solve the right triangle with 50° and 15

The evaluations of the given expressions are:

(a) ln e⁻³ = -3

(b) e^(ln 5) = 5

(c) e^(ln √3) = √3

(d) ln (1 / e⁵) = -5

From the question, we are to evaluate the given expressions.

The given expressions contain natural logarithm and exponential functions.

The natural logarithm is the inverse of the exponential function.

Thus,

ln eˣ = x

Likewise

e^(ln x) = x

Applying these rules to the given expressions, we get

(a) ln e⁻³ = -3

(b) e^(ln 5) = 5

(c) e^(ln √3) = √3

(d) ln (1 / e⁵)

This can be written as

ln (e⁻⁵) = -5

Thus,

ln (1 / e⁵) = -5

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Answer: It is not possible for the length of the third side of a triangle to be an integer when the lengths of the other two sides are not integer.

Step-by-step explanation:

When the other two sides of a triangle are 5.3 and 0.4 in length, the third side cannot possibly have an integer length. This is so because any two sides of a triangle must have lengths that are greater than the length of the third side. In this instance, 5.3 + 0.4 = 5.7, which still falls short of any integer number for the third side's length.

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Answer: 5

Step-by-step explanation:

5.3+0.4=5.7

5.3-0.4=4.9

4.9<x<5.7

The only possible integer between these two numbers is 5, so the correct answer is 5.

The volume of the display case is 60 + 120 = 180. The correct answer is B. 36.

Volume is a measure of the three-dimensional space something occupies or contains. It is often expressed as a calculation of length x width x height. It can also refer to the amount of something, such as the volume of a liquid, or the amount of space a container holds. Volume is an important concept in mathematics, science, engineering, and many other fields. It is used to measure the size of a solid, liquid, or gas, and to quantify the amount of material in an object or a space.

The volume of a rectangular prism is determined by multiplying its length, width, and height. The volume of a display case made of one rectangular prism stacked on top of a second rectangular prism is equal to the sum of the volumes of each rectangular prism.

The volume of the first rectangular prism is 3 x 4 x 5 = 60.
The volume of the second rectangular prism is 4 x 5 x 6 = 120.

Therefore, the volume of the display case is 60 + 120 = 180. The correct answer is B. 36.

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The values of Sin A, Cos B and Tan A are: 41.8, 2.8 and 6.9 respectively

The ratios of the sides of a right triangle are called trigonometric ratios.", if in trigonometry the ratios of the sides of a triangle are called 'trigonometric ratios' then what if the triangle is not a right triangleA =

In triangle 1

SinA = Opposite/Hypothenuse

Son A = 6/9

Sin A = 0.6669

A = Sin ⁻¹0.6667

A = 41.8⁰

For triangle 2

Cos B = Adjacent /Hypothenuse

Cos 45 = x/4

AB = 4*0.7071

AB = 2.8

For triangle 3

Tan a = Opp/Adjacent

Tan60 = AB/4

AB = 4*Tan60

AB = 4* 1.7321

AB = 6.9

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Answer:

OD:24

Step-by-step explanation:

3*3”2 = 27

-(4+3) = -7

8divided by 2= 4

27 + 4 -7=24

To find the greatest common factor of these three terms, we need to factor each one and identify the highest power of each factor that is common to all three. Then, we can multiply those factors together to find the GCF.

Let's begin by factoring each term:

1/4n^2m^3 = (1/4) * n^2 * m^3

5/20n^7m^8 = (1/4) * n^7 * m^8

3/12n^2m^8 = (1/4) * n^2 * m^8

Now, we can see that each term has a common factor of 1/4, so we can factor that out:

1/4 * (n^2 * m^3)

1/4 * (n^7 * m^8)

1/4 * (n^2 * m^8)

To find the highest power of each factor that is common to all three terms, we need to look at the exponents. The highest power of "n" that is common to all three terms is 2, and the highest power of "m" that is common to all three terms is 3. Therefore, the GCF is:

1/4 * n^2 * m^3

This simplifies to:

n^2m^3/4

So, the correct option is (c) n^2m^3/4.

Hence ,10 Hispanic students in Ms. Vitals Wednesday night aerobics class.

Aerobics is a form of physical exercise that combines rhythmic aerobic exercise with strength and stretching training routines with the goal of improving all elements of fitness ( cardio-vascular fitness, flexibility and muscular strength ).

The percentage  can be  found by  dividing the  value by the total value and then multiplying the  result by 100. The formula  used to  calculate  the  percentage is: [tex]\frac{value}{total value}[/tex]×100%.

To find out  how many of the  students in Ms.  Vitals aerobics class are Hispanic,

first of all to determine  the percentage of students  are not African American or Caucasian.

The percentage  of students are African American is 30%, and the percentage are Caucasian is 45%. Therefore, the percentage of students are not African American or Caucasian is;

100% - 30% - 45% = 25%

So, 25% of  the students in the aerobics class are Hispanic.

To find the number of students are Hispanic,  we need to calculate 25% of the total number of  students;

25% of 40 students = [tex]\frac{25}{100}[/tex] x 40 = 0.25×40=10 students

Therefore, there are 10 Hispanic students in Ms. Vitals Wednesday night aerobics class.

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Answer:28 or 29 can't tell if the x is supposed to be on the 28 or 29

Step-by-step explanation:

Answer:

Step-by-step explanation:

D

Answer: p=[tex]\frac{4m}{3}[/tex]  last one

Step-by-step explanation:

Varies directly means y=kx

here p=km

m= 1 1/2 =3/2

p=2

plug to solve for k

2=k(3/2)

k=4/3

plug back in p=4m/3

In summary |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.

How to solve?

|-13.5 - (-4 1/5)| = |-13.5 + 4 1/5| [Subtracting a negative is equivalent to adding a positive]

= |-9 4/5|

= 9 4/5

Now, we can substitute the values and simplify the expression:

|-13.5 - (-4 1/5)| × 1.4 + (-2)²2

= 9 4/5 × 1.4 + (-2)²2

= 13 3/5 + 4

= 17 3/5

Therefore, |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), connected by an equal sign (=).

For example, the equation 3x + 5 = 14 is an equation that shows that the expression 3x + 5 is equal to the expression 14. This equation can be solved for x to find the value of x that makes the equation true.

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The probability of selecting a car from the rental parking lot is 0.6 or 60%.

Probability of selection refers to the likelihood or chance of selecting a particular item or event from a group or population. It is a mathematical concept used in statistics, mathematics, and science to describe the likelihood of an event occurring, given the set of possible outcomes.

The probability of selecting a car from the rental parking lot can be found by dividing the number of cars by the total number of vehicles:

P(Car) = Number of Cars / Total Number of Vehicles

In this case, there are 5 trucks, 9 cars, and 1 van, so the total number of vehicles is:

Total Number of Vehicles = 5 + 9 + 1 = 15

Number of Cars = 9

Therefore, the probability of selecting a car from the rental parking lot is:

P(Car) = Number of Cars / Total Number of Vehicles

           = 9 / 15

           = 3 / 5

            = 0.6

So the probability of selecting a car from the rental parking lot is 0.6 or 60%.

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Answer:

A = 15.87 m²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 6.9 and h = 4.6 , then

A = [tex]\frac{1}{2}[/tex] × 6.9 × 4.6 = 3.45 × 4.6 = 15.87 m²

The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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Answer: C. 3/(t-1)

Step-by-step explanation:

Answer:

[tex] \dfrac{3}{t - 1} [/tex]

Step-by-step explanation:

[tex] \dfrac{t^2 - 2t - 3}{t^2 - 1} \cdot \dfrac{3t - 3}{t^2 - 4t + 3} = [/tex]

Start by factoring every numerator and denominator.

[tex] = \dfrac{(t - 3)(t + 1)}{(t + 1)(t - 1)} \cdot \dfrac{3(t - 1)}{(t - 3)(t - 1)} [/tex]

Every factor that exists in both a numerator and denominator can be eliminated.

[tex] = \dfrac{1}{t - 1} \cdot \dfrac{3}{1} [/tex]

Multiply numerators together. Multiply denominators together.

[tex] = \dfrac{3}{t - 1} [/tex]

1.The set of all mathematical concepts .

2.The set of possible weather conditions in which an area can experience.

3.The set of countries that make up the North American continent.

Sets, in mathematics , are a coordinated assortment of articles and can be addressed in set-manufacturer structure or list structure. Curly braces are typically used to represent sets.

1- Mathematics:

The collection of all mathematical concepts and guiding principles pertaining to the investigation of quantity, structure, space, and change. Math, algebra, geometry, trigonometry, calculus, probability, and statistics are all included in this.

2- Rain, Snow, Sunny:

The arrangement of conceivable weather patterns where a region can insight. This includes rain, which is the term used to describe the liquid water droplets that fall from clouds; snow, which refers to ice crystals falling from clouds; and sunny, a weather condition characterized by abundant sunlight and clear skies.

3- Canada, Mexico, United States:

The group of nations that make up the continent of North America. Canada, which is in the north of the continent, is included in this. Mexico, which is in the continent's southernmost region; and the United States of America, which is in the middle of the continent. The numerous cultures, histories, and geographies of these nations define them.

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Answer:

9207 divided by 4 = 2301 with a remainder of 3

Step-by-step explanation:

  (check the attached document)

The scale of the drawing is 1 cm = 4.5 m. This means that each centimeter in the drawing represents 4.5 meters in the actual field. The length of the field in the drawing is 7.2 cm, so the actual length of the field is 7.2 cm × 4.5 m/cm = 32.4 m. The width of the field in the drawing is 3 cm, so the actual width of the field is 3 cm × 4.5 m/cm = 13.5 m. The area of a rectangle is found by multiplying its length by its width, so the area of the actual field is 32.4 m × 13.5 m = 437.4 m²

Note :- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √[tex](b^2 - 4ac)[/tex]) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √[tex]((-12)^2 - 4(2)(20)))[/tex] / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √[tex](144 - 160)[/tex]) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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Answer:

Step-by-step explanation:

(0,0)

i hope this helps

Answer:

10x^2 - 4x - 32

Step-by-step explanation:

(2x - 4)(5x + 8)

10x^2 + 16x - 20x - 32

10x^2 - 4x - 32

Answer:

the abswer is D

Step-by-step explanation:

[f○g](x)=(9x+12)/9+8/3=x+8/3

[g○f](x)=9(x/9 + 4/3)+12=x+24

so for the same x they are not inverses

Both the domain and range of the transformed function are the same as those of the parent function.

What are Range and Domain?

The collection of all potential output values that a function can generate given its domain is known as its range.

The set of all potential input values for which a function is specified is referred to as its domain.

The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.

Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.

A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.

Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.

A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well

So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.

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The selection method that assures a fair chance of being selected to go first between Carla and Hattie is A) Flip a fair coin. If it lands on heads, Carla will go first. If it lands on tails, Hattie will go first.

A fair chance is based on an equal probability of being selected.

A fair coin of head and tail offers a fair chance to two contenders on who should play the game first.

In this situation, since Carla gets the heads, he has 50% chance of being selected to go first.

Equally, Hattie has a 50% chance to go first getting the tails.

Thus, the correct selection method is Option A.

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Tyler invested $5800 in the first account and $3900 in the second account.

Simple interest is interest that is calculated solely on a loan's or investment's principal amount, without taking into account any interest that has accrued over time. For instance, regardless of how long you keep the money in the account, if you deposit $1,000 in a savings account that offers 5% simple interest annually, you will make $50 in interest each year. Contrarily, compound interest accounts for both the original principal and the interest that has accrued over time. This means that interest is calculated on the new, higher balance after the interest collected during each period is applied to the principal amount.

Let us suppose the amount invested in first account = x.

The amount in second account = y.

Thus, according to the statements we have:

x + y = 9700 (total amount invested is $9700)

0.10x + 0.09y = 931

Now from the first equation we can write:

y = 9700 - x

Substituting the value of y we have:

0.10x + 0.09(9700 - x) = 931

0.10x + 873 - 0.09x = 931

0.01x = 58

x = 5800

Now, substituting the value of x we have:

y = 9700 - 5800

y = 3900

Hence, Tyler invested $5800 in the first account and $3900 in the second account.

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Answer:

C. 9 times larger

Explanation:

where, r = radius of a cylinder and h = height of the cylinder. This means that the volume of a cylinder will be 9 times larger if the radius is multiplied by 3.

Answer:

B.

Step-by-step explanation:

Since the line is from the top left to bottom right it's negative but if it was the opposite it would be positive.