The length, L, of a rectangular garden is twice its width, W. The perimeter of the garden is 36 feet.

Answer:

324 ft

Step-by-step explanation:

[tex]v=\sqrt{2gh}[/tex]

[tex]v^2=(\sqrt{2gh})^2[/tex]

[tex]v^2=2gh[/tex]

[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]

[tex]\frac{v^2}{2g}=h[/tex]

[tex]\frac{144^2}{2(32)}=h[/tex]

[tex]\frac{20736}{64}=h[/tex]

[tex]324=h[/tex]

Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.

I clarify this because the question uses plural “drawing white socks”. Ok, in our language practice one does usually say socks instead of sock because they usually come in pair.

If it means 1 draw of 1 sock then the probability is 6out of 21. Or about 28.57%

But if it is to draw twice with one sock being drawn in each draw to get a pair of white socks then the probability is 6/21 * /20 = 30/420 = 1/14 or about 7.14%

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250 bicycles must be manufactured to minimize the cost.

The cost C in dollar of manufacturing x bicycles at a production plant is given by:

C(x) = 3x² - 1500x + 198,500

a. To find number of bicycle that can minimize the cost

differentiate C(x) with respect to x

C'(x) = 6x - 1500

equating C'(x) = 0

6x - 1500 = 0

x = 1500/6

x = 250 , is our stationary point

Differentiate C'(x) = 6x - 1500 again and put x = 250,

C''(x) = 6 (positive)

At x = 250 , cost is minimum

Therefore , 250 bicycles must be manufactured to minimize the cost.

b. C(x) = 3x² - 1500x + 198,500

putting x = 250,

C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500

= $11,000 is the minimum cost

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Answer:

r ≤ -21.75

Step-by-step explanation:

Forming the equation,

→ r ÷ (-2.5) ≤ 8.7

Then the value of r will be,

→ r ÷ (-2.5) ≤ 8.7

→ r ≤ 8.7 × (-2.5)

→ r ≤ -21.75

Hence, value of r is -21.75.

The x-intercepts of the quadratic function g(x) = x² - 10x + 24 are given as follows:

(4, 0) and (6, 0).

A function crosses the x-axis when the numeric value of the function is of y = 0, hence these points are called the x-intercepts of the function.

In this problem, the definition of the function is given as follows:

g(x) = x² - 10x + 24.

This function can be simplified as follows:

g(x) = (x - 6)(x - 4).

Applying the inverse of the Factor Theorem, the x-intercepts are given as follows:

Hence the x-intercepts of the function are given by the third option, which is of (4, 0) and (6, 0).

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Answer: C

Step-by-step explanation: trust me

An airplane can fly 374.4 miles in 3 hours.

A small airplane flew 104 miles in 50 minutes.

So, the rate would be,

rate  = distance / time

rate = 104/50

rate = 2.08 miles/minute

We need to find the distance the airplane can flay in 3 hours.

3 hours = 180 minutes

t = 180 minutes

r = d/t

2.08 = d/180

d = 2.08 * 180

d = 374.4 miles

Therefore, an airplane can fly 374.4 miles in 3 hours.

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Answer:

v = -6

Step-by-step explanation:

½v + 8 = 3 - ⅓v

Collect like terms

½v + ⅓v = 3 - 8

⅚v = -5

Divide both sides by ⅚

⅚v/⅚ = -5/⅚

v = -5 × 6/5

v = -30/5

v = -6

Answer:

A = Ao * (1+ i)^n       amount Ao invested for n yrs at i/yr

14900 = 4500 (1.07)^n

3.311 = (1.07)^n

log 3.311 = n log 1.07 = n* .0294

n = log 3.311 / .0294 = .52 / .0294 = 17.6 yrs

Check:

Money will double about very 70 / 7 = 10 yrs

At 10 yrs around 9000 return

At 20 yrs 18,000 return - result appears reasonable

Answer:

Step-by-step explanation:

28xy

The measure of the angle ACB is 87°.

Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.

An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.

When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.

In triangle ADE and triangle ACB, the triangles are similar.

So,

∠AED/ ∠ABC = ∠DAE/∠CAB

∠AED = ∠ABC

11x-2 = 6x + 13

11x - 6x = 13 + 2

5x = 15

x = 15/5

x = 3

So, the measure of angle ABC is

∠ ABC = 6(3)+13

∠ ABC = 18+13

∠ ABC  = 31°

Now, consider triangle ABC, the sum of all angles = 180°

So, 62° + 31° + ∠ACB = 180°

∠ACB + 93° = 180°

∠ACB =  180° - 93°

∠ACB = 87°

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The measures, using the normal distribution, are given as follow:

a) Probability that a wedding costs less than $20,000: 0.257 = 25.70%.

b) Probability that a wedding costs between $20,000 and $32,000: 0.659 = 65.90%.

c) Minimum cost of the most expensive 5% of weddings:  $33,564

Normal Probability Distribution

The z-score of a measure X of a variable that has to mean symbolized by  and standard deviation symbolized by  is given by the rule presented as follows:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

The z-score represents how many standard deviations measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.

Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of measure X in the distribution.

The mean and the standard deviation for the wedding prices are given as follows:

μ = 23858, σ = 5900

a) The probability that a wedding costs less than $20,000 is the p-value of Z when X = 20000, hence:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z = (20000 - 23858)/5900

Z = -0.65

Z = -0.65 has a p-value of 0.257.

The probability that it costs between $20,000 and $32,000 is the p-value of Z when X = 32000 subtracted by the p-value of Z when X = 20000, found above, hence:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z = (32000 - 23858)/5900

Z = 1.38

Z = 1.38 has a p-value of 0.816.

0.916 - 0.257 = 0.659.

The minimum cost for a wedding to be in the most expensive 5% of weddings is the 95th percentile, which is X when Z = 1.645, hence:

1.645 = (X - 23858)/5900

X - 23858 = 1.645 x 5900

X = $33,564.

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Answer: 90 x 4 x 1

Step-by-step explanation:

90 x 4 x 1 = 360

Please thank and rate <3

Answer:

360

Step-by-step explanation:

2³x3²x5

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Step-by-step explanation:

Simplify Calculator. Step 1: Enter the expression you want to simplify into the editor. The simplification calculator allows you to take a simple or complex expression and see fro googlle bro

Answer:

16 - 11i

Step-by-step explanation:

When Adding or Subtracting any Complex Number

we Add or Subtract the Real Parts together and Add or Subtract the Imaginary Parts together

So for our Question

( 9 - 9i ) - ( -7 + 2i ) = ( 9 - (-7) ) + ( -9 - 2 )i = 16 - 11i

Answer:

Step-by-step explanation:

um ok so

Answer:

x=0

Step-by-step explanation:

the rest of this is so i can reach twenty characters.

The inequality expression given as -x/3 < 5 has a solution of x > -15

From the question, the inequality is given as

-x/3 < 5

The above inequality can be re-written as follows

-x/3 < 5

There is no constant to add or subtract in the expression

So, we start by multiplying both sides of the expression by a constant

Multiply both sides by 3

expression

-x < 15

Divide both sides by -1

So, we have the following representation

x > -15

Hence, the solution to the expression is x > -15

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Answer: D

Step-by-step explanation:

5 x 3 = 15

8 x 3 = 24

the multipliers are both 3

so they are "similar shapes".

The other options don't have the same multipliers so they aren't right :)

The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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Answer:

Step-by-step explanation:

Considering the volume of the rectangular prism given the dimensions, it is found that:

The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width w, the height h and the length l, that is:

V = l x w x h.

In this problem, the dimensions are given as follows:

Hence the polynomial expression for the volume of the prism is given as follows:

V = w(w - 5)(w - 3)

V = w(w² - 8w + 15)

V = w³ - 8w² + 15w.

The features of the polynomial function are given as follows:

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The equation of the graph in point slope form is y + 2 = -3(x - 1)

The equation of the graph in point slope form can be represented as follows;

y - y₁ = m(x - x₁)

where

using two point let's find the slope

(0, 1)(-1, 4)

Hence,

m = 4 - 1 / -1 - 0

m = 3 / -1

m = -3

Therefore, the slope of the line is - 3.

Therefore, using one coordinates(1, -2) from the graph, the equation of the graph in point slope form is y + 2 = -3(x - 1)

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x-intercept

The x-intercept is where y=0.

[tex]-7x+10(0)=35\\\\-7x=35\\\\x=\boxed{-5}[/tex]

y-intercept

The y-intercept is where x=0.

[tex]-7(0)+10y=35\\ \\ 10y=35\\\\y=\boxed{7/2}[/tex]

The interior angle and the exterior angle of triangle XYZ is 68° and 112° respectively.

A triangle is a plane shape that has three sides.

Recall that, the sum of a interior angle and an exterior angle of a triangle is 180°.

Using the formula,

Where:

From the question,

Given:

Substitute these values into equation 1

Solve for g

Hence, interior angle of X = (5×10)+18 = 50+18 = 68° and exterior angle of X = (8×10)+32 = 80+32 = 112°

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Answer: I belive the answer is A

Step-by-step explanation: i could be wrong

The equation 22+(d-1)0.5 = 30 may be used to determine how many days it will take the plant to reach a height of 30 cm. The value of d is 17, and it stands for the number of days.

There are two definitions for an arithmetic sequence. It is a series where the differences between every two succeeding terms are identical or each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term.

The following details are available to us:

A 22 cm tall basil plant that is gaining half a centimeter daily was purchased by Matteo.

We now have the arithmetic progression shown below with the common difference, indicated by the letter d:

22, 22.5, 23, 23.5, ...

The formula for calculating the nth term:

When an is the first term, a(n) = a+(n-1)d.

A) 22+(d-1)0.5 = 30

B) The plant still needs to develop 8 cm, as there is a difference of 8 cm between 30 and 22.

C) D's value:

22+(d-1)0.5 = 30

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Answer:

Step-by-step explanation:

dees

Answer:get a tutor

Step-by-step explanation:

its free

The angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 200 feet above sea level will be 87.36 degrees.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.

Here,

The cell phone tower's peak will be at a height of 1300 + 110 = 1410 feet above sea level.

Assuming that the user of a cell phone is 200 feet above sea level, the distance between them is 1410 feet- 200 feet, or 1210 feet.

The distance between them horizontally is 5 miles, or 5 * 5280, or 26400 feet.

The opposite cathetus is 26400 feet away and the neighboring cathetus is 1210 feet away.

the angle is 87.376 degrees, or tan(angle) = 26400 / 1210 = 21.82

A cell phone user 5 horizontal miles away and 200 feet above sea level will be depressed at an angle of 87.36 degrees from the top of the tower.

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The mean of the triangular dots is 4, the median is 8 and the range is 6.

How to determine the Measures of central tendency?

A measure of central tendency is defined as a single value that attempts to describe a set of data by identifying the central position within the given set of data.

From the question, the parameters are dots that will form triangle as

                  .

             .   .    .

         .    .    .   .    .

      .   .   .     .   .    .   .

Total mumber of dots is 1+3+5+7=16

These parameters are represented as follows:

The mean is the average of all the dots that formed the triangle

Mean value of the set of data = [tex]\frac{16}{4} =4[/tex]

The median is the middle number when arranged in ascending or descending order of magnitude

The median is [tex]\frac{16}{2} =8[/tex]

The range is the highest value minus the lowest value in the dots

The range is 7-1=6

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Answer:

$2.34

Step-by-step explanation:

2.75 x 0.85 = $2.3375

Since we are rounding, it will round up to $2.34.

Answer:

Step-by-step explanation:

Cost of 2.75 pounds of potato =.

2.75x0.85

 = $2.3375

Answer:

$6.72

Step-by-step explanation:

1 us liquid pint =2 us cups

3.36*2 cups