PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!
Find the probability of drawing a green, then yellow, with replacement.
A bag has 4 green blocks, 6 red blocks, 7 blue and 3 yellow.

Answers

Answer 1

The probability of drawing a green block followed by a yellow block with replacement is 0.03, or 3%.

What is probability?

The probability of an event is calculated by dividing the total number of possible outcomes by the number of possible outcomes.

The likelihood of drawing a green block on the main draw is:

P(green) = (number of green blocks) / (total number of blocks)

P(green) = 4 / (4 + 6 + 7 + 3)

P(green) = 4 / 20

P(green) = 0.2

Since the blocks are replaced after each draw, the probability of drawing a yellow block on the second draw is still:

P(yellow) = (number of yellow blocks) / (total number of blocks)

P(yellow) = 3 / (4 + 6 + 7 + 3)

P(yellow) = 3 / 20

P(yellow) = 0.15

To find the probability of both events happening, we multiply the probabilities:

P(green, then yellow) = P(green) * P(yellow)

P(green, then yellow) = 0.2 * 0.15

P(green, then yellow) = 0.03

As a result, replacing a yellow block with a green one has a chance of 0.03, or 3%, being drawn.

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Related Questions

1. Which number is the greatest? 20 -100 -45 50

Answers

Answer:

D) 50

Step-by-step explanation:

-100 <-45 < 20 < 50

Answer:

50

Step-by-step explanation:

any numbers approaching negative (before 0) in an increasing manner are the lowest, whereas numbers approaching positive in a increasing manner are the greatest.

The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.
-3, 4, -1, 6, 7
The mean temperature for all 7 days of the week was 0°F.
What was the mean of the temperatures for the two missing days?
a. -13
b. -10.5
c. -6.5
d. 0

Answers

The value of the mean of the temperatures for the two missing days are,

= - 6.5

We have to given that;

The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.

-3, 4, -1, 6, 7

And, The mean temperature for all 7 days of the week was 0°F.

Now, We can assume that,

Last two days temp. are x and y.

Hence, We get;

(- 3 + 4 + (-1) + 6 + 7 + x + y) / 7 = 0

- 3 + 4 - 1 + 6 + 7 + x + y = 0

x + y = - 13

Divide both side by 2;

(x + y)/2 = - 13/2

(x + y)/2 = - 6.5

Thus, The value of the mean of the temperatures for the two missing days are,

= - 6.5

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An area of land measures 735 metres by 756 metres. It is to be divided up into
square plots of equal size.
(a) What is the area of the largest squares that will fit on it?
(b) How many squares will fit on it?

Answers

Answer:

See below!

Step-by-step explanation:

Given:

Length = 735 meters

Width = 756 meters

Finding the area:

Area = length × width

Area = 735 × 756

Area = 555660 m²

Part a)

To find the area of largest square, we first need to find the highest common factor of 735 and 756.

HCF of 735 and 756:

= 21

This means the length of largest square will be 21 m.

Now,

Area of largest square:

= length × length

= 21 × 21

= 441 m²Part b)

No. of squares = Total area / Area of largest square

No. of squares = 555660 / 441

No. of squares = 1260 squares

[tex]\rule[225]{225}{2}[/tex]

Angulo de 38 grados y 25 grados

Answers

El ángulo entre 38 grados y 25 grados es de 13 grados.

pls!! :(( a golf ball has been hit off of the tee at an angle of elevation of 30 degrees and an initial velocity of 128 ft/sec

how long is the ball in the air (hang time)?

what is the maximum height of the ball?

how far, horizontally, does the ball travel in the air?

Answers

According to the information, the horizontal distance traveled by the ball is 443.404 feet.

How to calculate the distance traveled by the ball?

We can use the kinematic equations of motion to solve for the hang time, maximum height, and horizontal distance traveled by the golf ball.

First, we need to resolve the initial velocity vector into its horizontal and vertical components. The vertical component will determine the maximum height and hang time, while the horizontal component will determine the horizontal distance traveled.

The initial velocity can be represented as:

v0x = v0 cos(theta) = 128 cos(30) = 110.851 ft/secv0y = v0 sin(theta) = 128 sin(30) = 64 ft/sec

where v0 is the initial velocity, theta is the angle of elevation, v0x is the horizontal component of the initial velocity, and v0y is the vertical component of the initial velocity.

Now we can use the kinematic equations to solve for the hang time, maximum height, and horizontal distance traveled.

Hang time (time in air):

We can use the vertical motion equation to solve for the time when the ball reaches its maximum height:

v = v0y - gt0 = 64 - 32tt = 2 seconds

Since the ball will be in the air for twice the time it takes to reach its maximum height, the hang time is:

2t = 4 seconds

Maximum height:

We can use the vertical motion equation to solve for the maximum height reached by the ball:

y = v0y t - 1/2 gt^2y = 64(2) - 1/2 (32)(2)^2y = 64 ft

Therefore, the maximum height of the ball is 64 feet.

Horizontal distance traveled:

We can use the horizontal motion equation to solve for the horizontal distance traveled by the ball:

x = v0x t

x = 110.851(4)

x = 443.404 ft

Therefore, the horizontal distance traveled by the ball is 443.404 feet.

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I need help with this to find x and y value ​

Answers

Answer:

x = 360°/8 = 45°

y = 2 × 45° = 90°

A theatre contains 457 seats and the ticket prices for a recent play were ​$54 for adults and ​$17 for children. If the total proceeds were ​$14,984 for a​ sold-out matinee, how many of each type of ticket were​ sold?

Answers

Answer: 195 adult tickets and 262 children tickets

Step-by-step explanation:

     Let a be adult tickets and c be children tickets.

We know there are 457 seats.

     a + c = 457

We also know the cost of the tickets and how much money was made.

     $54a + $17c = $14,984

Now, we have a system of equations we can use to solve.

     a + c = 457

     $54a + $17c = $14,984

Lastly, we will graph this system, see attached. The point of intersection, or where the lines intersect, is our answer.

     195 adult tickets and 262 children tickets.

Answer:

Chidden tickets were 262 and adult tickets were 195 tickets

Step-by-step explanation:

Let x = the number of children tickets

Let y = the number of adult tickets.

x + y = 457

17x + 54y = 14984

Use substitution

x + y = 457 Solve for y

y = 457 -x  Substitute 457 -x for y in the equation 17x + 54y = 14984

17x + 54y = 14984

17x + 54(457 -x) = 14984  Solve for x  Distributer the 54

17x + 24678 - 54x = 14984  Combine like terms

-37x = -9694   Divide both sides by -37

x = 262

The number of children tickets.

x + y = 457  Substitute 262 for x and solve for y

262 + y = 457  Subtract 262 from both sides

y = 195

The number of adult tickets.

Helping in the name of Jesus.

θ=1 rad when S=r. If θ=2 rad then what is the condition? :::::::(S means arc length)

Answers

If θ=2 rad then the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

In this problem, we are given that when the arc length is equal to the radius (S=r), the angle is 1 radian (θ = 1 rad). Now, we are asked to find the condition when the angle is 2 radians (θ = 2 rad).

If Θ=1 rad when S=r, it means that when the angle subtended by an arc of length r is 1 radian, then the radius of the circle is also r.

Now, if θ=2 rad, we can use the same proportionality to find the arc length S that corresponds to this angle. Since the angle has doubled, we can expect the arc length to double as well. Therefore, we have:

θ/Θ = S/r

2/1 = S/r

S = 2r

Thus, the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

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Match the equation or expression to the number of terms, the coefficients and the constants.

Answers

 [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

  Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

How to break down mid point?

To break down each equation or expression and identify the number of terms, coefficients, and constants.

[tex]1.[/tex] Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: 4. There are four terms in this equation separated     by addition and subtraction operators.

Coefficients: [tex]6,4,10[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (xt, yz, a) in each term.

 Constants: [tex]-3,1[/tex]. These are the constants, which are the numerical values without any variables that are added or subtracted in the equation.

[tex]2.[/tex]  Expression:[tex]25abc -2b +3ac -6bc +25[/tex]

   Number of terms: [tex]5[/tex] There are five terms in this expression separated by addition and subtraction operators.

  Coefficients: [tex]25,-2,3,-6[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (abc, b, ac, bc) in each term.

  Constants: [tex]25[/tex]. This is the constant, which is the numerical value without any variables that is added in the expression.

[tex]3.[/tex]  Equation: [tex]25y -3xy+5x = 100[/tex]

    Number of terms:[tex]3[/tex]. There are three terms in this equation separated by addition and subtraction operators.

    Coefficients: [tex]25,-3,5[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (y, xy, x) in each term.

   Constants: [tex]100[/tex]. This is the constant, which is the numerical value without any variables on the right-hand side of the equation.

Therefore,   [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

   Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

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Find the volume of a tissue box that has the following dimensions:

Length=20 cm

Width= 5 cm

Height= 12 cm

Volume=______

Answers

Answer:

1,200

Step-by-step explanation:

The formula is Length x Width x Height so it will be 20 x 5 x 12 and you get 1,200.

Hope this helps!

V=l*w*h
V=20*5*12
V=1,200cm^3

Calcular el área de un triángulo equilátero si su base es de 8 m y una altura de 5 m

Answers

Answer:

[tex]tringle = \frac{1}{2} \times base \times hieght[/tex]

1/2 × 8×5

0.5×40

=20m

is it true that 5 2/3 - 3 3/4= 1+2/3+3/4

Answers

In linear equation., both quantities are different from each other.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Taking LHS

  5 2/3 - 3 3/4= 17/3 - 15/4

  17/3 - 15/4 =  68 - 45/12  = 23/12

 

now solving RHS

  1+2/3+3/4  = 12 + 8 + 9/12  = 29/12

clearly, LHS≠ RHS

hence both quantities are different from each other.

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I need help with this math

A right triangular pyramid has a height of 14 yards. Its base has a leg that is 8 yd. The volume of the pyramid is 168 cubic yd. The other leg of the base is ___ yd.

Answers

Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 3 yards long.

What does volume actually mean?

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.

Here,

Let's use "x" yards to represent the other leg of the right triangle pyramid's base.

A pyramid's volume can be calculated using the following equation: => Volume = (1/3) * Base Area * Height

In this instance, we are informed that the pyramid has a volume of 168 cubic yards and a height of 14 yards.

=> 168 = (1/3) * 14 * base area

The base area can be estimated as (8 * x)/2 = 4x because we know that one leg of the base is 8 yards long and the other leg is designated as "x" yards.

=> 168 = (1/3) * 4x * 14

=> 168 = (4/3)x * 14

=>  168 = (4/3) * 14x

=> 168 = 56x

=> x = 168/56

=> x = 3

Therefore, the other leg of the right triangular pyramid's base is 3 yards long.

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a circle has a circumerence of 6 and an arc with a 60 degree central angle. what is the length of the arc

Answers

The length of the arc is 1 unit.

What is length of an arc?

The distance that runs through the curved line of the circle making up the arc is known as the arc length.

length of an arc is expressed as;

l = tetha/360 ×2πr

the circumference of circle is expressed as ;

C = 2πr

6 = 2×3.14 × r

r = 6/6.28

r = 0.955 units

Therefore length of the arc

= 60/360 × 6

since 2πr is the circumference,

l = 360/360 = 1 unit

therefore the length of the arc is 1 unit.

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you are renting a condominium at 1,700 a month. Your annual expenses are insurance, $325; lost interest, $50 and utility bills, $5,940. You also pay a monthly fee for all maintenance and what is his average monthly expense?

Answers

Answer:

$526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.

Step-by-step explanation:

To calculate your average monthly expense, we need to first add up all of your annual expenses and divide by 12 (the number of months in a year) to find the monthly average.

Annual expenses:

Insurance: $325

Lost interest: $50

Utility bills: $5,940

Total annual expenses = $325 + $50 + $5,940 = $6,315

To find the average monthly expense, we divide the total annual expenses by 12:

Average monthly expense = Total annual expenses / 12

Average monthly expense = $6,315 / 12

Average monthly expense = $526.25

In addition to the annual expenses, you also pay a monthly rent of $1,700 and a monthly fee for all maintenance. Let's assume that the monthly maintenance fee is $100.

Therefore, your total monthly expense would be:

Total monthly expense = Monthly rent + Monthly maintenance fee + Average monthly expenses

Total monthly expense = $1,700 + $100 + $526.25

Total monthly expense = $2,326.25

So, your average monthly expense is $526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.

What is 25% of 32?
Hint: We can think of 25% as a common
fraction.

Answers

Answer:8%

Step-by-step explanation:

you divide 25 by 32 and round to nearest tenth

hope this helps :)

Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.

Answers

Answer:

yes it is if you bisect 5m on a 12m line

A ship leaves a port with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns 90° towards the North with the same speed in 2 hours. What is the bearing to the ship from the port (due North)? How far is the ship from the port now?

Answers

The bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.

Since the ship travels at a constant speed, we can use the formula:

distance = speed × time

For the first hour, the ship travels at a bearing of S80°E, which is equivalent to a bearing of N10°E. Therefore, the ship travels 15 nautical miles in a direction N10°E. This gives us:

PA = distance = speed × time = 15 × 1 = 15 nautical miles

After the first hour, the ship turns 90° towards the North. This means that the ship is now heading due East. Therefore, for the next 2 hours, the ship travels 15 × 2 = 30 nautical miles in an easterly direction. This gives us:

AB = distance = speed × time = 15 × 2 = 30 nautical miles

Now, we can use the Pythagorean theorem to find the value of y:

y² = x² + (AB)²

y² = 15² + 30²

y² = 225 + 900

y² = 1125

y ≈ 33.54 nautical miles

To find the bearing of B from P, we can use trigonometry. The bearing is the angle between the line PA and due North. Let θ be this angle. Then we have:

tan(θ) = x / y

θ = tan^-1(x / y)

Using the values we have found, we get:

tan(θ) = 15 / 33.54

θ ≈ 24.65°

Therefore, the bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.

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What is the solution of the equation (x-5)2 + 3(x-5)+9=0? Use u substitution and the quadratic formula to solve.
-3±3-√3
2
O x-
7±3-√√3
2
Ox-2
Ox=8

Answers

Answer: there is no solution

Step-by-step explanation:

The solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

What is a quadratic equation?

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.

The general form of the quadratic equation is: ax² + bx + c = 0

Given that, a quadratic equation (x-5)² + 3(x-5) + 9 = 0, we need to solve it,

So, put x-5 = u

Therefore,

u² + 3u + 9 = 0

Solving using quadratic formula,

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}} {2a}[/tex]

Here a = 1, b = 3 and c = 9

Therefore,

[tex]u=\frac{-3 \pm \sqrt{3^2-4(9)}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{9-36}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{-27}} {2}[/tex]

[tex]u=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

Put u = x-5,

Therefore,

[tex]x-5=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

[tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Hence, the solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

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How many times does 13 go into 26

Answers

Answer: 2

Step-by-step explanation:

2 times with a remainder of 0

What is the area of a circle with diameter of 16 meters? Leave the answer in terms of pi

Answers

Answer:

64π

Step-by-step explanation:

Use the formula for an area of a circle
[tex]A = \pi r^2[/tex]
Half of 16 is 8.
8*8 = 64.

The area of a circle with a diameter of 16 meters is equal to 64π or 200.96 square meters.

How to calculate the area of a circle?

Mathematically, the area of a circle can be calculated by using this formula:

[tex]\text{Area} = \pi \text{r}^2[/tex]

Where:

[tex]\text{r}[/tex] represents the radius of a circle.

[tex]\text{Note:} \ \text{Radius} = \dfrac{\text{diameter}}{2} = \dfrac{16}{2} = 8 \ \text{meters}.[/tex]

By substituting the radius into the formula for the area of a circle, we have the following;

[tex]\text{Area of circle} = \pi \times 8^2[/tex]

[tex]\bold{Area} \ \text{of circle} = 64\pi \ \text{or} \ 200.96[/tex] square meters.

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At the school's holiday craft fair, Colette and her classmates get to make gingerbread houses. Their teacher divides a bag of licorice ropes evenly among the 9 students at the table. Each student gets 3 licorice ropes to decorate the roof of his or her gingerbread house.

Answers

Answer: So, what are you asking?

Step-by-step explanation:

HELPP SOMEONE PLEASE

Answers

Answer:

8. mArc ED = 38°

9. mArc EA = 142°

10.mArc BDC = 308°

Step-by-step explanation:

The measure of an a central angle and it's intercepted arc are equal

So if the measure of the angle for the angle that intercepts Arc ED is 38° the arc is also 38°

Same thing with Arc EA, the central angle that intercepts it is 142° so the measure of Arc EA is 142°

Arc BDC is a major arc so it is greater than 180°. It goes around the circle from point B to point C and point D is one of the points on the arc.

We could find the value of the arc two ways. We could add all the angles  the that make up the central angle it is intercept by or we could simply subtract the 52° that isn'tt a part of the arc and subtract that from 360°

360 - 52 = 308

So the central angle intercepting Arc BDC is 308° so the arc also has a measure of 308°.

4 ft
6 ft
T4ft-
8 ft
1. List the shapes that make up the front of the house.

Answers

The answer on shape of house is , (1) A rectangle for the main structure of the house. (2) A triangle for the roof. (3) A rectangle for the front porch. (4) Two trapezoids for the roof of the front porch. (5) A rectangular door.

What is Trapezoid?

A trapezoid is a four-sided geometric shape with two parallel sides, called the bases, that are of different lengths, and two non-parallel sides that connect the bases. The non-parallel sides are also called legs, and they may or may not be equal in length.

Trapezoids are often encountered in geometry and in real-life situations, such as in construction and architecture. They can be classified as either right trapezoids or oblique trapezoids depending on whether one of the angles formed by the bases and a leg is a right angle or not.

Based on the image provided, the shapes that make up the front of the house are:

A rectangle for the main structure of the house. A triangle for the roof.A rectangle for the front porch.Two trapezoids for the roof of the front porch.A rectangular door.

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6/5/8 - 2/3/8 estimate

Answers

The estimated value of the expression [tex]6/5/8 - 2/3/8[/tex] is approximately [tex]0.5082[/tex].

How can we calculate the multiple fraction?

In Mathematics, fractions are defined as the parts of a whole. The whole can be an object or a group of objects

To estimate 6/5/8 - 2/3/8, we can convert the fractions to decimals and then perform the subtraction.

6/5/8 is equivalent to 6 ÷ 5.8, which is approximately 1.0345. 2/3/8 is equivalent to 2 ÷ 3.8, which is approximately 0.5263.

Therefore, 6/5/8 - 2/3/8 is approximately 1.0345 - 0.5263 = 0.5082.

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Calculate the ratio​

Answers

Where the conditions above are given with regard to the above triangle, the ratio AD:DB is 1:1.

What is the explanation for the above response?

Since D is the midpoint of AB, we have:

AD = DB

Let M and N be the midpoints of OA and OB, respectively. Then we have:

AM = MO = x/2

BN = NO = y/2

Also, from the given information, we have:

OD = 3/7x + 4/7y

Since D is the midpoint of AB, we have:

AD + DB = AB

Substituting AD = DB, we get:

2AD = AB

Therefore:

AD = AB/2

We can express AB in terms of x and y using the law of cosines:

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos(BOA)

Since M and N are midpoints, we have:

OM = OA/2 and ON = OB/2

Therefore, using the law of cosines, we have:

MN^2 = OM^2 + ON^2 - 2(OM)(ON)cos(MON)

Substituting OM = OA/2 and ON = OB/2, we get:

MN^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

But MN = OD, so we can also express this as:

OD^2 = (3/7x + 4/7y)^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

Substituting OD^2 = (3/7x + 4/7y)^2 and simplifying, we get:

9x^2 + 16y^2 = 49(OA^2 + OB^2) - 42(OA)(OB) cos(BOA)

Substituting AB^2 = OA^2 + OB^2 - 2(OA)(OB) cos(BOA) and simplifying, we get:

9x^2 + 16y^2 = 49AB^2

Substituting AD = AB/2, we get:

9x^2 + 16y^2 = 49(2AD)^2

Simplifying, we get:

x^2 + 4y^2 = 28AD^2

We want to find the ratio AD:DB, which is the same as the ratio AD:(AB - AD). Substituting AB = 2AD, we get:

AD:(AB - AD) = AD:AD = 1:1

Therefore, the ratio AD:DB is 1:1.

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What is the image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin?

Answers

The image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

What is the image of the point?

To rotate a point counterclockwise about the origin, we can use the following formulas:

(x', y') = (y,-x)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the rotated point

In this case, we want to rotate the point (-1, 2) by 270° counterclockwise about the origin.

So, we have

(x', y') = (2,1)

Therefore, the image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

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I'm having a hard time finding the period, amplitude, and sinusoidal equation of this graph. I don't know if I'm supposed to use sine or cos. Please help me

Answers

The period of the sinusoidal equation of the graph is 4 months.

The amplitude of the sinusoidal equation of the graph is 84 degrees Celsius.

What is the period and amplitude of a wave?

The period and amplitude are two important characteristics of a wave.

Period: The period of a wave is the time it takes for one complete cycle of the wave to occur. The period of a wave determines its frequency, which is defined as the reciprocal of the period.

Amplitude: The amplitude of a wave is the maximum displacement of the wave from its equilibrium position. In simpler terms, it represents the height or strength of the wave.

In then given graph, the period of the wave = 1 complete cycle in 4 months = 4 months/cycle = 4 months

Amplitude = 84 degrees Celsius.

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In ΔFGH, f= 67 inches, m∠G=66° and m∠H=30°. Find the length of g to the nearest inch

Answers

Answer:

38 inches

Step-by-step explanation:

We can use the Law of Sines to solve for the length of side g:

sin(66°)/67 = sin(30°)/g

Cross-multiplying, we get:

g*sin(66°) = 67*sin(30°)

Dividing both sides by sin(66°), we get:

g = 67*sin(30°)/sin(66°) ≈ 38 inches (rounded to the nearest inch)

Therefore, the length of side g is approximately 38 inches.

< ^2 − 3
^2 ≥ x^2/2 -12


Is this a system of linear inequalities?

Answers

The linear inequalities in the given graph  is y ≥ x/2 -1 and  y< -1/2x -3.

What is Linear inequalities ?

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.

Here, we have,

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.

we have,

In the given graph, the area above solid line,

points, (-2 , -2) , (0 , -1)

slope = 1/2

so,  y ≥ x/2 -1

The area below dashed line ,

points, (-2 ,-2) , (0 ,-3)

slope= -1/2

so, y< -1/2x -3.

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