estimated position of a vehicle.

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Answer:

The basketball player made 8 free throws and scored two 2 point shots.

Step-by-step explanation:

Answer:

The basketball player made 8 free throws and scored two 2 point shots.

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

slope = rise/run

rise is a vertical distance

run is a horizontal distance

We need to find the rise and run between two points on the line.

Look at the point where the line crosses the y-axis. We need to go to another point on the line by going only vertically and horizontally.

Now start at that point, go 2 units up. The rise = 2. Now turn right and go 5 units to the right. The run = 5. You got to another point on the line.

rise = 2

run = 5

slope = rise/run

slope = 2/5

See the picture below.

Answer:

600

Step-by-step explanation:

+2  

2 5

2 4

---------

 First 5 x 4=20 which means add 2 to the equation 2 x 4

Second 4 x 2=8 + 2=10 do first 3 numbers are 100

third we put a 0 below the first 0 on first line.

fourth do 5 x 2=10 so we add 1 to 2 x 2

fifth 2 x 2 + 1= 5

sixth 100 + 500=600 and there's your answer

Hope this helps have a great afternoon:)

Answer:

Hollerith tabulating machine

Step-by-step explanation:

The Hollerith tabulating machine was invented by Herman Hollerith in other to assist in the data processing of the United States 1890 election. This machine was used to read and summarize the information stored on punchcards. This machine paved the way for the development of enhanced models which were employed for accounting and some other aspects related to business management.

Therefore, the probability that a randomly selected passenger has a waiting time less than 2.75 minutes is 0.55.

Since the waiting times between subway departure schedule and passenger arrival are uniformly distributed between 0 and 5 minutes, the probability density function of the waiting time can be expressed as:

f(x) = 1/5 for 0 <= x <= 5

0 otherwise

To find the probability that a randomly selected passenger has a waiting time less than 2.75 minutes, we need to calculate the area under the probability density function from 0 to 2.75:

P(X < 2.75) = ∫[0, 2.75] f(x) dx

= ∫[0, 2.75] (1/5) dx

= (1/5) [x]_[0, 2.75]

= (1/5) * 2.75

= 0.55

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Answer:

range

Step-by-step explanation:

Answer:

AE =15

Step-by-step explanation:

BC=16-12 = 4

AE=x

12/4 = x/5

Cross multiplication

4x=60

x=15

       4x3 = 12

       5x3 =15

Answer:

\(P=\left(\dfrac{1}{5},-\dfrac{12}{5}\right)\)

Step-by-step explanation:

We can use the internal section formula to find the coordinates of point P which divides the directed segment AB in the ratio of 3 : 2.

\(P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\)

where:

Given A (5, 0) and B (-3, -4) and the ratio 3 : 2:

Substitute the values into the formula:

\(\implies P(x,y)=\left(\dfrac{3 \cdot (-3)+2 \cdot 5}{3+2},\dfrac{3 \cdot (-4)+2 \cdot 0}{3+2}\right)\)

\(\implies P(x,y)=\left(\dfrac{-9+10}{5},\dfrac{-12+0}{5}\right)\)

\(\implies P(x,y)=\left(\dfrac{1}{5},-\dfrac{12}{5}\right)\)

Therefore, the coordinates of point P which partitions segment AB in a ratio of 3 : 2 are:

     \(\bullet\quad\left(\dfrac{1}{5},-\dfrac{12}{5}\right)\)

Note: The segment to be partitioned is a directed segment. Direction is important in a directed segment; it has a clear starting point and ending point. The starting point is the first letter of the segment and the ending point is the last letter of the segment. Therefore, if the directed segment AB is partitioned in a ratio 3 : 2 this means that point P is 3/5ths along the line from point A to point B.

The original number from the given decimal number is  0.02.

For the given question;

Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.

This results in:

10000x = 4.(1/x)

Simplifying.

x² = 4/10000

x > 0.

Taking square root of the number.

x = 2/100

x = 0.02

Thus, the original number from the given decimal number is  0.02.

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Answer: 55

Step-by-step explanation:

Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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After combining like terms in the equation, the next step would be to simplify and solve for 'x' by simplifying further.

In the given equation, "3 - 15x + 24 - 16x" on the left side of the equation is equal to "4x - 24 - 4x" on the right side. To continue solving, we need to simplify and combine like terms on both sides of the equation.

On the left side, combining like terms -15x and -16x gives us -31x. Similarly, combining like terms on the right side, 4x and -4x cancel each other out, leaving us with 0.

The simplified equation becomes -31x + 27 = 0. To finish solving for 'x', we would proceed by isolating the variable 'x' by performing further algebraic operations such as moving the constant term to the other side of the equation and dividing by the coefficient of 'x'. However, the next step would depend on the specific instructions or desired outcome of the equation.


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Answer: 4.15

Step-by-step explanation: