Susie, Meg, and Jane drive together to visit their grandma. Audit drive for 65 miles,and Meg drives 2 times as far as Susie. Then Jane drives twice as far as Susie and Meg combined. How far did Jane drive

To solve for the width of the rectangle, use the equation width = (2L - 1) / 2. Set up the equation L * width = 91 and simplify it to 2L² - L - 182 = 0. Solve the quadratic equation to find the possible values for L, which will give us the width of the rectangle.

To solve for the width of the rectangle, we can use the equation width = (2L - 1) / 2, where L is the length of the rectangle. Given that the area of the rectangle is 91 square feet, we can set up the equation as L * width = 91. Substituting the first equation into the second equation, we get:

L * ((2L - 1) / 2) = 91

Simplifying the equation, we have:

2L² - L - 182 = 0

We can then solve this quadratic equation to find the possible values for L, which will give us the width of the rectangle.

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The correct equation to solve for the width of the rectangle with an area of 91 square feet and a length that is one foot less than twice its width is 2x^2 - x - 91 = 0. Therefore, the correct answer is option C.

The student's question involves finding the width of a rectangle, given that the length is one foot less than twice its width and that the area of the rectangle is 91 square feet.

We can represent the width of the rectangle with x and the length as 2x - 1. The area of a rectangle is found by multiplying its length by its width, which gives us the equation x(2x - 1) = 91.

Expanding this equation, we get 2x^2 - x - 91 = 0. Therefore, the correct equation to solve for the width of the rectangle is 2x^2 - x - 91 = 0.

The probable question may be:

A rectangle has a length that is one foot less than twice its width. it the area of the rectangle is 91 square feet then which of the following equations could be used to solve for its the width of the rectangle?

O x² + 2x + 91 = 0
O 2x² + x + 91 = 0
O 2x² - x - 91 = 0

O x² - 2x - 91 = 0

Answer:the cost of each CD for a member is $5.25

Step-by-step explanation:

The membership costs $22 per year, and then a member can buy CDs at a reduced price.

Let x represent the cost of each CD for a member.

Let n represent the number of CDs that each member buys. This means that the total cost of buying n CDs for a member for a year would be

22 + nx

If a member buys 17 CDs in one year, the cost is $111.25. This means that

17x + 22 = 111.25

17x = 111.25 - 22 = 89.25

x = 89.25/175 = 5.25

Answer:

r  = 225 Mil/h     speed of the airplane in still air

Step-by-step explanation:

Then:

d  is traveled distance   and r  the speed of the airplane in still air

so the first equation is for a 4 hours trip

as  d = v*t

d  =  4 *  ( r  + 25)    (1)          the speed of tail wind  (25 mil/h)

Second equation the trip back in 5 hours

d  =  5  * ( r  - 25 )    (2)

So we got a system of two equation and two unknown variables  d  and

r

We solve it by subtitution

from equation (1)     d  =  4r  + 100

plugging in equation 2

4r  + 100  = 5r -  125    ⇒   -r  =  -225     ⇒    r  = 225 Mil/h

And distance is :

d  =  4*r  +  100         ⇒ d  =  4 * ( 225)  +  100

d  =  900 +   100

d  = 1000 miles

Pete needs 10.5 ounces of turkey.

Step-by-step explanation:

Given,

Number of friends = 2

One for Pete.

Total sandwiches to be made = 2+1 = 3

Quantity of turkey in one sandwiches = 3.5 ounces

For finding the quantity of turkey for three sandwiches, we will multiply.

Turkey for 3 sandwiches = 3*3.5 = 10.5 ounces

Pete needs 10.5 ounces of turkey.

Keywords: multiplication, addition

Learn more about addition at:

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The 95% confidence interval for the true mean score of all teenage boys is approximately 76,080 to 83,920.

To calculate the 95% confidence interval for the true mean score of all teenage boys, we'll use the formula for the confidence interval:

[tex]\[ \text{Confidence Interval} = \bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \][/tex]

where:

- [tex]\(\bar{x}\)[/tex] is the sample mean,

- Z is the Z-score corresponding to the desired confidence level,

- [tex]\(\sigma\)[/tex] is the population standard deviation, and

- n is the sample size.

For a 95% confidence interval, the Z-score is approximately 1.96.

Given:

- Sample mean [tex](\(\bar{x}\))[/tex] = 80,000

- Population standard deviation (\(\sigma\)) = 20,000

- Sample size (n) = 100

[tex]\[ \text{Confidence Interval} = 80,000 \pm 1.96 \left( \frac{20,000}{\sqrt{100}} \right) \][/tex]

Calculate the standard error (SE):

[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{20,000}{\sqrt{100}} = 2,000 \][/tex]

Now substitute the values into the formula:

[tex]\[ \text{Confidence Interval} = 80,000 \pm 1.96 \times 2,000 \][/tex]

[tex]\[ \text{Confidence Interval} = 80,000 \pm 3,920 \][/tex]

The 95% confidence interval is from 80,000 - 3,920 to 80,000 + 3,920.

Answer:

[tex]AB=9.02\ units[/tex]

[tex]BC=7.45\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

Remember that in a parallelogram opposites sides are parallel and congruent, opposites angles are congruent and consecutive angles are supplementary

step 1

Find the measure of angle ACB

we have

[tex]m\angle BAC=22^o[/tex] ----> given problem

[tex]m\angle ACB=m\angle DAC[/tex] ----> by alternate interior angles

[tex]m\angle DAC=27^o[/tex] ----> given problem

so

[tex]m\angle ACB=27^o[/tex]

step 2

Find the measure of angle ABC

The sum of the interior angles in any triangle must be equal to 180 degrees

In the triangle ABC of the figure

[tex]m\angle BAC+m\angle ACB+m\angle ABC=180^o[/tex]

substitute the given values

[tex]22^o+27^o+m\angle ABC=180^o[/tex]

[tex]49^o+m\angle ABC=180^o[/tex]

[tex]m\angle ABC=180^o-49^o[/tex]

[tex]m\angle ABC=131^o[/tex]

step 3

Find the length side AB

In the triangle ABC

Applying the law of sines

[tex]\frac{AC}{sin(ABC)}=\frac{AB}{sin(ACB)}[/tex]

substitute the given values

[tex]\frac{15}{sin(131^o)}=\frac{AB}{sin(27^o)}[/tex]

[tex]AB=\frac{15}{sin(131^o)}(sin(27^o))[/tex]

[tex]AB=9.02\ units[/tex]

step 4

Find the length side BC

In the triangle ABC

Applying the law of sines

[tex]\frac{AC}{sin(ABC)}=\frac{BC}{sin(BAC)}[/tex]

substitute the given values

[tex]\frac{15}{sin(131^o)}=\frac{BC}{sin(22^o)}[/tex]

[tex]BC=\frac{15}{sin(131^o)}(sin(22^o))[/tex]

[tex]BC=7.45\ units[/tex]

To find the lengths of AB and BC in the parallelogram ABCD, one can use the sine and cosine trigonometric ratios along with the given lengths and angles of the parallelogram. AB is calculated using the sine of angle DAC and the length of AC, while BC is equal to AD, which can be found using the cosine of angle DAC and the length of AC.

The student has a parallelogram ABCD with given measures and needs to find the lengths of sides AB and BC. To find side AB, we can use trigonometric ratios in the triangle ACD, as angle DAC is known and AC is the hypotenuse. For side BC, we could use the fact that opposite sides in a parallelogram are equal, thus BC will equal AD which is the adjacent side to angle DAC in triangle ACD.

For AB, which is the opposite side to angle DAC, we can use:
AB = AC × sin(angle DAC) = 15 × sin(27°).

The specific value can be computed with a calculator.

Since parallelogram ABCD has opposite sides equal:

BC = AD
Therefore, we can find AD using the trigonometric ratio involving the cosine of angle DAC:
AD = AC × cos(angle DAC) = 15 × cos(27°).

The computed value will be the length of side BC.

Answer:

The probability that sum of numbers rolled is a multiple of 3 or 4 is: [tex]\frac{7}{12}[/tex].

Step-by-step explanation:

The sample space for two fair die (dice) is given below:

[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]

From the above table:

Number of occurrence where sum is multiple of 3 = 12

Number of occurrence where sum is multiple of 4 = 9

Total number in the sample space = 36

probability(sum is 3) = 12/36

probability(sum is 4) = 9/36

probability(sum is 3 or 4) [tex]=\frac{12}{36} +\frac{9}{36} \\=\frac{12 + 9}{36} \\=\frac{21}{36}\\=\frac{7}{12}[/tex]

Answer:

25 miles

Step-by-step explanation:

Given: A boat sail 20 miles west of the port and then 15 miles south to an island.

Picture attached.

The distance from port to island could be measured in a straight line. It will form a hypotenous.

∴ we can use Pythogorean theorem to find the distance.

[tex]h^{2} = a^{2} +b^{2}[/tex]

Where, "a" is adjacent= 20 miles and "b" is opposite= 15 miles.

[tex]h^{2} = 20^{2} +15^{2}[/tex]

⇒ [tex]h^{2} = 400+225= 625[/tex]

⇒[tex]h^{2} = 625[/tex]

⇒[tex]h= \sqrt{625}= \sqrt{25^{2} }[/tex]

We know [tex]\sqrt{x^{2} } = x[/tex].

∴[tex]h= 25\ miles[/tex]

∴ Distance of Port from the Island is 25 miles.

Final answer:

Using the Pythagorean theorem, the straight-line distance from the port to the boat, after traveling 20 miles west and 15 miles south, is found to be 25 miles.

Explanation:

The problem presented involves calculating the straight-line distance, or 'hypotenuse', of a right-angled triangle formed by the boat's journey from the port, 20 miles west and then 15 miles south. We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².

Let's apply this formula to find the distance:

The distance travelled west (a) is 20 miles.

The distance travelled south (b) is 15 miles.

We can calculate the straight-line distance using the formula:

c² = 20² + 15²
c² = 400 + 225
c² = 625
c = √625
c = 25 miles

Therefore, the boat is 25 miles away from the port if measured in a straight line.

Answer:

  y = 2x +7

Step-by-step explanation:

We are given two points on the growth curve: (weeks, ounces) = (2, 11) or (4, 15).

These can be used to write the equation of a line using the 2-point form:

  y = (y2 -y1)/(x2 -1x)(x -x1) +y1

  y = (15 -11)/(4 -2)(x -2) +11

  y = 4/2(x -2) +11

  y = 2x +7 . . . . . y = weight in ounces x weeks after birth

_____

Comment on the problem

There are an infinite number of equations that can be written to go through the two given points. A linear equation is only one of them.

Answer:

  3√29 ≈ 16.155

Step-by-step explanation:

The distance formula can be used to find the length of the given side.

  d = √((x2-x1)^2 +(y2-y1)^2)

  PQ = √((3-1)^2 +(10-5)^2) = √(4 +25) = √29

The equilateral triangle has three same-length sides (the literal meaning of "equilateral"), so the perimeter is ...

  Perimeter = 3×PQ = 3√29

To find all x that satisfy the inequality (2x + 10)(x + 3) < (3x + 9)(x + 8), we expand and simplify the inequality, solve for x by considering the sign of each factor, and express the answer in interval notation. The solution is (-7, -6).

To find all x that satisfy the inequality (2x + 10)(x + 3) < (3x + 9)(x + 8), we will first expand and simplify the inequality. Then, we will solve for x by considering the sign of each factor.

The interval notation for the solution is (-7, -6). This means that all values of x between -7 and -6 (exclusive) satisfy the inequality.

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Answer:

ADB=72˚. base angles in an isosceles triangle are equal  

72+72=144  180-144=36  BAD=36 ˚Angles in a triangle =180˚

180-72=108˚ BDC=108˚ angles on a straight line=180˚

Step-by-step explanation:

only three marks for this one

By exploiting the properties of isosceles triangles and the sum of angles in a triangle, we deduce that triangle BCD is isosceles with BC = BD.

The student is asking how to prove that triangle BCD is isosceles given that triangles ABC and ABD are also isosceles with AB = BC and AB = AD, respectively, and angle ABD = 72 degrees. We can begin by noting that the sum of the angles in any triangle is 180 degrees. Because triangle ABD is isosceles with AB = AD, the angles ABD and ADB are equal, and since angle ABD is 72 degrees, angle ADB is also 72 degrees. Therefore, angle BAD, the remaining angle in triangle ABD, must be 180 - 72 - 72 = 36 degrees.

Since triangle ABC is also isosceles with AB = BC, angles ABC and BAC are equal. Angle BAD is part of angle BAC, which means angle BAC is also 36 degrees (since they both include angle BAD). Consequently, angle ABC is 36 degrees. The base angles of an isosceles triangle are equal, so angle BCA must also be 36 degrees. Because ABC is isosceles with AB = BC, and we have determined that angles ABC and BCA are equal, we conclude that angles BCD and CBD must also be equal, making triangle BCD isosceles, with BC = BD.

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Answer:

B. Yes, because 14.18/11.71 < 2.

Step-by-step explanation:

When the ratio of the largest sample standard deviation to the smallest sample standard deviation is less than 2, the condition is said to be met.

Step-by-step explanation:

Front footage of first lot = 180 ft

Area of each side lot = 19000 ft²

Depth of each side lot = 200 ft

We have

           Area = Depth x Front footage

           19000 = 200 x Front footage

           Front footage = 95 ft

Total front footage = Front footage of first lot + 2 x Front footage of each side lot

Total front footage = 180 + 2 x 95

Total front footage = 180 + 190

Total front footage = 370 ft

The total front footage of all three lots is 370 ft

Answer:

x = π/6, π/2, 5π/6, 3π/2

Step-by-step explanation:

cos x = sin(2x)

Use double angle formula.

cos x = 2 sin x cos x

Move everything to one side and factor.

cos x − 2 sin x cos x = 0

cos x (1 − 2 sin x) = 0

Set each factor to 0 and solve.

cos x = 0

x = π/2, 3π/2

1 − 2 sin x = 0

sin x = 1/2

x = π/6, 5π/6

The total solution is:

x = π/6, π/2, 5π/6, 3π/2

Final answer:

The solutions to the equation cos x = sin 2x in the interval [0, 2π) are π/6, π/2, 5π/6, and 3π/2, derived by using the identity sin 2x = 2 sin x cos x and considering cases for cos x = 0.

Explanation:

To find all solutions to the equation cos x = sin 2x in the interval [0, 2π), we first need to use a trigonometric identity to express both sides of the equation with either sine or cosine. The identity sin 2x = 2 sin x cos x can be used here. Substituting it into our original equation, we get:

cos x = 2 sin x cos x

To solve this equation, we can divide both sides by cos x, given that cos x ≠ 0:

1 = 2 sin x

sin x = 1/2

Using the unit circle or trigonometric tables, we know that sin x takes the value of 1/2 at x = π/6 and x = 5π/6 in the interval [0, 2π). Additionally, we must consider the case when cos x = 0 to avoid division by zero. This occurs at x = π/2 and x = 3π/2, which are also solutions to the original equation given that sin(2(π/2)) = sin(π) = 0 and sin(2(3π/2)) = sin(3π) = 0, which are equal to cos(π/2) and cos(3π/2) respectively. Thus, the complete set of solutions in the interval [0, 2π) is π/6, 5π/6, π/2, and 3π/2.

Yes because the number say on one side

yes because the numbers stay on one side of the number line

Final answer:

Ricky's best time running 200 meters is 23.34 seconds, and his worst time is 23.45 seconds. The difference between his best and worst times is 0.11 seconds.

Explanation:

The question asks what the difference is between Ricky's best and worst times running 200 meters. To find this, we need to identify the fastest (lowest) time and the slowest (highest) time from the provided times: 23.37 sec, 23.45 sec, 23.44 sec, and 23.34 sec. Ricky's best time is 23.34 seconds, and his worst time is 23.45 seconds. The difference between these times is calculated by subtracting the best time from the worst time.

Worst time (slowest): 23.45 sec

Best time (fastest): 23.34 sec

Difference: 23.45 sec - 23.34 sec = 0.11 sec

Therefore, the difference between Ricky's best and worst time is 0.11 seconds.

Answer:

Step-by-step explanation:

You need to pay very close attention to the triangle similarity statement.  This says that triangle NML is similar to triangle NVU.  But if you look at the way that triangle NVU is oriented in its appearance, it's laying on its side.  We need to set it upright so that angle N is the vertex angle, angle V is the base angle on the left, and angle U is the base angle on the right.  When we do that we see that sides NV and NM are corresponding and exist in a ratio to one another; likewise with sides VU and ML.  Setting up the proportion:

[tex]\frac{NV}{NM}=\frac{VU}{ML}[/tex]

Filling in:

[tex]\frac{12}{36} =\frac{9}{9x}[/tex]

Cross multiply to get

324 = 108x

and x = 3

Answer:

129

Step-by-step explanation:

Let a and b be two numbers.

We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as [tex]GCD(a,b)=3[/tex].

Their least common multiple is twelve times one of the integers. We can represent this information as [tex]LCM(a,b)=12a[/tex].

Now, we will use property [tex]GCD(x,y)*LCM(x,y)=xy[/tex].

Upon substituting our given values, we will get:

[tex]3*12a=ab[/tex]

[tex]36a=ab[/tex]

Switch sides:

[tex]ab=36a[/tex]

[tex]\frac{ab}{a}=\frac{36a}{a}[/tex]

[tex]b=36[/tex]

Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.

The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.

Similarly 96 is also not co-prime with 12 after dividing by 3.

We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.

Let us add 36 and 93 to find the largest possible sum of the required two integers as:

[tex]36+93=129[/tex]

Therefore, the required largest possible sum of the two integers is 129.

Answer:

YES

NO

NO

Step-by-step explanation:

The given polynomial is: [tex]$ f(x) =  x^3 + 4x^2 - 25x - 100 $[/tex]

(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.

To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.

∴ f(5) = 5³ + 4(5)² - 25(5) - 100

        = 125 + 100 - 125 - 100

        = 225 - 225

        = 0

We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.

Now, to check (x + 2) is a factor.

i.e., to check x = - 2 satisfies f(x) or not.

f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100

      = -8 + 16 + 50 - 100

     = -108 + 66

     ≠ 0

Therefore, (x  + 2) is not a factor of f(x).

To check (x - 4) is a factor.

∴ f(4) = 4³ + 4(4)² - 25(4) - 100

        = 64 + 64 - 100 - 100

        = 128 - 200

        ≠ 0

Therefore, (x - 4) is not a factor of f(x).

Answer:

The answers are (x-5) YES (x+2) NO (x-4) NO

Step-by-step explanation:

I took the test :)

Answer:

36.5

Step-by-step explanation:

s² = [∑(min value - median value)² + (max value - median value)²] / (N - 1)

s² = [(23 - 59.5)² + (96 - 59.5)²] / (3 - 1)

s² = 2664.5 / 2

s² = 1332.25

s = √1332.25

s = 36.5

Answer:

'x'  and 'y' have a positive association between them.

Step-by-step explanation:

We can see in the given data that as 'x' remains  constant or increases by 1 unit, or two units in it's two consecutive values, in each of the cases 'y' increases by 1 unit.

Hence, 'x'  and 'y' have a positive association between them.

Answer:

Step-by-step explanation:

Positive and negative association describe a relation between variables about a scatter plot.

A positive association happens when one variable increases while the other one also increases.

A negative association happens when one variable decreases while the other variable increases.

It's important to know that the variable that always increases is the independent variable, it increases no matter what.

In this case, we could say that we have a positive association, because while x increases, y also increases.

You could notice that there's some repetitive number. That's normal because a scatter plot doesn't describe a perfect linear relation at the beginning, actually, it's a bit messy, however, from such data we construct a linear relationship which is called "linear regression".

Therefore, the right answer is C.

Answer: The debt-to-equity ratio

Step-by-step explanation:

The debt-to-equity ratio is a company's debt as a percentage of its total market value. If your company has a debt-to-equity ratio of 50% or 70%, it means that you have $0.5 or $0.7 of debt for every $1 of equity

Answer:

[tex]T_{9hr}=-8 C[/tex]

[tex]T_{12hr}=-6 C[/tex]

[tex]T_{15hr}=-3 C[/tex]

[tex]T_{21hr}=-12 C[/tex]

Step-by-step explanation:

The initial temperature at 9 am:

[tex]T_{9hr}=-8 C[/tex]

At 12 hr is 2 degrees higher:

[tex]T_{12hr}=T_{9hr}+2 C=-6 C[/tex]

At 15 hr is 3 degrees higher than 12hr:

[tex]T_{15hr}=T_{12hr}+3 C=-3 C[/tex]

Finally, at 21 hr, is 9 degrees lower than 15 hr:

[tex]T_{21hr}=T_{15hr}-9 C=-12 C[/tex]

Answer:

C. 4

Step-by-step explanation:

f(c) = 28 = 2x² - 4

28 = 2x² - 4

32 = 2x²

16 = x²

±4 = x

x = 4

c = 4

Answer:

Option c) is correct

ie., c=4 represents the value of c suchthat function  [tex]f(c)=28[/tex]

Step-by-step explanation:

Given function f is defined by [tex]f(x)=2x^{2}-4[/tex]

To find the value of "c" such that  [tex]f(c)=28[/tex]

Therefore put x=c in the given function as

[tex]f(x)=2x^{2}-4[/tex]

[tex]f(c)=2c^{2}-4[/tex]

and we have [tex]f(c)=28[/tex]

Now equating the two functions

[tex]f(c)=2c^{2}-4=28[/tex]

[tex]2c^{2}-4=28[/tex]

[tex]2c^{2}=28+4[/tex]

[tex]c^{2}=\frac{32}{2}[/tex]

[tex]c^{2}=16[/tex]

[tex]c=4[/tex]

Therefore [tex]c=4[/tex]

Option c) is correct

ie., c=4 represents the value of c suchthat function  [tex]f(c)=28[/tex]

Answer: A. See photo for work.

Step-by-step explanation:

Answer:the cost of one burger is $1.4 and the cost of one fry is $1.6

Step-by-step explanation:

Let x represent the cost of one burger.

Let y represent the cost of one fry.

A man buys 3 burgers and 2 jumbo deluxe fries for $7.40. This means that

3x + 2y = 7.4 - - - - - - - - - 1

A woman buys one burger and 4 jumbo deluxe fries for $7.80. It means that

x + 4y = 7.8 - - - - - - - - -2

Multiplying equation 1 by 1 and equation 2 by 3, it becomes

3x + 2y = 7.4

3x + 12y = 23.4

Subtracting

- 10y = - 16

y = - 16/- 10 = 1.6

Substituting y = 1.6 into equation 2, it becomes

x + 4 × 1.6 = 7.8

x = 7.8 - 6.4 = 1.4

Understanding the representativeness of samples in surveys is crucial for drawing meaningful conclusions. In these examples, the lack of information about the characteristics of Remy's readers and the undercoverage bias in the radio station survey make the conclusions unreliable.

The question is about the representativeness of samples in surveys. In the case of Remy's blog survey, the fact that only female readers responded and that more information about their characteristics is needed suggests that no meaningful conclusion is possible without knowing something more about the characteristics of Remy's readers.

In the case of the local radio station survey, convenience sampling was used by only surveying people attending the concert events, which may not accurately represent the entire 20,000 listener population. Therefore, the survey is meaningless because of undercoverage bias.

Answer: [tex]\dfrac{1}{8}[/tex]

Step-by-step explanation:

The total outcomes of tossing a coin = 2

The total number of possible outcomes of flipping coin three times =2 x 2 x 2 = 8

Favorable outcome= (Head, tail, Head) in order

i.e. Number of Favorable outcomes = 1

We know that , Probability = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

Therefore , The required probability [tex]=\dfrac{1}{8}[/tex]

Hence , the probability she gets (Head, tail, Head) in that order[tex]=\dfrac{1}{8}[/tex]

Since it's a line we are talking about linear equation of a form

[tex]f(x)=mx+n[/tex]

where [tex]m[/tex] is slope and [tex]n[/tex] is y-intercept.

Our particular line has a form of

[tex]f(x)=6x+n[/tex]

So we are missing the y-intercept.

To find y-intercept [tex]n[/tex] we insert the coordinates of point [tex]P(x,f(x))\to P(1,4)[/tex] and solve for [tex]n[/tex]

[tex]

4=6\cdot1+n \\

n=-2

[/tex]

So the final form of the line is

[tex]y=6x-2[/tex]

Or as offered in the answers

[tex]y-4=6(x-1)[/tex]

The answer is B.

Hope this helps.

Answer:

The answer to your question is letter C

Step-by-step explanation:

Process

1.- Find two points of the dotted line

   A (0, 4)

   B (3, 5)

2.- Find the slope of the line

   [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

Substitution

   [tex]m = \frac{5 - 4}{3 - 0}[/tex]

   [tex]m = \frac{1}{3}[/tex]

3.- Write the equation of the line

   y - y1 = m(x - x1)

   y - 4 = 1/3(x - 0)

   y - 4 = 1/3x

   y = 1/3x + 4

4.- Write the inequality

    We are interested on the upper area so

    y > 1/3x + 4

Answer: C) y > 1/3x + 4

Step-by-step explanation: The line is dashed hence >. The slope is 1/3 and the y- intercept is 4. This makes the inequality y > 1/3x + 4.

Hope this helps!  :)