It is reported that the wild gorilla population has declined by 70% over the last 10 years. There are now 4,000 gorillas left in the wild. To the nearest thousand, how many gorillas were there 10 years ago?

Answer:

answer will be D i believe (As i cant see the graphs, I had too look for the graphs myself, thanks!)\

the graph will show a line chart -5 to 5+ THE HIGHLIGHTS will be between 1 and 3

Answer:

4

Step-by-step explanation:

3y=12  divide both sides by 3

y=4

Answer:

y = 4

Step-by-step explanation:

12 = 3(4)

12 = 12

The volume of the new right circular cylinder after change in the radius and the height is 44cm³.

Here we have to find the volume of the right circular cylinder when its radius gets twisted and the height gets half.

Given data:

Volume = 22 cm³³

h' = 1/2h

r' = 2r

The formula of the volume of a cylinder:

V= πr²h

V' = πr'² h'

V' = π (2r)² ( 1/2h)

= 2πr²h

= 2V

= 2 × 22

= 44cm³

Therefore the volume of the new right circular cylinder is 44cm³.

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Answer:

-3x + 549

Step-by-step explanation:

The order of operations is PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction)

So, according to PEMDAS, the first thing that we would do is solve the parenthesis. Since we can't solve the parenthesis because they aren't like terms, we're going to use distributive property to solve it instead.

-3(x+8) = -3(x) + -3(8) = -3x -24

Now we have: -3x - 24 ^ 2 -3

Our next step is to solve the exponent

24 ^ 2 or 24 x 24 = 576

Now we have: -3x - 24 + 576 -3

Our next step would be to add and subtract the like terms

-24 + 576 = 552 and 552 - 3 = 549

Now we have: -3x + 549

This would be the simplest form of the equation because -3x and 549 are not like terms

In complex number a+ib a is real and ib is the imaginary part.

Complex numbers are the numbers that are communicated as a+ib where, a,b are genuine numbers and 'I' is a fanciful number called "particle". The worth of I = (√-1). For instance, 2+3i is a complicated number, where 2 is a genuine number (Re) and 3i is a imaginary number (Im).

We have, a + ib is a complex number in mathematics

where a is the real part and ib is the imaginary part of the complex number.

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Answer:

10

Step-by-step explanation:

\( \sqrt{100} = 10\)

Hope it helps you in your learning process.

Based on the derivative, a function can cross the x-axis a certain number of times depending on the number of times the derivative changes sign.

A derivative is a mathematical tool that measures the rate of change of a function at a specific point. Specifically, it is the slope of the tangent line to the function at that point. The derivative can be used to determine where a function is increasing, decreasing, or reaching a maximum or minimum value.
When a function crosses the x-axis, it means that the y-value of the function is equal to zero. In order for a function to cross the x-axis, it must change sign from positive to negative or vice versa. This happens when the function passes through a maximum or minimum point.
If the derivative of the function is positive at a point, it means that the function is increasing at that point. If the derivative is negative, the function is decreasing. If the derivative is zero, it means that the function is neither increasing nor decreasing, and it could be at a maximum or minimum point.
Therefore, the number of times a function can cross the x-axis depends on the number of times the derivative changes sign. If the derivative changes sign twice, the function can cross the x-axis twice. However, if the derivative changes sign an odd number of times, the function can only cross the x-axis once.

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Answer:

180

Step-by-step explanation:

to work out all possibilities you multiple the amount of options.

4x5x9=180

The centroidal moments of inertia can be calculated by determining the moments of inertia for each component and applying the parallel axis theorem.



To determine the centroidal moments of inertia for the given built-up steel beam, we need to calculate the individual moments of inertia for each component and then use the parallel axis theorem to find the total centroidal moments of inertia.

First, we calculate the moment of inertia for the W18x97 wide flange beam using its properties. The moment of inertia for a wide flange beam can be found in engineering handbooks or online databases.Next, we calculate the moment of inertia for the vertical plate. Since it is centered on the web of the wide flange, its centroid coincides with the centroid of the wide flange.Similarly, we calculate the moment of inertia for the horizontal plate. Since it is also centered on the web, its centroid coincides with the centroid of the wide flange.

Finally, we use the parallel axis theorem to find the total centroidal moments of inertia. The parallel axis theorem states that the moment of inertia about any axis parallel to an axis through the centroid is equal to the sum of the moment of inertia about the centroidal axis and the product of the area and the square of the distance between the two axes.In this case, the total centroidal moments of inertia will be the sum of the moment of inertiainertia of the wide flange beam, the vertical plate, and the horizontal plate.

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Answer:

(2, - 2 )

Step-by-step explanation:

4x - y = 10 → (1)

x - 4 = y → (2)

substitute x - 4 = y into (1)

4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1

4x - x + 4 = 10

3x + 4 = 10 ( subtract 4 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2 - 4 = y

- 2 = y

solution is (2, - 2 )

Answer:

x = 2 , y = -2

Step-by-step explanation:

I will use the elimination method :

4x-y = 10 - Equation Number 1

x-4 = y  - Equation Number 2

For the second equation we add 4 to both sides and subtract y from both sides :

x = y + 4

x - y = 4 - Let's call this equation number 3 :

Now we can subtract the equation 1 with 3 to eliminate y :

3x = 6

x = 2

Now we substitute this value into equation 2 to solve for y :

(2)-4 = y

y = -2

Substitute these values into equation 1 to verify :

4(2) - (-2) = 10

8 + 2 = 10

10 = 10

So these values must be correct

Hope this helped and have a good day

Answer:

the original price was $53.33

Step-by-step explanation:

$x ---- 100%

$40 ------- 75% (this is because 25% of it's just 75% of the actual price)

\(75\cdot x = 100\cdot 40\\\\75x = 4000\\\\x=53.33\)

===============================================

Work Shown:

x = original price

25% = 25/100 = 0.25

25% of x = 0.25x = discount, or amount saved

final price = (original price) - (discount)

final price = (x) - (0.25x)

final price = 0.75x

0.75x = 40

x = 40/0.75

x = 53.333333

x = 53.33

The original price is $53.33

The discount, or amount saved, is 0.25*x = 0.25*53.33 = 13.3325 = 13.33 dollars.

This means the sale price is 53.33 - 13.33 = 40

We can also see this through computing 0.75*x = 0.75*53.33 = 39.9975 = 40, which matches with the given sale price.

Note how I'm rounding to the nearest penny when needed.

Check the picture below.

so, let's get the volume of the prism.

then let's get the volume of the smaller cube.

then let's see how many times the volume of the cube goes into the prism's volume, so in short a division.

\(\stackrel{\textit{prism's volume}}{\left( \frac{5}{2} \right)(2)(1)\implies 5~cm^3}~\hfill \stackrel{\textit{cube's volume}}{\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\implies \frac{1}{8}~cm^3} \\\\[-0.35em] ~\dotfill\\\\ 5\div \cfrac{1}{8}\implies \cfrac{5}{1}\div \cfrac{1}{8}\implies \cfrac{5}{1}\cdot \cfrac{8}{1}\implies 40~~cubes\)

OLAP is used for the analysis of accumulated data, and it requires a data warehouse.

while OLTP is used for transaction processing and requires a database optimized for real-time transaction processing. The analysis of accumulated data is known as Online Analytical Processing (OLAP), and it involves a data warehouse. OLAP is a business intelligence tool used for multi-dimensional analysis of large data sets, while a data warehouse is a central repository that stores historical and current data from multiple sources in a structured manner. OLAP allows users to perform complex queries on large data sets, analyze trends, and make informed business decisions. It is often used in data mining and decision support systems. OLAP tools can be used to slice and dice data, drill down to more detailed data, and roll up to higher levels of summary data. OLAP is primarily used for analytical purposes and is not designed for transaction processing. On the other hand, a data warehouse is designed to support OLAP and is used for storing large amounts of historical data that can be queried and analyzed. Data is extracted from various sources, transformed, and loaded into the data warehouse in a structured format, enabling efficient querying and analysis. OLTP (Online Transaction Processing), on the other hand, is a type of transaction processing that is designed for processing real-time transactions in databases. It is used for day-to-day operations such as order processing, inventory management, and customer management. OLTP is optimized for processing large volumes of transactions in real-time, and is not suitable for analytical purposes.

In summary, OLAP is used for the analysis of accumulated data, and it requires a data warehouse, while OLTP is used for transaction processing and requires a database optimized for real-time transaction processing.

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.

Step-by-step explanation:

The actual square root value is

12.7671453348...

But we Have taken only significant

figure and it is as 12.76

Answer:

a) 6x + 8 = 32

Step-by-step explanation:

Forming algebraic equation:

Let the number be 'x'.

      6 times x = 6 * x = 6x

6x is added to 8: 6x + 8

         6x + 8 = 32

Answer:

59 cm^3

Step-by-step explanation:

You can split the shape into two rectangular prisms.

3*3*1=9

10*5*1=50

9+50=59

Answer:

20%

Step-by-step explanation:

given the info, let's add up all of the marbles we have so far

7 + 4 + 2 + 3 = 16 marbles

the rest are white and the total number of marbles in the bag are 20

16 marbles + white marbles = 20 marbles

there must be 4 white marbles

putting this in a fraction is 4/20

to put in percentage multiply by 100

4/20 × 100 = 20%

Answer:

B 8÷2

Step-by-step explanation:

because of pemdas.

Answer:

B

Step-by-step explanation:

Follow the order of PEMDAS. So you gotta solve inside the prenthesis first following the order of pemdas and division comes first.

Parentheses

Exponent

Multiplication

Division

Addition

Subtraction

For the linear equations provided by the coordinates in the table;

The first equation of this system is y = -2x.

The second equation of this system is y = x - 3.

The solution to the system is (1, -2).

We have four points (-5,10), (-1,2), (0,0), and (11,-22) for first equation, and four points (-8,-11), (-2,-5), (1,-2), and (7,4) the second equation.

The slope (m) is given by the formula (y2 - y1) / (x2 - x1).

For the first line, we can use the points (-5,10) and (-1,2)

m1 = (2 - 10) / (-1 - (-5)) = -8/4 = -2.

the first equation is y = -2x

the second line, we can use the points (-8,-11) and (-2,-5)

m2 = (-5 - -11) / (-2 - -8) = 6/6 = 1.

the second line has a slope of 1,

the equation should have the form y = x + c.

To find c, we can use one of the points, for instance (-2,-5):

-5 = -2 + c => c = -5 + 2 = -3.

So, the second equation is y = x - 3.

the solution to the system, we need to find where the two lines intersect.

y = -2x

y = x - 3

Setting both equation equally

-2x = x - 3

=> 3x = 3

=> x = 1.

Substituting x = 1 into the first equation

y = -2(1) = -2.

the solution to the system of linear equation would be (1, -2).

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Answer:

Inequality is \(4x+3y\leq 87\)

Slope intercept form is \(y\leq 29-\frac{4}{3}x\)

Solutions are \((2,3)\,,\,(3,4)\)

Graph: attached to the question

Step-by-step explanation:

Given: Group dance numbers last 4 minutes and a solo performance lasts 3 minutes. The maximum duration for the recital is 87 minutes.

To find: inequality (in standard form) that describes the given situation, inequality in slope-intercept form, solutions for the inequality

To graph: the inequality

Solution:

x denotes the number of group dances on the program

y denotes the number of solo numbers on the program

Total duration of group dance numbers = \(4x\) minutes

Total duration of solo performance = \(3y\) minutes

According to question,

\(4x+3y\leq 87\)

Slope intercept form of equation is \(y\leq mx+c\) where m denotes slope of line and c denotes y-intercept of the line.

Slope intercept form of \(4x+3y\leq 87\) :

\(4x+3y\leq 87\\3y\leq 87-4x\\y\leq 29-\frac{4}{3}x\)

For \((x,y)=(2,3)\),

\(4(2)+3(3)\leq 87\\8+9\leq 87\\17\leq 87\,\,which\,\,is\,\,true\)

So, \((2,3)\) is a solution of the inequality.

For \((x,y)=(3,4)\),

\(4(3)+3(4)\leq 87\\12+12\leq 87\\24\leq 87\,\,which\,\,is\,\,true\)

So, \((3,4)\) is a solution of the inequality.

Graph: attached as image

The graph illustrates the supply and demand curves on a single graph to represent the equilibrium point in a market. The equilibrium point is where the quantity demanded equals the quantity supplied, resulting in a balance between buyers and sellers.

This point determines the market price and quantity exchanged in the market. The graph demonstrates the interplay between supply and demand, showcasing how changes in these factors can impact the equilibrium point and market outcomes.

The equilibrium point is the intersection of the supply and demand curves on the graph. At this point, the quantity demanded by buyers matches the quantity supplied by sellers. The equilibrium price is determined by the vertical position of the equilibrium point on the graph, while the equilibrium quantity is determined by the horizontal position.

If the market price is above the equilibrium price, there is excess supply, leading to a surplus. Sellers will be motivated to decrease prices to sell their goods, which, in turn, increases the quantity demanded. Conversely, if the market price is below the equilibrium price, there is excess demand, resulting in a shortage. Buyers will be incentivized to bid higher prices, increasing the quantity supplied by sellers.

The equilibrium point represents a state of market balance where the forces of supply and demand are in harmony. It reflects the price and quantity at which both buyers and sellers are satisfied, maximizing the efficiency of resource allocation in the market.

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The perimeter of Todd’s sandbox is; 20.8 feet.

Applying the similarity of triangles.

Consider 'x' and 'y' be the two unknown sides of triangle.

14/ x = 20/8 = 18/y

14/ x = 20/8

x = 14*8 / 20

x = 5.6

20/8 = 18/y

y = 18*8 / 20

y = 7.2

Perimeter of Todd’s sandbox,

= x + y + 8

= 5.6 + 7.2 + 8

= 20.8

Thus,  the perimeter of Todd’s sandbox is 20.8 feet.

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The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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Simple Random sampling  as each student is getting equal opportunity to get selected.

Describe random sampling.

A selection of participants from a community are chosen at random by the investigator using simple random sampling, a sort of sampling techniques. Every individual in the population has the same chance of being chosen. Then, information is gathered from as much of this randomly selected subgroup as possible.

Which four forms of random sampling are there?

Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main random (probability) sampling techniques.

What benefit may simple random sampling provide?

The benefits of a simple random sample include its simplicity and accuracy of depiction. Simple random sampling is the easiest way to select a study sample from a bigger population.

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Answer:

I think that the answer is 1 to1

Answer:

16

Step-by-step explanation:

448/28=16

if she did the work sheet for 28 days she answered 16 questions per day .

Answer:

it is 16

Step-by-step explanation:

448 ÷ 28 = 16 or 16×28=448

On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, the equation is -

1200=300+5x

900 = 5x

x=180

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Answer:

$160

Step-by-step explanation:

$100-$75=$25

$9*15=$135

$25+$135=$160

Hope this helps

The values of all the angles are shown:

(A) m∠1: 62°   (B) m∠2: 39°

(C) m∠3: 26°  (D) m∠4: 45°

(E) m∠5: 55°  (F) m∠6: 45°

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry.

Two rays can form angles in the plane where they are positioned.

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

So, the following values of the angles are:

(A) m∠1:

28 + 90 + ∠1 = 180

118 + ∠1 = 180

∠1 = 180 - 118

∠1 = 62°

(B) m∠2:

51 + 90 + ∠1 = 180

141 + ∠1 = 180

∠1 = 180 - 141

∠2 = 39°

(C) m∠3:

25 + (180-51) + ∠3 = 180

25 + 129 + ∠3 = 180

154 + ∠3 = 180

∠3 = 180 - 154

∠3 = 26°

(D) m∠4:

∠4 + ∠6 + 90 = 180

∠4 + ∠6 = 180 - 90

∠4 + ∠4 = 90 (∠4 and ∠6 are equal:  Isosceles triangle)

2∠4 = 90

∠4 = 90/2

∠4 = 45°

(E) m∠5:

35 + 90 + ∠5 = 180

125 + ∠5 = 180

∠5 = 180 - 125

∠5 = 55°

(F) m∠6:

∠4 = ∠6 = 45°

Therefore, the values of all the angles are shown:

(A) m∠1: 62°   (B) m∠2: 39°

(C) m∠3: 26°  (D) m∠4: 45°

(E) m∠5: 55°  (F) m∠6: 45°

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