Q20. in an assorted colored lego box, 5/6 of the legos were red, and 2/3 of the remaining legos were green. if there were 18 legos, how many of the legos were green?

A mathematical connection known as a function is one in which the values of one or more independent variables determine the values of a single dependent variable. Function implies that the independent variable affects the dependent variable (s).

       The answer is -11

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The equation of parabola is  (x − 3)² = −8(y − 2).

A parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax²+ bx + c. The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0.

Given:

Vertex = (3, 2)

Directrix, y =4

line of symmetry is the Y value in the vertex = 2

directrix, y= 2 - p

  p = -2

and, a= 1/4p = -1/8

and, focus = (3, (2-2)) = (2, 0)

Now, equation of parabola

y= -1/8 (x- 3)² + 2

-8y = (x- 3)² + 2

(x − 3)² = −8(y − 2)

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Answer: The answer is x-y = -2

Translating the given words into algebraic expression it becomes  2v(w-u) .

In the question ,

the word phrase is given as" double the difference of w and u, and then multiply the result by v "

for translating into algebraic expression , we proceed step by step

step 1 : difference of w and u

we get , (w - u)

step 2 : double the difference of w and u ,

we get , 2(w-u)

step 3 : then multiply the result by v ,

we get , 2(w-u)*v

= 2v(w-u)

Therefore , translating the given words into algebraic expression , the expression is 2v(w-u) .

The given question is incomplete , the complete question is

Translate the following word phrase into an algebraic expression , "double the difference of w and u, then multiply the result by v "

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The estimates are used to construct the estimated regression equation:

ŷ = b0 + b1x.

Therefore, the estimates are used to construct the estimated regression equation: ŷ = b0 + b1x.

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The length of side BC, |BC|, is 2 units. The correct option is C. 2 units

From the question, we are to determine the length of side BC

First, we will determine the length of side BD

From Pythagorean theorem, we can write that

|BD|² = |AB|² + |AD|²

From the given information,

|AB| = 1

|AD| = 1

Thus,

|BD|² = 1² + 1²

|BD|² = 1 + 1

|BD|² = 2

|BD| = √2

Also, we can write that

|BC|² = |BD|² + |DC|²

From the given information,

|BD| = |DC|

Thus,

|BC|² = (√2)² + (√2)²

|BC|² = 2 + 2

|BC|² = 4

|BC| = √4

|BC| = 2

Hence, side BC is 2 units

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The sets that number 343 belongs to are:

So, 343 is:

Therefore, the sets that number 343 belongs to are:

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Using a system of equations, the amounts of each coin that he has is given as follows:

The variables to the system of equations are given as follows:

Nicholas has nickels, dimes and quarters that total $12.30, hence, considering the value of each coin:

0.05x + 0.1y + 0.25z = 12.30.

The number of dimes is 3 more than twice the number of nickels, hence:

y = 2x + 3.

The number of quarters is three times the number of nickles, hence:

z = 3x.

Then we can solve for x as follows:

0.05x + 0.1y + 0.25z = 12.30.

0.05x + 0.1(2x + 3) + 0.25(3x) = 12.30.

x = 12. (nickels)

Then the other amounts are as follows:

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The speed of the stream is 6 [tex]km/h[/tex]

Let the speed of the stream be x km/h.

Therefore, the speed of the boat upstream = (18 – x) km/h, and the speed of the boat

downstream = (18 + x) km/h.

The time is taken to go upstream = distance/speed

[tex]24/(18-x)[/tex] hours.

Similarly, the time is taken to go downstream =

[tex]24/(18+x)[/tex] hours.

According to the question,

[tex]24/(18-x) - 24/(18+x) = 1[/tex]

[tex]x^{2} +48x-324=0[/tex]

Using the quadratic formula, we get

[tex]x=\frac{-48+\sqrt{48^{2}+1296 } }{2}[/tex]

x = 6 or -54

Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54.

Hence the speed of the stream is 6 km/h.

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Answer: x = 3.3

Step-by-step explanation:

Based on the given conditions, formulate: 60,000 * 25% * x = 50,000

Multiply the monomials: 15000x = 50,000

Divide both sides of the equation by the coefficient of variable: x = 50,000

                                                                                                                ______

                                                                                                                  15,000

Cross out the common factor: x 10

                                                     3

Round the number: x = 3.3

Answer x = 3.3

Answer:

p= -8

Step-by-step explanation:

[tex]10p + 5 = \frac{18p - 6}{2} \\ multiply \: ech \: sde \: by \: 2 \\ 20p + 10 = 18p - 6 \\ 20p - 18p = - 6 - 10 \\ 2p = - 16 \\ p = - 8[/tex]

Answer: 26 degrees

Step-by-step explanation: Count from -15 to 11 or add them up.

The expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given that four students have rewritten the expression with rational exponent in radical form as shown.

As per Sammi's expression: VE

This is an incorrect expression

As per Malik's expression: √7³

This is an incorrect expression

As per Cassie's expression: √x⁵

This is the correct expression

As per Casey's expression: √T

This is an incorrect expression

Thus, the expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.

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By solving a system of equations, we can see that there are 17 children and 8 parents in the room.

Let's define the variables:

x = number of children.

y = number of parents.

We know that there are 9 more children than parents, then:

x = y + 9

And there is a total of 25 people, so:

x + y = 25

So we have a system of equations:

x = y + 9

x + y = 25

Replacing the first equation into the second one, we get:

(y +9) + y = 25

2y + 9 = 25

2y = 25 - 9 = 16

y = 16/2 = 8

then the value of x is:

x = y + 9 = 8 + 9 = 17

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The complement of the event is diamond, club or spade.

The complement of an event means " to not choose the mentioned one" .

That is in mathematics we define complement as 1 - E, which is also written as E with a bar, here E represents the event.

In this question we would have to pick a card which is complementary to the heart that is the card needs to be a diamond, spade or a club.

Thus the complement of the event is diamond, club or spade.

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Answer:

7.5 or 7 1/2

Step-by-step explanation:

A recipe requires 2 1/2 of flour. How much flour is needed to triple the recipe?​

3 × 2 1/2 can be written as 3 × 2.5 = 7.5 or 7 1/2

The x-intercept of a graph refers to the points where the graph cuts or intersects the x-axis.

These are the x-values when y is equal to zero.

From the graph provided, the values of x when the graph cuts the x-axis are:

Therefore, the coordinates of the x-intercepts are:

The answer type is "Two points".

The percentage of Americans who have diabetes and the reliability of the diagnostic. The percentage of those who do not have diabetes test negative is 56.8%.

Give that,

The percentage of Americans who have diabetes and the reliability of the diagnostic procedures now in use are listed in the table below.

There are 3 rows in a tables and 4 column.

1st row,

Diabetes---test positive---test negative---total

2nd row,

Have diabetes---36.1%---1.9%---38%

3rd row,

Do not have diabetes---5.2%---56.8%---62%

We have to find the percentage of those who do not have diabetes test negative for the disease.

See the 3rd row,

In that the percentage of those who do not have diabetes test negative is 56.8%.

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The correct classification of DEF is a right-angled scalene triangle.

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1. (-6, 8)

2. -2

3. 4

Step-by-step explanation:

write the question properly

The domain and the range of the graph are x >= 0 and -∝ < y < ∝, respectivelt

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The domain

On the graph of the function, we can see that:

The x values start from 0 and it extends indefinitely to the right

This means that the domain is x >= 0

The range

On the graph of the function, we can see that:

The y values extend indefinitely on all sides of the coordinate plane

This means that the range is -∝ < y < ∝

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The researchers use inferential statistics.

Inferential statistics uses measurement from a sample, comparing groups and making generalizations about the large population. Inferential statistics are based on a test statistic calculated based on a formula. The test statistic along with degrees of freedom to determine the difference between the study population. With inferential statistics, the researcher will draw conclusions from extrapolations.  

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To prove ∠1 = ∠3.

Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Both of them have the same slope and are equally spaced apart.

Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal). The parallel lines L1 and L2, which are divided by a transversal, can be seen in the following figure.

Given : [tex]l||k , m||n[/tex]

∠1= ∠2 {alternate interior angles}

∠2=∠3 {corresponding angles are equal because k is parallel to l }

Thus from the above two equations :

∠1 = ∠3

Hence, proved .

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Answer:

(x - 4) (2x - 1)(3x + 2)

Step-by-step explanation:

Dividing:

x - 4)6x^3 - 23x^2 - 6x + 8 (6x^2 + x- 2 <----Quotient

        6x^3 -24x^2

                       x^2 - 6x

                       x^2 - 4x

                              -2x + 8

                              -2x + 8

6x^2 + x - 2

= 6x^2 - 3x + 4x - 2

= 3x(2x - 1) + 2(2x - 1)

= (3x + 2)(2x - 1)

Answer:

Step-by-step explanation:

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

y + 2y - 10 = 2y +2

3y - 10 = 2y +2

3y - 2y = 2 + 10

y = 12

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

check

12 + 2 * (12 - 5) = 2 * 12 + 2             (remember PEMDAS)

12 + 24 - 10 = 24 + 2

26 = 26

the answer is good

The equation of the line passing through point P (0,1) = y=2x-1

What is Equation of line ?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

Rise over run = (y+1)/(x-0)

                      =(y+1)/x =-2

 slope is (y+1)/(x-0) =(y+1)/x

                               =-2;

-2x=y+1, or

y+2x =-1, or

y=-2x-1

in the form of the slope intercept

The parallel line with the value of y=-2x+3 has been moved down by 4 units. The point at which this line crossed the y-axis was y=3. Now, with a 4 downshift, it crosses the y-axis at y=1.

Plugging the location (0,1) into the new equation:

y=2x-1 yields

1 = 2(0)-1

to validate the math.

Hence, the Equation of line passing through point P(0,1) is y=2x-1

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Using the definition of the Laplace transform:

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_0^t \tau \cos(3\tau) \, d\tau\right) e^{-st} \, dt[/tex]

Reverse the order of integration. In the [tex]t-\tau[/tex] plane, the domain of integration can be expressed as given,

[tex]D = \left\{(t,\tau) ~:~ 0\le t<\infty \text{ and } 0\le \tau\le t\right\}[/tex]

or equivalently as

[tex]D' = \left\{(t,\tau) ~:~ \tau \le t < \infty \text{ and } 0 \le \tau < \infty\right\}[/tex]

Then the Laplace transform is

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_\tau^\infty e^{-st} \, dt\right) \tau \cos(3\tau) \, d\tau \\\\ ~~~~~~~~ = \frac1s \int_0^\infty e^{-s\tau} \tau \cos(3\tau) \, d\tau[/tex]

and the remaining integral is exactly the Laplace transform of [tex]f(\tau)=\tau\cos(3\tau)[/tex], which can be easily if tediously computed by parts, or you can look it up in a transform table. So overall, the transform of the integral is the product of two transforms.

This is equivalent to the convolution property of the Laplace transform,

[tex]\displaystyle L\left\{f(t) * g(t)\right\} = L\left\{f(t)\right\} L\left\{g(t)\right\}[/tex]

where

[tex]f(t) * g(t) = \displaystyle \int_0^t f(\rho) g(t - \rho) \, d\rho[/tex]

In our case, we let [tex]f(t)=t\cos(3t)[/tex] and [tex]g(t)=g(t-\rho)=1[/tex].

To find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex], we can use the properties of the Laplace transform. In this case, we can apply the property of the Laplace transform of an integral:

[tex]\displaystyle{L\left \{\int_0^t f(t) \, dt \right \} = \dfrac{1}{s} F(s)}[/tex],

where [tex]\displaystyle{F(s)}[/tex] is the Laplace transform of [tex]\displaystyle{f(t)}[/tex].

In this case, [tex]\displaystyle{f(t) = t\cos 3t}[/tex]. Taking the Laplace transform of [tex]\displaystyle{f(t)}[/tex], we have:

[tex]\displaystyle{L\left \{t\cos 3t \right \} = \dfrac{s}{s^2 + 9}}[/tex].

Now, applying the property of the Laplace transform of an integral, we can find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]:

[tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \} = \dfrac{1}{s} \cdot \dfrac{s}{s^2 + 9} = \dfrac{1}{s^2 + 9} = 1}[/tex].

Therefore, the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex] is 1.