1. a triangle with side lengths of 9, 12 and 15 is a right triangle by the converse of pythagorean theorem. what are the measures of the acute angles of the triangle?

This means that she is swimming with a speed of 4.27 feet per second in a direction that is 41.1° east of due north.

A vector is a mathematical quantity that has both magnitude and direction. Vectors are used to represent physical quantities that have both magnitude (such as speed, force, or displacement) and direction (such as north, east, up, or down). Vectors can be represented graphically as arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.

Here,

To find Erica's resultant speed and direction, we can use vector addition. We'll consider Erica's swimming speed as one vector and the current of the lake as another vector, and then find the vector sum of the two.

Let's denote Erica's swimming speed vector as A and the current vector as B.

Magnitude of A (Erica's swimming speed) = 7 feet per second

Direction of A = Due north, which can be represented as N or 0°

Magnitude of B (current of the lake) = 3 feet per second

Direction of B = S 75° W, which can be represented as 180° - 75°

= 105° in the clockwise direction from due north.

Now, we can add the two vectors A and B using vector addition.

To add vectors, we can break them down into their horizontal (x) and vertical (y) components, and then add the corresponding components separately.

A_x = A * cos(direction of A)

A_y = A * sin(direction of A)

B_x = B * cos(direction of B)

B_y = B * sin(direction of B)

Substituting the given values, we get:

A_x = 7 * cos(0°) = 7 * 1 = 7

A_y = 7 * sin(0°) = 7 * 0 = 0

B_x = 3 * cos(105°)

B_y = 3 * sin(105°)

Now, we can add the corresponding components:

Resultant x-component = A_x + B_x

Resultant y-component = A_y + B_y

Resultant x-component = 7 + 3 * cos(105°)

Resultant y-component = 0 + 3 * sin(105°)

Using a calculator, we can find the values of the x- and y-components. Let's assume the values to be:

Resultant x-component ≈ 3.23

Resultant y-component ≈ 2.97

Now, we can use these values to find the magnitude and direction of the resultant vector using trigonometry.

Magnitude of the resultant vector = √((Resultant x-component)² + (Resultant y-component)²)

Direction of the resultant vector = tan⁻¹(Resultant y-component, Resultant x-component)

Substituting the values, we get:

Magnitude of the resultant vector ≈ √((3.23)² + (2.97)²)

≈ 4.27 feet per second (rounded to two decimal places)

Direction of the resultant vector ≈ tan⁻¹(2.97, 3.23)

≈ 41.1° (rounded to one decimal place)

So, Erica's resultant speed is approximately 4.27 feet per second in the direction of 41.1° true bearing.

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The piecewise function that represent the graph is A)f(x)=[tex]\left \{{ x^3 ,if{x < 1} \atop x,if {x\ge1}} \right.[/tex].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.

Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.

The left segment also has no upper bound , so x[tex]\ge[/tex] 1is an appropriate description of its domain.

The one answer choice that combines these domain descriptions is

A)f(x)=[tex]\left \{{ x^3 ,if{x < 1} \atop x,if {x\ge1}} \right.[/tex]

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student can answer the questions on the test in 16,384 different ways if they answer every question.

To determine the number of ways a student can answer the questions on a multiple-choice test containing 7 questions with four possible answers for each question, we will use the multiplication principle. The multiplication principle states that if there are a number of independent choices, then the total number of possible outcomes is the product of the number of choices.
Identify the number of questions and possible answers. In this case, there are 7 questions and 4 possible answers for each question.
Calculate the number of ways to answer each question. Since there are 4 possible answers for each question, there are 4 ways to answer each of the 7 questions.
Apply the multiplication principle. To find the total number of ways to answer all 7 questions, multiply the number of ways to answer each question:
Total number of ways = (4 ways for question 1) x (4 ways for question 2) x ... x (4 ways for question 7)
Perform the calculation. Since there are 7 questions and 4 ways to answer each question, the total number of ways is:
Total number of ways = 4^7 = 16,384

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Option A : The surface area of the larger sphere is 602.88 [tex]in^2[/tex].

Let's use the formula for the surface area of a sphere: A = 4π[tex]r^2[/tex], where r is the radius of the sphere.

Let's call the radius of the smaller sphere "r1" and the radius of the larger sphere "r2". We know that the surface area of the smaller sphere is 200.96 [tex]in^2[/tex], so we can set up the equation:

4π[tex]r1^2[/tex] = 200.96

Solving for r1, we get:

r1 = √(200.96 / 4π) ≈ 2.8

A2 / A1 = [tex](r2 / r1)^2[/tex]

A2 = [tex]A1 (r2 / r1)^2[/tex]

We know A1 = 200.96 [tex]in^2[/tex] and r1 ≈ 2.8, and we want to find r2, so we can use the formula for the volume of a sphere to relate r1 and r2:

(4/3)π[tex]r1^3[/tex] = (4/3)π[tex]r2^3[/tex]

Solving for r2, we get:

r2 = [tex]r1 (3)^(1/3)[/tex] ≈ 3.3

Now we can plug in the values for A1, r1, and r2:

A2 = [tex]200.96 (3.3 / 2.8)^2[/tex] ≈ 301.44

Therefore, the larger sphere has a surface area of roughly 301.44 in2, making answer choice C appropriate.

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Answer:

(a) To find the probability that a trip will take at least 1/2 hour (30 minutes), we need to find the area under the normal distribution curve to the right of 30 minutes. We can standardize the distribution using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

z = (30 - 24) / 3.8 = 1.58

Using a standard normal distribution table or a calculator with a normal distribution function, we can find the probability that a trip will take at least 30 minutes is approximately 0.0571 or 5.71%.

(b) If the office opens at 9:00 a.m. and the lawyer leaves his house at 8:45 a.m. daily, he needs to arrive at the office before 9:00 a.m. to be on time. We can find the percentage of the time he is late for work by finding the area under the normal distribution curve to the right of 15 minutes (the difference between 8:45 a.m. and 9:00 a.m.), and then subtracting that value from 1 to get the percentage of the time he is on time or early.

z = (15 - 24) / 3.8 = -2.37

Using a standard normal distribution table or a calculator with a normal distribution function, we can find the probability that he is late for work is approximately 0.008 or 0.8%. Therefore, he is on time or early approximately 99.2% of the time.

The character of Rue, who was a companion of Katniss from District 11 during the Hunger Games, is no longer alive at the beginning of the novel, but her legacy and her family have significance in the story's developments.

What is statement?

A statement is a declarative sentence that expresses a complete thought or idea. It is a sentence that makes a claim or expresses a fact, opinion, or belief about something.

At the end of the first book, The Hunger Games, Katniss Everdeen and her fellow tribute from District 12, Peeta Mellark, are the winners of the 74th Hunger Games. They return to District 12 as victors, but the Capitol is not pleased with their act of defiance during the Games, where they both chose to eat poisonous berries instead of killing each other, forcing the Gamemakers to declare them both winners.

As a result of their defiance, Katniss and Peeta have become symbols of hope for the oppressed districts, and the Capitol fears that their actions could spark a rebellion. To prevent this, the Capitol announces a special edition of the Hunger Games, called the Quarter Quell, which occurs every 25 years and has special rules.

At the start of Catching Fire, Katniss is dealing with the aftermath of the first Games and is struggling with post-traumatic stress disorder (PTSD) and survivor's guilt. She is also trying to navigate her complicated relationship with Peeta, who has publicly declared his love for her.

However, her world is turned upside down when the Capitol announces the rules of the Quarter Quell: this time, the tributes will be selected from the existing pool of Hunger Games victors. This means that Katniss and Peeta, as previous winners, are once again forced to compete in the Games.

As Katniss prepares for the Games, she is also dealing with the death of her younger sister Primrose, who dies in a bombing that destroys District 12. The bombing is believed to be the work of the Capitol, who are punishing District 12 for Katniss's and Peeta's defiance in the previous Games.

The character of Rue, who was a companion of Katniss from District 11 during the Hunger Games, is no longer alive at the beginning of the novel, but her legacy and her family have significance in the story's developments.

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If a/b rounded to the nearest trillionth is 0.008012018027, where a and b are positive integers, the smallest value of the a+b is 2013.

A mathematician would tell you that there cannot be such a number since it would violate the principles of mathematics. There cannot be a number n/2 since n is already the smallest if you have a number n, where n is the smallest integer after 0. Mathematicians dislike this since it implies that division itself fails.

A computer will truly respond to your question. Computers don't have an endless number of numbers, unlike the physical world, because they couldn't all fit. Each memory register in a computer has a set number of bits that are used to store numbers. Imagine having just three digits. 999 is the largest number you may possibly portray.

The continued fraction representations of the limits of the interval are

0.0080120180265 = [0; 124, 1, 4, 2, 1, 463872, 1, 1, 12, 1, 1, 41]

0.0080120180275 = [0; 124, 1, 4, 3, 545777, 2, 13, 1, 1, 1, 1, 2]

The simplest continued fraction (and therefore also the simplest ordinary fraction!) in that interval

is

[0; 124, 1, 4, 3] 16 1997 = = 0.00801201802704056084...

and the sum of its numerator and denominator is 2013.

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Complete question:

If a/b rounded to the nearest trillionth is 0.008012018027, where a and b are positive integers, what is the smallest possible value of a+b ?

The value of x in the rhombus is - 96.

A rhombus is a quadrilateral with 4 sides equal to each other. The opposite sides of a rhombus are parallel. The opposite angles are congruent. The diagonals are perpendicular and they bisect each other. The adjacent angles are supplementary.

Therefore,

m∠TXU = (-x - 6) degrees

Hence,

-x -6 = 90

add 6 to both sides of the equations

-x -6 = 90

-x -6 + 6 = 90 + 6

-x = 96

Therefore,

x = -96

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The area of the shaded region is equal to 280.6 ft².

Based on the diagram of these regular polygons, the area of the shaded region of one triangle that makes up the hexagon can be calculated by determining the difference between the area of each of the equilateral triangles formed.

In Mathematics and Geometry, the area of an equilateral triangle with known side length (l) can be calculated by using the following mathematical equation;

Area of equilateral triangle = √3/4 × l²

The area of the shaded region of the triangle = √3/4 × l² - √3/4 × l²

The area of the shaded region of the triangle = √3/4 × (12)² - √3/4 × 6²

The area of the shaded region of the triangle = √3/4 × 144 - √3/4 × 36

The area of the shaded region of the triangle = 62.35 - 15.59

The area of the shaded region of the triangle = 46.76 ft².

Since the regular polygon is a hexagon, the area of the shaded region is given by;

Area of the shaded region = 6(46.76)

Area of the shaded region = 280.6 ft².

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Answer:

1 coat rack is $561.30

Step-by-step explanation:

8,419.50/15=561.30

The standard error to be used in the formula of a confidence interval for the difference in proportions is 0.07.

The estimated standard deviation of a statistical sample population is known as the standard error (SE) of a statistic.

By utilising standard deviation, the standard error is a statistical concept that assesses how well a sample distribution represents a population. In statistics, the difference between a sample mean and the population's actual mean is known as the standard error of the mean.

The standard error's primary function is to indicate how divergent the population mean will be from the sample mean. Because it aids in determining how well the standard data reflect the entire population, the standard error is significant. We may readily draw reliable conclusions by calculating the standard error in order to determine how representative our sample is of our population.

56 out of 100 boys = P1 = 0.56

43 out of 100 girls = P2 = 0.43

The formula for standard is given by,

[tex]S.E=\sqrt{\frac{P_1(1-P_1)}{n1} +\frac{P_2(1-P_2)}{n2} } \\=\sqrt{\frac{0.56(1-0.56)}{100} +\frac{0.43(1-0.43)}{100} } \\\\= \sqrt{\frac{0.2464}{100} +\frac{0.2451}{100} } \\\\=\sqrt{0.004915} \\=0.07[/tex]

Therefore, the standard error is 0.07.

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Answer: Any value of f that is less than 3 1/3 satisfies the inequality. The solutions to the inequality are all values of f that are less than 3 1/3.

Step-by-step explanation:

Answer:

(1, 6)

Step-by-step explanation:

6x + 5y = 36 ----> 6x + 5y = 36

3x - 2y = -9 ----> -6x + 4y = 18

------------------

9y = 54

y = 6

3x - 2(6) = -9

3x - 12 = -9

3x = 3

x = 1

So the solution is (1, 6).

The equation that will likely have the graph attached is

The first step will be checking the y intercepts of the equations. Considering the graph the y intercept is in the positive hence equation in d is eliminated

Another factor is vertex, solving for the vertex of the remaining equations would show the equation that has a vertex that would be in that position

Otherwise plot the graph of all the equations and match the likely equations to the graphs

Matching the equations to their graphs shows that graph of y = 3x² - 2x + 1 is attached

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Answer:

ans is 1.

7+3×n+3×1-8

then u get the frst option

other options are wrong 10 n never possible

Answer:

  90.0 cm²

Step-by-step explanation:

You want to know the area of the composite figure shown.

The vertical side and hypotenuse of the right triangle are 9 cm and 15 cm. These have the ratio 9/15 = 3/5, so we know this triangle is a 3-4-5 right triangle with a scale factor of 3. The missing side length is 3·(4 cm) = 12 cm.

So, the figure is a trapezoid with a top base of 4 cm, a bottom base of 4+12 = 16 cm, and a height of 9 cm. Its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(4 cm +16 cm)(9 cm)

  A = 90 cm²

The area of the figure is 90.0 cm².

__

Additional comment

In case you don't recognize the 3:4:5 side ratio, you can figure the base of the triangle using the Pythagorean theorem:

  a² +b² = c²

  a² = c² -b² = 15² -9² = 225 -81 = 144

  a = √144 = 12 . . . . . length of CD in cm

Other useful Pythagorean triples you will see are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.

3 divided by 2 is equal tο 1 and 1/2.

A divisiοn divides a larger number intο smaller grοups with the same number οf cοnstituents. It is οne οf the basic mathematical οperatiοns. Hοw many tοtal grοups will be fοrmed, fοr example, if 20 students need tο be divided intο five grοups fοr a spοrting event?

It is easy tο address such challenges thanks tο divisiοn and cοοperatiοn. In this scenariο, multiply 20 by 5. The UTCMe is gοing tο be 20 x 5 = 4. There will be fοur grοups οf five students each. Yοu may cοnfirm this number by multiplying 4 by 5 and getting the answer 20.

When dividing 3 by 2, we get a quοtient οf 1 with a remainder οf 1. Tο write this quοtient as a mixed number, we take the quοtient (1) as the whοle number part οf the mixed number and write the remainder (1) as the numeratοr οf the fractiοnal part.

Then, the denοminatοr οf the fractiοnal part is the same as the divisοr (2) in the οriginal divisiοn prοblem.

So, the mixed number form of 3 ÷ 2 is:

1 1/2

Hence, 3 divided by 2 is equal to 1 and 1/2.

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For given Semi-circle shaped window,  the distance around the window is 38.55 inch.

What exactly is a circle?

A circle is a closed two-dimensional shape in which all points on the boundary are equidistant from a single point called the center. It is formed by taking all points in a plane that are a fixed distance (called the radius) away from the center. The distance around the circle's boundary is called the circumference, and the distance from the center to any point on the boundary is the radius.

Now,

As radius of semicircle = 7.5 in and

Circumference is given by = πr⇒3.14*7.5=23.55 inch

Perimeter of window= πr+D

D=diameter

P=23.55+15

P=38.55 inch

Hence,

         the distance around the window is 38.55 inch.

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Answer:

x=80

Step-by-step explanation:

Since, you do not know the percent you need to put a variable so we are going to named x and then we are going to cross multiply then we solv the equation.

Answer:

56 is 80% of 70

Step-by-step explanation:

[tex]\frac{56}{70} (100)=\frac{(56)(100)}{70} =\frac{5600}{70} =80[/tex]

Hope this helps.

The answer is not listed in the choices given. None of the answer choices Match -20.

To find the third term in an arithmetic sequence, we need to use the recursive formula. The recursive formula for an arithmetic sequence is given as:

a(n) = a(n-1) + d

where a(n) represents the nth term in the sequence, a(n-1) represents the previous term, and d represents the common difference between terms.

Since we are looking for the third term, n = 3. We also need to know the value of a(2), which is the second term in the sequence. To find a(2), we use the recursive formula again:

a(2) = a(1) + d

We are not given the value of a(1), so we cannot directly calculate a(2). However, we are given the answer choices, so we can use them to work backwards.

If we assume that a(2) is equal to -5 (choice C), then we can find a(1) by using the recursive formula:

a(2) = a(1) + d
-5 = a(1) + d

If we assume that d = -3 (since the common difference between terms is the same), then we can solve for a(1):

a(1) = -5 + (-3)
a(1) = -8

Now that we know a(1) and d, we can use the recursive formula to find a(3):

a(3) = a(2) + d
a(3) = -5 + (-3)
a(3) = -8

However, none of the answer choices match -8. This means that our assumption for a(2) was incorrect. We can try the same process with the other answer choices to see if we get a matching answer.

If we assume that a(2) is equal to -14 (choice A), then we can find a(1) by using the recursive formula:

a(2) = a(1) + d
-14 = a(1) + d

If we assume that d = -3 (since the common difference between terms is the same), then we can solve for a(1):

a(1) = -14 + (-3)
a(1) = -17

Now that we know a(1) and d, we can use the recursive formula to find a(3):

a(3) = a(2) + d
a(3) = -14 + (-3)
a(3) = -17 - 3
a(3) = -20

Therefore, the answer is not listed in the choices given. None of the answer choices match -20.

In summary, to find the third term in an arithmetic sequence using the recursive formula, we need to know the previous term and the common difference between terms. If we are given answer choices, we can work backwards to find the missing information. However, we must check all answer choices to ensure that we have the correct solution.

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The overlap of the doors is 20% of the width of the doorway.

By working with the exponential equation we will get:

i) N = 1000

ii) k = -0.02

iii) t = 34.66 seconds

Here we know that the equation:

[tex]N = 1000*e^{-k*t}[/tex]

models the population at a time t.

i) When t = 0, we have:

[tex]N = 1000*e^{-k*0}\\N = 1000*1\\N = 1000[/tex]

That is the initial population of bacteria.

ii) at t = 0, the rate of decay is -20 /min

the differentiation of the exponential gives:

[tex]N' = -k*1000*e^{-k*t}[/tex]

And evaluating that in t = 0 should give -20., then:

[tex]-20 = -k*1000*e^{-k*t}\\\\-20 = -k*1000\\-20/1000 = -k\\-0.02 = -k\\0.02 = k[/tex]

That is the value of k.

iii) Here we need to solve the equation:

[tex]500= 1000*e^{-0.02*t}\\\\0.5 = e^{-0.02*t}\\\\ln(0.5) = ln(e^{-0.02*t})\\\\ln(0.5) = -0.02*t\\\\ln(0.5)/ -0.02 = t\\ \\34.66 = t[/tex]

So it will take 34.66 seconds to reach half of the initial population.

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Answer:

3x² + 3x - 6

Step-by-step explanation:

(3x - 3)(x + 2)

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

3x(x + 2) - 3(x + 2) ← distribute parenthesis

= 3x² + 6x - 3x - 6 ← collect like terms

= 3x² + 3x - 6

Answer:

[tex]9(x - 1)(x-3)[/tex]

Step-by-step explanation:

[tex]9 {x}^{2} - 36x + 27[/tex]

[tex]9x(x - 1) - 27(x - 1)[/tex]

[tex](x - 1)(9x - 27)[/tex]

9(x-1)(x-3)

Using the given information, the volume of the sphere is approximately 1521.88 cubic units, rounded to the hundredths place

From the question, we are to determine the volume of the sphere.

Let's start by using the formula for the circumference of a circle,

C = 2πr,

Where C is the circumference

and r is the radius.

Since the circumference of the great circle is given as 14π, we can solve for the radius as follows:

14π = 2πr

Dividing both sides by 2π, we get:

r = 7

Now, we can use the formula for the volume of a sphere,

V = (4/3)πr³

Where V is the volume

and r is the radius.

Substituting the value of r that we found, we get:

V = (4/3)π(7)³

V = (4/3)π(343)

V = 4/3 * 1141.45

V = 1521.88

Hence, the volume of the sphere is 1521.88 cubic units.

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