The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are ( r, 67.4°). What is the value of the polar coordinate r in this case?

Answer:

Step-by-step explanation:

If you simply need to identify the inequality, it is

n + 5 ≥ 12

since "sum" means to add and "at least" is the inequality sign that is greater than or equal to.

If you are solving it, then the solution set will be

n ≥ 7

Answer:

5 + n ≥ 12.

Step-by-step explanation:

Given  :  sum of five and a number n is at least 12.

To find : Write expression .

Solution : We have given sum of five and a number n is at least 12.

According to given statement :

Sum of 5 and n

5 + n

At least 12 mean the number is 12 or greater than 12

So ,

5 + n ≥ 12.

Therefore, 5 + n ≥ 12.

Answer:

[tex]x^{2} \neq -\frac{1}{14}[/tex]

Step-by-step explanation:

The equation will hold true as long as the denominator does not equal zero:

so take the denominator and set it equal to zero and find x. when you find x, that will be your answer:

-14x^2 -1=0

-14x^2=1

-x^2=1/14

x^2=-1/14

Answer:

The length is 78 feet and the width is 30 feet.

Step-by-step explanation:

The perimeter of a rectangle can be calculated with this formula:

[tex]P=2l+2w[/tex]

Where "l" is the length and "w" is the width.

Since we know that the perimeter of the playing field is 216 feet and its length is 48 feet longer than the width ([tex]l=w+48[/tex]), we can substitute them into the formula and solve for "w":

[tex]216=2(w+48)+2w\\\\216=2w+96+2w\\\\216-96=4w\\\\\frac{120}{4}=w\\\\w=30\ ft[/tex]

Finally, substitute the width into [tex]l=w+48[/tex] to find the length. This is:

[tex]l=30+48\\\\l=78\ ft[/tex]

Final answer:

To find the dimensions of the playing field, we identify the width as w feet and the length as w + 48 feet. By using the perimeter formula and solving the resulting equation, we determine that the width is 30 feet and the length is 78 feet.

Explanation:

The student is asking to find the dimensions of a rectangle given its perimeter and the relationship between its length and width. The perimeter of the rectangle is known to be 216 feet, and the length is specified to be 48 feet longer than the width.

Let's call the width w feet. Then, the length would be w + 48 feet. Since the perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width, we can set up the following equation:

2(w + w + 48) = 216

Solving this equation, we find:

4w = 120

Therefore, the width of the playing field is 30 feet. To find the length, add 48 feet to the width:

Length = w + 48 = 30 + 48 = 78 feet.

The dimensions of the playing field are 30 feet in width and 78 feet in length.

Answer:

A.

[tex]y - 5 = -2(x-6)[/tex]

Negative reciprocal gives you the perpendicular slope so negative reciprocal of 1/2 is -2.

Then apply point-slope form.

B. The answer is x = 6.

The midpoint of JK is

[tex]\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{8+ 4}{2}, \frac{4 + 4}{2} \right) = \left(6,4\right)[/tex]

The line that goes through JK is just a horizontal line [tex]y = 4[/tex] because the y-coordinate does not change. So its perpendicular bisector is the vertical line that goes through the x-coordinate of the midpoint, that is, [tex]x = 6[/tex].

Final answer:

The probability of getting exactly one topping on a hamburger, when up to 7 toppings are possible and each choice is unique, is 1 in 8 or 0.125.

Explanation:

When considering the probability of getting exactly one topping on a hamburger when the toppings could range from 0 to 7, and each topping is unique, we apply the concept of theoretical probability. The scenario implies there are 8 different events that could occur - getting no toppings to getting all 7 toppings. We are interested in the event where we get exactly one topping. Since each of these events - from getting 0 toppings to 7 toppings - is equally likely, the probability of getting exactly one topping is 1 in 8 or 0.125, when expressed as a decimal number rounded to four decimal places.

Answer with explanation:

For, a 3 × 3, matrix

[tex]r_{1}=(3,-2,0)\\\\r_{2}=(0,1,1)\\\\r_{3}=(2,-1,0)[/tex]

which are entries of First, Second and Third Row Respectively.

So, if written in the form of Matrix (A)

 [tex]A=\left[\begin{array}{ccc}3&-2&0\\0&1&1\\2&-1&0\end{array}\right][/tex]

⇒Adjoint A= Transpose of Cofactor of A

[tex]a_{11}=1,a_{12}=2,a_{13}=-2\\\\a_{21}=0,a_{22}=0,a_{23}=-1\\\\a_{31}=-2,a_{32}=- 3,a_{33}=3\\\\Adj.A=\left[\begin{array}{ccc}1&0&-2\\2&0&-3\\-2&-1&3\end{array}\right][/tex]

⇒≡ |Adj.A|=1 ×(0-3) -2×(-2-0)

            = -3 +4

            =1     --------(1)

⇒For, a Matrix of Order, 3 × 3,

| Adj.A |=| A|²---------(2)

[tex]|2 A^{-2}|=2^3\times |A^{-2}|\\\\=2^3\times |A|^{-2}\\\\=\frac{8}{|A^{2}|}\\\\=\frac{8}{|Adj.A|}\\\\=\frac{8}{1}\\\\=8[/tex]

                                              --------------------------------------------(Using 1 and 2)

[tex]\rightarrow|2 A^{-2}|=8[/tex]

Step-by-step explanation:

First, use trig to find the height of the slide.

The slide forms a right triangle.  We know the hypotenuse is 8.80 ft, and the angle opposite of the height is 25.0°.  So using sine:

sin 25.0°  = h / 8.80

h = 3.72 ft

Converting to meters:

h = 3.72 ft × (1 m / 3.28 ft)

h = 1.13 m

Potential gravitational energy is:

PE = mgh

where m is the mass, g is the acceleration due to gravity, and h is the relative height.

At the bottom of the slide, h = 0:

PE = (63.0 kg) (9.8 m/s²) (0 m)

PE = 0 J

At the top of the slide, h = 1.13 m:

PE = (63.0 kg) (9.8 m/s²) (1.13 m)

PE =  700 J

The change is the final potential energy minus the initial potential energy.

ΔPE = 0 J - 700 J

ΔPE = -700 J

Step-by-step explanation:

Let's say the position of the fire is point C.

Bearings are measured from the north-south line.  So ∠BAC = 55°, and ∠ABC = 60°.

Since angles of a triangle add up to 180°, ∠ACB = 65°.

Using law of sine:

190 / sin 65° = a / sin 60° = b / sin 55°

Solving:

a = 181.6

b = 171.7

Station A is 181.6 miles from the fire and station B is 171.7 miles from the fire.

Answer:

The logarithmic function modeled by the given table:

f(x) = log₃x

Step-by-step explanation:

Given Table:

x     f(x)

9     2

27    3

81    4

We can see that x increases as powers of 3. And f(x) is the power.

We assume that f(x) = log₃x

Checking using the table:

for x = 9

f(x) = log₃9 = 2

for x = 27

f(x) = log₃27 = 3

for x = 81

f(x) = log₃81 = 4

Hence proved.  

-10x - 3 = -10 - 3x

Bring -10x to the other side by adding it to both sides

(-10x + 10x) - 3 = -10 + (-3x + 10x)

0 - 3 = -10 + 7x

-3 = -10 + 7x

Bring -10 to the oposite side by adding 10 to both sides

-3 + 10 = (-10 + 10) + 7x

7 = 0 + 7x

7 = 7x

Isolate x by dividing 7 to both sides

7/7 = 7x/7

x = 1

Hope this helped!

~Just a girl in love with Shawn Mendes

-10x-3= -10-3x

-10x+10x-3= -10x+10x-3x

-3=-3x

divide by -4 for -3 and -3x

-3/-3= -3x/-3

1=x

x= 1

check answer by using substitution method

-10x-3= -10-3x

-10(1)-3=-10-3(1)

-13=- 13

Answer is x= 1

Answer: C. -4 percent

Step-by-step explanation:

Nominal interest rate is the interest rate before taking inflation into account.

Real interest rate takes the inflation rate into account.

The equation that links all three values is

nominal rate - inflation rate = real rate

6 - 10 = -4

-4 percent

The real interest rate can be calculated by subtracting the inflation rate from the nominal interest rate. In this case, the real interest rate is -4%, suggesting an investor would lose value due to inflation.

The calculation of the real interest rate involves subtracting inflation from the nominal interest rate. This is essential since inflation erodes the purchasing power of money, making it an important factor to consider when dealing with interest rates. In this case, you need to subtract the inflation rate (10 percent) from the nominal interest rate (6 percent).

So, performing this calculation:
6% (Nominal Interest Rate) - 10% (Inflation Rate) = -4%

Thus, in this scenario, the correct option would be C. -4 percent. This implies that an investor would actually lose ground when considering the effect of inflation.

https://brainly.com/question/34393655

#SPJ3

Answer:

n = 22

Step-by-step explanation:

We will use the formula for the present value of an ordinary annuity :

[tex]P.V.=P(\frac{1-(1+r)^{-n}}{r})[/tex]

where P = periodic payment

          r = rate per period

          n = number of periods

Given P = PMT = $400, P.V. = $8,000, i = 0.01, and we have to find n.

Now we put the values in the formula

[tex]8000=400(\frac{1-(1+0.01)^{-n}}{0.01})[/tex]

After rearranging we have

[tex]\frac{8000\times 0.01}{400}=1-1.01^{-n}[/tex]

[tex]20\times 0.01=1-1.01^{-n}[/tex]

[tex]1.01^{-n}[/tex] = 1 - 0.2

[tex]1.01^{-n}[/tex] = 0.8

Taking log on both sides

-n log 1.01 = log 0.8

[tex]n=\frac{-log0.08}{log1.01}[/tex] = 22.4257

Therefore, n = 22

So there are total 22 payments

Answer:

481/600

Step-by-step explanation:

Since the delay is exactly 10 min, or 600 seconds, the delay must be more than 480. Taking this, the probability of it not being 480 seconds or less becomes 481/600. (Since you can't have 480)

The probability is 481/600

Since the delay is exactly 10 min, or 600 seconds, the delay must be more than 480. Taking this, the probability of it not being 480 seconds or less becomes 481/600. (Since you can't have 480)

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Learn more about Problem-solving here: brainly.com/question/13818690

#SPJ2

Answer:

25.8

Step-by-step explanation:

The cost to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017 is:

                   4.45 cents

Electric power costs 17.8 cents per kWh in Los Angeles in July 2017.

Now we are asked to find the cost to run  a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017.

We know that: 1 w=0.001 kW

This means that:

   1500 W= 1.500 kW

Also, it is used for 10 minutes

i.e. 1/6 hours

Hence, the electric power used to run the hair dryer is: 1.500×(1/6)

i.e. Electric power to used by hair dryer is: 0.25 kWh

Cost of 1 kwh is: 17.8 cents

This means that cost of 0.25 kwh is: 17.8×0.25

                                                        =  4.45 cents

Hence, the answer is:

                      4.45 cents

Answer:

[tex]\large\boxed{\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\left(\dfrac{1}{4}\right)^2=r^2-\dfrac{1^2}{4^2}=r^2-\dfrac{1}{16}[/tex]

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

[tex]\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}[/tex]

Answer:

a_n=-\frac{1}{4 a_{n-1}

Step-by-step explanation:

The recursive formula for the geometric sequence is given by:

a_n = a_{n-1} \cdot r

where,

r is the common ratio terms

-16, 4, -1, ...

This is a geometric sequence.

Here,  and

Since,

ans so on .....

Substitute the given values we have;

⇒

Therefore, the recursive formula for the following geometric sequence is,

Answer:

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

Step-by-step explanation:

Formulate the recursive formula for the following geometric sequence.

{-16, 4, -1, ...}

Here the common difference of two terms are not same.

LEts find the common ratio. To find common ratio, divide the second term by first term

[tex]\frac{4}{-16} =\frac{-1}{4}[/tex]

[tex]\frac{-1}{4} =\frac{-1}{4}[/tex]

So common ratio is -1/4

Recursive formula is

[tex]A_n= A_{n-1} (r)[/tex]

'r' is the common ratio.

Recursive formula becomes

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

Answer: 90.5%

Step-by-step explanation:

Given: Mean : [tex]\mu = 1\text{ inch}[/tex]

Standard deviation : [tex]\sigma = 0.003\text{ inch}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 0.995

[tex]z=\dfrac{0.995-1}{0.003}=-1.66666666667\approx-1.67[/tex]

The P Value =[tex]P(z<-1.67)=0.0474597[/tex]

For x= 1.005

[tex]z=\dfrac{1.005-1}{0.003}=1.66666666667\approx1.67[/tex]

The P Value =[tex]P(z<1.67)= 0.9525403[/tex]

[tex]\text{Now, }P(0.995<X<1.005)=P(X<1.005)-P(X<0.995)\\\\=P(z<1.67)-P(z<-1.67)\\\\=0.9525403-0.0474597=0.9050806[/tex]

In percent ,

[tex]P(0.995<X<1.005)=0.9050806\times100=90.50806\%\approx90.5\%[/tex]

the probability that an elevator rail will meet the specifications is about 90.5%, which is 0.9525 - 0.0475.

The student is asking for the fraction of all elevator rails produced by Smalltown Elevator that will meet the given specifications, assuming that the diameter of an elevator rail follows a normal distribution with a mean of 1 inch and a standard deviation of 0.003 inches. To meet specifications, the diameter must be between 0.995 inches and 1.005 inches.

The z-score for the lower specification limit (0.995 inches) is calculated as: (0.995 - 1) / 0.003. This gives us a z-score of -1.67. The z-score for the upper specification limit (1.005 inches) is calculated as: (1.005 - 1) / 0.003. This gives us a z-score of 1.67.

Using the standard normal distribution table, we find that the cumulative probability for a z-score of 1.67 is approximately 0.9525, and for -1.67 is approximately 0.0475. Thus, the probability that an elevator rail will meet the specifications is about 90.5%, which is 0.9525 - 0.0475.

Answer:

The price is $3.36 per infinity stone

Step-by-step explanation:

we know that

Five infinity stones cost $16.80

so

To find the price of each infinity stone (unit rate) divide the total cost by five

[tex]\frac{16.80}{5} =3.36\frac{\$}{infinity\ stone}[/tex]

Answer:

Step-by-step explanation:

What level of math is this?

To determine if H is a subspace, we need to check three properties: the presence of the zero vector, closure under vector addition, and closure under scalar multiplication.

1. Does H contain the zero vector of V? The answer is no, because the zero vector (0,0) does not lie in the second or fourth quadrants.

2. Is H closed under addition? The answer is no. For example, the vectors (-1, 1) from the second quadrant and (-1, -1) from the fourth quadrant would sum to (-2, 0), which is not part of either quadrant.

3. Is H closed under scalar multiplication? The answer is no, as multiplying a vector in H by a negative scalar will place it in the opposite quadrant, which is outside H. For example, the scalar -1 and the vector (-1, 1) will yield the vector (1, -1), which is not in the second or fourth quadrants.

4. Is H a subspace of the vector space V? The answer is no, because it does not meet the required properties mentioned in parts 1-3.

Answer:

3

Step-by-step explanation:

there are two solutions in the given system of two equations:

a=10; b=7 and a=7; b=10.

|a-b|=3.

Answer:

50% chance

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

There are 3 coins, and each coin has 2 possible outcomes.  So there are a total of 6 possible outcomes.

Of these 6 outcomes, 3 are heads.  Of these 3, only 1 has tails on the opposite face.

So the probability is 1/3.

We can also show this using conditional probability:

P(A|B) = P(A∩B) / P(B)  

Probability that A occurs, given that B has occurred = Probability that both A and B occur / Probability that B occurs

Here, A = tails on opposite face and B = heads.

P(A|B) = (1/6) / (3/6)

P(A|B) = 1/3

Answer:

C

Step-by-step explanation:

The Pythagorean Theorem tells us that

a^2 + b^2 = c^2

a = b = s because a right angle and a 45 degree angle leaves only 45 degrees which means that both acute angles are 45 degrees

c = 2

2s^2 = 2^2         Divide by 2

s^2 = 4/2

s^2 = 2                Take the square root of both sides.

sqrt(s^2) = sqrt(2)              

s = sqrt(2)

Answer:

C: square root of 2.

Step-by-step explanation:

Ignore the picture that shows option D, jcherry99's description is correct.

Answer:

[tex]y =( x +9 )\times 4[/tex]

simplified

[tex]y = 4x + 48[/tex]

Step-by-step explanation:

first know that the result would be y or f(x), because it's the function applied to x that makes it y. so its starts with either y= or, f(x)=

increasing by a number is multiplying, the word and is used for addition so

+9 ×4 will be in the equation

used PEMDAS, distribution, and combining like terms to simplify

Answer:

The average rate of change is [tex]\frac{18}{5}[/tex]

Step-by-step explanation:

Given function that shows the population of a culture of cells,

[tex]P(t)=\frac{90t}{t+1}------(1)[/tex]

Where, t represents the number of weeks.

Thus, the average rate of change in the population over the interval [0,24],

[tex]m=\frac{P(24)-P(0)}{24-0}[/tex]

From equation (1),

[tex]=\frac{\frac{90\times 24}{24+1}-\frac{90\times 0}{0+1}}{24}[/tex]

[tex]=\frac{\frac{2160}{25}-\frac{0+1}{0}}{24}[/tex]

[tex]=\frac{2160}{25\times 24}[/tex]

[tex]=\frac{2160}{600}[/tex]

[tex]=\frac{18}{5}[/tex]

Answer:

A) 4/33 hour

Step-by-step explanation:

This is a distance = rate * time problem

We are given the distance and the rate, now we need to solve for the time:

[tex]\frac{4}{7}=4\frac{5}{7}t[/tex]

Let's change that mixed fraction into an improper one:

[tex]\frac{4}{7}=\frac{33}{7}t[/tex]

Now to solve for t we can multiply the 33/7  by its recirocal:

[tex](\frac{7}{33})\frac{4}{7}=\frac{33}{7}(\frac{7}{33})t[/tex]

Multiplying a fraction by its reciprocal = 1, so that leaves only a t on the right:

[tex](\frac{7}{33})\frac{4}{7}=t[/tex]

The 7's cancel out on the left and that leaves you with

[tex]t=\frac{4}{33}hr[/tex]

Answer:

  7

Step-by-step explanation:

The function can be written in vertex form as ...

  f(x) = -(x +1)^2 +7

The vertex is then identifiable as (-1, 7). The y-coordinate is 7.

_____

Vertex form is ...

  f(x) = a(x -h)^2 +k

where "a" is the vertical scale factor, and (h, k) is the vertex point. It is convenient to arrive at this form by factoring "a" from the first two terms, then adding and subtracting the square of the remaining x-coefficient inside and outside parentheses.

  f(x) = -(x^2 +2x) +6

  f(x) = -(x^2 +2x +1) + 6 -(-1) . . . . completing the square

  f(x) = -(x +1)^2 +7 . . . . . . . . . . . . vertex form; a=-1, (h, k) = (-1, 7)

The y-coordinate of the vertex of the parabola defined by the function f(x)= -x² - 2x + 6 is 3. This is found by using the vertex formula and then substituting the x-coordinate back into the original function.

To find the y-coordinate of the vertex of the parabola defined by the quadratic function f(x)= -x² - 2x + 6, we can use the vertex formula for a parabola in standard form, which is y = ax² + bx + c. The x-coordinate of the vertex is given by the formula -b/(2a), and the y-coordinate can then be calculated by applying the x-coordinate to the original function.

First, let's find the x-coordinate of the vertex:

x-coordinate of the vertex, x_v = -(-2)/(2*(-1)) = -(-2)/(-2) = 1

Now, substitute x_v back into the function to find the y-coordinate:

y-coordinate of the vertex, y_v = f(1) = -1² - 2*1 + 6 = -1 - 2 + 6 = 3

Therefore, the y-coordinate of the vertex is 3.

The graph approaches positive infinity at a constant rate.

The end behavior of this graph is:

As x → -∞, f(x) → +∞

For the first notation it looks at the behavior of the left side of the graph. As x approaches negative infinity (or positive xs) y or f(x) approaches positive infinity (or positive ys)

and

As x → +∞, f(x) → +∞

For the second notation it looks at the behavior of the right side of the graph. As x approaches positive infinity (or positive x's) y or f(x) approaches positive infinity (or positive ys)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: The graph approaches positive infinity at a constant rate.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’s nothing