The mass of a tumor grows at a rate proportional to its size. The first measurement of its size was 4. 0 grams. Four months later its mass was 6. 76 grams. How large was the tumor six months before the first measurement? If the instrument can detect tumors of mass 1 gram or greater, would the tumor have been detected at that time?

Required value of s(4), s(7), s(5), s(9) are V(4) + C, V(7) + C, V(5) + C, V(9) + C respectively where c is the constant.

To determine the values of s(t) at different time points, we need to integrate the velocity function v(t) with respect to time. Based on the values you provided, it seems like you have already performed the integration correctly. However, since the values you provided are the definite integrals, we need to find the antiderivative or the indefinite integral of the velocity function to determine s(t) explicitly.

Let's assume the indefinite integral of v(t) is V(t). Then, we have:

s(t) = V(t) + C

where C is the constant of integration. To determine the constant C, we can use the initial condition s(0) = -3. Substituting t = 0 into the equation, we get:

s(0) = V(0) + C

-3 = V(0) + C

Since the constant of integration is the only unknown term, we can solve for C:

C = -3 - V(0)

Now, we can find the position function s(t) for different values of t using the indefinite integral and the constant C:

s(4) = V(4) + C

s(7) = V(7) + C

s(5) = V(5) + C

s(9) = V(9) + C

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If the point (3, -2) were reflected across the y-axis what would be the new y-coordinate is same as before, which is -2.

If a point (x, y) is reflected across the y-axis, its x-coordinate becomes its opposite (-x), while its y-coordinate remains the same.

In this case, the point is (3, -2). If we reflect this point across the y-axis, its x-coordinate will become its opposite, which is -3. The new coordinates of the reflected point will be (-3, -2).

Therefore, the new y-coordinate is still -2, as the point is only being reflected across the y-axis and not moving up or down in the y-direction. The change is only in the x-coordinate, which becomes its opposite.

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Answer:

\(0.1\)

Step-by-step explanation:

\(1-0.9\)

\(=0.1\)

Answer:

0.1

WHY DO I HAVE TO WRITE AT LEAST 20 CHARACTERS?!?!?!?!?!?!?!?! THIS IS MAD!!!

The required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line is called a parabola.

Given that, a parabola has the directrix x=6 and the focus (3,-5), we need to find the equation of the parabola,

The standard form of a left-right parabola is given as:

4p(x-h) = (y-k)²

Focus = (p+h, k)

Therefore,

h+p = 3....(i)

Directrix =

x = h-p

h-p = 6...(ii)

Solving the equations we get,

h = 9/2

p = -3/2

Substitute into the standard form:

4p(x-h) = (y-k)²

4(-3/2)(x-9/2) = (y+5)²

-6(x-9/2) = (y+5)²

\(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

Hence, the required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

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The question is incomplete so, i solved for the attached question

Answer:

4.5

Step-by-step explanation:

60.82 kilos are equal to 134 pounds. To convert from pounds to kilogram multiply the amount of pounds by 0.45359237 because one pound is equivalent to 0.45359237 kilogram .

134 lbs * 0.45359237 = 60.82 kg

It's easy to convert 134 pounds to kilos. Simply multiply the number of pounds by 0.45359237 to convert from pounds to kilogrammes. One pound is equal to 0.45359237 kilogram .134 lbs multiplied by the an

0.45359237 in this instance equals 60.82 kilos. Hence, 134 pounds are equivalent to 60.82 kilos.  You would just reverse the process and divide the amount of kilogram by 0.45359237 to convert from kilogram to pounds. If you were to convert 90 kilogram to pounds, for instance, you would divide 90 by 0.45359237, which would give you 199.6 lbs. It only takes a fundamental grasp of multiplication and division to convert between the two units.

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We have to find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1.

To find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1, we have to integrate x^(1/2) and x^(1/3) with respect to x. That is, Area = ∫0¹ [x^(1/2) - x^(1/3)] dx= [2/3 x^(3/2) - 3/4 x^(4/3)] from 0 to 1= [2/3 (1)^(3/2) - 3/4 (1)^(4/3)] - [2/3 (0)^(3/2) - 3/4 (0)^(4/3)]= 0.2857 square units

Therefore, the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1 is 0.2857 square units. Note: The question  but the answer has been provided in the format requested.

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The graph with a line y+3=2(x+3) is

A coordinate plane with a line passing through the points (0, 3) and (-2, -1) with a slope of 2.

The answer is the fourth option: the slope of the line y - 4 = 5/2(x - 2), is

To find the graph that matches the equation y+3=2(x+3), we need to rewrite the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

y + 3 = 2(x + 3)

y + 3 = 2x + 6

y = 2x + 6 - 3

y = 2x + 3  slope-intercept form

The equation is now in slope-intercept form, y = 2x + 3,

where

The graph of this equation should be a line that passes through the y-axis at 3 and has a slope of 2. From the attached graph we can see point (-2, -1)

To find the slope of the line whose equation is y - 4 = 5/2(x - 2), we can rewrite the equation in slope-intercept form.

y - 4 = 5/2(x - 2)

y - 4 = 5/2x - 5

y = 5/2x - 5 + 4

y = 5/2x - 1  slope-intercept form

The equation is now in slope-intercept form, y = 5/2x - 1,

where the slope is 5/2.

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Answer:

y = 127 + 5x

Step-by-step explanation:

Today Olivia has $127 in her savings account. She will deposit $5 into the account each week given x < 0

Let x = number of weeks Olivia deposits money.

y = Total pint of money that Olivia has in her account after x weeks

Hence, the function represents the amount in Olivias savings account after x weeks is ;

y = $127 + $5 × x

x < 0

y = 127 + 5x

Answer:

y=2.89

explanation

square root of 24=square root of (6)^2+(y-8)^2

4.89=6+y-8

4.89-2=y

2.89=y

Answer:

C. 164

Step-by-step explanation:

its self explanitory

Answer:

Sorry i really need points you can report me but i just want you to knw that I REALLY need points

Considering all the given information, the probability of a widget being less than or equal to 56 is approximately 0.1587

The formula for converting a value to a standard score, also known as a z-score, is:

z = (x - μ) / σ

Where x is the value of interest, μ is the mean, and σ is the standard deviation.

To find the probability of a widget being less than or equal to 56, we first find the corresponding z-score:

z = (56 - 65) / 9 = -1

We can then use the cumulative distribution function (CDF) of the standard normal distribution to find the probability of a z-score being less than or equal to -1:

P(z ≤ -1) = 0.1587

So the probability of a widget being less than or equal to 56 is approximately 0.1587, or 15.87%.

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Answer:

-8+7x

Step-by-step explanation:

-1-6-1=-8

-3x+10x=7x

Equation employing the slope-intercept method for two points

The slope-intercept version of the equation may be used to calculate the two-point Y-intercept.

The shape of a point-slope is\(\mathbf{Y-Y_{1} = m(X-X_{1})}.\)

Steps to find the y-intercept with two ordered pairs?

Determine the slope using two points.

\(Slope = \frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{Rise}{Run} = \frac{\bigtriangleup Y}{\bigtriangleup X}\)

As an illustration, two points are (3, 5) and (6, 11)

Slope = \(\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{11 - 5}{6 - 3} = \frac{6}{3} = 2\)

In the slope-intercept form of the equation, substitute the slope(m).

\(\\y = mx+b \\y = 2x+b\)

Either point may be substituted in the equation. You may either use (3,5) or (6,11).

\(\\y = 2x+b \\5 = 2(3)+b\)

Find the answer to the equation for b, the line's y-intercept.

\(\\5 \ \ \ = 2(3) + b \\5 \ \ \ = 6 + b \\\underline{-6\ = -6 \ \ \ \ \ \ \ } \\-1 = b\)

Substitute b,  into the equation.

\(\\y = 2x + b \\y = 2x - 1\)

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Step-by-step explanation:

I guess option 4 is the correct answer.

A line, line segment, or ray that divides an angle into two congruent angles is called an angle bisector.

What are supplementary angles example?

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.

What do you mean by angle bisector?

If the angle is divided by the line and the angle is divided such that the angles are equal to each other then the line is called the angle bisector.

The word congruent means equal of the things. In this, the angles are congruent to each other which means the angles are equal to each other.

Thus, the black space is to be filled by the angle bisector.

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Answer:

1st option

Step-by-step explanation:

Calculate the distance using the absolute value function, that is

distance = | 4.7 - (- 11.2) | = | 4.7 + 11.2 | = | 15.9 | = 15.9

or

distance = | - 11.2 - 4.7 | = | - 15.9 | = 15.9

Answer:

The first answer

Step-by-step explanation:

I just know it was the right answer on k12

Answer:70

Step-by-step explanation:30 divided by 6 equals 5. And 420 divided by 6 equals 70

The median number of minutes Alejandra spent working on homework is 30 minutes.

What is median ?

In statistics, the median is a measure of central tendency that represents the middle value in a set of data when the data points are arranged in ascending or descending order. It is the value that separates the higher half and lower half of the data.

Based on the data provided, the median number of minutes Alejandra spent working on homework can be calculated as follows:

Arranging the time spent on homework in ascending order:

22, 22, 38, 40

Since the number of data points is even, the median is calculated as the average of the two middle values. In this case, the two middle values are 22 and 38.

Median = (22 + 38) ÷ 2 = 60 ÷2 = 30

So, the median number of minutes Alejandra spent working on homework is 30 minutes.

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The limit of 8(x) can be computed to be infinity.  This limit is a vertical asymptote as x approaches infinity.

The limit of 8(x) as x approaches infinity is equal to infinity. We can show this by observing that the function 8(x) grows without bound as x approaches infinity. When x gets larger and larger, 8(x) gets larger and larger, and it will never stop growing. This means that there is no finite limit for the function 8(x) as x goes to infinity. Instead, the function approaches infinity.

A vertical asymptote is a straight line that represents a function's behavior near an essential singularity, or a point where a function cannot be defined due to mathematical restrictions. A vertical asymptote can be described as a vertical line x=a, where the function's value either approaches infinity or negative infinity as x approaches a. It is a type of asymptote that occurs when the denominator of a fraction approaches zero while the numerator approaches a finite number.

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The given series is of the form $$\sum_{n = 1}^{\infty}6^{n}$$The common ratio, $$r = 6 > 1$$Therefore the series is divergent, since the absolute value of the common ratio is greater than 1.The sum of the series is given by $$S_{n} = \frac{a(1 - r^{n})}{1 - r}$$where $a$ is the first term and $r$ is the common ratio.

The series is divergent, therefore the sum does not exist. That is, the value of $S_{n}$ keeps on increasing, if more and more terms are added, but there is no finite limit to which it tends. Therefore, we can say that the given series is divergent.

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The percentage of people who filed their taxes during the week of tax day is 10%

I can estimate how many people filed their taxes during the week of April 15th using a percentage of 100 is a/b * 100.

A percentage is a portion of a sum divided into 100 equal parts.

Calculate (Number of persons who submitted their taxes during the week of April 15th / total people who filed their taxes that year) times 100 to get the percentage of people who filed during that week.

Let :

a represents the total number of taxpayers during the week of April 15th.

b represents the total number of taxpayers for that year.

The original equation is reduced to

a/b× 100

As an illustration, 100 individuals submitted their taxes the week of April 15th and

Let's say that year, 1000 persons filed their taxes.

= 100/1000 = 10%

Thus, 10% of Americans submitted their taxes during the week of April 15th, or 100 out of 1,000.

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Answer:

6,139,468

Step-by-step explanation:

do the ones tens thpusand place value. write out all the numbers in order then for every 3 numbers put a comma

The range of the data set is, 28

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The data set is,

74, 64, 90, 74, 92, 68, 71

Now, We know that;

Range of data set is calculating by subtracting the lowest value from highest value.

Hence, The range is,

⇒ Highest value - Lowest value

⇒ 92 - 64

⇒ 28

Thus, The value of range = 28

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Answer:

801.66

Step-by-step explanation:

calculator

Answer:

801.6632653061

Step-by-step explanation:

.......

a. This is easily determined from examining the plot. \(p(x)\) is clearly increasing for \(4\le x\le12\) and \(x\ge19\) (more or less).

b. The population was 10000 wherever the plot of \(p(x)\) intersects the horizontal line \(p=100\). This happens twice at around \(x\approx1.5\) and \(x\approx7\).

c. The years 1994 and 2002 correspond to \(x=4\) and \(x=12\), respectively. Judging by the plot, we have \(p(4)\approx50\) and \(p(12)\approx150\), so the average rate of change in the population is

\(\dfrac{p(12) - p(4)}{12 - 4} \approx \dfrac{150 - 50}8 = \dfrac{25}2 = 12.5\)

i.e. the population increased at an average rate of 12,500 fruit bats per year between 1994 and 2002.

d. We have \(p(0)\approx180\) and \(p(20)\approx110\), so the average rate of change over the duration of the study is

\(\dfrac{p(20) - p(0)}{20 - 0} \approx \dfrac{110 - 180}{20} = -\dfrac72 = -3.5\)

i.e. the population decreased at an average rate of 3,500 fruit bats per year between 1990 and 2010.

a. \(4\leq x\leq 12\) and \(x\geq 19\)

b. x ≅ 15 and x ≅ 7 because  the plot of \(p(x)\)  intersects or meets the horizontal line \(p= 100\) at both intervals

c. 12. 5

The population increased at an average rate of 12,500 fruit bats per year between 1994 and 2002

d. -3. 5

The population decreased at an average rate of 3,500 fruit bats per year between 1990 and 2010

a. This is easily determined from examining the plot.  is clearly increasing for  and  (more or less).

\(4\leq x\leq 12\) and \(x\geq 19\)

b. The population was 10000 wherever the plot of \(p(x)\)  intersects or meets the horizontal line \(p= 100\) . This happens twice at x ≅ 15 and x ≅ 7 .

c. The years 1994 and 2002 correspond to x = 4  and x = 12 , respectively.

From the plot, we have p(4) ≅ 50  and p(12)≅ 150

The average rate of change in the population is:

\(\frac{p(12) - p(4)}{12 -4}\)

= \(\frac{150 - 50}{12 - 4}\)

= 12. 5

Thus explains that the population increased at an average rate of 12,500 fruit bats per year between 1994 and 2002.

d. We have p(0) ≅ 180 and p(20)≅ 110, so the average rate of change over the duration of the study is;

= \(\frac{p(20)- p(0)}{20 - 0}\)

= \(\frac{110 - 180}{20}\)

= -3. 5

Hence, the population decreased at an average rate of 3,500 fruit bats per year between 1990 and 2010

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