Kinsley bought 8.01 ounces of chocolate. 3.89 ounces of it was milk chocolate and the
rest was dark chocolate. How much dark chocolate did Kinsley buy?

The time used for the return trip is t / 3

He drove to the nearest hospital with an average speed of v meters per seconds in t seconds.

Therefore,

average speed  = distance / time

average speed = v

time used = t

d = distance covered

Therefore,

v = d / t

d = vt

He drives home on the same path, but with an average speed of 3v meters/second. The time used for the return trip is as follows:

Recall he covered the same distance.

Therefore,

average speed = 3v

time used for the return trip = x

d = distance

Hence,

3v = vt / x

x = vt / 3v

x = t / 3

Therefore,  the time used for the return trip is t / 3

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Answer: A

Step-by-step explanation:

A. 2.6x 10^-7

Answer:

a

Step-by-step explanation:

because you move the decimal 7 times to the right to put it into scientific notation

The equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex] is [tex]y=6[/tex]

As per the question statement, we are supposed to find the equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex].

Before solving that, we need to know that the given line [tex]x = 11[/tex] is parallel to the y-axis as no point is passing through y axis hence the slope [tex]m_{1}[/tex] of the given line will be [tex]\frac{1}{0}[/tex].

The required line is perpendicular to the given line, so it will be parallel to the x-axis and hence it's slope would be slope [tex]m_{2}[/tex] = [tex]0[/tex]

We know the equation of the line passing through a some point [tex]x_{1}[/tex] and [tex]y_{1}[/tex] having slope m is given by:

[tex]y-y_{1} =m_{2} (x-x_{1})[/tex]

Here the required line is passing through (7,6), hence substituting the values of [tex]x_{1}, y_{1} ,m_{2}[/tex], we get

[tex]y-6=0(x-7)[/tex]

or [tex]y-6=0[/tex]

or [tex]y=6[/tex]

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Answer:

Use distance formula between these points to find length of one side of the square.....then multiply by 4 sides

sqrt( 5^2 + 12^2 ) =   13 units  side length

Step-by-step explanation:

And i think you can go from there if not please ask me to do the rest for you

The fraction of the brownies left is 1/12.

We need to find out what fraction of the brownies is left.

Let " r " denote the fraction that is left.

Then we have r + 1/4 + 2/6 + 1/3 = 1

⇒ r + 1/4 + 1/3 + 1/3 = 1 (Writing the fraction 2/6 in the simplest form)

⇒ r + 1/4 + 2/3 = 1

⇒ r + (3 + 8)/12 = 1 (taking LCM of 4, 3 and adding the fractions 1/4 and 2/3)

⇒ r + 11/12 = 1

⇒ r = 1 - 11/12

⇒ r = (12 - 11)/12

⇒ r  = 1/12.

Therefore, the fraction of the brownies left is 1/12.

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Disclaimer:

The fractions provided in the question are not clear.

Assuming the following to answer the given question.

Molly ate 1/4 of the brownies,

Milo ate 2/6 of the brownies, and

Morgan ate 1/3 of the brownies.

Answer:

LK = 7

Step-by-step explanation:

NK = NM + ML + LK ( substitute values )

23 = x - 6 + 9 + 2x - 19

23 = 3x - 16 ( add 16 to both sides )

39 = 3x ( divide both sides by 3 )

13 = x

Then

LK = 2x - 19 = 2(13) - 19 = 26 - 19 = 7

Two hikers are 22 miles apart and walking toward the each other, they meet in 4 hours. The rate of each hiker if one hiker walks 3.3 mph faster than the other are 2.2mph, 2.2mph, 3.3mph.

Distance divided by time is the dimension of speed. The SI measure of speed is the meter per second (m/s), although the most widely used unit in daily life is the kilometer per hour (km/h), or miles per hour in the US and the UK (mph). The knot is a popular choice for air and sea travel.

The instantaneous speed serves as the upper bound of the average speed as the duration of the time period gets closer to 0. The distance traveled by an object during a period of time divided by the length of the period gives the average speed of an object throughout that period. Velocity and speed are not the same thing.

Time divided by distance are the speed-related metrics. The kilometer per hour (km/h), or miles per hour in the US and UK, is the unit of speed that is most frequently used in daily life. The meter per second (m/s) is the metric unit of speed (mph). The knot is often used in air and sea transportation.

Since the hikers are moving at varying speeds, they collide in a location other than the center.

Let the distance travelled by Hiker A (slower) be x at speed s.

So, the distance travelled by Hiker B (faster) is (22 - x) at a speed (s + 1.1).

s = x / 4

s + 1.1 = 22 - x / 4

After resolving equations 1 and 2, we obtain:

x = 8.8m and s = 2.2mph

Therefore,

Speed of the Hiker A = 2.2 mph

Speed of the Hiker A = 2.2 mph

Speed of the Hiker B = 3.3 mph

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The two points that also lie on the circle are:

A (-3,-4) and D (5,0)

We know that a all the points on a circle are equidistant to the center of the circle, and in this case, the center is the origin (0, 0).

We know that the point (4, -3) lies on the circle, so the radius of the circle is:

R = √( (4 - 0)^2 + (-3 - 0)^2) = √25 = 5

So, any point that is at 5 units of the origin will also lie on the circle.

These points are:

A: (-3, -4)

R = √(  (-3 - 0)^2 + (-4 - 0)^2) = √25 = 5

And the point D: (5, 0)

R = √( (5 - 0)^2 + (0 - 0)^2) = √25 = 5

So the correct options are A and D.

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Answer:

Step-by-step explanation:

Given that

To find

So, according the question,

We have

So, the money he loss to don't sell that Jackets in 30 days is the total cost of all jackets.

∴     The Total cost of all Jackets    = 75 × 5

                                                           = $375.

Answer: Retailer will loss $375.

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Answer:

The change in direction or bending of a light wave passing from one transparent medium to another; caused by the change in wave's speed is known as “Refraction”. Pencil appears bent in water because of the refraction of light rays

Step-by-step explanation:

By applying the Tangent Secant Theorem to this circle, the value of x to the nearest tenth is equal to: A. 5.7.

The Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have:

(x + x + 3) × x = 9²

(x + 3)x = 81

2x² + 3x = 81

2x² + 3x - 81 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-3\; \pm \;\sqrt{3^2 - 4(2)(-81)}}{2 \times 2}\\\\x = \frac{-3\; \pm \;\sqrt{9 + 648}}{4}\\\\x = \frac{-3\; \pm \;\sqrt{657}}{4}[/tex]

x = 5.7 or -7.2

Since the line segment cannot be negative, the value of x to the nearest tenth is equal to 5.7.

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Answer: The total weights of the two animals is  11. 92 × 10² Ibs

Step-by-step explanation:

Answer:

1e+21

Step-by-step explanation:

I believe this the answer

The amount each contestant will receive is as follows:

This year $52,000 college scholarship is being divided between the top two contestants .

Therefore,

Total amount to share to the top winners = 52000 dollars

The winner receives three times as much as the runner-up.

Therefore,

let

x = Amount received by the runner-up

Hence,

Amount the winner received = 3x

Therefore,

52,000 = 3x + x

52,000 = 4x

divide both sides by 4

4x / 4 = 52,000 / 4

x = 13000 dollars

Hence,

Amount the winner received =3(13000) = $39000

Amount received by the runner-up = $13,000

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Answer:

2

Step-by-step explanation:

What you do to one side, you must do to the other.

When you add the 2 on one side of the = sign then you have to add the 2 on the other side. when you do that you will get 7 + 2. so the number in the green is 2. hope this helped a little!

The statement  that "If two adjacent angles form a right angle, then the angles are complementary", is true

The conditional is given as:

If two adjacent angles form a right angle, then the angles are complementary

As a general rule, complementary angles add up to 90 degrees i.e. right angle

This means that adjacent angles that add up to 90 degrees are complementary angles

Hence, the statement  that "If two adjacent angles form a right angle, then the angles are complementary", is true

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The probability that the number showing is a 3 is [tex]\frac{1}{6}[/tex].

Probability refers to the possibility of the occurrence of an event.

P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]

Now,

According to question, number of favorable outcomes = 1, i.e., the number 3 shows up on the die

And the total number of outcomes = 6

Hence, The probability that the number showing is a 3 is [tex]\frac{1}{6}[/tex].

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The comparison of the mean and median of the data set of the dot plot in the first part and the variability and outlier of the dataset in the box and whiskers plot in the second part are;

First part;

1. The median is greater than the mean.

2. Both the mean and median will increase

Second part;

1. School 1 has greater variability

2. The maximum value of school 1 is not an outlier

3. The new athlete needs to spend 21 hours or more

First part;

1. The value in the dot plot are;

10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 19

The number of data points = 36

The mean = The sum of the above data divided by 36

Using an online calculator of data sets, we have;

Therefore;

2. The addition of 60 to the dataset will increase the number of data points from 36 to 37, thereby changing the median, which is the middle value to the 19th number, which is 16, while the mean value will also increase to 16.405, therefore;

Second part;

1. A measure of variability of a box plot is the range, which is the difference between the largest and smallest values.

The range of school 1 is; 16 - 1 = 15

The range of school 2 is; 14 - 1 = 13

Therefore;

2. The maximum value of school 1 is 16

The inter quartile range of school 1 is; IQR = 10 - 4 = 6

An outlier = Q3 + 1.5 × IQR

Which gives;

An outlier ≥ 10 + 1.5 × 6 = 19

3. Q3 for school 2 = 12

IQR for school 2 = 12 - 6 = 6

Which gives;

Outlier for school 2 ≥ 12 + 1.5 × 6 = 21

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Answer:

Step-by-step explanation:

The answer to this my friend would be valid by the law of syllogism because our P is an angle bisector and our q is km. Our r is connecting to our p and says that they are congruent. Therefore if An angle bisector divides an angle into two congruent angles, then JKM and KML are congruent.

Hope this helps!

The Conclusion: ∠J K M ≅ ∠M K L is valid

Given data

An angle bisector divides an angle into two congruent angles. →KM is an angle bisector of ∠J K L .

Bisection is a term in mathematics that refers to dividing into two equal parts. This term is used more in the branch of mathematics called geometry.

Bisection can be done for an angle or line, for a line the given line is divided into two equal parts. Angle bisector divides the given angle into two equal parts to give two equal angles

When angle JKL is bisected by line KM. The line will lead to two angles which are:

These two angles are congruent and are represented by the formula below: ∠J K M ≅ ∠M K L

Hence we can say that the conclusion is valid

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Answer:

Mpq= (

[tex] \frac{4 \times \frac{1}{3} + - 2 \times \frac{1}{5} }{2} and \frac{3 \times \frac{1}{6} + 3 \times \frac{2}{3} }{2} [/tex]

[tex] \frac{16}{15} \: and \frac{41}{12} [/tex]

midpoint for PQ is (16/15; 41/12)

If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x

Given,

The initial fee of taxi cab = $2.85

The charges per mile = $2.70

Consider the number of miles as x

Then,

The equation of the fare = 2.85+2.70x

Hence, If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x.

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The inverse of the given linear function is of:

R^(-1)(x) = (x - 2)/3

The graph is given at the end of the answer.

A linear function is modeled by the following rule:

y = mx + b

In which:

For function R, in blue, we have that when x = 0, y = 2, hence the intercept is of b = 2 and:

R(x) = mx + 2.

When x = 1, y= 5, when x = 2, y = 8, that is, when x changes by 1 y changes by 3, meaning that the slope is of m = 3, and:

R(x) = 3x + 2.

To find the inverse function, we exchange x and y in the original function, then isolate y.

For function R(x), we have that:

y = 3x + 2.

Then the inverse is found as follows:

x = 3y + 2

3y = x - 2

y = (x - 2)/3

R^(-1)(x) = (x - 2)/3

The graph of R(x) in blue and of R^(-1)(x) in blackis given at the end of the answer. Since they are inverses, they are symmetric over the line y = x.

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To solve the equation, divide both sides by 5. The solution is c = 4.

A linear equation is an equation of which the highest degree of its variables is 1.

Steps to solve linear equations:

The given problem:

Solve 5c = 20

Notice that the variable, c, is already isolated on the left side.

Divide both sides by 5:

5c : 5 = 20 : 5

c = 4 (solved)

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Answer:

Negative 2.5 greater-than negative 1.5

C

Step-by-step explanation:

-2.5 < -2

Answer:

Step-by-step explanation:

z³/xy²

Answer:

Both Choice C, D

Step-by-step explanation:

A: Choice A cannot be the correct answer due to it being negative.

B: Choice B also cannot be part of the correct answer because 8 x 3 = 24

C: Choice C is part of the correct answer

D: Choice D is also part of the correct answer

The expression for modelling the pattern is n² + 2

Charlie can observe 38 guppy fish in month 6.

Given,

Number of guppy fish in Charlie's fish tank for the first time = 3

Number of guppy fish after one month = 6

Number of guppy fish in the following month = 11

The increasing pattern of guppy fish in the tank:

First month = 6 - 3 = 3

Second month = 11 - 6 = 5

So, we get that the number of guppy fish is increasing by odd numbers.

That is, 3, 6, 11, ........

Now, we have to find an expression for this pattern.

First term is 3.

That is, first term² + 2 = 1² + 2 = 3

Let n be the number of term.

n = 3

So, third term be:

3² + 2 = 9 + 2 = 11

So the expression for modelling the pattern is n² + 2

Now, we have to find the number of guppy fish in month 6.

That is,

n = 6

So,

n² + 2

6² + 2 = 36 + 2 = 38

That is, Charlie can observe 38 guppy fish in month 6.

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a) [tex]x^{2}[/tex]+8kx +k=0,   b) k=1/16

Here we have equation is 2x -y = 1 , [tex]x^{2}[/tex]+4ky+5k=0

To show that [tex]x^{2}[/tex] +8kx +k =0, we have two equation 2x-y=1 and [tex]x^{2}[/tex] +4ky + 5k=0

So from the equation 2x - y = 1 we can find y

Therefore y = 2x-1

Now we will put the value of y in the equation [tex]x^{2}[/tex] + 4ky + 5k =0

a) We have [tex]x^{2}[/tex] + 4k(2x-1) +5k=0

              [tex]x^{2}[/tex] + 8kx -4k + 5k=0

             [tex]x^{2}[/tex] +8kx +k=0

b) Now we have to find the value of k, and as from the question it is given that [tex]x^{2}[/tex] + 8kx +k =0 have equal roots

Therefore we get [tex]b^{2}[/tex] + 4ac = 0 is the condition of the linear equation in two equal roots.

So from this we have b= 8k, a = -1, c= k

           [tex](8k)^{2}[/tex] - 4× 1×k =0

           64[tex]k^{2}[/tex] -4k =0

           4k(16k -1) =0

           16k-1=0

            k = 1/16

As k is a non-zero constant therefore we have not taken k=0. Therefore the value of k is 1/16.

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The complete question is:

Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant a)show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots., b) find the value of k.

The Domain of the given function is −2≤x≤2 and the range of the given function are −2≤y≤3.

The domain of a graphical function refers to all the input values which are shown or plotted on the x-axis. The domain of a function may be defined as the set of values that are assumed for the function.

The range of a graphical function refers to all the input values which are shown or plotted on the y-axis. The range of a function may be defined as the set of values that the function gives after assuming the input values for the function.

Here in the graph, the set of input values on the x-axis are from -2 to 2. Thus, the domain is −2≤x≤2. Also, the set of input values on the y-axis is from -2 to 3. Thus, the range is −2≤y≤3.

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