at the valentines day dance the sponsors handed out candy kisses to each person entering the dance. one group received a total of 20 candy kisses as they entered. another group of dancers received a total of 52 candy kisses. each person received the same amount of candy. what was the greatest possible number of candy kisses each person could have received

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.

for such more question on distance

https://brainly.com/question/7243416

#SPJ8

Answer:

A

Step-by-step explanation:

It is option A: -2, -1, 0, 1

Answer:

x = 10, AB = 57

Step-by-step explanation:

In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. From this, we have:

\( \frac{1}{2} (5x + 7 + 8x - 11) = 63\)

\(13x - 4 = 126\)

\(13x = 130\)

\(x = 10\)

\(5(10) + 7 = 50 + 7 = 57\)

The values accurate to two decimal places for -2  standard deviation, mean, and +2  standard deviation are 0.30, 0.40, and 0.49, respectively.

We can use the following formulas to calculate the mean and standard deviation of the sampling distribution:

Mean: μ = p = 0.40 (since the population proportion is 0.40)

Standard deviation: σ = √((p(1-p))/n)

σ = √((0.40(1-0.40))/165)

σ = 0.049

Now we can calculate the values for -2SD, mean, and +2SD as follows:

-2SD: μ - 2σ = 0.40 - 2(0.049) = 0.30

Mean: μ = 0.40

+2SD: μ + 2σ = 0.40 + 2(0.049) = 0.49

Learn more about standard deviation at: https://brainly.com/question/24298037

#SPJ1

Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )

Answer:

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Step-by-step explanation:

Answer:

7.28 units

Step-by-step explanation:

To find the distance between two points, we use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates given, we can plug in the values:

d = √((-5 - 2)^2 + (5 - 7)^2)

d = √((-7)^2 + (-2)^2)

d = √(49 + 4)

d = √53

Therefore, the distance between (2,7) and (-5,5) is approximately 7.28 units (rounded to two decimal places).

I hope this is clear enough , although I did not arrive at the same answer using x in both equation .

Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.

This shows, with dots, the number of times that each of the measures appears in a data set.

For finding the dot plot, we have that:

The shortest conifer measures 6 and 1/4

= 6.25 inches.

The tallest conifer measures 9.5 inches.

The difference is:

9.5 - 6.25 = 3.25 inches.

Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.

More can be learned about a dot plot at;

brainly.com/question/24912483

#SPJ1

Answer:

4.5 inches on the map would represent 60 actual feet.

Step-by-step explanation:

Given that:

1.5 inches on map represents 20 feet in the park.

x be the inches on map that represents 60 feet in the park.

Ratio of distance on map to actual distance :: Ratio of distance on map to actual distance

1.5 : 20 :: x : 60

Product of mean = Product of extreme

20*x = 1.5*60

20x = 90

Dividing both sides by 20

\(\frac{20x}{20}=\frac{90}{20}\\x=4.5\)

Hence,

4.5 inches on the map would represent 60 actual feet.

Answer:

b

Step-by-step explanation:

Answer:

The answer is C, 2/9

Step-by-step explanation:

Since there 18 marbles in total and 4 blue marbles, that makes the probability 4/18. Although, 4/18 has to be simplified, which is 2/9

Answer:

its c just so u know

Step-by-step explanation:

The value of 3¾ft in yards would be = 1 6/25 yard

A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.

To convert to yards;

1 ft = 0.33 yard

3¾ = X yards

make x yards the subject of formula;

X yards = 3¾ × 0.33

X yards = 3.75×0.33

X yards = 1.24 yards

X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.

Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25

Learn more about mixed numbers here:

https://brainly.com/question/21610929

#SPJ1

The odds in favor of drawing a 7 are 1 to 12.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

There are four 7s in a deck of 52 cards, so the probability of drawing a 7 is 4/52, which simplifies to 1/13. The odds in favor of drawing a 7 are the ratio of the probability of drawing a 7 to the probability of not drawing a 7, which is:

(1/13) : (12/13

We can simplify this ratio by dividing both terms by the greatest common factor, which is 1:

(1/13) : (12/13) = 1 : 12

Therefore, the odds in favor of drawing a 7 are 1 to 12.

To know more about probability visit :

https://brainly.com/question/13604758

#SPJ1

The length of e is 29.53 inches.

In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".

Given:

f= 33 inches

<F= 140, <D = 5

Now,

<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35

Using Sine law

sin F / f = sin E/ e

sin 140 / 33 = sin 35 / e

0.642/ 33 = 0.573 / e

0.0194 e= 0.573

e= 29.53 inches

Hence, the length of e is 29.53 inches.

Learn more about sine law here:

https://brainly.com/question/17289163

#SPJ1

Now

\(\\ \rm\Rrightarrow P(E)=\dfrac{|E|}{|S|}\)

\(\\ \rm\Rrightarrow P(E)=\dfrac{7}{14}=1/2\)

Answer:

\(\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}\)

Given:

\(\implies \mathsf{Probability \ of \ red\ hair= \dfrac{7}{14}=\dfrac12=0.5}\)

Step-by-step explanation:

Diameter (d) = 22 km

circumference(c)

= π d

= 3.14 * 22

= 69.02 km

Hope it will help :)

An arithmetic progression is a set of numbers with a fixed difference between any two succeeding numbers (A.P.). Examples of A.P. include 3, 6, 9, 12, 15, 18, and 21.

A.P. and G.P. application: A series of terms known as an arithmetic progression (AP) have identical differences. In a geometric progression (GP), the common ratio is multiplied by the previous term to produce each succeeding term.

Given,

a₁ = x

a₂ = 2x + 1

a₃ = 11

a₂ - a₁ = a₃- a₂

(2x + 1) - (x) = 11 - (2x + 1)

2x - x + 1 = 11 - 2x - 1

x + 1 = -2x + 10

2x + x = 10 - 1

3x/3 = 9/3

x = 3  

The arithmetic sequence:  3, 7, 11

Common difference: 4

To know more about arithmetic progression visit:-

brainly.com/question/29259404

#SPJ1

The layout of the fast-food restaurant of dimensions 6 by 8 5 feet squares is presented in the attached table created with Sheets.

The dimensions of the facility are;

Horizontal = 6 squares

Vertical = 8 squares

The side length of each square = 5 feet

Therefore;

Area of each square = 5² ft.² = 25 ft.²

Number of squares, n, required by each dependent are therefore;

CB department, n = 300 ÷ 25 = 12 squares

CF department, n = 200 ÷ 25 = 8 squares

PS department, n = 8 squares

DD department, n = 8 squares

CS department, n = 12 squares

A layout for the fast-food restaurant is therefore;

Please see the attached table layout created using Sheets.

Learn more about finding the area of regular figures here:

https://brainly.com/question/316492

#SPJ1

Answer:

78

Step-by-step explanation:

JT = half the distance so JT x 2 = CT

JT = 39

39 x 2 = 78

Michael must contribute $7,849.55 quarterly during the first 12 years in order to achieve his retirement goals.

The idea that money now is worth more than the same amount of money in the future owing to the potential earning capacity of money over time is known as the time value of money, and it is a basic concept in finance. The notion behind the concept is that money may be invested to produce interest or other returns, and that over time, inflation and other variables affect how much money is worth.

Given that, the contributions are made for 12 years.

The future value is thus given by:

\(FV = P[((1+r)^n - 1)/r]\)

The number of periods are:

12*4 = 48 periods.

The interest rate per quarter is 8%/4 = 2%.

Substituting the values we have:

\(FV = P[((1+r)^n - 1)/r] \\\\=P[((1+0.02)^48 - 1)/0.02] \\\\= P[67.242]\)

Now, for present value of an annuity, we get:

\(PV = C[(1-(1+r)^-n)/r] \\\\= 10000[(1-(1+0.02)^-40)/0.02] \\\\=528,113.20\)

Setting the two values equal we have:

P[67.242] = 528,113.20

P = 7,849.55

Hence, Michael must contribute $7,849.55 quarterly during the first 12 years in order to achieve his retirement goals.

Learn more about future value here:

https://brainly.com/question/28952696

#SPJ1

We can solve the inequality by isolating the variable, we will get:

x < 8

This is just like an equation, what we need to do is isolate the variable in one of the sides.

Here we have the inequality:

3x - 5 < 19

To solve it, let's isolate the variable x.

We can start by adding 5 in both sides, then we will get:

3x < 19 + 5

3x < 24

Now let's divide both sides by 3, so we will get:

x < 24/3

x < 8

Laern more about inequalities at:

https://brainly.com/question/24372553

#SPJ1

Answer:D: 48

Step-by-step explanation:

Answer:

\(a.\ \dfrac{3}{5}\)

Step-by-step explanation:

We can see the fractions \(\frac{5}{4}\) and \(\frac{3}{4}\) of cups.

It can be seen that denominator has 4 i.e. the fraction \(\frac{1}{4}\).

Let us suppose, a unit is equal to \(\frac{1}4\) of a cup.

Susan was supposed to use \(\frac{5}{4}\) of a cup.

i.e. 5 units of butter was to be used.

But, actual recipe has only 3 units of butter.

\(\text{Fraction of butter used} = \dfrac{\text{Units of butter used}}{\text{Unit of butter Susan was supposed to use}}\)

a. \(\text{Fraction of butter used} = \dfrac{3}{5}\)

Alternatively, we could have directly divided the given fractions:

\(\dfrac{\dfrac{3}{4}}{\dfrac{5}{4}} = \dfrac{3}{5}\)

The fraction of the butter that she should have used did Susan actually use is :

Fractions =5/4 and 3/4 of cups.

Denominator = 4 i.e. the fraction 1/4

Let us suppose,

A unit is equal to 1/4 of a cup.

Susan was supposed to use 5/4 of a cup.

5 units of butter was to be used.

But, actual recipe has only 3 units of butter.

Fraction of butter used=unit of butter used/unit of butter                        

                                                                 that was supposed to      

                                                                         be use

                                        =3/4/5/4

                                        =3/5

The fraction of the butter that she should have been used is 3/5.

Find out more information about "Fractions":

https://brainly.com/question/9047718referrer=searchResults

Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Answer:

every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false

Answer:

The walkway should be 2ft wide.

Step-by-step explanation:

Let x be the width of the walkway surrounding the pool.

The area including the pool is 560ft².

Let's solve for the value of x.

The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.

A = lw

560 = (24 + 2x)(16 + 2x)

560 = 384 + 48x + 32x + 4x²

4x² + 80x + 384 - 560 = 0

4x² + 80x - 176 = 0

Divide the whole equation by 4

x² + 20x - 44 = 0

(x + 22)(x -2) = 0

x = -22; x = 2

Since we are dealing with dimensions, take the one with the positive value.

x = 2ft

Let's check

560ft² = (24ft + 2x)(16ft + 2x)

560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))

560ft² = (24ft + 4ft)(16ft + 4ft)

560ft² = (28ft)(20ft)

560ft² = 560ft² ✔

Answer:

The perimeter of this rectangle is 10 cm.

Answer:

-6

Step-by-step explanation: