.
An investment pays 14% interest compounded weekly. What percent, as a decimal, is the effective annual yield? Enter your
answer as a decimal rounded to four decimal places.
Provide your answer below:

Answer: [tex](f \cdot g)(x) = x^4-11x^2+30.[/tex]

Step-by-step explanation:

We want to find the value of [tex]f(g(x)).[/tex] To do this, we plug in [tex]g(x)[/tex] into the expression for [tex]f(x).[/tex] This gives us:

[tex]f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.[/tex]

Answer: 6 units

Step-by-step explanation: To find the mass of the lamina, we need to integrate the density function fi(x,y,z) over the volume of the lamina. The lamina is a portion of the cone z=sqrt(x^2+y^2) between the planes z=1 and z=3. We can express this volume using cylindrical coordinates, where rho is the distance from the origin to the point (x,y,z), phi is the angle between the positive x-axis and the line connecting the origin to the point (x,y,z), and z is the height of the point (x,y,z) above the xy-plane.

We have:

1 <= z <= 3

0 <= rho <= 3sin(phi)

0 <= phi <= 2pi

The density function is given by fi(x,y,z) = x^2z. In cylindrical coordinates, we have x = rhocos(phi), y = rhosin(phi), and z = z. Therefore, we can express the density function as:

fi(rho, phi, z) = (rhocos(phi))^2 * z = rho^2cos^2(phi) * z

The mass of the lamina is given by the triple integral of the density function over the volume of the lamina:

M = ∭ fi(rho, phi, z) dV

= ∫∫∫ rho^2cos^2(phi) * z dz dA

= ∫∫[1,3] ∫[0,2pi] ∫[0,3sin(phi)] rho^2cos^2(phi) * z dz d(phi) drho

= ∫[0,2pi] ∫[0,3] ∫[0,rhosin(phi)] rho^2cos^2(phi) * z dz drho d(phi)

= ∫[0,2pi] ∫[0,3] (1/3)rho^3sin(phi)cos^2(phi) d(phi) drho

= ∫[0,2pi] (1/3)[9sin(phi)cos^2(phi)] d(phi)

= (1/3)[9(2/3)]

= 6

Therefore, the mass of the lamina is 6 units.

The given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.

A number's power or exponent, in other words, tells how many times it must be multiplied by itself.

Any integer, fraction, or decimal can serve as the basis in this situation.

Additionally, the exponent might have either a positive or negative value.

Subtract the exponents to divide exponents (or powers) with the same base.

Given that division is the inverse operation of multiplication, it stands to reason that, just as exponents are added when multiplying numbers with the same base, exponents are subtracted when dividing numbers with the same base.

So, we have the exponents as;
9⁻³/9¹²

Then, solve as follows:

9⁻³/9¹²

9⁻³⁻¹²

9⁻¹⁵

Therefore, the given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.

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Answer:

a. 110°

Positive coterminal angles: 110° + 360° = 470°, 110° + 2(360°) = 830°

Negative coterminal angles: 110° - 360° = -250°, 110° - 2(360°) = -610°

b. 165°

Positive coterminal angles: 165° + 360° = 525°, 165° + 2(360°) = 885°

Negative coterminal angles: 165° - 360° = -195°, 165° - 2(360°) = -555°

c. -10°

Positive coterminal angles: -10° + 360° = 350°, -10° + 2(360°) = 710°

Negative coterminal angles: -10° - 360° = -370°, -10° - 2(360°) = -730°

Step-by-step explanation:

When an angle is in the standard position, it means that the initial side of the angle is the positive x-axis, and the terminal side of the angle is located in one of the four quadrants of the coordinate plane.

To find coterminal angles, we need to add or subtract multiples of 360 degrees to the given angle while keeping the terminal side in the same position. This is because a full rotation around the origin in the coordinate plane is 360 degrees.

For positive coterminal angles, we add multiples of 360 degrees to the given angle. In the case of 110 degrees, we can add 360 degrees once or twice to get 470 degrees or 830 degrees, respectively.

For negative coterminal angles, we subtract multiples of 360 degrees from the given angle. In the case of -10 degrees, we can subtract 360 degrees once or twice to get -370 degrees or -730 degrees, respectively.

It's important to note that there are infinitely many coterminal angles for any given angle, but we usually restrict our answers to the smallest positive and negative angles that differ from the given angle by a multiple of 360 degrees.

Answer:

the on side to side is the x axes and the y one is up and down

Step-by-step explanation:

The cube's volume can be expressed as V = s³ = x³ since the height of the cube is x and all sides have equal length. The surface area of the cube can be expressed as SA = 6s² = 6x².

b. The sphere's volume can be expressed as V = (4/3)πr³, where r is half the diameter or x/2. Therefore, V = (4/3)π(x/2)³ = (1/6)πx³.

The surface area of the sphere can be expressed as SA = 4πr² = 4π(x/2)² = πx².

c. The ratio of the cube's volume to its surface area can be expressed as V/SA = (x³)/(6x²) = x/6, with the restriction that x > 0.

d. The ratio of the sphere's volume to its surface area can be expressed as V/SA = [(1/6)πx³]/(πx²) = x/6, with the restriction that x > 0.

e. Since the ratios of the volumes to the surface areas of the containers are the same, the efficiency of the packaging will depend only on the amount of material required for each shape. The cube will require less material since it has a smaller surface area, making it the more efficient choice.

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The equation of exponential function of following table is represented by the table below is y = A(Bˣ).

An exponential function is a mathematical function denoted by f(x) = eˣ (where the argument x is written as an exponent). Unless otherwise stated, the term usually refers to positive-valued functions of real variables, but can be extended to complex numbers and generalized to other mathematical objects such as matrices and Lie algebras. Although the exponential function arose from the notion of exponentiation (iterative multiplication), its modern definition (which has several equivalent characterizations) allows it to be extended exactly to any real argument, including irrational numbers. Its ubiquitous appearance in pure and applied mathematics has led mathematician Walter Rudin to believe that the exponential function is "the most important function in mathematics."

To find the equation of exponential form:

For case 1,

Exponential form: y = A(Bˣ)

y = 0.1, x = 0

[tex]0.1 = A(B^{0})[/tex]

0.1 = A(1)

A = 0.1

For case 2,

Exponential form: y = A(Bˣ)

y = 0.05, x = 1

[tex]0.05 = 0.1(B^{1})[/tex]

B = 0.5

For case 3,

y = 0.025, x = 2

[tex]A = 0.1(B^{2})[/tex]

[tex]0.025 = 0.1(0.5^{2})[/tex]

0.025 = 0.025

For case 4,

y = 0.0125, x = 3

0.0125 = 0.1(0.5³)

0.0125 = 0.1(0.125)

0.0125 = 0.0125

We calculated the value of A and B, and proved it in case 3 and case 4.

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The complete question is as follows:

Find the equation of the exponential function represented by the table below:

The inequality |x + 7| ≥ 2 has the solution set x ≤ –9 or x ≥ –5, as required.

We can write an absolute value inequality with the given solution set as follows:

|x + 7| ≥ 2

Here's how we arrived at this inequality:

First, we find the midpoint of the given solution set:

midpoint = (-9 + (-5)) / 2 = -7

Next, we find the distance from the midpoint to each endpoint of the solution set:

distance to -9 = |-7 - (-9)| = 2

distance to -5 = |-7 - (-5)| = 2

The maximum distance is 2, so we use c = 2 in the inequality.

Since the midpoint is to the left of both endpoints, we use the form |x - b| ≥ c.

Plugging in b = -7 and c = 2, we get:

|x + 7| ≥ 2

This inequality has the solution set x ≤ –9 or x ≥ –5, as required.

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Answer:

40

Step-by-step explanation:

Hope this helps! =D

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The volume of the triangular prism will be 400 cubic feet.

Given that:

Width, W = 15 feet

Height, h = 8 feet

Base length, b = 6²/₃ feet

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The volume of the triangular prism is calculated as,

V = 1/2 · b · h · W

V = 0.5 · 6²/₃ · 8 · 15

V = 400 cubic feet

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To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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A sampling distribution is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population.

To get the possible samples, use the formula "N choose n", where N is the population size, and n is the sample size to be taken. The total probability of the sample mean must be equal to 1.

Since the mean of all possible samples must be equal to the population mean. The sampling distribution is an important concept in statistics as it allows us to make inferences about the population based on the characteristics of the sample, and helps us estimate parameters and test hypotheses.

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Answer:

∠ A = 76°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

9x - 5 - 5 + 6x + 55 = 180

15x + 45 = 180 ( subtract 45 from both sides )

15x = 135 ( divide both sides by 15 )

x = 9

Then

∠ A = 9x - 5 = 9(9) - 5 = 81 - 5 = 76°

Answer:

Angle 1 = 51.6°

Angle 2 = 38.4°

Step-by-step explanation:

All complimentary angles add up to 90°.

If two complimentary angles were congruent then their measures would both be 45°.

Since one angle's measure is 6.6° more than the other's measure, it's measure is 6.6° more than 45°

Vice versa for the second angle, its measure will be 6.6° less than 45°

Answer:

Yes

Step-by-step explanation:

we all know there is 60 minutes in an hour. So in order to answer this question we need to know the percentage of 15 to 60 which is really really just 15/60=0.25 so Henry's answer is correct:
6.25 Hours are 6 hours and 15 minutes

and 0.25 really is just a quarter because 4 x 0.25 = 1 so in fraction it is 1/4 so Jenny is also correct on :

6 1/4 hours are 6 hours and 15 minutes

Answer:

60 seconds

Step-by-step explanation:

Let's start by finding how much more water needs to be added to the solution to reach a total of 10 ml of water:

10 ml - 5.8 ml = 4.2 ml

Now we can use the formula:

time = amount of water added / rate of addition

to calculate the time it will take to add 4.2 ml of water at a rate of 0.07 ml/s:

time = 4.2 ml / 0.07 ml/s

time = 60 seconds (rounded to the nearest second)

Therefore, it will take 60 seconds to add enough water to the solution to make a total of 10 ml of water.

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1. Por lo tanto, la suma de las dos expresiones es 9x² + 5x + 18.

2. Por lo tanto, el resultado de la expresión es -22.

3. Por lo tanto, el resultado de la expresión es 24.

4. Por lo tanto, el valor de x es 3.

5. Por lo tanto, el resultado de la expresión es 45.

1. Para sumar las dos expresiones, simplemente sumamos los términos semejantes:

(4x² + 8x +12) + (5x² − 3x + 6) = 9x² + 5x + 18

Por lo tanto, la suma de las dos expresiones es 9x² + 5x + 18.

2. Evaluando la expresión numérica:

5 - 21 + (-3) (2) = 5 - 21 + (-6)

Luego, sumamos los términos:

= -16 - 6 = -22

Por lo tanto, el resultado de la expresión es -22.

3. Evaluando la expresión numérica:

(-3) (-2) (-1) (4) = 24

Por lo tanto, el resultado de la expresión es 24.

4. Para encontrar el valor de x, debemos despejarlo de la ecuación:

18 + 3x = 27

Restando 18 de ambos lados, obtenemos:

3x = 9

Dividiendo ambos lados por 3, obtenemos:

x = 3

Por lo tanto, el valor de x es 3.

5. Evaluando la expresión numérica:

3² + 4 (3)² = 3² + 4 (9)

Primero elevamos al cuadrado 3, luego multiplicamos 4 por 9 y sumamos ambos términos:

= 9 + 36

Por lo tanto, el resultado de la expresión es 45.

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Answer:

Part a 6 and 9

Step-by-step explanation:

Part B is 7.3 because u just find the sq root of 54 which can't go down the easiest is finding the decimal form

Johannes will need to pay $8.61 for 5 pounds of ground beef

Since Johannes needs 5 pounds of ground beef, and the available pounds are 1.5, 2, 3, and 3.75 pounds.

To reduce the cost, he need to select the package with the lowest cost per pound.

The cost per pound for each package is:

Package 1: $5.58 / 1.5

              = $3.72 per pound

Package 2: $7.44 / 2

              = $3.72 per pound

Package 3: $1.16 / 3

              = $0.39 per pound

Package 4: $13.95 / 3.75

                = $3.72 per pound

Therefore, the package with the lowest cost per pound is Package 3 and package 2  which will give us 5 pounds

So he can do it as:

$1.16 + $7.44

= $8.6

Or

(1 package of 3 pounds x $0.39 per pound) + (1 package of 2 pounds x $3.72 per pound)

= $1.17 + $7.44

= $8.61

Therefore, Johannes will need to pay $8.61 for 5 pounds of ground beef.

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The graph of the piecewise function can be seen in the image attached below where (x+2)² terminates at x = -1,  |x - 1| between the interval of x = -1 to x = 1, and  [tex]-\sqrt[3]{x}[/tex] from +x-axis to infinity [tex]\infty[/tex]

A piecewise function is a type of function that has different expressions or formulas for different parts or intervals of its domain. This means that the formula that defines the function changes depending on which part of the domain we are looking at.

Now, to graph the piecewise function, we need to start by identifying the different intervals on which the function is defined and the corresponding expressions that define the function on each interval.

If we have a piecewise function f(x) defined as:

The graph of the piecewise function can be seen in the image attached below.

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The answer is Option 2: The measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.

An angle that, when combined with another angle, creates a straight angle (measuring 180 degrees), is known as a supplementary angle. In other words, if the sum of the measurements of two angles is 180 degrees, they are supplementary. Contrarily, a complimentary angle is one that, when combined with another angle, creates a right angle (which has a 90-degree angle). In other words, if the sum of the measurements of two angles is 90 degrees, they are complimentary. A straight angle and a right angle are not the same thing, hence it is crucial to understand that one angle cannot be both supplementary and complimentary at the same time.

From the given figure we see that the measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.

Hence, option 2 is correct.

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The complete question is:

Answer:

Step-by-step explanation:

Okay but seriously though, you would have to write the whole question down.

Since p and q are real numbers, the value of q is 21.

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 8x - 5 = 0

x² - 8x = 5

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 8x + (-8/2)² = 5 + (-8/2)²

x² - 8x + 16 = 5 + 16

x² - 8x + 16 = 21

By simplifying, we have;

(x - 4)² = 21

p = 4 and q = 21

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The formula for the nth term of the arithmetic sequence is an = 4n + 2

Let d be the common difference of the arithmetic sequence, and let a1 be the first term. Then we have:

a4 = a1 + 3d = 10

a6 = a1 + 5d = 18

We can solve this system of equations to find a1 and d. Subtracting the first equation from the second, we get:

2d = 8

d = 4

Substituting this into either of the original equations, we get:

a1 + 12 = 18

a1 = 6.

So the arithmetic sequence is:

6, 10, 14, 18, ...

To find the nth term of this sequence, we can use the formula:

an = a1 + (n - 1)d

Substituting in the values of a1 and d, we get:

an = 6 + 4(n - 1)

Simplifying, we get:

an = 4n + 2

Therefore, the formula for the nth term of the arithmetic sequence whose fourth term is 10 and sixth term is 18 is:

an = 4n + 2

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Start at -2 on the number line and move 7 to the left.

A number line is a visual representation of the real numbers as a straight line. It is a useful tool for understanding and comparing numbers, as well as for performing operations on them.

The number line is typically drawn horizontally, with zero in the center and positive numbers to the right of zero and negative numbers to the left of zero. The distance between any two points on the number line represents the difference between the corresponding numbers.

The number line is also commonly used for representing fractions, decimals, and irrational numbers. For example, fractions can be represented as points on the number line by dividing the line into equal segments, with each segment representing one unit fraction. Decimals can be represented as points on the number line by marking off the appropriate place value.

In addition to basic arithmetic operations such as addition, subtraction, multiplication, and division, the number line can be used to perform more advanced operations such as finding absolute value, calculating distance between two points, and solving linear equations.

Overall, the number line is a powerful visual tool that helps to deepen our understanding of the real numbers and their relationships.

Start at -2 on the number line and move 7 to the left.

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The complete question is:

The equation for the best fit of the scatter plot is y = x - 3

What is the scatter plot?

In a scatter plot, dots are used to represent the values of two different numerical variables. The values of each data point are represented by the position of each dot on the horizontal and vertical axes. Use scatter plots to see how different variables are related to one another.

Given data,

Let the scatter plot be represented as A

Now, the value of A is plotted below

where the slope of the plot is given by

m = y / x

m = 1

And, the y-intercept of the plot is when x = 0

So , when x = 0 , y = -3

Hence, the scatter plot is y = x - 3

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