What is the range of 5,28,16,32,5,16,48,29,5,35

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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total number of students = 51

total number of accounting students = 23

total number of chemistry student = 17

number of students that takes both accounting and chemistry = 4

total number of probabilities = 23 + 17 - 4

= 36

the probability of randomly chosen student taking accounting or chemistry

= 36/51

= 12/17

therefore, the probability of randomly chosen student taking accounting or chemistry is 12/17

The solution to the system of equations is x = 4 and y = 0. In summary, the correct substitution step for the system is: -4x - 6(x - 4) = -16 .C answer is correct

To solve the given system of equations:

1) y = x - 4

2) -4x - 6y = -16

We can use the substitution method to eliminate one variable and solve for the other.

Step 1: Solve the first equation (1) for y in terms of x.

  y = x - 4

Step 2: Substitute the expression for y from equation (1) into equation (2).

  -4x - 6(x - 4) = -16

Step 3: Simplify and solve for x.

  -4x - 6x + 24 = -16

  -10x + 24 = -16

  -10x = -16 - 24

  -10x = -40

  x = -40 / -10

  x = 4

Step 4: Substitute the value of x back into equation (1) to solve for y.

  y = 4 - 4

  y = 0

Therefore, the solution to the system of equations is x = 4 and y = 0.

In summary, the correct substitution step for the system is:

-4x - 6(x - 4) = -16

By substituting the expression for y from equation (1) into equation (2) and simplifying, we obtain the equation -4x - 6y = -16, which can be further solved to find the values of x and y. C answer is correct

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Answer:

x = -4.5

Step-by-step explanation:

\(20 = 2 - 4x\)

\(18 = - 4x\)

\( - 4.5 = x\)

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

The calculated value of x at g(x) = 2 is x = 2.5

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

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Answer:

3200 of 768 is 416.67%

Step-by-step explanation:

There's your answer hope this helps.

Answer: -2.5

Step-by-step explanation: The absolute value of 0.5 is "0.5".

Therefore; if you subtract the value "3" from "0.5", you will end up with -2.5 as an answer.

Answer:

x=-6

Step-by-step explanation:

2x=-4-8

2x=-12

2x/2=-12/2

x=-6

Answer:

x = - 6

Step-by-step explanation:

2x+8 = 4

Subtract 8 from both sides:

2x+8-8 = - 4 - 8

Simplify :

2x = -12

Divide both sides by 2 :

2x/2 = -12/2

Simplify  :

-12/2 : -6

x = -6

Hope it Helps :) !!

Answer:

2.00 grams

Step-by-step explanation:

1.66 + 0.34 = 2.00

2.00 grams

Answer:

18 degrees.

Step-by-step explanation:

12 - (-6)

= 12 + 6

= 18.

Answer: 18 degrees

Step-by-step explanation:

The easiest way to solve this problem is to first get the temperature to 0 and then add the current temperature. 0-(-6) = 6. 6+12 = 18.

Answer:

1

Step-by-step explanation:

1.  One way to do this is converting both into improper fractions.  To do this, multiply the whole number by the denominator and add that to the numerator.

2 3/5 --> 2*5 is 10 --> 10+3 is 13.  --> 13/5

2.  This leaves us with 13/5 - 8/5

3.  Subtract the numerators

13/5 - 8/5 = 5/5

4.  Simplify.  If the numerator is the same number as the denominator, it's a whole number.

5/5 = 1

If the original amount is 390 and the new amount is 546, the amount of increase is 156 and the percent increase is 40%. This indicates that the new amount is 156 units higher than the original amount, representing a 40% increase.

To find the amount of increase and the percent increase between the original amount and the new amount, we can follow these steps:

1. Start with the original amount: 390.

2. Determine the increase by subtracting the original amount from the new amount: 546 - 390 = 156.

3. The amount of increase is 156. This means that the new amount is 156 units greater than the original amount.

4. To calculate the percent increase, divide the amount of increase by the original amount and then multiply by 100: (156 / 390) * 100 = 40.

5. The percent increase is 40%. This means that the new amount is 40% greater than the original amount.

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Solving the quadratic equation, it is found that:

A quadratic function is given according to the following rule:

\(y = ax^2 + bx + c\)

The solutions are:

\(x_1 = \frac{-b + \sqrt{\Delta}}{2a}\)

\(x_2 = \frac{-b - \sqrt{\Delta}}{2a}\)

In which:

\(\Delta = b^2 - 4ac\)

If a < 0, the graph, which is a parabola, is concave down, that is, it is positive only between the two roots.

In this problem, the equation is:

\(y = -16t^2 + 176t - 384\)

Then, the solution is:

\(-16t^2 + 176t - 384 = 0\)

The coefficients are \(a = -16, b = 176, c = -384\), then:

\(\Delta = (176)^2 - 4(-16)(-384) = 6400\)

\(x_1 = \frac{-176 + \sqrt{6400}}{-32} = 3\)

\(x_2 = \frac{-176 - \sqrt{6400}}{-32} = 8\)

Considering that the parabola is concave down, we have that:

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Check the picture below.

so let's recall that the area of a circle is just πr² where r = radius, so since the sizes of each pizza are 10, 14, 18 and 22, that's simply their diameter, so that means they each have a radius half of that, or namely 5, 7, 9 and 11, as you see in the picture, so, hmmm which radius gives us the most area per the fraction provided, namely per slices provided?

\(\cfrac{4}{8}\pi 5^2\implies \cfrac{25\pi }{2} ~~ \approx ~~ 39.26~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{8}\pi 7^2\implies \cfrac{147\pi }{8} ~~ \approx ~~ 57.73~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{8}\pi 9^2\implies \cfrac{81\pi }{4}~~ \approx ~~ 63.62~in^2 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}\pi 11^2\implies \cfrac{121\pi }{8}~~ \approx ~~ 47.52~in^2\)

Answer: Large

Step-by-step explanation:  Hope it helps Good luck!!!

Answer:

1 milimiter

Step-by-step explanation:

that the answer

The exponential function can be rewritten as:

f(x) = 48*e^(0.0198*x)

Here we start with the exponential function:

f(x) = 48*(1.02)^x

And we want to write this in the general form:

f(x) =a*e^(kx)

Notice that we can write the second form as:

f(x) = a*[e^k]^x

So, comparing this with the given exponential, we will get:

a = 48

e^k = 1.02

Apply the natural logarithm in both sides:

ln(e^k) = ln(1.02)

k*ln(e) = ln(1.02)

k = ln(1.02) = 0.0198

Then the exponential function is:

f(x) = 48*e^(0.0198*x)

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Answer:

54932540-476715.jpeg

A study of stroke patients who survived 6 months after the stroke found that 6/45 men and 22/63 women lived in an institution (e.g., nursing home or assisted living facility).  What is the risk difference of living in an institution between men and women (using men as the reference group)?

Data (1=males, 2 =females)

temp sex Heart rate

96.3 1 70

96.7 1 71

96.9 1 74

97 1 80

97.1 1 73

97.1 1 75

97.1 1 82

97.2 1 64

97.3 1 69

97.4 1 70

97.4 1 68

97.4 1 72

97.4 1 78

97.5 1 70

97.5 1 75

97.6 1 74

97.6 1 69

97.6 1 73

97.7 1 77

97.8 1 58

97.8 1 73

97.8 1 65

97.8 1 74

97.9 1 76

97.9 1 72

98 1 78

98 1 71

98 1 74

98 1 67

98 1 64

98 1 78

98.1 1 73

98.1 1 67

98.2 1 66

98.2 1 64

98.2 1 71

98.2 1 72

98.3 1 86

98.3 1 72

98.4 1 68

98.4 1 70

98.4 1 82

98.4 1 84

98.5 1 68

98.5 1 71

98.6 2 77

98.6 1 78

98.6 1 83

98.6 2 66

98.6 1 70

98.6 1 82

98.7 2 73

98.7 1 78

98.8 1 78

98.8 1 81

98.8 2 78

98.9 1 80

99 2 75

99 2 79

99 1 81

99.1 1 71

99.2 1 83

99.3 1 63

99.4 1 70

99.5 1 75

96.4 2 69

96.7 2 62

96.8 1 75

97.2 1 66

97.2 2 68

97.4 2 57

97.6 1 61

97.7 2 84

97.7 1 61

97.8 2 77

97.8 2 62

97.8 2 71

97.9 1 68

97.9 2 69

97.9 2 79

98 2 76

98 1 87

98 2 78

98 2 73

98 2 89

98.1 2 81

98.2 2 73

98.2 2 64

98.2 2 65

98.2 2 73

98.2 2 69

98.2 2 57

98.3 2 79

98.3 2 78

98.3 2 80

98.4 2 79

98.4 2 81

98.4 2 73

98.4 2 74

98.4 2 84

98.5 2 83

98.6 2 82

98.6 2 85

98.6 2 86

98.6 2 77

98.7 2 72

98.7 2 79

98.7 2 59

98.7 2 64

98.7 2 65

98.7 2 82

98.8 2 64

98.8 2 70

98.8 2 83

98.8 2 89

98.8 2 69

98.8 2 73

98.8 2 84

98.9 2 76

99 2 79

99 2 81

99.1 2 80

99.1 2 74

99.2 2 77

99.2 2 66

99.3 2 68

99.4 2 77

99.9 2 79

100 2 78

100.8 2 77

Step-by-step explanation:

To know the area of a figure, you would like to know its shape and estimations. The steps to take on how to draw a figure with the use of a ruler and a pencil is given below.

Begin by selecting the kind of figure you need to draw. Make use of a ruler to draw the sides of the figure. Make sure that the lines are straight and have the right length.

E.g. If the figure may be a rectangle or a parallelogram, you wish to create beyond any doubt that inverse sides are parallel to each other. If the figure is triangle, you would like to draw three lines that shows at three distinctive points. At last, name the sides and vertices of the figure.

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The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,

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

f(x) = x²

g(x) = (4x)²

Mathematically, these equations can be represented as

g(x) = f(4x)

The above equations implies that, we have the transformation to be:

The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4

Hence, the transformed function is (a)

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Answer:

Regina paid $4.70 more that Kyle

Step-by-step explanation:

To be able to make our choice, we first have to find out how much Regina and Kyle pay! We already know that Kyle bought it $47.50 but we are told that Regina pays $58 with a discount of 10%

This means that he pays 90% making our multiplier 0.9!

Now we have to find the difference between our results.

Hope this helps, have a lovely day! :)

Answer: Regina paid $4.70 more than Kyle

Step-by-step explanation:

To be able to make our choice, we first have to find out how much Regina and Kyle pay! We already know that Kyle bought it for $47.50 but we are told that Regina pays $58 with a discount of 10%

This means that he pays 90% making our multiplier 0.9!

58 x 0.9 = 52.2

Meaning Kyle paid $52.20

Now we have to find the difference between our results.

52.20 - 47.50 = 4.70

This means that Regina paid $4.70

Answer:

\(x\geq - \frac{16}{3}\)

Step-by-step explanation:

x +2/2 ≥ -7 - x/2

= x ≥ -16/3 (sign doesn't change since you didn't divide by a negative number).

Ace Carlos

Answer:

\(x\geq \frac{-16}{3}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Looks good

Answer:

I think it is correct and also check to your teacher also

Answer:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Step-by-step explanation:

Total expenses for this year: $214.00

The child fee will be: $x

and the adult fee will be $(x+2)

Last year the number of children was 44

and the number of adults was 33

this year also has the same number of children and adults.

which means the entrance fee total for children will be $44x and for adults will be $33(x+2).

44x + 33(x+2) = 214

--> 44x + 33x + 66 = 214

--> 77x = 214 - 66 = 148

--> x = 148/77 = 1.92

So children's price is $1.92 and adults price is $1.92 + 2

hence:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)

Linear Equation                   General Form                    Example

Slope intercept form             y = mx + b                            y + 2x = 3

Point–slope form                   y – y1 = m(x – x1 )              y – 3 = 6(x – 2)

General Form                            Ax + By + C = 0               2x + 3y – 6 = 0

Intercept form                        x/a + y/b = 1                 x/2 + y/3 = 1

As a Function f(x) instead of y      f(x) = x + C                         f(x) = x + 3

The Identity Function                      f(x) = x                     f(x) = 3x

Constant Functions                      f(x) = C                       f(x) = 6

Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:

(x - 2i)² = x² - 4xi + 4i²

Note that i² = -1, so we can simplify this expression to:

(x - 2i)² = x² - 4xi - 4

Substituting this expression and the given values into the original expression, we get:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Grouping the real and imaginary terms, we get:

(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)

Simplifying the real part, we get:

-2x² - 1

Simplifying the imaginary part, we get:

-7i - 4x

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Answer:

6 and 12 have the greatest common factor of 2

Answer:

4

Step-by-step explanation:

The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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Answer:

The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 47

Standard deviation of 7

What is the approximate percentage of lightbulb replacement requests numbering between 47 and 68?

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% of the above.

Between 47 and 68:

68 = 47 + 7*3

So 68 is three standard deviations of the mean.

Of the 50% above the mean, approximately 99.7% are between the mean of 47 and 3 standard deviations above the mean, which is 68. So

0.5*0.997 = 0.4985

0.4985*100 = 49.85%

The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.

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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