A jacket with an original price of $160 is on sale for 15% off what is the sale price

The probability that exactly 2 out of the 20 older adults prefer organic is approximately 0.2707.

To calculate the probability that exactly 2 of the 20 older adults prefer organic, we need to use the binomial probability formula. The formula for the probability of exactly k successes in n trials, where the probability of success is p, is given by:

P(X = k) = \((n choose k) * p^k * (1-p)^{(n-k)\)

In this case, we want to find the probability that exactly 2 of the 20 older adults prefer organic. The probability of an older adult preferring organic is given as 22%, or 0.22.

Using the formula, we substitute the values into the equation:

P(X = 2) = (20 choose 2) * 0.22² * (1-0.22)²⁰⁻²

Calculating this expression, we find:

P(X = 2) ≈ 0.2707

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Complete question is:

A restaurant chain wants to create dishes that will attract new clientele. They are interested in adding some organic options to their menu. A survey revealed that 22% of people over 50 and 32% of people under 50 prefer organic foods. The restaurant wants to poll their clientele. 60 clients were randomly selected: 20 older adults and 40 younger adults. Let X be the number of older adults (out of 20) who prefer organic. Let Y be the number of younger adults (out of 40) who prefer organic. Let Z be the total number in the sample who prefer organic (out of 60).

What is the probability that exactly 2 of the 20 older adults prefer organic?

Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       \(0=\frac{1}{3} x-1\)

       \(1=\frac{1}{3} x\)

       \(x=3\)

So x-intercept is the point (3,0).

Mr. Woodstock will need to purchase 144 meters of wire to fully encircle his land. He will need to measure the length of the four sides of the land and add them together. The four sides measure 36 meters + 36 meters + 16 meters + 16 meters, which equals a total of 104 meters. He should buy enough wire to cover an additional 40 meters to account for any extra material he may need. Therefore, he needs to purchase 144 meters of wire for his fencing.

Step-by-step explanation:

we can make it as a ratio

90/100=27/total Q

total Q= (27*100)/90=30

So wrong questions=30-27=3

hope this helps!

Answer:

- 72 - 48i

Step-by-step explanation:

note that i² = - 1

(6i)(- 2i)(- 6 - 4i)

= - 12i²(- 6 - 4i)

= - 12(- 1)(- 6 - 4i)

= 12(- 6 - 4i) ← distribute parenthesis by 12

= - 72 - 48i

Carly has $2342.67 in her account in 2047.

Growth rate of the account is 3.75% per year.

To get amount of money Carly has in her account in 2047, we need to substitute t = 2047 into equation \(P = 600(1.0375)^t.\)

Years = 2047 - 2010

Years = 37

\(P = 600*(1.0375)^{37}\\P = 600*(3.90445030158)\\P = 2342.67018095\\P = $2342.67\)

The growth rate is calculated by finding the exponent coefficient in the equation \(P = 600(1.0375)^t\)

Growth rate = (1.0375 - 1) × 100

Growth rate = 0.0375 × 100

Growth rate = 3.75%

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Answer: 240 gumdrops

Step-by-step explanation:

1 house: 15 gumdrops

16 houses : 240 gumdrops

1 x 16 = 16

15 x 16 = 240

Answer: I'm pretty sure its 14.

Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14

The domain of the equation include the following: D. all real numbers.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-4, ∞}

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The least distance by Pythagorean theorem is equal to √5. (Correct choice: B)

In this problem we find the representation of a point and a line on Cartesian plane. There is a least distance between the point and the line when the line segment between them is perpendicular to the line. The line segment AC fulfill these features. Given the location of points A and C, we can determine the distance by means of Pythagorean theorem:

d = √[(Δx)² + (Δy)²]

Where:

If we know that A(x, y) = (1, 3) and C(x, y) = (3, 2), then the least distance between the point and the line:

d = √[(3 - 1)² + (2 - 3)²]

d = √[2² + (- 1)²]

d = √5

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Answer:

a) We can use similar triangles to find PB in terms of a and b. Let x be the length of AD. Then, using the fact that AP = 4PC, we have:

PC = CP = x - b

AP = 4(x - b)

Also, using the fact that DC = (1/4)AB, we have:

AD = x

AB = 4DC = x/4

BC = AB - AD = x/4 - x = -3x/4

Now, consider the similar triangles PBC and ABD:

PB/AB = BC/AD

PB/(x/4) = (-3x/4)/x

PB = -3/4(x/4) = -3x/16

Finally, substituting x = a + b, we have:

PB = -3(a + b)/16

b) Using the same similar triangles as in part (a), we have:

DP/DC = PB/BC

DP/(1/4)AB = PB/(-3x/4)

DP = -3/4(PB)(DC/BC)AB

DP = -3/4(PB)(1/4)/(AB - AD)AB

Substituting the expressions for PB, AB, and AD from part (a), we get:

DP = -3(a + b)/16 * 1/4 / (-3(a + b)/4) * (a + b)/4

DP = -3/16 * 1/4 * 4/(3(a + b)) * (a + b)

DP = -3/16

So, DP = -3/16(a + b)

c) To check if DPB forms a straight line, we need to verify if the slopes of DP and PB are equal. Using the expressions we found in parts (a) and (b), we have:

Slope of PB = Δy/Δx = (-3/16(a+b) - 0)/(0 - (-3(a+b)/16)) = 3/16

Slope of DP = Δy/Δx = (-3(a+b)/16 - (-3/16(a+b)))/(1/4 - 0) = -3(a+b)/4

Since the slopes are not equal, DPB does not form a straight line.

Answer:

14 is the correct answer

Step-by-step explanation:

just took the test!! mark me brainliest!!!

The length of the line segment AC is 14.

Option C is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

The triangle is an equilateral triangle.

This means,

Two sides are equal and the angles opposite to the sides are also equal.

Now,

∠B = ∠C

So,

AB = AC

2x = 3x - 7

Solve for x.

2x = 3x - 7

3x - 2x = 7

x = 7

AC.

= 3x - 7

= 3 x 7 - 7

= 21 - 7

= 14

Thus,

The length of the line segment AC is 14.

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Answer:

7/2

Step-by-step explanation:

2x+5=12

2x=7

x=7/2

Answer:

p = 6 , q = 43

Step-by-step explanation:

x² + 12x - 7

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

=x² + 2(6)x + 36 - 36 - 7

= (x + 6)² - 43 ← in the form (x + p)² - q

with p = 6 and q = 43

Answer: Option (2)

Step-by-step explanation:

We need the angle to be included between the two mentioned sides.

Also, the sides need to be corresponding for the ratio, and both sides of the triangle need to be in either the numerators or the denominators.

Answer:

no

Step-by-step explanation:

8a+8b are not equivalent 6a+5b

Answer:

500

Step-by-step explanation:

Answer:

20$

Step-by-step explanation:

because 20*5 =100 which 20 times 5 is the same thing as adding 20+20

+20+20+20 witch is 20$ per dog he walks. hope this helps!

Answer:

From left to right picture,

Scale factor = 2/3

x = 24

y = 12

z = 21

Step-by-step explanation:

Look at the two figures and identify the sides where both lengths are known.

That is the top right-hand side.

Scale factor is hence 18/27 = 2/3

Next, find x, y and z:

Bottom left-hand side:   16/x = 2/3

                                            x = 3/2 x 16

                                             x = 24

Bottom right-hand side:    y/18 = 2/3

                                            y = 18 x 2/3

                                             y = 12

Top left-hand side:       14/z = 2/3

                                           z = 3/2 x 14

                                            z = 21

Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

Answer:

The graph of a linear equation is a straight line.  The "solution" to a system of two linear equations is the point where the two lines cross.  If the two lines are parallel, they never cross; hence parallel lines have no solution.  Two lines are parallel if they have the same slope (the m value in y = mx+b).  One of your equations is y = -2x + (you left the y-intercept out).  The slope is -2.  So any line with a slope of m = -2 will be parallel to this line and will not cross it.  The second line also needs a different value of b, the y-intercept.  Otherwise it is the same line and every point is a solution.  So if your equation is:

y = -2x + 1

Then any equation of the form y = -2x + b, b≠1 will create a system with no solution.  Hence the values of m and b are m = -2, b ≠ 1.

For binomial probability mass function formula and compound interest formula, These both involve the use of exponents, they are not otherwise related to each other in any significant way.

What is Compound interest?

Compound interest is the interest that is earned not only on the initial principal amount of an investment, but also on any interest that has accumulated over time. In other words, it is interest that is "compounded" or added to the principal amount at specific intervals, such as daily, monthly, quarterly, or annually.

Now,

The binomial probability mass function formula and the compound interest formula are not directly related to each other, as they are used to model different types of phenomena.

The binomial probability mass function is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure) and the probability is same. The binomial probability mass function is

P(x) = pˣ (1-p)ⁿ⁻ˣ

where X is the number of successes, k is the specific number of successes we are interested in, n is the total number of trials, p is the probability of success on each trial, and represents the binomial coefficient.

The compound interest formula, on the other hand, is used to calculate the value of an investment over time, assuming a fixed interest rate and compounding periods. The future value is

FV = PV x (1 + r/n)ⁿˣ

where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), n = number of times interest is compounded per year, and x = number of years.

While both formulas involve the use of exponents, they are not otherwise related to each other in any significant way.

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The binomial probability mass function formula and the compound interest formula are not directly related to each other.

The binomial probability mass function formula is used to calculate the probability of observing a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant across all trials. The formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where X is the random variable representing the number of successes, k is the number of successes we want to observe, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

On the other hand, the compound interest formula is used to calculate the value of an investment that earns a fixed interest rate over a certain period of time, assuming that the interest is compounded at regular intervals. The formula is:

A = P * (1 + r/n)^(nt)

where A is the final amount of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the number of years, and (1 + r/n)^(nt) represents the growth factor of the investment.

While both formulas involve exponents and use the terms (1 - p) and (1 + r/n), they are fundamentally different in their purpose and application.

Answer:

VW = 6

Step-by-step explanation:

To find x, set up the following equation:

(5x - 4) + (2x) = 5x

Solve out left side

7x - 4 = 5x

Subtract 5x from both sides

2x - 4 = 0

Add 4 to both sides

2x = 4

Divide both sides by 2

x = 2

Plug into 5x - 4

5(2) - 4

10 - 4

6

Answer:

6

Step-by-step explanation:

5x - 4 + 2x = 5x

7x - 4 = 5x

-4 = -2x

2 = x

5(2) - 4

10 - 4

6

Answer:

(-2,-11)

Step-by-step explanation:

3x-2(4x-3)=16

3x-8x+6=16

-5x=10

x=-2

Plug back in

y=4(-2)-3

y=-8-3

y=-11

Answer:

(-2,-11)

Step-by-step explanation:

y= 4x-3

3x-2y=16 <— substitute y from above

——————————————————————————-

3x-2y = 16

3x-2(4x-3) = 16

3x-8x+6 = 16

-5x + 6 = 16

-5x ÷ 10

x = -2

——————————————————-

Substitute the x from above to any equation to get the y value

3x-2y=16

3(-2)-2y=16

-6 - 2y = 16

-2y = 22

y = -11

——————————————————-———————

(-2,-11)

Answer:

Radius = 25.5 units

Diameter = 51 units

Step-by-step explanation:

r = radius of circle

d = Diameter of circle

  = \(2r\)

Circumference of circle = \(2\pi r\)

Substitute the provided value of the circumference:

                               \(51\pi = 2\pi r\)

r is to be isolated and made the subject of the formula:

                                 \(r = \frac{51\pi}{2\pi}\)

\(\pi\) in the numerator and denominator cancel each other outcompletely:

                                 \(r = \frac{51}{2}\)

                          ∴r = radius of circle = 25.5 units

This also means that:

\(d = 2r\)

\(d = 2(25.5)\)

∴d = Diameter of the circle = 51 units

Answer:

r=26

Step-by-step explanation:

22/11=r/13

11r=286

r=26

Answer:

The square root of 50 is approximately 7.07.

Answer:

7.07106781187...

Step-by-step explanation:

its an irrational number

Estimated volume of the tree as per given height and circumference using trapezoidal rule is equal to 30907.5 cubic inches.

As given in the question,

Given height 'x' and circumference 'y=f(x)',

Height (inches)  'x'            :       0    15     30    45      60      75      90

Circumference (inches) 'y=f(x)':      31   28    21    17      12      8        2

Trapezoidal rule :

Δx = (b - a ) n

Here b = 90

a = 0

n =6

Δx = ( 90 - 0)/6

    = 15

Substitute the value to get the volume using trapezoidal rule:

T₆=(Δx/2)[f(x₀)²+ 2{f(x₁)²+ f(x₂)²+f(x₃)² + f(x₄)²+f(x₅)²}+ f(x₅)²]

   = (15/2)[ 31² + 2 (28² + 21² + 17² + 8²) + 2² ]

   = ( 15/2) [961 + 2{ 784+ 441 + 289 + 64} + 4]

   = 15 × 2060.5

   =   30907.5 cubic inches

Therefore, the volume of the tree as per given given table using trapezoidal rule is equal to 30907.5 cubic inches.

The above question is incomplete , the complete question is:

The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree using the trapezoid rule. There needs to be six subdivisions in the trapezoid rule.

Height (inches) :                  0    15     30    45      60      75      90

Circumference (inches):      31   28    21    17      12      8        2

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Answer:

1810

Step-by-step explanation:

362+362+362+362+362=1810

Answer:

it's b

Step-by-step explanation:

literally twelve minus m

Answer:

B

Step-by-step explanation:

12 minus m is, 12 - m