Can you use the Law of Cosines in the triangle below? Why or why not?

Answer:

  $257.95

Step-by-step explanation:

We have assumed the payment is made at the end of each month, and the last payment will bring the balance to $1 million.

Answer:

see attached graph on the graph tool

Step-by-step explanation:

The equation of the parabola is

x²-6x-16y+25=0

vertex at (3,1) and focus at (3,5)

Answer:

3,238

Step-by-step explanation:

1,685+1,356+197=3,238

Using the Central Limit Theorem, it is found that the standard deviation of the sampling distribution of this sample mean is of 96.6 hours.

The Central Limit Theorem states that for a sample of size n, from a population of standard deviation [tex]\sigma[/tex], the standard deviation of the sampling distribution is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that: [tex]\sigma = 1356, n = 197[/tex]

Then

[tex]s = \frac{1356}{\sqrt{197}} = 96.6[/tex]

The standard deviation of the sampling distribution of this sample mean is of 96.6 hours.

A similar problem is given at https://brainly.com/question/15122730

Answer:

Probability of missing two passes in a row is 0.08.

Step-by-step explanation:

Event E = A football player misses twice in a row.

P(E) = ?

Event X = Football player misses the first pass

P(X) = 0.4

Event Y = Football player misses just after he first miss

P(Y) = 0.2

Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:

P(E) = P(X).P(Y)

P(E) = 0.4*0.2

P(E) = 0.08

Answer:

Probability of missing two passes in a row is 0.08.

Step-by-step explanation:

Event E = A football player misses twice in a row.

P(E) = ?

Event X = Football player misses the first pass

P(X) = 0.4

Event Y = Football player misses just after he first miss

P(Y) = 0.2

Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:

P(E) = P(X).P(Y)

P(E) = 0.4*0.2

P(E) = 0.08

Answer:

1) 6 cm

2) 117°

Step-by-step explanation:

1) Draw a picture of the rhombus.  The distance between opposite sides is the height of the rhombus.  If we draw the height at the vertex, we get a right triangle.  Using trigonometry:

sin 30° = h / 12

h = 12 sin 30°

h = 6 cm

2) Draw a picture of the rectangle.

∠KML is the angle the diagonal makes with the shorter side ML.  This angle is 54°.  ∠NKM is the angle the diagonal makes with the shorter side NK.  ∠KML and ∠NKM are alternate interior angles, so m∠NKM = 54°.

The angle bisector of angle ∠NKM divides the angle into two equal parts and intersects the longer side NM at point P.  So m∠PKM = 27°.

KLMN is a rectangle, so it has right angles.  That means ∠KML and ∠KMN are complementary.  So m∠KMN = 36°.

We now know the measures of two angles of triangle KPM.  Since angles of a triangle add up to 180°, we can find the measure of the third angle:

m∠KPM + 36° + 27° = 180°

m∠KPM = 117°

Answer:E 83[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

50% of the apartment in a certain building have windows and hardwood floors.

25% of the remaining 50% apartment without window have hardwood floors.

40% of the apartment do not have hardwood floors i.e. 60 % have hardwood floor

Therefore percent of the apartments with windows have hardwood floors is

[tex]=\frac{50 percent of total\ apartment }{60\ percent\ of\ apartment}[/tex]

=83[tex]\frac{1}{3}[/tex]%

Answer:

B. f(x) = x^2

Step-by-step explanation:

The only quadratic equation in the choices is the answer.

B. f(x) = x^2

Answer:

8793

Step-by-step explanation:

Multiply and divide first, making the equation 8811-17-1. Now subtract. This leaves 8793

Answer:

8793

Step-by-step explanation:

99×89-34÷2-1 = 8793

Multiply: 99 x 89 = 8811

Divide: 32 ÷ 2 = 17

Add: 17 + 1 = 18

Subtract: 8811 - 18 = 8793

Answer:

13%

Step-by-step explanation:

took all numbers add them together than divided by 3

Answer: the answer would be -4

Step-by-step explanation: it is going down 4 units

Answer:

  -8

Step-by-step explanation:

x = -2 is in the range -3 ≤ x ≤ -1, so the definition f(x) = 4x applies.

  f(-2) = 4(-2) = -8

Answer:

-8

Step-by-step explanation:

The value of f(-2) is -8.

            -2 if x < -3

f(x) -     4x if -3 < x < -1

            x^2 if x> -1

Answer:

im not sure I understand the question.

Step-by-step explanation:

Answer:

equidistant from the endpoints of the segment.

Step-by-step explanation:

Answer:

609

Step-by-step explanation:

Standard deviation = [tex]\sigma[/tex] = $30

Margin of error = E = $2

Confidence level = 90%

Since the distribution is said to be normal, we will use z scores to solve this problem.

The z score for 90% confidence level = z = 1.645

Sample size= n = ?

The formula to calculate the margin of error is:

[tex]E=z\frac{\sigma}{\sqrt{n}}\\\\\sqrt{n}=z\frac{\sigma}{E}\\\\n=(\frac{z\sigma}{E} )^{2}[/tex]

Using the values in above equation, we get:

[tex]n=(\frac{1.645 \times 30}{2} )^{2}\\\\ n = 608.9[/tex]

This means, the minimum number of observations required is 609

Answer:

52 minutes and 30 seconds

Step-by-step explanation:

You know that Yuto has ridden for 5.25 miles when Riko left their house and you need to know and what time they will be together:

Then you can say that:

5.25 miles+(yutos speed)*t= (Rikos speed)*t

when t=Time in minutes when they will be together

5.25 miles+(0.25miles/min)*t= (0,35miles/min)*t

5.25miles=(0.35miles/min-0.25miles/min)*t

5.25miles/(0.35miles/min-0.25miles/min)=t

t=52.5 min =52 minutes and 30 seconds

Answer:

The solution means that Riko will be behind Yuto from the time she leaves the house, which corresponds to t = 0, until the time she catches up to Yuko after 52.5 minutes, which corresponds to t = 52.5. The reason that t cannot be less than zero is because it represents time, and time cannot be negative.

Hope this helps!!! :) Have a great day/night.

Answer:

  7x

Step-by-step explanation:

This illustrates the meaning of a logarithm.

The natural log of 7x is the power to which e must be raised to give 7x. When you raise e to that power, you get 7x.

[tex]\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y=-2(x-\stackrel{h}{3})^2+\stackrel{k}{4}\qquad\qquad \stackrel{vertex}{(\underline{3},4)}\qquad \qquad \stackrel{\textit{axis of symmetry}}{x=\underline{3}}[/tex]

From the equation of the parabola in vertex-form, it's line of symmetry is given by:

[tex]l: x = 3[/tex]

The equation of a parabola of vertex (h,k) is given by:

[tex]y = a(x - h)^2 + k[/tex]

The line of symmetry is given by:

[tex]l: x = h[/tex]

In this problem, the parabola is modeled by the following equation:

[tex]y = -2(x - 3)^2 + 4[/tex]

Hence, the coefficients of the vertex are [tex]h = 3, k = 4[/tex], and the line of symmetry is:

[tex]l: x = 3[/tex]

A similar problem is given at https://brainly.com/question/24737967

Answer:

452.16 units^2

Step-by-step explanation:

Given

Radius = r= 6 units

The formula for finding the surface area of a sphere is:

[tex]A = 4\pi r^2\\A= 4 * 3.14 * (6)^2\\A=12.56*36\\A = 452.16[/tex]

In the formula, π is taken as 3.14.

So, the surface area of the given sphere is 452.16 units^2 ..

Answer:

452.39 units²

Step-by-step explanation:

To get the surface area of a sphere, all you need is the radius. The formula for the surface area is:

V=4πr²

So all you need to do is plug in the values:

V = 4πr²

V = (4)(π)(6)²

V = 4π36

V = 452.39 units²

BUT WAIT! If your teacher set the value of π to 3.14, the answer would be 452.16 units².

Answer:

(3)x+(3)

Step-by-step explanation:

Answer:

The height of the red prism must be twice the height of the blue prism

Step-by-step explanation:

The height of the red prism must be twice the height of the blue prism.

Since the height of the blue prism is twice that of the red prism, the height of the red prism must be twice as much as that of the blue prism to make the volumes equal.Volume of a prism can be calculated as the area of the base multiplied by the height.

V= b*h....

[tex]\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{\stackrel{\textit{difference of squares}}{(x^3-y^2)(x^3+y^2)}+2y^4}\implies [(x^3)^2-(y^2)^2]+2y^4 \\\\\\ x^6-y^4+2y^4\implies \boxed{x^6+y^4}[/tex]

Answer:

a) [tex](x^3-y^2)(x^3+y^2)+2y^4=x^6+y^4[/tex] is an identity.

Step-by-step explanation:

Most of the left hand sides are in this form:

[tex](a-b)(a+b)[/tex].

When you multiply conjugates you do not have to use full foil.  You can just multiply the first and multiply the last or just use this as a formula:

[tex](a-b)(a+b)=a^2-b^2[/tex].

Choice a), b), and d). all have the form I mentioned.

So let's look at those choices for now.

a) [tex](x^3-y^2)(x^3+y^2)+2y^4[/tex]

[tex](x^6-y^4)+2y^4[/tex]  (I used my formula I mentioned above.)

[tex]x^6+y^4[/tex]  

So this is an identity.

b)  [tex](x^3-y^2)(x^3+y^2)[/tex]

[tex]x^6-y^4[/tex] (by use of my formula above)

This is not the right hand side so this equation in b is not an identity.

d) [tex](x^3-y^2)(x^3+y^2)+2y^4[/tex]

[tex](x^6-y^4)+2y^4[/tex]

[tex]x^6+y^4[/tex]

This is not the same thing as the right hand side so this equation in d is not an identity.

Let's look at c now.

c) [tex](x^3+y^2)(x^3+y^2)[/tex]

There is a formula for expanding this so that you could avoid foil. It is

[tex](a+b)(a+b) \text{ or } (a+b)^2=a^2+2ab+b^2[/tex].

Just for fun I'm going to use foil though:

First: x^3(x^3)=x^6

Outer: x^3(y^2)=x^3y^2

Inner: y^2(x^3)=x^3y^2

Last: y^2(y^2)=y^4

---------------------------Add.

[tex]x^6+2x^3y^2+y^4[/tex]

This is not the same thing as the right hand side.

Answer:

56060550

Step-by-step explanation:

555x101010=56060550

That’s a lot of zombies and I’m scared now.

Answer:

56,060,550

Step-by-step explanation:

The mastodon bones are approximately 6764 years old, determined by calculating carbon-14 decay, with 42.1% of the original carbon-14 remaining after losing 57.9%, and using the known half-life of 5750 years.

The procedure to determine the age of the mastodon bones involves the principle of radioactive decay, specifically using carbon dating. Carbon-14, a radioactive isotope of carbon with a half-life of 5750 years, is used to date materials that were once part of a living organism.

Since the mastodon bones have lost 57.9% of their original Carbon-14, less than one half-life has passed. By using the exponential decay formula, we find that the remaining amount of Carbon-14 is 100% - 57.9% = 42.1%. One half-life (5750 years) would result in 50% remaining, and since 42.1% is a bit less than 50%, we need to determine how much less in terms of time. The calculation requires solving the following equation: N/N_0 = (1/2)^(t/T), where N is the remaining amount of Carbon-14, N_0 is the original amount, t is the time passed, and T is the half-life of Carbon-14.

To solve for t, we rearrange the equation to t = T * (log(N/N_0) / log(1/2)). Substituting the known values (T = 5750, N/N_0 = 0.421), we can calculate the time t that has passed since the death of the mastodon. When we perform this calculation, we find the bones to be slightly older than one half-life, equating to approximately 6764 years old.

The correct answer is A

Explanation:

A Venn diagram is a type of diagram used in mathematics and other fields to show sets and their relationship, because of this, Venn diagrams include at least two sets that are presented in two overlapped circles, in this each circle represents the elements that exclusively belong to each set, while the elements that belong two both sets are placed in the overlapped sections and the elements that do not belong to any of the sets are outside the circles. This implies, in the Venn diagram presented the elements that belong to swamp are in section B, the ones that belong to rainforest are in section D, the elements bot sets share are in section C and those that do not belong to any of the sets presented or that are different from the are in section A, as these elements are outside the circles and therefore do not belong to any of the sets that are represented by the circles.

To find the intervals on which a function is increasing or decreasing, analyze the sign of the derivative. The function is increasing on (-infinity, -1) and (2, infinity), and decreasing on (-1, 2).

To find the intervals on which a function is increasing or decreasing, we need to analyze the sign of the derivative of the function. In this case, the derivative of f(x) is f'(x) = 6x^2 + 6x - 12. We can find the critical points by setting the derivative equal to zero: 6x^2 + 6x - 12 = 0. Solving this equation gives us x = -1 and x = 2.

To determine the intervals of the function, we can create a sign chart:

x-2-1023f'(x)+0-0+

From the sign chart, we can see that the function is increasing on the intervals (-infinity, -1) and (2, infinity), and decreasing on the interval (-1, 2).

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(a) Intervals of Increase:

[tex]\[ (-\infty, -3) \cup (2, \infty) \][/tex]

Interval of Decrease:

[tex]\[ (-3, 2) \][/tex]

(b) Local Minimum and Maximum:

Local Maximum: [tex]\( x = -3 \)[/tex]

Local Minimum: [tex]\( x = 2 \)[/tex]

(c) Inflection Point:

[tex]\[ \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \][/tex]

(d) Concavity:

Concave Up: [tex]\( (-\infty, -\frac{1}{2}) \)[/tex]

Concave Down: [tex]\( (-\frac{1}{2}, \infty) \)[/tex]

(a) To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to examine the sign of its derivative, [tex]\( f'(x) \)[/tex].

[tex]\[ f(x) = 2x^3 + 3x^2 - 12x \][/tex]

First, let's find[tex]\( f'(x) \)[/tex]:

[tex]\[ f'(x) = 6x^2 + 6x - 12 \][/tex]

To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to find the critical points where [tex]\( f'(x) = 0 \)[/tex] or is undefined.

Setting [tex]\( f'(x) = 0 \)[/tex]:

[tex]\[ 6x^2 + 6x - 12 = 0 \][/tex]

[tex]\[ x^2 + x - 2 = 0 \][/tex]

This quadratic equation can be factored as:

[tex]\[ (x + 2)(x - 1) = 0 \][/tex]

So, the critical points are [tex]\( x = -3 \)[/tex] and [tex]\( x = 2 \)[/tex].

Now, let's test the intervals between and beyond these critical points:

For [tex]\( x < -3 \)[/tex]:

[tex]\[ f'(-4) = 6(-4)^2 + 6(-4) - 12 = 6(16) - 24 - 12 > 0 \][/tex]

Since [tex]\( f'(-4) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on[tex]\( (-\infty, -3) \)[/tex].

Between [tex]\( -3 \)[/tex] and [tex]\( 2 \)[/tex] :

[tex]\[ f'(0) = 6(0)^2 + 6(0) - 12 = -12 < 0 \][/tex]

Since [tex]\( f'(0) < 0 \)[/tex], [tex]\( f(x) \)[/tex] is decreasing on [tex]\( (-3, 2) \)[/tex].

For [tex]\( x > 2 \)[/tex]:

[tex]\[ f'(3) = 6(3)^2 + 6(3) - 12 = 6(9) + 18 - 12 > 0 \][/tex]

Since [tex]\( f'(3) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on [tex]\( (2, \infty) \)[/tex].

So, the interval on which [tex]\( f(x) \)[/tex] is increasing is [tex]\( (-\infty, -3) \cup (2, \infty) \)[/tex] , and the interval on which [tex]\( f(x) \)[/tex] is decreasing is [tex]\( (-3, 2) \)[/tex].

(b) To find the local minimum and maximum values of [tex]\( f(x) \)[/tex] :

we need to examine the critical points and the endpoints of the intervals we found.

Since [tex]\( f(x) \)[/tex] changes from increasing to decreasing at [tex]\( x = -3 \)[/tex], [tex]\( f(x) \)[/tex] has a local maximum at [tex]\( x = -3 \)[/tex] .

And since [tex]\( f(x) \)[/tex] changes from decreasing to increasing at [tex]\( x = 2 \)[/tex], [tex]\( f(x) \)[/tex] has a local minimum at [tex]\( x = 2 \)[/tex] .

(c) To find the inflection point:

we need to examine the concavity of [tex]\( f(x) \)[/tex], which is determined by the sign of the second derivative, [tex]\( f''(x) \)[/tex].

First, let's find [tex]\( f''(x) \)[/tex]:

[tex]\[ f''(x) = 12x + 6 \][/tex]

Setting [tex]\( f''(x) = 0 \)[/tex]:

[tex]\[ 12x + 6 = 0 \][/tex]

[tex]\[ x = -\frac{1}{2} \][/tex]

Since [tex]\( f''(x) \)[/tex] is positive for [tex]\( x < -\frac{1}{2} \)[/tex] and negative for [tex]\( x > -\frac{1}{2} \), \( f(x) \)[/tex] is concave up on [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and concave down on [tex]\( (-\frac{1}{2}, \infty) \)[/tex].

So, the inflection point is [tex]\( \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \)[/tex], and the intervals on which [tex]\( f(x) \)[/tex] is concave up and concave down are [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and [tex]\( (-\frac{1}{2}, \infty) \)[/tex] respectively.

Answer:

The focus point is (2 , 0) ⇒ answer D

Step-by-step explanation:

* Lets revise the equation of the parabola in standard form

- The standard form is (x - h)² = 4p(y - k)

- The focus is (h, k + p)

- The directrix is y = k - p

- If the parabola is rotated so that its vertex is (h , k) and its axis of

 symmetry is parallel to the x-axis, it has an equation of

 (y - k)² = 4p(x - h)

- The focus is (h + p, k)

- The directrix is x = h - p

* Lets solve the problem

∵ The equation of the parabola is y = 1/8(x² - 4x - 12)

- Lets make x² - 4x completing square

∵ √x² = x  

∴ The 1st term in the bracket is x

∵ 4x ÷ 2 = 2x

∴ The product of the 1st term and the 2nd term is 2x

∵ The 1st term is x

∴ the second term = 2x ÷ x = 2

∴ The bracket is (x - 2)²

∵  (x - 2)² = (x² - 4x + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out  

  the bracket to keep the equation as it

∴ (x² - 4x + 4) - 4 = (x - 2)² - 4

- Lets put the equation after making the completing square

∴ y = 1/8 [(x - 2)² - 4 - 12]

∴ y = 1/8 [(x - 2)² - 16] ⇒ multiply both sides by 8

∴ 8y = (x - 2)² - 16 ⇒ add 16 to both sides

∴ 8y + 16 = (x - 2)² ⇒ take from the left side 8 as a common factor

∴ 8(y + 2) = (x - 2)²

∴ The standard form of the equation of the parabola is

   (x - 2)² = 8(y + 2)

∵ The standard form of the equation is (x - h)² = 4p(y - k)

∴ h = 2 , k = -2 , 4p = 8

∵ The focus is (h , k + p)

∵ h = 2

∵ 4p = 8 ⇒ divide both sides by 4

∴ p = 2

∴ The focus = (2 , -2 + 2) = (2 , 0)

* The focus point is (2 , 0)

Answer:

D 2,0

Step-by-step explanation:

Answer: 120

Step-by-step explanation: to get this answer you do 5! (5 factorial), which means you multiply that number by all those which are lower down to one, or 5x4x3x2x1 in this case, which is 120

Answer: 240

Step-by-step explanation: 5 x 4 x 3 x 2 x1 = 240

Answer:

  about 6.418 seconds

Step-by-step explanation:

You apparently want to find t when h=0:

  0 = -16t^2 +84t +120

  0 = 4t^2 -21t -30 . . . . . . divide by -4

  t = (-(-21 ±√((-21)² -4(4)(-30)))/(2(4)) = (21±√921)/8 . . . . only the positive time is of interest

  t = 2.625+√14.390625 ≈ 6.419 . . . . seconds

It takes about 6.42 seconds for the rock to hit the water.

Answer:

6.4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Adjacent angles are supplementary. If one of them is 90°, then they both are. Another name for a 90° angle is "right angle." In this geometry, all 8 of the angles are right angles, including interior, exterior, vertical, linear, adjacent, and any other pairing you might name.

Any statement restricting the congruent angles to "only" some subset will be incorrect. Any and every subset of the angles contains congruent angles.

Answer:

A. All the angles are congruent.

C. All the angles are right angles.

E. All the interior angles are congruent.

This should be right.

Step-by-step explanation:

Answer:

  500%

Step-by-step explanation:

The percentage change is given by ...

  percent change = ((new value)/(old value) -1) × 100% = (180/30 -1)×100%

  = (6 -1)×100% = 500%

Mobile device sales increased 500% from 1998 to 2007.

Answer:

Number of mobiles sold in the year 1998=30 million

Number of mobiles sold in the year 2007=180 million

Percentage increase in mobile sale from year 1998 to 2007 will be

           [tex]=\frac{\text{final}-\text{Initial}}{\text{Initial}}\\\\=\frac{180-30}{30}\times100\\\\=\frac{150}{30} \times 100\\\\=\frac{15000}{30}\\\\=500\text{Percent}[/tex]

 =500%

Answer:

72

Step-by-step explanation:

If you find an interior angle, its supplement will be the exterior angle. That's one way to do the problem.

Another is to take 360 and divide it by the number of sides. That is the easier way to do it.

Exterior angle = 360 / divided by the number of sides

Exterior angle = 360 /5

Exterior angle = 72

---------------

The other way is done by

(n - 2) * 180 = 540

That's the total number of degrees in the interior of the pentagon.

1 interior angle = 540 / 5 = 108

The supplement of this angle is 180 - 108 = 72

Same answer 2 different ways.