Please need help with this assignment… thx

the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

what is right-angled triangle  ?

A right-angled triangle is a type of triangle that has one angle measuring exactly 90 degrees (a right angle). This angle is formed by the intersection of two sides of the triangle, which are called the legs or catheti, and it is opposite to the longest side of the triangle, which is called the hypotenuse. The hypotenuse is always opposite the right angle.

In the given question,

The area of a right-angled triangle is given by the formula:

Area = 1/2 x base x height

where the base and height are the two perpendicular sides of the triangle.

In this case, the adjacent side and opposite side of the right-angled triangle are both 2 units.

Let's call the hypotenuse of the triangle 'c'. Then, by the Pythagorean theorem, we have:

c² = 2² + 2²

c² = 8

c = √(8) = 2.8284 (rounded to 4 decimal places)

Now, we can use the trigonometric ratios to find the base and height of the triangle. In this case, we can use the tangent ratio:

tan(theta) = opposite/adjacent

tan(theta) = 2/2

tan(theta) = 1

theta = tan⁻¹(1) = 45 degrees

Therefore, the base and height of the triangle are:

base = adjacent x tan(theta) = 2 x tan(45) = 2 x 1 = 2

height = opposite x tan(theta) = 2 x tan(45) = 2 x 1 = 2

Now we can use the area formula to find the area of the triangle:

Area = 1/2 x base x height

Area = 1/2 x 2 x 2

Area = 2 square units

Therefore, the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

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Queremos encontrar el número total de árboles en un jardín botánico siendo que conocemos el porcentaje de un dado tipo de arbol, y cuantos de estos arboles tenemos.

Veremos que el número total de arboles es 250.

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

Para resolver esto, primero debemos analizar la información que se nos da:

Si definimos N como el número total de arboles, sabemos que el 18% de N es igual que 45.

Entonces podemos escribir:

(18%/100%)*N = 45

0.18*N = 45

Ahora podemos resolver esto para N:

N = 45/0.18 = 250

Es decir, hay 250 árboles en total.

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Given that the buffet is to have 19 desserts for every 16 people.

Let's find the number of desserts they should have if they plan for 320 people.

19 desserts = 16 people

x desserts = 320 people

Therefore, we have:

Divide both sides by 16:

Thereore, they should have 380 desserts if they plan for 320 people.

ANSWER:

380 desserts

tax is

$444.5 ---> 100%

x ------------> 6.5%

tax is $ 28.89, therefore the television cost with tax inclueded is

answer: C

Answer:

314.16cm²

Step-by-step explanation:

The average speed formula is given by:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)

Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is \(\displaystyle\sf 2 \times 120 = 240\) miles.

Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula \(\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}\).

For the journey from A to B:

\(\displaystyle\sf \text{Time}_1 = \frac{120}{30} = 4\) hours

For the return journey from B to A:

\(\displaystyle\sf \text{Time}_2 = \frac{120}{40} = 3\) hours

The total time for the round trip is the sum of the individual times:

\(\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7\) hours

Now, we can calculate the average speed:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240}{7} \approx 34.29\) miles per hour.

Therefore, the average speed for the round trip is closest to 34.29 miles per hour.

Answer: 32.21 (seattle resident has more than atlanta resident)

Step-by-step explanation:

The Seattle resident has $32.21/CPI more than the Atlanta resident.

The consumer price index is used to measure inflation. It measures the price of a basket of goods.

In order to compare the purchasing power, first adjust the incomes for inflation by dividing the incomes by the CPI.

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Answer:

-7x+15y+2x-6y

-5x+9y

Step-by-step explanation:

Answer:

-7x - ( -15y ) - ( - 2x) + ( -6y )

=> -7x + 15y + 2x - 6y

=> ( -7x + 2x ) + (15y - 6y)

=> -5x + 9y

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The measure of the minor arc m∡rv = 111°

Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c

Where a = ∡RV
b = ∡SU = 37°:

and c = ∠T (the angle between intersecting secants.

Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:

(a - 37) / 2 = 37

Multiplying both sides by 2 gives:

a - 37 = 74

Adding 37 to both sides gives:

a = 111

Therefore, a is equal to  m∡rv = 111°.

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Answer:

33%

Step-by-step explanation:

There are 33 squares out of 100 that are shaded

33/100

Percent means out of 100

33%

Or

A ratio that compares a number to 100 can be written as a percent. So in this problem, since the figure has 33 out of 100 boxes shaded, we have the ratio 33/100 which can be written as 33%.

Answer: C

Step-by-step explanation:

1. divide 3 by 2 to find out how many pounds of blueberries she picked each day. 3/2 is 1.5

2. multiply 1.5 by 16 to convert to ounces. 1.5x16 is 24.

3. she picked 24 ounces of blueberries each day.

Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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Answer:

0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

Assume the probability that a given registered voter will vote in the presidential election is 61%.

This means that \(p = 0.61\)

152 registed voters:

This means that \(n = 152\)

Mean and Standard deviation:

\(\mu = E(X) = 152*0.61 = 92.72\)

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{152*0.61*0.39} = 6.01\)

Probability that no less than 95 out of 152 registered voters will vote in the presidential election.

This is, using continuity correction, \(P(X \geq 95 - 0.5) = P(X \geq 94.5)\), which is 1 subtracted by the pvalue of Z when X = 94.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{94.5 - 92.72}{6.01}\)

\(Z = 0.3\)

\(Z = 0.3\) has a pvalue of 0.6179

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.

LM/PQ = MN/QR = LN/PR because triangle LMN and PQR are similar.

Similar triangles are triangles that have the same shape, but their sizes may vary. The conditions for two triangles to be similar are;

1. The corresponding angles of the similar triangles must be congruent i.e they must be equal.

2. The ratio of the corresponding sides are equal. The corresponding sides are :

LM and PQ, MN and QR , LN and PR

since LM/PQ = MN/QR = LN/PR , then we can say triangle LMN and PQR are similar.

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Answer:

6^2x+52

Step-by-step explanation:

Answer:

1. To round to the nearest tenth, we'll need to look at the digit to the right of the tenths place, the hundredths place. Since there's a three in the hundredths place, we will round down to 4.9. The mean absolute deviation of these eight values rounded to the nearest tenth is 4.9.

2. 1

Order the numbers in the data set and find the median.

2

Subtract the median from each number in the data set.

3

Take the absolute value of each difference.

4

Add up all of the positive differences.

5

Divide this sum by the number of data points in the set.

3.The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

4.

Step-by-step explanation:

Answer:

10 games

Step-by-step explanation:

The team can expect to win 6 matches.

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Given that, The ratio of wins to losses for the spartan football team is 3:5. and this trend continues, they play a total of 16 games,

Let they won 3k games and loose 5k games.

Then,

3k+5k = 16

8k = 16

k = 2

Therefore, they lose 5·2 = 10 matches and won 3·2 = 6 matches.

Hence, the team can expect to win 6 matches.

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Answer:

A. Reflection

Step-by-step explanation:

I believe the answer would be reflection

The maximum volume of the cylinder is approximately 1257 cubic centimeters.

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

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Answer:

A: (2, 11).

Step-by-step explanation:

For an ordered pair to be a solution of an equation, the ordered pair must "fit".

A: (2, 11).

11 = 3(2) + 5

11 = 6 + 5

11 = 11

So, (2, 11) is a solution.

B: (3, 13).

13 = 3(3) + 5

13 = 9 + 5

13 = 14

Since 13 is not the same thing as 14, (3, 13) is not a solution.

Since A works but B doesn't, choices C and D are both eliminated. A is your answer.

Hope this helps!

Answer:

C. a quadratic function with a negative value of a

Step-by-step explanation:

It is likely that a quadratic function with a negative value of a would be the best model for this data, as it would represent a parabolic shape that can accommodate a downward trend, followed by an upward trend, in the stock price. The value of "a" determines the direction of the parabola, with a negative value resulting in a downward-facing parabola, which is appropriate for a stock price that starts low and increases over time. This type of function would provide a good fit for the data, especially if there are fluctuations or ups and downs in the stock price over time.

Answer:

option 2 and 4 for the first slide

option 3 for the second slide

Step-by-step explanation:

Answer:

A, C, D

Step-by-step explanation:

For edge

Answer:

b. becomes narrower.

Step-by-step explanation:

Since the 95% confidence interval for a population mean could find out from 100 to 120

And based on this, the coefficient confidence level is declined to 0.90

Therefore the confidence interval for mean should become narrowed

As a 95% confidence interval represents narrower and 99% confidence interval represents wider

Therefore the option B is correct

Using confidence interval concepts, the correct option is:

b. becomes narrower

The margin of error of a confidence interval is given by:

\(M = z\frac{s}{\sqrt{n}}\)

In which:

The lower the confidence level, the lower the value of z, hence, the margin of error decreases and the interval becomes narrower, which means that option b is correct.

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Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

Answer:

Starting with the given inequality:

-4(r - 2/3) + 4 < -8

First, simplify the expression inside the parentheses:

-4r + 8/3 + 4 < -8

Combine the constants:

-4r + 20/3 < -8

Subtract 20/3 from both sides:

-4r < -8 - 20/3

-4r < -24/3 - 20/3

-4r < -44/3

Finally, divide both sides by -4, remembering to reverse the direction of the inequality since we are dividing by a negative number:

r > -44/3 ÷ -4

r > 11/3

So the solution to the inequality is r > 11/3, which means that any value of r that is greater than 11/3 will make the inequality true.

$40.50¢

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