A line passing through the points (-8, 13) and (-6, 19)

Answer:

4 kilometers is equal to 4000 meters.

Step-by-step explanation:

1 kilometer is equal to 1000 meters, so 4 kilometers is equal to 4 x 1000 = 4000 meters. This is because the prefix "kilo" means 1000, so 1 kilometer is equivalent to 1000 meters.

At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was 0 mg.

A limit is a value that a function or sequence approaches as the input or index approaches a certain value. Limits are a fundamental concept in calculus, and they are used to define important ideas such as derivatives and integrals. They are also used in other areas of mathematics, such as real analysis and mathematical analysis.

The rate at which the drug is being eliminated is the derivative of the amount of drug present at time t. We can write this as:

r(t) = dA(t)/dt = 50(e^-0.1 t - e^-0.20 t) mg/hr

If we integrate both sides of this equation with respect to t, we get:

A(t) = ∫r(t) dt = ∫50(e^-0.1 t - e^-0.20 t) dt

This integral can be evaluated using integration by parts. Let u = e^-0.1 t and dv = e^-0.20 t. Then du = -0.1 e^-0.1 t and v = -1/(0.2) * e^-0.20 t = -5e^-0.20 t. We can then write:

A(t) = -5 ∫e^-0.1 t * e^-0.20 t dt + (1/0.2) ∫e^-0.1 t dt

The first integral on the right-hand side can be evaluated using the substitution y = -0.3t, which gives:

A(t) = -5 ∫e^y dy + (1/0.2) ∫e^-0.1 t dt

The first integral is simply -5e^y, and the second integral is -5e^-0.1 t. Substituting these results back into the expression for A(t) gives:

A(t) = -5(-5e^-0.3 t) + (1/0.2)(-5e^-0.1 t)

Combining constants and simplifying gives:

A(t) = 25e^-0.1 t - 25e^-0.3 t

We are told that all the drug is eventually eliminated, so A(t) approaches 0 as t approaches infinity. This means that the original dose A(0) must be equal to the limit of A(t) as t approaches 0.

Taking the limit as t approaches 0 gives:

A(0) = lim t → 0 [25e^-0.1 t - 25e^-0.3 t]

This limit is equal to 25 - 25 = 0, so the original dose was 0 mg.

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The phrase describes the variable expression 7 ÷ s is the quotient of 7 and s.

The correct option is (d).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Expression: 7 ÷ s

We know that the division results to quotient.

So, the expression shows the 7 is divided by s to give the quotient.

Hence, the answer is the quotient of 7 and s.

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The volume of the cone is 144π units³.

The volume of a cone can be calculated as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore, the height of the cone is 27 units and the radius of the cone is given as 4 units.

Let's find the volume using the formula,

r = 4 units

h = 27 units

Therefore,

volume of a cone = 1 / 3 πr²h

volume of a cone = 1 / 3 × π × 4² × 27

volume of a cone = 1 / 3 × π × 16 × 27

volume of a cone = 432 / 3 π

Therefore,

volume of a cone = 144π

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Answer: 51/100

Step-by-step explanation:

I'm assuming that the numerator is supposed to be a whole number, because there is an infinite number of answers if it is not a whole number. 5/10 can be rewritten as 50/100 by multiplying the numerator and denominator by 10. The only fraction with a whole number numerator between 50/100 and 52/100 is 51/100.  Hope this helped!

The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.

1. The integral is given as an area under a graph.

2. The graph has labeled regions.

3. The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure.

4. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.

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Answer:

Step-by-step explanation:

How to find the mean of the probability distribution: Steps

Step 1: Convert all the percentages to decimal probabilities. For example: ...

Step 2: Construct a probability distribution table. ...

Step 3: Multiply the values in each column. ...

Step 4: Add the results from step 3 together.

In general, the improvements that we can make refer to optimizations that can be applied in a context.

In a particular process or context, the best are optimizations that are done to make something more efficient or to improve the quality of an element.

For example, some improvements that we could make in our community are:

¡Hope this helped!

The probability of the cumulative distribution function  to meet the specification of the components is given by P( X = 0 ) = 0.0304 ,

P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.

As given in the question,

Let probability of the first component to meet the specification be P (M)

= 0.81

And probability of the second component to meet the specification be P (N)

= 0.84

Probability of the first component do not meet the specification be P ( M' )

= 1 - 0.81

= 0.19

Probability of second component do not meet the specification be P(N' )

= 1 - 0.84

= 0.16

X defined the number of components to the meet the specifications

Here X = 0, 1, 2

P( X = 0 ) represents components do not meet any specifications

= P( M' ∩ N' )

= P(M') P(N')   ( Independent )

= 0.19 × 0.16

= 0.0304

P( X= 1) represents components meet only one specification

= P( M∩N') ∪ P( M'∩N)

= P( M∩N') + P( M'∩N)

=  P(M) P(N')  +  P(M') P(N)  

= 0.81(0.16) + (0.19)(0.84)

= 0.1296 + 0.1596

= 0.2892

P( X=2) represents components meet both the specification

= P( M ∩ N )

= P(M) P(N)

= 0.81(0.84)

= 0.6804

Therefore, the probability of the cumulative distribution function is given by P( X = 0 ) = 0.0304 , P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.

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Because the object is moving slowly toward the bottom and the positive y-direction points upward, the object has a positive value for ay.

Motion is the shift in an object's location with regard to time. Motion can be quick or slow, but motion is still present. Due to the significance of motion in the physical world, it is crucial that we pay proper attention to the study of motion. Generally speaking, the following phrases are used to describe motion

With the use of equations and derivations, understanding the numerical of physics can be tedious, but with the aid of graphs, it is both entertaining and simple to understand what the answer is describing.

Since they are used in nearly all of the topics in physics, graphs are essential. Give us more information about various graphs in this article.

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If a radius is drawn to the point of tangency of a tangent line, then the radius is basically perpendicular to the tangent line.

Given that the radius is drawn to the point of tangency of a tangent line.

We are required to fill the blank with the appropriate word.

Radius is basically the line segment which joins the center to any point on the circumference of the circle.

Tangent line is basically a line which is drawn from an outside point on the circumference of the circle.

When the radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.

Hence if a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.

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Answer:

$368 per week

Step-by-step explanation:

[tex]8 \times 40 \times 1.15 = 368[/tex]

The set U can be rewritten by listing its elements as follows:

U = {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}

In this notation, the "..." symbol indicates that the set continues in both the negative and positive direction, and that all integers from negative infinity to positive infinity are included in the set. This notation is commonly used to represent sets of integers or other infinite sets in mathematics.

A line of best fit for this problem is y = 5.08x + 46.59. The number of ice cream cones that you would expect the shop to sell if the temperature one day is 106 degrees is; 585 cones

A graph of the scatter plot and line of best fit is as shown in the attached file.

The temperature in this problem is the independent variable, or x.  This is due to the fact that we are assuming that the particular number of ice cream cones sold will depend on the temperature. Therefore, we can say that the number of ice cream cones will be the dependent variable, or y.

Therefore in our graphing calculator, we will enter temperature in the first list and then the number of cones in the second.

Sequel to drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax + b:

a = 5.08

b = 46.59

Therefore, the equation is;

y = 5.08x + 46.59.

Entering our temperature of 106 degrees, for x gives;

y = 5.08(106) + 46.59

= 585.07

≈ 585

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The sequence  is f(n)=3[tex]n^{2}[/tex]−n.

Sequences are ordered collections of numbers, often known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, thus we may now continue the process. There are formulae for sequences that show us where to locate any given term.

We have 2 10 24 44 70 (which we refer to as the first column)

If we have 10 - 2 = 8, 24- 10 = 14, 44- 24 = 20, and 70- 44 = 26,

(this is second column)

The third column is now 14 - 8 = 6, 20 - 14 = 6, and 26 - 20 = 6.

First, create the second column sum formula.

Sum(x)

S(x)=8+6(x1)=6x+2 is the second digit of the phrase.

Next make the first column formula f(n)

f(n)= 2+[tex]sum_{n-1}[/tex]

=2+(n−1)[3(n−1)+5]

=2+(n−1)(3n−3+5)

=2+(n−1)(3n+2)

=2+3[tex]n^{2}[/tex]+2n−3n−2

=3[tex]n^{2}[/tex]−n

The sequence  is f(n)=3[tex]n^{2}[/tex]−n.

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The differentiation of y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x is cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))

In mathematics, differentiation is the process of finding the derivative of a function. The derivative of a function is a measure of how the function changes as its input (or independent variable) change

Given: y = logx - cosecx + 5ˣ + 3/(x^(3/2))

Thus, the derivative will be:

d/dx [logx - cosecx + 5ˣ + 3/(x^(3/2))]

= d/dx [logx] -  d/dx [logx]  +  d/dx [5ˣ]  +  3d/dx[(x^(3/2))]

= 1/x -  (-cotx)cosecx + log(5).5ˣ + 3(-3/2)x^((3/2) -1)

=  cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))

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Step-by-step explanation:

1 , 14x=-6+21

14x=15 , divide both sides by q4 to get the value of x

x=15/14

2 , x1=x

-x=9-12

-x=-3 , divide both side by -1

x=3

3, 13x=6_61

13x= 55 , divide both sides by 13

x=55/13

4, 1-2x+81=1+81_2x

82_2x=0

-2x=-82 , divide both sides by -2

x=41

So, all of them have a solution

Answer:

There were a total of 7 + 1 + 11 + 5 + 2 + 19 + 9 = 44 voters in this election.

To get a majority, a candidate would need at least 44 / 2 + 1 = 23 first place votes.

The candidate with the most first-place votes is A, with a total of 7 + 1 + 5 = 13 first-place votes.

The candidate with the least first-place votes is X, with a total of 1 first-place vote.

The candidate with the most last-place votes is G, with a total of 9 + 2 + 9 = 20 last-place votes.

The candidate with the least last-place votes is X, with a total of 0 last-place votes.

Step-by-step explanation:

a) The standard error is of: 0.0167.

b) The test statistic is of: 2.99.

c) The p-value is of 0.0013, representing the probability of finding a sample proportion of at least 55%.

At the null hypothesis, it is tested if there is not enough evidence that a majority of the population supports the measure, hence:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that a majority of the population supports the measure, hence:

[tex]H_1: p > 0.5[/tex]

The equation that defines the test statistic is given as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

The values of these parameters in this problem are given as follows:

[tex]p = 0.5, n = 900, \overline{p} = 0.55[/tex]

Then the standard error is calculated as follows:

Standard error = square root (0.5 x 0.5/900) = 0.0167.

Then the test statistic is calculated as follows:

z = (0.55 - 0.5)/0.0167 = 2.99.

We have a right-tailed test, as we are testing if the mean is different of a value, hence the p-value represents the probability of finding a sample proportion of at least 0.55.

Using a z-distribution calculator, with z = 2.99, the p-value is of:

0.0013.

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Answer:

4k because is right is the best answer

The leg-leg (LL) theorem of congruency states that if the legs of a right triangle are equal to the legs of a second right triangle, then the two triangles are congruent.

We know that two triangles are congruent if and only if they have three pairs of equal sides.

In the case of the LL congruence theorem,

the two triangles have two pairs of equal sides (the legs) and one pair of equal angles (the right angles).

Therefore by the Side-Angle-Side (SAS) congruence criterion, the 2 triangles are congruent.

Alternatively

If the legs are of equal length then

Their squares would be equal to

Hence, the sum of these squares too would be equal.

Now taking a root over these would give us the hypotenuse for these triangles, which in turn should be equal.

Hence, by SSS congruence criteria

the triangles would be congruent.

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Answer:

Step-by-step explanation:

5+ 20= 25

Because when you set them up and add them properly you get 25

(Not sure if that was the question you wanted us to answer..)

The scatter plot for provide data is shown above in figure. The slope-intercept form of the equation of the line that best fits the data is

y = - 0.3319 x + 312.16

Scatter charts are similar to line charts in that they use horizontal and vertical axes to represent points of data. However, they have a very specific purpose. The scatterplot shows how much one variable is influenced by another. The relationship between two variables is called their correlation. There are three types of correlation: positive, negative, and none (no correlation).

• Positive correlation: when one variable increases, the other also increases. ...

• Negative correlation: an increase in one variable causes a decrease in the other variable. ...

• No Correlation: nothing displayed

We have the following observations,

X Y

10 20

10 630

30 390

40 160

90 210

100 370

Now , we construct a scatter plot for the provide data. The constructed scatter plot is shown above. As we see in plot that there is no increase or decrease with increasing values of one variable .So, there is no correlation between two variables. Now, equation of the line that best fits the data, A best line of fit never connect all the points on the scatter plot. but it connects only a few points. There will have data points above and below the line. The equation of a line of best fit can be represented as y = mx+b y = m x + b , where m is the slope and b is the y-intercept.

here, y = - 0.3319 x + 312.16

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The linear relationship between the number of shirts, n ,it can sell and the price, p is p = (-1/250)x + 79

The linear equation is

y = mx + b

Where m is the slope of the line

b is the y intercept

Here p is the total price

n is the number of shirts

The equation will be

p = mn + b

The price of 6000 shirts = $55

The price of 8000 shirts = $47

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The slope of the line = (47-55) / (8000-6000)

= -8/2000

= - 1/250

Substitute the point (6000, 55) in the equation

55 = (-1/250)(6000) +  b

55 = -24 + b

b = 55 + 24

b = 79

Substitute the values in the equation

p = (-1/250)x + 79

Therefore, the linear relation in the form of p is p = (-1/250)x + 79

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{48, 55, 73} and  {10, 23, 26} do not represent a right angle triangle.

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

Now,

48² + 53² = 73².

2304 + 2809 = 5329.

5113 ≠ 5329 so do not represents a right-angle triangle.

Similarly,

39² + 80² = 89² represents a right-angle triangle.

42² + 56² = 70² represents a right-angle triangle.

10² + 23² ≠ 26²so do not represent a right-angle triangle.

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The  answer is 7525381507

The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” And the formula is given by [tex]_n C_r=\frac{n !}{r ! (n-r) !}[/tex]        [tex]_n C_r[/tex]= number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Given here, select 8 cards out of a possible 52 thus using the formula we get

[tex]=\frac{52 !}{8 ! (52-8) !}[/tex]

[tex]=\frac{52 !}{8 ! (44) !}[/tex]

= 7525381507

Hence the answer is 7525381507

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Answer:

3, 4, 5

Step-by-step explanation:

The side lengths satisfy the Pythagorean theorem.

If we consider  a pair of integers (a b) and the given operations, then the java program that depicts it is as written below.

The program that carries out the required operations on the pair of integers is;

static LinkedList<Pair<Integer,Integer>> pairs = new LinkedList<Pair<Integer, Integer>>();

   public static String isItPossible(Integer a, Integer b, Integer c, Integer d){

       pairs.addLast(new Pair<Integer, Integer>(a,b));

       while (!pairs.isEmpty()){

           Pair<Integer,Integer> pair = pairs.poll();

           Integer key = pair.getKey();

           Integer value = pair.getValue();

           if(key.equals(a) &&

                   value.equals(b)){

               return "YES";

           }

           int sum=key+value;

           if (sum<=c){

               pairs.addLast(new Pair<Integer, Integer>(sum,value));

           }

           if (sum<=d){

               pairs.addLast(new Pair<Integer, Integer>(key,sum));

           }

       }

       return "NO";

   }

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Complete question is;

Consider a pair of integers, (a, b). The following operations can be performed on (a, b) in any order, zero or more times:

• (a, b)(a + b, b)

• (a, b) → (a, a + b)

Return a string that denotes whether or not (a, b) can be converted to to (c,d) by by performing zero or more of the operations specified above. Example

(a, b) = (1, 1)

(c,d) = (5,2)

Perform the operation (1,1 + 1) to get (1, 2), perform the operation (1 + 2, 2) to get (3, 2), and perform the operation (3+2, 2) to get (5,2). Alternatively, the first operation could be (1+1, 1) to get (2, 1) and so on.

Complete the function is possible in the editor below. isPossible has the following parameter(s): int a: first value in (a, b) int b: second value in (a, b) int c: first value in (c,d) int d: second value in (c,d) Returns: str: Return 'Yes' if (a, b) can be converted to (c,d) by performing zero or more of the operations specified above, or 'No' if not Constraints • 1 sa,b,c,ds 1000

The line with a slope of 1 and y - intercept -7 will have an equation of y = x - 7

Given,

Slope of the line. m = 1

Y - intercept = -7

We have to determine the linear equation for the line;

Linear equation;-

A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here,

Equation of line in slope intercept form;

y = mx + b

Here,

-7 = 1x + b

Let b = y intercept (begins from 0)

Then,

y = x - 7

That is,

The linear equation is y = x - 7

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Given question is improper. Proper question is;

Write a linear equation with a slope of 1 and the y-intercept of -7