if f(x)= -6x+6 then f^-1(x)=

To graph an absolute value function with a given vertex and 'a' value, first plot the vertex. Then use the 'a' value to find and plot other points. Connect the points to create the graph.

To graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½, you first plot the vertex on the graph. This point will be the lowest (if 'a' is positive) or highest (if 'a' is negative) point on the graph. The vertex of the absolute value function is the point of reflection. Next, create a table to find extra points on the graph. Because 'a' is ½, count over 1 and up (or down depending on if 'a' is positive or negative) half the distance. Similarly, count over 2 and up (or down) the distance to find more points. Once you've plotted these points, you'll see the absolute value function starting to take shape. Connect the dots to create the two arms of the absolute value function that point upwards or downwards depending on the value of 'a'. This will result in a 'V' shaped graph if 'a' is positive or an upside-down 'V' shape if 'a' is negative.

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The domain of the function y = ln (-x + 3/2) is all real numbers less than 3/2, represented in interval notation as (-∞, 3/2). This is because the argument of the logarithm must be positive, leading to an inequality that restricts x to be less than 3/2.

The domain of a function refers to the complete set of possible values of the independent variable. For the function y = ln (-x + 3/2), we must consider where the argument of the natural logarithm, -x + 3/2, is greater than zero. This is because the natural logarithm function is defined only for positive arguments.

To find the domain, set the argument of the logarithm function greater than zero: -x + 3/2 > 0. Solving this inequality, we find -x > -3/2, hence x < 3/2. This means that the domain of the function is all real numbers less than 3/2, which can be written in interval notation as (-∞, 3/2).

The domain of a function is the set of all possible input values. In the function y = ln(-x + 3/2), the natural logarithm function is defined only for positive numbers, so to find the domain, we need to identify the values of x that make the argument of the logarithm greater than zero.

Solve for the argument inside the logarithm to be greater than zero: -x + 3/2 > 0

Simplify the inequality to find the valid domain: x < 3/2

Therefore, the domain of the function y = ln(-x + 3/2) is x < 3/2.

An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.

Basing from the graph, we can actually see that the interval is:

10 Fahrenheit degrees

for a, make a dot on the line plot at each of the given lengths

b) there are more fishes greater than 1 1/2

The time required for the principal amount to double is 13 years 10 months and 10 days approx.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The term "compound" is crucial here.

CI Formula. C.I. = Principal (1 + Rate)^time − Principal.

Given, A sum of $5000 is invested at an interest rate of 5% per year.

hence, principle = 5000

Amount = 10000

rate = 5%

let's assume the time is x

Let's solve for time

A(t)= 10000 = 5000* e⁵ˣ/¹⁰⁰

2 = (e)^x/20

taking logs on both sides

ln 2 = x / 20

x = 20 ln2

time required = 20 ln2 = 20 * 0.69 = 13.86

Therefore, To make the amount double at the interest rate of 5% we need time approx 13 years 10 months, and 10 days.

Learn more about compound interest here:

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Answer:

2.1 +2x=7.5

Step-by-step explanation:

a) The probability is approximately 0.9973.

b) The store takes in at most [tex]$\$ 15,600.00$[/tex].

a) To estimate the probability that the store's revenues were at least [tex]$\$9,500$[/tex], we need to find the z-score corresponding to this revenue value and then find the probability associated with that z-score in the standard normal distribution.

First, we calculate the z-score:

[tex]\[ z = \frac{X - \mu}{\sigma} = \frac{9500 - 3200}{2000} = \frac{6300}{2000} = 3.15 \][/tex]

Using a standard normal distribution table or a calculator, we find that the probability corresponding to [tex]$z = 3.15$[/tex] is approximately 0.9987.

So, the estimated probability that the store's revenues were at least [tex]$\$9,500$[/tex] is approximately 0.9987.

b) To find out how much the store takes in on the worst [tex]$10\%$[/tex] of such days, we need to find the revenue value corresponding to the [tex]$90\%$[/tex] percentile of the distribution.

Using the standard normal distribution table or a calculator, we find that the [tex]$90\%$[/tex] percentile corresponds to a z-score of approximately 1.28.

Now, we can find the revenue value:

[tex]\[ X = \mu + z \times \sigma = 3200 + 1.28 \times 2000 = 3200 + 2560 = 5760 \][/tex]

So, on the worst [tex]$10\%$[/tex] of such days, the store takes in at most [tex]$\$5,760.00$[/tex].

The correct question is:

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of [tex]$\$ 32$[/tex] and a standard deviation of [tex]$\$ 20$[/tex]. Suppose the store had 294 customers this Sunday.

a) Estimate the probability that the store's revenues were at least [tex]$\$ 9,500$[/tex].

b) If, on a typical Sunday, the store serves 294 customers, how much does the store take in on the worst [tex]$10 \%$[/tex] of such days?

a) The probability is [tex]$\square$[/tex].

b) The store takes in at most [tex]$\$ \square$[/tex].

Answer:

The correct option is A.

Step-by-step explanation:

Given information: Length of Arc TR is 116° and the measure of ∠WSX is 45°.

According to the angle of Intersecting Secants Theorem,

[tex]\text{Angle of Intersecting Secants}=\frac{1}{2}(\text{Major arc - Minor arc})[/tex]

Using this property we get

[tex]45^{\circ}=\frac{1}{2}(Arc(TR)-Arc(WX))[/tex]

[tex]45^{\circ}=\frac{1}{2}(116^{\circ}-Arc(WX))[/tex]

Multiply 2 on both the sides.

[tex]90^{\circ}=116^{\circ}-Arc(WX)[/tex]

[tex]Arc(WX)=116^{\circ}-90^{\circ}[/tex]

[tex]Arc(WX)=26^{\circ}[/tex]

The measure of arc WX is 26°. Therefore the correct option is A.

The sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].

To find the sum of all 3-digit whole numbers that are divisible by 13, we can use the arithmetic series formula.

1. Identify the first and last 3-digit numbers divisible by 13:

  - The smallest 3-digit number divisible by 13 is 104 (since [tex]\( 13 \times 8 = 104 \)[/tex]).

  - The largest 3-digit number divisible by 13 is 988 (since [tex]\( 13 \times 76 = 988 \)[/tex]).

2. Calculate the number of terms in the series:

  - Use the formula for the number of terms n in an arithmetic sequence:

[tex]\[ n = \frac{\text{last term} - \text{first term}}{\text{common difference}} + 1 \][/tex]

  Here, the common difference d = 13:

[tex]\[ n = \frac{988 - 104}{13} + 1 = \frac{884}{13} + 1 = 68 + 1 = 69 \][/tex]

3. Find the sum of the arithmetic series:

  - The sum [tex]\( S_n \)[/tex] of the first n terms of an arithmetic series is given by:

[tex]\[ S_n = \frac{n}{2} \times (\text{first term} + \text{last term}) \][/tex]

  Substitute the values:

[tex]\[ S_{69} = \frac{69}{2} \times (104 + 988) \][/tex]

  Simplify the calculation:

[tex]\[ S_{69} = \frac{69}{2} \times 1092 = 34.5 \times 1092 = 37674 \][/tex]

Thus, the sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].

0.5x-9 = 4x+5

add 9 to both sides

0.5x = 4x+14

subtract 4x from each side

-3.5x =14

x = 14/*3.5

x = -4

The Correct Answer is A:-5 :)

divide 9 by 1200

9 / 1200 = 0.0075 = 0.75%

Answer:

The new mean height will be greater than 65.4 inches.

Step-by-step explanation:

The mean height of a group of students is 65.4 inches. A student joins the group who is 73 inches tall.

Mean is 65.4 inches

A student joins the group who is 73 inches tall.

73 is greater than the means 64.4 inches

So mean will increase definitely

Mean will vary depends on the total number of students

The new mean height will be greater than 65.4 inches.

Answer with explanation:

Smallest Polygon = Triangle , which has 3 sides

Sum of angles of triangle = 180°→→, Using the angle sum property of triangle.

We can find the Sum of angles of triangle, using the formula

   = (n-2)×180°

  = (3-2)×180°

 = 1 × 180°

 = 180°

A Quadrilateral has four sides.

Sum of angles of Quadrilateral = 360°

Or , using the formula

=(4-2)×180°

=2 × 180°

=360°

For, n sided Polygon

Sum of it's Interior angles = (n-2) × 180°

To prove this, we should divide that polygon into triangles, and multiply number of triangles by angle of 180°.

For, example, Quadrilateral can be divided into two triangles , sum of interior angles of Quadrilateral =2 × 180°=360°

(3^8 *2^-5 *9^0)^-2 *  (2^-2/3^3)^4 * 3^28 =

(6561 * 0.03125 * 1)^-2 * (0.25/27)^4 * 2.287679245x10^13 =

0.0000237881 * 0.00000000073503 * 2.287679245x10^13 =

0.40000008, round to 0.4

Answer:

Area of the triangle will be 162.3 cm²

Step-by-step explanation:

From the figure attached,

In the triangle ABC angle ACB = 23°, side BC = 27.6 cm and hypotenuse AC = 30 cm

Now we have to calculate the area of the given right angle triangle.

Since area of a right angle triangle is represented by

Area = [tex]\frac{1}{2}\times b\times h[/tex]

Where b = adjacent side

h = opposite side

To calculate the opposite side of the triangle we will apply Pythagoras theorem in the ΔABC.

AC² = AB² + BC²

AB² = AC² - BC²

AB² = (30)² - (27.6)²

      = 900 - 761.76

      = 138.24

AB = √138.24

     = 11.76

Area of the triangle = [tex]\frac{1}{2}(AB)(BC)[/tex]

                                 =  [tex]\frac{1}{2}(11.76)(27.6)[/tex]

                                 = 162.28 cm² ≈ 162.3 cm²

3 girls to 5 boys

3+5 =8

120/8 = 15

3 *15 = 45 girls