Evaluate the function f at the indicated value.
3)
6x + 7, if x ≤ 0 f(4)forf(x)= 4-3x,if0 3)
x, if x ≥ 3

The slope of line p is: 3

The slope of line q is: -3.

To find the slope (m) of any given line, what we need is the coordinates of any two points on the given line. The formula to apply to find the slope (m) of the line is given as:

Slope (m) = change in y / change in x = y2 - y1 / x2 - x1.

Slope (m) of line p with points (2, 2) and (0, -4):

Slope (m) of line p = -4 - 2 / 0 - 2 = -6/-2

Slope (m) of line p = 3

Slope (m) of line q with points (0, 2) and (2, -4):

Slope (m) of line q = -4 - 2 / 2 - 0 = -6/2

Slope (m) of line q = -3

Therefore, the slope of line p is: 3

The slope of line q is: -3.

Learn more about the slope of a line on:

https://brainly.com/question/3493733

#SPJ1

The statistical technique used to estimate future values by successive observations of a variable at regular intervals of time that suggest patterns is called trend analysis.

Trend analysis is a statistical technique that helps identify patterns and tendencies in a variable over time. It involves analyzing historical data collected at regular intervals to identify a consistent upward or downward movement in the variable.

By examining the sequential observations of the variable, trend analysis aims to identify the underlying trend or direction in which the variable is moving. This technique is particularly useful when there is a time-dependent relationship in the data, and past observations can provide insights into future values.

Trend analysis typically involves plotting the data points on a time series chart and visually inspecting the pattern. It helps in identifying trends such as upward or downward trends, seasonality, or cyclic patterns. Additionally, mathematical models and statistical methods can be applied to quantify and forecast the future values based on the observed trend.

This statistical technique is widely used in various fields, including finance, economics, marketing, and environmental sciences. It assists in making informed decisions and predictions by understanding the historical behavior of a variable and extrapolating it into the future.

Learn more about: Statistical technique

brainly.com/question/32688529

#SPJ11

Answer:

The answer is 60

Step-by-step explanation

54

55

56

59

60 The middle number

62

65

66

68

Answer:

60

Step-by-step explanation:

"Median in the middle"

put the set of numbers in order from least to greatest. If you end up having an even amount of numbers in the set, you add the two numbers in the middle then divide by 2 to find the median.

54, 55, 56, 59, 60, 62, 65, 66, 68

55, 56, 59, 60, 62, 65, 66

56, 59, 60, 62, 65

59, 60, 62

60

Answer:

b dhrjdhfjrjribdhdjdiekw

Answer:

X= -5

y= -9

Step-by-step explanation:

7x -4y = 1

4(5x -y = -16)

(7x - 4y = 1) - (20x -4y = -64)

X= -5

y= -9

Answer:

Step-by-step explanation:

2\

Answer:

Solution Given:

C is the interest point of AD and EB.

AC ≅ EC and ∠A ≅ ∠E

To prove:

AB ≅ ED

Proof:

In ∆ABC and ∆EDC

∠BAC= ∠CED Given

AC = CE Given

∠ACB= ∠ECD Vertically opposite angle

∆ABC ≅ ∆EDC By ASA axiom

Therefore,

AB ≅ ED

Since the corresponding side and corresponding angle of a congruent triangles are congruent or equal.

Hence Proved:

Refer to the attachment! v

As per the above given question the reflection of m∠O=112°.

A process of introspection or self-examination is reflection. It entails reflecting critically on one's thoughts, feelings, and experiences in order to comprehend oneself better. Self-awareness and insight can be developed through reflection, which can result in personal development and change.

In a larger sense, reflection also refers to the bouncing back of light, sound, or other waves from a surface and is employed in many disciplines, including arithmetic, computer science, and optics. The capacity of a computer program to review and alter its own structure and behavior at runtime is known as reflection in computer programming.

According to question:

Here are given m∠G=61 m∠f=7

From angle sum property of triangle, we get in ΔGFA

m∠G+m∠F+m∠O=180°

⇒61+7+m∠O=180

⇒68+m∠O=180

Therefore m∠O=180-68=112

To know more about Reflection visit:

https://brainly.com/question/30270479

#SPJ1

Answer: the width is 8 miles

Step-by-step explanation:

The value of x from given quadrilateral ABCD is 27°.

In the given quadrilateral ABCD, ∠A=3x+5, ∠B=2x+15, ∠C=4x and ∠D=4x-10.

We know that, the sum of interior angles of quadrilateral is 360°.

Here, ∠A+∠B+∠C+∠D=360°

3x+5+2x+15+4x+4x-10=360°

13x+10=360°

13x=350°

x=350/13

x=26.9

x≈27°

Therefore, the value of x from given quadrilateral ABCD is 27°.

Learn more about the quadrilaterals here:

https://brainly.com/question/29934440.

#SPJ1

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

What is a Normal distribution in statistics?

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.

Given data:

X: height of seaweed.

       X~N (μ;σ²)

       μ= 10 cm

       σ= 2 cm

We have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

              P(X ≤ x) = 0.30

              P(X ≥ x) = 0.70

Now by using the standard normal distribution,

we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula

        Z = (X - μ)/σ

translates the Z value to the corresponding X value.

           P(Z ≤ z) = 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

                  z= -0.52

Now you have to clear the value of X:

        Z= (X - μ)/σ

        X= (Z * σ) + μ

       X = (-0.52 * 2) + 10

         = 8.96

hence, the value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

To learn more about normal distribution, visit:

brainly.com/question/23418254

#SPJ4

#a

\(\\ \rm\Rrightarrow f(-4)\)

\(\\ \rm\Rrightarrow 3(-4)+2\)

\(\\ \rm\Rrightarrow -12+2\)

\(\\ \rm\Rrightarrow -10\)

#b

#1

\(\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}\)

Find y

\(\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}\)

Inverse is

\(\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}\)

#2

\(\\ \rm\Rrightarrow gof(x)\)

\(\\ \rm\Rrightarrow g(f(x))\)

\(\\ \rm\Rrightarrow g(3x+2)\)

\(\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+3}{3}\)

If we factor out

\(\\ \rm\Rrightarrow \dfrac{2x+1}{1}\)

\(\\ \rm\Rrightarrow 2x+1\)

#c

\(\\ \rm\Rrightarrow f(x)=g(x)\)

\(\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow 3(3x+2)=2x-1\)

\(\\ \rm\Rrightarrow 9x+6=2x-1\)

\(\\ \rm\Rrightarrow 7x=-7\)

\(\\ \rm\Rrightarrow x=-1\)

Answer:

Given functions:

\(f(x)=3x+2\)

\(g(x)=\left(\dfrac{2x-1}{3}\right)\)

Part (a)

\(\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}\)

Part (b)(i)

\(\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}\)

Part (b)(ii)

\(\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}\)

Part (c)

\(\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}\)

Given the expression that models the tip amount for a total bill of $102:

You know that "x" represents the dollar amount of the tax.

You also know that Mr. Jaxon tips $23.50.

Therefore, knowing all that information, you can set up the following equation to represent that situation:

Now you have to solve for "x" in order to find its value:

Hence, the answer is:

Answer:

$1920

Step-by-step explanation:

Simple interest = principal x time x interest rate

8000 x 0.06 x 4 = $1920

There were a total of 3 and 1/4 pizzas, and 5 students each ate 1/4 of a pizza for lunch, so the total amount of pizza eaten was 5 * 1/4 = 5/4 pizzas.

The amount of pizza remaining after the 5 students ate is equal to the original amount minus the amount eaten, which is 3 and 1/4 - 5/4 = 2 pizzas.

To find the amount of pizza remaining after the 5 students ate, we first multiply the number of students by the amount each student ate to find the total amount of pizza eaten. In this case, 5 students each ate 1/4 of a pizza, so the total amount of pizza eaten was 5 * 1/4 = 5/4 pizzas. Next, we subtract this amount from the original amount of pizza to find the amount remaining.

The original amount was 3 and 1/4 pizzas, so the amount remaining after the students ate is 3 and 1/4 - 5/4 = 2 pizzas. This means that there are 2 whole pizzas remaining after the students ate.

Learn more about Simple Maths:

https://brainly.com/question/13442477

#SPJ4

Answer:

20

Step-by-step explanation:

length x width = area

4 x 5 = 20

(not 100% sure, but I hope this helps)

Answer:

The million dollar cube will be 10.79 cm tall

Step-by-step explanation:

Let the sides of the gold cube representing the tallness of the cube  be s

volume of the gold cube V = s³

Then :

\(\mathbf{s = \sqrt[3]{V} }\)  --- (1)

Similarly; we know that , density ρ = mass m/Volume V

making volume the subject of the formula, then ;

V = m/ρ

Replacing that into (1) above , we have:

\(\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }\)

Given that:

At the time, gold is selling for $1282 per troy ounce

∴ In a million-dollar cube of gold, the number of troy ounce that can be bought with a million dollar = 1000000/1282 = 780.03 troy ounce

Since 1.0000 troy ounce equals 31.1035 g

∴ 780.03 troy ounce = 780.03  × 31.1035 g

= 24261.66 g

From the tables 12.1 of Gold , the density of Gold is obtained as 19.3 g/cm³

∴

\(\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }\)

\(\mathbf{s = \sqrt[3]{\dfrac{24261.66}{19.3}} }\)

\(\mathbf{s = \sqrt[3]{1257.080829} }\)

\(\mathbf{s = 10.79 \ cm }}\)

The million dollar cube will be 10.79 cm tall

To find the vertex of a parabola with its focus at (1, 8) and directrix y = -2, you need to calculate the midpoint between the focus and directrix. This midpoint will be the vertex of the parabola.

The vertex is at (1, 3).

Step 1: Determine the coordinates of a point on the directrix. Since the directrix has the equation y = -2, we can choose any x-value for a point on the directrix. Let's choose x = 1. This gives us a point on the directrix, which is (1, -2).

Step 2: Find the midpoint between the focus and the point on the directrix. The midpoint formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Using the focus (1, 8) and the point on the directrix (1, -2), plug in the values:
Midpoint = ((1 + 1)/2, (8 + (-2))/2)

Step 3: Calculate the midpoint:
Midpoint = (2/2, 6/2) = (1, 3)

So, the vertex of the parabola is at the point (1, 3).

Know more about parabola click here:

https://brainly.com/question/31142122

#SPJ11

The angle ∠2 is a vertically opposite angle to the angle 145°, so they are congruent:

∠2 = 145°

The angles 1 and 3 are supplementary angles to the angle 145°, so they are equal to:

180° - 145° = 35°

∠1 = 35°

∠3 = 35°

The angle 8 is a corresponding angle to the angle 145°, so they are congruent:

∠8 = 145°

The angle ∠6 is a vertically opposite angle to the angle ∠8 so they are congruent:

∠6 = 145°

The angles 5 and 7 are supplementary angles to the angle ∠8, so they are equal to:

180° - 145° = 35°

∠5 = 35°

∠7 = 35°

If your opponent goes first, you are guaranteed to win with 8 gems if

your opponent takes 1, 2, or 3 gems on their first turn.

In general, if there are n gems, you can guarantee a win if your opponent

takes n/2 or fewer gems on their first turn when you go second.

Let's consider the starting configuration of gems with 8 gems total.

If you go first, the maximum number of gems you can take on your first

turn is 4 (either 4 diamonds or 4 rubies or 2 of each).

If you take 4 diamonds, your opponent can take all 4 rubies, leaving you

with no choice but to take the remaining 4 diamonds on your next turn,

which means your opponent will take the last 4 rubies and win. Similarly,

if you take 4 rubies on your first turn, your opponent can take all 4

diamonds and win.

If you take 2 diamonds and 2 rubies on your first turn, your opponent can

mirror your move and take 2 diamonds and 2 rubies, leaving you with 2

diamonds and 2 rubies left. At this point, no matter what you do, your

opponent can take the remaining gems and win.

So, if you go first, there is no way to guarantee a win with 8 gems.

Now let's consider the case where your opponent goes first. If your

opponent takes 1, 2, or 3 gems on their first turn, you can mirror their

move and take the same number of gems, leaving 4, 5, or 6 gems left

respectively.

At this point, no matter what your opponent does, you can take enough

gems to ensure that you take the last gem and win. For example, if there

are 4 gems left, you can take 2 diamonds (or 2 rubies) to leave 2 gems,

and then take the remaining 2 gems on your next turn. Similarly, if there

are 5 gems left, you can take 1 diamond and 1 ruby to leave 3 gems, and

then take the remaining 3 gems on your next turn. And if there are 6

gems left, you can take 2 diamonds and 2 rubies to leave 2 gems, and

then take the remaining 2 gems on your next turn.

for such more questions on maximum number

https://brainly.com/question/29795588

#SPJ11

Answer:

i think it is d

Step-by-step explanation:

Robbie’s brother has 12 baseball cards.

How do I solve for x in equation?

Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let x be the baseball Card that Robbie brother has.

Then Robbie has 12x baseball cards.

According to question,

12x= 144

x= \(\frac{144}{12}\)

x= 12

So, Robbie brother has 12 baseball cards

To know more about solve for x in equation:

brainly.com/question/18067015

#SPJ1

Answer:

30

Step-by-step explanation:

the street and the diameter of the bike are not measured in the same units. We have to convert them to the same units

1 feet = 12 inches

157 x 12 = 1884

circumference of a circle = 2nr

2 x 3.14 x 10 = 62.8 in

Number of revolutions = 1884/62.8 = 30

The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:

Step 1: Calculate the amount of discount = Regular Price × Discount rate

Discount rate = 35/100

Simplifying the value we have:

Discount rate = 0.35

Amount of discount = 91 × 0.35

Amount of discount = $31.85

Step 2: Calculate the sale price

Sale price = Regular price − Amount of discount

Sale price = $91 − $31.85

Sale price = $59.15

Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

Learn more about percentage here:

https://brainly.com/question/29763752

#SPJ11

Molly conjectured that for any number x greater than 0, x^3 is always greater than 3x^3. However, we need to find a counterexample that disproves her conjecture. We can test the given values -5, 0, 2, and 10 to see if any of them satisfy the inequality.

To determine a counterexample, we substitute the values -5, 0, 2, and 10 into the inequality x^3 > 3x and check if the inequality holds true for any of them.

For -5, we have (-5)^3 = -125 and 3(-5) = -15. Since -125 is not greater than -15, -5 is not a counterexample.

For 0, we have 0^3 = 0 and 3(0) = 0. Since 0 is not greater than 0, 0 is not a counterexample.

For 2, we have 2^3 = 8 and 3(2) = 6. Since 8 is greater than 6, 2 is not a counterexample.

For 10, we have 10^3 = 1000 and 3(10) = 30. Since 1000 is greater than 30, 10 is a counterexample.

Therefore, the value 10 is a counterexample to Molly's conjecture, as it satisfies the inequality x^3 > 3x.

Learn more about conjectured  here : brainly.com/question/29381242

#SPJ11

Answer:

false

Step-by-step explanation:

False.

Access supports a wide range of built-in functions and operators that can be used to create calculated fields. These functions and operators include mathematical functions (such as multiplication, division, exponentiation), string functions (such as concatenation, trimming, and formatting), date and time functions, aggregate functions (such as sum, average, count), and more.

In addition, Access also allows you to create user-defined functions using VBA (Visual Basic for Applications), which can be used to perform custom calculations on your data.

Therefore, the statement "the only calculated fields you can create in Access are those involving addition and subtraction" is false.

learn more about 'function'

#SPJ11

The product Sc will be an m x r matrix times an r x r diagonal matrix, which gives an m x r matrix as the result. Therefore, Sc is an rxr-matrix.

True.

If A has rank r, then we can find r linearly independent columns in A. Let these columns be denoted as\(a_1, a_2, ..., a_r.\) Then, we can express any other column in A as a linear combination of these r columns. Let's call the coefficients in this linear combination \(c_1, c_2, ..., c_r\). Then, we can write:

\(A = c_1 * a_1 + c_2 * a_2 + ... + c_r * a_r\)

Each of the terms on the right-hand side is a rank 1 matrix, and there are r of them, so A can indeed be written as the sum of r rank 1 matrix.

For the second question, the answer is: Sc is an rxr-matrix.

Since A has rank r, its compact SVD UV will have U as an m x r matrix, V as an n x r matrix, and S as an r x r diagonal matrix. So, the product Sc will be an m x r matrix times an r x r diagonal matrix, which gives an m x r matrix as the result. Therefore, Sc is an rxr-matrix.

learn more about linear combination

https://brainly.com/question/30888143

#SPJ11