1. Which of the drawings described below would create a line of reflection that takes the point A to point B?
a.
Draw the perpendicular bisector of segment AB.
b. Draw a line through B perpendicular to segment AB.
c. Draw the line passing through A and B.
d. Draw a line parallel to line AB.

Answer:

Use the SOH CAH TOA

Step-by-step explanation:

Angle = 60°

x = opposite o

y = adjacent a

10√ 3 = hypotenuse h

To find x we use SOH {sineø = o/h}

Sin 60° = x/10√ 3

x=10√ 3 * sin 60

X=15

You can use Pythagoras theorem or CAH{cosø = a/h}

Cos 60°= y/10√ 3

y=Cos 60° * 10√ 3

y=5√ 3

The rate of change in the given graph is 21/4.

The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:

Rate of change = Δy / Δx

To calculate the rate of change of the given graph, we need to identify 2 points first. We take:

(0, 0)

(4, 21)

Rate of change = Δy / Δx

Rate of change = y₂ - y₁

                             x₂ - x₁

Rate of change = 21 - 0

                               4 - 0

Rate of change = 21/4

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Answer:

114

Step-by-step explanation:

j k  / j + k

612/ 6 + 12

   104 + 12

       114

3x = 18

Divide both sides by 3 and simplify

x=6

Answer:

Step-by-step explanation:

assuming  that you need to find the value of x

3x = 18

-divide both sides by 3

3x/3 = 18/3

-use the facts that 3/3 =1 and 18/3 = 3*6/3 = 6

x = 6

A frequency distribution in which there are too many scores at the extremes of the distribution is said to be platykurtic distribution.

What is frequency distribution?

Frequency tables or charts are used to represent frequency distributions.

Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.

We are given a frequency distribution in which there are too many scores at the extremes of the distribution

This distribution is said to be platykurtic distribution because a distribution with a negative excess kurtosis value is referred to as "platykurtic." Since there are fewer extremely positive or negative events, a platykurtic distribution will have thinner tails than a normal distribution.

Hence, this type of distribution is said to be platykurtic distribution.

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4= b) 20

210-190=20

5= a) 8

142-134=8

6= b) driver 2 drove the least amount of miles in one day

B is false, driver 2 drove the most amount in one day so, b is correct.

Hope this helps and so sorry if I'm wrong.

Two options are given to Tina. We find how much she pays for each option, and the one in which she pays less offers the better value.

Tina sends 12 text messages each day in June

June has 30 days, so in June, Tina sent 12*30 = 360 text messages.

Package A:

First 100 messages cost 3p, the next 100 cost $2 and after that each costs $1.

She sends 360 messages, with:

The first 100 costing 3p.

The next 100 costing 2p.

The final 360 - 200 = 160 costing 1p.

She pays:

\(100*3 + 100*2 + 160*1 = 660\)

Package B:

2p for each message, 360 messages, so:

360*2p = 720p.

Which package is better?

Package A costs less, thus, it offers her the better value for money in 30 days.

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After conversion we get,

17. 120° = 0.2988 radian.

The  given measure is,

17.20 degree

A radian is a unit of measurement for angles. Angles are measured using two units: degrees and radians. You may have been using degrees to measure the sizes of angles up to this point. Angle measures in advanced mathematics, on the other hand, are typically described using a unit system other than the degree system for a variety of reason.

A single radian, as seen here, is about equal to 57.296 degrees. When we wish to compute the angle in terms of radius, we use radians instead of degrees. In the same way that '°' is used to denote a degree, rad or c is used to represent radians. 1.5 radians, for example, is written as 1.5 rad or 1.5c.

Then 1 degree = 0.0175 radian

Now,

17.120 degree = 0.0175x17.120

                        = 0.2988 radian.

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Answer:

128

Step-by-step explanation:

The expected value (EV) of betting $3 on red is -$0.16

The standard deviation (SD) of betting $3 on red is 2.995

The expected value of the bet is calculated as follows:

there are 18 red slots out of 38 total, so the probability of winning a bet on red is 18/38, or 0.4737.

The probability of losing the bet is 1 - 0.4737, or 0.5263.

If the ball lands on red, the player wins $3, and if it lands on black or green, the player loses $3.

The expected value (EV) f betting $3 on red is:

EV = (probability of winning * amount won) + (probability of losing * amount lost)

EV = (0.4737 * $3) + (0.5263 * -$3)

EV = $1.42 - $1.58

EV = -$0.16

The standard deviation (SD) of betting $3 on red is:

SD = √[(probability of winning * (amount won - EV)²) + (probability of losing * (amount lost - EV)²)]

SD = √[(0.4737 * ($3 - (-$0.16))²) + (0.5263 * (-$3 - (-$0.16))²]

SD = √[(0.4737 * $9.98) + (0.5263 * $8.06)]

SD = √[$4.728 + $4.245]

SD = √($8.973)

SD = $2.995

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The correct option is B. The trips will each bus has to make to get everyone to the stadium is 40 trips.

The number of fans who will need to use satellite parking is:

150,000 x 0.52 = 78,000

Each bus can carry 65 fans, so the total number of trips required is:

78,000 / 65 = 1200

Therefore, each bus will need to make 1200/30 = 40 trips

Satellite parking typically offers lower rates than the central parking area and provides a shuttle service to transport passengers to and from the main terminal. This type of parking is a popular option for travelers who need to park their car for an extended period of time, such as those going on vacation or business trips.

Satellite parking can be located either on-site or off-site, depending on the transportation hub. Some airports have several satellite parking lots located at various distances from the main terminal, while others have a single satellite parking area. Overall, satellite parking is an important component of transportation infrastructure, as it provides a convenient and affordable parking solution for travelers while also helping to alleviate congestion in the main parking area.

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The third term of the expansion is 6a²b²

The expression is given as

(a+b)^4

Rewrite properly

So, we have the following representation

(a + b)⁴

The a-th term of a binomial expansion is represented as

Tₐ₊₁ = ⁿCₐ xⁿ⁻ᵃ * yᵃ

For the third term, we have the following equation

Third term = ⁴C₂ a² * b²

Apply the combination formula

Third term = 4!/2!2! * a² * b²

Evaluate

Third term = 6a²b²

Hence, the third term is 6a²b²

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Answer:

h(3) = -7

Step-by-step explanation:

h(3) = - 3 - 4 = -7

Answer:

Step-by-step explanation:

The number of simple events in this experiment is 16.

The correct answer to the given question is option c.

The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.

The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.

Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

Therefore, the number of simple events in this experiment is 16, which is option (c).

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Yes, the sequence is an arithmetic sequence.

the common difference is 4

The given sequence in the problem include: 7, 11, 15, 19, ...

The common difference is the constant amount by which each term increases (or decreases) from the previous term in the sequence.

The common difference is solved by comparing the successive terms as below

first term = 7

second term = 11

common difference = d

7 + d = 11

d = 11 - 7 = 4

check

7 + 4 = 11

11 + 4 = 15

15 + 4 = 19

In this case, the common difference is 4, because each term is 4 more than the previous term.

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Since 1/2 is distributed over 1/3 and 1/4 hence the law applied is the distribution law of addition.

Given the following integers A, B and C. According to the distribution law;

A(B + C) = AB + AC

This shows that the  value A is distributed over B and C

Given the expression

1/2 + (1/3*1/4) = (1/2*1/3) + (1/2*1/4)

From the result, you can see that 1/2 is distributed over 1/3 and 1/4 showing that the law applied is the distribution law of addition

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Answer:

x = 8√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to solve for the missing length.

Step 2: Identify Variables

Leg a = 8

Leg b = 8

Hypotenuse c = x

Step 3: Solve for x

The tank with the smallest surface area has dimensions of 6ft.

s = 12ft and h = 6ft.

A(s) = s² + 4 × (V ÷ s)

The rectangular tank has a capacity of 864 feet.

Let the square base's long sides be.

Let h represent the tank's height.

Let A represent the tank's whole area.

A = (Base Area) + (4 × Lateral Area)

Lateral Area = s × h

Lateral Area = s × (V ÷ s²)

Lateral Area = (V ÷ s)

Base Area = s²

Compared to the objective function,

A(s) = s² + 4 × (V ÷ s)

A(s) = s² + 4 × (864 ÷ s)

The area function's derivative,

A'(s) = 2s - (3456 ÷ s²)

The smallest surface area is now.

A'(s) = 0

2s - (3456 ÷ s²) = 0

2 × \(s^{3}\) = 3456

\(s^{3}\) = 3456

s = \(\sqrt[3]{3456}\)

s = 12ft

The volume is,

V = s² × h

864 = 12² × h

h = 6ft

As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.

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The question is -

A rectangular tank with a square​ base, an open​ top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.

The margin of error would be larger, since a decrease in the sample size will increase the standard error. As the sample size decreases, the amount of error that can be expected in the sample estimate increases.

The margin of error would be larger, since a decrease in the sample size will increase the standard error. As the sample size decreases, the amount of error that can be expected in the sample estimate increases.Therefore, the margin of error would increase as well, indicating that the results are less precise and less reliable.
Hi! If the sample size were 85 rather than 100, the margin of error would be larger. This is because a decrease in the sample size will increase the standard error, resulting in a larger margin of error.

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Answer:

  B.  False

Step-by-step explanation:

For independent events, it must be true that ...

  P(B|A) = P(B)

__

The probability of B does not depend on A. That is what makes them independent.

Answer:

33°

Step-by-step explanation:

In triangle ABC,

<ABC +<BAC+<ACB =180°[Sum of three angles of a triangle]

2x+15+2x+x=180

5x=180 - 15

x=165/5

x=33°

Hope this helps!!

Answer:

The answer is there are 30 glazed donuts

Step-by-step explanation:

there are 12 donuts to a dozen therefore 12 * 12 = 144 donuts all together.

donuts with chocolate icing

\(144 \times \frac{3}{8} = 54\)

with white icing and sprinkles

\( 144 \times \frac{1}{4} = 36\)

donuts with pink icing

\(144 \times \frac{1}{6} = 24\)

Total donuts minus donuts with icing equal glazed donuts

\(144 - 54 - 36 - 24 = 30\)

Step-by-step explanation:

you did not say what needs to be done.

simplify ?

sqrt(12/b²)

12 = 4×3

4 is a square number (2² = 4).

3 is not.

b² is per definition a square "number".

in a multiplication or division we can apply the square root (or any root) individually to the different factors involved.

so,

sqrt(12/b²) = sqrt(12)/sqrt(b²) = sqrt(4×3)/b =

= 2×sqrt(3)/b

FYI - about your question : if somebody does not know (how to get) the answer, he/she will also not be able to doubtlessly determine, if a specific answer is right ...

Answer:

5

Step-by-step explanation:

13² - 12² = 25

√25 = 5

Have a great day <3

To find the total income from the machines over the first 6 years, we need to calculate the definite integral of the given function f(t) = 150e^(0.08t) over the interval [0, 6]. This integral represents the accumulated income over the given time period.

The given function represents the annual rate of flow of money into the machines, with f(t) = 150e^(0.08t) in thousands of dollars per year.

To find the total income over the first 6 years, we need to calculate the definite integral of f(t) from 0 to 6:

∫[0,6] 150e^(0.08t) dt.

Evaluating this integral, we get [150/0.08 * e^(0.08t)] evaluated from 0 to 6. Simplifying further:

= [1875 * e^(0.08t)] evaluated from 0 to 6

= 1875 * [e^(0.08 * 6) - e^(0.08 * 0)].

Evaluating the exponential terms, we have:

= 1875 * [e^(0.48) - e^(0)]

≈ 1875 * [1.616 - 1]

≈ 1875 * 0.616

≈ 1155.

Therefore, the total income from the machines over the first 6 years is approximately 1155 thousand dollars. Rounded to the nearest thousand dollars, the answer is 1155 thousand dollars.

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Bisection method is a numerical method used to find the root of a function by repeatedly bisecting an interval and determining which subinterval the root lies in, until the root is found.

To find the time at which the number of people in the museum is at a maximum, we need to find when the rate at which people are entering the museum (f'(t)) is equal to the rate at which people are leaving the museum (g'(t)).

Setting f'(t) = g'(t), we get:

380(1.02^t) = 240 + 240 sin (π(t-4)/12)

Simplifying, we get:

1.58(1.02^t) = 1 + sin(π(t-4)/12)

We can use a graphing calculator or numerical methods to solve for t.

Using a graphing calculator, we can graph the functions y = 1.58(1.02^x) and y = 1 + sin(π(x-4)/12) and find the point of intersection on the interval 1 ≤ x ≤ 11.

Alternatively, we can use numerical methods such as the bisection method or Newton's method to approximate the solution.

Using either method, we find that the solution is t ≈ 9.446.

Therefore, the answer is (C) 9.446.

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The approximation of cos(1) using the fifth-degree Taylor polynomial is 1 - 1/2 + 1/24.

The approximation of the value cos(1) obtained by using the fifth-degree Taylor polynomial about x=0 for cos(x) is 1 - 1/2 + 1/24.

The Taylor series expansion for cos(x) centered at x=0 is given by:

cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + (x^8)/8! - ...

To approximate cos(1), we consider the terms up to the fifth-degree polynomial:

cos(x) ≈ 1 - (x^2)/2! + (x^4)/4!

Substituting x=1 into the polynomial, we get:

cos(1) ≈ 1 - 1/2 + 1/24

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Answer:

D

Step-by-step explanation:

From the given figure it is clear that angle MNO is formed by segments MN and NO.

It says that angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′.

Answer:

v=24

Step-by-step explanation:

V= 3\(\sqrt{10^{2} - 6^{2} }\)

V= 3\(\sqrt{100-36}\)

V= 3\(\sqrt{64}\)

V= 3×8

V= 24

The solution to the given absolute value problems is:

1) x > 0 and x < 0

2) x > 0 and x < 0

3) y = |x| + 2

The absolute value which is also referred to as modulus | x | of a real number x is the non-negative value of x without any regard given  to its sign. For example, the absolute value of 4 is 4, and the absolute value of −4 is also 4. The absolute value of a number may be referred to as its distance from zero along real number line.

1) |x - 5| if x > 5

Using the concept of absolute value functions, we have:

For (x - 5) if x > 5: x > 0

For -(x - 5) if x > 5: x < 0

Thus, the solution is: x > 0 and x < 0

2) |x - 5| if x > 5

Using the concept of absolute value functions, we have:

For (x - 5) if x > 5: x > 0

For -(x - 5) if x > 5: x < 0

Thus, the solution is: x > 0 and x < 0

3) When we translate a function by two units upwards, then it means that we add 2 to the function.

Thus, we have:

y = |x| + 2

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