5. Calculate the following in Z..
(a) 2 +3
(b) 2+2+2
(c)-3

Answer:

The projected world population in 2015 was 8,705,121,030 people.

Step-by-step explanation:

Given that the population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year, assuming that the world population follows an exponential growth model, to find the projected world population in 2015 the following calculation must be performed :

5,000,000,000 x 1.02 ^ (2015-1987) = X

5,000,000,000 x 1.02 ^ 28 = X

5,000,000,000 x 1.741024 = X

8,705,121,030 = X

Therefore, the projected world population in 2015 was 8,705,121,030 people.

Answer:

depends on the size of the food

Step-by-step explanation:

Answer:

108 mangoes

Step-by-step explanation:

divide 180 by 2 and the subtract 18 from 90 which equals to 72 add the 18 to the mangoes which will be 108

Answer:

15%

Step-by-step explanation:

To calculate the margin of error, we can adopt this formula

Margin of error = critical value* (standard deviation/sqrt of sample size)

Where critical value is 2.33, sd is 0.78 and sample size is150.

Thus, we have:

Margin of error = 2.33*(0.78/√150)

Margin of error = 2.33*(0.78/12.2474)

Margin of error =2.33*0.06369

Margin of error = 0.1484 which is a 15% margin of error

Answer:

b

Step-by-step explanation:

-a-(a-b)

Distribute the negative sign to get -a+a+b

-a cancels out a, and you're left with b.

Answer:a²-ab

Step-by-step explanation:

since the negative symbol is on the outside of the parenthesis all values inside the parenthesis get reversed. so:

-a(-a+b)

Then multiply by -a:

a²-ab

Answer:

a 0, 16, 64,144 graph A edge

Step-by-step explanation:

The graph that best represents the equation is option A.

What is an Equation?

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The equation is

s = 16t²

The table is

s              t

0             16*0 = 0

1              16 * 1 = 16            

2              16 * 4 = 64

3               16 * 8 = 108

The points represents a parabola opening upwards, vertex is at (0,0) and goes through the point (-1,16)

This has been confirmed by the graph plotted for the equation.

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Answer:

AB= 7.45

Anwer C)

Step-by-step explanation:

Cos (angle) = Nearest side / Huypothenuse

Cos(20)      = 7 / AB

Cos(20) * AB = (7 /AB) * AB

Cos (20) * AB = 7

(Cos(20) *AB) / Cos(20) = 7 / Cos(20)

AB = 7 / cos(20)

AB=    7.45

Answer:

h = 231 feet

Step-by-step explanation:

Given that,

A person standing 248 feet from the base of a church, x = 248 feet

The angle of elevation to the church's steeple to be 43°.

We need to find the tall of the church. Let the length of the church is h. Using trigonometry to find it.

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=248\times \tan(43)\\\\=231.26\ \text{feet}\)

or

h = 231 feet

So, the height of the church is 231 feet.

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

The equation to model the given work is 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.

The teams will share 5.4 liters of olive oil. To find out how much each team will receive, we can divide the total amount of olive oil by the number of teams:

5.4 liters ÷ 10 teams = 0.54 liters per team

However, it's usually more convenient to express this in grams for equation, so we need to convert liters to grams.

The conversion factor for olive oil is approximately 0.92 grams per milliliter (or 920 grams per liter). So, we can multiply 0.54 liters per team by 920 grams per liter to get:

0.54 liters per team × 920 grams per liter = 497.28 grams per team

Therefore, each team will receive 497.28 grams of olive oil as per the work.

Equation: 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.

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Answer:

67766788786686

Step-by-step explanation:

86686868686867

Answer:

-95

Step-by-step explanation:

The each fitness class pass costs $5.

What is Average total cost ?

Average total cost is referred to as the sum total of all production costs divided by the total quantity of output.

Let's assume that the cost of each fitness class pass is x dollars. Then we can set up the following equation to represent the total amount of money Monica collects:

15x + 18 = 93

Simplifying this equation, we get:

15x = 75

Dividing both sides by 15, we get:

x = 5

Therefore, each fitness class pass costs $5.

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Answer:

I'm pretty sure its 1/5

Step-by-step explanation:

because 5 friend's and half of a whole pizza

The center of mass for the system (x, y) is \(\left(\frac{a m+b M}{m+M}, 0\right)\).

What is center of mass?

The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.

The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.

Centre of mass is

\(x=\frac{m a+M b}{m+M}\)

and y=0

\((x, y)=\left(\frac{a m+b M}{m+M}, 0\right)\)

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Answer:203

Step-by-step explanation:

102+79+22 = 203

Answer:

$203

Step-by-step explanation:

Answer:

The area of the quadrilateral ABCD is 114 square units

Step-by-step explanation:

We must calculate the area of each triangle and then add these areas so we calculate the area of the quadrilateral ABCD

First for the BAD right triangle:

AD = sqrt [BD ^ 2 - AB ^ 2]

AD = sqrt [15 ^ 2 - 12 ^ 2]

AD = sqrt [225-144]

AD = sqrt [81]

AD = 9

The area of a triangle is half the product of the base times the height, that is:

A1 = AB * AD / 2 = 12 * 9/2 = 54

Then for the second triangle in the right triangle BDC:

DC = sqrt [BC ^ 2 - BD ^ 2]

DC = sqrt [17 ^ 2 - 15 ^ 2]

DC = sqrt [289 - 225]

DC = sqrt [64] = 8

We calculate the area

A2 = DC * BD / 2 = 8 * 15/2 = 60

The total area then is:

AT = A1 + A2

AT = 54 + 60 = 114

Which means that the area of the quadrilateral ABCD is 114 square units

The length of PZ is 7 units.

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the side midpoints.

Given:

As, Centroid is the point where all median of a Triangle intersect.

Here, we have centroid 'P'.

Now, using the property of Centroid that the Centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

So, SP = 1/3 SZ => SZ = 3SP

and, PZ = 2/3 SZ => SZ = 3/2 PZ

Then, 3SP = 3/2 PZ

3(3.5) = 3/2 PZ

10.5 x 2 = 3 PZ

21 = 3PZ

PZ = 7 units

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Area and circumference of the circle are 78.5 m² and 31.4 m respectively.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that, a circle have a radius 5 m

Area of a circle = π × radius²

Circumference = 2π×radius

Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²

Circumference = 3,14 × 2 × 5 = 31.4 m

Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.

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the equation of the Linear function will be f(x) = -19x + 14.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a data set of a linear function

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept (the value of y, at x = 0)

since, slope = (y - y')/(x -x')

In our case,

Slope = (128 -90)/ (-6 + 4)

Slope = 38/-2

Slope = -19

And b = 14 (Given)

Thus,

The equation of Line:

y = -19x + 14

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Answer:

-5°C < 5°C

The temperature was higher on Wednesday than on Tuesday.

The algorithm justifies the answer of 3/5 as the fraction each person gets.

Representation of the fractions on the second row:

From what you described, two of the loaves were divided into thirds.

This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.

Therefore, each person receives one fifth from this remaining third.

So, the representation of the fractions on the second row would be:

Each person receives 1/3 (one third) from the two loaves.

Each person receives 1/5 (one fifth) from the remaining third.

Algorithm/Abstract strategy to justify the 3/5 found as the answer:

To find the final answer of 3/5, we can follow the steps you provided:

Divide two loaves into thirds, giving each person 1/3.

Divide the remaining third from the second loaf into fifths, giving each person 1/5.

Combining the fractions, each person has 1/3 + 1/5.

To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:

1/3 = 5/15 (multiplying numerator and denominator by 5)

1/5 = 3/15 (multiplying numerator and denominator by 3)

Now, we can add the fractions:

5/15 + 3/15 = 8/15

Therefore, each person receives 8/15 of a loaf.

Simplifying this fraction, we get 3/5.

Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.

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Answer:

9 laps takes 5 minutes 25 seconds.

Step-by-step explanation:

Here is given:

4 laps takes 6 minutes 12 seconds.

We have to find how long 1 lap takes.

4/4 6/4 12/4 --> 1 lap takes 2 minutes 33 seconds.

Now, multiply each by 9 because you want to find 9 laps, so:

1x9 2x9 33x9 --> 9 laps takes 5 minutes 25 seconds.

Hope this helps :)

Answer:

14 and 10

Step-by-step explanation:

We have the equation x(x-4)=140. We can distribute the x to everything in the parenthesis so it's easier to work with.

x(x-4)=140

\(x^2-4x=140\)

Let's move 140 to the left side, so we can solve this equation better by finding the zeros of the equation.

\(x^2-4x-140=0\)

To find the zero, we have to find TWO values that multiply to -140 but add to -4.

(x-14)(x-10)=0

To find the zeros. make both of those parenthesis equal to zero.

x=14, 10

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

B.

Step-by-step explanation:

the x intercept passes through -5 and the y intercept passes through 3

The correct comparison as shown in the figures are:

From the given diagram, we are to fill in the blank spaces with a < or > symbol.

21) The measure of the angles is a function of the measure of the sides.

Since the angle facing the side QR is less than that of QS, hence QR < QS

22) Similarly for this figure, the angle facing the side AB is greater than that of CD, hence AB >  CD

23) Also, for this figure, the side facing the angle m<FJG is greater than the side facing the angle m<HJG, hence m<FJG > m<HJG

24) Also, for this figure, the side facing the angle m<QSP is greater than the side facing the angle m<QSR, hence m<QSP > m<QSR

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Answer:

411

Step-by-step explanation:

Answer:

411 is the answer!!:))

The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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