A presidential candidate plans to begin her campaign by visiting the capitals and three of 43 states. What is the probability that she selects the route of three specific capitals

Answer: To rewrite the fractions 2/3 and 4/15 with the least common denominator (LCD), we need to find the smallest multiple that both denominators, 3 and 15, divide into evenly.

The prime factorization of 3 is 3, and the prime factorization of 15 is 3 * 5.

To find the LCD, we take the highest power of each prime factor that appears in either denominator. In this case, the highest power of 3 is 3, and the highest power of 5 is 5.

The LCD is the product of these highest powers: LCD = 3 * 5 = 15.

Now, we can rewrite the fractions with the least common denominator:

2/3 = (2/3) * (5/5) = 10/15

4/15 = (4/15) * (1/1) = 4/15

Therefore, the fractions 2/3 and 4/15 can be rewritten with the least common denominator as 10/15 and 4/15, respectively.

Step-by-step explanation:

Using the slope-intercept form, the equation of the lines are

a. 2y = x + 9

b. 3y = x + 1

c. y = x - 6

d. y = x + 10

e. y = -1/2x + 1

In the given question, we have the coordinate of a point and the slope of the line.

To determine the equation of the straight line, we have to use the formula of slope-intercept which is given as; y = mx + c.

Plugging the values into the formula.

a. (3, 6) and slope = 1/2

equation of line = y = mx + c = 6 = 1/2(3) + c

6 = 3/2 + c

c = 9/2

The equation of line is y = 1/2x + 9/2 ; 2y = x + 9

b. The point is (2,1) and slope is 1/3

Equation of line is;

y = mx + c

1 = 1/3(2) + c

c = 1 - 2/3

c = 1/3

Equation of line is y = 1/3x + 1/3; 3y = x + 1

c. The point is (4, -2) and slope is 1

y = mx + c

-2 = 1(4) + c

c = -2 - 4 = -6

y = x - 6

d. The point is (-2, 8) and slope is 1

y = mx + c

8 = 1(-2) + c

c = 10

y = x + 10

e. The point is (-4, 3) and slope is -1/2

y = mx + c

3 = -1/2(-4) + c

3 = 2 + c

c = 1

y = -1/2x + 1

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The  names of the siblings from shortest to longest time are:

Rafael= 75min = 1 hour and 15 minutes.

Leanne= 1 hour and 25 minutes

Ray= 1 3/4 =  1 hour and 45 minutes.

To be able to compare 1 hour and 25 minutes with  1 3/4 (1.75 hours), one need convert the minutes to hours. 1 hour is equal to 60 minutes, so 1 hour and 25 minutes is equivalent to 1.42 hours.

1.42 hours is smaller than 1.75 hours. hence Ray has the longest time.

So according to the given information, note that:

Hence, the siblings' names listed from shortest to longest time are Rafael, Leanne, and Ray.

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The line of reflection that would make A'B'C'D' the image of ABCD is line 3

From the question, we have the following parameters that can be used in our computation:

Rectangles ABCD and A'B'C'D'

Also, we can see that

Both rectangles are in opposite quadrants

This means that the line of reflection must be slant line in the adjacent quadrants

In this case, the line is line 3

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The velocity represented by vector AC of Michelle's canoe is approximately option C. 11.2 miles per hour.

To determine the velocity, represented by vector AC, of Michelle's canoe, use the concept of vector addition.

Break down the motion into its components:

1. Paddling due east at 10 miles per hour: This motion can be represented by a vector pointing in the positive x-direction with a magnitude of 10 mph.

2. Wind blowing due south at 5 miles per hour: This motion can be represented by a vector pointing in the negative y-direction with a magnitude of 5 mph.

To find the resultant velocity, add these two vectors. Using the Pythagorean theorem, calculate the magnitude of the resultant velocity:

AC² = AB² + BC²

AB (paddling east) = 10 mph

BC (wind blowing south) = -5 mph (negative sign due to opposite direction)

AC² = (10 mph)² + (-5 mph)²

AC² = 100 mph² + 25 mph²

AC² = 125 mph²

Taking the square root of both sides:

AC ≈ √(125) mph

AC ≈ 11.2 mph (rounded to the nearest tenth)

Therefore, the velocity represented by vector AC of Michelle's canoe is approximately 11.2 miles per hour.

The correct answer is option C: 11.2 miles per hour.

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Answer:

[tex]x^2+2y=1[/tex]

Step-by-step explanation:

The equation of a parabola with a vertical axis of symmetry,

focus (h, k+p), and directrix x=h-p is given by:

[tex](x - h)^2 = 4p(y - k)[/tex]

In this case, the focus is (0, 1) and the directrix is x =3.

Comparing this to the general equation,

we have

h = 0, k = 1, and x = h - p = 3.

From x = h - p, we can solve for p:

3 = 0 - p

p = -3

Substituting the values of h, k, and p into the equation, we get:

[tex](x - 0)^2 = 4(-3)(y - 1)[/tex]

Simplifying further:

[tex]x^2 = -12(y - 1)[/tex]

[tex]x^2=-12y+1[/tex]

[tex]x^2+12y=1[/tex]

Therefore, the parabola equation is [tex]x^2+2y=1[/tex]

Answer:

See below for answers and explanations

Step-by-step explanation:

[tex]\displaystyle \lim_{x\rightarrow1^{-}}f(x) = 4-(1)-(1)^2=4-1-1=3-1=2\\\\\lim_{x\rightarrow1^{+}}f(x) = 2(1)-1=2-1=1\\\\\lim_{x\rightarrow1}f(x) = DNE[/tex]

Note that [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)[/tex] represents the left-side limit (so the limit of f(x) as x approaches 1 from the left), and [tex]\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex] represents the right-side limit (so the limit of f(x) as x approaches 1 from the right)

Because [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)\neq\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex], then [tex]\displaystyle \lim_{x\rightarrow1}f(x)=DNE[/tex]

I hope this helped!

Answer:

carnival one
elevation = SWT
depression = RTW

deer one
elevation = ABC
depression = DCB

Step-by-step explanation:

Answer:

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

Given a right triangle with two legs known.

Find the missing angle using tangent function:

Substitute values to get:

Answer: B

Step-by-step explanation: 63.3 in^2

The two other positive angles of rotation that take Point A to Point B on the unit circle is (5π/6) and (5π/6) + 2π .

Given data ,

To find two other positive angles of rotation that take Point A to Point B, we need to consider the angle values that yield the same coordinates as (1, 0) after rotating counterclockwise.

The position of Point A is (1, 0) on the unit circle.

Now, let's find the coordinates of Point B after rotating (7π/6) radians counterclockwise.

To rotate counterclockwise by (7π/6) radians, we can subtract (7π/6) from the angle of Point A. So, the angle for Point B would be:

Angle of Point B = 0 - (7π/6) = - (7π/6)

Now , for positive angles of rotation, we can add multiples of 2π to the angle of Point B while keeping the same coordinates. Adding 2π to the angle gives us:

Angle of Point B = - (7π/6) + 2π = (5π/6)

Hence , two other positive angles of rotation that take Point A to Point B are (5π/6) and (5π/6) + 2π. Both of these angles yield the same coordinates as Point B, which is (1, 0) on the unit circle.

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Answer:

[tex]a_{n}[/tex] = - 7n + 47

Step-by-step explanation:

there is a common difference between consecutive terms , that is

33 - 40 = 26 - 33 = - 7

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 40 and d = - 7 , then

[tex]a_{n}[/tex] = 40 - 7(n - 1) = 40 - 7n + 7 = - 7n + 47

Answer:

Step-by-step explanation:

Hello!

We want to know the area of the original circle - the now circle.

The original circle's diameter is 110 meters.

To figure out the area you use this formula: [tex]r^2*pi[/tex]

The diameter is 107 meters, so the equation is [tex]55^2[/tex][tex]*\pi[/tex].

The area is about 9503.3 meters.

The next area is the "now circle".

The now circle's diameter is 107 meters.

When you use this formula, you end up with  [tex]53.5^2*\pi[/tex].

The area is about 8892 meters.

So it's just basic subtraction!

I'll let you figure out the rest.

:)

Answer:

-7/4

Step-by-step explanation:

we can see that every time the value of x increases by 4, the value of y decreases by 7.

let's pick two sets of coordinates (first two will be fine).

that is (-4, 6) and (0, -1)

Slope = (change in y values) / (change in x values)

= (-1 - 6) / (0 - -4)

= -7 / (0 + 4)

= -7/4.

so our slope (gradient) is -7/4

1) The value of A ∪ B is,

A ∪ B = {<, +, =, /, >, x }

2) The value of A ∩ M is,

A ∩ B = {2}

3) The value of B ∩ C is,

B ∩ C = { }

4) The value of M - J is,

M - J = {soap}

5) The complement of set A is,

A' = (to, combat, coronavirus}​

Now, WE can simplify as;

1) We have;

A = {<, +, =, x) and B = {=, +, /, >}

Hence, We get;

The value of A ∪ B is,

A ∪ B = {<, +, =, /, >, x }

2) Given that,

A = {1, 2, 4) and M = {2, 3, 5}

Hence, The value of A ∩ M is,

A ∩ B = {2}

3) Given that;

B = {C, O, U, G, H) and C = {F, E, V, E, R)

Hence, The value of B ∩ C is,

B ∩ C = { }

4) Given that;

M = {soap, alcohol, sanitizer, mask) and J = {alcohol, sanitizer, mask, gloves}

Hence, The value of M - J is,

M - J = {soap}

5) Given that;

U = {Frontliners, sacrifice, their, lives, to, combat, coronavirus) and A = {Frontliners, sacrifice, their, lives)

Hence The complement of set A is,

A' = U - A

A' = (to, combat, coronavirus}​

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Answer:

6

Step-by-step explanation:

The correct answer is C. 6.

If we substitute 6 for x in the equation, we get 4(8-6) = 4(2) = 8.

This is the only value of x that makes the equation true.

Answer:

The median is the middle value in the set. Since there are 5 values in this set, the middle value is the third value, which is 6.

Therefore, the median of the set {2, 4, 6, 8, 10} is 6.

Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).

In order to find the missing expression in Step 1, let's analyze the given steps and the final expression.

Step 1: ?

Step 2: -9 + 2 + 3

Step 3: -7 + 3

To find the missing expression in Step 1, we need to work backwards from Step 3 to Step 1.

In Step 3, the expression "-7 + 3" gives us a result of -4.

In Step 2, the expression "-9 + 2 + 3" gives us a result of -4.

So, the missing expression in Step 1 should also evaluate to -4 when performed correctly.

Let's check the available options:

[-10 + -1 + 2] + (2 + 3) = -11 + 2 + 5 = -4

[-8 - 1] + (2 + 3) = -9 + 5 = -4

[-10 + 1] + (2 + 3) = -9 + 5 = -4

[8 + 1] + (2 + 3) = 9 + 5 = 14

Out of the given options, only option 2, [-8 - 1] + (2 + 3), correctly evaluates to -4. Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).

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The value of x in the given figure is 15.

In the given figure

The length of section of chords are given

We have to find the value of x

In order to find the value of x

Apply the intersecting chord theorem,

The intersecting chords theorem, often known as the chord theorem, is a basic geometry statement that defines a relationship between the four line segments formed by two intersecting chords within a circle. It asserts that the products of the line segment lengths on each chord are equal.

Therefore,

From figure we get,

⇒ 10/x = 8/12

⇒ x = 120/8

⇒  x = 15  

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Answer:

Therefore, the expression becomes:

7/1 - 2/6

Now, we need to find a common denominator for the fractions, which is 6:

7/1 - 2/6 = (76)/(16) - 2/6

= 42/6 - 2/6

= (42 - 2)/6

= 40/6

Finally, we can simplify the fraction:

40/6 = 20/3

So, the difference between 5 2/6 and -2 4/6 is 20/3.

Step-by-step explanation:

First, let's subtract the whole numbers: 5 - (-2) = 5 + 2 = 7.

Next, let's subtract the fractions: 2/6 - 4/6 = (2 - 4)/6 = -2/6.

Combining the whole number and fraction results, we have:

7 - 2/6

Now, to simplify this result further, we can express 7 as a fraction with a common denominator of 6:

7 = 7/1

The perimeter of the dilated rectangle C'D'E'F' is 200 units.

To find the perimeter of the dilated rectangle C'D'E'F', we need to determine the new coordinates of its vertices after the dilation.

Given that the scale factor is 5 and the dilation is centered at (0, 0), each coordinate of the original rectangle CDEF will be multiplied by 5 to obtain the corresponding coordinate of the dilated rectangle C'D'E'F'.

The original coordinates of CDEF are:

C (-10, 10)

D (5, 10)

E (5, 5)

F (-10, 5)

To find the coordinates of the dilated rectangle C'D'E'F', we multiply each coordinate by 5:

C' = (-10 × 5, 10 × 5) = (-50, 50)

D' = (5 × 5, 10 × 5) = (25, 50)

E' = (5 × 5, 5 × 5) = (25, 25)

F' = (-10 × 5, 5 × 5) = (-50, 25)

Now, we can calculate the perimeter of the dilated rectangle C'D'E'F' by summing the lengths of its sides.

Length of side C'D':

√[(-50 - 25)² + (50 - 50)²] = √[(-75)² + 0²] = √[5625] = 75

Length of side D'E':

√[(25 - 25)² + (50 - 25)²] = √[0² + 625] = √[625] = 25

Length of side E'F':

√[(25 - (-50))² + (25 - 25)²] = √[75² + 0²] = √[5625] = 75

Length of side F'C':

√[(-50 - (-50))² + (25 - 50)²] = √[0² + 625] = √[625] = 25

Now, we add up the lengths of all four sides to find the perimeter:

Perimeter = C'D' + D'E' + E'F' + F'C'

= 75 + 25 + 75 + 25

= 200

Therefore, the perimeter of the dilated rectangle C'D'E'F' is 200 units.

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If we know that <C is congruent to <E, we can say that: (a). the two triangles are similar by SAS.

from the question, we have the following parameters that can be used in our computation:

The triangles (see attachment)

Two triangles are similar when the ratio of their corresponding sides are equal and their corresponding angles are congruent.

So, we have

Ratio = BC/AC = 6/3 = 2.

Ratio = FE/DE = 4/2 = 2.

Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.

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The correct equations are:

1. Two one-step equations:

[tex]\[3x + 2 = 11\]\[5y - 7 = 18\][/tex]

2. Two equations that contain fractions:

[tex]\[\frac{2}{3}x - \frac{1}{4} = \frac{5}{6}\]\[\frac{3}{5}y + \frac{2}{7} = \frac{1}{3}\][/tex]

3. One equation with distributive property:

[tex]\[2(4x - 3) = 10\][/tex]

4. One equation with decimals:

[tex]\[0.5x + 0.25 = 1.75\][/tex]

5. Real-world problem solved by an equation:

A bakery sells cakes for $[tex]15[/tex] each. Let's say the total cost of cakes sold in a day is $[tex]180[/tex]. We can use the equation [tex]\(15x = 180\)[/tex] to find the number of cakes sold, represented by the variable [tex]x[/tex]. Solving the equation, we find [tex](x = 12\)[/tex]), indicating that the bakery sold [tex]12[/tex] cakes that day.

Here's a basic explanation for the real-world problem:

Imagine there is a bakery that sells cakes for $[tex]15[/tex]each. We want to find out how many cakes the bakery sold in a day if the total revenue from cake sales is $[tex]180[/tex]. To solve this problem, we can use an equation. Let's represent the number of cakes sold as [tex]x[/tex].

The equation [tex]\(15x = 180\)[/tex] is used to express that the total cost of the cakes sold [tex](\$15\ per \ cake)[/tex] is equal to $[tex]180[/tex]. To solve the equation, we divide both sides by [tex]15[/tex] to isolate the variable [tex]x[/tex]. The equation simplifies to [tex]\(x = 12\),[/tex] which means that the bakery sold [tex]12[/tex] cakes that day.

By using the equation, we can determine the number of cakes sold based on the given information and calculate the desired result.

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The equation is written as z = 7 + (20 -4x²/2)

From the information given, we have that the equations as;

x²-2y=5   ( 1)

4y+z=7     (2)

From equation (1), make y the subject of formula, we have;

-2y= 5 - x²

Divide both sides by the coefficient of the variables, we have;

y = 5 - x²/-2

y = -5 + x²/2

Now, substitute the value of y in (2), we have;

4 (-5 + x²/2) + z = 7

expand the bracket

-20 + 4x²/2 + z = 7

collect the like terms, we have;

z = 7 + (20 -4x²/2)

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Although the rectangles have the same base lengths, the heights and areas are not directly proportional in this case.

Let's denote the base length of both rectangles as 'b'. If one rectangle has a height that is twice the height of the other rectangle, we can denote the heights as 'h' and '2h', respectively.

The area of a rectangle is calculated by multiplying the base length by the height. Therefore, the area of the first rectangle with height 'h' would be A₁ = b * h, and the area of the second rectangle with height '2h' would be A₂ = b * (2h) = 2b * h.

Comparing the two areas, we have A₁ = b * h and A₂ = 2b * h. It is evident that the areas are not proportional because the area of the second rectangle is twice the area of the first rectangle.

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The box that would be able to hold all the cubes if Robin's teacher had 200 cubes is given as follows:

Box B.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

Hence the volumes for each box in this problem are given as follows:

As 216 > 144, Box B is the box that could hold all of the 200 cubes.

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The probability of event B would likely be greater when event A is true, reflecting the tendency of professional basketball players to be taller.

To determine the probabilities in question, we need to consider the information provided and make some assumptions based on general knowledge about the population of the United States.

P(B) when you have no other information:

Without any other information, we cannot accurately determine the probability of event B, which represents "The woman is taller than 5 feet 4 inches." We would need additional data on the height distribution of women in the United States to calculate this probability.

P(B) when you know A is true:

If we know that event A is true, meaning "The woman is a professional basketball player," we can make some assumptions based on the nature of professional basketball players.

Generally, professional basketball players tend to be taller than the average population due to the physical requirements of the sport. Therefore, the probability of event B, "The woman is taller than 5 feet 4 inches," would likely be greater when we know event A is true.

P(B) when you know A is false:

If event A is false, meaning "The woman is not a professional basketball player," we cannot make any definitive conclusions about the probability of event B, "The woman is taller than 5 feet 4 inches." The height of an individual is not solely determined by their profession, so without further information, we cannot determine if event B is more or less likely when event A is false.

In summary, based on the given information, we can conclude that the probabilities of event B are not equal under different scenarios. The probability of event B would likely be greater when event A is true, reflecting the tendency of professional basketball players to be taller. However, without any other information, we cannot determine the probability of event B or make comparisons when event A is false.

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Length of JN = 10

x = 6

Given ,

S is the center of the circle.

JK = 20

LM = 3x + 2

SN = 12

SP = 12

Now ,

SN and SP are perpendicular to the chords JK and LM respectively .

Perpendiculars drawn from the center of circle to the chords bisect chords into two equal halves .

Thus,

JN = JK/2

JN = 10

Now join SJ,

In ΔSJN ,

Apply pythagoras theorem,

SN² + NJ² = SJ²

12² + 10² = SJ²

SJ = 14.52

SJ =Radius of the circle .

Now,

LP = LM/2

LP = 1.5x + 1

Now join  SL,

In ΔSLP

SP² + PL² = SL²

SL = SJ (radius of circle)

So,

12² + (1.5x + 1)² = 244

x = 6

Hence the value of x is 6 and JN is 10 .

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