Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c) constant.
y =f(x)

Step-by-step explanation:

A set is a collection of distinct elements, and a subset is a collection of elements taken from a larger set. In this case, the set is {10, 15, 14, 20, 11}.

To calculate the number of subsets, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, the number of subsets of the set {10, 15, 14, 20, 11} is 2^5 = 32.

To calculate the number of proper subsets, we need to exclude the empty set (Ø) and the set itself from the total number of subsets. So, the number of proper subsets is 32 - 2 = 30.

Therefore, there are 32 subsets and 30 proper subsets of the set {10, 15, 14, 20, 11}.

The next step in the solution to this equation is to evaluate the exponents

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

The steps 1 to 4

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

Step 4: (3x - 11)² =(√4x)²

At this point,, we open the bracket

This is done by evaluating the exponents

So, we have

9x² - 66x + 121 = 4x

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The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

(3/5) (30x - 15) = 72

Solve the linear equation with a single variable for 'x', then we have

(3/5) (30x - 15) = 72

3(6x - 3) = 72

18x - 9 = 72

18x = 81

x = 4.5

The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.

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The relative frequency of sophomores at this high school is 39/128.

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).

We are given that;

Total students=1152

Freshmen=391

Sophomores=351

Juniors=208

Seniors=202

Now, to find frequency of sophomores

=number of sophomores/total number of students

=351/1152

=117/384

=39/128

Therefore, the relative frequency will be 39/128.

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Answer: OD. 13

Step-by-step explanation:

The value of CD is 9.92 cm

Given:

Find: CD

Triangle ABC is an isosceles triangle with base AB, because AC = BC. In isosceles triangle angles adjacent to the base are congruent. So,

m<A = <mB = 72°

The sum of the measures of all interior angles is 180°, thus

m<C =  180° -72° - 72° = 36°

The area of the triangle ABC is

AABC= 1/2AC.BC.sin<C

If we expand,

AC = 10.43cm

Consider right triangle ACD. In this triangle,

sin <A = CD/AC

sin 72° = CD/10.43

therefore,

CD = 9.92 cm.

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Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72°

Find: CD

Answer:

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Answer:

Bryce is 10 years old

Step-by-step explanation:

The age of Brice is given by B = 10 years old

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as B

Now , the value of B is

Substituting the values in the equation , we get

The age of Aida = 15 years

The age of Brice = 5 years younger than Aida

On simplifying the equation , we get

So , age of Brice = 15 - 5 = 10 years

The age of Henry = three years younger than Aida

So , the age of Henry = 15 - 3 = 12 years

Hence , the age of Brice is 10 years old

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The order of the numbers from greatest to least are 3.406 > 305 / 100 > 99 × 1/100

Descending order refers to the arrangements of numbers from the greatest to the least.

On the other hand, ascending order is the arrangement of numbers from the least to the greatest.

3.406

305 / 100

= 3.05

99 X 1/100

= 99 × 0.01

= 0.99

Therefore, the arrangements from greatest to least is 3.406, 305 / 100, 99 × 1/100

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A quotation isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2.

The option (a) is correct.

Famous people who discuss their opinions on a given subject often employ quotation marks around their words. The brief nature of a quotation allows it to share individuality. The citation served as a means of sharing ideas and serving as a source of historical information.

The quotation, which is sometimes referred to as "quote vomit," was cut off from the remainder of the text.

The sentences are directed at their objective. Understanding how the universe functions and how we fit into it can be done through the metaphor of weaving.

As a result, the quote isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2. Therefore, option (a) is correct.

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The x-intercepts of the graph of the given polynomial function as described is; 2, 3 and -5.

The x-intercepts of a polynomial function are otherwise termed, roots, solutions or zeroes of the polynomial function.

On this note, the x-intercepts of the polynomial function which is as described in this scenario are;

x - 2 = 0; x = 2.

x - 3 = 0; x = 3.

x + 5 = 0; x = -5.

Ultimately, the x-intercepts of the polynomial function in discuss are; 2, 3 and -5.

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The average rate of change over each specified interval is 8/3 and -10.

The average rate shows the change in the function per unit, over an interval.

Given that, find the average rate of change over each specified interval.

The average rate of change is given by

f(b)-f(a) / b-a

a) [2, 5] :-

To find the average rate of change we will take the change in the function over the change in x,

f(5)-f(2) / 5-2 = 24-16 / 3 = 8/3

Therefore, the average rate of change in interval [2, 5] is 8/3

b) [3.8, 4] :-

Similarly,

f(4)-f(3.8) / 4-3.8 = 17-19 / 0.2 = -2/0.2

= -10

Therefore, the average rate of change in interval [3.8, 4] is -10

Hence, the average rate of change over each specified interval is 8/3 and -10.

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The measurement closest to the area of the circle in meters is 379.94 sq. meters.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area. The majority of forms and things have corners and edges. When computing the area of a certain form, both the length and width of these edges are taken into account.

Given that,

diameter = 22m

radius = 22/2 = 11m

The area of the circle is:

A = πr²

Substituting the value of π = 3.14 and r = 11 we have:

A = (3.14)(11)²

A = 379.94

Hence, the measurement closest to the area of the circle in meters is 379.94 sq. meters.

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The number of ways 3 man and 3 woman line up at the counter in a store is 720 ways.

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.

Given that, three men and three women line up at a checkout counter in a store.

a) Number of ways = 6!

= 6×5×4×3×2×1

= 720 ways

b) The first person in line is a woman, and then the line alternates by gender that is a woman, a man, a woman, a man, a woman, a man, and so on

There are 3 number of ways for woman standing in the odd position and for men standing in the even position.

So, number of ways = 3!×3!

= 3×2×1×3×2×1

= 36 ways

c) There are 3 men and 3 women.

Probability first is a woman is 3/6

Probability second is a man is 3/5

Probability third is a woman is 2/4

Probability fourth is a man is 2/3

Probability fifth is a woman is 1/2

Probability sixth is a man is 1/1

Multiply all these probabilities together and you get:

3/6 × 3/5 × 2/4 × 2/3 × 1/2 × 1/1 = 0.05

Therefore, the number of ways 3 man and 3 woman line up if the first person in line is a woman, and then the line alternates by gender that is a woman is 36 ways.

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Answer:

Both of them are correct.

Step-by-step explanation:

Let's review both of their methods and check their validity.

This method is the most straight forward and seems to be correct as we're simply calculating the total value of each, and then subtracting the difference. We can write the expression as: [tex]2.25(4.25)-2.25(2.85)[/tex] and this should give us the difference assuming the prices and math is done correctly.

While this method is a bit difference, it actually does work! Think of this way, we first calculate the difference in the prices and then for each pound we increase it by, the difference also increases by this amount. It also helps to look at our original expression: [tex]2.25(4.25)-2.25(2.85)[/tex], notice how we have a factor of 2.25 on both sides? Well we can just factor that out to get: [tex]2.25(4.25 - 2.85)[/tex] and this is essentially what Ariel's method is. This should give us the difference in prices and is likely easier than Kaylee's method as we do less multiplication and with smaller numbers.

Answer:

  1/(ab) if a ≠ 0, b ≠ 0, and (a+b) ≠ 0

Step-by-step explanation:

You want the simplified form of 1/(a²+ab) +1/(ab+b²) and any applicable conditions.

The expression is simplified by writing it over a common denominator and cancelling any common terms from numerator and denominator.

  [tex]\dfrac{1}{a^2+ab}+\dfrac{1}{ab+b^2}=\dfrac{1}{a^2+ab}\cdot\dfrac{b}{b}+\dfrac{1}{ab+b^2}\cdot\dfrac{a}{a}=\dfrac{b+a}{a^2b+ab^2}\\\\=\dfrac{a+b}{ab(a+b)}=\boxed{\dfrac{1}{ab}\quad a\ne0,b\ne0,(a+b)\ne0}[/tex]

The given conditions ensure the denominator(s) will not be zero.

Answer:

t = 21 + (-4)h

Step-by-step explanation:

t = temp. at hour h

h = # of hours past midnight

t = 21° + (-4°/hr)h

Answer:

(a) highest number of groups  = 5

(b) out how many, of each color marble, will be in each group.
5 red

3 blue

2 yellow

Step-by-step explanation:

The GCF of 25, 15, 10 gives you the greatest number of groups you can form with those numbers

GCF of 25, 15 and 10 can be found as follows by finding factors of each number:

25 = 5 x5

15 = 5 x 3

10 = 5 x 2

Choose the highest number that is common in each group and this is 5

So John can make a maximum number of 5 groups

Divide each number by the GCF to find how may in each group

25/ 5 = 5 red marbles
15/5 = 3 blue marbles

10/5 = 2 yellow marbles

So there are 5 groups max possible each group containing 5 red, 3 blue and 2 yellow marbles

The value of y from x= 0 to x = 3 is: y = 5(2)⁰ = 5, y = 5(2)¹ = 10, y = 5(2)² = 20, y = 5(2)³ = 40. The most rapid rate of change is: y = 7ˣ. The constant 1.20 is greater than 1 thus, the function is exponential growth.

The formula for an exponential function is f (x) = axe, where x is a variable and an 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.

The given function is:

y = 5(2)ˣ

The value of y from x= 0 to x = 3 is:

y = 5(2)⁰ = 5

y = 5(2)¹ = 10

y = 5(2)² = 20

y = 5(2)³ = 40

The most rapid rate of change as x increases beyond 0 is:

y = 7ˣ

This is observed as the graph increases rapidly with change in value of x.

3. y = (1.20)ˣ

The constant 1.20 is greater than 1 thus, the function is exponential growth.

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The outliers in a set of data is the maximum value 41.6.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

Given that Minimum: 1

Q1: 5

Median: 19.45

Q3: 31.5

Max: 41.6

Range = Maximum - minimum

Range =41.6 -1

= 40.6

Since Mean not including the outlier.

The outliers in a set of data is 41.6.

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Answer:

option

Step-by-step explanation:

f(x)=-3x²-4x+15

if (-3,-2) is substitute

x=-3 x=-2 is substitute in above given equation we get real zero.

The GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.

What is Interest?

Interest is the income that is returned to the holder of capital. Different kinds of interest include gross interest and net interest.

To find GI (Gross Income), we add wages and interest:

GI = Wages + Interest = $145,000 + $2500 = $147,500

To find AGI (Adjusted Gross Income), we subtract the contributions towards retirement from GI:

AGI = GI - Contributions towards Retirement = $147,500 - $3000 = $144,500

To find TI (Taxable Income), we subtract exemptions and deductions from AGI:

TI = AGI - Exemptions - Deductions = $144,500 - $4100 - $2800 = $137,600.

Therefore, the taxable income is $137,600.

Hence, GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.

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Answer:

The correct answer is:

e = 0.25 t + 1.75 .

A structure may lack structural integrity if it experiences overloading and material degradation.

A structure may lack structural integrity if it experiences:

Overloading, where the loads placed on the structure exceed its design capacity, leading to failure of some structural components or members.

Material degradation, where the structural materials lose their strength and stiffness over time due to environmental factors such as corrosion or excessive temperature.

ii. The basic types of structural systems are:

Frame Structures, where the structural components are arranged in a series of interconnected frames that can resist lateral and gravity loads. Examples include steel frames and concrete frame structures.

Load-Bearing Wall Structures, where the structural components are arranged in a series of interconnected walls that bear the weight of the structure and transfer loads directly to the foundation. Examples include masonry and concrete walls.

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Answer: 1,652.8 calories

Step-by-step explanation:

620 divided by 6 = 103.3 calories per inch

103.3 times 16 inches = 1,652.8 calories

The expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.

A polynomial expression is an algebraic expression made up of variables and coefficients, combined using only the operations of addition, subtraction, and multiplication. The variables are raised to a power, which is a non-negative integer, and the coefficients are real numbers. A polynomial can have any number of terms, but it always has a degree, which is the highest power of the variables in the expression.

For the polynomial expression, (1/2)x⁵ - 6 - x⁴ - 5x⁴

There are 4 terms which are: (1/2)x⁵, - 6, - x⁴, and - 5x⁴.

The constant term is -6

The leading term is (1/2)x⁵

The coefficient of the leading term is 1/2.

In conclusion, the expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.

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Answer:

quadrinomial, 4, -6, 1/2x^5, 1/2

Step-by-step explanation:

quadrinomials are polynomials with 4 terms

constant is the number with no variable

leading term is the term at the beginning

leading coefficient is the number at the beginning

Answer:

x[tex]\geq[/tex] 3

Step-by-step explanation:

-4x -2 ≤ -14
-4x ≤ -12
x ≥ 3

Answer:

is not a solution to the system of equations.

Step-by-step explanation:

Sure! Here's a step-by-step solution to determine if the point (-6, 3) is a solution to the system:

Substitute the x and y values into the first equation:

y = 1/2x + 6

3 = 1/2(-6) + 6

Simplify the right side of the equation:

3 = -3 + 6

Solve for the value of y:

3 = 3

The first equation is satisfied, so now let's substitute the x and y values into the second equation:

2y = -x - 3

2 * 3 = -(-6) - 3

6 = +6 - 3

Simplify the right side of the equation:

6 = -3

The second equation is not satisfied, so the point (-6, 3) is a not solution to the system.

The area of the shaded region is 20 square units for the given rectangle frame.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

Dimensions of the inside rectangle, are as follows:

Length L₁ = 5 units

Width W₁ = 3 units

Since the frame is 2 units wide,

So, the dimensions of the outside rectangle, are as follows:

Length L₂ = 5 + 2 = 7 units

Width W₂ = 3 + 2 = 5 units

The area of the shaded region = area of the outside rectangle - area of the inside rectangle

The area of the shaded region = L₂ x W₂ - L₁ x W₁

The area of the shaded region = 7 x 5 -  5 x 3

The area of the shaded region = 35 - 15

The area of the shaded region = 20 square units

Thus, the area of the shaded region is 20 square units.

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The question seems incomplete, the missing figure is attached below.