Mathematics High School

Which of the following values could represent the probabilities of complementary events and 28% and 82% and 10% and 80%
1/7and2/7
2/5and3/5

Answers

Answer 1
The answer is 2/5 and 3/5 as they both add up to 1.00 or 100%
Answer 2

Answer:

2/5 and 3/5

Step-by-step explanation:

Complementary events have probabilities that sum to 100%, or 1.

28+82 = 110; this is not 100.

10+80 = 90; this is not 100.

1/7+2/7 = 3/7; this is not 1.

2/5+3/5 = 1; this is correct.

Related Questions

How would paying off the lowest outstanding balance credit card first be beneficial over paying off the one with the highest interest rate?

Answers

Final answer:

Paying off the lowest outstanding balance credit card first can be beneficial for motivation and momentum, even if it's not the most mathematically efficient approach.

Explanation:

When paying off credit card debt, it can be beneficial to start by paying off the credit card with the lowest outstanding balance. This approach is called the Snowball Method and is popularized by financial expert Dave Ramsey. The Snowball Method focuses on tackling the smallest debt first, regardless of the interest rate, as it provides a psychological boost and motivates individuals to continue paying off their debts.

By paying off the smallest debt first, you can quickly eliminate one of your credit card balances. This can give you a sense of accomplishment and momentum to continue paying off your other debts. It's important to note that while the Snowball Method may not be the most mathematically efficient approach in terms of saving on interest payments, it can be effective in helping individuals stay motivated and committed to paying off their debts.

The volume, V, of a soap bubble is related to its surface area, A. In cubic centimeters, this relationship is shown by the formula V = 0.094A 3/2. What is the surface area of a bubble with a volume of 5 cm3 ?

Answers

First let's rewrite the volume expression correctly:
 V = 0.094 * (A) ^ (3/2)
 Now we clear the area:
 (A) ^ (3/2) = V / 0.094
 A = (V / 0.094) ^ (2/3)
 We now replace the volume:
 A = (5 / 0.094) ^ (2/3)
 A = 14.14364782 cm ^ 2
 Answer:
 The surface area of a bubble with a volume of 5 cm3 is:
 A = 14.14364782 cm ^ 2

The surface area of a soap bubble with a volume of 5 cm³, given the relationship V = 0.094 [tex]A^{3/2[/tex], can be calculated by rearranging and solving the formula, resulting in an approximate surface area of 36.3 cm².

To find the surface area of a soap bubble with a volume of 5 cm³, using the given relationship V = 0.094 [tex]A^{3/2[/tex], we need to rearrange the formula to solve for A (the surface area). We will take the following steps to find A:

First, divide both sides of the equation by 0.094 to isolate [tex]A^{3/2[/tex] on one side:

[tex]A^{3/2[/tex] = V / 0.094

Next, substitute V = 5 cm³ into the equation:

[tex]A^{3/2[/tex] = 5 / 0.094

Calculate the right-hand side:

[tex]A^{3/2[/tex] ≈ 53.19

Finally, raise both sides of the equation to the power of 2/3 to solve for A:

A = [tex](53.19)^{2/3[/tex]

Calculating the right-hand side gives us the surface area A. After performing these calculations, we find that the surface area of a bubble with a volume of 5 cm³ is approximately 36.3 cm².

Use the quadratic formula to determine the exact solutions to the equation.

x^2−2x−4=0



Enter your answers in the boxes.

x=__ or x=___

Answers

Answer:  " x = 1  + √5 " or " x = 1 − √5" .
______________________________________________________
Given:
______________________________________________________

   " x² − 2x − 4 = 0 " ;
______________________________________________

Solve for "x" by using the "quadratic formula" :

Note:  This equation is already written in "quadratic format" ; that is:

  " ax² + bx + c = 0 " ;  { "a [tex] \neq [/tex] 0" } ;

in which:   "a = 1" {the implied coefficient of "1" ;
                         since "1", multiplied by any value, equals that same value};

                 "b = -2 " ;

                 "c = -4 " ;
_______________________________________________________
The quadratic equation formula:

x = { - b ± √(b² − 4 ac) } / 2a ;   {"a[tex] \neq [/tex]0"} ;
______________________________________________________
Substitute our known values:
______________________________________________________

   →  x = { - (-2) ± √[(-2)² − 4(1)(-4)] } / 2(1) ; 

       →  x  = { 2 ± √(4 − 4(-4) } / 2 ; 

       →  x  = { 2 ± √(4 − (-16) } / 2 ;

       →  x  = { 2 ± √(4 + 16) } / 2 ;

       →  x  = { 2 ± √(20) } / 2 ;

       →  x  = { 2 ± √4 √5} / 2 ;

       →  x  = { 2 ± 2√5} / 2 ;

       →  x = 1 ± √5 ; 

_______________________________________________________
→  "x = 1 + √5"  or  "x = 1 − √5" .
_______________________________________________________

The measure of dispersion which is not measured in the same units as the original data is the
a. variance
b. standard deviation
c. median
d. coefficient determination

Answers

Variance is not expressed in the same units as the original data.

Variance is measured by:

Finding the difference between the mean of a data set and the variables in the data set Squaring this difference Summing up the squares

Because variance is squared, it is no longer the same units as the rest of the data set. For instance, if the data set is in centimeters, the variance will be in centimeters².

In conclusion, the variance of a data set is not measured in the same unit as the data set.

Find out more at https://brainly.com/question/20317994.

Final answer:

The measure of dispersion which is not measured in the same units as the original data is the variance.

Explanation:

The measure of dispersion which is not measured in the same units as the original data is the variance. The variance is a squared measure and does not have the same units as the data. On the other hand, the standard deviation is derived from the variance and it measures the spread in the same units as the data.

Then again, the standard deviation, which is the square foundation of the fluctuation, is estimated in similar units as the first information. It gives a proportion of the spread of the information that is all the more effectively interpretable. The middle is a proportion of focal inclination and doesn't give data about the scattering or spread of the information.

The coefficient of assurance, otherwise called R-squared, is a proportion of how well the relapse line fits the information and isn't straightforwardly connected with scattering.

Complete the statement If x/7 = 5/3, then x+7/7 =?

Answers

Lets get started :)

[tex] \frac{x}{7} = \frac{5}{3} [/tex]
We can cross multiply, to find the value of x
3x = 7 x 5
3x = 35
We have to divide by 3 on either sides to isolate x
[tex] \frac{3x}{3} = \frac{35}{3} [/tex]
3 and 3 cancels out

x = [tex] \frac{35}{3} [/tex]

Then, x + [tex] \frac{7}{7} [/tex]  ( 7 divided by 7 is 1)
[tex] \frac{35}{3} [/tex] + 1   = [tex] \frac{38}{3} [/tex]


Given cos A = 0.25 find angle A in degrees. Round your answer to the nearest hundredth.

34.12°

123.98°

56.78°

75.52°

Answers

we have that
cos A=0.25
so
A=arc cos (0.25)-------> using a calculator----> A=75.5225°
Round to the nearest hundredth-----> A=75.52²

the answer is
the option 75.52°

All side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units. Is this a rigid transformation?

No, there is no one-to-one mapping of all the points of the pre-image to the image.
No, at least one segment length is not preserved, making this a nonrigid transformation.
Yes, the vertices of the pre-image map to the vertices of the image.
Yes, all of the side lengths of the pre-image are proportionate to the image.

Answers

no because at least one segment length is not preserved.
rigid means everything stays the same, but orientation sometimes changes.

No, at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.

What is geometric transformation?

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that, all side lengths of ΔJKL equal 2 units. A transformation maps ΔJKL to ΔJ'K'L'. The length of side J'K' is 5 units.

A transformation that leaves a geometric figure's size or shapes unchanged is known as a rigid transformation. It is a unique type of metamorphosis in which a figure's size or shape is left unchanged.

From the definition, it is obtained that there is no rigid transformation because at least one segment length is not preserved.

Thus, no at least one segment length is not preserved, making this a nonrigid transformation. Option B is correct.

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What is the domain of the relation graphed below? GET 50 POINTS!

Answers

Answer:
domain {-5, -4, -3, 1, 2, 5}

Explanation:
Domain is defined as the inputs to a certain function.
In other words, for a certain function f(x), the domain would be the x values for this function.

Now, the domain for the given graph would simply be all the x values which have a corresponding y-value on the graph which are: -5, -4, -3, 1, 2 and 5

Hope this helps :)

Answer:

Domain is the set of x values

so domain is {-5 , -4 , -3 , 1 , 2 , 5}

describe the vertical asymptotes) and holes) for the graph of y=(x+2)(x+4)/(x+4)(x+1)
A. asymtotes: x=-1 and hole: x=4
B. asymtotes: x=2 and hole: x=-1
C. asymtotes: x= -1 and hole: x=-4
D. asymtotes: x=1 and hole: x=4
Can someone plzzzz help me!??

Answers

For this case what you should do is check the points where the function is NOT defined.
 The function is not defined for those values where the denominator is equal to zero.
 We have then:
 y = (x + 2) (x + 4) / (x + 4) (x + 1)
 Studying the denominator:
 (x + 4) (x + 1) = 0
 x = -4
 x = -1
 Answer:
 C. asymtotes: x = -1 and hole: x = -4

If a 16 in. by 24 in. window has a wooden frame 3 inches wide surrounding it, what is the total area of the window and frame?

Answers

16 + 3 = 19
24 + 3 = 27

19 * 27 = 513

Answer: 513 in squared

Hope this helped!

Answer:

The CORRECT answer is 660 sq inches

Step-by-step explanation:

Compute the requested average. Tim Worker receives the following income monthly from a second job. Jan. Feb. Mar. Apr. May June $200 $150 $250 $260 $285 $380 What is his average pay? (To the nearest hundredth.)
254.17255.37257.83259.85

Answers

To find the average, simply add up the values of the money that Tim earned and divide it by the six months that he worked. In this case, it would be (200 + 150 + 250 + 260 + 285 + 380) = (1525 / 6 = 254.166). This gives a closest value of choice (A), which is $254.17 per month. or Ok,  all you have to do is add all the money together then divide it by how many numbers there are which is 12.
200 + 150 + 250 + 260 + 285 + 380 + 200 + 225 + 200 + 250 + 220 + 150 = 2770 

2770 divided by 12 =230.83 is the average




In finding the average of the monthly income, simply sum up all the values and divided by the total number of months. Hence, 200+150+250+260+285+380=1525. Divide 1525 dollars by 6 months. The answer is 254.17 dollars which is his average monthly pay.

Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?
A) f has a relative minimum at x = 1.5
B) f has relative maximum at x = -1.5
C) f is decreasing on the interval from x = 1 to x = 2
D) none of these are true
https://seminole.flvs.net/webdav/assessment_images/educator_apcalcab_v14/08_01_04.gif

Answers


the derivitive is just the slope

minimum happens when the derivitive goes from negative to positive, imagine a slope of the function, the minimum is where the slope goes from neative to positive, and to get there, it has to pass through 0

max happens when the derivitive goes from positive to negative

increaseing is when the derivitive is positive



so, based on what you said, the slope of f(x) is 0 at x=-3, x=1 and x=2 since those are where the derivitive is 0 (derivitive is just the slope)

A and B are wrong because the derivitive isn't 0 at those points

C is correct because increasing means that the derivitive is positive, and so therefo since the only hoirontal place in between 1 and 2 is 1.5, it must remain positive throughout and not dip down, C is right

D is wrong then




answer is C

The only statement that is true as regards the graph of f ′(x) is;

C:  f is decreasing on the interval from x = 1 to x = 2

We are told that the graph of f ′(x) has x-intercepts at x = –3, x = 1 and x = 2.

Now, f'(x) is simply the derivative of f(x) and the derivative of f(x) is defined as the slope.

Since x-intercepts of the derivative are at x = –3, x = 1 and x = 2. It means that the values of x that will make the slope to be zero are  x = –3, x = 1 and x = 2.

Now, the minimum for the derivative graph usually happens when the the graph goes from negative to positive. This means that the graph is decreasing when the x-intercepts of the slope is positive

In contrast the graph is increasing when the x-intercepts of the slope is negative.

Let us look at the options;

Option A; This is not correct because the derivative has to be zero at minimum point.

Option B; This is not also correct because the derivative has to be zero at maximum point.

Option C; This is correct because slope is positive when the graph is decreasing and from x = 1 to x = 2 is positive interval.

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Which values are solutions to the inequality below?
Check all that apply.
√x ≤ 11

a) 121
b) 120
c) 111
d) -10
e) 122
f) no solutions

Answers

Final answer:

The values that are solutions to the inequality √x ≤ 11 are 121, 120, and 111.

Explanation:

To find the values that are solutions to the inequality √x ≤ 11, we first need to square both sides of the inequality. This gives us x ≤ 121. So any value of x that is less than or equal to 121 will be a solution.

Now let's check each option:

a) 121: 121 is equal to 121, so it is a solution.b) 120: 120 is less than 121, so it is a solution.c) 111: 111 is less than 121, so it is a solution.d) -10: Negative numbers do not have real square roots, so -10 is not a solution.e) 122: 122 is greater than 121, so it is not a solution.f) no solutions: This option is not a valid solution.

In summary, the values that are solutions to the inequality √x ≤ 11 are: 121, 120, and 111.

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A customer buys 3 bottles of water for ninety-nine cents each seven percent tax on each bottle what is the total bill

Answers

$3.18 when the tax is applied to each bottle separately or at the end of the bill.

 
The bill before tax is
.. 3*$0.99 = $2.97

The tax is
.. 0.07*$2.97 = $0.2079 ≈ $0.21

The total bill, including tax is
.. $2.97 +0.21 = $3.18

______
This is how every bill is computed wherever you may shop. It is a good idea to figure this out.

The price of 6 pretzels is $5.10. Simon and Sofia bought 8 pretzels an shared the cost equally. How much did each person pay?

Answers

Answer:

$3.40

Step-by-step explanation:

To find out the amount each person paid, let's find the total cost of the pretzels first.

6 pretzels ----- $5.10

1 pretzel ----- $5.10 ÷6= $0.85

8 pretzels ----- 8($0.85)= $6.80

The total cost of 8 pretzels is thus $6.80.

Since the total cost was shared equally amongst two people, each person paid half of the total cost.

Amount each person paid

= $6.80 ÷2

= $3.40

By taking a quotient between the total cost and the number of people, we can see that each one pays $3.40

How much did each person pay?

We know that the price of 6 pretzels is $5.10, then the price for each pretzel is given by the quotient:

$5.10/6 = $0.85

We know that Simon and Sofia bought 8 pretzels, so they pay:

P = 8*$0.85 = $6.80

And they divide that evenly between the two, so we can take the quotient:

p = $6.80/2 = $3.40

That is the amount that each person pays.

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Anton must pay a co-pay of $30 for an office visit. His insurance company will then pay 85% of the cost of the visit. How much will Anton pay for an office visit that costs $270? (Points : 1) $36.00 $40.50 $56.00 $70.50

Answers

your answer will be D $70.50

Given:

Anton must pay a co-pay of $30 for an office visit.

His insurance company will then pay 85% of the cost of the visit.

Office visit costs $270

Solution:

[tex] co-pay \; =\; \$30 [/tex]

[tex] Insurance \; Company \; pay = 85\% \; of\; 270 = \frac{85}{100} \cdot 270 = \frac{22950}{100}=\$ 22950\\ \\ Anton \; Pay\; remaining \; of\; what\; Insurance\; Company\; pay.\\ \\ So, \; Anton \; Pay = \$270 - \$229.50=\$40.5\\ \\ [/tex]

Conclusion:

Anton totally Pay = Remaining amount for office visit + Co-pay for office visit

[tex] Anton \; pay \; for\; an \; office \; visit \; that\; costs \; \$270\; = \; \$30 \; + \; \$40.5\; =\; \$70.5 [/tex]



Find two numbers their sum is −7 and their difference is 14

PLZ HELP FAST

Answers

-2 and -14 I hope this is what you are asking

Use the chart above to determine the premium for 10-year term insurance. $10,000 policy for a 35-year-old male. Premium = _____?

6.11

61.10

611.00

6,110.00


Answers

Answer:

Option B 61.10

Step-by-step explanation:

Given is a chart giving the premium to be paid for 10 year term insurance for different age groups for an amount of 1000 policy.

We have to calculate the premium for a 35 year old man for 10 year term insurance for 10000 policy.

From the chart we find that for a 35 year old man premium = 6.11

This premium is for 1000 dollars.

Since here sum assured is 10000 dollars, we get the premium

=6.11(10) = 61.10 dollars

Option B is correct

Premium = 61.10 dollars

Find the equation of the line with the given properties: slope of 2, contains the point ( 4, -3).

Answers

Answer:

y = 2x - 11

Step-by-step explanation:

We are given that a line has a slope of 2 and passes through the point (4, -3).

As the question doesn't specify, we can write the equation of the line in any format.

There are 3 ways to write the equation of the line. They are:

Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0 and a cannot be negative. Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.

Although while all of these choices are valid, let's write the equation in slope-intercept form, as that is the most common way to write the equation of the line.

As we are already given the slope of the line, we can immediately plug it into the equation as m.

Replace m with 2.

y = 2x + b

Now we need to find b.

As the line contains the point (4, -3), we can use its values to help solve for b.

Substitute 4 as x and -3 as y.

-3 = 2(4) + b

Multiply.

-3 = 8 + b

Subtract 8 from both sides.

-11 = b

Substitute -11 as b in the equation.

y = 2x - 11

Topic: finding the equation of the line

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Add the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).

Answers

To find the reciprocal of a mixed number, we first convert it to an improper fraction.  1 1/5 = 5/5 + 1/5 (remember that 1 whole would have the same numerator and denominator) = 6/5.
The reciprocal is this number flipped, so 5/6.
To find the sum of 1.25 and -1 3/4, we will convert the decimal to a fraction. 0.25 is read as "twenty-five hundredths," so the fraction would be 25/100.  This will simplify to 1/4, so 1.25 = 1 1/4.
1 1/4 + -1 3/4 = -2/4 = -1/2.
Now we add 5/6 + -1/2:
Find the least common denominator (LCD).  6 is the first number that both 6 and 2 will divide into evenly.  This gives us 5/6 + -3/6 (we multiply 2 by 3 to get 6, so we multiply the numerator, -1, by 3 as well).  This equals 2/6 which simplifies to 1/3.

The answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The fraction is 1 1/5 = 6/5

The reciprocal of the above fraction = 5/6

= 1.25 - 1 3/4 + 5/6

= 1.25 - 7/4 + 5/6

= 1.25 - 11/12

= 4/12

= 1/3

Thus, the answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).

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Help me ASAP
THANKS




IF YOU DON’T KNOW THE ANSWER DON’T ANSWER! RANDOM ANSWERS WILL BE MODERATED!

Answers

Asked and answered elsewhere.
https://brainly.com/question/9006279

What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth?

x ≈ −3.23 and x ≈ 0.23
x ≈ −2.72 and x ≈ −0.28
x ≈ 0.28 and x ≈ 2.72
x ≈ −0.23 and x ≈ 3.23

Answers

First 
[tex] 4x^{2} + 12x + 3 = 0 [/tex]
determine if this equation were factorable, it's not for this one
so I use quadratic formula, try to search the formula online

[tex]x1 = \frac{-12 + \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 + 4\sqrt{6} }{8} = \frac{4(-3 + \sqrt{6}) }{8} = \frac{-3 + \sqrt{6}}{2} = - 0.28[/tex]
[tex]x2 = \frac{-12 - \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 - 4\sqrt{6} }{8} = \frac{4(-3 - \sqrt{6}) }{8} = \frac{-3 - \sqrt{6}}{2} = - 2.72[/tex]

x ≈ −2.72 and x ≈ −0.28 is the solution

the inverse of an exponential function is the quadratic function? true or false?

Answers

False.

The inverse of an exponential function is a logarithmic function.


Hope this helps!

What is the smallest integer greater than -1/2 .

Answers

0 is greater than - 1/2 and zero is an integer.

The correct answer to your question is... 0

what is the approximate distance between the points (-5 1) and (-2 3) on a coordinate grid

Answers

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -5 &,& 1~) % (c,d) &&(~ -2 &,& 3~) \end{array}~~ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-2-(-5)]^2+[3-1]^2}\implies d=\sqrt{(-2+5)^2+(3-1)^2} \\\\\\ d=\sqrt{3^2+2^2}\implies d=\sqrt{13}[/tex]

This figure shows circle Z with chords AB and RS . mAR=55° mRB=66° AB=8 m RS=8 m What is mRS?

Answers

m AR = 55°
m RB = 66°
Like AB=8 m =RS →m RS = m AB

m AB = m AR + m RB
m AB = 55° + 66°
m AB = 121°

m RS = m AB
M RS = 121°

Answer: m RS is 121°

Answer:

The correct answer is, mRs = 121°

Step-by-step explanation:

From figure we get ,

mAR=55° mRB=66° AB=8 m RS=8 m

To find mRS

Using given information we can write,

mAB = mAR + mRB = 55 + 66 = 121°

Since AB=8 m RS=8 m,

AB = RS

⇒ mAB = mRS

mAB = 121°

Therefore mRS = 121°

The correct answer is given by,

mRS = 121°

Group of kids rode horses to canyon. 20 eyes 30 legs between them. How many horses

Answers

If all were kids, there would be 20 legs. A horse has 2 more legs than a kid. The extra 10 legs can be attributed to there being 5 horses.

Final answer:

To solve this problem, we set up equations based on the total number of eyes and legs. By solving the system, we find that the group consists of 5 horses.

Explanation:

The question asks us to solve a problem involving a group of kids and horses by using the given information about the total number of eyes and legs. Since humans have two eyes and two legs, and horses have two eyes and four legs, we can set up a system of equations to find the solution.

Let's denote the number of kids as 'k' and the number of horses as 'h'. Since each human and horse has two eyes, the total number of eyes is given by the equation: 2k + 2h = 20. Similarly, the total number of legs is given by the equation: 2k + 4h = 30. Solving these equations will give us the number of kids and horses in the group.

Solving for 'k' from the first equation gives us k = 10 - h. Substituting this into the second equation gives us 2(10 - h) + 4h = 30. Simplifying this equation results in 20 - 2h + 4h = 30, which further simplifies to 2h = 10, and thus h = 5. Therefore, there are 5 horses in the group.

Johnny is five years older than his brother. the sum of their ages is 37. how old is Johnny

Answers

Johnny is 21 years old.
If you take 21 and add 16, you get 37. 

21+16= 37
21-16= 5



johnny is 21 years old

At a local department store, pants have been reduced to $26. this price is at 68.4% of the original price for pants. given this, what was the original price of the pants?

Answers

The way you should go is to divide the twenty-six dollars by the percentage, (in decimal form).
[tex]26 \div .684 = a[/tex]

Calculus HELP PLEASE? A highway runs due north. A car traveling at 50 mph exits the highway at a 30° angle. After driving another 1.5 hours at the same speed and direction, how far away is the car from the highway?

Answers

check the picture below.

notice that the car exits the northbound highway, and whilst going at 50mph for 1.5 hours, that simply means going for 75 miles.

make sure your calculator is in Degree mode.

Answer:

37.5 miles is the answer.

Step-by-step explanation:

Since car is travelling with a speed = 50 mph

Angle between the highway and the track on which the car is travelling = 30°

Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track

Distance traveled by the car in 1.5 hours = speed × time

                                                                   = 50 × 1.5 = 75 mi.

Therefore sin 30° = x/75

x = 75×sin30° = 75 × 1/2 = 37.5 mi.

Therefore the answer is 37.5 mi away.

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