In RST, the measure of ZT=90°, the measure of ZR=6°, and RS = 3.6 feet. Find the
length of ST to the nearest tenth of a foot.

Answer: y = 8/3x + 4

Answer:

9

Step-by-step explanation:

Let the ratio's unit be x. We have:

3x:2x:x. We add these up to get 6x. 6x=18, so x=3. 3*3 (since the wins is 3 in the ratio 3:2:1) is 9, so there's your answer! We can double check because 3*2 = 6 losses, and 3*1 = 3 draws, and 9:6:3=3:2:1, and 9+6+3=18!

The total rebound distance is 2 + 1 + 0.5 + 0.25 = 3.75 ft.

A super ball dropped from a height of 8 ft rebounds half of the distance fallen. After rebounding 4 times, what is the total rebound distance?The initial height = 8 ft

After the first bounce, the ball rebounds half the distance fallen.The distance fallen during the first bounce = 8/2 = 4 ft The rebound height = 4/2 = 2 ft

Therefore, the ball rebounds to a height of 2 ft on its first bounce.Since the ball rebounds half the distance fallen, it falls to a height of 1 ft after the second bounce.                                                                                                                                                                                                        The distance fallen during the second bounce = 4/2 = 2 ft ,The rebound height = 2/2 = 1 ft

Therefore, the ball rebounds to a height of 1 ft on its second bounce.

Repeating the above process, the third and fourth bounces are as follows:

During the third bounce: Distance fallen = 2 ft, rebound height = 0.5 ft

During the fourth bounce: Distance fallen = 1 ft, rebound height = 0.25 ft

Therefore, the total rebound distance is 2 + 1 + 0.5 + 0.25 = 3.75 ft.

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So, there are 20 different mix-and-match plates that can be created by combining one savory and one sweet dish from Alejandra's Tapas Bar's menu.

To determine the number of different mix-and-match plates that can be created from Alejandra's Tapas Bar's menu, we need to calculate the number of options for both the savory and sweet dishes and then multiply them together.
Let's assume that there are 5 savory dishes and 4 sweet dishes on the menu. To create a mix-and-match plate, we need to choose one savory and one sweet dish. The number of options for the savory dish is 5, and the number of options for the sweet dish is 4. Therefore, the total number of different mix-and-match plates that can be created is:
5 x 4 = 20
Customers can choose any combination they like and can enjoy a unique dining experience each time they visit the restaurant.

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Answer:

15,6

Step-by-step explanation:

15×104/100=15,6

She make 15,6$ per hour

Answer:

D. the exponent can be odd

Step-by-step explanation:

A. (-4)² = 16 ⇒ -4 is even and the product is positive.

B. (-5)² = 25 ⇒ -5 is odd and the product is positive.

C. (-5)⁴ = 625 ⇒ The exponent 4 is even and the product is positive.

D. (-5)⁵ = -3125 ⇒ The exponent 5 is odd and the product is negative.

So, the answer is D.

Hope this helps.

The equation of the required perpendicular line is y = (-5/4)x - 30.

We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation of the given straight line is y = (4/5)x + 23. We need to find the equation of the straight line that is perpendicular to the given line and passes through the point that has coordinates (-40, 20).

The slope of the given line is 45. Let the slope of the required perpendicular line be represented by the variable "m". The slope of the perpendicular line must be the negative reciprocal of the slope of the given line.

m = -1/(4/5)

m = -5/4

The equation of the required line is of the form y = mx + c.

y = (-5/4)x + c

We know that this line passes the point (-40, 20).

20 = (-5/4)(-40) + c

20 = 50 + c

c = -30

Hence, the equation of the required line is y = (-5/4)x - 30.

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The angle B in the triangle is 67.5 degrees.

The sum of angles in a triangle is 180 degrees. A triangle is a polygon that three sides.

Therefore, let's find the angle B in the triangle as follows:

Hence, let's find x

2x + 3x + 3x  = 180

8x = 180

divide both sides of the equation by 8

x = 180 / 8

x = 22.5

Therefore,

angle B = 3(22.5)

angle B = 67.5 degrees.

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In a simple random sample, every member of the population has an equal chance of being selected. This sampling method helps ensure unbiased representation and allows for accurate statistical analysis.

In a simple random sample, every member of the population has an equal chance of being selected. This is one of the key characteristics of a simple random sample. Additionally, in a simple random sample, the population is assumed to be approximately normal with the mean, median, and mode being approximately equal. This assumption allows for easier analysis of the data collected from the sample. It is important to note that the mean of N (the sample size) is not always equal to the standard deviation. However, the mean of the sample can be used as an estimate of the population mean with a certain level of confidence.
In a simple random sample, every member of the population has an equal chance of being selected. This sampling method helps ensure unbiased representation and allows for accurate statistical analysis.

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Answer:

40

Step-by-step explanation:

80/2= 40

Answer:

third

Step-by-step explanation:

Answer:

11 and 12

Step-by-step explanation:

the square root of 125 is 11.18

The length of r, to the nearest 10th of an inch, is 2.4 inches.

The relationship between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it states that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.

Given that in ΔQRS, s = 5.2 inches, ∠S=129° and ∠Q=30°. The value of side r will be calculated by using the sin angle theorem.

The value of r is,

r / sin21 = s / sin129

r = 5.2 x ( sin21/sin129)

r = 5.2 x 0.46

r = 2.4 inch

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The hypothesis test is a Left-tailed test and the parameter being​ tested is known as a Population mean.

What is a null and alternative hypotheses?

A null hypothesis predicts no effect between variables while an  alternative hypothesis predict an effect or relationship between variables of the study.

What is the given hypothesis test?

In the question, the given hypothesis test includes "H0​: σ=110" and "H1​: σ<110"

Hence, based on the test above, the hypothesis test is a Left-tailed test and the parameter being​ tested is known as a Population mean.

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Answer:

ok Let’s calculate the money Sam makes per week, not including sales (or Assuming $0 in sales):

Money per week =$6.45/hour×37.5 hours/week= $241.88/week  

The money he Gains from sales must make up the difference, So

money from sales = $400−$241.88 = $158.12  

This Money is only 6% or 0.06 of the total sales though, so

Total sales = $158.120.06 = $2635.33  

of course, this is Assuming that the money per week is rounded up from $241.875 to $241.88 instead of down to $241.87, in which case Sam would Have to make $2635.50 in sales (about 17 cents more).

Step-by-step explanation:

have a nice day.

Answer:

C.) 16.86 degrees

Step-by-step explanation:

Tan = opposite over adjacent

10/33

arctan(10/33)

C.) 16.86 degrees

Answer:

∠2 and ∠5

∠6 and ∠3

Step-by-step explanation:

Vertical angles are a pair of non-adjacent angles formed by intersecting two straight lines.

Looking at the options, the answers are ∠2 and ∠5, ∠6 and ∠3

Now the state-space representation is

\([ΔθΔθ˙]=[001Ib​kIb​][ΔθΔθ˙]+[0Hω] cos(θ0​ + Δθ\)

\()≈[0Hω] cos(θ0​) + [0−Hω sin(θ0​)] Δθ + [0Hω] cos(θ0​) Δθ˙ + [001Ib​kIb​][ΔθΔθ˙]\)

This is the state space representation of the system if the input is ω(t) and the output is \(θ(t).\)

Given that the differential equation of the system is \(Iθ¨ + bθ˙ + kθ = Hω cosθ.\)

Here, I is the moment of inertia, b is the coefficient of damping, k is the spring constant, θ is the angular displacement, H is the torque constant and ω is the angular frequency.

The state-space representation of the above system is given by:

\([θθ˙]=[001Ib​kIb​] [θθ˙]+[0Hω]cosθ\).The linearization of the state equation can be obtained by taking the first order Taylor series expansion of the equation about the equilibrium point. At the equilibrium point \(θ0​=0\),

\(θ˙0​=0\) and

ω0​=0, the linearized state equation is given by

:\(Δθ¨ + bΔθ˙ + kΔθ = Hω cosθ or Δθ¨ + bΔθ˙ + kΔθ\)

= HωFor linearization,

\(Δθ = θ - θ0\)​ and

\(Δθ˙ = θ˙ - θ˙0​Δθ\)

\(= θ\)and

\(Δθ˙ = θ\)˙

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Answer:

Step-by-step explanation:

When the stick is placed along the diagonal  of the cuboid , shortest possible length will extend out above top of the crate .

Length of the diagonal

= \(\sqrt{36^2+36^2+60^2}\)

= 78.69 cm

the length of the stick that extends out of the crate

= 90 - 78.69

= 11.31 cm

If θ be the angle made by stick with the base

cosθ = hypotenuse of base / diagonal of cuboid

=\(\frac{\sqrt{2}\times36 }{78.69}\)

= \(\frac{50.90 }{78.69}\)

θ = 50°

Answer: This is the answer to B) 47.9 degrees

Step-by-step explanation:

Pythagoras: a^2+b^2=c^2

36²+36²=C²

√2592=C

C=50.9cm

Used Trigonometry: SOH CAH TOA

Tan=Opposite/Adjacent

Tan=60/50.9

The angle stick makes when it meets the base:

Tan^-1(60/50.9)

=49.7˚

No, y=23ex−4e−2x is not a solution of the differential equation y' + 2y = 2ex, as it does not satisfy the equation.

To check whether y = 23ex−4e−2x is a solution of the differential equation y' + 2y = 2ex, we need to verify that y satisfies the equation.

First, let's find y':

y' = (23)ex - (42)e-2x

Next, let's substitute y and y' into the differential equation:

y' + 2y = (23)ex - (42)e-2x + 2(23ex-4e-2x)

Simplifying this expression, we get:

y' + 2y = 6ex - 8e-2x + 2(3ex-2e-2x)

y' + 2y = 6ex - 8e-2x + 6ex-4e-2x

y' + 2y = 12ex - 12e-2x

So we can see that y = 23ex−4e−2x is not a solution of the differential equation y' + 2y = 2ex, since y does not satisfy the equation.

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The unknown angle x in the triangle is 80 degrees

From the question, we have the following parameters that can be used in our computation:

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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The correct option of the given question is option(c) becomes narrower.

Based on the given information, when the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes narrower. So, the correct answer is option c. becomes narrower.

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When the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes wider.

This is because a higher confidence level implies a narrower interval to provide a higher level of certainty in capturing the true population mean. Conversely, when the confidence level is decreased, the interval needs to be wider to allow for a larger margin of error and account for the reduced confidence requirement.

Widening the interval ensures that the estimate is more conservative and includes a broader range of possible values for the population mean. Therefore, the confidence interval for μ becomes wider as the confidence level is lowered.

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Answer and Step-by-step explanation:

Area of triangle:

A = \(\frac{bh}{2}\) (Base times height, all divided by 2)

Area of Rectangle/Square

A = bh (base times height)

Triangle:

\(\frac{7*24}{2} = \frac{168}{2} = 84\)

Rectangle:

A = 12.5 * 13 = 162.5

162.5 + 84 = 246.5

#teamtrees #WAP (Water And Plant)

The employer chooses at random, and three of the candidates are women, there are 80 possible ways to fill the four positions.

We may use the combination formula to address this issue,

which is:

nCr = n! / (r! * (n-r)!)

where r is the number of things being picked, n denotes the total number of items, and! denotes factorial, which is the sum of all positive integers up to that number. For example, 4! = 4 x 3 x 2 x 1 = 24.

Six women will be chosen, and one person will be selected from the remaining four (who must be a man). The result is:

Number of ways to choose 3 women from 6 women = 6C3 = 20

Number of ways to choose 1 man from 4 men = 4C1 = 4

Since these two numbers are independent options, we must multiply them together to determine the total number of alternatives to fill the four seats. Which is:

There are a total of four slots that can be filled, including 3 women and 1 man. = 20 * 4 = 80

Therefore, the employer chooses at random, and three of the candidates are women, there are 80 possible ways to fill the four positions.

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A: The height of the street sign is obtained by indirect measurement method as 15 feet.

B: The two proportions Betsy can use is 5/1.5 = x/4.5 and 5/.x = 1.5/4.5

C: Using both the proportions height of the street sign is obtained as 15 feet.

What is indirect measurement?

A mathematical technique called as an indirect measurement is used to discover unknown measures of items that are challenging to measure. A direct measurement is something that can easily be measured, like a toddler's height.

The height of Betsy is h = 5 feet.

The shadow of Betsy is h' = 1.5 feet.

The height of the street sign is H = x feet.

The height of the shadow of street sign is H' = 4.5 feet.

The two proportions are -

h/h' = H/H' and h/H = h'/H'

These two can be used to find the measurement of the street sign.

To find the height of the street sign use the method of indirect measurement -

h/h' = H/H'     h/H = h'/H'

Substitute the values in the given equation -

5/1.5 = x/4.5            5/x = 1.5/4.5  

1.5 × x = 5 × 4.5      5 × 4.5 = 1.5 × x

1.5x = 22.5              22.5 = 1.5x

Simplify the equation further -

x = 22.5/1.5             x = 22.5/1.5

x = 15                       x = 15

Therefore, the value of the x is obtained as 15 feet.

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The absolute maximum value of the function f(x, y) = \(x^2\) + xy + \(y^2\) on the disc\(x^2\) + \(y^2\) ≤ 1 is 1, and the absolute minimum value is 0.

To find the absolute maximum and minimum values of the function on the given disc, we need to consider the extreme points of the disc.

First, let's analyze the boundary of the disc, which is defined by the equation \(x^2\) +\(y^2\) = 1. Since the function f(x, y) = \(x^2\)+ xy + \(y^2\) is continuous and the boundary of the disc is a closed and bounded region, according to the Extreme Value Theorem, the function will attain its maximum and minimum values on the boundary.

Next, we consider the points inside the disc. Since the function is a quadratic polynomial, it will have a minimum value at the vertex of the quadratic form. The vertex of \(x^2\) + xy + \(y^2\) is at the origin (0, 0), and the function value at this point is 0.

Therefore, the absolute maximum value of the function on the disc\(x^2\) + \(y^2\) ≤ 1 is 1, which occurs on the boundary of the disc, and the absolute minimum value is 0, which occurs at the center of the disc.

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Explanation:- When they had asked, Round 468986 to the nearest thousand, You should know that :-

Th H T O

4 6 8 9 8 6

So, Here In Thousand place we have 8.

Then see the all numbers after 8 That is :-

8986

So 8986 is nearest to 9000

Therefore, answer will be 469000.

the answer is 469000 hope it help's

So the direction that the boat should be pointed is 28.3 degrees to the left of straight across the river.

We can see that there are two forces acting on the boat:

the rowing force, which points straight ahead, and the force of the river current, which points to the right.

We want to find the direction that the boat should be pointed in order to reach the other side of the river.

Let's call this angle θ.

Using trigonometry, we can set up the following equation:

tan θ = opposite/adjacent

where opposite is the force of the river current (0.6 m/s) and adjacent is the rowing force (1.1 m/s).

tan θ = 0.6/1.1θ

        = tan⁻¹(0.6/1.1)θ

        ≈ 28.3°

So the direction that the boat should be pointed is 28.3 degrees to the left of straight across the river.

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To find the probability that the equipment is functioning properly, we need to consider the cases where 6, 7, 8, or all 9 components are operational.

Let's calculate the probability for each case and add them together.
For 6 components to be operational, we have to choose any 6 out of the 9 components. The probability of each chosen component working is p, and the probability of each unchosen component failing is (1 - p). So, the probability for 6 operational components is (9 choose 6) * \(p^6 * (1 - p)^3.\)
Similarly, for 7 operational components, the probability is (9 choose 7) \(* p^7 * (1 - p)^2.\)
For 8 operational components, the probability is (9 choose 8) * \(p^8 * (1 - p).\)
Lastly, for all 9 components to be operational, the probability is\(p^9.\)
Adding up these probabilities will give us the overall probability that the equipment is functioning properly.

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The discriminant of the quadratic equation is q · (q + 8) < 0. The solution set of this inequality is (0, - 8).

The nature of the roots of quadratic equations of the form a · x² + b · x + c = 0 can be inferred by the understading of its discriminant under the following condition:

b² - 4 · a · c < 0

Where a, b, c are the coefficients of the polynomial.

If we know that a = 2 · q, b = q and c = - 1, then the equation of the discriminant is:

q² - 4 · (2 · q) · (- 1) < 0

q² + 8 · q < 0

And by algebraic handling, we find the set of possible values of q:

q · (q + 8) < 0

The solution set of this inequality is (0, - 8).

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The row vectors of the matrix are [-2 -3 1 0], and the column vectors are:

In a matrix, row vectors are the elements listed horizontally in a single row, while column vectors are the elements listed vertically in a single column. In this case, the given matrix is a 1x4 matrix, meaning it has 1 row and 4 columns. The row vector is [-2 -3 1 0], which represents the elements in the single row of the matrix. The column vectors, on the other hand, can be obtained by listing the elements vertically. Therefore, the column vectors for this matrix are -2, -3, 1, and 0, each listed in a separate column.

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