GEOMETRY PLEASE HELP!! for 30 points!
Looking up, Joe sees two hot air balloons in the sky as shown. He determines that the hot air balloon is 700 meters away, at an angle of 38 degrees from the vertical. The higher hot air balloon is 1,050 meters away, at an angle of 26 degrees from the vertical. How much higher is the balloon on the right than the balloon on the left?

Do not round any intermediate computations. Round your answer to the nearest tenth.

Note that the figure below is not drawn to scale.

The dimensions of section B are 36 inches by 48 inches, and the area of the piece of sheet metal after both sections are cut and removed is 6336 square inches.

Given the width and length of a rectangular piece of sheet metal as 60 inches and 44 inches, we need to find the dimensions of section B and the area of the piece of sheet metal after both sections are cut and removed.

The length of rectangle B can be found as TR = SR - ST = PQ - ST, where SR and PQ are opposite sides of the rectangle. Here, PQ is the length of the rectangular sheet metal, which is 60 inches, and ST is the width of the rectangle WVTX, which is 24 inches. Therefore, the length of rectangle B is:

TR = PQ - ST = 60 - 24 = 36 inches

The breadth of rectangle B can be found as UR = QR - QV - VT - TU. Here, QR and PS are opposite sides of the rectangle PQRS, so QR = PS = 144 inches. Also, QV is the width of rectangle WVTX, which is 36 inches, and VT and TU are the lengths of rectangle WVTX, which are both 24 inches. Therefore, the breadth of rectangle B is:

UR = QR - QV - VT - TU = 144 - 36 - 24 - 36 = 48 inches

So, the dimensions of section B are 36 inches by 48 inches.

Next, we need to find the area of the piece of sheet metal after both sections are cut and removed.

The area of rectangle B is the product of its length and breadth, which is:

Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches

The area of rectangle WVTX is the product of its length and breadth, which is:

Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches

The area of rectangle PQRS is the product of its length and breadth, which is:

Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches

Therefore, the area of the piece of sheet metal after both sections are cut and removed is:

Area of the piece of sheet metal = Area of rectangle PQRS - Area of rectangle B - Area of rectangle WVTX

= 8640 - (1728 + 576)

= 8640 - 2304

= 6336 square inches

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For made a fruit punch, Kim used the 3 batches of this fruit punch recipe. From unit conversion, the total quantity in litres used to fruit punch is equals to the 2.570 L.

We have Kim made 3 batches of this fruit punch recipe. It includes the combination of following,

quantity of strawberry juice = 70 mL

quantity of apple juice = 2 L

quantity of pineapple juice = 500 mL

We have to determine the number of liters of fruit punch he made. Using the unit conversion,

one liters = 1000 mililiters

=> 1 mL = 0.001 L ( conversion factor)

so, quantity of strawberry juice = 70 mL = 70× 0.001 L = 0.070 mL

quantity of pineapple juice = 500 mL = 500× 0.001 L = 0.500 L

So, total quantity of fruit punch made by Kim in liters = strawberry juice + pineapple juice + apple juice

= 0.070 L + 0.500 L + 2 L

= 2.570 L

Hence, the required value is 2.570 liters.

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The standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

To find the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students, we need to use the binomial distribution.

Given that 71.6% of all first-time, full-time freshmen believe that same-sex couples should have the right to legal marital status, the probability (p) that a randomly selected student from this population believes this is:

p = 0.716

Since we are interested in the number of students in a sample of nine who believe this, we can model this using the binomial distribution with parameters n = 9 and p = 0.716.

The formula for the standard deviation of a binomial distribution is:

σ = sqrt(n * p * (1 - p))

Substituting in the values of n and p, we get:

σ = sqrt(9 * 0.716 * (1 - 0.716))

σ = 1.168

Therefore, the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

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Answer:

Step-by-step explanation:

The number in your question is expressed in scientific notation, which is typically used to express numbers that are either too large or too small.  The number in scientific notation is expressed as a power of 10.  A positive exponent means the # is large whereas if the exponent is negative, then the # is small.

3.652 x 10-4 --> negative exponent, therefore, # is small.

All you need to do is to convert this number to standard notation by moving the decimal 4 places to the left.

3.652 x 10-4 = 0.0003652

f(x,y) = x + y; if both x & y are even f(x,y) = x - y; if both & y are odd f(x, y) = 2x – y2, if any one of them is odd & other is = even. Then the result of f(2,3) - f(2,4) is -11, which corresponds to option c).

Determining f(2,3)

Since x = 2 (even) and y = 3 (odd)

Then, the function definition for this case is f(x,y) = 2x - y²

f(2,3) = 2(2) - 3² = 4 - 9 = -5

Determining f(2,4)

Since x = 2 (even) and y = 4 (even)

Then, the function definition for this case is f(x,y) = x + y.

f(2,4) = 2 + 4 = 6

Now, Calculating f(2,3) - f(2,4)

f(2,3) - f(2,4) = -5 - 6 = -11

Therefore, the answer is option c) -11.

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For a bounded martingale Xₙ and stopping time T (not necessarily bounded), E[XT] = E[X] is proved by considering the stopping times Tₙ= min(T, n) and using the Optional Stopping Theorem.

To prove that E[XT] = E[X], we can utilize the Optional Stopping Theorem.

First, we know that since Xₙ is a bounded martingale, it satisfies the conditions for the Optional Stopping Theorem stating that for any stopping time T, [tex]E[X_{T}] = E[X_{0}][/tex], where [tex]X_{0}[/tex] is the initial value of Xₙ.

Now, taking into consideration stopping times Tn = min(T, n). As Tn is a bounded stopping time, we utilize the Optional Stopping Theorem to get:

[tex]E[X_{Tn}] = E[X_{0}][/tex]

We can rewrite this as:
[tex]E[X_{Tn}] - E[X_{0}] = 0[/tex]

Now, if we take the limit as n→∞.As Xn is a bounded martingale, it follows that E[|Xn|] < infinity for all n. Thus, utilizing Dominated Convergence Theorem, we get:

[tex]lim_{n} E[X_{Tn}] = E[lim_{n} X_{Tn}] = E[XT][/tex]

Similarly, [tex]lim_{n} E[X_{0}] = E[X].[/tex]

Therefore, taking the limit as n→∞ in our previous equation, we get:

E[XT] - E[X] = 0

Or, equivalently:

E[XT] = E[X]

So, E[XT] = E[X] by considering the stopping times Tn= min(T, n)].

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i. To find the component form of the vector AB, we subtract the coordinates of A from the coordinates of B:
AB = <52 - 12, 33 - 41> = <40, -8>
To find the magnitude of the vector AB, we use the formula:
|AB| = sqrt((40)^2 + (-8)^2) = sqrt(1600 + 64) = sqrt(1664) ≈ 40.79

ii. Similarly, we find the component form of AB:
AB = <12 - 8, 3 - 14> = <4, -11>
And the magnitude of AB:
|AB| = sqrt((4)^2 + (-11)^2) = sqrt(157) ≈ 12.53

iii. To find the component form of AB in 3D space, we subtract the coordinates of A from the coordinates of B:
AB = <8 - 9, 5 - (-2), 11 - 5> = <-1, 7, 6>
To find the magnitude of AB, we use the formula:
|AB| = sqrt((-1)^2 + (7)^2 + (6)^2) = sqrt(86) ≈ 9.27

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Answer:

Volume formal= L × W × W

Volume formal= 6 × 8 × 9

Answer= 6×8×9= 432

On a coordinate plane, kite HIJK with diagonals is shown. Point H is located at (-3, 1), point I is at (-3, 4), point J is at (0, 4), and point K is at (2, -1). The diagonals of this kite connect points H and J, and points I and K, creating an intersecting pattern within the shape.

Based on the information provided, we know that a kite shape has been loaded onto a coordinate plane with points h, i, j, and k located at specific coordinates. The coordinates for point h are (-3, 1), for point i are (-3, 4), for point j are (0, 4), and for point k are (2, -1). Additionally, we know that the kite has diagonals, but we are not given any information about their lengths or intersection points.

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Answer:

B is the answer

Step-by-step explanation:

The measure of angle x in the given right triangle is 71.8°

From the question, we are to determine the measure of angle in the given triangle

The given triangle is a right triangle

We can determine the value of angle x by using SOH CAH TOA

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

In the given triangle,

Adjacent = 5

Hypotenuse = 16

Thus,

cos (x) = 5/16

x = cos⁻¹ (5/16)

x = 71.7900°

x ≈ 71.8°

Hence, the measure of angle x is 71.8°

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The probability of obtaining 126 or more individuals with the characteristic, P(p ≥ 0.63) is 0.5.

The binomial distribution is used to approximate the probability.

The mean of the binomial distribution is np is 200 * 0.63

mean = 126

The standard deviation is √(np(1-p)) = √(200 * 0.63 * 0.37)

standard deviation = 5.18.

Standardize the random variable p as follows:

z = (x - μ) / σ

z = (126 - 126) / 5.18 = 0

Using a calculator to find the probability of z being greater than or equal to 0, the given probability is 0.5.

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Tom increased his investment by 16.67% percent when he sold the merchandise at the flea market.

Given that Tom bought $72 worth of merchandise at a yard sale

Tom sold it for $84 at a flea market.

We have to find the percent did he increase his investment

Tom's initial investment was $72, and he sold the merchandise for $84. The difference between these amounts is:

$84 - $72 = $12

To express this difference as a percentage of his initial investment, we can use the formula:

percent increase = (difference / initial investment) x 100%

Substituting the values we have:

percent increase = ($12 / $72) x 100%

= 0.1667 x 100%

= 16.67%

Hence,  Tom increased his investment by approximately 16.67% when he sold the merchandise at the flea market.

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Answer:

(x-5)(3x+1)=0

x= 5, x= -1/3

Step-by-step explanation:

3x²-14x=5

3x²-14x-5=0

The factor that goes in are 1 and -15 which equal the sum and products.

Sum: -14

Product: -15

Therefore:

3x²+x-15x-5 = 0

Factor by grouping:

x(3x²+x)  -5(-15x-5)

x(3x+1) -5(3x+1)

(x-5)(3x+1) = 0

Use Zero Product Property to solve for X

x-5 = 0  3x+1 = 0

x= 5, x= -1/3

In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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(a) The values of u is 140 g and o is 13.42 g. (b) The value of K in (300 - K. 300 + K) grams is 27.15 g. C) The weights of the middle 96.6% of fruit cups are between (L1, L2) grams. The values of LI is 272.85 g and L2 is 327.15 g.

(a) The mean weight of blueberries is:

300 g - 160 g = 140 g

The standard deviation of the weight is:

Var(X + Y) = Var(X) + Var(Y)

Adding the variances:

15^2 = 10^2 + o^2

Solving for o:

o = sqrt(15^2 - 10^2) = 13.42 g

Therefore, the values of u and o are u = 140 g and o = 13.42 g.

(b) Since the distribution is normal, we can use the standard normal distribution to find K.

The middle 96.6% of a standard normal distribution corresponds to the interval (-1.81, 1.81) (using a table or calculator). Therefore,

K = 1.81 * 15 = 27.15 g

Therefore, the weights of the middle 96.6% of fruit cups are between 300 - 27.15 = 272.85 g and 300 + 27.15 = 327.15 g.

(c) Using the standard normal distribution to find the corresponding interval on the standard normal scale:

(-1.81, 1.81)

We can then scale this interval to the distribution of the weight of fruit cups by dividing by the standard deviation and multiplying by 15 g:

L1 = 300 + (-1.81) * 15 = 272.85 g

L2 = 300 + 1.81 * 15 = 327.15 g

Therefore, the weights of the middle 96.6% of fruit cups are between 272.85 g and 327.15 g.

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The answer is B.

In order to get the answer, you replace the letter n to 5 and workout the problems to see which one is true.

B is the answer because n + 3 = 8

5 + 3 = 8

Answer:

B

Step-by-step explanation:

n+3 =

5+3=

The value of the identity sin N = 3/5

To determine the value of the identity, we need to know the different trigonometric identities. These identities are;

From the information given, we have that;

The angle of the triangle is N

The opposite side of angle N is 3

The hypotenuse side of angle N is 5

Using the sine identity, we have;

sin N = 3/5

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Answer:

The given question is on trigonometry which requires the application of required function so as to determine the value known. So that the length of the guy wire is 67.0 feet.

Trigonometry is an aspect of mathematics that requires the application of some functions to determine the value of an unknown quantity.

Let the length of the guy wire be represented by l, and the angle that the guy wire makes with the stake be θ. So that applying the appropriate trigonometric function to determine the value of θ, we have:

Tan θ =

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

adjacent

opposite

=

11

4

4

11

Tan θ = 2.75

θ =

�

�

�

−

1

Tan

−1

2.75

= 70.0169

θ =

7

0

�

70

o

Considering triangle formed by the tower and the stake to determine the value of l, we have;

Cos θ =

�

�

�

�

�

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

hypotenuse

adjacent

Cos

7

0

�

70

o

=

23

�

l

23

l =

23

�

�

�

7

0

�

Cos70

o

23

=

23

0.3420

0.3420

23

l = 67.2515

l = 67 feet

The length of the guy wire is 67 feet.

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The value of x is equal to 17.

In Mathematics, the exterior angle theorem or postulate is a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the triangle BHY is equal to the measure of angle x (∠NYB);

m∠BHY + m∠HBY = m∠NYB

(2x + 7)° + (8x - 18)° = (4x + 91)°

10x - 11 = 4x + 91

10x - 4x = 91 + 11

6x = 102

x = 102/6

x = 17.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

In/out

-18, -19

-17, -18

-15, -16

-7, -8

0, -1

14, 13

Step-by-step explanation:

the rule states "subtract 1" so if you look at the In, -15 for example goes to -16 for the out which proves that -15-1 is -16. so for all the In's you subtract each number by 1. to FIND a In from the out you just add 1. So just follow the rules and look at the rules carefully!

The percent markup is 20%

The selling price of the Nu is 900

The cost price of the Nu is 750

The percent markup can be calculated as follows

= 900-750/750 × 100

= 150/750 × 100

= 0.2 × 100

= 20%

Hence the percent markup is 20%

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The number 7.1 x 10⁴ in standard form is: 71,000

In standard form, a number is expressed as a coefficient multiplied by a power of 10, where a coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 represents the number of places the decimal point must be moved to obtain the number's value.

In this case, the coefficient is 7.1, which is greater than or equal to 1 and less than 10. The power of 10 is 4, which means that the decimal point must be moved 4 places to the right to obtain the value of the number. Therefore, we get 71,000.

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The area of the rectangle is 13, 950 square unit.

We have,

length = 150

width= 93

So, Area of rectangle

=  length x width

= 150 x 93

= 13950 square unit.

Thus, the required Area is 13, 950 square unit.

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The p-value is 0.00002. (a) The average output voltage is less than 130 since our t-statistic is less than the critical value therefore,  we can reject the null hypothesis. The p-value is 0.007.

To find the p-value for a z-test, you need to use a z-table or a calculator that can give you the area under the standard normal curve to the left of your test statistic.

In this case, your test statistic is z = -4.22. Using a standard normal table, the area to the left of z = -4.22 is approximately 0.00002.

Therefore, the p-value for this test is p = 0.00002.

(a) Using a one-sample t-test to test the hypothesis that the average output voltage is 130 against the alternative that it is less than 130.

With a sample size of 40 and a sample mean of 128.6, the t-statistic is calculated as:
t = (128.6 - 130) / (2.1 / sqrt(40)) = -2.67

Using a t-table with 39 degrees of freedom (df = n - 1), the critical value for a one-tailed test with a level of significance of 0.05 is -1.685.

Since our t-statistic is less than the critical value, we can reject the null hypothesis and conclude that the average output voltage is less than 130.

Using a t-distribution calculator, the one-tailed p-value for a t-statistic of -2.67 with 39 degrees of freedom is approximately 0.007.

Therefore, the p-value for this test is p = 0.007.

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The values of the missing sides and angles are;

<D = 32 degrees

d = 8. 75

e = 16. 50

To determine the value we need to note that the sum of the angles in a triangle is 180 degrees.

From the information given, we have;

<E + <D + <F = 180

substitute the values

90 + 58 + <D = 180

collect the like terms

<D = 32 degrees

Using the sine identity

sin 58 = 14/x

cross multiply the values

x = 16. 50

Using the tangent identity;

tan 58 = 14/y

cross multiply

y = 8. 75

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The probability assigned to each experimental outcome must be: b. between zero and one

The probability assigned to each experimental outcome must be between zero and one. This is because probability is a measure of how likely an event is to occur, and it cannot be negative or greater than 100%. A probability of zero means that the event will not occur, while a probability of one means that the event is certain to occur. Probabilities between zero and one indicate the likelihood of an event occurring, with higher probabilities indicating greater likelihood. It is important for probabilities to add up to one across all possible outcomes, as this ensures that all possible events are accounted for and that the total probability is normalized. Probability theory is used in many fields, including statistics, finance, and engineering, and is essential for making informed decisions based on uncertain events. By assigning probabilities to different outcomes, we can calculate expected values and make predictions about future events, helping us to better understand the world around us.

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An inequality representing v, the number of visits Nayeli needs to make to get a free movie ticket is 40 + 14.5v ≥ 185.

Inequality describes a mathematical statement that states that two or more algebraic expressions are unequal.

Inequalities are represented as:

The rewards points Nayeli has just for signing up = 40

The points earned per visit to the movie theater = 14.5

The total number of points required for a free movie ticket ≥ 185

Let the number of visits Nayeli needs to make too get a free movie ticket = v

40 + 1.45v ≥ 185

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The table that shows a linear function include the following: B. table B.

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

In this context, we have:

Slope = (0 - 2)/(-3 + 5) = (2 - 0)/(-3 + 1) = -1

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The use of regression modeling in retail analytics can help businesses make data-driven decisions that ultimately lead to increased profits and growth.

Based on the information given, it seems that the large sports supplier is interested in predicting the annual revenue of a particular store based on various factors, such as population, promotion expenditure, and distance from the city center. This is a common approach in retail analytics, where regression models are often used to predict sales or revenue based on different variables.

By constructing a regression model, the sports supplier can gain valuable insights into which factors are most strongly associated with revenue, and how they can optimize their operations to increase sales. For example, they may find that stores located closer to the city center tend to have higher revenue, or that increased promotion expenditure leads to a greater increase in revenue in smaller towns.

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The zeroes of the function as required to be determined in the task content are; 0, 2, -4, 4.

It follows from the task content that the zeroes of the given function; f(x) = -5x (x - 2) (x² - 16) is to be determined.

To determine the zeroes; we have;

-5x = 0; x = 0

x - 2 = 0; x = 2

x² - 16 = 0; x² = 16; x = ± 4.

Ultimately, the zeroes of the function are; 0, 2, -4, 4.

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