A park is in the shape of a rectangle 300 feet long 50 feet wide Amaya is standing at one corner of the park at point x he then walks in a straight line to the opposite corner at point y how far does he walk rounded to the nearest tenth

Answer: 2. Linear pair postulate

4. 60 + mACB=180

5. mACB=120

6. definition of obtuse angle

The value of straight angle ∠BCD = 180° thus the angle ∠ACB = 180°- 60° = 120° therefore, the given triangle ABC is the obtuse triangle.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given triangle ABC with extended line CD.

Since CD is colinear with BC, therefore, BCD will be a single straight-line segment.

The ∠BCD is straight angle so it will be 180°.

∠BCD = ∠ACB + ∠ACD

∠ACB + 60 = 180

∠ACB = 180 - 60 = 120°.

An obtuse triangle is a triangle whose one or more interior angle is greater than 90°.

Since∠ACB > 90° therefore triangle ABC is an obtuse angle.

Hence "The value of straight angle ∠BCD = 180° thus the angle ∠ACB = 180°- 60° = 120° therefore, the given triangle ABC is the obtuse triangle".

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The value of "x" in the expression 5ˣ⁻² = 8; by using the change of base formula is approximately 3.2920.

We have to find the value of "x" in the "logarithmic-expression" : 5ˣ⁻² = 8; for which we have to use the change-of-base formula, which is \(log_{b} (y) = \frac{log(y)}{log(b)}\).

we take "log" on both sides of 5ˣ⁻² = 8;

We get,

⇒ (x-2)log(5) = log(8),

⇒ x-2 = log(8)/log(5),

By using the "change of base formula",

We get,

⇒ x-2 = log₅(8),

⇒ x-2 = 1.2920

⇒ x = 1.2920 + 2;

⇒ x ≈ 3.290,

Therefore, the value of x is approximately 3.2920.

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The given question is incomplete, the complete question is

Find the value of "x" in the expression 5ˣ⁻² = 8 . Using the change of base formula \(log_{b} (y) = \frac{log(y)}{log(b)}\).

Answer:

x= 75*2

x= 3/4*200

(The options arent very clear)

Step-by-step explanation:

The equation is

x= 75/100 *200

= 75*2

or 3/4 * 200

Answer:

The answer is B.

Step-by-step explanation:

Answer:

y=22

Step-by-step explanation:

y=20+2

Answer: I calculated the surface area of a cube whose edge is 4.2 m

Step-by-step explanation: hope this helps

Answer:

sqaure root

Step-by-step explanation:

aka radical of cat

Answer:

|-2| + 2

Step-by-step explanation:

-4 / 2-5i

cos (x) / 1 - sin squared (x)

|-2| + 2

Answer:

Step-by-step explanation:

\(\sf -5x^5*y^5 *(-6xy^3) = (-5)*(-6) *x^{5+1}*y^{(5+3)}\\\)

                               \(\sf = 30x^6y^8\)

The instantaneous rate of change of r with respect to θ when θ=0 is zero.

The instantaneous rate of change of a polar curve with respect to θ at a point is given by the derivative of the equation of the curve with respect to θ at that point.

To find this instantaneous rate of change of r with respect to θ when θ=0, we first take the derivative of the equation of the curve with respect to θ:

dr/dθ = (-200/(θ^3))/((θ^2)+1)^2

Then, we substitute θ=0 into this expression, which gives us:

dr/dθ|θ=0 = (-200/(0^3))/((0^2)+1)^2

Since any division by zero is undefined, we cannot evaluate this expression directly. However, we know from the definition of limits that if the limit of a function exists as x approaches a certain value, then we can use this limit to define the behavior of the function at that value.

In this case, as θ approaches 0, the denominator of the expression becomes (0^2 + 1)^2 = 1, while the numerator remains -200/θ^3. Therefore, we have:

dr/dθ|θ=0 = limit as θ approaches 0 of (-200/(θ^3))/((θ^2)+1)^2

= limit as θ approaches 0 of (-200/θ^3)/(θ^4 + 2θ^2 + 1)

Using L'Hopital's rule, we can simplify this expression as follows:

= limit as θ approaches 0 of (600/θ^4)/(12θ^2)

= limit as θ approaches 0 of 50/θ^2

Since the denominator becomes smaller and smaller as θ approaches 0, the limit approaches infinity. Hence, the instantaneous rate of change of r with respect to θ when θ=0 is undefined or infinite.

Answer: The instantaneous rate of change of r with respect to θ when θ=0 is undefined or infinite.

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The final image will fit in a similar portfolio with an area of 160 square inches.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

The dimensions for this problem are given as follows:

24 inches, 36 inches.

With the reduction with a scale factor of 1/3, the dimensions are given as follows:

8 inches,  12 inches.

With the enlargement by a factor of 1.25, the dimensions are given as follows:

10 inches and 15 inches.

Hence the area is given as follows:

15 x 10 = 150 square inches.

As the area of 150 square inches is less than 160 square inches, the final image will fit in a similar portfolio with an area of 160 square inches.

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Slope-intercept form: y = mx + b

m = the slope

y = the y-intercept

In our problem,

y = -4/3x - 1

m = -4/3

The slope is -4/3

Answer:  AE = 5

Step-by-step explanation:

I sketched the triangle based on the information provided.

since ∠A = 90° and is divided into three equal angles, then ∠BAD, ∠DAE, and ∠CAE = 30°

Since AB = 5 and BC = 10, then ΔCAB is a 30°-60°-90° triangle which implies that ∠B = 60° and ∠C = 30°

Using the Triangle Sum Theorem, we can conclude that ∠ADB = 90°, ∠ADE = 90°, ∠ AED = 60°, AND ∠ AEC = 120°

We can see that ΔAEC is an isosceles triangle. Draw a perpendicular to divide it into two congruent right triangles. Label the intersection as Z. ΔAEZ and ΔCEZ are 30°-60°-90° triangles.

Using the 30°-60°-90° rules for ΔABC we can calculate that AC = 5√3.

Since we divided ΔAEC into two congruent triangles, then AZ = \(\dfrac{5\sqrt 3}{2}\)

Now use the 30°-60°-90° rules to calculate AE = 5

The ∠G and ∠J are congruent because they are bisector  angles.

ΔGHI and ΔJKL are congruent because of the similar triangle theorem.

When two lines in a plane do not cross at any point, they are said to be parallel. Thus, lines that never cross each other's paths and do not have a common junction point are said to be parallel.

From the given information, segments GH and JK are parallel and congruent and segments GL, LI, and IJ are congruent.

If we see the figure according to the statements,

The ∠G and ∠J are congruent because they are bisector  angles.

ΔGHI and ΔJKL are congruent because of the similar triangle theorem.

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Answer:

D (D)

Step-by-step explanation:

We can know from the question that each face has two A, two B, and two C, two D, and two E. And these three faces are the sides of the triangular pyramid (Each face vertex is D).

∴ We can get the picture of the fourth face.

∴ There are two A, two B, two C, one D, and two E in the picture.

∴ The middle of the fourth face is D.

*See the attachment*

Answer:

D

Step-by-step explanation:

A patent is a form of intellectual property that gives an individual or organization the exclusive right to manufacture, use, and/or sell an invention for a set period of time.

The length of a patent varies by country, but generally lasts for 20 years from the date the patent is filed with the government. This period can be extended in certain cases if the patent office grants a patent term extension.

The formula for calculating the length of a patent is: Length of Patent = Initial 20 Year Period + Extension. The initial 20 year period starts from the filing date of the patent application and is the same for all countries. However, the length of the extension varies depending on the country and the circumstances of the patent. For example, some countries may offer a 5-year extension, while others may offer a 10-year extension.

The length of a patent must be carefully calculated so that the patent owner can maximize the benefits of the patent. By calculating the patent length and extension, the patent owner can ensure that they are able to take advantage of their exclusive right to the invention for the maximum amount of time possible.

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The cars pass each other at approximately 4:30 PM.

The first car, traveling from Boston to New York, is moving at a steady rate of 50 mph.

It starts at 1:00 PM and travels for a certain amount of time, which we'll call "t" hours.

The second car, traveling from New York to Boston, is moving at a steady rate of 40 mph. It starts at 1:30 PM, which is half an hour after the first car, and also travels for "t" hours.

Now, let's calculate the distance each car has traveled when they meet:

Distance traveled by the first car = Speed × Time = 50 mph × t hours

Distance traveled by the second car = Speed × Time = 40 mph × (t-0.5) hours

Since the total distance between Boston and New York is 295 miles, the sum of the distances traveled by the two cars must equal 295 miles:

50t + 40(t - .5) = 295

50t + 40t -20 = 295

90t = 295 + 20

90t = 315

t = 315/90

t = 3.5 hours later

So, the cars pass each other approximately 3.5 hours after the first car starts from Boston.

To find the time at which they pass, we add this time to the starting time of the first car:

1:00 PM + 3.5 hours = 4:30 PM (rounded to the nearest minute)

Therefore, the cars pass each other at approximately 4:30 PM.

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She can save $432 each year.

Now, According to the question:

Li-Mei thinks she can save money on electricity by changing all her bulbs from incandescent bulbs to fluorescent bulbs.

Incandescent bulb - 150 hours monthly use $.05 per hour Fluorescent bulb - 150 hours monthly use $.02 per hour.

We have to following statement.

Incandescent: 0.05 × 150 × 12 × 8=720

Fluorescent: .02 × 150 × 12 × 8=288

720-288=$432 less per year

Hence, She can save $432 each year.

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The complete question is this:

Li-Mei thinks she can save money on electricity by changing all her bulbs from incandescent bulbs to fluorescent bulbs. Based on the following energy cost table, how much can she save each year if she replaces 8 bulbs? Incandescent bulb - 150 hours monthly use $.05 per hour Fluorescent bulb - 150 hours monthly use $.02 per hour

The null hypothesis (H0) assumes that the proportion of people who own cats is equal to or greater than 60%, while the alternative hypothesis (H1) suggests that the proportion is smaller than 60%.

To test the claim that the proportion of people who own cats is smaller than 60% at the 0.025 significance level, we need to set up the null and alternative hypotheses.

Let's start with the null hypothesis (H0), which assumes that the proportion of people who own cats is equal to or greater than 60%.

The alternative hypothesis (H1) will be that the proportion is smaller than 60%.

H0: p ≥ 0.6
H1: p < 0.6

The null hypothesis assumes that the proportion of people who own cats is 60% or higher, while the alternative hypothesis suggests that the proportion is smaller than 60%.

We will conduct a hypothesis test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

To conduct the hypothesis test, we would collect a sample of data and calculate the test statistic, which in this case would be the proportion of people in the sample who own cats.

We would then compare this test statistic to the critical value or p-value associated with the 0.025 significance level.

If the test statistic falls in the critical region (below the critical value) or if the p-value is less than 0.025, we would reject the null hypothesis in favor of the alternative hypothesis.

This would indicate that there is enough evidence to suggest that the proportion of people who own cats is indeed smaller than 60%.

On the other hand, if the test statistic does not fall in the critical region (above the critical value) or if the p-value is greater than or equal to 0.025, we would fail to reject the null hypothesis.

This would suggest that there is not enough evidence to conclude that the proportion of people who own cats is smaller than 60%.


To summarize, the null hypothesis (H0) assumes that the proportion of people who own cats is equal to or greater than 60%, while the alternative hypothesis (H1) suggests that the proportion is smaller than 60%.

By conducting a hypothesis test and comparing the test statistic to the critical value or p-value associated with the 0.025 significance level, we can determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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The solution to the equation below rounded to 2 decimal places is 22.20.

Given the logarithmic expressions

ln x = 3.1

We are to determine the value of "x"

ln x = 3.1

Take the exponent of both sides

e^ln x = e^3.1

The exponent will cancel out the log function to have:

x = e^3.1

x = 22.197

Hence the solution to the equation below rounded to 2 decimal places is 22.20.

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Segment CP is tangent to circle C at point B.

How to prove that the line is tangent to a circle?

Draw circle C with center at point A and radius AD = CD = DE.

Draw point P outside the circle C.

Draw segment AP and extend it to intersect the circle at point B.

Draw segment BD.

Draw segment CP.

Note that triangle BCD is isosceles, since CD = BD. Therefore, angle BDC = angle CBD.

Since angle BDC is an inscribed angle that intercepts arc BC, and angle CBD is an angle that intercepts the same arc, then angle BDC = angle CBD = 1/2(arc BC).

Since CD = DE, then angle CED = angle CDE. Therefore, angle DCE = 1/2(arc BC).

Since angles BDC and DCE are equal, then angles BDC and CBD are also equal, and triangle BPC is isosceles. Therefore, segment BP = segment PC.

Since BP = PC, then segment CP is perpendicular to segment BD, by the Converse of the Perpendicular Bisector Theorem.

Therefore, segment CP is tangent to circle C at point B.

Hence, the proof is complete.

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Answer:

Step-by-step explanation:

congruent angles:

angle A = H

B = J

K = C

L = D

proportional side :

AB proportional HJ

AD proportional HL

JK proportional  BC

KL proportional CD

hope it helps

if it does so then please mark me as brainliest

Answer:

c

Step-by-step explanation:

the parabola crosses the x axis at (0,0) and (4,0)

Based on the given information, the regression that represents the estimated production function model for firm output in the industry is:

c. log(Q1) = 10.74 + 0.032 Li

The regression equation in option c represents a logarithmic relationship between the output (Q1) and the number of workers employed (Li). Taking the logarithm of the output variable allows for a more flexible functional form and captures potential diminishing returns to labor.

In the regression equation, the constant term (10.74) represents the intercept or the level of output when the number of workers is zero. The coefficient of 0.032 (0.032 Li) indicates the relationship between the logarithm of output and the number of workers employed.

Since the question states that employing another worker leads to a 32 percent increase in output, this aligns with the coefficient of 0.032 in the regression equation. It suggests that a 1 percent increase in the number of workers (Li) leads to a 0.032 percent increase in output, which is equivalent to a 32 percent increase.

Therefore, the regression equation in option c best represents the estimated production function model in this scenario.

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In the context of this poem, people overcome adversity through hope.

Hope is described as a bird with feathers that perches in the soul and never stops singing. It is a source of comfort and solace, heard in the chillest lands and on the strangest seas, even in extremities. Despite the challenges people may face, the presence of hope is enough to keep them warm and to overcome adversity.

In my own experience, hope has been a driving force in overcoming adversity. When faced with challenges, having a positive outlook and focusing on a brighter future can help to overcome difficulties and find resilience.

This idea is echoed in other literature and art, where hope is often depicted as a source of strength and comfort in the face of adversity.

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--The given question is incomplete; the complete question is

"In the context of this poem, how do people overcome adversity? Use evidence from the poem 'hope is the thing with feathers', your own experience, and other literature or art in your answer. The poem is

"Hope" is the thing with feathers

That perches in the soul

And sings the tune without the word

And never stops - at all-

And sweetest in the gale is heard

And sore must be the storm

That could abash the little bird

That kept so many warm

I've heard it in the chillest land

And on the strangest sea

Yet never in extremity.

It asked a crumb of me."--

If 150 town residents were asked about their age and yogurt , then the probability that a randomly selected customer prefers Swirl if age is at least 25 years old is 0.66 .

let X be = the selected customer that prefers swirled yogurt or is at least 25 years old ;

The sum of all the customers that are "at least 25 years old" = 21 + 30 + 24 = 75 ;

the sum of all the customers that " like Swirl Yogurt" is = 24 + 24 = 48 ;

the total number of residents = 150 students ;

So , the probability is calculated as : ( 75+48 -24)/150 = 0.66 .

Therefore , the required probability is 0.66 .

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The given question is incomplete , the complete question is

The 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next.

     Age                               Chocolate      Vanilla      Swirl

under 25 years old                  22                 29             24

at least 25 years old                21                  30             24

What is the probability a randomly selected customer prefers Swirl Yogurt given he or she is at least 25 years old ?

The arc made by the hand is 38.47 inches.

In this question we have been given the tip of a 7 in. minute hand of a clock sweeps out circular arcs.

We need to find the length of the arc made by the tip of the minute hand between 8:45 am to 9:00 am.

For the minute hand to 60 minutes is a full rotation of the clock, or 360°.

9:00 - 8:45 = 15 minutes.

15 minutes is 1/4 of 60 minutes, so 15 minutes is 1/4 of 360° = 90°.

Now we can calculate the arc length using the angle of 90°.

here, radius r = 7 in.

Arc length = (90/360)(πr^2)

                 = (1/4) * (3.14) * (7^2)

                 = 38.47 in 

Therefore, the length of the arc made by the hand is 38.47 inches.

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Answer:

-7\(x^{3}\) + 9\(x^{2}\) -4x

Step-by-step explanation:

-4\(x^{3}\) + 8\(x^{2}\) - 4x - 3\(x^{3}\) + \(x^{2}\)

-7\(x^{3}\) + 9\(x^{2}\) -4x