In these triangles, the largest angle and the
largest side have been measured. What do
you notice?


The shortest distance between two points is a straight line.
It would obviously be shorter to walk distance c than to walk
a plus b. The Triangle Inequality says that a + b > c. What
other two inequalities could you write?

Answer:

Step-by-step explanation:

The international company has 21,800 employees in one country, which represents 32.2% of the company's total employees. We can use this information to find the total number of employees by solving for the missing value.

Let's call the total number of employees in the company "X".

If the 21,800 employees in one country represent 32.2% of the total employees, we can write an equation to represent this relationship:

0.322 * X = 21,800

Next, we'll isolate X by dividing both sides of the equation by 0.322:

X = 21,800 / 0.322

Using a calculator, we can find that:

X = 68,062.5

Rounding to the nearest whole number, the company has 68,063 employees in total.

So, that's how you can use a percentage to find the total number of employees in the company. By knowing the number of employees in one country and the percentage that this represents of the total, we can find the total number of employees in the company.

The correlation coefficient when Claudia records the hours she spent studying and her test scores for 5 tests is 0.85. This is a strong positive correlation.

Any statistical association between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.

Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.

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Claudia records the hours she spent studying and her test scores for 5 tests.

What is the correlation coefficient?

-0.85-0.840.840.85

What is the strength of the model?

Answer:

  0.255 or 25.5%

Step-by-step explanation:

You want the scale factor that reduces 5.1 inches to 1.3 inches.

The scale factor is the ratio of the image size to the original size:

  1.3/5.1 ≈ 0.254902 ≈ 0.255 = 25.5%

__

Additional comment

A scale factor of 0.255 would give an image of 1.3005 inches. That's probably close enough. Rounding to the nearest percent, it would be 25%, which would give an image size of 1.275 inches.

For the information provided, the total kinetic energy of both gliders after collision is 13.5 J. In an elastic collision, both momentum and kinetic energy are conserved.

The momentum conservation principle states that the total momentum of the system before the collision is equal to the total momentum after the collision. Mathematically, we can write this as:

m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f

where m₁ and v₁i are the mass and initial velocity of glider 1, m₂ and v₂i are the mass and initial velocity of glider 2, and v₁f and v₂f are their velocities after the collision.

Using this equation and the given values, we can solve for the final velocities:

(7.0 kg)(2.0 m/s) + (4.0 kg)(-5.0 m/s) = (7.0 kg)v₁f + (4.0 kg)v₂f

14.0 kg·m/s - 20.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f

-6.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f ---(1)

The kinetic energy of an object is given by the equation:

KE = 1/2 mv²

Therefore, the total kinetic energy of both gliders after the collision can be calculated as:

KE_total = 1/2 m₁ v₁f² + 1/2 m₂ v₂f²

Substituting the values of m₁, m₂, v₁f, and v₂f from equation (1) into this equation, we get:

KE_total = 1/2 (7.0 kg) (0.86 m/s²) + 1/2 (4.0 kg) (5.14 m/s²)

KE_total = 13.5 J

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The table to represents the total cost for the different numbers of books ordered is:

Number of books     Spending     Total cost

1                                     $41            $44

2                                    $65           $71

3                                    $125          $134

An expression is written with one or more terms with addition, subtraction, multiplication, and division.

Example:

2.2 + 3x + 4y = 7 is an expression.

3 + 5x = 9 is an expression.

We have,

The book cost = $3

Now,

Spendings = $41, $65, or $125

Now,

Table:

Number of books     Spending     Total cost

1                                     $41            41 + 3 = $44

2                                    $65           65 + 6 = $71

3                                    $125          125 + 9 = $134

Thus,

The table for the total cost is given above.

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Answer:

The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.

So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).

Therefore, the values that are solutions to the inequality x < -2 are:

• all real numbers less than -2, such as -3, -4, -5, etc.

Note that -2 itself is not part of the solution set, since it is not less than -2.

Step-by-step explanation:

On the region, (-oo,0.5), the graph formes a upside U shaped , this mean the graph is concave down on this region. this implies that our second derivative is negative and our first derivative is changing negatively.

The graph is concave up from (0.5,oo) since the graph formes a U shape.

This also implies that (0.5) is a inflection point

The function crosses the x axis at -1,0,3

So the 2nd,3rd,6th, 7th options are correct

Answer:a

Step-by-step explanation:

The coordinates that lie on the equation of line y = 1 - 2x are P ( -3 , 7 ) and Q ( 6, -11)

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , 7 )

Let the second point be Q ( 6 , -11 )

The equation of line is y = 1 - 2x

Substituting the values of x and y in the equation , we get

when x = -3

y = 1 - 2 ( -3 )

y = 1 + 6

y = 7

when x = 6

y = 1 - 2 ( 6 )

y = 1 - 12

y = -11

Hence , the coordinates of the equation of line are P ( -3 , 7 ) and Q ( 6, -11 )

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Approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.

A logarithmic equation is an equation that involves a logarithmic function. A logarithmic function is the inverse of an exponential function, and it represents the exponent to which a given base must be raised to obtain a given number.

The formula that relates the energy released by an earthquake to its magnitude is given by:

logE = 5.24 + 1.44M

To find the amount of energy released by a magnitude 5 earthquake, we can substitute M = 5 into the formula and solve for E.

logE = 5.24 + 1.44(5)

logE = 5.24 + 7.2

logE = 12.44

Now we need to convert this logarithmic value to a regular value of E. We can do this by taking the antilogarithm (or exponentiating) both sides of the equation.

10⁽ˡᵒᵍᴱ⁾ = 10⁽¹²ॱ⁴⁴⁾

E = 2.51 x 10¹² joules

Therefore, approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.

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Answer:

Step-by-step explanation:

The function f(x) = |x − 1| is a absolute value function that calculates the distance of a number x from the number 1 on the number line. On the number line, numbers to the left of 1 are negative and numbers to the right of 1 are positive.

To find the value of f(x), we first subtract 1 from x to find the distance between x and 1. If the result is positive, then x is to the right of 1 and the absolute value of the result is equal to the distance. If the result is negative, then x is to the left of 1 and the absolute value of the result is equal to the distance.

For example, let's find f(-5):

f(-5) = |-5 - 1| = |-6| = 6

The interpretation of f(-5) is that the number -5 is a distance of 6 units away from the number 1 on the number line.

Now let's find f(3):

f(3) = |3 - 1| = |2| = 2

The interpretation of f(3) is that the number 3 is a distance of 2 units away from the number 1 on the number line.

The domain of the function is all real numbers. The range of the function is all non-negative real numbers.

Answer:

he constant of proportionality is $1.80, since for every 3 lemons the total cost increases by $1.80.

The equation that relates the total cost, y, and the number of lemons, x, is:

y = 1.80 * (x/3) + b

where b is the y-intercept, which represents the cost of 0 lemons. We'll need additional information to determine the value of b.

Here is a table with the values of y and x, assuming b = 0:

x (Number of Lemons) y (Total Cost)

0 0

3 1.80

6 3.60

9 5.40

... ...

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

- (3x + 1) + 7 = 4 - (3x + 2) ← distribute parenthesis on both sides

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

- 3x + 4 = 2 - 3x ( subtract 4 from both sides )

- 3x = - 2 - 3x ( add 3x to both sides )

0 = - 2 ← false statement

this false statement indicates the equation has no solution

-(3x+1)+7=4-(3x + 2)

-3x-1+7=4-3x-2

-3x+6=-3x+2

-3x+3x=-4

0=-4

no solution

The final inequality is x > - 1.

Option D is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

√(x + 2) > -1

Squaring both sides.

x + 2 > (-1)²

x + 2 > 1

Subtracting 2 on both sides.

x > 1 - 2

x > -1

Thus,

x > - 1 is the final inequality.

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Answer:

= 60°

Step-by-step explanation:

Exterior angle =

[tex] = \frac{360}{n} [/tex]

[tex] = \frac{360}{6} \\ = {60}^{o} [/tex]

= 60°

The probability that the person is under 18 or employed part-time is 179/864.

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

where,[tex]P_e(E)[/tex] is denoting experimental probability of occurrence of E.

Given that;

The table of age, full time, part time, unemployed

Now,

Total number of people who are between the age group 35-49

= 581+179+104

= 864

Number of people who are employed part time= 179

Number of people employed part time in age group 35-49/ Total people in age group 35-49

= 179/864

Therefore, the probability will be 179/864.

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Answer:

9

Step-by-step explanation:

divide 27 by 3

It equals 9

9 x 2 = 18 boys

27-18= 9 girls

Answer: The shape of the supply curve for tickets to football games at the stadium with 70,000 seats is upward-sloping. This means that as the price of tickets increases, the quantity of tickets supplied also increases.

The reasoning behind this is simple: when the price of tickets is high, there is more incentive for the sellers (e.g. the stadium, ticket resellers, etc.) to sell more tickets. They have the ability to supply more tickets as the demand for tickets at the high price is likely to be higher, thus increasing their profits.

However, it is important to note that the upward slope of the supply curve is not necessarily linear. The supply curve for tickets to football games is likely to be more elastic in the higher price range, meaning that as the price continues to increase, the quantity supplied may increase at a slower rate. This is because at some point, even if the price continues to rise, there will be a limit to how many tickets can actually be sold due to a decrease in demand.

Overall, the upward-sloping shape of the supply curve for tickets to football games at the stadium with 70,000 seats reflects the basic principle of supply and demand: as the price increases, the quantity supplied will also increase, but at some point, the increase in price will lead to a decrease in demand, limiting the quantity supplied.

Step-by-step explanation:

The vertical intercept of the graph is 100,000

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e, is called an exponential function.

Given that, the population p of migrating butterflies satisfies the exponential function p = 100,000 (4/5)ⁿ, where n is the number of weeks,

So, we need to find the vertical intercept of the graph,

We know that, vertical intercept = intercept

To find the y-intercept of a line, we will put x = 0,

here x is n,

So, the y-intercept of the graph is = 100,000 (4/5)⁰ = 100,000×1 = 100,000

Therefore, the vertical intercept of the graph is 100,000

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Answer:

6.25 x h = 50.000

Step-by-step explanation:

Answer:

8 headbands.

Step-by-step explanation:

Winnie needs to sell AT LEAST 8 headbands. 50 divided by 6.25 is 8. Remember that the phrase "at least" is represented by a greater-than-or-equal-to symbol.

The total area of the two circles will be 168316.9 square feet.

The circle is defined as a two-dimensional figure having a fixed point and the number of the points is traced around the curved path at an equal distance from the fixed point. The overall figure is called a circle.

The area of the circle is calculated by the formula:-

Area = πr²

Given that the south side of the highway needed to be compacted in order to create two circles of various sizes for a specific four-leaf clover. The two circles on the north side of the road have a 128-foot radius, whereas the two on the south side have a 102-foot radius.

The total area will be calculated as:-

Area = 2 x π x 128² + 2 x π x 102²

Area = 102943.25 + 65370.25

Area = 168316.9 square feet

Hence, the total area will be 168316.9 square feet.

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Value of system after 'x' years = [tex]3000*(0.85)^x[/tex]

The value of the computer after 3 years is $1842.375

The formula for an exponential function is f(x) =[tex]a^x[/tex], where 'x' is variable and 'a' is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given that, computer system values at $3000 decrease at a rate of 15% each year.

If the value decreases by 15%, it means that the new value is 85% of the old value.

new value = old value * (85/100)

new value = old value * 0.85

value in 1st year = $3000

value after 1st year = $3000 * 0.85

value after 2nd year = $3000 * 0.85 * 0.85

value after nth year = $3000 * [tex]0.85^n[/tex]

Value of the system after 3 years = $3000 * [tex]0.85^3[/tex]

= $3000 * 0.614125

= $1842.375

Therefore, The value of the computer system after 3 years  is $1842.375

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Answer:

<1 and <2

Step-by-step explanation:

Adjacent means angles that are next to each other.  This is not the only pair, but <1 and <2  are adjacent.

Step-by-step explanation:

an arithmetic progression or arithmetic sequence is a sequence of terms, where the difference bergen neighboring terms is a constant d for the whole sequence.

a1 = 29

a2 = 29 + d

a3 = a2 + d = a1 + d + d = 29 + 2d

...

an = 29 + (n-1)d

a7 = -13 = 29 + 6d

-42 = 6d

d = -42/6 = -7

therefore,

a10 = 29 + 9×-7 = 29 - 63 = -34

Answer: Looks like a positive correlation with an outlier in the lower left.

Step-by-step explanation:

The simplification of the given expression would be = 210

A fraction is defined as the expression of part of a whole value in the form of a denominator and a numerator.

The above statement can be expressed above mathematically as follows:

= 7/8 × 16 × 1/2× 30

= 3360/16

= 210

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Answer:

Below

Step-by-step explanation:

5000   *   2.4 x 10^-6  =

12 000 x 10^-6  g

= .012 g

The number as decimal is 26583.0

From the question, we have the following parameters that can be used in our computation:

Number = 26583

Also, we have the required value of 5 to be

Required = 100

Using the above as a guide, we have the following:

The number 5 must have a value of 100 in the new number i.e. 500

So, we have

Number = 26583

Rewrite as

Number = 26500 + 83

This means that we add 5 at the end

So, we have

Number = 26583.0

Hence, the new number is  26583.0

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Another form of representing the cost of the book is (75/100)×D.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know, Percentages and decimals are related.

10% in decimal form is equivalent to (10/100) - 0.1 in decimal.

An expression that represents the sale day book price is 0.75D.

Another expression that would represent the cost of the book priced 'D' would be,

= (75/100)×D.

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