in the 3rd century bc the egyptians used their body parts to measure things.Why do you think peoplebinvented measurement system if body parts can be used to measure?


PLEASE ANSWER IT I REALLY NEED THANKYOU ​

If sin(x) = 3a/2 and 0 ≤ x ≤ π/2, then x = arcsin(3a/2). The condition on x here is useful because it makes the sin and arcsin functions exacts inverses of one another: if y = sin(x), then arcsin(y) = x.

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Also because 0 ≤ x ≤ π/2, we know both sin(x) > 0 and cos(x) > 0. So from the Pythagorean identity, it follows that

sin²(x) + cos²(x) = 1

==>   cos(x) = √(1 - sin²(x)) = √(1 - 9a ²/4) = 1/2 √(4 - 9a ²)

Then we have

x/4 - sin(2x) = x/4 - 2 sin(x) cos(x)

… = 1/4 arcsin(3a/2) - 2 (3a/2) (1/2 √(4 - 9a ²))

… = 1/4 arcsin(3a/2) - 3a/2 √(4 - 9a ²)

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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The value of function f(x) = 3x² + 8x-10 at f(2) is  18 .

We have given an function f(x) = 3x² + 8x-10

Putting x = 2 into this function , we get

 f(2) = 3(2)²+ 8x -10

        =3(4) + 8(2) -10

        = 12 + 16 -10

        = 18

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Answer:

y=1

Step-by-step explanation:

we can find what w is equal to first

2w=8

/2. /2

w=4

Now we fill in w to find y

4=4y

/4. /4

1=y

Hopes this helps please mark beainliest

Answer:

d

Step-by-step explanation: bc i said

The possible error of measurement is half of the smallest unit on the tape measure, which is half an inch, option B is correct.

Two or more expressions with an Equal sign is called as Equation.

The possible error of measurement refers to the smallest unit of measurement on the tape measure.

In this case, the tape measure is marked every half inch, so the smallest unit of measurement is 0.5 inches.

Therefore, the possible error of measurement is also 0.5 inches.

This means that any measurement taken using this tape measure may be off by up to 0.5 inches due to the limitations of the instrument used.

Hence, the possible error of measurement is half of the smallest unit on the tape measure, which is half an inch. Therefore, the answer is B. 0.5 in.

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Answer:

\(34.5575191895\)

Step-by-step explanation:

\(2\pi r(180/360)\\2\pi *11*1/2\\=11\pi\)

The arc length of the semicircle is half the circumference i.e., 11π.

The circumference is the perimeter of a circle.

Formula of Circumference = 2πr.

= Arc length of a semicircle  

= half of the circle's circumference

= 2πr/2

= πr

=11r

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This is the answer to your problem

Answer: B

Step-by-step explanation:

A  $70 is fixed, we have to add $50 each hour. So, it will be 70 + 50x. If he charged $285 overall, this means that 70 + 50x = 285

50x = 285 - 70

50x = 215

x = 215/50 = 4.3

Answer: no like this

Step-by-step explanation:

There are two questions to be solved, therefore, I'll solve the buckets one first and then I'll solve the other one. To solve both we need to apply LCM (least common multiple).

There are three buckets with differente capacities, one with 15 litres, one with 18 litres and one with 24 litres. Since they can fill a drum in an exact number of times, this means that the capacity of the drum is a multiple of the capacity of each bucket, therefore we should break each number into their multiples and find the common ones as shown below.

We now need to multiply all the common multiples:

For the second problem we have three items a book, a pen and a box. They cost respectively 36, 45 and 54. We need to then find the smallest sum of money that could buy a exact number o each item. We need to apply LCM once again as shown below:

We now need to multiply all the common multiples:

The set of parametric equations to model the path of the rocket include:

x(t) = 0

y(t) = -4.9t^2 + 26.5t + 6

The time it takes for the rock to hit the ground again is 5.26 seconds.

It should be noted that to find t in the formula y(t) = 0, we can substitute y(t) with 0 and solve for t. The resulting quadratic equation will be -4.9t^2 + 26.5t + 6 = 0; solving this involves utilizing the quadratic formula: t= (-b ± sqrt(b^2-4ac))/2a where a=-4.9, b=26.5, and c=6.

Substituting them into the quadratic formula and simplifying further leads us to t=5.26 seconds rounded off to two decimal places. Therefore, it would take approximately 5.26 seconds before the rocket hits the ground again based on the given parameters.

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a)  These two hypothesis tests differ in terms of their research questions, assumptions, and the types of variables that are involved in each test.

The arithmetic calculations and statistical procedures for (a) the test of homogeneity and (b) the test of independence are not the same. They are different from each other. These two hypothesis tests differ in terms of their research questions, assumptions, and the types of variables that are involved in each test. This is because they deal with different types of data. Below are the examples of a research question that would require a test of homogeneity and an example that would require a test of independence. These examples show the distinguishing characteristics that are involved in each of these tests. Research question that would require a test of homogeneity: A researcher would like to determine whether there is any significant difference between the proportions of men and women who voted for the two main political parties in an election. The research question can be framed as follows: Are the proportions of men and women who voted for the two main political parties homogenous or different? Assumptions: Samples are independent, observations are nominal or categorical, and the variable of interest has more than two categories (i.e., nominal or ordinal).Test of homogeneity:It is used to determine whether two or more populations have the same proportion or distribution of a nominal or categorical variable.Example that would require a test of independence:A researcher is interested in knowing whether there is any relationship between gender and drug addiction among high school students in a particular area. The research question can be framed as follows: Is there a relationship between gender and drug addiction among high school students?Assumptions:Samples are independent, observations are nominal or categorical, and the variable of interest has only two categories (i.e., nominal).Test of independence: It is used to determine whether there is any relationship between two nominal or categorical variables.

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Answer:

6384

Step-by-step explanation:

Since the question is only talking about fruit, I'm going to ignore which type and add the fruits together.

3+4+7+14=7+7+14=14*2=28

I have 28 fruits, and my friend give me 5 times that, so my friend gives me 5*28, or 140 fruits. So in all, I have 140 plus my original 28, or 168 all together

Then, my other friend gives me 75 times more. Wow. I don't think I've seen this many fruits all in one place, but this is the world of math, so who cares?

75*168=(70*168)+(5*168)=7000+4200+560+500+300+40=11760+840=

12600 fruits that your friend gives you. In addition to the 168 that you had before. Pardon my french, but why the ...

12600+168=12768 fruits at the height of your fruity domination.

Then, your friend takes half

12768/2=6384 fruits.

The graph 2 1/2 on a cording plane is shown below.

To graph 2 1/2 on a coordinate plane, you will need to use the number line to locate the point 2 1/2, which is halfway between 2 and 3.

First, draw a horizontal number line with tick marks at each integer value. Label the tick marks as 0, 1, 2, 3, and so on.

Next, locate the point 2 on the number line and mark it with a dot. Then, locate the point 3 on the number line and mark it with another dot.

Finally, locate the point halfway between 2 and 3 on the number line, which is 2 1/2, and mark it with a third dot. This dot represents the point (2 1/2, 0) on the coordinate plane.

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Answer:

Step-by-step explanation:

ok im not gonna give A step by step but this is answer A for sure and imma see that the oil up center is shut down(crying emoji) and then that the well rom the ring is not  there anymore so thtas a dossie also thats what drake would say lets go hop this helps ;)

Step-by-step explanation:

Start with   3x + 20 + 5x+40  = 180    ( supplementary angles add to 180)

                         8x = 120

     x = 15           <=====NOT what you sked for...you are looking for 'y'

Then    3x +20    + y   = 180      (supplementary angles again)

                shows y = 115 degrees  

Two positive integers whose product is 24,999,999 are 4999 and 5001

Given

The product of two numbers should be 24,999,999.

The positive difference should be small

There are many ways to obtain those two numbers but an easiest way would be taking the square root of the given number and making decision by trial and error.

This may take few iterations but this is the optimal way to solve.

Square root of 24,999,999 is 4999.99

Hence try multiplying a number less than and a number equal to 4999.99.

Eventually we will reach to a conclusion 4999 x 5001 whose product is 24,999,999.

The difference of the numbers is 5001 - 4999 = 2

Hence the positive difference is small.

Hence the two numbers are 4999, 5001.

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Answer:

Yes

Step-by-step explanation:

I think so

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

To find the area of the surface of the part of the plane x + 2y + 3z = 1 that lies inside the cylinder x^2 + y^2 = 3, we can use a parametric representation for the plane and cylinder intersection.

Let x = r * cos(θ) and y = r * sin(θ), where r^2 = 3 (from the cylinder equation). Now, we can find z in terms of r and θ using the plane equation:

z = (1 - x - 2y) / 3
z = (1 - r * cos(θ) - 2r * sin(θ)) / 3

Now, we have the parametric representation of the intersection: (r * cos(θ), r * sin(θ), (1 - r * cos(θ) - 2r * sin(θ)) / 3). To find the surface area, we need to calculate the partial derivatives with respect to r and θ and then find the magnitude of the cross product.

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

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So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

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To find the point on the plane x - 2y + 3z = 6 that is closest to the point (0, 1, 1), we can use the concept of orthogonal projection. The closest point will be the projection of the given point onto the plane.

The equation x - 2y + 3z = 6 represents a plane in three-dimensional space. We are required to find the point on this plane that is closest to the point (0, 1, 1).

To find the closest point, we can use the concept of orthogonal projection. The projection of a point onto a plane is the point on the plane that is closest to the given point. This can be achieved by finding a vector that is orthogonal (perpendicular) to the plane.

The normal vector of the plane is (1, -2, 3) since it represents the coefficients of x, y, and z in the plane equation. We can use this normal vector to calculate the projection of the given point onto the plane.

The projection of the point (0, 1, 1) onto the plane is given by the formula:

Projection = (0, 1, 1) - [(0, 1, 1) dot (1, -2, 3)] / ||(1, -2, 3)||² * (1, -2, 3)

Simplifying the equation and performing the calculations will yield the coordinates of the point on the plane that is closest to (0, 1, 1).

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Answer:

Step-by-step explanation:

4

The range of a function is the possible output values the function can have.

The range of the function is all real values except 0

The function is given as:

\(\mathbf{y = \frac{1}{4x + 1}}\)

When the denominator of the function is 0, the function would not have a real value.

This means that:

\(\mathbf{y \ne 0}\)

i.e. the value of y cannot be 0.

Hence, the range of the function is all real values except 0

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As a result of answering the given question, we may state that When we expressions compare the finished square form\(2(x - 1/4)^2 + 143/8\) to the answer alternatives, we see that option \(D: 2(x - 1/16)`^2.\)

In mathematics, an expression is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or value. Expressions might be simple, like "3 + 4", or complex, like "(\(3x^2\) - 2) / (x + 1)". They may also include functions such as "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and carrying out the mathematical operations in the given order. For instance, if x = 2, the formula "3x + 5" is 3(2) + 5 = 11. In mathematics, expressions are widely used to explain real-world situations, build equations, and simplify complex mathematical issues.

expression is equivalent -

\(2(x^2 - 1/2x) + 18\\2(x^2 - 1/2x + 1/16 - 1/16) + 18\\2((x - 1/4)^2 - 1/16) + 18\\2(x - 1/4)^2 - 1/8 + 18\\2(x - 1/4)^2 + 143/8\\\)

When we compare the finished square form\(2(x - 1/4)^2 + 143/8\) to the answer alternatives, we see that option \(D: 2(x - 1/16)`^2.\)

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Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

The population was growing at a rate of 500,000 people per year at the start of 2011.

We can use the formula for exponential growth:

N = N0 \(\times 2^{(t/T)\)

where N is the population at time t, N0 is the initial population, and T is the doubling time.

In this case, we know that N0 = 3,500,000, T = 7 years, and we want to find the rate of growth at time t = 0.

Taking the derivative of both sides with respect to time, we get:

dN/dt = (N0 / T) \(\times 2^{(t/T)\)

At t = 0, this becomes:

dN/dt = (3,500,000 / 7) \(\times 2^{(0/7)\) = 500,000

Therefore, the population was growing at a rate of 500,000 people per year at the start of 2011.

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Answer:

1 7/95

Step-by-step explanation:

convert the fractions into improper fractions

3 2/5 = 17/5

3 1/6 = 19/6

\(\frac{17}{5}\) divided by \(\frac{19}{6}\) - invert second term and multiply

so 17 * 6 = 102

5* 19 = 95

answer is 102/95, or 1 7/95

Answer:

____________

is it 1700 miles ?

Answer:

b. F' (3, 0), G' (-6, -1), H' (-5, -3)

Answer:

$5.22

Step-by-step explanation:

you would subtract so 5.60-.38=$5.22

Answer:

$5.22

Step-by-step explanation:

$5.22-0.38

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