What is the slope that passes through (-9,-8) and (-15,-16)

Answer:

3 3/5

Step-by-step explanation:

First, convert 1 4/5 into an improper fraction. It would turn into 9/5, then you can make 2 as 2/1 because any whole number can be put over 1 and still keep the same value. Then, multiply 2/1*9/5 to get 18/5.

The simplest form is 3 3/5.

Hope this helps!

The correct solution to the differential equation 4y+y′′=0 is y=5cos⁡(2x).

To solve this differential equation, we can first write it in the form y′′=-4y. Then, we can use the characteristic equation r^2+4=0 to find the roots of the equation. The roots are r=±2i. Since the roots are imaginary, we know that the general solution to the differential equation will be in the form y=c1cos(2x)+c2sin(2x).

Now, we can compare the given solutions to the general solution to see which one is correct. The first solution, y=3sin(2x), does not have a cosine term, so it is not a solution. The second solution, y=5cos⁡(2x), matches the general solution with c1=5 and c2=0, so it is a solution. The third solution, y=e2x, does not have either a cosine or sine term, so it is not a solution.

Therefore, the correct solution is y=5cos⁡(2x).

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Answer:

61 ft squared

Step-by-step explanation:

To solve the area of this equation, it would be easy to break it into separate rectangles/squares.

The first rectangle will be the one with the dimensions 10 x 4.

This makes the area 40 ft.

The next rectangle will have the dimensions 5 x 3.

This makes the area 15 ft.

The last rectangle will have the dimensions 3 x 2.

This makes the area 6 ft.

Add it all up and you get 61 ft squared.

Answer:

the answer is 61 feet squared

Step-by-step explanation:

The distance between the given 2 points using the distance formula is 4√2.

So, the Distance formula: \(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)

Substitute values in the distance formula as follows:
\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\d=\sqrt{\left(0-(-4)\right)^2+\left((-2)-2\right)^2}\\d=\sqrt{\left(4\right)^2+\left(-4\right)^2}\\\\d=\sqrt{16+16}\\d=\sqrt{32}\\\\d=\sqrt2*2*2*2*2\\d=2*2\sqrt2\\\\d=4\sqrt2\)

Therefore, the distance between the 2 points is 4√2.

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Answer:

$ 251,619.37        

Step-by-step explanation:

Given that :

Loan = $ 268,000

Interest rate = 4.4 % per annum

4.4%/12 months =   0.366% per month

\($3/27$\) : \($3$\) years to pay and \(27\) years amortization

\(27\) years x 12 months = \(324\) months

Calculating the amount for he monthly amortization,

\($A=P \times \frac{r(1+r)^n}{(1+r)^n-1}$\)

\($A=268,000 \times \frac{0.00366(1+0.0366)^{324}}{(1+0.00366)^{324}-1}$\)

\($A=268,000 \times \frac{0.0119}{2.266}$\)

A = 1407.41

Therefore, the future value is given by :

\($FV=PV(1+r)^n-P\left[\frac{(1+r)^n-1}{r}\right]$\)

where, FV = future value ( balloon balance)

            PV = present value (original balance)

            P = payment

            r = rate per payment

            n = number of payments

\($FV=268,000(1+0.00366)^{36}-1407.41\left[\frac{(1+0.00366)^{36}-1}{0.00366}\right]$\)

\($FV = 305670.10- 54050.73 $\)

FV = 251619.37

Therefore, Stuart's balloon payment will be $ 251,619.37

Answer:

39858075

Step-by-step explanation:

Hello,

One basic way to see it is to compute the values.

   75 = 25 * 3

   225 = 75 * 3

   675 = 225 * 3

   etc ...

We can notice that this is multiplied by 3 every 10 years so we can compute as below.

year         population

1970 25

1980 75

1990 225

2000 675

2010 2025

2020 6075

2030 18225

2040 54675

2050 164025

2060 492075

2070 1476225

2080 4428675

2090 13286025

2100 39858075

So the correct answer is 39858075

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

c

Step-by-step explanation:

i think

Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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Answer:

This is like asking x/-x = -1, where x∈N.

No matter what number you choose that is a nonzero number, negative or positive when divided by its negated self will always be -1. Therefore this statement is always true.

x=3 i guess thats it

The justification for each step in the flowchart proof is given as:

A. given

B. definition of congruent

C. definition of bisect

A segment that divides an angle into two equal halves is known as an angle bisector.

In the image attached below, we want to prove that BC is an angle bisector of angle ABD.

The following justofy each step in the flowchart proof:

m∠ABC ≅ ∠CBD (given)

m∠ABC ≅ ∠CBD (definition of congruent)

BC bisects ABD (definition of bisect)

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Answer:

Step-by-step explanation:

Answer:

C.

yes; y = 1.8x

Step-by-step explanation:

Answer for the question :

Yes, Y varies directly with X, and the equation is :

Y = 1.8X

NOTE : For every value of X, when you multiply them with 1.8, you will get the corresponding Y.  

Y = 1.8 x X

5.4 = 1.8 x 3

12.6 = 1.8 x 7

21.6 = 1.8 x 12   (Q.E.D.)

That’s the answer, good luck in solving the question!

:-)

ideal all you ought to do is to divide the y via potential of x and u get the equation working occasion #a million y=32 / x=4 then u have y/x=32/4 ----> y=8x and do the comparable indoors something so #2 y=-20 & x=-20 so y/x=-20/-20 y=x etc

The linear equation is given as y = 1.8x, Then the correct option is C.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

The table is given below.

x         y

3      5.4

7      12.6

12     21.6

Then the linear equation is given as,

\(\rm (y - 5.4) = \left [\dfrac{5.4-12.6}{7-3} \right] (x-3)\)

Simplify the equation, then we have

y - 5.4 = 1.8(x - 3)

y - 5.4 = 1.8x - 5.4

y = 1.8x

The linear equation is given as y = 1.8x, Then the correct option is C.

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Answer:

-11/3= -3.6 repeating

Step-by-step explanation:

Plz mark B R A I N L I E S T

Answer:

Exact Form:

-11/3

Decimal Form:

-3.6

Mixed Number Form:

NEGATIVE 3 AND 2 THIRDS

Step-by-step explanation:

Answer:

1 7/8

Step-by-step explanation:

KCF method.

\(\sf 3 \dfrac{3}{8}-2\dfrac{1}{4} \div 1\dfrac{1}{2}= \dfrac{27}{8}-\dfrac{9}{4}\div\dfrac{3}{2} \\\\\)

                       \(\sf = \dfrac{27}{8}-\dfrac{9}{4}*\dfrac{2}{3}\\\\=\dfrac{27}{8}-\dfrac{3}{2}\\\\=\dfrac{27}{8}-\dfrac{3*4}{2*4} \ [\text{LCM of 2 and 8 is 8}]\\\\=\dfrac{27}{8}-\dfrac{12}{8}\\\\=\dfrac{27-12}{8}\\\\=\dfrac{15}{8}\\\\=1\dfrac{7}{8}\)

Answer: See the diagram below

Specifically, refer to figure 4.

==========================================================

The set U is the universal set. It represents every teacher. Let's draw this as a rectangle. Divide the rectangle so that one portion represents female teachers, and the other represents male teachers. I'll use a vertical line to divide the universal set.

Now draw a circle such that one portion of the circle is in the "male teacher" region and the other portion of the circle is in the "female teacher" region. Lastly, shade the region inside the circle that is also in the male teacher region. The diagram below shows the step by step process.

Figure 1 is the rectangle representing the universal set, which in this case is the set of all teachers.

Figure 2 splits up set U into female teachers on the left and male teachers on the right.

Figure 3 adds a circle, set M, to represent all math teachers. This circle spans the male and female teacher regions, since we can have either male or female math teachers.

Figure 4 adds labels A,B,C,D such that

There are no gaps or overlaps between any of the A,B,C,D regions. We consider these regions to be mutually exclusive. If a person is in region B for instance, then they cannot be in any other region. This is assuming no person teaches more than one subject. Note how regions A,B,C,D completely fill the set U, and do so without any gaps or overlaps. So we can say that set U is partitioned into those four regions.

lowest control limit (LCL^{R} ) for R chart is equal to 0.068 inches

and 0.068 is less than 1 .So the correct answer is( A) less than or equal  to 1 .

What is  lowest control limit?

The lower control limit on a control chart is a line that runs parallel to the centerline and denotes the value below which any particular data point would be deemed to be outside statistical control due to special cause variation.

Total sample = 25

sample size =  8 observation

mean length of the zippers = 15 inches

average range = 0.5 inches

D3 for R chart = 0.136

Formula =  \(LCL^{R}\) = D₃ R

        Put the values

              R = 0.5 Inches

             D₃ = 0.136

LCL^{R} =  D₃ R

            = 0.136 * 0.5 = 0.068  inches

Thus lowest control limit (LCL^{R} ) for R chart is equal to 0.068 inches

and 0.068 is less than 1 .

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There are 8 different colorings that can be made.

Color each of the six faces of a cube with either blue or red. note that two colorings are regarded the same if the cube looks identical after some rotation.

The number of colorings can be calculated by using the equation 2^6 = 64. This is because each of the six faces of the cube can be colored either blue or red, giving two options for each face.

As there are six faces, the total number of colorings is 2^6 = 64. However, some of these colorings are the same after a rotation, so the total number of distinct colorings is 8.

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Answer:

6x - 9

Step-by-step explanation:

We can use the distributive property to solve.

3(2x - 3)

(3 * 2x) + (3 * -3)

6x - 9

Best of Luck!

3(2x-3)

Multiplying each term in the parentheses by 3

3×2x-3x-3

calculate the product

6x-3×3

multiply the number

6x-9

The depth of trail mix box that is shaped like a rectangular prism must be 2.4 inches.

We are going to use the formula for determining volume to work out the depth of the rectangular prism.

The volume of a rectangular prism is given by the formula:

V = l × w × h

where:

V = the volume

l = the length

w = the width

h = the height.

Given:

w = 7.5 inches

h = 9 inches

V = 162 cubic inches

Now, we are to find the value of d, the depth of the box, which corresponds to the length of the rectangular prism.

Substituting the values into the formula for volume:

162 = d × 7.5 × 9

Simplifying the right-hand side:

162 = 67.5d

Dividing both sides by 67.5, we get:

d = 162 ÷ 67.5

d = 2.4 inches

Therefore, the depth of the box shaped as rectangular prism = 2.4 inches.

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Answer:

c(x) = 5x + 20

Step-by-step explanation:

there is a fixed membership fee of 20$ and each day cost 5$

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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a) Probability P[Y(1) < 0.25, 0.4 < Y(2) < 0.6, Y(3) > 0.8] = 0.25 * 0.2 * (1 - 0.8) = 0.25 * 0.2 * 0.2 = 0.01. b) Subtracting the CDF value at 0.4 from the CDF value at 0.6 gives us the desired probability.

a) To find the probability P[Y(1) < 0.25, 0.4 < Y(2) < 0.6, Y(3) > 0.8], we can use the independence property of the random variables.

Since Y1, Y2, Y3 are independent and uniformly distributed on (0, 1), we can calculate the probability of each event separately and then multiply them together.

The probability that Y(1) < 0.25 is simply 0.25, as Y(1) follows a uniform distribution.

The probability that 0.4 < Y(2) < 0.6 is the difference between the cumulative distribution functions (CDF) evaluated at 0.6 and 0.4. Since Y2 is uniformly distributed, the CDF is simply the difference between the two values: P[0.4 < Y(2) < 0.6] = 0.6 - 0.4 = 0.2.

The probability that Y(3) > 0.8 is 1 - P[Y(3) ≤ 0.8]. Since Y3 is uniformly distributed, P[Y(3) ≤ 0.8] is simply 0.8.

Now, we multiply these probabilities together: P[Y(1) < 0.25, 0.4 < Y(2) < 0.6, Y(3) > 0.8] = 0.25 * 0.2 * (1 - 0.8) = 0.25 * 0.2 * 0.2 = 0.01.

b) To find the probability P[0.4 < Y(2) < 0.6] for Y1, Y2, Y3 being independent and following a Beta(2, 1) distribution, we can use the properties of the Beta distribution.

The probability P[0.4 < Y(2) < 0.6] can be calculated by finding the difference between the cumulative distribution function (CDF) values at 0.6 and 0.4 for the Beta(2, 1) distribution.

Using a statistical software or tables for the Beta distribution, we can find the CDF values corresponding to 0.4 and 0.6 for the Beta(2, 1) distribution. Subtracting the CDF value at 0.4 from the CDF value at 0.6 gives us the desired probability.

Please note that the specific calculations for the Beta distribution require the use of numerical methods or software, as they involve integrating the Beta probability density function.

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Answer:

7/54

Step-by-step explanation:

Answer:

Option b) Use the results from the 2014 survey.

Step-by-step explanation:

Using the results from the 2014 survey can reduce the sample size needed for the new survey, as it provides a good estimate of the population proportion. This reduces the margin of error and increases the confidence level of the new survey.

As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:

\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)

Therefore, t(0) = (3, 3, 0).

To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:

\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)

Substituting 0 for t in r''(t), we have:

\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)

Therefore, r''(0) = (12, 12, 12).

Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:

\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)

\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)

Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

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The situation can be represented by the equation y = 3x

A) How to write an equation for the situation

The given parameters are

Total amount = $30

Cost of bag of popcorn = $5 each

Cost of each drink = $2.5

\(Y=\frac{30-5\times X}{2.5} =12-2\times X\)

Let the bag of popcorn be x and the number of drinks be y

5·X + 3·Y = 30

3·Y = 30 - 5·X

\(Y=\frac{30-5\times X}{2.5} =12-2\times X\)

Y = 12 - 2·X

The point corresponding to the y-intercept is the point that gives the

maximum number of drinks Judy can buy if she does not buy popcorn is

12 drinks. The number of drinks she can buy reduces by 2 for each bag of popcorn she buys, such that she can buy 6 bags of popcorn and no drinks which is the x-intercept.

Using the above equation, the graph of popcorn and drinks bought by

Judy is plotted with MS Excel and attached here

(a)F(x) = P(X ≤ x) = ∫[0, x] f(t) dt

(b) f(x) is equal to the PDF f(x) itself.

(c) The probability that a cellphone is located within a distance of 0.5R from the base station is approximately 0.159 or 15.9%.

Step-by-step explanation:

(a) F(x) is the cumulative distribution function (CDF) of the distance X of a cellphone from a base station, given that cellphone location are randomly distributed within the disk with radius R.

To find F(x), we need to integrate the probability density function (PDF) f(x) over the range [0, x], where x is the distance from the base station:

F(x) = P(X ≤ x) = ∫[0, x] f(t) dt

(b) The PDF f(x) is the derivative of the CDF F(x):

f(x) = d/dx F(x)

To find f(x), we differentiate F(x) with respect to x:

f(x) = d/dx F(x) = d/dx ∫[0, x] f(t) dt

Using the fundamental theorem of calculus, we get:

f(x) = F'(x) = f(x)

Therefore, f(x) is equal to the PDF f(x) itself.

(c) P(x < 0.5R) is the probability that a cellphone is located within a distance of 0.5R from the base station.

To find P(x < 0.5R), we need to integrate the PDF f(x) over the range [0, 0.5R]:

P(x < 0.5R) = ∫[0, 0.5R] f(x) dx

We do not have an explicit formula for f(x) without knowing the distribution of cell phones within the disk. However, if we assume that cellphones are uniformly distributed within the disk, then the PDF of X is given by:

f(x) = (1/πR^2) if 0 ≤ x ≤ R, and 0 otherwise.

Using this PDF, we can find F(x) and P(x < 0.5R) as follows:

F(x) = P(X ≤ x) = ∫[0, x] f(t) dt

= ∫[0, x] (1/πR^2) dt

= x/πR^2 if 0 ≤ x ≤ R, and 1 if x > R.

Therefore, for 0 ≤ x ≤ 0.5R,

P(x < 0.5R) = ∫[0, 0.5R] f(x) dx

= ∫[0, 0.5R] (1/πR^2) dx

= 0.5/π = 0.159.

Hence, the probability that a cellphone is located within a distance of 0.5R from the base station is approximately 0.159 or 15.9%.

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To make the 2% solution of tetracaine hydrochloride isotonic, a 0.9% solution of sodium chloride should be used.

The amount of the 0.9% sodium chloride solution needed can be calculated by setting up a proportion based on the concentration percentages.

Let's assume x represents the volume of the 0.9% sodium chloride solution needed in milliliters.

Since the 0.9% solution is isotonic, it means that the concentrations of tetracaine hydrochloride and sodium chloride should be equal. Therefore, the proportion can be set up as follows:

(0.9 / 100) = (2 / 100) * (x / 30)

Simplifying the proportion, we have:

0.009 = 0.02 * (x / 30)

To solve for x, we can multiply both sides of the equation by 30 and divide by 0.02:

x = (0.009 * 30) / 0.02

x ≈ 13.5 mL

Therefore, approximately 13.5 milliliters of the 0.9% sodium chloride solution should be used in compounding the prescription to make the 2% tetracaine hydrochloride solution isotonic.

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