which of the following expressions are equivalent to…

The height of the antenna found using trigonometric ratios is about 8 meters

Trigonometric ratios indicates the ratio of the sides of a right triangle, and have values based on the lengths of the sides of a right triangle, drawn on the coordinate plane.

The distance from the building at which Brooklyn stands = 23 meters

Angle of elevation from her eyes to the roof, θ = 24°

Angle of elevation from her eyes to the top of the antenna = 38°

Height of her eyes from the ground = 1.66 meters

[tex]tan(\theta) = \dfrac{Opposite}{Adjacent} = \dfrac{Height}{Horizontal \, distance}[/tex]

Therefore;

Height = Horizontal distance × tan(θ)

Height to the top of the roof, H₁ = Horizontal distance × tan(θ)

Therefore;

H₁ = 23 × tan(24°) ≈ 10.24

Height to the top of the antenna, H₂ = 23 × tan(38°) ≈ 17.97

Height of the antenna ≈ 17.97 - 10.24 ≈ 8

Height of the antenna is about 8 meters

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Answer: 9x - y = -5

Step-by-step explanation:

For Cameron's job, the restrictions on the domain are 168 hours for the hourly rate.

The total number of hours affects how much money is made.

This suggests that the amount of money made is the result of the number of hours put in.

A week can only have a total of 168 hours (24 x 7).

Thus, the domain for the hourly wage of Cameron.

24 x 7 < 168

Since 168 hours is the maximum that can be completed in a week, this represents the constraint mostly on domain.

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The correct Option (B). Succession may be defined as the change in the ecological community of the species with respect to time. Two main types of succession are primary succession and secondary succession.

The living things that accumulate in the succession is from the simple organism to the complex organism. First lichens will evade in the land. After lichens grass then shrubs and finally the trees will cover the area and convert into the forest.

Primary succession occurs in basically dead areas—regions where the soil is incapable of supporting life due to causes such as lava flows, newly created sand dunes, or glacier-left boulders.

Pioneer microorganisms, plants (lichens and mosses), grassy stage, smaller shrubs, and trees are all stages of primary succession. When there is food available, animals begin to return. The climax community stage is reached when the ecosystem is fully functional.

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Full Question :

After a town is abandoned, the concrete parking lots remain empty and inactive for hundreds of years. What is the most likely order of ecological succession in that area?

A.grass → trees → lichens → moss

B.lichens → grass → shrubs → trees

C.lichens → grass → trees → shrubs

D.shrubs → grass → trees → lichens

Observed proportions (relative frequencies) from a sample are statistics that can be used to estimate probabilities.

a) Thre is 99.73% proportion of observations is in between 190 and 310 .

b)there is 95.44% proportion of observations is in between 210 and 290 .

We have given that,

Mean of population, μ = 250

standard deviations, σ = 20

we have to calculate proportion of observations in the given interval pair.

a) pair of values are 190 and 310

Using Z-score formula,

Z =( x - μ) /σ

=> Z = (190 - 250) / 20 = -3

Similarly, Z = (310 - 250)/20 = 3

So, -3 < z < 3 and from Z score we found p-value

P(190<X<310) = P( 190-u/sd < X-u/sd < 310-u/sd)

= P( X< 310 ) - P(X<190) = P(Z < 3) - P( Z< -3 )

=0.99865 - 0.00135 0.9973 = 99.73%

b) pair is 210 and 290

Z-Score = (210-250)/20 = -2

Z-score = (290-250)/20 = 2

so, -2 < z < 2

From Z score we found p-value

P(210<X<290) = P(X<290) - P(X<210)

= P(Z< 2) - P(Z< -2)

= 0.9772 - 0.0228 = 0.9544 = 95.44%

So, the required proportion are 99.73% and 95.44% proportion of observations in each given pair.

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Complete question:

If the mean of a population is 250 and its standard deviation is 20, approximately what proportion of observations is in the interval between each pair of values? a 190 and 310 b. 210 and 290.

The approximate probability that the sample mean is within 48 and 51 is 0.82.

n = sample size = 81

σ = standard deviation = 9

μ = population mean = 50

Probability is a chance of something event can occur, for this case the probability measure of the chance of sample mean is between 48 and 51 can occur. So, the probability of the sample mean is between 48 and 51 is,

P(48 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])

= P([tex]\frac{48-50}{\frac{9}{\sqrt{81}}}[/tex]≤ z ≤ [tex]\frac{51-50}{\frac{9}{\sqrt{81}}}[/tex])

= P(-2 ≤ z ≤ 1)

= P(z ≤ 1) - P(z ≤ -2)

using z table and we get,

= 0.8413 - 0.0228

= 0.8185

= 0.82

Thus, the probability is 0.82 for the sample mean is within 48 and 51.

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The measure of the largest angle of quadrilateral is 140°.

We have given that,

the ratio of angles of a quadrilateral is 2:3:6:7.

And we have to find the largest angle of quadrilateral.

We know that the sum of all the interior angles of quadrilaterals 360°.

Let the common multiple of angles be x,

therefore  

2x + 3x + 6x + 7x = 360°

                      18x = 360°

                         x = [tex]\frac{360}{18}[/tex]

                         x = 20°

so the angles becomes,

2(20°) = 40°

3(20°) = 60°

6(20°) = 120°

7(20°) = 140°

Hence the largest of these angles is 140°.

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If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg according to given standard deviation.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = x- υ/σ

Given that μ = 55, σ = 6;

For x = 49:

z = 49 - 55/6

z = -1

If the dog has a z-score of -1.09, his weight is:

-1.09 = x -55/6

x - 55 = -6.54

x = 48.46

If the dog has a z-score of 1.09, his weight is:

1.09 = x - 55/6

x -55 = 6.54

x = 61.54

Hence ,If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg

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When a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.

The binomial distribution's PMF is;

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

Following are the results of a calculation using a binomial distribution to determine the likelihood of receiving at least 9 heads.

P(X ≥ 9) = P(X = 9) + P(X = 10)

P(X ≥ 9) = ¹⁰C₉. (0.6)⁹ (1 - 0.6)¹ + ¹⁰C₁₀. (0.6)¹⁰ (1 - 0.6)⁹

P(X ≥ 9) = 0.0403 + 0.0060

P(X ≥ 9) = 0.0463

Thus, when a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.

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The complete question is-

A biased coin is tossed 10 times and the probability of obtaining heads is 0.6.

Find the probability of obtaining at least 9 heads. Round answer to the nearest ten-thousandth.

The maximum number of aphids in the cherry orchard is 1508.

What is population growth?

Population growth is the term used to describe the relative increase in population over a period of time. The growth rate is defined as growth per unit of time.

Given, N(t) = 1500-3t*ln(0.1t)-t

For maximum/minimum,  [tex]\frac{dN}{dt} =0[/tex]

or, -3*ln(0.1t) - [tex]\frac{3t}{0.1t} *0.1[/tex] - 1 = 0

or, -3*ln(0.1t) = 4

or, ln(0.1t) = -4/3

or, t = 2.64

Then, [tex]\frac{d^{2} N}{dt^{2} } = \frac{-3*0.1}{0.1t} = \frac{-3}{t}[/tex] at t = 2.64

= -1.1381 < 0

Hence, it is maximum.

For the maximum number of Aphids put t = 2.64, we get

N = 1508

Hence, the maximum number of aphids in the cherry orchard is 1508.

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Answer:y=2x+-1

Step-by-step explanation:

y= slopex + y-intercept, the y-intercept is at the point (0,-1) as the y-intercept is when the x coordinate is 0 and the y coordinate gets touched by the y axis, therefore 2x+-1

Answer:

5 miles

Step-by-step explanation:

Perimeter of a square = 4s

Where s = side length

We are given that the square has a side length of 1.25 (so s = 1.25)

Plugging this into the formula we acquire perimeter = 4(1.25) = 5 miles

Pretty sure it's C!!! :))))))))))))

Susan would charge $7.50 to babysit 5 kids.

The unitary method is used to calculate the value of a single unit from a given multiple. If the cost of 40 pens is Rs. 400, how do you calculate the value of one pen? The unitary method can be used to accomplish this. Furthermore, once we've determined the value of a single unit, we can multiply that value by the number of units needed.

Given,

Amount charged for 3 kids =$4.50

then,

Amount charged for 1 kid will be [tex]\frac{4.50}{3}=$1.50[/tex]

now, amount charge to babysit 5 kids =1.50*5=$7.50

Thus, Susan would charge $7.50 to babysit five children..

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In interval estimation, when the sample size have become larger then the interval estimate then it will becomes narrower. Option (c) is correct.

A large sample of pattern length or decrease variability will bring about a tighter self belief c program interval with a smaller margin of error. A smaller pattern length or a better variability will bring about a much wider self belief c program interval with a bigger margin of error. The stage of self belief additionally impacts the c program interval width. The large your pattern, the greater certain you may be that their solutions genuinely mirror the population.

This suggests that for a given self belief stage, the bigger your pattern length, the smaller your self belief c program language period. The width of the self belief c program interval for an character observe relies upon to a massive volume at the pattern length. Larger research generally tend to provide greater unique estimates of effects (and therefore have narrower self belief intervals) than smaller research.

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Correct Question:

In interval estimation, as the sample size becomes larger, the interval estimate

a). remains the same, because the mean is not changing.

b). gets closer to 1.96.

c). becomes narrower.

d). becomes wider.

Adjacent angles of a parallelogram are supplementary.

[tex]3x+10+8x+5=180 \\ \\ 11x+15=180 \\ \\ 11x=165 \\ \\ \boxed{x=15} \\ \\ \\ \\ 5y+3(15)+10=180 \\ \\ 5y+55=180 \\ \\ 5y=125 \\ \\ \boxed{y=21}[/tex]

Reason:

Every exponent shown for choice A is an even number, which by extension points us to an even polynomial function.

Choice D has all odd exponents (think of [tex]\text{x}[/tex] as [tex]\text{x}^1[/tex]), which means choice D is an odd polynomial function.

Choices B and C have a mix of even and odd exponents for their terms. This means B and C are neither even nor odd.

List could be the one Akeem created is option D . 0.21  22%  1/4  0.35  3/8  38%.

Given:

Akeem created a list by correctly putting a group of fraction in percentage and decimals order from least to greatest value.

Least to greatest value:

Option D :

0.21  22%  1/4  0.35  3/8  38%

= 22 %

= 22 / 100

= 0.22

1/4 = 0.25

3/8 = 0.375

38 = 38 / 100

= 0.38

0.21 < 0.22 < 0.25 < 0.35 < 0.375 < 0.38.(least to greatest)

Hence Option D is correct.

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Full question:

Is in the image uploaded.

Answer:

3 cupcakes per person

Step-by-step explanation:

first we need to find the total number of cupcakes so in order to do that we need to multiply the number of mixes and the number of cupcakes each mix would make so:

total number of cupcakes = 6 * 12 = 72

now we can divide it by the total number of people who attended the party  so:

72/24 = 3 cupcakes per person

98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

What does a statistical random sampling entail?

P = x/n

= 89/168

= 0.53

α= 0.02

∴ Zc = Zi - α/2

= 2.326

Now, C.I = P ± Zc * √[P(1-P)/n]

= 0.5 ± 2.326 *√[(0.53(1-0.53)) / 168

= (0.440, 0.619)

∴98% C.I. = 0.440 < P < 0.619

Hence, 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

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Answer:

divide 59.36 by 12 to get through cost of one = 4.95

Step-by-step explanation:

unit cost is the cost of one product

The circle's radius circumscribed through points, A,D and E are 2 units.

Look at the image  of the figure attached below for a better understanding of the solution :

From the given figure, we can conclude the following data:

AP = √3/2(a)  → 1 length of the median for the triangle of side a.

by putting the value of a. we get:

AP = √3/2(2)  = √3

AQ = AP + PQ = √3 + 2

Area of triangle AEΔ = 1/2 × EΔ × AQ = 1/2(2) (√3+2)

AE = AD = √(EQ)² + (AQ)²

= √(1)² + (2+√3)² = √1+4+3+4√3 = √8+4√3

= 2√2+√3

We know that,

R = abc/4Δ

R = 2(2×√2+√3)  (2√2+√3) / 4{1/2×2×(√3+2)}

R= 2{4(2+√3)} / 4(√3+2)²

On solving the above equation we get ,

R = 2 units.

As a result, the radius of the circle is 2 units when it is defined by the points A, D, and E.

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The probability that the people came for the match live were born within 30 miles be, 0.197

Given, while watching a basketball game of lakers in a cafe near L.A live, we observe someone who is clearly supporting lakers in the game.

we have to find the probability that the person we observed born within 30 miles of L.A downtown.

As, the area of L.A downtown is 15.13 km².

1.6 km = 1 mile

2.56 km² = 1 miles

15.13 km² = 5.91 miles

Probability that the person was born within 30 miles be,

P = favorable area / total area

P =5.91/30

P = 0.197

Hence, the probability that the people came for the match live were born within 30 miles be, 0.197

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The Union of South American Nations (UNASUR) is not a regional alliance.

What is the Union of South American Nations?

The Union of South American Nations was formed in 2008 to further the interests of South American nations. It was an intergovernmental union and that was meant to bring more prosperity to the region.

There are also plans to make UNASUR a single-currency union. The Union of South American Nations was never meant to be a regional alliance however.

complete question is

the union of south american nations (unasur) is considered all of the following except (5 points) group of answer choices a supranational organization an intergovernmental union a single-currency union a regional alliance

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Set S should contain 137 number of integers so that at least 35 integers in S have same remainder when divided by 4.

According to the pigeonhole principle in mathematics, at least one container must hold more than one item if n things are placed into m containers, where n &gt; m. As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

Given: Set S = {}, least number of integers having same remainder when divided by 4=35

As we know, any number when divided by 4 has following remainder = 0, 1, 2, 3.

Least number of integers having same remainder when divided by 4 = 35.

∴ Number of integers in set S = 35×4

                                                =  140

but 3 is to be subtracted from 140 as it is the last different remainder after which the remainders repeat in manner 0, 1, 2 &amp; 3.

∴ Total number of integers in set S = 140-3  

                                            = 137                                                

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Answer:

= –179/9

or –19 ^8/9

Step-by-step explanation:

–19²/9 –4¹/9 –(–3⁴/9)

–(173/9) –37/9 + 31/9

=L.c.m = 9

–173–37+31/9

= –210+31/9

= –179/9

or –19 ^8/9

i hope i was able to helped

Answer:

Parallel

Step-by-step explanation

Put into y=mx+b

Equation 1:

14x=2y-6

add 6

14x+6=2y

Divide by 2

7x+3=y

Equation 2:

8/7=y-7x

add 7x

7x+8/7=y

Look at the slope of each equation (the x)

1: 7x    and     2. 7x

The slopes are the same so the lines are parallel

Hope this helped!

BC IF YOU MULIPLY 3X3=9 AND 7X3=21 so yes its is proprational

Step-by-step explanation:

Hope you have a good day :D

The volume of the balloon will be 9.3 L and the volume of the tire in the morning will be 10.93 L.

Heat is the result of the movement of kinetic energy within a material or an item, or from a power source to a material or an object. Three ways exist for such transfer of energy to take place: Convection, radiation, and conduction

As per the given information in the question,

1.

Volume, V1 = 5 L

Temperature, T1 = 200 K and,

Temperature, T2 = 373 K

V1/T1 =V2/T2

5/200 = V2/373

V2 = 9.3 L

2.

Pressure, P1 = 80 KPa

Pressure, P2 = 250 KPa

Volume, V2 = 3.5 L

P1V1 = P2V2

80(V1) = 250(3.5)

V1 = 10.93 L

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