a rectangular field is X to the second power - 150 x + 5400 the width in feet is x - 60 what is the length in feet​

In using quarterly time series data, Quarter two  can serve as the base period for interpretation of dummy variables.

What do you mean by interpretation?

The process of interpreting anything involves elaborating, rephrasing, or otherwise demonstrating your own understanding of it.

                           Because they are explaining what someone is saying to someone who doesn't understand, a person who translates one language into another is known as an interpreter.

What are examples and variables?

A trait that is measurable and capable of taking on several values is known as a variable. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling.

                                 The two primary categories of variables are categorical and numeric.

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Answer:

Step-by-step explanation:

16 cups= 1 gallon

16 cups=8 cakes

8 x 3=24

24 chocolate pudding cakes can  be made by Abdul with 3 gallons of milk

An equation is an expression used to show the relationship between two or more variables and numbers.

Given that 2 cups of milk is used to make a chocolate pudding cake.

Amount of cake made from 3 gallons = 48 cups *  1 cake per 2 cups = 24 cakes

24 chocolate pudding cakes can  be made by Abdul with 3 gallons of milk.

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The events A and B are not disjoint (i.e. mutually exclusive) events

The sections on the dice are given as

S = {1, 2, 3, 4, 5, 6}

These sections mean that:

n(3) = 1 and n(4) = 1

Recall that:

A be the event that the number rolled is a 3 or a 4.

So, we have

P(A) = P(3) + P(4)

This gives

P(A) = 1/6 + 1/6 = 1/3

Also, we have

Coin = {Head, Tail}

Where

B be the event that a head is flipped.

This means that

P(B) = 1/2

The occurrence of an event in event A does not hinder the occurrence of another occurrence in event B

This means that the events are not disjoint

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Answer:

126

Step-by-step explanation:

because after point no. greater than 5 will definitely

be 1 no. more than that

Answer:

12

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The  base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

1. The solution to the system of equations is v = -3 and w = 4.

2. The solution to the system of equations is y = 6 and z = -2.

To eliminate v, we can add the two equations:

(-v + w) + (v + w) = 7 + 1

2w = 8

w = 4

Substitute w = 4 into one of the equations to solve for v:

v + 4 = 1

v = -3

To eliminate z, we can add the two equations:

(y + z) + (y - z) = 4 + 8

2y = 12

y = 6

Substitute y = 6 into one of the equations to solve for z:

6 + z = 4

z = -2.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Probability of mutation = 2% = 0.02

Number of samples(n) = 18

nCk × (p^k) × (1 - p)^(n-k)

P = probability of success

n = number of trials

k = number of success desired

A) P(n, k) = p(18, 0) = 18C0 × 0.02^0 × 0.98^18

P(18,0) = 1 × 1 ×0.6951353 = 0.6951

0.6951 × 100% = 69.50%

B.) At most one Sample is mutated

P(x =0) + p(x = 1)

P(18,0) = 69.5%

P(18, 1) = 18C1 × 0.02^1 × 0.98^17

P(18,0) = 18 × 0.02 × 0.70932176618 = 0.25535

0.2553 × 100% = 25.5%

69.5% + 25.5% = 95.00%

C) More than half the samples are mutated

Half of samples (18 / 2) = 9

P(x> 9) : p(x = 9) + p(x = 10)... +p(x = 18)

Using the binomial distribution calculator to save time ;

P(x > 9) = 0.00

Answer: Consider me the brainiest. The answer is... Decimal form =4.083

Exact form= 49/12

The mixed number form=4 1/12

How do we solve fractions step by step?

Conversion a mixed number 2  1/3 to a improper fraction: 2 1/3 = 2  1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator

A;   Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one-third are seven-thirds.

Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7

c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.

Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It

is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions.  The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12.  It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling.  In other words - seven thirds plus seven quarters is forty-nine twelfths.

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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The length of the side GF is equal to 0.96 according to Pythagoras's Theorem.

Given angle ∠E = 16°

Length of side GE = 3.5

Also the given angle is right angled triangle. So ∠F = 90°.

Now we need to find the length of side GF.

Use Pythagoras's theorem to find the length GF.

Formula: \(C^{2} =A^{2} +B^{2}\)

i.e., \(GE^2=GF^2+EF^2\)

Now, according to trigonometric rules, sinФ= opposite /hypotenuse

cosФ = adjacent / hypotenuse

tanФ = opposite / adjacent

Now, sum of all angles = 180°

So ∠G = 180°-90°-16° = 74°

∠G = 74°

Now, sin 16° = x/3.5 = opposite / hypotenuse

x = 0.275 x 3.5

x= 0.96

Therefore, the length of the side GF (x) is equal to 0.96.

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Answer:

B,

Step-by-step explanation:

The height of a rectangle is 12 units. The rectangle has an area greater than 25 square units. What are the possible values for the base of the

rectangle, n?

Step-by-step explanation:

3 1/2 = 7 /2

2 1/2 = 5 /2

7/2 - 5/2

= 2/2 = 1

hope it helpful

The slope of (3,1) and (4 , 2) is 1

The standard form of  equation of line in slope-intercept form is = y =mx + b

where, m is slope of line

b is y-intercept of line

The slope , m represents the steepness of a line. It is also termed as gradient

The y-intercept, b represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Given that line passes through (3,1) and (4,2)

Slope of line is given by = y₂ - y₁ / x₂ - x₁

here x1 = 3 , x2 = 4 and y1 = 1 and y2 = 2

slope : m = 2 - 1 / 4 - 3

m = 1 /1 => 1

Hence , the slope of line is 1

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The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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As per the binomial distribution, the probability that every insect will die is 0.22%.

Binomial distribution:

Binomial distribution refers a discrete probability distribution that gives only two possible results in an experiment, either success or failure.

The formula for calculating binomial distribution is

P = ⁿCₓ pˣ qⁿ⁻ˣ

P = binomial probability

x = number of times for a specific outcome within n trials

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

Given,

A certain insecticide kills 80% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment.

Here we need to find the probability that every insect will die and round off it into four decimal places.

While we looking into the given question we have identified that it is the binomial type probability distribution.

And we have identified the following values,

The number of trials n= 12

Probability of the success trial = 0.8,  

Number of success trials k = 12

Now, we have apply the values on the binomial distribution formula, then we get,

=> P = ¹²C₁₂ x (0.6)¹² x (1 - 0.6)¹²⁻¹²

When we simplify it then we get,

=> P = 1 x 0.0022 x (0.4)⁰

=> P = 0.0022

When we convert this into percentage then we get, 0.22%

Therefore, the resulting probability is 0.22%.

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the distance from the center of the circle to a point on the circle is simply its radius, thus

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{(~~-4 - (-2)~~)^2 + (~~1 - 1~~)^2} \implies r=\sqrt{(-4 +2)^2 + (1 -1)^2} \\\\\\ r=\sqrt{( -2 )^2 + ( 0 )^2} \implies r=\sqrt{ 4 + 0 } \implies r=\sqrt{ 4 }\implies \stackrel{ radius }{r=2} \\\\[-0.35em] ~\dotfill\)

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{1}{k})}\qquad \stackrel{radius}{\underset{2}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-1 ~~ )^2~~ = ~~2^2\implies (x+2)^2 + (y-1)^2 = 4 \\\\\\ (x^2+4x+4) + (y^2 - 2y + 1) = 4\implies \boxed{x^2+4x +y^2 -2y + 1 = 0}\)

The average speed on the first 30 minutes is 0.2 km per min.

Here we have the graph for the position of a bycicle rider on a 42-minute trip.

On the vertical axis we can see the position, and on the horizontal axis we can see the time.

Remember that:

speed = distance/time.

To find the average speed on the first 30 min, we need to take the quotient between the position after 30 minutes and 30 min.

At 30 min we can see that the position is at 6 km, then the speed will be:

S = 6km/30min = 0.2 km per min.

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Answer:

6 is the answer because it is

Number of lines of symmetry in snowflake design would be,

⇒ 6

We have to given that,

A snowflake design is shown in image.

Since, We know that,

Exactly dividing a form in half, a line of symmetry exists. This indicates that the form would fold perfectly in half if you did so along the line.

Hence, By definition of line of symmetry,

Number of lines of symmetry in snowflake design would be,

⇒ 6

Thus, Number of lines of symmetry in snowflake design would be,

⇒ 6

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Answer:

Step-by-step explanation

Sort the data: 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97

Find the median (Q2): 53

Split the data set into two parts: Q1 (25th percentile) and Q3 (75th percentile)

Q1: 41, 41, 43, 43, 45, 50, 52, 53

Q3: 54, 62, 63, 63, 67, 75, 97

Find the median (Q1) of Q1 and the median (Q3) of Q3:

Q1 = 45

Q3 = 63

Finally, calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 63 - 45 = 18

So, the interquartile range of the given data set is 18. This means that 50% of the data falls within a range of 45 + 18 = 63 and 45 - 18 = 27.  

Answer:

14

Step-by-step explanation:

(4+(16-1)/5)*2

(4+15/5)*2

(4+3)*2

7*2

14

Answer:

See explanation

Step-by-step explanation:

Given

f(r) => Number of people in the bus after 8am

Required

Interpret f(5) = 23

Going by the analysis in the question, the interpretation goes this:

5 hours after 8 am, there are 23 riders on a bus

We can also interpret as:

There are 23 riders on a bus at 1 pm

Since 1 pm = 5 hours after 8am

The methods to reduce the risk of tuberculosis include Educating patients on respiratory hygiene

What is tuberculosis?

Mycobacterium tuberculosis is the bacteria that causes tuberculosis (TB). TB germs often attack the lungs, but they can attack any region of the body, including the kidney, spine, and brain.

When an infected individual coughs or sneezes, the germs that cause tuberculosis spread. The majority of people who are infected with the germs that cause tuberculosis do not show symptoms. When symptoms do appear, they are typically accompanied by a cough (sometimes blood-tinged), weight loss, night sweats, and fever.

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Answer:

15 quarters and 10 nickels

Step-by-step explanation:

\(q+n=25\)

\(0.25q+0.05n=4.25\)

multiply the first equation by -0.25 and add the second equation to it

\(-0.25q-0.25n=-6.25\\0.25q+0.05n=4.25\)
________________
                \(-0.2n=-2\)

\(n=\frac{-2}{-0.2} =10\)   has 10 nickels

\(q=25-n=25-10=15\)  has 15 quarters

10(.05) +15(0.25) = 0.5 + 3.75 = 4.25

Hope this helps

Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

The probability of exactly 90 defective washers is approximately 0.021, and the probability of at least 2 defective items is approximately 0.985.

A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. The probability of exactly 90 defective washers being chosen and the probability of at least 2 defective items being found can be calculated using the hypergeometric distribution formula.

A. The probability of exactly 90 defective washers being chosen can be calculated using the hypergeometric distribution. The probability mass function of the hypergeometric distribution is given by:

P(X = 90) = (400 choose 90) * (1100 choose 110) / (1500 choose 200)

Substituting the given values, we get:

P(X = 90) ≈ 0.021

B. The probability of at least 2 defective items can be calculated as 1 minus the probability of 0 or 1 defective item. The probability of 0 defective items is given by:

P(X = 0) = (1100 choose 200) / (1500 choose 200)

The probability of 1 defective item is given by:

P(X = 1) = (400 choose 1) * (1100 choose 199) / (1500 choose 200)

Substituting these values, we get:

P(X >= 2) = 1 - P(X = 0) - P(X = 1) ≈ 0.985.

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The complete question is:

A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. Two hundred washers are chosen at random (without replacement) and classified as defective or non-defective_ a) What is the probability that exactly 90 defective washers are found? (Do NOT compute out:) b) What is the probability that at least 2 defective items are found?

Answer:

hmm mybe 28k

Step-by-step explanation:

Answer:

it would be C

Step-by-step explanation: