A whale is swimming due north at a speed of 40 kilometers per hour. Just 6 kilometers away,
a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 83
kilometers per hour. How long will it be before they meet?

The slope of the line is given by the equation slope m = 3/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the first point be P = P ( 0 , 1 )

Let the second point be Q = Q ( 2 , 4 )

Now , the slope of the line between the two points is

Slope m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 4 - 1 ) / ( 2 - 0 )

On simplifying the equation , we get

Slope m = ( 3 / 2 )

Therefore , the value of m is 3/2

Hence , the slope of the line is 3/2

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Answer:

x-intercept:  (-56, 0)

y-intercept:  (0, -14)

Step-by-step explanation:

The x-intercept is the point at which the line crosses the x-axis, so when y=0.  To find the x-intercept, substitute y=0 into the given equation:

[tex]\begin{aligned}y=0\implies x+4(0)&=-56\\x+0&=-56\\x&=-56\end{aligned}[/tex]

Therefore, the x-intercept of the given linear equation is:

The y-intercept is the point at which the line crosses the y-axis, so when x=0.  To find the y-intercept, substitute x=0 into the given equation:

[tex]\begin{aligned}x=0\implies 0+4y&=-56\\4y&=-56\\y&=\dfrac{-56}{4}\\y&=-14\end{aligned}[/tex]

Therefore, the y-intercept of the given linear equation is:

According to probability, total number of handshakes will be 36.

Handshakes equal n * (n - 1)/2. This is the case because a handshake between two people is not counted twice and each of the n people can shake hands with n - 1 people (they wouldn't shake their own hand). Any number of people can be calculated using this formula.

The first person will need to shake eight (8) people's hands. Only seven (7) hands will need to be shook by the second person because the first handshake will not be repeated. Due to the same factors as mentioned above, only six (6) people will require a handshake from the third person. This continues until the final person has no one left to shake hands with because everyone has already done so.

The formula to calculate how many handshakes were exchanged is n = 8 + 7 + 6 +... + 1 = 36.

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If frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week.

a. When they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

b. Based on the calculation both of them has the same amount of weight.

a. Weight

Let d represent the number of dieting days for this happen.

Since Frank gains 2 lb a day or a total of 2d lbs and John loses 3 lb a day for a total of 3d lbs

So,

John's weight = Frank's weight

Hence,

208 - 3d = 160 + 2d

Combine like terms

208 - 160 = 2d + 3d

48 = 5d

Divide both side by 5d

d = 48/5

d = 9.6 dieting days

The amount the weigh

Using John equation

Weigh = 208 - 3(9.6)

Weigh = 208 - 28.8

Weigh = 179.2 lbs

b. The amount they both weigh is the same as John weigh 179.2ilb and Frank as weigh the same.

Using Frank's equation

Weigh = 160 + 2(9.6)

Weigh = 160 + 19.2

Weigh = 179.2 lbs

Therefore when they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

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The absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

population mean assumed to be 2925

sample mean = 2515

standard deviation of sample = 585.

sample size = 15

t-score is indicated because the standard deviation is taken from the sample rather than from the population.

t-score = (x - m) / s

x is the raw score

m is the raw mean of the population

s = standard deviation of sample/sqrt (sample size) = 585/sqrt(15) = 151.6217 rounded to 4 decimal places.

degrees of freedom = 15 minus 1 = 14.

t-score = (2515 - 2925)/151.6217 = -2.7123 rounded to 4 decimal places.

you need to know the confidence level.

at a 95% confidence level, the two-tailed critical t-score with 14 degrees of freedom = plus or minus 1.7613 rounded to 4 decimal places.

since the absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol.

A few more constant examples are :

The number of days in a week represents a constant.

Substitute:

m*o+b=18

m+b=20

Apply Zero Property of Multiplication:

b=18

m+b=20

Substitute into one of the equations:m+18=20

Rearrange unknown terms to the left side of the equation:m=20-18

Calculate the sum or difference:m=2

The solution of the system is:

b=18

m=2

The answer is b=18 m=2

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Answer:

v = 1/-3

Step-by-step explanation:

cross multiply

-3v = 1

then:

divide through by the coefficient of v which is -3

-3v/-3 = 1/-3

[tex]-1=\dfrac{1}{3} v[/tex]

Flip:

[tex]\dfrac{1}{3} v=-1[/tex]

Multiply both sides by 3:

[tex]3\times(\dfrac{1}{3} v)=3\times(-1)[/tex]

[tex]\fbox{v = -3}[/tex]

To translate a triangle with vector (-5/2), you need to subtract 5/2 from the x-coordinate and add 2 to the y-coordinate of each vertex of the triangle. This will move the triangle 5 units to the right and 2 units up.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

To translate a triangle with a vector, you can use the vector to adjust the coordinates of the triangle's vertices.

For example, if the triangle has vertices at (x1, y1), (x2, y2), and (x3, y3), you can translate it by the vector (-5/2) by subtracting 5/2 to the x-coordinates of the vertices. The new coordinates of the translated triangle would be (x1-5/2, y1), (x2-5/2, y2), and (x3-5/2, y3).

This will move the triangle 5/2 units to the left along the x-axis.

It is important to note that the translation vector you provided only has one component, which is -5/2. Since the vector only has x component, the translation will only occur along the x-axis and the y-coordinate of the vertices will not change.

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Therefore , the solution of the given problem of triangle comes out to be  A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).

The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.

Here,

The image A'B'C' is formed by our transformation rule, (+3,y-2)

So:

1. Describe the updated coordinates for points A', B', and C'?

In order to locate these new positions, we have:

A' (-23, 2-2)  =>    A'(1, 0) (1, 0)

B' => (-23, 4-2)    =>   B'(1, 2) (1, 2)

C'=> (0+3,0-2) => C'(3,-2) (3,-2)

2. Explain the qualities that would emerge if the respective vertices were linked together by lines.

We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.

The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.

Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.

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It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

Solve the inequities:

k^2-7k+12. 25>0

2. 25y^2-3y+1<0

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

So Whenever you find two conclusions which are false Just check for these two symbols . In Most of the case where two conclusions are false and these two signs are not there respectively than that statement, you can call it as Neither Nor.

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Probability that one of the girls (Piper as well as Sedona) will be able to attend the performance is one in five.

For the stated question-

Out of the six grandchildren, two are to be chosen.

There are 6C2 different ways to choose 2 out of 6 grandchildren.

6C2  = 6! / (6 - 2)!*2!

6C2  = 15

2C1 = 2

There are two different ways to choose one of the two girls.

Number of methods for choosing both girls = 2C2

Number of methods for choosing both girls equals one.

Probability of choosing 1 of the 2 grandchildren is 1/15.

The likelihood of choosing both girls is 2/15.

Probability that one of the females (Piper and Sedona) will be able to attend the performance is:

=  1/15 + 2/15.

= 3/15.

Thus, Probability that atleast one of girls (Piper as well as Sedona) will be able to attend the performance is one in five.

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a) The number of traders who sell only one fruit is given as follows: 88.

b) The number of traders who sell only two fruits is given as follows: 9.

The amounts are obtained using Venn sets in the context of this problem.

The sets are given as follows:

10 sell all three fruits, hence:

A ∩ B ∩ C = 10.

15 vendors sell apples and mangoes, hence:

(A ∩ C) + (A ∩ B ∩ C) = 15

(A ∩ C) = 5.

14 vendors sell apples and oranges, hence:

(A ∩ B) + (A ∩ B ∩ C) = 14

(A ∩ B) = 4.

Hence the number who sell two of them is of:

(A ∩ B) + (A ∩ C)  = 4 + 5 = 9.

50 vendors sell mangoes, hence:

C + (A ∩ C) + (A ∩ B ∩ C) = 50

C = 35.

46 vendors sell oranges, hence:

B + (A ∩ B) + (A ∩ B ∩ C) = 46

B = 32.

40 vendors sell apples, hence:

A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 40.

A + 9 + 10 = 40

A = 21.

Hence the number of vendors who sell only one fruit is given as follows:

A + B + C = 21 + 32 + 35 = 88.

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Answer:

The answer is x=g/6

Step-by-step explanation:

When solving an equation like this, you want to move x over to the left of =, which leaves g, and 6. now always remeber that the next variable, g for instance, will be the one divided by the factor, 6

The Solving we get the difference of the given polynomials [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] as [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]   .

What is a Polynomial ?

The polynomial is defined as the expression that is composed of variables, constants and exponents, which are combined by using mathematical operations such as addition, subtraction, multiplication and division .

Based on number of terms present in polynomial , they can be classified as  monomial, binomial, and trinomial .

For Example : [tex]3x^{2} +4x[/tex]  .

The polynomial is given as : [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] ;

On simplifying the above given polynomial ,

we get ,

= [tex]5x^{3} + 4x^{2} - 6x^{2} + 2x + 9[/tex]

On subtracting the like terms together  in above equation ,

we get ;

= [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]

Therefore , the difference of the polynomials is (d)  [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .

The given question is incomplete , the complete question is

What is the difference of the polynomials?

[tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex]

A. –x³ + 6x² + 9

B. –x³ + 2x² – 9

C. 5x³ – 2x² – 2x – 9

D. 5x³ – 2x² + 2x + 9

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The value of x is 10.66

Complementary angles  is when the sum of two angles is equal to 90 degrees. for example, 30 degrees and 60 degrees are complementary angles.

If the sum of two angles is 90 degrees then we say that they are complementary. Thus, the complement of an angle is obtained by subtracting it from 90. for example the complement of 40° is 90° - 40° = 50°

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

Collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Therefore, the value of x is 10.66

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The sum of all the positive two-digit integers where one of the digits is three times the other is 630.

To arrive at this result, the numbers can be broken down into two groups. The first group consists of numbers with 3 as the first digit, and the second group consists of numbers with 3 as the second digit.

For the first group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9. This gives a sum of 3+6+9+12+15+18+21+24+27 = 135.

For the second group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9 and then reversing the digits. This gives a sum of 30+60+90+12+51+81+21+42+72 = 495.

The total sum of all the positive two-digit integers where one of the digits is three times the other is 135+495 = 630.

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By using the triangular inequality, we will get the possible lengths:

a) 6km < x < 16km

b) 0mi < x < 24mi

c) 15yd < x < 30yd

If A, C, and D are the lengths of the sides of a triangle, then the triangular inequality says that:

A + C > D

A + D > C

C + D > a

Now, if the two sides are 5km and 11 km, and the other side is x, then we can write:

x + 5km > 11km

x + 11km > 5km

11 km + 5 km > x

From these inequalities we can get:

16km > x

x > 11km - 5km

x > 6km

Then the possible lengths of the third side are:

6km < x < 16km

b) Now the sides are 12 mi and 12mi, then the inequalities are:

x + 12mi  > 12mi

12mi + 12mi > x

The first one gives:

x > 0mi

The second:

24mi > x

The possible lenghts are 0mi < x < 24mi

c) 25 yd and 10 yd

Here we will get:

25yd + 10yd > x  ----- >  30yd > x

x + 10 yd > 25yd -------> x > 15yd

The possible lengths are:

15yd < x < 30yd

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The answer choice which represents a number line for the intersection of the given intervals is; (-∞, 2).

The answer choice which represents a number line for the union of the given intervals is; (-∞, ∞).

It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.

Since the given intervals are; (-∞, 2) and [0,∞).

It follows that the intersection of both intervals is the interval; (-∞, 2).

Also, the interval which represents the union of both intervals is; (-∞, ∞).

Hence, the image which represents both scenarios is attached.

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Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.

1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.

2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).

3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.

4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.

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The slope of a logarithmic graph depends on the type of logarithm used.

For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.

For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.

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To create a frequency polygon calculate the midpoint,  locate the midpoints and connect them with lines.

A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.

So, we must determine the midpoint or average of the range for each category.

0 < t < 10 = 5

10 < t < 20 = 15

20 < t < 30 = 25

30 < t < 40 = 35

2. Add a point where the data of the axis Y and X form an intersection.

3. Connect the points.

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Answer:

the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

Step-by-step explanation:

To find out how many minutes it will take for a bus to cover 5km at a speed of 9km/h, we need to use the formula:

time = distance / speed

In this case, the distance is 5 km, and the speed is 9 km/h. To convert the speed to km/min we can divide 9 by 60.

9 km/h = 0.15 km/min (by dividing 9 by 60)

Now we can substitute the distance and speed into the formula:

time = 5 km / 0.15 km/min = 33.33 min

So, the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

It's important to note that in this problem km/h is the speed and the distance is given in km, so you need to convert it to km/min in order to find the time. Also the time you get will be in minutes.

The lower left-hand corner of the graph is the third quadrant.

It contains the negative values of both x and y.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.

Cartesian system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

coordinates

Coordinates are numbers which determine the position of a point or a shape in a particular space.

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Ericka’s mistake is in ''Step 2.''

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Ericka was solving an exponential equation, and upon finishing, she realized her answer was incorrect when she substituted -5 back into her original equation.

Now,

Since, Ericka was solving an exponential equation.

Clearly, The equation is,

⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴

Step 1;

⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴

⇒ 5 ⁹ˣ⁺⁶ = 5 ² ⁽³ˣ ⁻ ²⁴⁾

Step 2;

⇒ 9x + 6 = 2 (3x - 24)

So, Ericka’s mistake is in Step 2.

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On solving the provided question we can say that the new Mean = 610 mean .

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). is 50.

What is mean?

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean).

The mean score is calculated by dividing the total number of tests taken by all of the scores. The mean will therefore rise if you give each test a higher mark. The standard deviation is calculated as the square root of the product of the power of two of all test results, multiplied by the number of tests, and then subtracted from the mean.

Each score you raise by 10 will result in a 10 change in the mean. But as there will be no change in the distance between each score and the mean, the standard deviations will also not change.

Mean = 600

Average deviation is 50.

Scores went up by 10

Mean = 610

Average deviation is 50.

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Answer:

-x

Step-by-step explanation:

3x - y = -2y

add y to both sides

3x = -3y

divide both sides by -3

-x = y

For a roll of paper with dimensions 3 feet cut to any desire length,

a) The value of perimeter when cut to 2.5 feet is 11 feet.

b) The complete table with filled perimeter column is present above . The function notation for perimeter is , P =2(L+ W)

c) P(11) , represents the length of paper cut to 11 feet in this situation. It's value i.e., P(11) = 28 feet .

Perimeter is defined as the sum of all boundary length of any geometry. We have a roll of paper with dimensions 3 feet ( i.e, width) is cut to any length. From, it we conclude that that paper is like quadrilateral shape but not square.

a) when the paper cut in a length of 2.5 feet , so, length (L) = 2.5 feet

The perimeter of quadilateral ( rectangle in this case ) is 2(L+W) so, perimeter

= 2( 2.5 + 3)

= 11.0 feet

b) Now, we have to complete "perimeter coulmn ," in the table and side lengths are provided.

Width (w) = 3 feet

length (l) = 1 feet

perimeter = 2(4) = 8

similarly, side lengths (ft.) perimeter ( ft.)

2.5 11

1 8

2 10

11 28

L 2( L + W)

The functional notation for perimeter is

P = 2(L+W) .

c) P(11) represents the length of paper in feet when the paper is cut at a length of 11 feet . It's value is 28 feet . So, the value of P(11) is 28 feet.

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Complete question:

A roll of paper that is 3 feet wide can be cut to any length.

a. If we cut a length of 2.5 feet, what is the perimeter of the paper?

b. Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation.

c) what does P(11) represent in this situation? What is its value?

Answer:

  36.9°

Step-by-step explanation:

You want to know the pitch angle of a staircase with a riser height of 6 inches and a tread depth of 8 inches.

The tangent of an angle is the ratio of the side opposite to the side adjacent:

  Tan = Opposite/Adjacent

The tangent of the staircase angle to the floor will be the ratio of the riser height to the tread depth:

  tan(α) = (6 in)/(8 in) = 3/4

The angle is found using the inverse tangent function.

  α = arctan(3/4) ≈ 36.9°

__

Additional comment

You need to be a little bit careful here. Different authors define "tread depth" differently. For the purpose of this question, it must be defined as the horizontal distance between corresponding points on adjacent treads, as shown in the attached illustration.

Some authors define tread depth as the distance from the nosing to the riser. If that definition is used, the "run" of the step will be the tread depth less the nosing depth. The pitch angle will be the arctangent of the ratio of riser height to "run".

The tread depth of 8 inches is a little too narrow to be in compliance with some building codes. A more usual minimum is about 10 inches with a riser height of 7 1/2 inches.

Answer:

0.75 tangent 0.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

so

120 = 2x

x = 120 : 2

x = 60

120 = 2 x 60

120 = 120