six distinct integers are selected at random from 2018 2019 2020 2027 what is the probability that among those selected the second smallest in 2020

The amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups. So, option D is correct.

A mixed fraction is one that is represented by both its remainder and quotient. Two is the quotient and one is the remainder in the mixed fraction 2/3, for instance.

You can write mixed numbers with or without the word "and," for example, 5 and 3/4 . The mixed number must have a valid fraction as its fractional component. A correct fraction, such as 37, has a numerator that is less than the denominator.

Given,

The amount of orange juice= 3 [tex]\frac{1}{3}[/tex] cups

The amount of grape juice=6 [tex]\frac{1}{2}[/tex] cups

The amount of cherry juice= 4 [tex]\frac{1}{8}[/tex] cups

The amount of club soda=1 [tex]\frac{1}{4}[/tex] cups

So, 3 [tex]\frac{1}{3}[/tex]+6 [tex]\frac{1}{2}[/tex] + 4 [tex]\frac{1}{8}[/tex]

=(10/3)+(13/2)+(33/8)

=(10/3)+(13/2)+(33/8)

=(80+156+99)/24

=335/24

=13.95

≈14 cups approximately

Therefore, the amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups.

So, option D is correct.

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The fracion 12k⁸/4(k⁵)² expressed in its simplest form is the expression 3/k².

To simplify fraction, we need to factorise the denominator and numerator, and then look for common factors in the numerator and denominator and cancel.

Given the fraction;

12k⁸/4(k⁵)² = 3 × 4 × k⁸/k² × 4 × k⁸ {expressed to get a common factor}

12k⁸/4(k⁵)² = 3 × 4k⁸/k² × 4k⁸

4k⁸ is a common factor to the numerator and denominator, so we cancel it out

12k⁸/4(k⁵)² = 3/k²

Therefore, the simplest form of the fracion 12k⁸/4(k⁵)² is derived as the expression 3/k.

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The surface area, A, is changing at a rate of 288 km/min decreasing.

Given,

Base length, l = 6 km

Height, h = 10 km

dl/dt = -9 km/min

dh/dt = 12 km/min

Surface area of a prism, A = 2 × (lw + lh + wh)

For a square prism,

Length, l = width, w = 6km

A = 2 × (l² + lh + lh)

= 2(l²) + 4lh

A = 2(l²) + 4 lh

= 2 × (l² + 2lh)

dA/dt = 2 × (2I × dI/dt + 0 × dh/dt + 2 × 2h × dl/dt + 2l × dh/dt)

dA/dt = 2 × (2l × dl/dt + 0 + 2 × 2h × dl/dt + 2l × dh/dt)

= 2 × (2(6) × (-9) + 2(10) × (-9) + 2(6) × (12))

= 2 × (- 108 + -180 + 144)

= 2 × -144

= -288 km/min

The rate of change of the surface area, A is decreasing by 288 km/min.

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Question is incomplete. Completed question is given below;

The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 9 kilometers per minute and the height h(t)h(t)h, (, t, )of the prism is increasing at a rate of 12 kilometers per minute. At a certain instant t_0t 0 ​ t, start subscript, 0, end subscript, the base's side is 6 kilometers and the height is 10 kilometers. What is the rate of change of the surface area A(t)A(t)A, (, t, )of the prism at that instant?

Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

The line in slope-intercept form that is perpendicular to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex].

As we know the slope of line is

[tex]y=mx+c[/tex]

where [tex]m[/tex] is the slope and [tex]c[/tex] is the y intercept.

Given points are [tex](-6,11)[/tex].

If we want to describe the perpendicular line to the original line then the slope of line is

[tex]m_2=-\frac{1}{m_1}[/tex]

In our given slope of line

[tex]y = -x -18[/tex]

where [tex]m_1=-1[/tex]

So,

[tex]m_2=-\frac{1}{m_1}\\\\m_2=-\frac{1}{-1}\\\\m_2=1[/tex]

Now for the slope of second line we use the point slope from the construct equation then,

[tex]y-y_1=m_2(x-x_1)\\\\y-11=1(x-(-6))\\\\y-11=x+6\\\\y=x+6+11\\\\y=x+17[/tex]

Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].

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Answer:

m=-6

Step-by-step explanation:

use slope formula to solve

m= rise/run=y2-y1/x2-x1

Answer: It is an obtuse triangle.

Answer: No

Step-by-step explanation:

To know if a triangle is a right triangle, we can use Pythagorean Theorem to test.

Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

[tex]4^2+6^2=8^2[/tex]                [exponents]

[tex]16+36=64[/tex]                [add]

[tex]52\neq 64[/tex]

Therefore, this is not a right triangle.

The value of the polynomial p(x) = -2x + 3x + 4 when x is 5 will be 9

A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division.

A polynomial is an expression made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.

p(x) = -2x + 3x + 4

when x = 5

= -2x + 3x + 4

= -2(5) + 3(5) + 4

= -10 + 15 + 4

= 9

Note that the information you gave wasn't complete.

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It can be seen that the radius and circumferance are not proportional.

        y = mx

        m = y/x

        [m] is called constant of proportionality.

Given is a graph as shown in the figure.

For the proportional relationship -

(25 - 18)/(4 - 3) should be equal to (38 - 25)/(6 - 4)

7/1 = 13/2

7/1 = 6.5

7 ≠ 6.5

Therefore, it can be seen that the radius and circumferance are not proportional.

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The domain the function is In interval notation [7,  ∞). The range of the function is in the interval  (-1, ∞).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A "vertical line test" can be used when examining a graph to determine whether a relation is a function. The relation is not a function if any point on the graph can be used to draw a vertical line that crosses the relation twice.

Here,

y=√(x-7)-1

x-7≥0

x≥7

at x=7

y=√(7-7)-1

y=-1

The function's domain is represented by the interval notation [7, ∞). The function's range falls within the range [-1, ∞).

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Answer:

[tex]y=\frac{1}{2} x-2[/tex]

The area of the semicircle table after it is cut in half  [tex]=\frac{9}{2}\pi[/tex] square units.

A semicircle is a 2 -D shape which is obtained by cutting a circle along with its diameter. a circle has 2 semicircles when it is cut along with its diameter.

The formula for finding the area of a semicircle is half of the area of a circle with the same radius.

area of semicircle = [tex]\frac{\pi r^{2} }{2}[/tex] square units

Given:

A table with a round top is cut in half so now its shape is a semicircle.

After it is cut, the edge along the wall is 6 ft means that the diameter of the semicircle is = 6 ft

Diameter = 6 ft

Radius = diameter / 2

Radius = 6/ 2

Radius = 3 ft

Therefore now we can calculate the area of the table after it is cut in half

Area of the semicircle table after it is cut in half =

[tex]=\frac{\pi r^{2} }{2} \\=\frac{\pi 3^{2} }{2} \\=\frac{9\pi }{2}\\= \frac{9}{2}\pi[/tex]

The area of the semicircle table after it is cut in half  [tex]=\frac{9}{2}\pi[/tex] square units.

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A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 feet. What is the area of the table after it is cut in half? Give your answer in terms of pi.

[tex]\angle R \cong \angle STV[/tex]: Alternate interior angles theorem

[tex]\angle TSV \cong \angle U[/tex]: Alternate interior angles theorem

[tex]\angle R \cong \angle TSV[/tex]: Transitive property of congruence

[tex]\angle R \cong \angle U[/tex]: Transitive property of congruence

Answer:

<AFC

Step-by-step explanation:

Vertical angles are pairs of opposite angles that are created by two intersecting lines. As an example, the other pair of vertical angles are <CFD and <AFE.

On average, it is going to take DJ 7.27 hours to get to the beach.

Average refers to the quotient when a numerator is divided by a denominator.

In this situation, the average refers to the time, which is the quotient of the distance and speed.

The total distance going to the beach from his family = 800 km

The average speed = 110 km/hr

The time to cover the distance of 800 km at 110 km/hr = 7.27 hours (800/110).

Thus, DJ will take 7.27 hours to cover 800 km at 110 km/hr.

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Answer: As Devansh Sehta has calculated, there are 82 terms and  82=7×11+5.  When each term of  S  is divided by 7, the remainders, in order are 6, 3, 0, 4, 1, 5, 2, and these repeat.

Step-by-step explanation:

For any arithmetic sequence, record the remainders when successive terms are divided by n. Then the sum of every set of n consecutive remainders is divisible by 7. In this case, the first 77 terms add to a multiple of 7 as do the 5 remaining terms.

It is important to state the restrictions before simplifying rational expressions because the simplified expression may be defined for restrictions of the original.

What is rational expressions?

The ratio of two polynomials is a rational expression. F can be expressed in the form p/q, where p and q are polynomials, if f is a rational expression.

Fractional terms are seen in rational expressions. We include constraints because with some x values, the equation may become undefined. Undefined inquiries are hypothetical or ideal. The seven expressions for undefined words are  (∞-∞),∞^∞, N/0, 0⁰, 1^∞, ∞/∞ and 0×∞ respectively. N/0 is the most typical constraint on rational expressions. Any number divided by 0 is therefore undefined. For instance, if you substitute 0 for x in the case of the function f(x) = 6/x2, the outcome is 6/0, which is undefined. If you graphed this function, you would see a break at x=0.

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the Pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables (scale variables) such as those depicted conceptually by scatter diagrams: True.

A measure of the degree and direction of relationship between two variables assessed on at least an interval scale is the Pearson product-moment correlation coefficient, or Pearson's correlation.

If you want to determine whether there is a linear relationship between two quantitative variables, you may use Pearson's correlation. The expectation of a linear relationship between those variables is the sole part of the study hypothesis.

This approach finds the precise amount or degree of correlation between any two variables and tells if there is or is not any correlation between them.

Thus, the given statement is true.

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If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.

The quadratic formula includes the discriminant, which comes after the square root. The discriminant of a quadratic equation is important because it indicates the quantity and kind of solutions.  

The formula for the Discriminant of a Quadratic Equation ax²+bx +c = 0 is given by

Here we have

x² + 16x + c = 0 equation has only one real solution

Compare given equation with ax²+ bx + c = 0

=> a = 1, and b = 16  

As we know when an equation has only one real solution

then its Discriminant will be equal to zero

=> b² - 4ac = 0

By the above values,

=> 16² - 4(1)c = 0  

=> 256 - 4c = 0

=> 4c = 256

=> c = 256/4

=> c = 64

Therefore,

If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.

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The interest charged for 3 years would be $75 ($500 x 0.05 x 3). The total amount Ariane has to pay back would be $575 ($500 + $75).

Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.

To calculate simple interest, multiply the principal sum by the time period, interest rate, and time period. Simple interest is calculated as follows: "Simple Interest = Principal x Interest Rate x Time." This equation provides the simplest method for calculating interest.

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Answer:

NO=6

Step-by-step explanation:

If MP=16 and NP=13 that means MN=3 and MO=9 so that makes NO=6

Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.

A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

calculation

a) µ =     48    

σ =     12    

n=    115    

X =    45    

Z =(X - µ )/(σ/√n)  =     (45-48)/(12/√115)=    -2.68

P(X<45) = P(Z<-2.68) =         0.0037

b) µ =     48.00    

σ =     12.00    

n=    115.00    

P(X ≤ x) =    0.2500    

z value at  0.25=    -0.674        (excel formula =NORMSINV(0.25))

z=(x-µ)/(σ/√n)        

X=z * σ/√n +µ= -0.674*12/√115+48=        47.25

Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.

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The required solution of the given expression is 1/3 [m²-2m-6].

Given that,
To simplify the [2m⁵ -5m₄ +2m² -8m²]/[m²+1], when  m² + 1 = 3m.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= [2m⁵ -5m₄ +2m² -8m²]/[m²+1]
When substituting the value m² + 1 = 3m in the above expression we get.
= m/3 [m²-2m-6]

Thus, the required solution of the given expression is 1/3 [m²-2m-6].

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The way Jason's position relative to the leader changed per minute is; 6²/₅ ft/minute

We are told that Jason's position was 11 ¹/₅ feet relative to the leader after 1 ³/₄minutes.

Now, the fractions are in mixed fraction form and so let us convert them to improper fractions to get;

⁵⁶/₅ and ⁷/₄

Thus, the way Jason's position relative to the leader changed per minute is; ⁵⁶/₅ ÷ ⁷/₄

= ⁵⁶/₅ * ⁴/₇

= 32/5

= 6²/₅ ft/minute

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Point ( 0 , -27 ) on the line and  ( -9 , 0 ) are not on the line

Given :

Madison is reeling in her string at a steady rate the linear equation 3y - 9x = -81 can be used to find y the number of feet of kite string she still needs to reel in after x seconds .

Points ( 0 , -27 )

when x = 0

3y - 9 * 0 = -81

3y - 0 = -81

3y = -81

y = -81 / 3

y = -27

so point ( 0 , -27 ) on the line .

when y = 0

3 * 0 - 9x = -81

0 - 9x = -81

-9x = -81

x = 81/9

x = 9

so ( -9 , 0 ) are not on the line

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Answer: the rectangle is 23 x 41

Step-by-step explanation:

x = length

2x - 5 =  width

A = length x width = (x)(2x-5) = 943

2[tex]x^{2}[/tex] - 5x - 943 = 0

use quadratic equation to solve for x:

a = 2, b = -5, c = -943

roots are 23, -20.5

x = 23 (length)

2x - 5 = 2(23) - 5 = 46 - 5 = 41 (width)

The total distance travelled by the particle is 24 units.

What is displacement?

Displacement is defined as a change in an object's position. An object's displacement is defined as how far it has moved from its starting point. The dependent variable in the displacement time graph is displacement, which is represented on the y-axis, and the independent variable is time, which is represented on the x-axis. Position-time graphs are another name for displacement time graphs.

The displacement curve is given for 0 ≤ t ≤ 18.

We need to find the total distance of the curve, it will be the positive sum of all displacements.

So, total distance = (7-0) + (3-0) + (2+3) + (2+4) + (7-4)

                             = 7 + 3 + 5 + 6 + 3

                             = 24

Hence, the total distance is 24 units.

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Answer:

Below

Step-by-step explanation:

a^2 + b^2 = c^2       subtract  a^2 from both sides

b^2 =  c^2 - a^2    

   take the positive sqrt of both sides ( since you can't have a negative length)

b = sqrt (c^2 - a^2)    

The speed of boat is 14 miles per hour and the speed of current 35 mile per hour

Speed:

The general formula to calculate the speed is written as

Speed = Distance/Time

Given,

A boat travel 42 mile uptream in 3 hour looking for a lot diver. It then travel downstream 70 mile in 2 hour.

Here we need to find the speed of boat and the speed of current.

While we looking into the given question, we have identified the following values,

Distance = 42 mile

time = 3 hour

Then the speed is calculated as,

=> speed = 42/3

=> speed = 14 miles per hour

Similarly, for the current is

distance = 70 miles

time = 2 hour

Then the speed is calculated as,

=> speed = 70/2 = 35 miles per hour.

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The monthly base fee of the situation is $0

From the question, we have the following parameters that can be used in our computation:

Charges per minute = $0.50 per minute

Number of minutes = 200 minutes

Total charges = $100

The above parameters mean that

Total charges = Monthly Base fee + Charges per minute x Number of minute

Substitute the known values in the above equation, so, we have the following representation

Monthly base fee + 0.50 * 200 = 100

This gives

Monthly base fee + 100 = 100

Subtract 100 from both sides

Monthly base fee = 0

Hence, the monthly base fee is $0

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