The table below models a particular physical situation.
X: -8, 1, 4, 10
Y: 2, -3, 1, -3
Find the piecewise linear equation that models the data above. Round to three decimal places if needed.

_____x + ____ -8 ≤ x ≤ 1
Y= _____x + ____ 1 < x ≤ 4
_____x + ____ 4 < x ≤ 10

The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

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

First = tan(θ)

Second = cos(θ)

The basis trigonometry identity is

sin²(θ) + cos²(θ) = 1

Divide through the equation by cos²(θ)

So, we have

tan²(θ) + 1 = 1/cos²(θ)

Subtract 1 from both sides

tan²(θ) = - 1 + 1/cos²(θ)

Take the square root of both sides

tan(θ) = √[-1 + 1/cos²(θ)]

Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

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The required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.

Given that the heights of adult parrots are normally distributed with a mean height of 34 cm and standard deviation of 8 cm.

The formula used to calculate the z-score for the height of 18 cm is

z = (x - mean) / standard deviation

By substituting the value of mean and standard deviation gives,

z = (18 - 34) / 8.

On simplification of numerator gives,

z= -16 / 8 = -2.

To find the proportion of parrots more than 18 cm tall by calculating the area under the standard normal curve to the right of z = -2 by the standard normal distribution table.

That implies, proportion = area to right of z = -2 is approximately equal to 0.9772.

The formula used to calculate the number of parrots that is more than 18 cm tall is  proportion × total number of parrots.

That implies, the number of parrots out of 400 birds which are more than 18 cm tall is 0.9772 × 400 = 390.88 ≈ 391.

Therefore, the required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.

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Answer:

  see attached

Step-by-step explanation:

You want the possible lengths of the third side of a triangle with side lengths 20 m and 18 m.

If the third side is length c, the triangle inequality requires ...

  18 +c > 20   ⇒   c > 2

  20 +c > 18   ⇒   c > -2

  18 +20 > c   ⇒   c < 38

The possible lengths for the third side (c) are ...

  2 < c < 38

That is, the third side must lie between the difference and the sum of the given sides.

The attachment shows the values on the list that are in this range.  

The expression [tex]3log_b(8) - log_b(7)[/tex] written as a single logarithm is [tex]log_b(\frac{512}{7})[/tex].

Given the logarithmetic expression in the question:

[tex]3log_b(8) - log_b(7)[/tex]

To rewrite the expression [tex]3log_b(8) - log_b(7)[/tex] as a single logarithm, we can use the properties of logarithms.

Using the quotient rule property, which states that:

logₙ(a) - logₙ(b) = logₙ(a/b)

Applying the quotient rule:

First, rewrite [tex]3log_b(8) - log_b(7)[/tex] as:

[tex]log_b(8^3) - log_b(7)[/tex]

Now, since the base of the logarithm is the same (b), we can combine the two logarithms using the power rule, which states that logₙ(aᵇ) = b × logₙ(a).

[tex]log_b(\frac{8^3}{7})[/tex]

Simplify

[tex]log_b(\frac{512}{7})[/tex]

Therefore, the single logarithm is [tex]log_b(\frac{512}{7})[/tex].

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The value of x is equal to 15.1 units.

In Mathematics and Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical equation:

Interior angle = [180 × (n - 2)]/n

Where:

n represents the number of sides of a regular polygon.

Since this regular polygon can be decomposed into 46 triangles, it ultimately implies that it has 46 x 3 = 138 sides.

Therefore, the value of each interior angle can be calculated as;

Interior angle = [180 × (n - 2)]/n

Interior angle = [180 × (138 - 2)]/138

Interior angle = 169.6⁰

For the value of x, we have:

9.5x + 26.2 = 169.6

9.5x = 143.4

x = 15.1 units.

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Complete Question:

Suppose there is a regular polygon that can be decomposed into 46 triangles. The measure of one of its interior angles is (9.5x+26.2).

What is the value of x?

Answer: x = 0

Step-by-step explanation:

Anything divided by 0 equals 0

Multiply -9 to the other side

x = 0 × -9

Anything Multiplied by 0 equals 0

x = 0

The margin of error for the two-proportion 95% confidence interval is 0.0662.

The margin of error for a two-proportion 95% confidence interval can be calculated using the following formula:

ME = z√(p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂)

where ME is the margin of error, z is the z-score corresponding to the level of confidence (in this case 1.96 for a 95% confidence interval), p₁ and p₂ are the sample proportions, and n₁ and n₂ are the sample sizes.

Using the given information, we have:

Sample 1: n₁ = 250, p₁ = 0.90

Sample 2: n₂ = 275, p₂ = 0.85

Level of confidence: 95%

Substituting these values into the formula, we get:

ME = 1.96√[(0.90×0.10 / 250) + (0.85 × 0.15 / 275)]

ME = 0.0662

Therefore, the margin of error for the two-proportion 95% confidence interval is 0.0662.

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The profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.

The profit generated by the company manufacturing lawn mowers is the difference between the revenue and the cost, so we can subtract the cost polynomial C= 38x+300 from the revenue polynomial R= -0.5x²+91x to obtain the profit polynomial:

P(x) = R(x) - C(x)

P(x) = (-0.5x²+91x) - (38x+300)

P(x) = -0.5x² + 53x - 300

Therefore, the profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.

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Answer:

$3,080 for each person

Step-by-step explanation:

9,240 / 3 = 3,080

The area of the regular polygon, given the apothem and the side length, would be 52. 5 in².

To find the area of a regular pentagon with a given apothem (a) and side length (s), we can use the formula:

Area = ( Perimeter × Apothem ) / 2

Perimeter would be :

= 5 x sides

= 5 x 6

= 30 inch

The area is therefore :

= ( Perimeter × Apothem ) / 2

= ( 30 in x 3. 5 in ) / 2

= 105 / 2

= 52. 5 in²

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Answer: 2.667

Step-by-step explanation:

Answer:

Can you mark me brainiest.

Step-by-step explanation:

Instead of me telling you the answer I will make it easy for you go to M a th way its very easy.

Or 2.667

The value of P (B) = 0.8

The probability of event A, P (A) = 0.68

The probability of events A and B, P (A ∩ B) = 0.544

The probability of event B, P (B) = ?

We know that Independent events are those where the probability of A event occurring doesn't affect the probability of B event. In other words, they don't depend upon each other and are independent.

By formula;

P (A ∩ B) = P (A) . P (B)

By substituting the values to the above equation, we get;

0.544= 0.68 * P (B)

P (B) = 0.8

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Sharon is correct in classifying the shape as a square, rectangle, and quadrilateral.

The shape satisfies the criteria for each classification: it has equal sides and right angles, making it a square; it has right angles, making it a rectangle; and it has four sides, making it a quadrilateral. Therefore, the shape can be accurately described and categorized using all four classifications.

Moreover, as a quadrilateral, this shape satisfies the general criteria of having four sides. Its defined boundaries encompassing an enclosed area are emblematic of a quadrilateral.

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The cost per pound of sausage, s, and brisket, b is 10s + 14b = 100.5

We are given that;

First customer order= $21

Second customer order= $100.50

Now,

The two equations that can be used to create a system of equations are:

2s + 3b = 21 10s + 14b = 100.5

These equations are obtained by multiplying the cost per pound of sausage and brisket by the number of pounds ordered by each customer and setting them equal to the total cost for each customer. The variables s and b represent the cost per pound of sausage and brisket, respectively.

Therefore, by the equation the answer will be 10s + 14b = 100.5

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Answer:

8) b. 15 m²

9) c. 63.5 ft²

Step-by-step explanation:

Area of composite figure:

8) To find the area of the composite figure, we have to add the area of rectangle, area of the top triangle and the area of the below triangle.

Rectangle:

            length = 3m

            width = 2.5 m

          [tex]\boxed{\text{\bf Area of rectangle = length * width}}[/tex]

                                           = 3 * 2.5

                                           = 7.5 m²

Area of triangle:

              [tex]\boxed{\text{\bf Area of triangle =$ \dfrac{1}{2}*base*height$}}[/tex]

       Triangle1:

                    base = 3 m  ; height = 1.5 m

                   [tex]\sf Area \ of \ triangle1 = \dfrac{1}{2}*3*1.5[/tex]

                                             [tex]= 2.25 \ m^2[/tex]

       Triangle2:

               base = 3 m ; height = 2.5 + 1 = 3.5 m

               [tex]\sf Area \ of \ triangle2 = \dfrac{1}{2}*3*3.5[/tex]

                                          = 5.25 m²

Area of the figure = 7.5 + 2.25 + 5.25

                               = 15 m²

_______________________________________________________

9) To find area of the given area, add the area of rectangle1 and area of rectangle2.

      length = 5 ft ;  width =  5.5 ft

Rectangle1:

         Area of rectangle1 = 5 * 5.5

                                         = 27.5 ft²

Rectangle2:

           length = 8ft

           width = 10 - 5.5

                      = 4.5 ft²

           Area of rectangle2 = 8 * 4.5

                                           = 36 ft²

Area of the given figure = area of rectangle1 + area of rectangle2

                                       = 27.5 + 36

                                        = 63.5 ft²

We can see here that the dollar doesn't belong to the box.

We can see here that in order to known if the dollar belongs to the box or not, here is an explanation:

Let the single tickets = x

and the couples tickets = y

Note: $8 = 2 tickets (for couples),

Thus, 1 ticket = $4

5x + 4y = 200  -------(1)

x + y = 47 ----------- (2)

-4 × (2)

5x + 4y = 200  -------(1)

-4x - 4y = 188

x = 12

Substituting 12 in (2)

12 + y = 47

y = 47 - 12 = 35

y = 35

So, 5x + 4y = 200

5 (12) + 4 (35) = 200

60 + 140 = 200.

Thus, we see here that the dollar doesn't belong to the box.

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Answer:

h = -10

Step-by-step explanation:

The solution to the equation is h = -10. To solve for h, we need to isolate h on one side of the equation. We do this by adding 9 to both sides, subtract 4h from both sides, and add 5 to both sides. This gives us:

Negative 3 (h + 5) + 2 + 9 = 4 (h + 6) - 9 + 9

Negative 3h + 14 = 4h + 15

Negative 3h - 4h = 15 - 14

-7h = 1

h = -1/7

h = -10

A. The greatest number of packages that can fit the truck is 24000

B. The volume of the part that is filled is 375 cubic feet

Given that

Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft

Also, we have

Package = 1/4 foot cube

So, we have

Number of packages = (8 * 6 1/4 * 7 1/2)/(1/4 * 1/4 * 1/4)

Evaluate

Number of packages = 24000

This means that the greatest number of packages is 24000

Recall that

Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft

So, we have

Volume = (8 * 6 1/4 * 7 1/2)

Evaluate

Volume = 375

Hence, the volume is 375 cubic feet

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The value of p when q is 2 is 1

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means that has x increases y will decrease and vice versa.

If p is inversely proportional to q , then p = kq

when p = 2, q = 4

2 = k4

k = 2/4

k = 1/2

When q = 2

p = 1/2 × 2

p = 1

Therefore the value of p is 1

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Answer:

0.1429

Step-by-step explanation:

The formula for the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]. a = 0, b = 7, f(a) = 2, and f(b) = 3, We plus the numbers into the formula and get 0.1429 as our answer.

Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

Human actions and behaviors towards our surroundings can have significant implications for human health, leading to the emergence of various health problems.

Our choices and activities encompassing lifestyle, pollution, and resource utilization exert direct impacts on our overall well-being. For instance, our exposure to environmental pollutants, encompassing air and water contaminants, toxic substances, and hazardous waste, can engender respiratory ailments, cancer, and an array of severe health conditions.

Similarly, the degradation of natural habitats, deforestation, and unsustainable practices contribute to the proliferation of infectious diseases, disrupt ecological balance, and undermine the stability of our food systems.

Moreover, unhealthy dietary patterns, sedentary behaviors, and limited access to healthcare services compound the complexities of prevailing health issues.

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The value of x is -1 which makes the model true

The equation from the given model will be 5x+6=1

We have to find the value of x

5x+6=1

Subtract 6 from both sides

5x=-5

Divide both sides by 5

x=-1

Hence, the value of x is -1 which makes the model true

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Answer:

Step-by-step explanation:

For Company C, the total cost in dollars, denoted as t, can be calculated using the following equation:

t = 27n + 18

In this equation, 27n represents the cost of the bracelets (charging $27 per bracelet), and 18 represents the flat rate for shipping any number of bracelets. By summing these two components, we obtain the total cost of the friendship bracelets from Company C in terms of the number of bracelets, n.

The theoretical probability of Constance getting an orange ring from the coin-operated machine is 0.182. This means that out of all the possible outcomes, there is an 18.2% chance that Constance will get an orange ring.

To find the theoretical probability of Constance getting an orange ring from the coin-operated machine, we need to first understand what theoretical probability means. Theoretical probability is the likelihood or chance of an event happening based on the number of possible outcomes. In this case, the possible outcomes are the different colored rings that the machine contains.

We are given that the machine contains 5 white rings, 6 orange rings, 7 purple rings, and 15 pink rings.

Therefore, the total number of rings in the machine is 5 + 6 + 7 + 15 = 33.

The probability of Constance getting an orange ring can be calculated by dividing the number of orange rings by the total number of rings in the machine.

Therefore, the theoretical probability of Constance getting an orange ring is:

6 / 33 = 0.181818...

To express this as a decimal, we can round it to the nearest thousandth, which is 0.182.

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Note that from the coordinates of the above triangle, we can state that the triangle is an Isoceles triangle.

We can also state emphatically that it is NOT a right triangle.

a) we now that the triangle is a scalene triangle because all three sides have unequal lengths.

This can be determined with the use of distance formula.

d = √((x2 - x1)² + (y2 - y1)²)

PQ = √((2-4)² + (7-1)²)

= 6.32455532034

PQ ≈ 6. 33

Using the same steps above,

QR = 6.33

Using the same steps

RP = 5.66

From the above as well as is show on the attached graph, we can see that the triangle has two equal sides hence an Isosceles triangle.


b) We know for a fact using the graphical method that the above triangle is NOT a right triangle.

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The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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The outcome of 4 occurred 3 more times than expected. This is the resulting probability. Therefore, the correct option is option A.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which anything is probable to happen is basically what probability means. The outcome of 4 occurred 3 more times than expected.

Therefore, the correct option is option A.

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The equivalent value of the expression is A = ( -16y + 12 + 7 ) / 8x

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -2y+ 3/2x + 7/4

On simplifying , we get

A = ( -4y + 3 )/2x + 7/4

Taking LCM on both sides , we get

A = ( -16y + 12 + 7 ) / 8x

Hence , the expression is A = ( -16y + 12 + 7 ) / 8x

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The expression has no solution when k < - 5.

Hence, option B is correct.

The given inequality is

|2x + 7|-k ≤ 5

We know that,

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.

A function with absolute values is another name for it.

No matter what input was provided to this function, the outcome is always favorable.

Now adding k both sides of inequality,

⇒ |2x + 7| ≤ 5 + k

When we take value of k less than -5

Then the expression |2x + 7| becomes negative.

Since it always gives absolute value,

Therefore,

There is no any solution when k < -5.

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