What is the volume of a rectangular prism with a length of 12ft, a width of 10ft, and a height of 18ft?

We follow the inclusive rule, The answer to the question is (A) that is

if y>=10 and y <=50

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.

The intervals used are:

(a , b) , All the numbers between a & b without including them.

[a, b] , All the numbers between a & b including them.

y lies in [10,50].

And since it means that it includes 10 and 50 and all the numbers between them.

The final answer is (A) that is if y>1=10 and y <=50.

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Answer:

Step-by-step explanation:

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Answer and Explanation:

No, they did not use a ruler to compute the values of trig functions. They used geometry to prove theorems about trigonometry, then used those results and ordinary computations involving addition, subtraction, multiplication, division, and square roots to determine the entries in trigonometric tables.

Claudius Ptolemy (85 C.E.–165) created the first trig tables that we know of, and he included proofs of the theorems he used. One of the main theorems he used is what is now called Ptolemy’s theorem.

In order to prove his sum and difference forumlas, Ptolemy first proved what we now call Ptolemy’s theorem.

Ptolemy’s theorem. The product of the diagonals of a cyclic quadrilateral is equal to the sum of the products of the opposite sides.

A cyclic quadrilateral is a quadrilateral inscribed in a circle as ABCD. Ptolemy’s theorem says:

AC ⋅ BD = AB ⋅ CD + AD ⋅ BC

When one of the diagonals (like ) is a diameter of the circle, that gives you a way to determine the trig functions for sum and differences of angles.

Sometimes, the sum and difference formulas for sine and cosine are still called Ptolemy’s formulas.

sin(α + β) = sin α cos β + cos α sin β

cos(α + β) = cos α cos β − sin α sin β

sin(α − β) = sin α cos β − cos α sin β

cos(α − β) = cos α cos β + sin α sin β

Ptolemy started with angles he knew the trig functions for. These included angles in various isosceles triangles: 45°-45°-90°, 60°-60°-60°, and 36°-72°-72°, the last one described by Euclid in Proposition IV.10. That gave him the trig functions for 36°, 60°, and 90°. Using half-angle formulas (mentioned by Hipparchus (190–120 B.C.E.), he could compute trig functions for half of those angles and a quarter of those angles. Then using the sum and difference formulas he computed the rest of the numbers in his trig table.

Hope this helps! :)

The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

We know that the method to find the axis of the symmetry of the parabola is given by:

x = - b / 2 a

We have the general equation of the parabola as:

y = a x² + b x + c

We have the equation of the parabola as:

y = - 4 x² + 24 x - 35

Comparing from this equation, we get that:

a = - 4

b = 24

c = - 35

Now, substituting the values, we get that:

x = - 24 / 2 (- 4)

x = - 24 / - 8

x = 24 / 8

x = 3

Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

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Answer:

Step-by-step explanation:

Answer:

I believe A and B

Step-by-step explanation:

C cant be it due to the blueberry price being more and I dont believe its D

Graph [1] will represent the cost of raspberries and blueberries perfectly.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of straight line also represents direct proportionality as -

y = mx

m = y/x    

[m] is constant of proportionality.

We have Raspberries (R) cost twice as much as blueberries (B). The prices of blueberries and raspberries represent proportional relationships.

We can write the relation as -

y[R] = 2 x[B]

Graph [1] will represent the cost of raspberries and blueberries perfectly. The slope of the line representing raspberry is 2 times that of blueberry.

Therefore, Graph [1] will represent the cost of raspberries and blueberries perfectly.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

Area of trapezoid:

12 + 6<-- your two bases of the trapezoid = 18

18 x 4 = 72, 72 divided by 2 = 36

now we multiply by 2 since there are 2 trapezoids:

36 x 2 = 72

Area of rectangle in front:

6 x 3 = 18

Area of the 2 rectangles on the sides:

5 x 3 = 15

(multiply by 2 since there are two rectangles on both sides)

15 x 2 = 30

Area of rectangle on the back:

12 x 3 = 36

Now lets add up all the areas:

72 + 18 + 30 + 36 = 156 in2 is your answer.

The amount insurance company will pay is $700000.

We are given that

Age of Mr. lewis= 63

Policy value= $700,000

Now,

If Mr. Lewis dies after paying for the policy for 24 months, he would have paid a total of 24 * $72 = $1728 in premiums. Since he has a five-year level-term life insurance policy with a face value of $700,000, his beneficiaries would receive the full face value of the policy if he dies within the five-year term.

Therefore, by algebra the answer will be $700000.

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Answer:

0.0954 = 9.54% probability that the combined sample tests positive for the​ virus. This probability is higher than 5%, and thus, it is not unlikely for such a combined sample to test​ positive.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they test positive, or they do not. The probability of a person testing positive is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The probability of a randomly selected adult in one country being infected with a certain virus is 0.005.

This means that \(p = 0.005\)

Samples from 20 people

This means that \(n = 20\)

What is the probability that the combined sample tests positive for the​ virus? Is it unlikely for such a combined sample to test​ positive?

Probability of at least one positive test, which is:

\(P(X geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.005)^{0}.(0.995)^{20} = 0.9046\)

Then

\(P(X geq 1) = 1 - P(X = 0) = 1 - 0.9046 = 0.0954\)

0.0954 = 9.54% probability that the combined sample tests positive for the​ virus. This probability is higher than 5%, and thus, it is not unlikely for such a combined sample to test​ positive.

Answer:

The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Step-by-step explanation:

hope this helped:)

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The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Here, we have,

The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54, then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.

Factors of 54: 1,2,3,6,9,18,27 and 54

Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number.

To find the factors of a number, 54, we will use the factorization method.

To find factors of 54, we have to divide 54 by all natural numbers from 1 to 54.

54 ÷ 1 = 54

54 ÷ 2 = 27

54 ÷ 3 = 18

54 ÷ 6 = 9

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The function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.

Given is that f(x) = 2x² + 1 and g(x) = 3x - 5.

We have to find -

f{g(2)}

Now -

g(2) = g(2) = 3 x 2 - 5 = 6 - 5 = 1

g(2) = 1

f{g(2)} = 2x² + 1 = 2 x 1 x 1 + 1

f{ g(2) } = 3

Therefore, the function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.

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Answer:

1 1/4

Step-by-step explanation:

Answer:

First, let's find the fraction of people wearing green or red shorts:

1/4 + 1/6 = 3/12 + 2/12 = 5/12

This means that 5/12 of the people are wearing either green or red shorts. To find the fraction of people wearing blue shorts, we need to subtract this from 1 (since the three options are exhaustive):

1 - 5/12 = 7/12

So, 7/12 of the people are wearing blue shorts. To find out how many people this represents, we can multiply this fraction by the total number of people in the race:

7/12 x 24 = 14

Therefore, 14 people are wearing blue shorts.

Step-by-step explanation:

Answer:

To use a tape diagram, we can start by drawing a rectangle to represent the total number of people in the race. Then, we can divide it into four equal parts to represent the people wearing green shorts and into six equal parts to represent the people wearing red shorts.

Let's use the letter "B" to represent the number of people wearing blue shorts. We know that the total number of people is 24, so we can write:

4 parts + 6 parts + B parts = 24

Simplifying this equation, we get:

10 + B = 24

Subtracting 10 from both sides, we get:

B = 14

Therefore, 14 people are wearing blue shorts.

To double-check our answer, we can add up the number of people in each category:

4 parts out of 24 = 6 people wearing green shorts

6 parts out of 24 = 4 people wearing red shorts

B parts out of 24 = 14 people wearing blue shorts

6 + 4 + 14 = 24, which matches the total number of people in the race.

Answer:

A(3,3), B(3,7), C(8,7), D(8,3)

Step-by-step explanation:

it was the correct answer hope this helps!!

Answer:

Amar pays the most

Step-by-step explanation:

Amar pays the most, because Mira and Raja split the bill, so they onyl need to pay 1/5 each. However, Amar needs to pay 2/5 which is the most.

Hope this helps!

Answer: 90, 180, 270

Step-by-step explanation: 90 es divisible por todos esos números. Para obtener dos números más que sean divisibles por esos, simplemente multiplique 90 por 2 y 3.

The interest amount is $622.85

The given parameters are:

The interest amount is calculated as:

I = P(1 + r/n)^(nt) - P

This gives

I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000

Evaluate the products and the quotient

I = 1000 * (1 + 0.045)^(11) - 1000

Evaluate the sum

I = 1000 * (1.045)^(11) - 1000

Solve

I = 622.85

Hence, the interest amount is $622.85

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Answer:

distance = 14.4222

midpoint = (1, -2)

Step-by-step explanation:

distance between two points:

sqrt(x₂ - x₁)² + sqrt(y₂ - y₁)²

sqrt((5 - (-3))² + sqrt(-8 - 4)²

sqrt(8)² + sqrt(-12)²

\(\sqrt{64 + 144}\)

\(\sqrt{208}\)

distance = 14.4222

midpoint:

\((\frac{-3 + 5}{2} , \frac{4 + -8}{2})\)

(1, -2)

Answer:

x = -3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+2(3x−7))=22x−65

Step 1: Simplify both sides of the equation.

4(x+2(3x−7))=22x−65

(4)(x)+(4)(2(3x−7))=22x+−65(Distribute)

4x+24x+−56=22x+−65

(4x+24x)+(−56)=22x−65(Combine Like Terms)

28x+−56=22x−65

28x−56=22x−65

Step 2: Subtract 22x from both sides.

28x−56−22x=22x−65−22x

6x−56=−65

Step 3: Add 56 to both sides.

6x−56+56=−65+56

6x=−9

Step 4: Divide both sides by 6.

6x = -9

6       6

x =  -3/2

Answer:

x<−

​9

​--

​16

​​

and x≤−

​13

​--

​19

​​

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Use slope formula:

m = (y2 - y1) / (x2 - x1)

m = (-2 - 1) / (-3 - 1)

m = -3/-4

Negative + Negative = Positive

m = 3/4

Answer:

Standard Form: 2x - y = -2

Step-by-step explanation:

A set is a collection of distinct elements, and a subset is a collection of elements taken from a larger set. In this case, the set is {10, 15, 14, 20, 11}.

To calculate the number of subsets, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, the number of subsets of the set {10, 15, 14, 20, 11} is 2^5 = 32.

To calculate the number of proper subsets, we need to exclude the empty set (Ø) and the set itself from the total number of subsets. So, the number of proper subsets is 32 - 2 = 30.

Therefore, there are 32 subsets and 30 proper subsets of the set {10, 15, 14, 20, 11}.

Answer: 3

You are breaking up the 8 into 5 and another number. The other number plus 5 has to equal 8. Using 8-5, we know that that other number must be 3.

:)

the missing number Is 3

40=25+(_×5)

40-25=_×5

15=_×5

_=15/5

_=3

Answer:

y = -6x-8

Step-by-step explanation:

Answer:

Option A and B

Step-by-step explanation:

- - 10 / - 9 is same as - 10 / 9.

It can also be written as 10 / - 9.

Answer:

36

Step-by-step explanation: