4) Assume that the rate of decay of a radioactive substance is proportional to the amount of substance present. That is, if x(t) is the amount of substance present at time t , then its rate

From the portion of a four-year amortization schedule the principal has been paid off after twenty-five payments, is $9543.97.

Loan amount is the amount or sum of money, which is borrowed by one at some rate of interest for a period of time.

Here, the principal has to be calculated after twenty-five payments. At 25 months, the balance of the loan is 10,356 dollars and 3 cents. It can be written as $10356.03.

As, the loan amount or principal is 19,900 dollars. This balance is the total amount of the loan. If we substrate the remaining loan amount from the total amount of loan, the result will be the paid loan amount.

Suppose the paid loan amount is P. Therefore,

\(P=19900-10356.03\\P=9543.97\)

Thus, from the portion of a four-year amortization schedule the principal has been paid off after twenty-five payments, is $9543.97.

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Answer:

(-6 , 4.5 )

Step-by-step explanation:

We have to find the mid-point of the line segment joining the points (-2,-3) and (-10,12). A mid-point divides a line segment into 2 equal parts with equal ratio i.e. 1 : 1 .

According to the Section Formula , the mid-point of a line segment joining two points (x¹,y¹) & (x²,y²) is :-

\((x' , y') = (\frac{x^1+x^2}{2} , \frac{y^1+ y^2}{2} )\) where ( x' , y' ) is the co-ordinate of the mid-point of the line segment.

Here in the question ,

x¹ = -2

y¹ = -3

x² = - 10

y² = 12

Putting all these values in the formula ,

\((x',y') = (\frac{-2-10}{2} , \frac{-3+12}{2} ) = ( \frac{-12}{2} , \frac{9}{2} ) = (-6,4.5)\)

Answer:

x = -7

Step-by-step explanation:

Given parameters:

Slope of the line = \(\frac{4}{3}\)

 Coordinates =  (5,x) and (2,-3)

Unknown:

X= ?

Solution:

  To find slope, use the expression below;

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

y₂ = -3  y₁ = x

x₂ = 2   x₁ = 5

   \(\frac{4}{3}\)  = \(\frac{-3 - x}{2 - 5}\)

           3(-3-x) = 4(-3)

            -9 -3x = 12

                -3x = 21

                  x = -7

The two angles are vertical angles, which mean they are the same.

6s-2 = 94

Add 2 to both sides:

6s = 96

Divide both sides by 6:

S = 96/6

S = 16

At the end of December, Cory will have approximately $38.97.

We have,

To calculate the amount of money Cory will have at the end of December, we need to consider the monthly savings and the duration from June to December.

Cory plans to save 10% of his money each month, starting with $20.

Let's calculate the savings for each month:

June: $20 + 10% of $20 = $20 + ($20 x 0.1) = $20 + $2 = $22

July: $22 + 10% of $22 = $22 + ($22 x 0.1) = $22 + $2.2 = $24.2

August: $24.2 + 10% of $24.2 = $24.2 + ($24.2 x 0.1) = $24.2 + $2.42 = $26.62

September: $26.62 + 10% of $26.62 = $26.62 + ($26.62 x 0.1) = $26.62 + $2.662 = $29.282

October: $29.282 + 10% of $29.282 = $29.282 + ($29.282 * 0.1) = $29.282 + $2.9282 = $32.2102

November: $32.2102 + 10% of $32.2102 = $32.2102 + ($32.2102 x 0.1) = $32.2102 + $3.22102 = $35.43122

December: $35.43122 + 10% of $35.43122 = $35.43122 + ($35.43122 x 0.1) = $35.43122 + $3.543122 = $38.974342

Therefore,

At the end of December, Cory will have approximately $38.97.

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Answer:

D

Step-by-step explanation:

1T=2000lb

9000lb= 4.5T

Answer:

it is d my friend

Answer:

x ≈ 16.6 units

Step-by-step explanation:

The angle between a tangent and the radius at the point of contact is 90° , so

Δ ABC is a right triangle at ∠ B

Using Pythagoras' identity in the right triangle

x² + 7² = 18²

x² + 49 = 324 ( subtract 49 from both sides )

x² = 275 ( take the square root of both sides )

x = \(\sqrt{275}\) ≈ 16.6 ( to the nearest tenth )

This study can be best described as Controlled Placebo Experiment

What is a Controlled Placebo Experiment?

A controlled placebo experiment is a type of research method that is used to check the effectiveness of a drug in a patient. This is done by selecting a sample group, then randomly divide the two group into a placebo group (this are the group that will receive the drug treatment ) and the controlled group (these are the group that will receive a colored mixture that looks like the drug, but does not have any effect). Without the groups knowledge about the real drugs and the colored mixture, but are followed up and tested.

According to the given question:

This is a controlled placebo experiment, because 400 student has been chosen as the sample, and are divided into a placebo group and a controlled group, to check the effectiveness of a drug on their memory.

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Answer:

Lin will run 1 mile in 8/55 of an hour

Noah will run 1 mile in 2/13 of an hour

Step-by-step explanation:

Here;

Lin ran 2 3/4 miles in 2/5 of an hour

he will run 1 mile in x hour

x * 2 3/4 = 2/5 * 1

2 3/4 = 11/4

x * 11/4 = 2/5

x = 2/5 * 4/11

x = 8/55 hour

For Noah

8 2/3 miles in 4/3 of an hour

1 miles in y hours

y * 8 2/3 = 4/3 * 1

y * 26/3 = 4/3

y = 4/3 * 3/26

y = 4/26 = 2/13

He will run 1 mile in 2/13 hours

Answer:

33

Step-by-step explanation:

1254 divided by 38 is 33

Answer:

944 cm²

Step-by-step explanation:

get the area of each side: 12*10+10*16+12*16= 472

2 sets of each side: 944

Answer:

Below

Step-by-step explanation:

Slope-y-axis -intercept form is  y = mx + b

y = - 2/5 x + 3     Done.

A ratio variable should be transformed into a dichotomous variable represented with dummy coding when the research question or analysis requires a simplified comparison between two distinct groups, the relationship between the ratio variable and the outcome variable is non-linear, there is a meaningful cutoff or threshold value, or specific statistical methods necessitate dichotomous variables.

A ratio variable may be transformed into a dichotomous variable represented with dummy coding under the following conditions:

Simplification of Analysis: When the research question or analysis requires a simplified comparison between two distinct groups or categories based on the ratio variable.

Nonlinearity: If the relationship between the ratio variable and the outcome variable is non-linear, it may be beneficial to dichotomize the ratio variable to capture the presence or absence of a certain condition or threshold.

Practical Interpretation: When there is a meaningful and interpretable cutoff or threshold value for the ratio variable that divides the population into two distinct groups.

Statistical Analysis Requirements: Certain statistical methods or models may require dichotomous variables for analysis, and transforming a ratio variable into a dichotomous variable allows for the use of these methods.

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Answer:

Your answer would be:
13.25

128 books in use + 84 books in the collection box =212 reference books on the shelf

212 books / 16 shelves =13.25 per shelf

Logically the answer 13.25 wouldn't make sense because you can't put a 25th of a book on a shelf, so that means you will need to put the "0.25 book" away. Technically your answer would be 13. Due to the question, however, it would be 13.25.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

The average velocity of Gwen over the time interval 0 < t is zero. We need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer.

Given that Gwen runs back and forth along a straight track and her velocity, in feet per second, is modeled by the function v(t) during the time interval 0 < t < 45 seconds; We are to determine the first time at which Gwen changes direction and find her average velocity over the time interval 0 < t.Firstly, we know that velocity is a vector quantity and has both magnitude and direction.

Since she is running back and forth along a straight track, her displacement at any given time t is given by the function s(t), which is the integral of her velocity function v(t).That is, s(t) = ∫v(t)dtWe can find the displacement by taking the definite integral of v(t) from 0 to t. Since Gwen is running back and forth, her displacement will be zero at the times when she changes direction.

Therefore, we need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer. Therefore,t = 45n/πwhere n is an integer. Since we are looking for the first time at which Gwen changes direction, we need to take the smallest positive value of n, which is n = 1.

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Answer:

-75

Step-by-step explanation:

f(x)=7x-5

f(-10)=7(-10)-5

f(-10)=-70-5

f(-10)=-75

Answer:

f(-10) -75

Step-by-step explanation:

f(x)=7x-5   f(-10)

    =7(-10)-5

    =-70-5

f(-10)= -75

Hope this helps :)

Answer: Ben's garden is 8.4 m long.

Step-by-step explanation:

Let's define:

B = length of Ben's garden.

A = length of Amy's garden

F = length of Faisal's garden.

We know that:

"Ben’s garden is 1.9 m shorter than Faisal’s garden"

This can be written as:

B = F - 1.9m

"Amy’s garden is three and a half times longer than Faisal’s garden."

A = 3.5*F

"Amy’s garden is 36.05 m long"

A = 36.05 m

Then we have the system of equations:

B = F - 1.9m

A = 3.5*F

A = 36.05 m

To solve this, we need to first replace the last equation into the second one, and in that way we can find the value of F.

A = 3.5*F

36.05m = 3.5*F

(36.05m)/3.5 = 10.3m = F

Now that we know the value of F, we can replace it in the first equation:

B = F - 1.9m

B = 10.3m - 1.9m = 8.4m

Ben's garden is 8.4 m long.

Rafael is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 16 feet and its width is 13 feet. Suppose each bag of fertilizer covers 26 square feet. How many bags will he need to cover the garden?​

step 1

Find the area of the garden

Remember that the area of a rectangle is equal to

A=L*W

we have

L=16 ft

W=13 ft

substitute

A=16*13

A=208 ft^2

step 2

we know that

each bag of fertilizer covers 26 square feet

so

Applying proportion

1/26=x/208

solve for x

x ----> number of bags

x=(1/26)*208

x=8 bags

therefore

Answer:

g(x) is shifted left by two units

Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

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Slope = (y2-y1) / (x2-x1)

9) (7 - -6)/(-11- 17) = 13/-28

10) (-5-4)/(-4-3)= -9/-7

11) (15-14)/(17- -20) = 1/37

12) (-7 - -18) /(-1 -11) = 11/-12

Step-by-step explanation:

x(x-4) = 192

the Equation:

x²-4x -192 =0

=> (x-16) (x+12) =0

x= 16 or x= -12

since the x should be a possitive, so x = 16

the dimension :

the length = 16 m

the width = 12 m

Step-by-step explanation:

2:10:16=2/10=1/5÷16

\(1 \div 5 \div 16\)

1/5×1/16

=1/80

The minimum value of z is 17, and the optimal values of x1 and x2 are 5 and 3, respectively.

To solve the given linear programming problem using the simplex method, let's set up the initial tableau:

Cj    4   -1   0

-----------------

       |    

  2    |   1    1   <=   8

  1    |   0    1   <=   5

  0    |   1   -2   <=   4

Here, Cj represents the coefficients of the objective function z, and the bottom row represents the right-hand side (RHS) values of the constraints.

Step 1: Select the most negative coefficient in the bottom row as the pivot column. In this case, it is -2.

Step 2: Determine the pivot row by selecting the smallest non-negative ratio from the RHS values divided by the corresponding entries in the pivot column. In this case, the smallest ratio is 4/(-2) = -2.

Step 3: Perform the pivot operation to make the pivot element (in this case, -2) equal to 1 and eliminate all other elements in the pivot column. The pivot row becomes the new row with the pivot element.

Pivot column: x2

          |  

  2    |   1    1   <=   8

  1    |   0    1   <=   5

  0    |   1   -2   <=   4

Pivot row: R2

          |  

  2    |   1    1   <=   8

  0    |   0    1   <=   3

  0    |   1   -2   <=   4

Step 4: Update the tableau by performing elementary row operations to eliminate other elements in the pivot column.

          |  

  2    |   1    1   <=   8

  0    |   0    1   <=   3

  0    |   1   -2   <=   4

R1 = R1 - R2

          |  

  2    |   1    0   <=   5

  0    |   0    1   <=   3

  0    |   1   -2   <=   4

Step 5: Check if the current solution is optimal. If there are no negative coefficients in the top row (except for z = 0), the solution is optimal. In this case, the solution is optimal since all coefficients are non-negative.

Step 6: Read the optimal solution from the tableau. The values of x1 and x2 can be found in the right-most column of the variables' columns.

Optimal solution:

x1 = 5

x2 = 3

Step 7: Calculate the value of the objective function z using the optimal solution.

z = 4x1 - x2

z = 4(5) - 3

z = 20 - 3

z = 17

Therefore, the minimum value of z is 17, and the optimal values of x1 and x2 are 5 and 3, respectively.

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(a) t ≤ 2.5 minute she can take.

(b) the probability that she will miss exactly three items is:0.073

(c)  the Probability distributive function (pdf) for the waiting time between items is 0.195

Probability Distributive function (PDF) :

In probability theory and statistics, a probability distribution is a mathematical function that gives the probability of occurrence of different possible outcomes of an experiment. It is a mathematical description of random phenomena in terms of sample space and event probability (subset of sample space).

a) if she wishes to sneak out to have a coffee but will not allow the expected value of the number of items she misses to be greater than 5, Then, t ≤ 2.5 minute she can take.

λt ≤ 5

2t ≤ 5

t ≤ 5/2

t ≤ 2.5 min

(b) if she leaves for two minutes, then the probability that she will miss exactly three items is:

P(N(1)-N(0)=2) * P(N(2)-N(1)=1) =

= e× 2²/ (2)! × e(-2×1) × 2¹/(1!)

= 0.0729

≈ 0.073

(c) The probability that she will miss exactly three items

P(N(2)-N(0)=3) = e²*² ×(2×2)³/(3)!

≈ 0.195

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Answer:

c on edge

Step-by-step explanation:

its not congruent, i got 100 on quiz btw

Answer:

its C

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = x² - 2x + 5

Yo find f(-2) substitute the value of x that's - 2 into f(x) that is for every x in f (x) replace it with - 2

So we have

f( - 2) = (-2)² - 2(-2) + 5

= 4 + 4 + 5

= 8 + 5

We have the final answer as

Hope this helps you

Answer: 10p + 8c ≤ 300

Step-by-step explanation:

From the question, we are informed that Pepperoni pizza (p ) costs $10 per pizza and cheese pizza (c ) costs $8 per pizza and that the coach has a budget of $300 to spend on the pizza.

The inequality that represents the number of each type of pizza he can purchase without going over his budget would be:

10p + 8c ≤ 300

This shows that the combination of both types of pizza shouldn't be more than $300.