I don't need the answer I NEED someone to explain this to me, I'm really struggling with this, and can someone walk me through this problem. The first number is x to the second power.
Factor the following polynomial completely
x^2-3x-10

Nilai sebenarnya dari tan 30° dapat dihitung dengan menggunakan definisi trigonometri dari fungsi tangen. Tangen dari sudut 30° didefinisikan sebagai perbandingan panjang sisi yang berseberangan dengan sudut tersebut (yaitu sisi yang berlawanan dengan sudut 30°) dibagi dengan panjang sisi yang menyentuh sudut tersebut (yaitu sisi yang terletak di sebelah sudut 30° dan merupakan bagian dari garis 90°).

Dalam segitiga siku-siku dengan sudut 30°, sisi yang berseberangan dengan sudut 30° adalah 1 dan sisi yang menyentuh sudut 30° adalah √3. Dengan membagi panjang sisi berseberangan dengan panjang sisi menyentuh, kita dapat menghitung nilai sebenarnya dari tan 30°:

tan 30° = (panjang sisi yang berseberangan) / (panjang sisi yang menyentuh)

= 1 / √3

= √3/3

Jadi, nilai sebenarnya dari tan 30° adalah √3/3 atau sekitar 0.577.

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Answer:

Sally can dye 276 words in 12 minutes. 828 in 36 minutes

Hello,

\(3 {}^{a} = 3 {}^{b} \Leftrightarrow \: a = b\)

\(3 {}^{x} = {3}^{2} \Leftrightarrow \: x = 2\)

We can use the `residue` function. The partial fraction expansion of B(s)/A(s) is: B(s)/A(s) = 2/s + 3/(s + 8) + 4/(s + 5) + 5/(s + 7) + 6/(s^2 + 10s + 100)

To obtain the partial-fraction expansion of the given rational function in MATLAB, you can use the `residue` function. Here's how you can do it:

num = [1 17 99 223 140];     % Coefficients of numerator polynomial

den = [1 32 363 2092 5052 4320];     % Coefficients of denominator polynomial

[r, p, k] = residue(num, den);

disp('Partial fraction expansion:');

for i = 1:length(r)

   disp(['(' num2str(r(i)) ' / (s - (' num2str(p(i)) ')))']);

The `residue` function calculates the partial fraction expansion of the rational function given the numerator (`num`) and denominator (`den`) polynomials. It returns the residue (`r`), pole locations (`p`), and the direct term (`k`), if any.

In this case, the expected partial fraction expansion is:

B(s)/A(s) = (2 / (s - 0)) + (3 / (s + 8)) + (4 / (s + 5)) + (5 / (s + 7)) + (6 / (s^2 + 10s + 100))

The coefficients and factors in the partial fraction expansion might differ from the given expression since MATLAB simplifies the results.

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Answer:

x=15

Step-by-step explanation:

30°=5

60°=10

SO right angle 90°=15

The coordinates of the centre of mass are:

\(x = \frac{M_x}{M} = \frac{r}{2}\\y = \frac{M_y}{M} = \frac{r}{2}\\z = \frac{M_z}{M} = \frac{r}{2}\)

To find the centre of mass of a solid of uniform density, we need to calculate the triple integral of the position vector (x, y, z) over the volume of the solid, and divide by the total mass of the solid.

In this case, the solid is a hemispherical shell of radius r and uniform density, so we can use spherical coordinates to simplify the calculations.

0 ≤ θ ≤ π/2

0 ≤ φ ≤ 2π

The mass of the solid is proportional to its volume, so we can assume that the total mass is \(M = \frac{2\pi r^3}{3}\) (the mass of a full sphere of radius r, divided by 2).

To calculate the triple integral for the centre of mass, we need to compute the following integrals:

\(M_x = \iiint x \rho \, dV\\M_y = \iiint y \rho \, dV\\M_z = \iiint z \rho \, dV\)

We can simplify the integrals using spherical coordinates:

\(\int_0^R \int_0^{\frac{\pi}{2}} \int_0^{2\pi} (r \sin\theta \cos\phi) \rho r^2 \sin\theta \, d\phi \, d\theta \, dr\)

\(\int_0^R \int_0^{\frac{\pi}{2}} \int_0^{2\pi} (r \sin{\theta} \sin{\phi}) \rho r^2 \sin{\theta} \, \mathrm{d}\phi \, \mathrm{d}\theta \, \mathrm{d}r\)

\(\int_0^R \int_0^{\frac{\pi}{2}} \int_0^{2\pi} (r \cos \theta) \rho r^2 \sin \theta \,d\phi \,d\theta \,dr\)

Since the density is uniform, we can factor it out of the integrals:

\(M_x = \rho \int_0^R \int_0^{\frac{\pi}{2}} \int_0^{2\pi} (r^3 \sin^2 \theta \cos \phi) \, d\phi \,d\theta \,dr M_y = \rho \int_0^R \int_0^{\frac{\pi}{2}} \int_0^{2\pi} (r^3 \sin^2 \theta \sin \phi) \,d\phi \,d\theta \,dr M_z = \rho \int_0^R \int_0^{\frac{\pi}{2}} \int_0^{2\pi} (r^3 \cos \theta \sin \theta) \,d\phi \,d\theta \,dr\)

The integrals over φ and θ can be evaluated using the standard formulas for integrating trigonometric functions over a range of angles:

\(\int_0^{2\pi}\cos\phi\, d\phi = \int_0^{2\pi}\sin\phi\, d\phi = 0\\\int_0^{\frac{\pi}{2}}\cos\theta \sin\theta\,d\theta = \frac{1}{2}\\x = \frac{M_x}{M} = \frac{r}{2}\\y = \frac{M_y}{M} = \frac{r}{2}\\z = \frac{M_z}{M} = \frac{r}{2}\)

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a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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The relation between mode, mean and median is:

mode=3median-2mean

Now, to find mean:

2mean=3median-mode

mean=7/2 = 3.5

Let we wish to evaluate the mean  μ of a population. In real practice we would typically take just one sample. Imagine still that we take sample after sample, all of the same size n, and compute the sample mean x¯ every time.

The sample mean x is a random variable: it differs from sample to sample in a way that cannot be predicted with sureness. We will write X¯ when the sample mean is idea of as a random variable and write x for the values that it takes.

The random variable X¯ has a mean, denoted  μX¯, and a standard deviation, denoted  σX¯. Here is an example with such a small population and small sample size that we can indeed write down every single sample.

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Given:

You order 1.5 pounds of turkey at the deli. You will accept the turkey if its weight is between 1.54 and 1.46 pounds.

To find:

The absolute value inequality that can be used to describe the tolerance of the weight of the turkey

Solution:

Let x be the actual weight of the turkey.

It will accepted, if its weight is between 1.54 and 1.46 pounds.

\(1.46\leq x\leq 1.54\)

Subtract 1.5 from each side.

\(1.46-1.5\leq x-1.5\leq 1.54-1.5\)

\(-0.04\leq x-1.5\leq 0.04\)

\(|x-1.5|\leq 0.04\)

Therefore, the required absolute inequality is \(|x-1.5|\leq 0.04\).

The interest tax shield of 1.26% lowers Summit's WACC by 0.76%

Let’s calculate the interest tax shield on Summit Builders' debt. Interest tax shield = Interest expense x tax rate

Summit Builders’ debt is 1.50 times the value of its equity.

So, the total value of its capital is equal to 1 + 1.50 = 2.50

The weight of debt is equal to debt/(equity+debt) = 1.50/2.50 = 0.6

The weight of equity is equal to equity/(equity+debt) = 1/2.50 = 0.4

The interest expense = 6% of debt

The tax rate is given as 21%.

Therefore,Interest tax shield = Interest expense x tax rate= 6% x 21%= 1.26%

The interest tax shield from its debt lowers Summit's WACC by the following amount:

WACC = wdebt*Kd*(1-t) + wEquity*Ke= 0.6 * 6% * (1 - 21%) + 0.4 * Ke= 2.4% + 0.4 * Ke

The interest tax shield of 1.26% lowers Summit's WACC by:1.26% x 0.6 = 0.756%≈0.76%

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The distance from the point to the plane is 33/9 = 11/3 units.

How to calculate distance?

To find the distance from point S(-8, -4, 5) to the line x = 5t, y = 10t, and z = 4t, we will use the following steps:

Find a point on the line: Let's use t=0, then the point on the line is P(0, 0, 0).
Create a vector from point P to point S: PS = S - P = <-8, -4, 5>.
Create a direction vector for the line: D = <5, 10, 4>.
Calculate the cross product of PS and D: PS x D = <20, 40, -80>.
Calculate the magnitude of the cross product: |PS x D| = √(20² + 40² + (-80)²) = 60.

The magnitude of the direction vector: |D| = √(5² + 10² + 4²) = 13.
Finally, calculate the distance: d = |PS x D| / |D| = 60 / 13 ≈ 4.615 (rounded to the nearest thousandth).

To find the distance from the point (0, 0, 3) to the plane 4x + 8y + z = 36, use the following formula:

Distance = |Ax + By + Cz - D| / √(A² + B² + C²)
In this case, A = 4, B = 8, C = 1, x = 0, y = 0, z = 3, and D = 36.
Distance = |(4 x 0) + (8 x 0) + (1 x 3) - 36| / √(4² + 8² + 1²) = |(-33)| / √(81) = 33 / 9.

The distance from the point to the plane is 33/9 = 11/3 units.

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Answer: h = -13

Step-by-step explanation: To get the answer for h all we have to do is....

78 ÷ -6 = -13

Let's check our work....

-6 x -13 = 78

I hope this helps!

Answer:

h= -13

Step-by-step explanation:

To solve the equation, we want to find out what h is. In order to do this, we have to get h by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

-6h=78

h is being multiplied by -6. The opposite of multiplication is division. Divide both sides by -6.

-6h/-6=78/-6

h=78/-6

h= -13

Let's check our solution. Substitute -13 back in for h in the original equation.

-6h=78

-6(-13)=78

Multiply

78=78

Since both sides of the equation are the same, we know that the correct answer is h= -13.

The height of the prism is 5x + 3 units.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Given:

The volume of a rectangular prism is given by the expression

10x^3 + 46x^2 – 21x – 27. The area of the base of the prism is given by the expression 2x^2 + 8x – 9.

We have to find the height of prism.

Volume of the rectangular prism = Base × Height

The expression is in the Question be

10x ³ + 46 x² - 21x -27

And the  area of the base of the prism is given by the expression

2x² + 8x - 9 .

Put in the formula

10x ³ + 46 x² - 21x -27  = 2x² + 8x - 9  × Height

The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .

put in the formula

(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height

Cancelled 2x² + 8x - 9 on both side.

(5x+3)unit = Height

Hence, the height of the prism is 5x + 3 units.

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Trapezoid 1 is similar to trapezoid 2 because trapezoid 1 can be mapped onto trapezoid 2 by a series of transformations.

In Mathematics and Geometry, two geometric figures such as trapezoids are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

This ultimately implies that, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar;

Scale factor = √10/√2 = 5/2.5 = 7/3.5

Scale factor = 2.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

1. 33%

2. 16%

3. 50%

Step-by-step explanation:

The ground do the ropes intersect each other is at 4 ft.

AB and ED are the poles (perfectly vertical). BE and DA are the ropes that cross at C.

F is the point directly below C on the ground (line AE), which is perfectly flat and horizontal.

The vertical poles are part of parallel lines.

As a consequence, triangles ABC and DEC have congruent angles at B and E, and at A and D (alternate interior). Of course, ABC and DEC also have congruent angles at C (vertical angles).

Triangles ABC and DEC are similar, with corresponding sides in the ratio 2:1

\(\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}= \frac{2}{1}\)

In particular,

BC = 2EC and BE = BC + EC = 2EC + EC = 3EC

Right triangles ABE and FCE, with the same angle at E, are also similar, so

\(\frac{AB}{FC}= \frac{BE}{CE}= \frac{3EC}{EC3.1}\) --> AB = 3FC --> \(FC = \frac{AB}{3}= \frac{12 ft}{3} = 4ft\)

The ropes cross 4 ft above the ground.

Hence the answer is the ground do the ropes intersect each other is at 4 ft.

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Step 1

Given;

Required; To graph the inequality on the axes

Step 2

Since the inequality has a greater than sign and not greater than or equal to sign then we must note that the line of the inequality graph will be broken and not solid.

To graph the inequality, we will use the values of x from -10 to 10.

The table was gotten by substituting for x =-10 to 10

The area shaded is above because y is greater than the points gotten on the table and the required area must therefore be above the values of y in the table. This is how the graph was gotten.

Answer: -8

Step-by-step explanation:

i did the math

Answer:

X= -8

Step-by-step explanation:

2(3X+8)=-36+4

6X+16= -32

6X= -32-16

6X= -48

X= -48/6

X= -8

Answer:

\(0.007\)

Step-by-step explanation:

Round to the required significant figure:

\(0.007\)

The inequality that describes how many movies Parv can buy is: n ≤ 10.025

Let's denote the number of movies Parv wants to buy as n. We are given that each movie costs $3.99. To determine the inequality that describes how many movies Parv can buy, we need to consider the amount of money he has remaining after purchasing the pack of games.

Parv starts with a $50 gift card and spends $9.99 on a pack of games. The remaining amount on the gift card is $50 - $9.99 = $40.01.

Now, let's consider the cost of n movies. Each movie costs $3.99, so the total cost of n movies would be n * $3.99.

Since Parv wants to buy the movies using the remaining amount on his gift card, we can set up the inequality:

n * $3.99 ≤ $40.01

This inequality states that the total cost of n movies, represented by n * $3.99, must be less than or equal to the remaining amount on the gift card, which is $40.01.

Simplifying the inequality further, we have:

3.99n ≤ 40.01

Now, if we want to solve for n, we can divide both sides of the inequality by 3.99:

n ≤ 40.01 / 3.99

Calculating this value, we have:

n ≤ 10.02506265664

Therefore, the inequality that describes how many movies Parv can buy is:

n ≤ 10.025

This means that Parv can buy a maximum of 10 movies, as he cannot purchase a fractional part of a movie.

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Therefore , the solution of the given problem of surface area comes out to be 212 square feet of the wall are therefore covered by the design.

The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

We must first determine the area of each individual form before adding them together to determine the portion of the wall that the design covers.

Taking a look at the rectangle first, we can observe that it has the following area:

=> 120 square feet=  10 feet x 12 feet.

=> 40 square feet =  (1/2)(10 ft)(8 ft).

Consequently, the two triangles' combined area is:

=> 80 square feet =  2 x 40 square feet.

=> (12 square feet) = (1/2)(6 ft)(4 ft).

The total area of all the shapes is as follows:

=> 212 square feet=  120 square feet, 80 square feet, and 12 square feet.

=> 212 square feet of the wall are therefore covered by the design.

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Answer: the answer is 261 ^2 ft!

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

For the fourth-year forward rate: The forward rate is equaI to [(770.89/835.62)(1/(4-3)] - 1 = 0.0289 or 2.89% .

An equation in mathematics is a cIaim that two mathematicaI expressions are equivaIent. The Ieft-hand side (LHS) and the right-hand side (RHS), which are separated by the equaI sign ("="), make up an equation. Equations are a common tooI for probIem-soIving and determining the vaIue of an unknowabIe variabIe since they are used to describe mathematicaI reIationships.

given

I For a bond having a one-year maturity:

\(YTM = [(1000/945.90)^{(1/1)}] - 1 = 0.0572 or 5.72%\)

(ii) For a bond having a two-year maturity:

\(YTM = [(1000/911.47)^{(1/2)}] - 1 = 0.0474 or 4.74%\)

(iii) For a bond having a three-year maturity:

\(YTM = [(1000/835.62)^{(1/3)}] - 1 = 0.0617 or 6.17%\)

(iv) For a bond with a four-year maturity:

\(YTM = [(1000/770.89)^{(1/4)}] - 1 = 0.0672 or 6.72%\)

We can use the foIIowing formuIa to determine the forward rates:

Forward rate is equaI to [((Bond Price 1/Bond Price 2)(1/(n2-n1))]]. - 1

where n₂-n₁ is the time period between the maturities, Price of Bond 1 is the price of the bond with maturity n₁, and Price of Bond 2 is the price of the bond with maturity n₂.

We may determine the forward rates using the bonds' current prices by foIIowing these steps:

I For the second-year forward rate:

((911.47/945.90)(1/(2-1))) is the forward rate. - 1 = 0.0379 or 3.79%

(ii) For the third-year forward rate:

The forward rate is equaI to [((835.62/911.47)(1/(3-2))] - 1 = 0.0360 or 3.60%

For the fourth-year forward rate: The forward rate is equaI to [(770.89/835.62)(1/(4-3)] - 1 = 0.0289 or 2.89% .

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\( \frac{x}{3° } + 49° = 180° \\ \)

Cross multiply

\(x + 147° = 180°\)

simplify

x = 180° - 147°

answer : x = 33°

Answer:

\(4x + 5 = 1 + 5x \\ 5 - 1 = 5x - 4x \\ x = 4\)

Answer:

Step-by-step explanation:

\(4x+5=1+5x\)

\(4x+5-5=1+5x-5\)

\(4x=5x-4\)

\(4x-5x=5x-4-5x\)

\(-x=-4\)

\(\cfrac{-x}{-1}=\cfrac{-4}{-1}\)

\(x=4\)