Evaluate the function.
f(x) = -3x2 – 20
Find f(-9)

By using the concept of Compound interest, Number of payment periods in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = 12

What is Compound interest?

The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

This problem can be solved by using the concept of compound interest

Number of  payment periods are in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = \(6 \times 2 = 12\)

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We apply the pythagorean theorem to find this answer.

a = 11 and b = 6 are the given legs

c = unknown hypotenuse

So,

a^2+b^2 = c^2

c = sqrt( a^2+b^2 )

c = sqrt( 11^2 + 6^2 )

c = sqrt( 121 + 36 )

c = sqrt( 157 )

c = 12.52996 approximately

c = 12.5

Side note: once you replace 'a' and b with 11 and 6, you can compute everything with a calculator in one single step more or less. The steps above are shown if you wanted to find the exact value sqrt(157).

Answer:

Good luck with math

The sum of the numbers is  (2x + z) + (2y + 10)i. If the difference of two complex number is -10i and the product is 34.

Let the two complex numbers be x + yi and z + wi, where x, y, z and w are real numbers.

We are given that their product is 34, thus

(x + yi) (z + wi) = 34

z(x + yi) + wi(x + yi) = 34 + 0i_____(1)

We are also given that their difference is -10i, thus

(x + yi) - (z + wi) = -10i

(x - z) + (y - w)i = 0 - 10i_____(2)

Simplifying equation (2), we get

x - z = 0 and y - w = -10

We are asked to find the sum of the numbers, thus

(x + yi) + (z + wi) = 2x + 2yi___(3)

We can simplify equation (1) as follows:

34z + wi = 34x + 34yi - wi - yi

We can substitute equation (2) into the above equation:

34z + wi = 34x + 34yi + yi - 10i

We can further simplify the above equation as:

34z + wi = 34x + 35yi - 10i

We can then use the fact that x - z = 0 to express one variable in terms of the other.

Solving for w in equation (2), we get:

w = y + 10

Thus, we can substitute w = y + 10 into equation (3) and simplify as follows:

(x + yi) + (z + (y + 10)i)

= 2x + 2yi + z + 10i

= (2x + z) + (2y + 10)i

The sum of the numbers is thus (2x + z) + (2y + 10)i.

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Answer:

X=2

Step-by-step explanation:

Answer:

82%

Step-by-step explanation:

Answer:

B

Step to Step Explaintion:

Answer:

Step-by-step explanation:

Simplifying

12y + 2x = 24

Reorder the terms:

2x + 12y = 24

Solving

2x + 12y = 24

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12y' to each side of the equation.

2x + 12y + -12y = 24 + -12y

Combine like terms: 12y + -12y = 0

2x + 0 = 24 + -12y

2x = 24 + -12y

Divide each side by '2'.

x = 12 + -6y

Simplifying

x = 12 + -6y

La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.

Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:

Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:

Nota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:

Opciones:

A. Multiplicar (6)(4)

B. Multiplicar (7.5)(4.5)

C. Multiplicar (9)(6)

D. Multiplicar (9.5)(4.5)

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Answer: $180

Step-by-step explanation: you first divide $240 by 20 to get 12 so you multiply 12 and 15 together to get $180

The margin of error (E) at 95% confidence for estimating μ with n = 66, mean = 1.72 oz, and σ = 0.66 oz is approximately 0.15 oz.

To calculate the margin of error (E) for estimating the population means (μ) at a 95% confidence level, we use the formula: E = Z * (σ / √n), where Z is the critical value corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Given n = 66, mean = 1.72 ounces, and σ = 0.66 ounces, we need to find the critical value Z for a 95% confidence level. The Z-value for a 95% confidence level is approximately 1.96.

Plugging in the values, we get E = 1.96 * (0.66 / √66). After evaluating the expression, the margin of error (E) is approximately 0.15 ounces when rounded to two decimal places. This means that we can expect the true population mean to be within 0.15 ounces of the estimated mean at a 95% confidence level.

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Yes. \(f(x)\) is a PDF if

• \(f(x) \ge 0\) for all \(x\) in the support; this is true, since \(e^{-x}>0\) for all \(x\), and multiplying a positive number \(x\) doesn't change this fact;

• the integral of \(f(x)\) over its support is 1; this is also true, since

\(\displaystyle \int_{-\infty}^\infty f(x) \, dx = \int_0^\infty xe^{-x} \, dx = 1\)

which can be computed by parts.

The equivalent equation in standard form is \(Y = ax^2 - 2ahx + ah^2 + k\)

The formula \(Y=a(x-h)^2+ k\) is a quadratic function in vertex form, where (h,k) is the vertex of the parabola.

Now, to rewrite this formula in standard form, which is the form \(ax^2 + bx + c\), we can expand the square and simplify:

\(Y = a(x-h)^2 + k\\Y = a(x^2 - 2hx + h^2) + k\\Y = ax^2 - 2ahx + ah^2 + k\)

where a, b, and c are:

a = a

b = -2ah

c = \(ah^2\) + k

Therefore, the equivalent equation in standard form is:\(Y = ax^2 - 2ahx + ah^2 + k\)

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Answer: R=5 D=10

Step-by-step explanation: If I am correct the radius is 5 while the diameter is 10. All you need to do is subtract 7 by 2 ( from the coordinates) giving you five. Now if you multiply 5 by 2 you get 10 which is the diameter. Hope this helps and best of luck.

The THREE true statements regarding the graph of B(w) are;

A) Based on the zeros of the function, the number of boxes of cereal sold is 0 after 0 weeks.

C) Based on the end behavior of the function, the number of boxes of cereal sold will keep falling after reaching the maximum.

E) Based on the asymptote of the function, the number of boxes of cereal sold will never reach 0 after the cereal is introduced in the store.

We are given the graph represented by the quadratic function;

B(w) = 120w/(150 + w²) for w ≥ 0 that models;

the number of boxes, B, in thousands, of the cereal sold after w weeks

From the graph, we can see that at the origin which is the coordinate (0, 0) that it remains so and as such the number of boxes of cereal sold is 0 after 0 weeks. Thus, option A is correct

Secondly, from the given graph, we see that the graph starts rising from zero to a maximum after which it keeps falling. Thus, we can say that option C is correct

Lastly, we see that the graph asymptote approaches 500 thousand boxes but never gets to zero and as such we can say that option E is correct.

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Taking onto account the definition of density, the apparent density of the unknown material is 0.894 g/mL.

The apparent density of a material or a body is the ratio between the volume and the dry weight, including voids and pores that it contains.

In other words, apparent density is defined as the mass of many particles of the material divided by the total volume they occupy, which includes the volume of particles, the void volume between particles, and the internal pore volume.

Apparent density is not an intrinsic property of a material, that is, it can change depending on how the material is handled.

The expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

density= mass÷  volume

In this case, a 112.6 g mass of unknown material is submerged in 102 mL of water to yield a final volume of 126 mL. This is, you know:

Replacing in the definition of apparent density:

density= 112.6 g÷  126 mL

density= 0.894 g/mL

Finally, the apparent density of the unknown material is 0.894 g/mL.

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Answer:

\(y=\frac{7}{3}-\frac{2}{3}x\)

Step-by-step explanation:

To solve for y, we will have to get y by itself on one side of the equation, with all of the other variables and values on the other side.

2x + 3y = 7

Subtract 2x to both sides of the equation.

3y = 7 - 2x

Divide both sides by 3.

\(y=\frac{7}{3}-\frac{2}{3}x\)

And now we have solved for y.

I hope you find my answer helpful.

Answer:

It depends what you are comparing that height to, but in general 0.5 meters is low.

Answer:

No

Step-by-step explanation:

Answer:

0 cannot go into 4

4 can go into 8

8 cannot go into 12

Answer:

1

Step-by-step explanation:

Answer:

1 is the slope

Step-by-step explanation:

Answer:

60 grams brudda

Step-by-step explanation:

Answer:6

Step-by-step explanation:If jayden made 5% of his free throws and he shot 120 free throws you have to find 5% of 120.

5% of 120 = 6  

So Jayden shot a total of 6 free throws during the season

The sample mean is -0.0417 standard deviations from the population mean.

Standard deviation is a measure of the dispersion or spread of a set of data.

The mean, also known as the arithmetic mean or average, is a measure of the central tendency of a dataset.

(sample mean - population mean) / standard deviation

Plugging in the values from the problem, we get:

(245.05 - 246) / 3.60 = -0.15 / 3.60 = -0.0417

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The Emma sold 5 T-shirts.

The function that expresses the sales of Emma is given as:I = 100 + 12J + 5T + 7S + 5H - 8M

where;I represents the amount of income earned by Emma.J represents the number of jeans sold by Emma.T represents the number of T-shirts sold by Emma.S represents the number of shorts sold by Emma.H represents the number of hats sold by Emma.

M represents the number of meals bought by Emma.Emma earned $205 in a week.Emma sold 6 pairs of jeans, 4 shorts, and 5 hats.She bought 5 of her meals.Hence, using the formula for Emma's income given above,I = 100 + 12J + 5T + 7S + 5H - 8M,

we can substitute the values and obtain the following equation:205 = 100 + 12(6) + 5T + 7(4) + 5(5) - 8M205 = 100 + 72 + 5T + 28 + 25 - 8M205 = 250 + 5T - 8M

Simplifying the equation gives:

5T - 8M = -45We can see that Emma sold 4 shorts and 6 jeans.Using this, we can determine the total cost of shorts and jeans sold by Emma:

Total cost = 12J + 7S

= 12(6) + 7(4)

= 72 + 28

= 100

Emma earned $205 during the week and spent $40 on meals.

So, the amount of money Emma made from sales is $205 - $40 = $165.We can determine the amount of money Emma made from selling hats as follows:

5H = $165H

= $33

If Emma sold T-shirts x, then, using the equation:

5T - 8M

= -45,5x - 8(5)

= -455x - 40

= -45x = (5/1)

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Answer:

If there's a common factor, divide both sides of the equation by that number to simplify the situation. If b = 0 (no bx term), go to the square root method. (if c is positive, there are no solutions). If c = 0, then one of your solutions is x = 0

Step-by-step explanation:

hope this helps!!!!

Answer:

Try the first option, 1, 10, 100, 1000 corresponding to 0, 1, 2, 3, and so on

Step-by-step explanation:

Answer:

Option C. 3√3

Step-by-step explanation:

Please see attached photo for brief explanation.

In the attached photo, we obtained the following:

Opposite = a

Adjacent = 3

Hypothenus = 6

Angle θ = 60°

We can obtain the value of 'a' as follow:

Tan θ = Opposite /Adjacent

Tan 60° = a/3

Cross multiply

a = 3 x Tan 60°

But: Tan 60° = √3

a = 3 x Tan 60°

a = 3 x √3

a = 3√3

Therefore, the length of the altitude of the equilateral triangle is 3√3.

The function of differentiable parameterization of arc length 2 in space is ∫√(1)² + (2t)² + (cos(t))² dt.

To set up a differentiable parameterization of arc-length 2 in space, we can use the arc-length formula:

s = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

where s is the arc length, t is the parameter, and (x, y, z) is the position vector.

We want the arc length to be 2, so we can set up the following equation:

2 = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

We can then choose a function for each component of the position vector, such as:

x = t

y = t²

z = sin(t)

We can now find the derivatives with respect to t:

dx/dt = 1

dy/dt = 2t

dz/dt = cos(t)

We can substitute these into the arc-length formula:

2 = ∫√(1)² + (2t)² + (cos(t))² dt

Solving this integral for t will give us the desired parameterization of arc-length 2 in space. However, this integral may not have a closed-form solution, so numerical methods may need to be used to approximate the solution.

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The question is -

Differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?

The length of ED is,  3√10

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

In a figure,

⇒ PB = BC = 6

Now, By the figure,

⇒ ΔFPD and ΔEMD are congruent.

Hence, We can formulate;

⇒ FP / EM = PD / MD

Let the length of MD = x

⇒ FP / EM = PD / MD

⇒ 6 / 3 = (9 + x) / x

⇒ 2x = 9 + x

⇒ 2x - x = 9

⇒ x = 9

Hence, The length of MD = 9

Now, In  ΔEMD;

⇒ ED² = EM² + MD²

⇒ ED² = 3² + 9²

⇒ ED² = 9 + 81

⇒ ED² = 90

⇒ ED = √90

⇒ ED = 3√10

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