Graph the function f(x)=1/2(2)^x on the coordinate plane.

Since the center of the circle lies on the y-axis, the x-coordinate of the center must be 0.

Also, since the diameter of the circle is 12 units, the radius is half of that, or 6 units.

Using the standard form of the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, we can substitute the values we know and simplify the equations to see which ones match.

The equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:

   x^2 + (y - 6)^2 = 36 (center is at (0, 6))

   x^2 + (y + 6)^2 = 36 (center is at (0, -6))

Therefore, the two options that represent the circles with the given properties are:

x^2 + (y - 6)^2 = 36 and x^2 + (y + 6)^2 = 36.

Answer:

Step-by-step explanation:

the range would be the answer as it shows the top and the bottom score.

The function is increasing on (4, 6).

The function is decreasing on (- 6, - 2).

The function is constant on (-2, 4).

The domain of the function is, (- 6, 6).

The range of the function is, (- 3, 1).

A function f(x) is said to be increasing if the increase in the independent variable results in an increase in the dependent variable.

A function f(x) is said to be increasing if the increase in the independent variable results in a decrease in the dependent variable.

The function is increasing on the intervals (4, 6).

The function is decreasing on the interval (- 6, - 2).

The function is constant on the interval (-2, 4).

The domain of the function is, (- 6, 6).

The range of the function is, (- 3, 1).

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Step-by-step explanation:

To calculate the future value of a loan with simple interest, we can use the formula:

A = P(1 + rt)

where A is the future value or total amount due, P is the principal, r is the interest rate, and t is the time period in years.

In this case, we have:

P = $1000

r = 5.0% = 0.05 (expressed as a decimal)

t = 6 months = 0.5 years (since there are 12 months in a year)

Plugging these values into the formula, we get:

A = $1000(1 + 0.05 x 0.5)

A = $1000(1.025)

A = $1025

Therefore, the future value or total amount due on the loan after 6 months is $1025.

Answer: To simplify the expression, we can apply the exponent rule for powers of powers which states that to raise a power to another power, we multiply the exponents.

So,

(4a^(-2))^(-1/2) = 4a^(-2 * (-1/2)) = 4a^(1) = 4a

Therefore, (4a^-2)^-1/2 simplifies to 4a.

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer:

2(x+3)

Step by Step:

2(x)=2x

2(3)=6

2x+6=2(x+3)

2(x)+2(3) =2 (x+3)

The value of f(g(2)) from the given table is -6.

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. Expressions of well-known functions can be found in many frequently used mathematical formulas. For instance, the calculation for a circle's area

Given that,

x –5 –4 –1 2 4 7

f (x) 0 2 7 –1 –6 –4

g(x) –8 –1 2 4 7 1

The value of g(2) = 4

The value of f(g(2)) = f(4) = -6

Hence, the value of f(g(2)) from the given table is -6.

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What is Function?

Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.

How to determine

Where F(x) = 2x^4 + x^2 - 10x + 1

So, to calculate f(-10)

f(x) = y

Where x = -10

f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1

f(-10) = 2(10000) + 100 + 100 + 1

f(-10) = 20000 + 100 + 100 + 1

f(-10) = 20201

For f(2),

f(x) = y

Where x = 2

f(2) = 2(2)^4 +2^2 -10(2) + 1

f(2) = 2(16) + 4 -20 + 1

f(2) = 32 + 4 -20 + 1

f(2) = 17

For f(3)

f(x) = y

Where x = 3

f(3) = 2(3)^4 + 3^2 -10(3) + 1

f(3) = 2(81) + 9 -30 + 1

f(3) = 162 + 9 - 30 + 1

f(3) = 142

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The system of linear equation has infinitely number of solutions

The collection of all ordered pairs that concurrently fulfill both equations makes up the graph of a system of linear equations. It is the collection of all points that are the solutions to both equations, in other words.

The system of linear equations in this issue is stated as

y = 1/2x + 3...eq(i)

2y = x + 6...eq (ii)

The graph demonstrates that the system has an infinite number of solutions and that both lines cross one another. This demonstrates that the system is intractable.

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Since the electorate have decided that Senator Wiggins is the best candidate for the position. The  logical form of this argument is option b. Disjunctive Syllogism

The argument is presented in the form of a disjunctive syllogism, which involves a logical form that states that either one of two alternatives must be true, and one of them has been found to be true; therefore, the other must be false.

In this case, the two alternatives are:

Thus, the logical form of the argument is:

Either A or B.

Not A.

Therefore, B.

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The cash discount is $353.20 and the net amount due is $17,306.80.

Conditions of sale are the rules that govern a business transaction, including the cost, the method of payment, the delivery, and any other pertinent information. Normally, they are specified in a sales contract or invoice and acknowledged in advance of the transaction. The conditions of sale might alter based on the type of products or services being exchanged, the volume and complexity of the deal, and other elements.

We know that,

Cash discount = amount x discount rate

Net amount due = amount - cash discount

For 2/10:

Cash discount = $17,660 x 2% = $353.20

Net amount due = $17,660 - $353.20 = $17,306.80

Hence, the cash discount is $353.20 and the net amount due is $17,306.80.

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The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x with a horizontal shift of 2 units to the right, a vertical stretch by a factor of 3, and a vertical shift of 5 units up.

The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x.

Here are the transformations that were applied to f(x) to obtain g(x):

1. Horizontal shift: The denominator of f(x) is x, which means that the vertical asymptote is at x = 0. By subtracting 2 from x in the denominator of g(x), we are shifting the vertical asymptote to x = 2. This is a horizontal shift of 2 units to the right.

2. Vertical stretch: The coefficient 3 in front of the fraction means that the function is stretched vertically by a factor of 3 compared to f(x). This means that the distance between the horizontal asymptotes (which are at y = 0 for f(x) and y = 5 for g(x)) is three times larger for g(x) than for f(x).

3. Vertical shift: The constant 5 added to the fraction means that the entire function is shifted vertically by 5 units compared to f(x). This means that the horizontal asymptote of g(x) is at y = 5 instead of y = 0.

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Answer:

Step-by-step explanation:

[tex]A=\pi r^2\\[/tex]

  [tex]=\pi \times 9^2[/tex]   (radius = 9 feet)

  [tex]=81\pi[/tex]

  [tex]\approx 254.47[/tex] feet

Answer:

To find the mean of a set of data, we need to sum up all the values in the set and divide by the number of values.

Sum of the data values = 19 + 23 + 35 + 41 + 42 = 160

Number of data values = 5

Mean = Sum of data values / Number of data values = 160 / 5 = 32

However, we are given that the mean is 36. Since the calculated mean is lower than the given mean, it means that we are missing a value that is higher than the other values in the set.

Let's call this missing value x. Then, we have:

(19 + 23 + 35 + 41 + 42 + x) / 6 = 36

Multiplying both sides by 6, we get:

19 + 23 + 35 + 41 + 42 + x = 216

Simplifying the left-hand side, we get:

160 + x = 216

Subtracting 160 from both sides, we get:

x = 56

Therefore, the missing value is 56, and the complete data set is:

19, 23, 35, 41, 42, 56

Now, we can calculate the mean as:

Mean = (19 + 23 + 35 + 41 + 42 + 56) / 6 = 216 / 6 = 36

So, the mean of the data values is indeed 36.

Answer:

32

Step-by-step explanation:

To find the mean of a set of numbers, we add up all the numbers and then divide by the total number of values.

Adding up the values:

19 + 23 + 35 + 41 + 42 = 160

We have a total of 5 values, so we divide the sum by 5:

160 / 5 = 32

Therefore, the mean of the given data values is 32, not 36.

There are 484 times more red blood cells than white blood cells in a cubic millimeter of blood.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, A lab technician draws a sample of blood.

A cubic millimeter of blood contains 22⁵ red blood cells and 22³ white blood cells.

The number of red blood cells in a cubic millimeter of blood is 22⁵,

and the number of white blood cells in the same volume is 22³.

To find out how many times more red blood cells there are than white blood cells, we need to divide the number of red blood cells by the number of white blood cells:

22⁵ / 22³ = 22⁵⁻³ = 22² = 484

Therefore, there are 484 times more red blood cells than white blood cells in a cubic millimeter of blood.

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Answer: 24 percent of 25 is 6.

Step-by-step explanation: The output of 24 percent of 25 is 6. To obtain this answer, we multiply 0.24 by 25.

Answer:10

Step-by-step explanation:3x2=6 and 4x1=4 4+6=10

Answer:

See below

Step-by-step explanation:

Perimeter = (7x2) + (2x2) = 18

Area (L x W) = Square + rectangle

= (3x2) + (4x1) = 6 + 4 = 10

The answer to the given problem can be stated as, "The quadrilateral is most specifically a square because all of its sides are equal and angles are right angle."

A square is type of rectangle of which all sides are equal.

The diagonals of a square are perpendicular bisector of each other.

The given diagram of the quadrilateral clearly shows the following information,

All the angles of the quadrilateral are equal to right angle,

And, all of its sides are equal.

The given information matches with the property of a square which implies that the given quadrilateral is a square.

Hence, the given quadrilateral is a square.

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Answer:

Step-by-step explanation:

We need to identify the quadrilaterals given in the question.

For first image , we can see that;

These are the properties of rhombus in which all sides and opposite angles are equal.

Hence in the first image quadrilateral is a " Rhombus" .

[tex]\rule{200}2[/tex]

In the second image , the most appropriate option is all sides are equal , as in rhombus all sides are congruent.

Answer:

The answer is $61.32

The simplification value of the expression is,

⇒ 5x³ - 12x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 2x³ - x² + 3 (x³ - 4x²)

Now, We can simplify the expression as;

⇒ 2x³ - x² + 3 (x³ - 4x²)

⇒ 2x³ - x² + 3x³ - 12x²

⇒ 5x³ - 12x²

Thus, The simplification value of the expression is,

⇒ 5x³ - 12x²

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The number of years for 21% to remain is 78years

The time required for half of the original population of radioactive atoms to decay is called the half-life.

half life = 0.693/decay constant

decay constant = 0.693/34

= 0.02

21% of N(o) = 21N(o)/100 = N(y)

from the formula

N(t) = Noe^-kt

21N(o)/100 = Noe^-kt

21N(o)=100 Noe^-kt

divide bother sides by N(o)

21 = 100e^-kt

e^-kt = 21/100

e^-kt = 0.21

-0.02 t= ln0.21

-0.02 t= -1.56t

t = 1.56/0.02

t = 78years

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Therefore , the solution of the given problem of equation comes out to be  y = 6x + 11.

Mathematical formulas frequently use the same letter to try to impose uniformity between two claims. Many variable academic numbers are shown to be equal using mathematical equations, also known as assertions. The normalise divides 12 and b + 6 into two parts using the result y + 6 = 12 as an illustration. It is possible to determine the connection between each sign component and the number of lines. The significance of a symbol usually contradicts itself.

Here,

In slope-intercept form, the provided equation y = -1/6x - 2 has a slope of -1/6. Consequently, this line's perpendicular inclination is as follows:

=> m2 = -(1/-1/6) = 6

Now that we know the desired line's slope and the spot through which it passes (-2, -1). To determine the solution of a linear equation, we can use its point-slope form:

=> y - y1 = m(x - x1) (x - x1)

where m is the slope 6 and (x1, y1) is the position (-2, -1). By replacing these numbers, we obtain:

=> y + 1 = 6(x + 2) y + 1

=> 6x + 12 y + 1

=> 6x + 11 y - (-1)

=> 6(x - (-2))

As a result, the equation for the line passing through the position (-2, -1) and perpendicular to y = -1/6x - 2 is y = 6x + 11.

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Tge coordinates of point c is - 3 and 1

Answer: The fourth vertex is D(8, 0)

Answer:

Let's use algebra to solve this problem:

Let's use the variable "m" to represent the number of markers that Martin has.

We know that Hiro has 4 fewer highlighters than Martin, so we can set up an equation:

18 = m - 4

This equation says that the number of markers Martin has (m) minus 4 is equal to the number of highlighters that Hiro has (18).

To solve for "m", we can add 4 to both sides of the equation:

18 + 4 = m

Simplifying this gives us:

22 = m

So Martin has 22 markers.

Answer:

Step-by-step explanation:

Angle sum of a triangle = 180°. So we get:

[tex]62+69+(4x+5)=180[/tex]

[tex]136+4x=180[/tex]

[tex]4x=44[/tex]

[tex]x=11[/tex]°

Answer:

x = 11

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Accordingly,

62 + 69 + 4x + 5 = 180

Combine like terms.

136 + 4x = 180

Subtract 136 from both sides.

4x = 180 - 136

4x = 44

Divide both sides by 4.

x = 11

let's recall, the x,y pairs are just the cosine,sine pairs.

[tex]\stackrel{ \cos(315^o) ~~ \sin(315^o) }{\left( \cfrac{\sqrt{2}}{2}~~,~-\cfrac{\sqrt{2}}{2} \right)}\hspace{4.5em}\tan(315^o)\implies \cfrac{\sin(315^o)}{\cos(315^o)} \implies \cfrac{ ~~ -\cfrac{\sqrt{2}}{2} ~~ }{\cfrac{\sqrt{2}}{2}}\implies \text{\LARGE -1}[/tex]

The solution of the given equation -4(n+5)=-32 is n=3.

What is equations ?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) between two expressions. The expressions on both sides of the equals sign have the same value. Equations are used to solve problems in mathematics and science.

To solve the equation, we need to isolate the variable n.

-4(n+5) = -32

Distribute -4 on the left side of the equation:

-4n - 20 = -32

Add 20 to both sides of the equation:

-4n = -12

Divide both sides by -4:

n = 3

Therefore, the solution of the given equation -4(n+5)=-32 is n=3.

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The p value is calculated as 0.116

Null u = 70

alternate u ≠ 70

The alternate is a two tailed test

the test statistic calculation

t = x - u / s/√n

x = 85 + 77 + 82 + 68 + 72 + 69 / 6

= 75.5

standard deviation s = [tex]\sqrt{\frac{(85- 75.5)^2+(77- 75.5)^2+...(69- 75.5)^2}{6-1} }[/tex]

= 7.01

Test stat = (75.5 - 70) / 7.01/√6

= 1.92

degree of freedom = 6 - 1 = 5

this is 2 tailed

p value using excel = tdist( 1.8, 5 , 2)

= 0.116

We fail to reject the null hypothesis because it is greater than the level of significance

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