If DE = 8, PS = 4, and PQ = 3, then what is the scale factor of DEFG to PQRS?

Please I just need you to explain it

The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

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Answer:

The set of all positive integers equal to or greater than 1

Step-by-step explanation:

n can take on the integer values 1 ... ∞

The formula for the nth term is a(n) = a(1) + 2(n - 1)

First term:  n = 1.  Then a(1) = 3 + 2(0) = 3 (as expected).

5th term:  n = 5.  Then a(5) = 3 + 2(5 - 1) = 3 + 8 = 11

...

and so on.

\(11x - 3 + 4x - 3 = 90 \\ 11x + 4 x = 90 \\ 15x = 90 \\ x = 6\)

The scale factor for the dilation shown above with the center of dilation at point A is 2.

To find the scale factor for a dilation, we compare the corresponding lengths of the pre-image and the image. In this case, we can compare the length of segment AB in the pre-image with the length of segment A'B' in the image. The coordinates of point A are (-8,9) and the coordinates of point A' are (-16,18). The length of AB is 14 units, and the length of A'B' is 28 units. Thus, the scale factor is determined by the ratio of the lengths: 28/14 = 2. Therefore, the scale factor for the dilation is 2.

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a) The mean of this distribution is 7 min

b) The standard deviation is 4.0414 min

a) The mean is the midpoint between the ends or 7 min

variance is (b-a)^2/12 or 196/12 or 16.3333 min

b) standard deviation is sqrt(V)= 4.0414 min

the complete question is

a bus comes by every 14 minutes. the times from when a person arives at the bus stop until the bus arrives follows a uniform distribution from 0 to 14 minutes. a person arrives at the bus stop at a randomly selected time. round to 4 decimal places where possible.

a) The mean of this distribution is

b) The standard deviation is

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Answer:

k = 3

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (2, 3 )

with k = 3

Answer:

I think it's 155 cm

Step-by-step explanation:

=(5×5×3)+(5×2×4)

= 75+40

= 155 cm2

Answer:

5x^2 - 2x - 3

Step-by-step explanation:

(x-1) (5x+3)

5x^2 + 3x - 5x - 3

5x^2 - 2x - 3

So, the answer is 5x^2 - 2x - 3

Answer:

\(Total = 25\ yd\)

Step-by-step explanation:

The given parameters can be represented as:

\(Length = 2\frac{1}{2}\)

\(Number=10\)

Required

The total yards

This is calculated as:

\(Total = Number * Length\)

\(Total = 10 * 2\frac{1}{2}\ yd\)

Convert fraction to decimal

\(Total = 10 * 2.5\ yd\)

\(Total = 25\ yd\)

The area of a parallelogram is A=base × height of the parallelogram.

The parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal)  and equal in length.

Examples of shapes that hold the same properties as parallelogram are: Rectangle

Rhombus

To calculate the area of a parallelogram:

Area of a parallelogram=Area = Base × Height

If the height of the parallelogram is unknown to us, then we can use this to find its area and the angle between the sides of the parallelogram is given.

Area = ab sin (x)Area of a Parallelogram

Using Diagonals: The area of any parallelogram can also be calculated using its diagonal lengths. There are two diagonals for a parallelogram that intersect each other. Suppose the diagonals intersect each other at an angle x"

Area = ½ × d1 × d2 sin (y)

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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The probability of selecting both red marbles without replacement is 0.0214.The probability of selecting a blue marble and a white marble without replacement 0.1143.  the probability of selecting a blue marble and a white marble with replacement is 16/441

(a) The probability that both marbles are red can be determined as follows:

Number of red marbles = 4 Probability of selecting one red marble out of 21 marbles = 4/21

Probability of selecting a second red marble out of 20 marbles after one has been removed = 3/20

Probability of selecting both red marbles without replacement = (4/21) * (3/20) = 3/140 = 0.0214 (rounded to thousandths place)

(b) The probability that the first marble is blue and the second is white can be determined as follows:

Number of blue marbles = 12 Probability of selecting one blue marble out of 21 marbles = 12/21

Probability of selecting a white marble after a blue one has been removed = 4/20

Probability of selecting a blue marble and a white marble without replacement = (12/21) * (4/20) = 12/105 = 0.1143 (rounded to thousandths place)

(c) No, we would not get the same answers from parts (a) and (b) if the sampling was done with replacement. If the sampling is done with replacement, the probability of selecting a marble does not change with each selection. As such, the probability of selecting two red marbles is still (4/21) * (4/21) = 16/441.

On the other hand, the probability of selecting a blue marble and a white marble with replacement is (12/21) * (4/21) = 16/441, which is different from the probability obtained without replacement.

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Answer:

2:3:5

Step-by-step explanation:

24:36:60

1) Find the greatest common factor

24 ⇒ 1, 2, 3, 4, 6, 8, 12, 24

36 ⇒ 1, 2, 3, 4, 6, 9, 12, 18, 36

60 ⇒ 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Therefore, the greatest common factor is 12.

2) Divide all values by 12

24 ÷ 12 = 2

36 ÷ 12 = 3

60 ÷ 12 = 5

Therefore, the simplified form of the ratio is 2:3:5.

I hope this helps!

Answer:

The answer is B: A captured boy learned there was a mine that contained a vein of pure gold.

Step-by-step explanation:

Took the test.

Answer:

The answer is B

Step-by-step explanation:

A captured boy learned there was a mine that contained a vein of pure gold.

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

f(2)= -2

g(2)= 12

Step-by-step explanation:

To solve this we use the substitution method. Since f(2) is your variable, we will plug the x-value of 2 into each equation

f(2)= 2(2)^2-5(2)

f(2)=8-10

f(2)= -2

If the same variable is used for both equations then g(x) would be g(2) as well leaving you with

g(x) = 3x^2

g(2)= 3(2)^2

g(2)=12

Answer:

The correct answer is 152

Container A that is full after the pumping is complete is 36.1%

Given,

In the question:

Container A has a radius of 9 feet and a height of 18 feet.

and, Container B has a radius of 7 feet and a height of 19 feet.

To find the what is the percent of Container A that is full after the pumping is complete?

Now, According to the question:

Radius of Container  A = 9 ft.

Height = 18 ft.

Radius of Container  B = 7 ft.

Height = 19 ft.

The formula Cylinder of Volume is

V = \(\pi r^2h\)

Substitute the values:

\(V_{A} = \pi . 9^2. 18 \\= 1458\pi \\\\V_{B} = \pi . 7^2. 19 \\ = 931\pi\)

Now, \(V_{A} - V_{B} = 1458\pi -931\pi =527\pi\)

\(\frac{527\pi }{1458\pi }\)× 100% = 36.1%

Hence, Container A that is full after the pumping is complete is 36.1%

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Answer:

Step-by-step explanation:

$31.10

The correct choice is B

Given the function f(x,y)=xy+y² and we need to determine the directions in which the derivative of the given function at P(8,7) is equal to zero.

The directional derivative of a multivariable function in the direction of a unit vector (a, b) can be determined by the following formula: D_(a,b)f(x,y)=∇f(x,y)•(a,b)

Where ∇f(x,y) represents the gradient of the function f(x,y).The partial derivatives of the given function are;∂f/∂x = y∂f/∂y = x + 2y

`Now, evaluate the gradient of the function at point P(8,7).∇f(x,y)

= <∂f/∂x , ∂f/∂y>

= Putting x = 8 and y = 7 in the above equation, we get,

∇f(8,7) = <7,22>

Therefore, the directional derivative of f(x,y) at P(8,7) in the direction of unit vector u = (a, b) isD_ u(f(8,7))

= ∇f(8,7) • u = <7,22> • (a, b)

= 7a + 22bFor D_u(f(8,7)) to be zero, 7a + 22b = 0 which has infinitely many solutions.

Thus the correct choice is B. There is no solution.

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The derivative of the function f(x,y) = xy + y^2 doesn't equal zero at point P(8,7). We found this by calculating the partial derivatives and checking if they can equal zero.

The function given is f(x,y) = xy+y^2. To find the points at which the derivative is zero, we need to first compute the partial derivatives of the function. The partial derivative with respect to x is y, and with respect to y is x + 2y.

The derivative of the function is zero when both these partial derivatives are zero. Therefore, we have two equations to solve: y = 0, and x + 2y = 0. However, the given point is P(8,7), so these values of x and y don't satisfy either equation. Thus, at point P(8,7) the derivative of the function is never zero.

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Answer:

n = 6

Step-by-step explanation:

To isolate n, subtract 1 from both sides:

4n + 1 = 25

4n = 24

Then divide by 4 on both sides:

4n = 24

n = 6

Hope this helped :)

Answer:

6

Step-by-step explanation:

4n+1= 25

or,4n= 25- 1

or,4n=24

or,n=24/4

so n= 6

Answer:

17.88

Step-by-step explanation:

18- 12/ 100=

447/24=

then simplify

Answer:

20.16

Step-by-step explanation:- 12% × 18 =

- 12 ÷ 100 × 18 =

- 12 × 18 ÷ 100 =

- 216 ÷ 100 =

- 2.16

Answer:

12/5hours=2.4 hours

Step-by-step explanation:

Sam:6hours

Tom:4hours

This is a rate problem

Sam's rate is one job completed in 6 hours which is 1/6

Tom's rate is one job completed in 4 hours which is 1/4

Together, they could complete 1/4+1/6 of the job in y hours

We are trying to find the rate at which Sam and Tom could complete the job together, or one job in x days, for a rate of 1/y

1/4+1/6=1/y

The least common denominator is 12y

Multiplying through by the LCD which gives:

12y(1/4)+ 12y (1/6)= 12y (1/y)

3y + 2y=12

5y = 12

y=12/5 hours=2.4hours

Therefore it will take 12/5 hours or 2.4 hours to complete the job if they work together

Answer:

x = - 6 ± \(\sqrt{37}\)

Step-by-step explanation:

Given

x² + 12x = 1

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(6)x + 36 = 1 + 36

(x + 6)² = 37 ( take the square root of both sides )

x + 6 = ± \(\sqrt{37}\) ( subtract 6 from both sides )

x = - 6 ± \(\sqrt{37}\) ← exact solutions