Find the nth term of this quadratic sequence 6, 16, 32, 54, ...​

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

Answer:

if not 24.5, it should be 31 yds

Step-by-step explanation:

ok so, I don't know how you want me to solve this but, if you're asking the distance diagonally, then it will be 24.5 yds. If you want the distance in straight lines, it will be 31 yds

lol there wasn't much information, sorry

Answer:

B. 65 MPH

Step-by-step explanation:

Each hour, the distance increased by 65 miles.

Answer:

65 mph

Step-by-step explanation:

Find a point on the graph where it perfectly intersects with the grid lines. This is (4,260), so in order to get that to one hour divide by 4, so 260 divided by 4 is 65.

To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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Answer:

7.22?

Step-by-step explanation:

Answer:

-7-63a

Step-by-step explanation:

-7(1 + 9a)

(use the distributive property of multiplication to simplify)

-7-63a

Answer:

A prime number is a number with exactly two factors. A prime number is only divisible by 1 and itself. Another way to think of prime numbers is that they are only ever found as answers in their own times tables.

Step-by-step explanation:

Answer:

Prime no.

Step-by-step explanation:

A number that only has two factors [ 1 and itself] is called a prime no.

For ex:

The factors of 2 are: 1,2

The factors of 3 is : 1,3

But if you look at the factors of 6, there are; 1,2,3,6 [ 4 FACTORS]

Thus, 6 is a composite no. [Has more than 2 factors]

The equation of a graph is a mathematical statement true only for points of that graph. The equation of specified circle is: x² + y² −41 = 0

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as: (x-h)²+(y-k)² = r²

For given case, we have h = 0, and k = 0,

We know that,

The shortest distance (straight line segment's length connecting both given points) between points (p, q) and (x, y) is:

D = √(x-p)² + (y-q)²  units.

Also,

Radius = distance between O and B as length of radius, which is

r = √[(4-0)² + (5-0)²] = √[16+25] = √41   units.

Thus, we have the equation as:

(x-h)² + (y-k)² = r²

x²+ y² = (√41)²

x² + y² = 41

x² + y² - 41 = 0

Hence, The equation of specified circle is: Option b) x² + y² - 41 = 0

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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a) The probability that the test comes back negative for all six people is  95.8%,

b)  The probability that the test comes back positive for at least one of the six people is 4.2%.

(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.

Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:

P(negative for all 6) = (0.993)^6 ≈ 0.958

Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.

(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.

The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.

The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:

P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042

Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.

In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.

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The 9th term of the given sequence is 78732.

The given sequence is 12, 36, 108... is a geometric sequence with a common ratio of 3.To find the 9th term of the given sequence, we will use the formula for the nth term of a geometric sequence, which is given by:

aₙ = a₁rⁿ⁻¹

Here, a₁ = 12 and r = 3.

Therefore, the formula for the nth term becomes:

aₙ = 12(3)ⁿ⁻¹

Now, we need to find the 9th term of the sequence. Hence, n = 9. Substituting the values of a₁ and r, and n in the formula, we get:

a₉ = 12(3)⁹⁻¹= 12(3)⁸= 12(6561)= 78732

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Answer:

96

Step-by-step explanation:

X be the total containers bought

Sales - cost = profit

4.08(X - 14) - 2.6X = 84.96

4.08X - 2.6X - 57.12 = 84.96

1.48X = 142.08

X = 96

Answer:

D -6, 15

Step-by-step explanation:

Because 3,11 is the middle, and 12,7 is the other end, you can do

12 - 3 = 9

3 - 9 = 6

then

11 - 7 = 4

11 + 4 = 15

so

6 is you x and 15 is your y

Answer: 1

Step-by-step explanation:

Diagonals of rectangles and squares are congruent, but not necessarily for a general parallelogram.

Answer: 115.42 ft

Step-by-step explanation:

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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Answer:

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of missing pulses and follows a Poisson distribution with parameter (μ = 0.50).

The probability mass function of X is as follows:

\(P(X=x)=\frac{e^{-\mu}\ \mu^{x}}{x!};\ x=0,1,2,3...\)

(a)

Compute the probability that a disk has exactly one missing pulse as follows:

\(P(X=1)=\frac{e^{-0.50}\ 0.50^{1}}{1!}=0.3033\)

Thus, the probability that a disk has exactly one missing pulse is 0.3033.

(b)

Compute the probability that a disk has at least two missing pulses as follows:

\(P(X\geq 2)=1-P(X<2)\\\)

                \(=1-[P(X=0)+P(X=1)]\\=1-[\frac{e^{-0.50}\ 0.50^{0}}{0!}+\frac{e^{-0.50}\ 0.50^{1}}{1!}]\\=1-0.6065-0.3033\\=0.0902\)

Thus, the probability that a disk has at least two missing pulses is 0.0902.

(c)

It is provided that the two disks selected are independent of each other.

The probability that a disk has no missing pulses is:

\(P(X=0)=\frac{e^{-0.50}\ 0.50^{0}}{0!}=0.6065\)

Compute the probability that neither of the two disks contains a missing pulse as follows:

\(P(X_{1}=0,\ X_{2}=0)=P(X_{1}=0)\times P(X_{2}=0)\)

                               \(=0.6065\times 0.6065\\=0.367842\\\approx 0.3678\)

Thus, the probability that neither of the two disks contains a missing pulse is 0.3678.

Answer:

Step-by-step explanation:

The dimensions of the rectangular field are given as follows:

The perimeter of a rectangle is given by twice the sum of the length and the width of the rectangle, as follows:

P = 2(l + w).

For this problem, the perimeter is of 582 yards, hence:

2(l + w) = 582

l + w = 291.

The length of the field is 4 yards less than quadruple the width, hence:

l = 4w - 4.

Then the width is obtained as follows:

4w - 4 + w = 295

5w = 295

w = 295/5

w = 59.

The length is obtained as follows:

l = 4 x 59 - 4

l = 232 yards.

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Answer:

Step-by-step explanation:

Quadratic means squared equation so

the first one is your answer.

y= 4x²

Answer:

They are collinear if they are on the same line

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Answer:

0.145

Step-by-step explanation:

Suppose λ = average number of an event occurring in an interval of a presented  length; &

x =  no. of events occurring in an interval length t

Thus, x has a Poisson distribution with parameter λt.

i.e.

\(P[X=k] = \dfrac{(\lambda t)^k\times e^{-\lambda t}}{k!} \ \ \ where; k = 0,1,2 ...\)

Given that:

The average number of call every 8 hours = 11

Then, the parameter for the Poisson process \(\lambda =\dfrac{11}{8}\)

where;

t = 2 hours

\(\lambda t = \dfrac{11}{8}\times 2\)

\(\lambda t = \dfrac{11}{4}\)

Also,

x = no. of calls occurring at an interval of length 2

The required probability is as follows:

P(x > 4) = 1 - [P ( x≤ 4) ]

\(=1 - [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) ]\)

\(= 1 - \bigg [ \dfrac{(\dfrac{11}{4})^0 \times e^{-11/4}}{0!}+\dfrac{(\dfrac{11}{4})^1 \times e^{-11/4}}{1!}+ \dfrac{(\dfrac{11}{4})^2 \times e^{-11/4}}{2!}+ \dfrac{(\dfrac{11}{4})^3 \times e^{-11/4}}{3!}+ \dfrac{(\dfrac{11}{4})^4 \times e^{-11/4}}{4!} \bigg ]\)

\(= 1 - \begin {bmatrix} 1 + \dfrac{11}{4} + \dfrac{\bigg (\dfrac{11}{4}\bigg)^2}{2}+\dfrac{\bigg (\dfrac{11}{4}\bigg)^3}{6}+\dfrac{\bigg (\dfrac{11}{4}\bigg)^4}{24} \end {bmatrix} e^{-11/4}\)

\(= 1 - [ 1 + 2.75 + 3.78125 + 3.466145833 + 2.3829] \ e^{-11/4}\)

= 1 - [13.38037]× 0.06393

= 1 - 0.855407

= 0.14459

≅ 0.145    ( to  3 decimal place)

Answer:

m∠RTS= 15°, m∠UTS= 15°, m∠RTU= 30°

Step-by-step explanation:

Since TS bisects RTS and UTS, that means the two angles are equal to each other. So let's find x first.

x+10=2x+5, subtract x to both sides

10=x+5, subtract 5 to both sides

x=5

Since RTU is basically RTS plus UTS, let's add the two angles together

x+10+2x+5, combine like terms

3x+15

Then we can plug in 5 for x

3(5)+15

15+15

=30

So, RTU is 30 degrees

Answer:

kjndnsadnsdnasnldnkasbdkbaskbjdbLol i dont caewnsnasdHBsadHKUsadkhsdkkbhaSKHChASKUCDKJGCHakbsDKskbhaKHDHU

Step-by-step explanation:

Answer:

no he is not

Step-by-step explanation:

17 tens + 9 ones

17(10) + 9(1)

170 + 9

179

he wrote 791 but the correct answer should be 179

The answer would be (C) 20.

Answer:

The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.

In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.

Option B, 12.5, is the correct answer.

Step-by-step explanation: