In Mr. Romano's class, the ratio of the number of girls to the number of boys is 3:2. A student is selected at random from
the class. The probability that the selected student is a boy is

F. 1/6
G. 1/3
H. 2/5
J. 3/5
K. 2/3

The number of white rabbits that are at the farm is 60

From the question, we are to determine the number of white rabbits that are at the farm

From the given information,

There are 210 rabbits at the farm

and

For every 5 gray rabbits, there are 2 white rabbits

Then, we can write that

5x + 2x = 210

Where x is the number of groups of 5 gray rabbits and 2 white rabbits

Then,

7x = 210

x = 210/7

x = 30

The number of white rabbits is 2x

∴ Number of white rabbits = 2×30

Number of white rabbits = 60

Hence, the number of white rabbits that are at the farm is 60

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Answer:

  about 94.41°

Step-by-step explanation:

The Law of Cosines can be used to find an angle in a triangle with three sides given.

The law of cosines relation generally relates the side opposite the angle to the other measures in the triangle:

  r² = p² +q² -2pq·cos(R)

We want to find the measure of angle R, so we solve the equation for that:

  2pq·cos(R) = p² +q² -r² . . . . . . add 2pq·cos(R)-r²

  cos(R) = (p² +q² -r²)/(2pq) . . . . divide by the coefficient of the cosine

We can fill in the given side lengths at this point:

  cos(R) = (13² +10² -17²)/(2·13·10) = -20/260 = -1/13

Then the angle can be found using the arccos function:

  R = arccos(-1/13) ≈ 94.41°

The measure of angle R is about 94.41°.

__

Additional comment

When you have done a few of these, you recognize that the angle opposite side 'c' is ...

  C = arccos((a² +b² -c²)/(2ab))

A calculator can make short work of this. The second attachment shows the evaluation of this expression with a=10, b=13, c=17. The calculator angle mode is set to degrees. The arccos function is the 2ND function of the Cos key.

Answer:

3/4

Step-by-step explanation:

The total number of children is 8 and the number of girls is 6. This can be represented as 6/8.

You would then need to simplify...

6/2=3

8/2=4

which which lead you to 3/4!

Answer:

Law of large Numbers

Step-by-step explanation:

The Law of large numbers.

The law of large numbers plays the main role in probability and statistics. It means that if you repeat an experiment independently so many times and average the result, what you get has to be close to the expected value.

An example of the Law of Large Numbers:

Let's assume that you rolled the dice three times and the outcomes were 6, 6, and 3. Then the average result is 5.

So, according to the law of the large numbers, if we roll the dice a large no. of times, then the average result should be closer to the expected value.

It also states that probability and statistics set a sample size that grows, and the mean of the sample size gets closer to the average of the entire population.

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Answer:

12

Step-by-step explanation:

the number of the available cases is :

3 × 4 = 12

The reflection over the y-axis only changes the sign of the x-component so the reflected point is A' (-3, -1)

Here we can't see the options, so I will teach you how to reflect any point over the y-axis.

Any point on the X-Y plane is defined by its coordinates (x, y).

If we reflect this point over the y-plane, we only change the sign of the x-component of the point.

So after the reflection, we get the point (-x, y).

Then if we apply that reflection to point A (3, -1). We will get the reflected point:

A' (-3, -1)

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The graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].

Suppose that the function is

[tex]f(x)=\log_2(x+c)+d[/tex]

Then there are two observations that we must consider from the figure

So,

[tex]-2=\log_2(-2+c)+d[/tex]

[tex]\implies -2+c=e^{-2-d} ...~...~(1)[/tex]

And,

[tex]0=\log_2(1+c)+d\\\implies 1+c=e^{-d} ~...~...~(2)[/tex]

Observe the figure given below we see that the graph of

[tex]\log_2(x)[/tex] passes through (1,0) but does not pass through (-2,-2) and the graph is to the right of (-2,-2) hence, we need the graph to move left.

When we increase c the graph  [tex]\log_2(x+c)+d[/tex]  moves left and

When we decrease d then the graph  [tex]\log_2(x+c)+d[/tex]  moves down.

That makes the graph required to be   [tex]\log_2(x+3)-2[/tex].

Hence, the graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].

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The answers to the questions are:

a. the straight-line method of depreciation

[tex]\frac{cost of machine - salvage}{useful life} * period[/tex]

= (240000 - 60000) / 4 * (9 / 12)

= $33,750

The debit is 33750 as well as the credit

b.  the units-of-production method of depreciation

(240000 - 60000) / 60000 * 12000

= $36000

c. the double-declining balance method of depreciation

(24000 *2 /4) * (9/12)

= $90000

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Hello,

g(x) = x² - 5x

g(-3) = (-3)² - 5 × 3 = 9 - 15 = - 6 ≠ 24 ⇒ not correct

g(-1) = (-1)² - 5 × (-1) = 1 - 5 = -4 ⇒ correct

g(5) = 5² - 5× 5 = 25 - 25 = 0 ⇒ correct

g(7) = 7² - 5 × 7 = 49 - 35 = 14 ⇒ correct

95% confidence interval is 1.96

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

For 95% confidence interval, we will keep 95% area in the center and will divide the remaining area equally on both sides.

From Standard Normal table,  P(-1.96 < Z < 1.96) = 0.95, i.e., there is a 95% probability that a standard normal variable, Z, will fall between -1.96 and 1.96.

Hence 95% percent confidence interval is 1.96

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User-generated content is the idea that you can empower players to seamlessly generate new content to a game continuously to keep the game fresh.

User-generated content (also known as UGC or consumer-generated content material) is original, emblem-particular content material created by customers and published on social media or other channels. UGC comes in many paperwork, inclusive of photos, films, opinions, a testimonial, or even a podcast.

User-generated content (UGC) has become an essential part of the content material advertising method within the present day era in which customers are prepared to rave about your products or services online. UGC refers to the content this is created through the users of a logo.

Types of User-Generated Content

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5000 square feet is the largest area that can be enclosed

It is given that a rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn there are and there is 200 feet of fence that is available.

One-fourth of the perimeter = 50

The other width also equals 50.

So the length of fencing = 200 - 50 - 50 = 100

So the area = 50 x 100 = 5000 square feet.

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The price of one pill is approximately $0.04.

Division is the mathematical operation used in grouping a number into equal parts using another number. The price of one pill can be determined by dividing the total cost of a number of pills by that number.

Price of one pill = cost of 50 pills / 50

$2.05 / 50 = $0.04

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[tex]\left(\sqrt{z^{2}+8} \right)^{2}=(1-2z)^{2}\\\\z^{2}+8=4z^{2}-4z+1\\\\0=3z^{2}-4z-7\\\\0=(z+1)(3z-7)\\\\z=-1, z=\frac{7}{3}[/tex]

We know that if z=7/3, the right-hand side will be negative, which means it is an extraneous solution as square roots cannot be negative.

Answer:

d. vertical line

Step-by-step explanation:

A line with an undefined slope is a vertical line

Slope is the change in y over the change in x

When the slope is undefined, it means that the x does not change, which is a vertical line

Answer:

Line D

Step-by-step explanation:

Slope is defined as rise/run. Since a vertical line has zero run and infinite rise the equation is infinity/0 and anything divided by zero is undefined.

Las expresiones matemáticas descritas son: (x-1)4=-4³ y 1/3(x+1)=(-10)-1.

Para identificar las expresiones matemáticas debemos organizar los datos proporcionados en el fragmento de la siguiente manera:

Luego debemos solucionar las expresiones matemáticas para encontrar el resultado final:

A. (x-1)4 = -4³

4x-4 = -64

4x = -64+4

4x = -60

x = -60/4

x = -15

B. 1/3(x+1) = (-10)-1

1/3x+1/3 = -11

1/3x = -11-1/3

1/3x = -32/3

x = -32/3•3

x = -32

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The option  that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO

Note that:

If ∆MNO  can be gotten  from ∆ABC  then ∆MNO ≅ ∆ABC  

To solve for Reflection (x axis), it will be:

The coordinate note for the reflection is (x, y) will be: (x,-y)

Since ∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).

Then the reflections will be:

M(-9, -4)- M1(-9,4)

N(-3, -4)- N1(-3,4)

O(-3,-15)-O1(-3,15)

To solve for Reflection (y axis), it will be:    

The coordinate note for the Reflection  is (x,y) will be (-x,y)

Since ∆M1N1O1  = M1(-9, 4), N1(-3, 4), and O1(-3, 15).

Then M1(-9, -4) - M2(9,4)

N1(-3, -4) - N2(3,4)

O1(-3,-15)- O2(3,15)

To solve for Translation

The coordinate note for the Translation is (x,y) will be (x+2,y+2)

Since ∆M2N2O2  = M2(9,4), N2(3,4), and O2(3, 15).

Then M2(9, 4) - M3(11,6)=A

N2(3,4) -  N3(5,6)=B

O2(3,15) - O3(5,17)=C

Hence  ∆MNO ≅ ∆ABC  

To know the congruent by a single rotation.

 If ∆JKL  can be gotten from ∆PQR

Then ∆JKL ≅ ∆PQR  

For Rotation of 90 degree in an anticlockwise position, then:

The coordinate note for the Rotation is (x,y) will be (-y, x)

So, ∆JKL  = J(17, -2), K(12, -2), and L(12, 7).

J(17, -2)-  J1(2,17)

K(12, -2) - K1(2,12)

L(12,7) - L1(-7,12)

To solve for translation

The coordinate note for the translation is (x,y) will be (x+10,y-14)

Then ∆J1K1L1 =  J1(2, 17), K1(2, 12), and L1(-7, 12).

Hence J1(2, 17) - J2(12,3) = P

K1(2, 12)- K2(12,-2) = Q

L1(-7, 12)- L2(3,-2) = R

So, ∆JKL ≅ ∆PQR.

So therefore, The option  that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO

See options below

___ can be shown to be congruent by a sequence of reflections and translations.

1)Pick one to go with the sentence.

a Triangle ABC and Triangle XYZ

b Triangle ABC and Triangle MNO

c Triangle JKL and Triangle ABC

d Triangle PQR and Triangle XYZ

___ can be shown to be congruent by a single rotation.

Pick one to go with the sentence.

a Triangle ABC and Triangle XYZ

b Triangle PQR and Triangle XYZ

c Triangle JKL and Triangle PQR

d Triangle JKL and Triangle XYZ

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Answer:

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

first know it in a simple way

that,3-1=2 right so if we add base and numbers in power , because it has same base when x i.e x to the power 1 goes up

Step-by-step explanation:

x^3/x^1

now

x^3 *x^-1

x^3-1

x^2

proved

Since in each option, each input is mapped to only one output, all the options are correct.

A relationship represents a function when each input is mapped to only one output.

In this problem:

Thus all the options are correct.

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Answer:

The slope is 3

Step-by-step explanation:

it is 3 up and 1 across, which is 3/1 = 3

Answer:

3

Step-by-step explanation:

Look at the two lower dots shown on the line.

slope = rise/run

The vertical distance from the lower point to the higher point is 3. That is the rise.

The horizontal distance from the lower point to the higher point is 1. That is the run.

slope = 3/1 = 3

Answer: 3

Answer:

The product is the difference of squares is [tex]$$\left(5-3x\right)\left(5+3x\right)=25-9{{x}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(5-3 x)(5+3 x)=(5)^{2}-(3 x)^{2} \\&(5-3 x)(5+3 x)=25-9 x^{2}\end{aligned}$$[/tex]

Answer:

  100 m²

Step-by-step explanation:

The scale factor for volume of similar figures is the cube of the scale factor for linear dimensions. The scale factor for area is the square of that linear dimension scale factor.

If the ratio of volumes is the cube of the scale factor, then the scale factor for the smaller figure in terms of the larger is ...

  [tex]k=\sqrt[3]{\dfrac{125\text{ m}^3}{729\text{ m}^3}}=\sqrt[3]{\dfrac{5^3}{9^3}}=\dfrac{5}{9}[/tex]

The area of the smaller figure is found from ...

  [tex]\dfrac{A}{324\text{ m}^2}=\left(\dfrac{5}{9}\right)^2=\dfrac{25}{81}\\\\A=(324\text{ m}^2)\cdot\dfrac{25}{81}=\boxed{100\text{ m}^2}[/tex]

The surface area of the smaller solid is 100 square meters.

__

Additional comment

The least surface area for a given volume is that of a sphere. The larger volume given corresponds to a sphere with a radius of about 5.583 meters. Such a sphere will have an area of about 391.7 square meters. There is no known physical object with a volume of 729 m³ that can have a surface area as little as 324 m².

Answer:

y=mx+b

Step-by-step explanation:

Slope intercept form is y=mx+b where "m" should be substituted with the slope and "b" stands for the y-intercept value. "x" and "y" are your input and output values respectively.

Answer:

32

Step-by-step explanation:

YZ = ⅗XY.

XY = 20

20 / 5 x 3 = 12

YZ = 12

XZ = YZ + XY

XZ = 20 + 12

XZ = 32

Work is attached. Hope it helps!

Utilizando el triangulo rectangulo como contraejemplo, veremos que esto es falso.

Primero, sabemos que para todo triangulo la suma de sus angulos internos es igual que 180°.

Ahora, vamos a el triangulo más comun. El triangulo rectangulo.

Este es el triangulo que tiene uno de sus angulos internos igual a 90°.

Digamos que los otros dos angulos internos son A y B, entonces tendriamos:

A + B + 90° = 180°

Despejando A + B obtenemos:

A + B = 180° - 90° = 90°

A + B = 90°

Entonces vemos que la suma de estos dos angulos internos es igual que el tercer angulo.

Encontramos un contraejemplo de la proposición, asi, concluimos que la proposición es falsa.

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