list the sides of ΔRST in ascending order
m∠R=2x+11°, m∠S=3x+23°, m∠T=x+42°
pls help

Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.

Given that, Juanita started collecting benefits at age 65.

Thus, her benefits reduced by 13.3%.

0.133 x $2,128 = $283.10

Deducting the reduction amount from the total:

$2,128 - $283.10 = $1,844.90

Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

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By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.

In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values ​​of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.  

Let's say a landscaper needs to use x gallons of an 80% pesticide solution.

The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.

After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.

Since we need a 55% pesticide solution, we can set the following formula:

[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]

Therefore, landscapers should use 35 gallons of an 80% pesticide solution.

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Answer:

ames have 18 litres of water. He poured unequally into 3 tank

I. Poured three quarter of water from tank one into tank 2

II. Poured half of the water that is now in tank 2 into tank 3

III. Poured one third of water that is now in tank 3 into tank 1

Find how much water is in each tanks

Step-by-step explanation:

Let's start with the amount of water in tank 1 as x liters.

I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.

II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.

III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.

We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.

3/8 * x + 3/8 * x + 1/8 * x = 18

Simplifying the equation, we get:

7/8 * x = 18

x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)

Therefore, the amount of water in each tank is:

Tank 1: 3/8 * x = 7.71 liters

Tank 2: 3/8 * x = 7.71 liters

Tank 3: 1/8 * x = 2.57 liters

The measure of ∠J in ΔJKL is approximately 57.5 degrees.

The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.

The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.

tan(∠J) = JK/KL

tan(∠J) = 7.3/4.7

∠J = arctan(7.3/4.7)

∠J = 57.5 degrees (rounded to the nearest tenth of a degree)

Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.

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Answer:

The simplified expression is sec^2a

Step-by-step explanation:

We can start by using the trigonometric identities:

cot^2 a + 1 = csc^2 a

tan^2 a + 1 = sec^2 a

Using these identities, we can rewrite the expression as:

(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)

= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))

= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)

Now we can use the identity:

sin^2 a + cos^2 a = 1

to rewrite the expression further:

= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)

= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)

= sin^2 a / sin^2 a (1 - cos^2 a)

= 1 / (1 - cos^2 a)

= sec^2 a

Therefore, the simplified expression is sec^2 a.

In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

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The sum of the geometric series is 3904/3125.

By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.

Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;

The first term, a = 4³/5³

Common ratio, r = 4/5

The number of terms, n = 3

We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;

S_n = a(1 - rⁿ) / (1 - r)

S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]

S₃ = {(64/125) [1 - (64/125)]} / [1/5]

S₃ = (64/125) [(125-64)/125] [5/1]

S₃ = (64/125) (61/125) (5)

Therefore, S₃ = 3904/3125.

Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.

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Answer:

I'm sorry, your question is not clear. Please provide more information or context so I can better understand what you are asking.

Step-by-step explanation:

The proof is completed using two column proof as follows

Statement                               Reason

QT ⊥ PT                                   Given

∠ QRP ≅ ∠ SRT = 90              definition of perpendicularity

∠ QPR ≅ ∠ STR                       Given

Δ PQR is similar to Δ TSR       AA similarity theorem

The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.

In the given triangle, the two angles given to be equal are

Hence the triangles are similar

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Answer:

:)

Hopefully this helps you guys :)

good luck :D

The total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.

To calculate the cost of compensated absences for Tamarisk Company, we need to calculate the number of vacation days and sick days earned by the employees in 2019 and 2020, and then calculate the cost of the days earned but not taken.

Each employee earns 9 vacation days per year. As they can be taken after January 15th of the year following the year in which they are earned, the vacation days earned by the employees in 2019 can be taken in 2020. Therefore, in 2019, no vacation days were taken by any employee.

In 2020, the employees took a total of 8 vacation days. As there are 9 employees, the total vacation days taken in 2020 were 9 x 8 = 72.

Sick Days:

Each employee earns 7 sick days per year, and unused sick days accumulate. In 2019, the employees used a total of 5 sick days. Therefore, the unused sick days at the end of 2019 were 9 x 7 - 5 = 58.

In 2020, the employees used a total of 6 sick days, and the unused sick days at the end of 2020 were 58 + 9 x 7 - 6 = 109.

To find the cost of compensated absences. The unused sick days and vacation days must be multiplied to get the hourly wage rate in effect in a year.

In 2019, the cost of compensated absences was 58 x $6 = $348.

In 2020, the cost of compensated absences was (72 + 109) x $7 = $1,399.

Therefore, the total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.

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Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

Hope this helps!

Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}.

The decision boundary is the line that separates the two classes. When it comes to the nearest neighbour method, the boundary of a class is determined by the closest data point in the other class.What is the nearest neighbour method?The nearest neighbour method (NNM) is a type of lazy learning method in which the data is stored and the computation is deferred until the classification phase.

The goal of the nearest neighbor technique is to use the pattern of the closest data point to classify a new sample. It's also one of the simplest non-parametric classification methods, and it's based on the assumption that the feature spaces used by each class are continuous regions.For Class 1, there are two labeled training data points: (0, 0)T and (0, 1)T. Similarly, for Class 2, there are two labeled training data points: (1, 0)T and (0, 0.5)T.

To generate decision boundaries, follow the steps below:Step 1: Plot the given labeled training data. They are shown in the figure below. Step 2: Label the data points according to their class: Class 1 and Class 2.Step 3: Now, we need to find the nearest neighbors. Find the nearest neighbor for each of the labeled training data points from the opposite class. The distances are calculated as follows:For the Class 1 data points, the nearest neighbor is Class 2's (1, 0)T data point.

For the Class 2 data points, the nearest neighbour is Class 1's (0, 1)T data point.Step 4: Connect the nearest neighbour's labeled training data points with a line. These are the decision boundaries. The red line represents the decision boundary between Class 1 and Class 2. The green line represents the decision boundary between Class 2 and Class 1. The slopes of the decision boundaries are -1 for the red line and 1 for the green line. These slopes are the result of the negative reciprocal of the nearest neighbour's slope. The break point for the red line is 0.5, while the break point for the green line is 0. A break point is the point at which the decision boundary intersects the y-axis.

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Answer:

equal

Step-by-step explanation:

An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

For each calculation, the smallest interval in which the result, using true instead of rounded values, must lie is as follows:

(a) 1.1062+0.947 = 2.0532 ≤ true result ≤ 2.053

(b) 23.46 - 12.753 = 10.707 ≤ true result ≤ 10.708

(c) (2.747) (6.83) = 18.6181 ≤ true result ≤ 18.6182

(d) 8.473/0.064 = 132.3906 ≤ true result ≤ 132.3907

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The perimeter of the smaller triangle would be = 28.1

A triangle can be defined as a three sided polygon that has a total internal angle of 180°.

To calculate the perimeter of the triangle is to find out the scale factor that exists between the two triangles.

The formula for scale factor = original object/new object

Scale factor= 8/7 = 1.14

The perimeter of the smaller triangle = 32/1.14

= 28.1.

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Answer:

169 - 144p²

Step-by-step explanation:

(13 - 12p) × (13 + 12p)

each term in the second factor is multiplied by each term in the first factor

13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis

= 169 + 156p - 156p - 144p² ← collect like terms

= 169 - 144p²

intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9Hence, P(AUB) = 0.9.

Probability of P(ANC)We know that events A, B and C are mutually exclusive.

Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C). Given, P(A) = 0.3,P(B) = 0.6,P(C) = 0.1

Therefore, P(A U B U C) = P(A) + P(B) + P(C) = 0.3 + 0.6 + 0.1 = 1Now, P(ANC) = 1 - P(A U B U C) = 1 - 1 = 0

Probability the intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9

Hence, P(AUB) = 0.9.ility of P(AUB)We know that events A, B and C are mutually exclusive.

Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C)

Now, we need to find P(AUB). If two events A and B are not mutually exclusive events, then the probability of their union P(A U B) can be found as follows; [tex]P(A U B) = P(A) + P(B) - P(A ∩ B)[/tex]We know that events A, B and C are mutually exclusive.

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Answer:

The answer to 1 + 1 is 2.

Very complicated problem, please mark brainliest!

Answer:

1+1 = 2

Or, 1=2-1

1=1

we know value of one is one

so,

1+1=11

Step-by-step explanation:

No,

if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular

A=πr2

A=3.142*36

A=113.112 cm3

Answer:

Step-by-step explanation:

Let h be the height of the trapezoid.

The area of a trapezoid is given by the formula:

Area = (1/2) × (sum of parallel sides) × (height)

In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:

21 = (1/2) × (5 + 9) × h

Simplifying this equation, we get:

21 = 7h

Dividing both sides by 7, we get:

h = 3

Therefore, the height of the trapezoid is 3 cm.

Answer:

Step-by-step explanation:

Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .

Shorter parallel side is 5 cm and the Longer Side is 9 cm.

As we know that formula of area of Trapezium is,

Where,

On substituting the values of area and the two parallel sides in the above formula we will get the required Height.

Substituting the values,

21 = ½ (5 + 9)h

21 = ½ × 14 × h

21 = 7 × h

h = 21/7

h = 3 cm

Therefore, Height of the Trapezium will be 3 cm respectively.

16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

Answer:

"9 more than A" is a verbal expression.

The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.

we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;

tan 68° = 125/x {opposite/adjacent}

x = 125/ tan 68° {cross multiplication}

x = 50.5033

tan 71° = y/50.5033

y = 50.5033 × tan 71°

y = 144.6722

height of the antenna = 144.6722 - 125

height of the antenna = 19.6722

Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.

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Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.

To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.

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Answer:

a=1/3

Step-by-step explanation:

First, expand the brackets by doing multiplication:

2+6a+3=3a+6

Then, move the unknown to the left and the numbers to the right:

3a=6-5

3a=1

a=1/3

The solution to the given equation is -1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2+3(2a+1)=3(a+2)

2+6a+3=3a+2

6a+5=3a+2

6a-3a=2-5

3a=-3

a=-1

Therefore, the solution to the given equation is -1.

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a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water.

a) Rotational speed at which the water just touches the bottom of the cylinder:

                  We will use the formula for centripetal force for a liquid with the volume of a cylinder to obtain the rotational speed at which the water just touches the bottom of the cylinder.

         The formula for centripetal force for a liquid with the volume of a cylinder is as follows:

                   F = (ρr²πh)ω²WhereF:

   Centripetal forceρ: Densityr: Radiush : Heightω: Rotational speed Substituting the given values,

we get: F = (1000 kg/m³ × (0.1m)² × π × 0.12m)ω²F

                = 377 Nω

                = √(F/m)ω

                = √(377 N/ 10 kg)ω

                = √37.7ω = 6.14 rad/sb)

      Pressure at points A and B:

                                We will use the formula for hydrostatic pressure for a liquid to calculate the pressure at points A and B. The formula for hydrostatic pressure for a liquid is as follows:

                         P = ρgh

  Where,

           P: Pressureρ: Densityg: Acceleration due to gravity: DepthSubstituting the given values for point A,

we get P = 1000 kg/m³ × 9.8 m/s² × 0.1 mP

                = 980 Pa

        Substituting the given values for point B,

we get P = 1000 kg/m³ × 9.8 m/s² × 0.22 mP

                = 2156 Pa

      The resulting pressure at point A is 980 Pa and the resulting pressure at point B is 2156 Pa.

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The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:

Step 1: Assume n = m², for some non-negative integer m.

Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².

Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.

Step 4: Let's assume m ≥ 1.

Step 5: Hence, n + 2 is not a perfect square.

The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.

In the final step, we conclude that n + 2 is not a perfect square.

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