The shorter leg of a 30°-60°-90° triangle is 12. what is the length of the hypotenuse?

Answer:

Step-by-step explanation:

[tex]n^{5}= 1254\\n^{5} = 2.3.11.19[/tex]

Therefore it is not possible that n is a perfect power of 5

           it is approximately 4.16

Answer:

n ≈ 4.165

Step-by-step explanation:

To solve this, you need to take the 5th root of both sides:

[tex]n^5=1,254[/tex]

[tex]\sf{\sqrt[5]{n^5} =\sqrt[5]{1254}}[/tex]

On the lhs we're only left with n as n^5 and the 5th root cancel each other out.

On the right-hand side we need to calculate:

[tex]n\approx4.165[/tex]

Answer:

4 cm

Step-by-step explanation:

Step: 1

Consider a circle inscribed in an isosceles triangle with legs of length 13cm and a base length of 10cm.

Step: 2

Draw-in altitude AD will pass through the center  O and bisects the base into two segments each in 5cm length.

So the triangle is isosceles so the segment BD is 6cm.

Draw in radius OB and radius OA  and length of  OD as h.

Refer to the attachment for step 3 and step 4

To learn more about triangles, please visit

https://byjus.com/maths/triangles/

Predicates are used to express statements, properties, or relationships between entities in a formal and systematic way, allowing for logical reasoning and analysis. They are an essential component of predicate calculus, which is a branch of mathematical logic.

In logic and linguistics, a predicate is a term used to describe or assert something about a subject. It is a fundamental concept in predicate logic, which is a formal system for reasoning about statements and their relationships.

In a logical statement, a predicate is typically a function or a relation that takes one or more arguments and returns a truth value (either true or false) when those arguments are substituted into it. The arguments of a predicate are usually referred to as its subjects.

For example, in the statement "Socrates is mortal," the predicate is "is mortal," which asserts the property of being mortal about the subject "Socrates." In this case, the predicate is a unary relation since it takes only one argument.

Predicates can also take multiple arguments. For instance, in the statement "John loves Mary," the predicate is "loves," which relates the subject "John" to the object "Mary." In this case, the predicate is a binary relation.

In general, predicates are used to express statements, properties, or relationships between entities in a formal and systematic way, allowing for logical reasoning and analysis. They are an essential component of predicate calculus, which is a branch of mathematical logic.

For such more questions on Predicate Meaning in Logic

https://brainly.com/question/30644755

#SPJ11

The option that shows the inverse's graph (with the correspondent domain and range) is option a.

Remember that for a function:

f(x) = y

The inverse f⁻¹(x) is defined as:

f⁻¹(y) = x

Here the original function is defined by the relation:

x: -1,  1,  3, 5, 7

y: 4, 2, 1, 0, 1

Then for the inverse function, the domain and range are:

x: 4, 2, 1, 0, 1

y: -1, 1, 3, 5, 7

Then the domain is 0 ≤ x ≤ 4

And the range is -1 ≤ y ≤ 7

the option with these two is a, so that is the correct option.

Learn more about inverses at:

https://brainly.com/question/3831584

#SPJ1

The Algebraic expression -3 * 15 simplifies to -45.

The product of -3 and 15 can be represented algebraically as (-3) * 15.

To simplify this expression, we can perform the multiplication operation:

(-3) * 15 = -45

Therefore, the product of -3 and 15 simplifies to -45.

In the given expression, we have multiplied -3 by 15, resulting in a negative value since one of the factors is negative. Multiplying a negative number by a positive number yields a negative product.

So, the algebraic expression -3 * 15 simplifies to -45.

To know more about Algebraic expression.

https://brainly.com/question/30318592

#SPJ11

The relation that represents a function is: ((- 6, 5), (- 3, 2), (1, 2), (6, 5))

A relation represents a function if each input (x-value) is associated with only one output (y-value).

1. {(0, 3), (2, 4), (0, 6)}:

This relation is not a function because the input 0 is associated with two different outputs, 3 and 6.

2. ((- 7, 5), (- 7, 1), (- 10, 3), (- 4, 3)):

This relation is not a function because the input -7 is associated with two different outputs, 5 and 1.

3. ((- 6, 5), (- 3, 2), (1, 2), (6, 5)):

This relation is a function since each input is associated with a unique output.

4. {(2, 0), (6, 2), (6, - 2)}:

This relation is not a function because the input 6 is associated with two different outputs, 2 and -2.

Learn more about Function here:

https://brainly.com/question/30721594

#SPJ1

Answer:

28

Step-by-step explanation:

2 30 mg pills for 60 mg

Twice a day is 4 pills and 7 days a week

So 4x7=28

Answer:

number is 2

Step-by-step explanation:

let the number be n then 8 times the number is 8n, subtract 1 from this and

8n - 1 = 15 ( add 1 to both sides )

8n = 16 ( divide both sides by 8 )

n = 2

that is the number is 2

The Mujib spent 60% of his money, while Prakash spent 20% of his money.The Mujib spent 60% of his money ($24 out of $40), and Prakash spent 20% of his money ($24 out of $120). Understanding percentages is an important skill, as it allows us to analyze and compare data in a meaningful way.

To work out the percentage of money each person has spent, we first need to determine the amount spent by each person. Both Mujib and Prakash spent $24 each. Now, let's calculate the percentage of money spent by each person.

Mujib had $40 initially and spent $24, so his total spending is $24. To find the percentage, we divide his spending by his initial amount and multiply by 100: ($24 / $40) * 100 = 60%. Therefore, Mujib spent 60% of his money.

Prakash had $120 initially and also spent $24, resulting in a total spending of $24. Similarly, we calculate the percentage of Prakash's spending by dividing his spending by his initial amount and multiplying by 100: ($24 / $120) * 100 = 20%. Hence, Prakash spent 20% of his money.

For such more questions on Percentages:

https://brainly.com/question/24877689

#SPJ11

The correct answer is: favorable outcomes divided by possible outcomes. The theoretical probability is a mathematical concept that represents the likelihood of an event occurring based on the ratio of favorable outcomes to the total number of possible outcomes.

The correct answer is: 1/5. Since there are five equally-sized pie shapes on the spinner, and only one of them is blue, the probability of landing on blue when you spin is 1 out of 5 or 1/5.

To predict how many out of 10,000 coffee drinkers will like the new coffee, we can use the concept of proportion. Since we know that 450 out of 1,000 coffee drinkers like the new coffee, we can set up the proportion:

450/1,000 = x/10,000

Cross-multiplying, we get:

1,000x = 450 * 10,000

Simplifying further:

1,000x = 4,500,000

Dividing both sides by 1,000:

x = 4,500

Therefore, out of 10,000 coffee drinkers, we can predict that approximately 4,500 will like the new coffee.

The expression x² + 17 represents the sum of x squared and 17.

The sum of x squared and 17 we have to write in expression

x squared is the term x² represents x squared.

It means that the variable x is being multiplied by itself.

If x = 3, then x² would be 3 squared, which is 9.

Similarly, if x = -2, then x² would be (-2) squared, which is 4.

The term + 17 represents the constant value 17 being added to x squared. Regardless of the value of x, 17 will always be added to the result of x squared.

By combining these two terms using the addition operator (+), we express the sum of x squared and 17 as a single mathematical expression, which is x² + 17

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

Answer:

[tex]\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}[/tex]

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

[tex]SA = 2( A_{\text{base}}) + A_\text{side}[/tex]

First, we can calculate the area of the circular base:

[tex]A_{\text{circle}} = \pi r^2[/tex]

[tex]A_{\text{base}} = \pi (0.75 \text{ in})^2[/tex]

[tex]A_{\text{base}} = 0.5625\pi \text{ in}^2[/tex]

Next, we can calculate the area of the rectangular side:

[tex]A_\text{rect} = l \cdot w[/tex]

[tex]A_\text{side} = (4\text{ in}) \cdot C_\text{base}[/tex]

Since the width of the side is the circumference of the base, we need to calculate that first.

[tex]C_\text{circle} = 2 \pi r[/tex]

[tex]C_\text{base} = 2 \pi (0.75 \text{ in})[/tex]

[tex]C_\text{base} = 1.5 \pi \text{ in}[/tex]

Now, we can plug that back into the equation for the area of the side:

[tex]A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})[/tex]

[tex]A_\text{side} = 6\pi \text{ in}^2[/tex]

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

[tex]SA = 2( A_{\text{base}}) + A_\text{side}[/tex]

[tex]SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2[/tex]

[tex]\boxed{SA = 7.125\pi \text{ in}^2}[/tex]

[tex]\boxed{SA \approx 22.4 \text{ in}^2}[/tex]

Randall's conversion is incorrect because centimetre value cannot be less than the meter value for an equivalent measurement.

Both meters and centimeters are used to measure the length of distances or objects. As distances becomes longer, the use of meters would be more preferable as they can represent this distances with smaller values than centimeters.

100 cm = 1 m

Therefore,

40 cm = (40/100) m

40cm = 0.4 m

This shows that centimeters values cannot be greater than equivalent meter values .

Hence, Randall is incorrect .

Learn more on conversion ; https://brainly.com/question/30850837

#SPJ1

The perimeter of the classroom in feet is 90 feet.

We are given that;

The corners of the classroom are (−12, 15), (−12, −9), (9, 15), and (9, −9).

Now,

Using the given coordinates, we can find the length and width of the rectangle. The length of the rectangle is the difference between the y-coordinates of two opposite corners, which is 15 - (-9) = 24 feet. The width of the rectangle is the difference between the x-coordinates of two opposite corners, which is 9 - (-12) = 21 feet.

P = 2(24 + 21) = 90 feet

Therefore, by the perimeter the answer will be 90 feet.

Learn more about perimeter here:

https://brainly.com/question/10466285

#SPJ1

In the given diagram, we have two parallel lines intersected by a transversal. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by parallel lines and a transversal.

From the diagram, we can observe the following angle relationships:

Angle A is corresponding to the angle (4x - 3)°.

Therefore, we can write: A = (4x - 3)°.

Angle B is alternate interior to the angle (7x + 9)°.

Therefore, we can write: B = (7x + 9)°.

Angle C is alternate interior to the angle 2x°.

Therefore, we can write: C = 2x°.

Since the sum of angles in a straight line is 180°, we can set up the equation:

A + B + C = 180°

Substituting the known values, we get:

(4x - 3)° + (7x + 9)° + 2x° = 180°

Simplifying the equation, we can solve for x:

4x - 3 + 7x + 9 + 2x = 180

13x + 6 = 180

13x = 174

x = 13.38

Therefore, the value of x is approximately 13.38.

Please note that this solution assumes the given diagram accurately represents the angle relationships.

The gradients of the lines AB, XY and PQ are 3S, -3 and 77/3 respectively.

To find the gradient of a line, we need to use the formula: gradient = (change in y)/(change in x).

For the first question, we have two points A (C3,1) and B (C6,10S). The change in y is 10S - 1 = 9S, and the change in x is C6 - C3 = 3. Therefore, the gradient of the line AB is 9S/3 = 3S.

For the second question, we have two points X (5,-1) and Y (3,5). The change in y is 5 - (-1) = 6, and the change in x is 3 - 5 = -2. Therefore, the gradient of the line XY is 6/-2 = -3.

For the third question, we have two points P (C3,-2) and Q (6,75). The change in y is 75 - (-2) = 77, and the change in x is 6 - C3 = 3. Therefore, the gradient of the line PQ is 77/3.

To learn more about : lines

https://brainly.com/question/24644930

#SPJ11

Step-by-step explanation:

a)   x = riders     y = racers       ( that is just what I picked...YMMV)

b)   x+y = 321        <======given

c)  25 x + 15 y =  6935    <=====given

Now just graph the two equations.....where they cross is the solution.

Graph below:

Answer:

To solve this problem, we can use the formula distance = rate x time.

For the first part of the trip on the highway, Jennifer travels at an average rate of 54 1/2 miles per hour for 3 hours, so the distance she covers is:

distance = rate x time

distance = (54 1/2) x 3

distance = (109/2) x 3

distance = 327/2

distance = 163.5 miles

For the second part of the trip on the smaller route, Jennifer travels at an average rate of 34.25 miles per hour for 3 hours, so the distance she covers is:

distance = rate x time

distance = 34.25 x 3

distance = 102.75 miles

The total distance Jennifer has driven after 6 hours is the sum of the distances she covered on both parts of the trip:

total distance = 163.5 + 102.75

total distance = 266.25 miles

Therefore, the answer is (A) 266.25 miles.

Answer: D (√x < 2)

Explanation: In interval notation, it reads:

0 < x < 4

It goes from 0 to 4.

Answer:

A C E

Step-by-step explanation:

judging by the fact that every game is $3.25 2 games is $6.50 3 is 9.75 and so on

Answer:

Step-by-step explanation:

mag jakol

(a). Rounded to three significant figures, the length of the side of the cube is 30.0 cm.

(b). Rounded to three significant figures, the height of the trapezoidal prism is 2.75 cm.

Let's solve this problem step by step:

First, let's calculate the volume of the fish tank when it is filled with water to two-thirds of its height.

The base dimensions of the fish tank are 72 cm by 48 cm, and the height is 52 cm.

Filling it with water to two-thirds of the height means the water level is at 2/3 × 52 = 34.67 cm.

The volume of a rectangular prism (the fish tank) is given by V = length × width × height.

Plugging in the values, we have V = 72 cm × 48 cm × 34.67 cm

≈ 112,430.08 cm³.

Now, let's calculate the volume of the cube.

The cube is placed in the fish tank the water level rises to three-quarters of the height is 3/4 × 52 = 39 cm.

The volume of the water that spilled can be calculated by subtracting the volume of the fish tank before the cube was placed from the volume of the fish tank after the cube was placed.

The volume of the cube is 112,430.08 cm³ - 39 cm × 72 cm × 48 cm = 28,861.92 cm³.

Since the volume of a cube is given by V = side³, we can solve for the length of the side of the cube.

Thus, side³ = 28,861.92 cm³ and by taking the cubic root of both sides, we find side ≈ 30.042 cm.

Now, let's calculate the height of the trapezoidal prism.

We know that the volume of water spilled when the trapezoidal prism is placed is 500 cm³.

Since the volume of a trapezoidal prism is given by V = (1/2) * (a + b) * h * base a and b are the lengths of the parallel sides of the trapezoid, h is the height of the trapezoid, and base is the distance between the parallel sides, we can rearrange the formula to solve for the height:

h = (2 × V) / ((a + b) × base).

The cross-sectional area of the trapezoidal prism is 928 cm², we can find the base.

Since the area of a trapezoid is given by A = (1/2) × (a + b) × h, we can rearrange the formula to solve for the base:

base = (2 × A) / (a + b).

Plugging in the values, we have base = (2 × 928 cm²) / (72 cm + 48 cm)

≈ 9.28 cm.

Now we can calculate the height of the trapezoidal prism:

h = (2 × 500 cm³) / ((72 cm + 48 cm) × 9.28 cm)

≈ 2.754 cm.

For similar questions on trapezoidal

https://brainly.com/question/1410008

#SPJ11

In the given triangle, we have a right triangle where one angle is 90 degrees (marked as a square symbol). To find the value of x, we can use the trigonometric ratios sine, cosine, or tangent.

Looking at the triangle, we can see that the side adjacent to the angle x is 8 cm, and the hypotenuse of the triangle is 10 cm.

Using the cosine ratio, which is defined as the adjacent side divided by the hypotenuse, we can set up the equation:

cos(x) = adjacent/hypotenuse

cos(x) = 8/10

To find the value of x, we can take the inverse cosine (arccos) of both sides:

x = arccos(8/10)

Using a calculator, we can determine the approximate value of x:

x ≈ 36.87 degrees

Therefore, the value of x in the given triangle is approximately 36.87 degrees.

To determine the probability of Luke getting all three prizes in three boxes of cereal, we need to find the probability of each individual event happening and then multiply those probabilities together.

The probability of getting a movie ticket coupon is 20% or 0.2.

The probability of getting a drink coupon is 30% or 0.3.

The probability of getting a popcorn coupon is 40% or 0.4.

Since Luke spins the spinner three times, the probability of getting all three prizes is calculated by multiplying the probabilities together:

P(all three prizes) = P(movie ticket) * P(drink) * P(popcorn)

= 0.2 * 0.3 * 0.4

= 0.024 or 2.4%

Therefore, based on the simulation, the probability that Luke gets all three prizes in three boxes of cereal is 2.4%.

The range of the cost of their family grocery bill is $119.91.

The range of the cost of the Michaels family grocery bill can be calculated by finding the difference between the highest and lowest values.

In this case, the highest value is $176.97, and the lowest value is $57.06.

Range = Highest value - Lowest value

Range = $176.97 - $57.06

Range = $119.91

Therefore, the range of the cost of their family grocery bill is $119.91.

For more such questions on range , Visit:

https://brainly.com/question/24326172

#SPJ11

Answer:

R5096÷98people

=R52 each

The instantaneous velocity of the coin, from the first derivative of the height function of the coin, is; v(2) = -20 m/s

The derivative of a function is the rate at which the function is changing with regards to the input variable, at a point within the domain of the function.

The height of the tower = 100 m

The function for the height of the coin is; h(t) = 100 - 5·t²

The instantaneous velocity of the coin is the rate of change of the height with respect to time, which is obtained from the derivative of the height function as follows;

The instantaneous velocity; v(t) = h(t)/dt = d(100 - 5·t²)/dt = -10·t

The instantaneous velocity for the coin at t = 2 seconds is therefore;

v(2) = -10 × 2 = -20

Learn more on instantaneous velocity here: https://brainly.com/question/17007399

#SPJ1

The volume of the pyramid is 18069333.33 cubic units

The area of the surface is 313280 square units

The volume of the pyramid is solved using the formula

= 1/2 * base area * height

Where

base area = 440 * 440 = 193600

height = 280

volume of the pyramid = 1/3 * 193600 * 280

volume of the pyramid = 18069333.33 cubic units

The surface area

The surface area is calculated using the formula

= 4 *  area of the triangles

= 4 * 1/2 * 440 * 356

= 313280 square units

Learn more about pyramid at

https://brainly.com/question/218706

#SPJ1

Answer:

[tex]\huge\boxed{\sf |AB|\approx 13.9 \ units}[/tex]

Step-by-step explanation:

Point 1 = (x₁, y₁) = (7, 12)

Point 2 = (x₂, y₂) = (2, -1)

So,

x₁ = 7

y₁ = 12

x₂ = 2

y₂ = -1

Using distance formula to solve the question.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\D=\sqrt{(2-7)^2+(-1-12)^2} \\\\D=\sqrt{(-5)^2+(-13)^2} \\\\D = \sqrt{23+169} \\\\D=\sqrt{194} \\\\|AB|\approx 13.9 \ units\\\\\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

To find out how many cuboids of dimension 5 cm x 5 cm x 3 cm are needed to form a cube, we need to calculate the volume of both the cuboid and the cube.

The volume of the cuboid is:

5 cm x 5 cm x 3 cm = 75 cubic cm

To form a perfect cube, the volume of the cube should be a multiple of the volume of the cuboid. The smallest cube that can be formed using a multiple of 75 cubic cm is a cube with a volume of 75 x 8 = 600 cubic cm.

To find the dimensions of this cube, we need to find the cube root of 600 cubic cm:

cube root of 600 = 8.66 cm

So, the dimensions of the cube are 8.66 cm x 8.66 cm x 8.66 cm.

To find how many cuboids are needed to form this cube, we need to divide the volume of the cube by the volume of the cuboid:

Volume of the cube = 8.66 cm x 8.66 cm x 8.66 cm = 658.39 cubic cm

Number of cuboids required = 658.39 cubic cm ÷ 75 cubic cm = 8.78

Since we can't use a fraction of a cuboid, Anuj will need 9 such cuboids to make a perfect cube.