Peaceful Travel Agency offers vacation packages. Each vacation package includes a city, a month, and an airline. The agency has cities, month, and airlines to choose from. How many different vacation packages do they offer?

Answer:

a) 1

b) [tex]\frac{4}{3}[/tex]

c) = 1

Step-by-step explanation:

We are given the following in the question:

[tex]\cos \theta = \dfrac{6}{8}[/tex]

θ is in the IV quadrant.

[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\sin \theta = \sqrt{1-\dfrac{36}{64}} = -\dfrac{2\sqrt7}{8}\\\\\tan \theta = \dfrac{\sin \theta}{\cos \theta} = -\dfrac{2\sqrt7}{6}\\\\\csc \theta = \dfrac{1}{\sin \theta} = -\dfrac{8}{2\sqrt7}[/tex]

Evaluate the following:

a)

[tex]\tan \theta\times \cot \theta =\tan \theta\times\dfrac{1}{\tan \theta} = 1[/tex]

b)

[tex]\csc \theta\times \tan \theta\\\\= -\dfrac{8}{2\sqrt7}\times -\dfrac{2\sqrt7}{6} = \dfrac{4}{3}[/tex]

c)

[tex]\sin^2 \theta + \cos^2 \theta = 1\\\text{using the trignometric identity}[/tex]

Answer:

10cm/s²

Step-by-step explanation:

Acceleration is the change in velocity of an object with respect to time.

Given velocity v(x) to be x³-2x+6

Acceleration = ∆v/∆x

Differentiating the velocity function to get acceleration we have,

Acceleration = dv/dt = 3x²-2

Acceleration of the particle at x = 2 will give;

dv/dt @ x = 2 is 3(2)²-2

= 12-2 = 10cm/s²

Answer:

a) Specific volume of the air in balloon is [tex]14.96 ft^3/lbm[/tex]

b)The weight of the air within the balloon is 1,126.09 lbf.

Step-by-step explanation:

Mass of air, m = 35  lbm

Volume of the air = V

Diameter of balloon = d = 10 ft

radius of the balloon = r= 0.5 d = 5 ft

Volume of balloon = V

[tex]V=\frac{4}{3}\pr r^3[/tex]

[tex]V=\frac{4}{3}\times 3.14\times (5 ft)^3[/tex]

Specific volume of the air in balloon = S

[tex]S=\frac{V}{m}=\frac{\frac{4}{3}\times 3.14\times (5 ft)^3}{35 lbm}[/tex]

[tex]S=14.96 ft^3/lbm[/tex]

Specific volume of the air in balloon is [tex]14.96 ft^3/lbm[/tex]

[tex]lbf=32.174 lbm ft/s^2[/tex]

Weight of the air = W

Acceleration due to gravity = [tex]32.174 lbm ft/s^2[/tex]

Weight = m\times g[/tex]

[tex]W=35 lbm\times 32.174 lbm ft/s^2[/tex]

[tex]W=1,126.09 lbf[/tex]

The weight of the air within the balloon is 1,126.09 lbf.

Answer:

[tex]y=-\frac{74}{21}x+452[/tex]

Step-by-step explanation:

Given:

The level of a lake is falling linearly.

On Jan 1, the level is 452 inches

On Jan 21, the level is 378 inches.

Now, a linear function can be represented in the form:

[tex]y=mx+b[/tex]

Where, 'm' is the rate of change and 'b' is initial level

[tex]x\to number\ of\ days\ passed\ since\ Jan\ 1[/tex]

[tex]y\to Lake\ level[/tex]

So, let Jan 1 corresponds to the initial level and thus b = 452 in

Now, the rate of change is given as the ratio of the change in level of lake to the number of days passed.

So, from Jan 1 to Jan 21, the days passed is 21.

Change in level = Level on Jan 21 - Level on Jan 1

Change in level = 378 in - 452 in = -74 in

Now, rate of change is given as:

[tex]m=\frac{-74}{21}[/tex]

Hence, the function to represent the lake level is [tex]y=-\frac{74}{21}x+452[/tex]

Where, 'x' is the number of days passed since Jan 1.

Final answer:

The lake level can be represented by a linear function L(t) = -3.7t + 452, where L(t) is the lake level in inches and t is the time in days from January 1st.

Explanation:

To find a function representing the lake level as it drops linearly over time, we need to determine the linear equation that corresponds to the change in the lake level.

We are given that the lake level is 452 inches on January 1st and 378 inches on January 21st.

First, we will define the variables where L(t) is the lake level in inches and t is the time in days with t=0 corresponding to January 1st.

We are given two points on the linear function: (0, 452) and (20, 378), since January 21st is 20 days after January 1st.

Next, we calculate the slope of the line using the formula:

slope = (change in lake level) / (change in time) = (378 - 452) / (20 - 0) = -74 / 20 = -3.7 inches per day.

Now, we can use the slope and a point to write the equation of the lake level as a function of time in the slope-intercept form:

L(t) = mt + b

where m is the slope and b is the y-intercept. Plugging in the slope and the point (0, 452):

L(t) = -3.7t + 452

This equation represents the function of the lake level over time.

Answer:

For a scaler variable, the Gaussian distribution has a probability density function of

p(x |µ, σ² ) = N(x; µ, σ² ) = 1 / 2π×[tex]e^{\frac{-(x-u)^{2}}{2s^{2} } }[/tex]

The term will have a maximum value at the top of the slope of the 1-D Gaussian distribution curve that is when exp(0) =1 or when x = µ

Step-by-step explanation:

Gaussian distributions have similar shape, with the mean controlling the location and the variance controls the dispersion  

From the graph of the probability distribution function it is seen that the the peak is the point at which the slope = 0, where µ = 0 and σ² = 1 then solution for the peak = exponential function = 0 or x = µ

Answer:

  $30.88

Step-by-step explanation:

The account value is given by ...

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, t is the number of years, n is the number of times interest is compounded per year.

The amount of interest earned is the account value less the initial investment:

  I = A - P = P(1 +r/n)^(nt) -P  = P((1 +r/n)^(nt) -1)

Filling in the given values, we get ...

  I = 500((1 +.03/12)^(12·2) -1) = 500(1.0025^24 -1) ≈ $30.88

The amount of interest earned is $30.88.

Answer:

17807cm2

Step-by-step explanation:

Surface area of a hexagonal prism is =( (3√3)/2) a^2 h

= 2.598 * 15.5^2 *28.5

= 2.598* 240.5* 28.5

=17807.34cm2

Answer: The answer is Correlation because its a connection between 2 or more things, or interdependence of variable quantities. Plus its in the definition, it says the process of establishing a relationship or connection between 2 or more measures.

Final answer:

The chicken quesadilla contains a total of 542 kilocalories, which is derived by summing the caloric contributions from protein, carbohydrate, and fat.

Explanation:

To calculate the number of kilocalories in a chicken quesadilla with 28 grams of protein, 40 grams of carbohydrate, and 30 grams of fat, we use the known caloric values for each macronutrient. Protein and carbohydrate each have 4 Calories per gram, while fat has 9 Calories per gram.

Protein: 28 grams × 4 Calories/gram = 112 Calories

Carbohydrate: 40 grams × 4 Calories/gram = 160 Calories

Fat: 30 grams × 9 Calories/gram = 270 Calories

Adding up these amounts, we have:

112 Calories (from protein) + 160 Calories (from carbohydrate) + 270 Calories (from fat) = 542 Calories

To convert Calories into kilocalories, we remember that 1 kilocalorie = 1 Calorie. Therefore, the chicken quesadilla contains 542 kilocalories.

Answer:

27° (as an integer)

Step-by-step explanation:

From the figure given;

DC = 8 units

BC = 4 units

We are required to determine m∠D

We need to use the appropriate trigonometric ratio;

In this case, DC is adjacent and BC is opposite to m∠D

Therefore, the appropriate trigonometric ratio is tangent;

That is;

Tan m∠D = BC ÷ DC

               = 4 ÷ 8

               = 0.5

Thus;

m∠D = Tan^-1 (0.5)

        = 26.57

         = 27 (as an integer)

Thus, m∠D is 27°

Answer:

3.75 gallons

Step-by-step explanation:

Answer:

dA/dt = 16 square inches per second

Step-by-step explanation:

Width of rectangle is w

Height of rectangle is h

width = twice height

w = 2h

Area = wh = (2h)*h

A = 2h^2

Differentiating the equation with respect to time

dA/dt = 2+2h dh/dt

dA/dt = 4h dh/dt

According to the given situation when width is 4 inches

h = w/2

h = 2

Rate of change of A is  

dA/dt = wh dh/dt

dA/dt = 4(2)(2)

dA/dt = 16 square inches per second

The rate of change of the area of the rectangle with respect to time at the specified instant is 16 square inches per second.

The question asks for the rate of change of the area of a rectangle with respect to time, where the rectangle's width is twice its height, both width and height are functions of time and the rate at which height is increasing is given.

The area A of the rectangle is given by the formula A = w*h. Substituting w = 2h into the formula gives A = 2h². The rate of change of the area with respect to time (dA/dt) can be found by differentiating A with respect to time. By the chain rule this gives dA/dt = 2*2h(dh/dt) = 4h*dh/dt.

At the given instant, where the width is 4 inches (so the height is 2 inches) and the rate of change of the height is 2 inches per second, we have dA/dt = 4*2*2 = 16 square inches per second. Therefore, the rate of change of the area of the rectangle with respect to time at that instant is 16 square inches per second.

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Answer:

Step-by-step explanation:

Let u represent the unit price of the 100 lb container. Then u+.06 is the unit price of the 75 lb container.

The difference in prices is ...

  100u - 75(u+.06) = 55.50

  25u -4.50 = 55.50

  25u = 60

  u = 60/25 = 2.40

The cost of the 100 lb container is 100u = 240. The cost of the 75 lb container is $55.50 less: 240 -55.50 = 184.50.

The 100 lb container costs $240. The 75 lb container costs $184.50.

Answer:

23

Step-by-step explanation:

We take a methodical approach by considering the different possible values of b when asqrtb is the simplest form of sqrtn.

Case 1: b=1. We can't forget the perfect squares! If n=100, for example, then sqrt100 can be written as 10sqrt1. So, we must include the perfect squares from 10^2=100 up through 22^2 = 484. (All greater squares are greater than 500.) There are 13 such squares.

Case 2: b=2. If b=2, then we have asqrtb = asqrt2 = sqrta^2 x sqrt2 = sqrt2a^2. We still must have a {>_} 10, but now we need 2a^2 to be no greater than 500. This means that a^2 must be no greater than 250, so a can be 10, 11, 12, 13, 14, or 15. There are 6 such values.

Case 3: b=3. We then have asqrtb = asqrt3 = sqrt3a^2. Since 3a^2 {<_} 500, we know that a^2 is less than 167. We still need a {>_} 10, so there are only 3 values of a in this case: 10, 11, 12.

We skip b=4 because then asqrtb would not be in simplest form.

Case 4: b=5. We then have asqrtb = sqrt5a^2, and a=10 is the only possible value for this case.

For any greater value of b, the resulting value of n is greater than 500 when a {>_} 10. So, there are no more possible numbers asqrtb that satisfy the problem. Since each of the 13+6+3+1 = 23 possibilities listed above represent different simplified forms, they give us 23 different possible values of n that satisfy the problem.

There are infinitely many positive integers less than 500 that have square roots in the form of a√b, where a and b are integers with a≥10.

The number of such positive integers n is infinite, as there is no finite value for the count.

Here,

We are looking for positive integers n that are less than 500.

The square roots of these integers can be expressed in the form a√b.

And [tex]a\ge 10[/tex]

To find the number of positive integers less than 500 that have square roots in the form of a√b,

Analyze the possible values of a and b separately:

For a,

We know that it must be an integer greater than or equal to 1. So,

We have a total of a = 10, 11, 12  ..., and so on. (since a ≥ 10)

As for b,

it can be any perfect square less than or equal to 500.

Let's list a few examples:

b = 1, since 1√1 = 1

b = 4, since 1√4 = 2

b = 9, since 1√9 = 3

b = 16, since 1√16 = 4

...

b = 484, since 1√484 = 22

Now, we can count the number of possibilities for a and b.

We have an infinite number of possibilities for a, but b has a finite number of perfect squares less than or equal to 500.

There are 22 perfect squares within this range.

Therefore, the total number of positive integers n, with n < 500, that have square roots in the form of a√b is 22 x infinity = infinity.

Since there are infinitely many possible values for n,

Hence,

We can conclude that there is no finite value for the number of positive integers n that satisfies this condition.

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Answer:

20 >= x + y

Step-by-step explanation:

Given:

- The length of garden = x

- The width of the garden = y

- Total fence available = 40 ft

- Rectangular garden

Find:

(a) Write and inequality representing the fact that the total perimeter of thegarden is at most 40 ft.

(b) Sketch part of the solution set for this inequality that represents all possiblevalues for the length and with of the garden.

Solution:

- The perimeter of the rectangular garden is P at most 40 ft:

                              P >= 2*x + 2*y

                              40 >= 2*x + 2*y

                              20 >= x + y

- The sketch of the graph will be all points in the shaded region denoted by the inequality as follows:

                               y =< 20 - x

- See the triangular shaded region.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since Rick has 40ft of fencing

Then, the perimeter cannot be more than 40ft if he decided to lay the block on a single layer and not on each other

Then if the length is x

And the breadth is y

Perimeter of a rectangle is 2(l+b)

Therefore,

Perimeter is less than or equal to 40ft

2(l+b)  ≤ 40

b.  2(l+b)≤ 40

Then divide both side by 2

l+b≤ 20.

Then l ≤ 20-b

Also, b ≤ 20-l

Check attachment for graph

Answer:

Step-by-step explanation:

The current global population is growing at an annual rate of 1.35 percent. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 6.1 × 10^9

r = 1.35% = 1.35/100 = 0.0135

t = 1

Therefore

A = 6.1 × 10^9(1 + 0.0135)^1

A = 6.1 × 10^9(1.0135)^1

A = 6182350000

The number of people that would be added is

6182350000 - 6100000000

= 82350000

If the world population were to keep growing at 1.35%, we number of people who would be added next year is 82,350,000 people.

The population of the world is growing at 1.35%. This means that next year, the number of people added will be 1.35% of the current population.

The current population is 6.1 billion so the number of people who will be added is:

= Population x Incremental rate

= 6,100,000,000 x 1.35%

= 82,350,000 people

In conclusion, 82,350,000 people will be added.

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Final answer:

To calculate the cost, multiply the amount of turkey per student (0.3 pounds) by the number of students (100), then multiply the total pounds needed (30) by the cost per pound ($0.79), resulting in a total cost of $23.70 for turkey for 100 students.

Explanation:

The question asks us to calculate the cost of providing turkey to 100 students if each student requires 0.3 pounds of turkey, and turkey costs $0.79 per pound. To find the total amount of turkey needed, we multiply the amount each student gets by the total number of students: 0.3 pounds/student × 100 students. This calculation results in 30 pounds of turkey required for 100 students.

Next, to determine the total cost, we multiply the total pounds of turkey needed by the cost per pound: 30 pounds × $0.79/pound. This calculation gives us a total cost of $23.70 for the turkey.

Therefore, it will cost $23.70 to give turkey to 100 students.

The volume of the square prism with a side of base decreasing at a rate of 7 km/min and height increasing at 10 km/min is decreasing at a rate of 344 cubic km/min.

In this problem, we're dealing with rates of change and the geometric properties of a square prism. A square prism can be characterized by the side length of its base (we'll call this length 's') and its height (h). The volume (V) of a square prism is given by the equation V = s^2 * h. We're told that the side length s is decreasing at a rate of 7 kilometers per minute (ds/dt = -7 km/min) and the height h is increasing at a rate of 10 kilometers per minute (dh/dt = 10 km/min).

To find the rate at which the volume is changing with respect to time, we can take the derivative of the volume equation with respect to time. Thus, dV/dt = 2*s*ds/dt*h + s^2*dh/dt. Substituting the given values, when s = 4 km and h = 9 km, we find: dV/dt = 2*4*(-7)*9 + 4^2*10 = -504 + 160 = -344 cubic kilometers per minute. Therefore, at the given instant, the volume of the square prism is decreasing at a rate of 344 cubic kilometers per minute.

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The rate of change of the surface area of the prism at that instant is -204 square kilometers per minute. Correct Option is Option C.

To solve this problem, let's first start by identifying the formula for the surface area (SA) of a square prism, which is given as [tex]2s^2 + 4sh[/tex] , where s is the side of the base and h is the height.

Now, let's find the rate of change of the surface area with respect to time, dSA/dt. We'll use the chain rule to differentiate the surface area formula:

1. Differentiate the given surface area formula:

[tex]SA = 2s^2 + 4sh[/tex]

[tex]d(SA)/dt = d(2s^2)/dt + d(4sh)/dt[/tex]

2. Apply the chain rule:

d(SA)/dt = 2 * 2s * (ds/dt) + 4 * (s * (dh/dt) + h * (ds/dt))

3. Plug in the given values: s = 4 km, ds/dt = -7 km/min, h = 9 km, dh/dt = 10 km/min:

d(SA)/dt = 4 * 4 * (-7) + 4 * (4 * 10 + 9 * (-7))

d(SA)/dt = -112 + 4 * (40 - 63)

d(SA)/dt = -112 + 4 * (-23)

d(SA)/dt = -112 - 92

d(SA)/dt = -204

The rate of change of the surface area of the prism at that instant is -204 square kilometers per minute. Correct Option is Option C.

Complete Question:- The side of the base of a square prism is decreasing at a rate of 7 kilometers per minute and the height of the prism is increasing at a rate of 10 kilometers per minute. At a certain instant, the base's side is 4 kilometers and the height is 9 kilometers. What is the rate of change of the surface area of the prism at that instant (in square kilometers per minute)? Choose 1 answer: A 204 B 148 C -204 D -148 The surface area of a square prism with base side 8 and height h is [tex]2s^2+4sh.[/tex]

Answer:

5.42 hours

Step-by-step explanation:

Let x represent time taken to complete 300 miles.

We have been given that Bryce a previous winner of the contest, made a trip of 360 miles in a 6.5 hours.

We will use proportions to solve our given problem since rates are same for both distances.

[tex]\frac{\text{Distance covered}}{\text{Time taken}}=\frac{360\text{ Miles}}{6.5\text{ Hours}}[/tex]

Upon substituting our given values in above proportion, we will get:

[tex]\frac{300\text{ Miles}}{x}=\frac{360\text{ Miles}}{6.5\text{ Hours}}[/tex]

Cross multiply:

[tex]x\cdot 360\text{ Miles}=300\text{ Miles}\times6.5\text{ Hours}}[/tex]

[tex]x=\frac{300\text{ Miles}\times6.5\text{ Hours}}{ 360\text{ Miles}}[/tex]

[tex]x=\frac{300\times6.5\text{ Hours}}{360}[/tex]

[tex]x=5.41666\text{ Hours}\approx 5.42\text{ Hours}[/tex]

Therefore, it will take approximately 5.42 hours to travel additional 300 miles.

Answer:

918

Step-by-step explanation:

Use distributive property.

(810) + (88) + (20) = 918

Answer:

918

Step-by-step explanation: hope it was helpful

Answer:

Discussed below.

Step-by-step explanation:

The headline states that 98% of all movies show imagery of drugs. There are a few assumptions that the wording can insinuate:

However, the story refers to a more specific statistic: that not 98% of all movies but 98% of the top movie rentals depicted drug use, drinking or smoking.

The key differences:

Thus, the headline misrepresents the content of the story which may lead one to make broader and misplaced conclusion about imagery of drugs in movies.

The headline accurately reflects the information provided in the news story, but the accuracy is dependent on the credibility and methodology of the government study.

The headline "Drugs shown in 98 percent of movies" accompanied a news story about a "government study" claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals.

First, it's important to note that the headline accurately reflects the information provided in the news story. However, the accuracy of the headline is dependent on the credibility and methodology of the government study being referenced.

Without additional information about the study, such as the sample size, selection criteria, and methodology, it is difficult to fully assess the accuracy of the headline. It's always important to critically evaluate the sources of information and consider multiple perspectives in order to draw accurate conclusions.

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Answer:22in2

Step-by-step explanation:

Answer:

Option A) 1.68                

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 100

p = 15% = 0.15

Number of bags overfilled , x = 21

First, we design the null and the alternate hypothesis  

[tex]H_{0}: p = 0.15\\H_A: p > 0.15[/tex]

Formula:

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{21}{100} = 0.21[/tex]

[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

Putting values, we get,

[tex]z = \dfrac{0.21-0.15}{\sqrt{\dfrac{0.15(1-0.15)}{100}}}\\\\z = 1.68[/tex]

Thus, the correct answer is

Option A) 1.68

To test the hypothesis H0: p = 0.15 versus Ha: p > 0.15, the test statistic is Z = 1.68.

To test the hypothesis H0: p = 0.15 versus Ha: p > 0.15, where p is the true proportion of overfilled bags, we can use the test statistic Z. The formula for the test statistic is Z = (P' - p) / √(p(1-p) / n), where P' is the sample proportion, p is the hypothesized proportion, and n is the sample size.

In this case, the sample proportion P' = 21/100 = 0.21, the hypothesized proportion p = 0.15, and the sample size n = 100.

Plugging these values into the formula, we get Z = (0.21 - 0.15) / √(0.15(1-0.15) / 100) = 1.68.

Therefore, the test statistic is Z = 1.68.

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Answer:

19

Step-by-step explanation:

If the scientist chooses 60 random eggs then the overall probability of selecting yellow eggs is 32%. So, there's a chance of he randomly collecting 60 eggs out of which 19 could be yellow.

(60/100) x 32 ~ 19...

The usual number of yellow dragon eggs expected in a sample of 60, given a 32% probability, is 19 when rounded to the nearest whole number.

The question at hand involves finding the expected number of yellow eggs in a sample size of 60, given a known probability of a yellow egg occurrence.

Since we know that 32% of the dragon eggs on planet Pern are yellow, we can calculate the usual number of yellow eggs in the samples by multiplying the sample size (60 eggs) by the probability of getting a yellow egg (0.32).

Therefore, the expected or usual number of yellow eggs in the sample would be 60 × 0.32 = 19.2.

Considering that we cannot have a fraction of an egg, the usual number of yellow eggs in samples of 60 eggs would typically be rounded to the nearest whole number, which is 19.

Answer:

  tan(23° -21°) = (tan(23°) -tan(21°))/(1 +tan(23°)tan(21°))

Step-by-step explanation:

The formula for the tangent of the difference of angles is ...

  tan(a-b) = (tan(a) -tan(b))/(1 +tan(a)tan(b))

Filling in the values a=23° and b=21°, you get the formula shown above.

The expression for tan(23°−21°) in terms of the tangents of 23° and 21° is: tan(23°−21°) = (tan 23° - tan 21°) / (1 + tan 23° * tan 21°).

To express tan(23°−21°) in terms of the tangents of 23° and 21°, we can use the angle subtraction formula for tangent, which is:

tan(α - β) = (tan α - tan β) / (1 + tan α * tan β)

Applying this to tan(23°−21°), we get:

tan(23°−21°) = (tan 23° - tan 21°) / (1 + tan 23° * tan 21°)

We can't directly calculate the values from the given table since 23° and 21° are not listed. However, we understand the formula required to express tan(23°−21°) in terms of the tangents of these two angles.

Answer:

[tex]\frac{3}{8}[/tex]  of a box of candy your friend eat.

Step-by-step explanation:

Given:

You and your friend are going to some candy.

You eat 3/4 of a box of candy.

Your friend eats 1/2 as much as you do.

Now, to find that how much of a box of candy does your friend eat.

Quantity of a box of candy you eat = [tex]\frac{3}{4}[/tex]

Quantity of candy your friend eat = [tex]\frac{1}{2} \ of\ \frac{3}{4}[/tex]

Now, to get how much the candy your friend eat we multiply 1/2 and 3/4:

= [tex]\frac{1}{2} \times \frac{3}{4}[/tex]

= [tex]\frac{3}{8}[/tex] .

Therefore, [tex]\frac{3}{8}[/tex]  of a box of candy your friend eat.

Answer:

The height of the wall is 52.2 feet.

Step-by-step explanation:

Given:

From the figure shown, HT is the height of Carlos, 'V' is the position of mirror.

So, TV = 4 ft, VS = 36 ft, HT = 5.8 ft.

Let the height of the wall be 'x'. So, JS = 'x'

Now, consider the two triangles HTV and JVS

Statements                                                               Reasons

1. ∠ HTV ≅ ∠ JSV                                           Right angles are congruent

2. ∠ HVT ≅ ∠ JVS                                          Given in the figure

Therefore, ΔHTV and Δ JVS are similar triangles by AA postulate.

Now, from definition of similar triangles, corresponding sides of two similar triangles are in proportion to each other. Therefore,

[tex]\frac{HT}{JS}=\frac{TV}{VS}=\frac{HV}{JV}[/tex]

Considering the first two pair of fractions, we have:

[tex]\frac{5.8}{x}=\frac{4}{36}\\\\36\times 5.8=4\times x\\\\x=\frac{36\times 5.8}{4}\\\\x=9\times 5.8=52.2\ ft[/tex]

Therefore, the height of the wall is 52.2 feet.

Answer:

The correct option is second one i.e 24 units.

Therefore the height of the triangle is

[tex]NR=24\ units[/tex]

Step-by-step explanation:

Given:

An equilateral triangle has all sides equal.

ΔMNO is an Equilateral Triangle with sides measuring,

[tex]NM = MO = ON =16\sqrt{3}[/tex]

NR is perpendicular bisector to MO such that

[tex]MR=RO=\dfrac{MO}{2}=\dfrac{16\sqrt{3}}{2}=8\sqrt{3}[/tex] .NR ⊥ Bisector.

To Find:

Height of the triangle = NR = ?

Solution :

Now we have a right angled triangle NRM at ∠R =90°,

So by applying Pythagoras theorem we get

[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]

Substituting the values we get

[tex](MN)^{2} = (MR)^{2}+(NR)^{2}\\\\(16\sqrt{3})^{2}=(8\sqrt{3})^{2}+(NR)^{2}\\\\(NR)^{2}=768-192=576\\Square\ rooting\ we\ get\\NR=\sqrt{576}=24\ units[/tex]

Therefore the height of the triangle is

[tex]NR=24\ units[/tex]

Answer:

b 24

Step-by-step explanation:

Answer:

Parallel lines do not intersect therefore the system of equations cannot have any solution. Therefore there no solutions to the given system of equations.

Step-by-step explanation:

Aaron and Blake both wrote down equation. Their equation has the same slope, But Aaron's y-intercept was negative and Blake's y-intercept was positive.

Therefore both equations will represent lines that are parallel.

Parallel lines do not intersect therefore the system of equations cannot have any solution.