six children are each offered a single scoop of any of 3 flavors of ice cream from the combinatorial creamery. in how many ways can each child choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least one child?

Answer:

  3.97%

Step-by-step explanation:

You want to know the annual interest rate, compounded daily, that will result in $43,000 growing to $75,000 in 14 years.

The formula for the account value is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r compounded n times per year for t years.

Filling in the given values, we can solve for r.

  75000 = 43000(1 +r/365)^(365·14)

  75/43 = (1 +r/365)^5110 . . . . . divide by 43000 and reduce the fraction

Taking the 1/5110 power gives ...

  (75/43)^(1/5110) = 1 +r/365 ≈ 1.00010886855

  r/365 = 0.0010886855 . . . . subtract 1

  r = 0.001086855·365 . . . . . multiply by 365

  r ≈ 0.039737 = 3.9737%

The required interest rate is about 3.97%.

Answer:

x = - 5;

y = 5;

Step-by-step explanation:

Identify the equation.

y = ( 2 / 3 )x + c;

Substitute a point.

5 = ( 2 / 3 )( - 2 ) + c;

5 = ( - 4 / 3 ) + c;

5 - ( - 4 / 3 ) = c;

5 + ( 4 / 3 ) = c;

19 / 3 = c;

y = ( 2 / 3 )x + ( 19 / 3 );

Substitute point A.

3 = ( 2 / 3 )x + ( 19 / 3 );

3 - ( 19 / 3 ) = ( 2 / 3 )x;

( 9 / 3 ) - ( 19 / 3 ) = ( 2 / 3 )x;

- ( 10 / 3 ) = ( 2 / 3 )x;

- ( 10 / 3 )( 3 / 2 ) = x;

( - 30 / 6 ) = x;

- 5 = x;

x = - 5;

Substitute point B. Use common sense and notice that point B is actually the same as the first point.

y = 5;

Answer:

x =  -5

y = 5

Step-by-step explanation:

You could write the equation in the point slope form of a line

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])

Use the slope they gave us 2/3.  Use the point they gave us for [tex]x_{1}[/tex] ( -2 ) and [tex]y_{1}[/tex] ( 5)

y -5 = 2/3(x - -2)

y - 5 = 2/3(x + 2)  Plug in 3 for y to solve for x

3-5 = 2/3(x + 2)

-2 = 2/3x + 4/3  subtract 4/3 from both sides of the equation

-2 - 4/3 = 2/3x

[tex]\frac{-6}{3}[/tex] - [tex]\frac{4}{3}[/tex] = 2/3x

[tex]\frac{-10}{3}[/tex] = 2/3 x  Multiply both sides by [tex]\frac{3}{2}[/tex]

([tex]\frac{3}{2}[/tex])[tex]\frac{-10}{3}[/tex] = ([tex]\frac{3}{2}[/tex])([tex]\frac{2}{3}[/tex]) x

-5 = x

substitute in -2 for x to solve for y

y - 5 = 2/3(x + 2)

y - 5 = 2/3(-2+2)

y - 5 = 2/3(0)

y - 5 = 0  Add 5 to both sides

y = 5

Firts get the equation

Second, write the equation in form of Ax +

Answer:

The slope would be 25/1 or 25.

Step-by-step explanation:

Use the formula y2-y1 over x2-x1. Or use rise over run.

Answer:5760

Step-by-step explanation:

48 beats per min and its 120 min in 2 hours so multiply 120×48=5760

Answer: Uncle Luke is at 50 years old

Step-by-step explanation: I went through trial and error first with simple t-charts.  In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:

[tex]\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.[/tex]

Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
[tex]\left \{ {{N=2} \atop {L=10}} \right.[/tex]        |             [tex]\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.[/tex]  (remember there are 1 increments)

Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50

Answer:

i d k 20???????????

Step-by-step explanation:

Answer:

The visitor attended no special exhibits and so paid a total of $10 just to get in.

An equation to represent the cost of admission could look like this:

f(x) is the total cost.

x is the number of special exhibits attended.

f(x) = 2x + 10

If I see no special exhibits on my visit,

x = 0, then

f(0) = 2•0 + 10

f(0) = 10

I only pay $10.

The most appropriate choice for reflection will be given by-

After reflection over y-axis, coordinate of K will become K' (6, -1)

After reflection over y-axis, coordinate of L will become  L' (0, -1)

After reflection over y-axis, coordinate of M will become M' (0, -2)

After reflection over y-axis, coordinate of J will become  J' (6, -2)

What is reflection?

Reflection of a figure about a line is a transformation in which a mirror image of the figure can be obtained over the line.

The line is called the line of reflection.

Here,

After reflection over the y - axis, sign of x coordinate will be same.

Coordinate of K = (-6, -1)

After reflection over y-axis, coordinate of K will become K' (6, -1)

Coordinate of L = (0, -1)

After reflection over y-axis, coordinate of L will become L' (0, -1)

Coordinate of M = (0, -2)

After reflection over y-axis, coordinate of M will become M' (0, -2)

Coordinate of J = (-6, -2)

After reflection over y-axis, coordinate of J will become J' (6, -2)

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The amount that Jane would earn for working for 60 hours is $630.

The given function is a linear function. A linear function is a function that changes at a constant rate. When a linear graph is drawn on a coordinate graph, it can slope either upward or downward.

The linear function that represents the total amount she earns is:

Total earnings = cost per hour x total number of hours worked

Total earnings = $10.50 x h  

Total earnings = $10.50 x 60 = $630

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Answer:

Every number that is greater than 6

Using the equation for the distance between two points, the distance between Ross and Rachel is given by the following option:

D. 19 miles.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, and the hypotenuse represents the distance between them.

Their coordinates in this problem are as follows:

Each unit on the plane represents a mile, hence their distance is given as follows:

[tex]D = \sqrt{(8 - (-4))^2+(-4 - 11)^2}[/tex]

D = 19.2 miles.

Rounded to 19 miles, hence option D is correct.

The complete problem is given by the image at the end of the answer.

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Answer:

y= x/(n-9)

Step-by-step explanation:

Move 9 to the right side to get n-9

Take y over to get x=y(n-9)

Then shift n-9 over to other side to get y= x/(n-9)

Answer:

see explanation

Step-by-step explanation:

consider the left side

(x + 2)² + (x - 2)² ← expand factors using FOIL

= x² + 4x + 4 + x² - 4x + 4 ← collect like terms

= 2x² + 8 ← factor out 2 from each term

= 2(x² + 4)

= right side , thus proven

Given

different choices

Find

Which of the following is not a condition necessary to create a valid probability distribution?

Explanation

Each discrete outcome can have different probability of occuring

Hence the option stating each discrete outcome hsould have equal probability of occuring is not necessary

Final Answer

option (a) is correct option

The height of the barometer on Sunday = 34.8 inches

How is the barometer height on Sunday calculated?

Consider the barometer height for one week,

The average height of a barometer during one week = 30.84 inches

The total height of a barometer during one week = 30.84 * 7

                                                                                  = 215.88

Consider the barometer height for 6 weekdays,

The average height of a barometer for 6 weekdays of the same week= 30.18 inches

The total height of a barometer for 6 weekdays = 30.18 *6

                                                                                =181.08

The barometer height  on Sunday = One week height- 6 days height

                                                         =215.88 - 181.08

                                                         =34.8  inches

What is a height?

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Answer:12:30,2:5 and 18:45

Step-by-step explanation:

Answer: 1.4 or just 1

Step-by-step explanation:

But we are going to a decimal point then go to 1.4, cause the 9 makes the 3 round-up. :)

Answer: 1.4

Step-by-step explanation:

I believe you're asking what 1.39 rounded to the nearest tenths place is, in that case it is 1.4

The triangle have shorter sides of 12.9 and 14.9 cm, respectively

From the question, the given parameters are:

Also, from the question, we have:

Two shaded sides of the triangle differ by 2

In this case, the shaded sides of the triangle are

Opposite and Adjacent

This can also be interpreted as

Base and Height

So, we have

Base - Height = 2

The area is calculated as

Area = 0.5 * Base * Height

So, we have

0.5 * Base * Height = 96

This gives

0.5 * (Height + 2) * Height = 96

Divide by 0.5

(h + 2) * h = 192

Using a graphing calculator, we have

h = 12.9

Substitute h = 12.9 in Base - Height = 2

Base - 12.9 = 2

Evaluate

Base = 14.9

Recall that the Opposite and Adjacent are the shorter sides of a right triangle

Hence, the shorter sides are 12.9 and 14.9 cm

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The given vertices are A(1,4), B(3,-2), and C(4,2).

The reflection over the x-axis is expressed as

This means we have to multiple each y-coordinate with -1. Let's do it!

Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to x³ -11x² +41x -51.

As given,

Standard form of the polynomial function:

f(x) = r(x-a)(x-b)(x -c)

r : leading coefficient

a, b, c are zeros

Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is given by

f(x) = 1(x -3) (x -(4+i))(x - (4-i))

⇒ f(x) = (x -3) (x-4 -i)(x -4 +i)

⇒ f(x) = (x-3) [(x-4)² -i²]

⇒f(x) = (x-3)(x² -8x +16+1)

⇒f(x) =(x-3)(x² -8x+17)

⇒f(x) = x³-11x² +41x-51

Therefore, polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to

x³ -11x² +41x -51.

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The slope for lot size is not different from 0.

We will let the slope of the size be β

So the hypothesis can be:  β = 0  (Null Hypothesis)  ,  β≠ 0 (Alternate Hypothesis)

If we consider a confidence level (the probability for which we can be confident that the null hypothesis is true) to be 95% (Probability = 0.95) then the level for which we are not confident that the null hypothesis is true will be (100 - 95)% = 5% (Probability = 0.05)

Thus, for this coefficient the P value is 0.5782.

As the p-value is more than the Probability for which we are not confident (0.05), so in this regard we can state then there is no such significance difference seen in this regard. Thus, we accept the null hypothesis here. This means that we can take the coefficient to be 0.

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Answer:

     y

-------------

  x²¹ z⁵

Step-by-step explanation:

 (x⁻⁹ y³ z⁻²)²

-------------------

   x³ y⁵ z

   x⁻¹⁸ y⁶ z⁻⁴

-------------------

   x³ y⁵ z

        y⁶

-------------------

 x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴

      y

-------------------

     x²¹ z⁵

I hope this helps!

After simplification by rule of exponent solution is,

⇒ y /  x²¹ z⁵

We have to given that;

The expression is,

⇒ (x⁻⁹ y³ z⁻²)² /  x³ y⁵ z

Now, We can simplify by rule of exponent as;

⇒ (x⁻⁹ y³ z⁻²)² /  x³ y⁵ z

⇒  x⁻¹⁸ y⁶ z⁻⁴ / x³ y⁵ z

⇒ y⁶ / x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴

⇒ y /  x²¹ z⁵

Thus, After simplification by rule of exponent solution is,

⇒ y /  x²¹ z⁵

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Answer:

u = 24

Step-by-step explanation:

-7/8u = -21

Solve for u

Multiply each side by -8/7

-8/7 *-7/8u = -21 *-8/7

u =3*8

u = 24

Answer:

u = 1/24

Write the equation:

–7/8u = –21

Get rid of fraction:

–7/2^3 • u = –21

–7 = ( – (8u) ) 21

Solve:

–7 = –8u + 21

–7 + 8u = –8u + 8u + 21

–7 + 8u = 21

–7 + 7 + 8u = 21 + 7

8u = 21 + 7

8u = 28

u = 1/24

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AAS = Angle , angle and one side of 2 congruent triangles

SSS = All 3 sides are measure same of the 2 triangles.

ASA = 2 angles and the side between them are same

HL = A right triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and one of its other legs.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions. For the two triangles to be congruent, they must be the same size and shape. It should be possible to superimpose the two triangles under examination. A triangle's position or appearance appears to change when we rotate, reflect, and/or translate it. In that situation, we must recognize the six components of a triangle.

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Simplified version of the given radical expression would be...

[tex]5x^2\sqrt{7x}[/tex]

Hope this helps!

The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.

There could be only two terms, but there could be one hundred, a thousand, or a million.

Here are always an integer number of terms in a summation.

As per the given,

Length of the trench on the first day = 18/20 meters

Length of the trench on the second day = 9/20

Total length of the trench = 18/20 + 9/20

Take LCM as 20

⇒ (18 + 9)/20 = 27/20

⇒ 1.35 which is closest among the given option by 1 1/2 meters.

Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".

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         The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

        A formula for the question at hand is 2x minus 20 divided by 3 Equals 2x, or (2x - 20) /3 = 2x.

The difference in degrees over the last 24 hours is represented by x in this equation, which predicts temperature change.

We must find x in the given equation.

(2x - 20) /3 = 2x \s (2x - 20) = 3(2x) (2x) ...........(Multiply by 3 on both sides)

2x - 20 + 20 = 6x + 20 ...........(Add 20 to both sides)

2x - 6x = 6x + 20 - 6x ..........(Subtract 6x from both sides) (

-4x = 20 \s x = -5 ..........(Divide by - 4 on both sides)

As a result, x = -5 for the given equation (2x - 20) /3 = 2x.

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