Mr. Mackinson has to choose 2 students to lead the class field trip. If he draws from a list of 6 boys and 6 girls, what is the probabilty that the names of 2 girls will be drawn?

For the two given graphs, the value for vector equation is obtained as [tex]\vec{w} = 2\vec{u} + \vec{v}[/tex].

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

From first graph it is seen that -

[tex]\vec{u}= < 1,1 >[/tex] and [tex]\vec{v}= < -1,2 >[/tex]

From second graph it is seen that -

[tex]\vec{w}= < 1,4 >[/tex]

So, it is obtained that -

[tex]a\vec{v}+b\vec{u}=\vec{w}[/tex]

Substitute all the values in the equation -

a<-1,2> + b<1,1> = <1,4>

<-a,2a> + <b,b> = <1,4>

<-a+b,2a+b> = <1,4>

The two equation obtained are -

-a + b = 1

2a + b = 4

Subtracting the equation 1 from 2 -

2a + b - (-a + b) = 4 - 1

2a + b + a - b = 3

3a = 3

a = 1

Substitute the value of a in equation 1 -

-1 + b = 1

b = 1 + 1

b = 2

So, the equation [tex]a\vec{v}+b\vec{u}=\vec{w}[/tex] becomes -

[tex]\vec{v} + 2\vec{u} = \vec{w}[/tex]

Therefore, the vector is obtained as [tex]\vec{w} = 2\vec{u} + \vec{v}[/tex].

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In total they knocked down 104 pins.

I got this by multiplying 26 by 3, which equals 78, then adding 26 to 78 to get the final answer, 104.

Hope this helps!

100%

You calculate the increase, which is the final amount minus the initial amount.

You then divide the value of increase by the original amount (in our case, this was 8÷8).

You then multiply that amount by 100 to put it into a percentage.

Hope this helps!

Answer:

r = 8

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

given a₁ = 3 and a₃ = 192 , then

a₁ = 3 → (1)

a₁r² = 192 → (2)

divide (2) by (1) on both sides

[tex]\frac{a_{1}r^2 }{a_{1} }[/tex] = [tex]\frac{192}{3}[/tex] ( cancel a₁ on numerator/ denominator of left side ), then

r² = 64 ( take square root of both sides )

r = [tex]\sqrt{64}[/tex] = 8

The factory sales of electronic goods from a certain country to dealers from 1990 to 2001 can be modeled using a mathematical equation .

Modeling factory sales of electronic goods from a certain country to dealers from 1990 to 2001 involves creating a mathematical equation to represent the data . To begin, one must collect the data from the sales of electronic goods from the given country to dealers from 1990 to 2001. This data should include the total amount sold for each year. Once the data is collected it must be organized into a visual representation, such as a line graph or a scatter plot. The visual representation should then be examined for patterns in the data which can be used to create a mathematical equation. This equation should be able to accurately describe the data and be able to predict future data points. The equation should then be tested to ensure accuracy before it is used to model the factory sales data.

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Answer: B. 0.058 hectometers

Step-by-step explanation: To convert millimeters to hectometers, you need to divide the number of millimeters by 10,000.

Given that there are 580 millimeters, the conversion to hectometers can be calculated as follows:

580 millimeters ÷ 10,000 = 0.058 hectometers

Quadrilateral FGHI is a scalene quadrilateral as none of the sides equal to each other from calculated slopes and lengths.

Coordinates of the quadrilateral FGHI are,

F (-1,-8), G(-3,2), H(0,1) and I(2,7)

Slope of side lengths of FGHI are:

Slope FG = ( 2 + 8)/ (-3 + 1)

               = -5

Slope GH = ( 1 -2)/ (0 + 3)

                = -1/3

Slope HI = ( 7 -1)/ ( 2 -0)

              = 3

Slope IF = ( 7 + 8 )/ (2 + 1)

              = 5

Product of slopes of perpendicular lines = -1

FG is perpendicular to IF

GH is perpendicular to HI

Measure of side lengths are:

FG = √(2+8)² + (-3+1)²

     = √104

     = 2√26

GH =√(1-2)² + (0 +3)²

     = √10

HI = √(7-1)² + (2-0)²

    = √40

    =2√10

IF = √(7+8)² + (2+1)²

   = √234

   = 9√26

Therefore, the given quadrilateral is scalene quadrilateral concluded using slopes and lengths.

The above question is incomplete, the complete question is:

The points F (-1,-8), G(-3,2), H(0,1) and I(2,7) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.

Slope of FG = __                            Length of FG = __

Slope of GH = __                            Length of GH = ___

Slope of HI= __                               Length of HI = ____

Slope of IF = __                               Length of IF = ____

Quadrilateral FGHI is ______

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Answer:

Step-by-step explanation:

ICA 2023

Answer:

she sold 100 cakes in all

Step-by-step explanation:

606 + 494 = 1100 ÷ 11 = 100

The 7 metric units are part of the International System of Units, and this are km, m, cm, mm, kg, g and L. Each unit is based on a multiple of 10, making it easy to convert between them.  For example, 1 kilometer is equal to 1000 meters, and 1 kilogram is equal to 1000 grams.

The 7 metric units are as follows:

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Answer:

See below

Step-by-step explanation:

Givens:

A (2,3)

B (4,2)

C (3,5)

1. Subtract each x and y value by 4: (x-4,y-4)

A (-2,-1)

B (0,-2)

C (-1,1)

2.  Flip the x and y values: (y,x)

A (3,2)

B (2,4)

C (5,3)

3. Multiply each point by 1.5: (1.5x,1.5y)

A (3,4.5)

B (6,3)

C (4.5,7.5)

Answer:

With the information given, I would say a dialation.

Step-by-step explanation:

Rotation of 180 degree around point (1, 0). Therefore, option (3) is the correct answer.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given that, the square with vertices (-1, 2), (-1, -2), (3, -2) and (3, 2).

(1) Reflection over the y-axis

Then the vertices become (1, 2), (1, -2), (-3, -2) and (-3, 2)

So, the transformation carries the square onto itself.

(2) Reflection over the x-axis

Then the vertices become (-1, -2), (-1, -2), (3, 2) and (3, -2)

So, the transformation carries the square onto itself.

(3) Rotation of 180 degree around point (1, 0)

(x, y) becomes (-y, x) 180° clockwise

So, the coordinate points are (-2, -1), (2, -1), (2, 3) and (-2, 3)

So, the transformation does not carries the square onto itself.

Therefore, option (3) is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

A square is graphed on the set of axes below, with vertices at (-1,2), (-1,-2), (3,-2), and (3.2). Which transformation would not carry the square onto itself.

(1) Reflection over the y-axis

(2) Reflection over the x-axis

(3) Rotation of 180 degree around point (1, 0)

(4) Reflection over the line y=x-1

A. Circle

B. Ellipse (which can resemble an oval)

Answer:

18.0

Step-by-step explanation:

this is correct!

The surface area of the given cylinder is 602.88 square centimeters.

The surface area of the cylinder is: A = 2πr(r+h)

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

The cylinder with a height of 10 cm and a radius of 6 cm.

⇒ A = 2πr(r+h)

Here h = 10 cm and r = 6 cm

Substitute the known values in the above formula,

⇒ A = 2(3.14)(6)(6+10)

⇒ A = (12.56)(6)(16)

Apply the multiplication operation, and we get

⇒ A = 602.88

Therefore, the surface area of the given cylinder is 602.88 cm².

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Answer:

the answer is a=15cm

Step-by-step explanation:

c²=a²+b²

where c=Hypothenuse,a=adjacent, b=opposite

a²=c²-b²

a²=39²-36²

a²=1521-1296

a²=225

take Square root of both sides

a=15cm

When the dimension of height is doubled, the volume of the cone also gets doubled.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.

Volume of a cone is given by,

V = πr²h/3

Where,

V = Volume,

r = radius of the base,

h = height of the cone.

Let, height at first be x, then volume would be,

V1 = πr²x/3

As the height is doubled, so height = 2x, then volume would be,

V2= πr²(2x)/3

We observe that:

V2 = 2(πr²x/3)

V2 = 2V1

Therefore, when the height is doubled, the volume of the cone also gets doubled.

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What is Null hypothesis?

The null hypothesis assumes that any difference between the selected attributes in a set of data is attributable to chance. For example, if the predicted earnings for the gambling game are genuinely zero, then any discrepancy between the data's average earnings and zero is due to chance.

(a) The appropriate null and alternative hypotheses for this setting are:

Null hypothesis: The actual mean systolic pressure (μ) of the individual is not greater than 130 (μ ≤ 130).

Alternative hypothesis: The actual mean systolic pressure (μ) of the individual is greater than 130 (μ > 130).

(b) Type I error occurs when the null hypothesis is rejected when it is actually true. In this case, it means that the device recommends that the person seeks medical attention when they do not actually need it. The consequence of this error is that the person may undergo unnecessary medical tests or treatments, which can be costly, time-consuming, and can cause anxiety or other negative effects.

Type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, it means that the device does not recommend medical attention when the person actually needs it. The consequence of this error is that the person may not receive the necessary medical attention and treatment, which can lead to serious health problems, including organ damage or failure, stroke, or heart attack.

(c) In this scenario, the cost of making a Type II error is likely to be much higher than the cost of making a Type I error. The reason is that failing to detect high blood pressure in a person can have serious health consequences. Therefore, it is better to make the Type I error probability smaller and the Type II error probability larger. This means that the device should be adjusted to have a higher threshold for recommending medical attention, which would decrease the likelihood of a false alarm, even if it increases the likelihood of missing some cases where medical attention is needed.

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The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge. According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.

A type I error (false-positive) occurs when a researcher rejects a null hypothesis that is actually true in the population; if the researcher does not do this When a null hypothesis is rejected even when it is false in the population, this is known as a type II error (false-negative).

Parameter Hypothesis testing is a second sort of statistical inference.

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The Average daily balance of the given scenario is $2083.

Suppose we're given that:

P_v = Present value of the loan amount

r = rate of interest (compound interest) per period of time

n = number of period of time in which loan is to be paid off

P = A fixed period payment needed to be done for paying off the loan in n number of periods.

Then, we get:

[tex]P = \dfrac{r\times P_v}{1 - (1 + r)^{-n}}[/tex]

Given;

APR= 25%

Cost of wheels and tires= $1500

Time=14days

Cost of brake calipers and leaking= $500

Time=30days

Now,

P= 25x2000/1-(1+25)^-30

P=50000/24

P=2083

Therefore, the monthly balance of loan will be $2083.

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Answer:

Step-by-step explanation:

im guessing youre finding the price of the favour.

(305-265)/8=answer

"/" means divide.

The best way to represents the change in the vertices of rectangle ABCD to rectangle A'B'C'D' in the attached graph is given by :

option A. (x, y ) → (2x, 2y).

From the attached graph we have,

Coordinates of rectangle ABCD are :

Coordinate of vertex A ( -3, -2 )

Coordinate of  vertex  B ( -3,  2 )

Coordinate of  vertex  C ( 3, 2 )

Coordinate of  vertex  D ( 3, -2 )

And coordinates of A'B'C'D' are:

Coordinate of  vertex  A' ( -6, -4 )

Coordinate of  vertex  B' ( -6, 4 )

Coordinate of  vertex  C' ( 6, 4 )

Coordinate of  vertex D' ( 6, -4 )

Coordinate of rectangle ABCD gets dilated by the scale factor of :

Scale factor of 'x' coordinate  = -6 / -3

                                                 = 2

Scale factor of 'y' coordinate  = -4 / -2

                                                 = 2

Change in the vertices of rectangle ABCD to A'B'C'D' is given by :

( x , y ) → ( 2x , 2y )

Therefore, the vertices of rectangle ABCD changed to A'B'C'D' is equal to option A. ( x , y ) → ( 2x , 2y ).

The above question is incomplete, the complete question is:

Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?

A) (x, y ) → (2x, 2y)

B) (x, y ) → (1. 5x, 1. 5y)

C) (x, y ) → (3x, 3y)

D) (x, y ) → (4x, 4y)

Graph is attached.

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Answer:7.2

Step-by-step explanation:

x-3=21/5=4.2

x=4.2+3=7.2

Answer: look at the image for the solution and the answer

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Second choice      at x = 0     it is = 6

  and as the exponent (x) gets more negative it gets larger meaning it has a coefficient of < 1     ( it is 3/4)

The quantity of shares you own can impact your dollar gains and losses, but not your rate of return. The length of time you hold the shares can have a significant impact on your rate of return, with longer holding periods generally leading to higher returns.

Investing in stocks can be a great way to earn money, but it's important to understand how your investments can impact your gains and losses. Two key factors that can impact your returns are the quantity of shares you own and the length of time you hold the shares. In this article, we'll explore how these factors can affect your rate of return.

The quantity of shares you own can have a direct impact on your dollar gains and losses. When the stock price goes up, the value of your shares also increases. Similarly, when the stock price goes down, the value of your shares also decreases. If you own more shares, the dollar amount of your gains and losses will be greater.

But, how does the quantity of shares impact your rate of return? Rate of return is the percentage change in the value of your investment over a certain period of time. It takes into account the gains and losses as well as the length of time you held the investment.

The length of time you hold the shares can have a significant impact on your rate of return. Generally, the longer you hold the shares, the higher your rate of return will be. This is because the stock market tends to go up over time, and the longer you hold the shares, the more time you have to benefit from this growth.

So, how does the quantity of shares you own impact your rate of return? As we mentioned earlier, the rate of return is only impacted by the percentage change in the stock price, not the quantity of shares. However, owning more shares can provide you with a higher dollar amount of gains, which can lead to a higher rate of return.

Additionally, the longer you hold the shares, the higher your rate of return will be. This means that if you own more shares and hold them for a longer period of time, you can potentially earn a higher rate of return.

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The probability that no two of them celebrate their birthday in the same month is very low.

There are 12 months in a year, so the probability that the first person has a birthday in a particular month is 1/12. The probability that the second person does not have a birthday in the same month is 11/12, since there are 11 months left that the second person's birthday can fall in. The probability that the third person does not have a birthday in any of the two previously chosen months is 10/12, and so on.

Therefore, the probability that none of the 12 people have a birthday in the same month is:

P = (1/12) x (11/12) x (10/12) x ... x (2/12) x (1/12)

which is approximately 0.00010578, or about 0.01%.

So the probability that no two of them celebrate their birthday in the same month is very low.

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the angle between the vectors is: θ = cos⁻¹ (- 12 / √145)

A quantity or phenomena with independent directions and magnitudes is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Science uses vectors to express everything with a direction and a magnitude. They are typically shown as pointed arrows, with the length of the arrow representing the magnitude of the vector.

Let, a(vector) = < -1, -2 >

a(vector) = -i -2j

||a(vector)|| = √(-1)² + (-2)² = √5

b(vector) = < -2, 5 >

b(vector) = -2i + 5j

||b(vector)|| = √(-2)² + (5)² = √29

Next, a(vector) . b(vector) = (-i -2j) . ( -2i + 5j)

a(vector) . b(vector) = (1 × (-2)) + (-2 × 5) = - 12

Thus, angle between these two vectors:

cosθ = a(vector) . b(vector) / ||a(vector)|| . ||b(vector)||

cosθ = - 12 / (√5 . √29)

cosθ = - 12 / √145

θ = cos⁻¹ (- 12 / √145)

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The solution of the expression x²-8x = 24 will be x = 4+√40. The correct option is D.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the quadratic expression is, x²-8x = 24. The expression will be solved as below,

x²-8x = 24

Solve the above expression by completing the square method.

x²-8x = 24

( x - 4 )² - 24 - 16 = 0

( x - 4)² =40

x - 4 = √40

x = √40 + 4

Therefore, the correct option is D.

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The solutions are given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Part A

the dotted line formes the thrid side of the triangle.

part B

The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.

part c

If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.

part D

You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.

part e

The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.

part f

Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters

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