The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data, using 7 classes.

Answer: 6.67

Step-by-step explanation: first you divide 4 and 3 to then get 1.3 and times that by 5

Answer:

lets denote x as 6

so,

(x-2)÷2

(6-2)÷2

4÷2

2(proved)

Only D satisfies both of the inequalities in the system represented by the graph. (Please check the graph attached)

Equations are not necessarily about having a "equal to" sign balanced evenly on both sides. It can occasionally refer to a "not equal to" connection, where one object is more than the other or less than. A connection that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical statements are classified as inequalities in the algebraic language.

To test point in that system satisfies both of the inequalities

The system of inequalities is shown by the graph.

While x + 2y is more than or equal to 3, 2x + 3y is less than or equal to 4.

Both of the system's inequalities represented by the graph are satisfied at the test point (4, -1).

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use real numbers for the proof

3^3 times 3^2 =

27 times 9 =

243 which is

3^5

Given

Answer:

m=-4/3

Explanation:

Given the points: (13,-4) and (1, 12)

To determine the slope of the line that joins the point, use the formula below;

Substitute the given points:

The slope is -4/3.

For function f(x) = (x − 1)³ and g(x) = 1-6x ,value of following function is:

a. (f ∘ g)(x)=-216x³

b. (g ∘ f)(x)=-6x³+18x²-18x+7

c. f(f(x))=(x³ -3x² +3x -2)³

d. f²(x)=(x-1)⁶

As given,

Given function :

f(x)=(x − 1)³

g(x)=1-6x

The value of following functions are:

a.(f ∘ g)(x)

=f(g(x))

=f(1-6x)

=(1-6x -1)³

=(-6x)³

=-216x³

b.  (g ∘ f)(x)

= g(f(x))

=g(x − 1)³

=1 -6(x − 1)³

=1 -6(x³ -3x² +3x -1)

=-6x³+18x² -18x+7

c. f(f(x))

=f(x-1)³

=((x-1)³ -1)³

=(x³ -3x² +3x -1-1)³

=(x³ -3x² +3x -2)³

d. f²(x)= (f · f)(x)

=f(x) × f(x)

=(x-1)³ × (x -1)³

=(x -1)⁶

Therefore, for function f(x) = (x − 1)³ and g(x) = 1-6x ,the value of following function is:

a. (f ∘ g)(x)=-216x³

b. (g ∘ f)(x)=-6x³+18x²-18x+7

c. f(f(x))=(x³ -3x² +3x -2)³

d. f²(x)=(x-1)⁶

The complete question is:

For function f(x) = (x − 1)³ and g(x) = 1-6x find the value of the following.

a. (f ∘ g)(x)

b. (g ∘ f)(x)

c. f(f(x))

d. f²(x)= (f · f)(x)

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The length of each side of the octagon would be 8.23 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

We are aware that one side of the square is 20 inches long and that one side is made up of the length of the octagon added. We also know that two sides of a right triangle have smaller angles inside that are 45 degrees, making those two sides equal to one another. Therefore, we add the two sides of the right angle triangle to the side of the octagon, which equals 20 inches, to determine the value of x, which is designated as the side of the octagon.

Since a side of the square is 20 inches

Here, y is the two equal sides of the right-angle triangle

So y + x + y = 20

Using Pythagoras's theorem for the right angle triangle

y² + y² = x²

2y² = x²

y² = (x²)/2

y = x /√2

So substitute the value of y = x /√2 in the equation

x /√2 + x + x /√2 = 20

2x /√2 + x = 20

2x /√2 + x√2 /√2 = 20

x[2/√2 + √2 /√2] = 20

x[(2 + √2) /√2] = 20

x(2 + √2) = 20√2

x = 20√2/(2 + √2)

x = 28.2843/3.4142 = 8.2343

Round to the nearest hundredth of an inch

x = 8.23

Therefore, the length of each side of the octagon would be 8.23 inches.

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If Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.

Given data  or information :

Product  = ( – 25. 31 ) (9. 61)

Now let estimate the product by first  approximating the product to the nearest tenth.

Approximation :

So,

-25.31 = - 25 ( Approximately )

9.61 =10 ( Approximately )

Hence , her estimate can be calculated as :

Estimate :

Estimate =  (-25) (10)

Estimate =-250

Therefore based on the information or data  given if  Seema  tend to make used of  compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.

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Answer:

7⁻²=[tex]\frac{1}{49}[/tex]

3⁻⁴ [tex]=\frac{1}{81}[/tex]

9⁰=1

11⁻¹=[tex]\frac{1}{11}[/tex]

Answer:

349.42499999998

Step-by-step explanation:

$232.95 divided by 22 hours of work = amount per hour = 10.588636363636

If you get paid 10.588636363636 per hour then multiply this by 33 hours to get the answer of : $349 and 42499999998 cents

Solve for (f - g)(x)

we have the equation

Solve for x

Step 1

squared both sides

The answer is x=5

Given:

Depreciation rate = 75% per year.

Let's find the value of the car in 2 years.

Given:

Cost = $16,500

Depreciation rate = 75%

From the equation we have:

Present value, a = 16500

x is the number of years = 2

Thus, we have:

Therefore, the value of the car in 2 years is $1,031

ANSWER:

$1,031

We use the following formula for integration:

We have the following integral:

Separate into two integrals:

Calculate the first integral. Take the coefficient out of the integral:

Apply the integration formula:

Calculate the second integral. Take the coefficient out of the integral:

Express the radical as a fractional exponent:

Apply the integration formula:

The total integral is:

(3x+5)-([tex]x^{2} - 3[/tex])=9

[tex]x^{2}[/tex]-3x-8=-9

[tex]x^{2}[/tex]-3x=-1

[tex]x^{2}[/tex]-3x+1=0

Answer:

Step-by-step explanation:

it is y

Answer: Y=0x +5

Step-by-step explanation

its going up by 0 so 0x and you start at 5 so plus 5

Answer:

13

Step-by-step explanation:

d) = √(-1 - -6)2 + (-4 - 8)2

= √(5)2 + (-12)2

= √169

= 13

Answer:

13

Step-by-step explanation:

We use the distance formula to find the distance between two points

d = sqrt ( (x2-x1)^2 + y2-y1) ^2)

Where ( x1,y1) and ( x2,y2) are the two points

d = sqrt( ( -1 - -6) ^2 + ( -4 - 8) ^2)

   = sqrt ( ( -1+6) ^2 + ( -12) ^2)

  = sqrt( 5^2 + 144)

 = sqrt ( 25+ 144)

 = sqrt ( 169)

 = 13

The the minimum and maximum possible measures of 31 centimeters is {30.5. 31.5}

To find it, one need to add the biggest possible inaccuracy to each measurement, then multiply to get the biggest volume you can. Also Subtract the largest potential mistake from each measurement, then multiply, to to know the smallest volume that can be produced.

Note that the smallest value in the data set is the minimum. The highest value in the data collection is called the maximum.

Since only one data set is given, the  possible measures can only be around it hence the largest and the smallest value close to it.

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Based on the equation, the value of x in 8x^2 + 9 = 313 is 6.2

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

8x^2 + 9 = 313

Subtract 9 from both sides of the quadratic equation

So, we have

8x^2 + 9 - 9 = 313 - 9

Evaluate the difference in the above equation

So, we have

8x^2 = 304

Divide both sides of the quadratic equation by 8

So, we have

8x^2/8 = 304/8

Evaluate the quotient in the above equation

So, we have

x^2 = 38

Take the square root of both sides

x = 6.2

Hence, the value of x in the quadratic equation given as 8x^2 + 9 = 313 is 6.2

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From the graph, we can determine that the function f(x) is quadratic. The function f(x) is defined as:

The graph of (a) 1/2 f(x):

This implies that f(x) is compressed vertically by a factor of 1/2.

Using the points:

(-4, 8) , (-2, 2), (0,0), (2,2), (4, 8)

The graph of the function using a graphing calculator is shown below:

The graph of (b) 2 f(x)

This implies that the original function was stretched vertically by a factor of 2

Using the points:

(-4, 32), (-2, 8), (0,0), (2,8), (4,32)

The graph using a graphing calculator is shown below:

The domain:

This is a set of allowable x-values

Using interval notation:

The range:

This is a set of allowable y-values:

Using interval notation:

Answer:

aaaaaaaaaa

Step-by-step explanation:

aaaaaaaa

The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is given by adding the two other ones, we will get:

862x^2 + 93x + 24,621

Here we have two polynomials:

Both of these are in gigawatts, so are in the same units, which means that we can directly add the two polynomials to get a polynomial for the total electricity.

-17x^2 + 165x + 14,481 + 879x^2 - 72x + 10,140

Now we group like terms:

(-17x^2 + 879x^2) + (165x - 72x) + (14,481 + 10,140)

862x^2 + 93x + 24,621

This polynomial represents the total electricity generated during 2002-2007

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3y - y= -5

2y= -5

y= -5/2

y= -2.5

rounded of answer is 3

The probability of getting 12 p events is 0.0139

The expected value, or mean, of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of successes (p), or n x p.

The binomial distribution formula is calculated as:

[tex]P(x:n,p) = ^nC_x * p^x*(1-p)^ {n-x}[/tex]

where:

n is the number of trials (occurrences)

X is the number of successful trials

p is probability of success in a single trial

is the combination of n and x. A combination is the number of ways to choose a sample of x elements from a set of n distinct objects where order does not matter and replacements are not allowed.

So, we have given that N = 15, P = 0.50 , and x = 12

So,

[tex]^{15}C_1_2 * (0.50)^{12}*(1-0.50)^ {15-12}\\^{15}C_1_2 * 0.50^{12}*(0.50)^ {3}\\[/tex]

=0.0139

Therefore, the probability of getting exactly 12 P events is 0.0139

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The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be 5/11.

It should be noted that probability simply means the likelihood that a particular event will happen.

In this case, there are there are 5 Democrats and 6 Republicans and rour of these people will be randomly chosen for early release.

The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be:

Number of Democrats = 5

Number of Republicans = 6

Total number = 5 + 6 = 11

This will be illustrated through the combination formula:

= (5C2 × 6C2) / 11C4

= (10 × 15) / 330

= 150/330

= 5/11

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Step 1 of the solution:

Let the parent function of the absolute value function is f(x) = |x|

Step 2 of the solution:

This function passes through (0, 0) and slope = 1 or -1.

Step 3 of the solution:

After transformation vertex (0, 0) becomes (-2, 3) and a point through which this function passes through is (-1, 0)

Step 4, let's find the slope of the absolute value funtion, this way:

Step 5: Interpretation

Since slope of the absolute value function is less than the parent function: -3 < -1

Therefore, the parent function will be dilated by a scale factor other than 1.

The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called turning point.

A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.

A turning point is a location on a graph where the trend shifts from rising to dropping or from decreasing to increasing (falling to rising). To determine the point, identify the leading term of the polynomial function if the function were enlarged. A polynomial of degree n will have at most n1 turning points. Next, determine the polynomial function's degree.

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$8,125 is the compound interest.

What is compound interest?

P = $6500

R = 25%

T = 1

compound Interest A = P( 1 + r/100)ⁿ

                                   = 6500( 1 + 25/100)¹

                                   = 6500( 5/4)

                                   = 6500 * 5/4

                                   = $8,125

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