What type of transformation is illustrated in the picture below? A. rotationB. translation

ANSWER

sin(2θ) + cos(2θ) = -31/25 = -1.24

EXPLANATION

If we do the inverse of the cosine to -3/5 we would get the angle θ. Then we can know the value of the sine:

So we have:

• sin(θ) = 4/5

• cos(θ) = -3/5

To find sin(2θ) + cos(2θ) we'll have to use the trigonometric identities:

Since we have the sine and cosine of theta, we can solve this:

The sum is:

Mrs. Richardson and Mr. Richardson have to make their hourly income 306.314 to live within their budget in Athens.

What is income?

Income is the amount of money that an individual or an organization gets in return for their services or goods offered. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.

Given in the question,

The Richardson family needs 990272 per year to in their budget.

Mrs. Richardson works 22 hours a week.

Mr. Richardson works 40hours a week.

We need to calculate their hourly income.

Lets first calculate total weeks in a year.

We know that, a year has 365 days and a week has 7

So, total no. of weeks in a year = 365/7 = 52.143 weeks.

no. of weeks in a year = 52.143 weeks

Their weekly income = yearly income/no. of weeks in a year

So, weekly income = 990272/52.143

weekly income = 18991.466

Their hourly income = weekly income/working hours per week

Their weekly income is 18991.466 and,

working hours = 22 + 40 = 62 hours.

Their hourly income = 18991.466/62

Hourly income = 306.314

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Given the standard form:

This can be expressef as a decimal by shifting the decimal point to the back 4 times (since the power is a negative 4) as shown:

Hence the equivalent value for the standard form is 0.0005. Option B is correct

Based on the system of equations, the cost of using 19 HCF of water is $35.43

An equation is a mathematical statement that two or more values are equivalent.

Equations are stated to show that two mathematical expressions are equal using the equation sign (=).

Cost of using 17 HCF of water = $32.13

Cost of using 35 HCF of water = $61.83

Total cost of 17 HCF water = 17x + a

17x + a = 32.13 ... equation 1

Total cost of 35 HCF water = 35x + a

35x + a = 61.83 ... equation 2

35x + a = 61.83

-17x + a = 32.13

18x = 29.70

18x = 29.7

x = 29.7/18

x = 1.65

17x + a = 32.13 ... equation 1

17(1.65) + a = 32.13

28.05 + a = 32.13

a = 4.08 (32.13 - 28.05)

= 19(1.65) + 4.08

= $35.43

Thus, using the equations above, we can conclude that 19 HCF of water costs $35.43.

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Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots e.t.c

Examples of radicals are

For exmaple,

Given the radical

To simplify into the simplest radical,

Factorize the perfect square

Then we take out the pairs

Simplify the result

Hence, the simplified radical of the example used is

EXPLANATION:

Given;

We are given a frequency table which displays a survey of numbers of customers that like hamburgers and burritos and those that do not like hamburgers and burritos.

Required;

We are required to analyze the table and use the values to answer the questions that follow.

Solution;

We shall begin by completing the table as follows;

Part A:

What percentage of the survey respondents do not like both burritos and hamburgers?

The percentage that do not like hamburgers is

The percentage that do not like burritos is

The percentage that does not like both burritos and hamburgers is;

Expressed as a percentage, this is

The marginal relative frequency of all customers that like hamburgers is the total of all hamburger lovers divided by the total of all respondents.

ANSWER:

Part (a) 26.34%

Part (b) 53.66%

The actual area of the reservoir in m² as required in the task content is; 0.5m².

It follows from the task content that the actual area of the reservoir is to be determined.

Hence, since it is given that the area of the reservoir on the map is 2cm² and the map has a scale of 1: 2500.

Hence, it follows from proportions that the area of the reservoir is; 2cm² × 2500 = 5000cm².

However, when expressed in m²; the actual area of the reservoir is; 5,000/10000 = 0.5m².

Ultimately, the area of the reservoir in m² is; 0.5m².

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According to the solving the probability are as follows:

a) Event "A or B": {1, 2, 3, 4, 6}

(b) Event "A and B": {2, 4}

(c) The complement of the event A: {5, 6}

The term "sample space" refers to a collection of probable results from a random experiment. The letter "S" indicates that this is the sample space. Events are a subset of what might happen in an experiment. Depending on the experiment, the outcomes in a sample area could change. In discrete or finite sample spaces, there are only a finite number of possible outcomes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

the sample space is, 1, 2, 3, 4, 5, 6 i.e., U = {1, 2, 3, 4, 5, 6}

Event A: The number rolled is less than 5

i.e., A = {1, 2, 3, 4}

Event B: The number rolled is even

i.e., B = {2, 4, 6}

Event A Or B A∪B = {1, 2, 3, 4} ∪ {2, 4, 6}

= {1, 2, 3, 4, 6}

Event "A and B"A∩B = {1, 2, 3, 4} ∩ {2, 4, 6}

= {2, 4}

Compliment of the event A

Comp(A) = U/ A = {1, 2, 3, 4, 5, 6} / {1, 2, 3, 4}

= {5, 6}

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Given:

The expression is 2p +5r = q.

The objective is to solve for p.

Explanation:

For the value of p, the expression can be solved as,

Hence, the expression for p is, (q-5r)/2.

Answer:

(99/8)

Step-by-step explanation:

      3

12 -------

      8

8 × 12 = 96

96 + 3 = 99

 99

-------

  8

I hope this helps!

we calculate the area of one trangle and multiply by 2

we apply formula of the triangle area

where b is the base and h the height of the triangle

then replacing

area of one triangle is 15.6square centimeters

Area of both triangles

Area of the two triangle bases is 31.2 square centimeters

SOLUTION

Define a variable for the unkwons

Then

6 dozen of doughnuts and 2 dozen of croissant cost $42, is written as

Similarly

$40 for 2 dozen of doughnuts and 5 dozen of croissant is witten as

Applying Elimination to solve the two system of equation, we have

Then, subtract the equation obtained above

Hence Y=6

Then you Eliminate Y from eqaution 1 an d 2 by

Multiplying equation 1 by 5 and equation 2 by 2

The sunbtract the equation obtained

Hence X=5

Therefore

A Dozen of doughnuts cost $5

A Dozen of Croisant cost $6

Answer:

[tex]\frac{3}{13}[/tex]

Step-by-step explanation:

the fraction is formed by the number who prefer historical movies to the total preferring all movies.

total = 24 + 18 + 6 + 30 = 78

number preferring historical movies = 18

then fraction preferring historical movies is

[tex]\frac{18}{78}[/tex] ( divide numerator/ denominator by 6 )

= [tex]\frac{3}{13}[/tex] ← in simplest form

Answer:

From the Graph the total number of students who preferred historical movies =  18.

Similarly total number of  students = 24+18+6+30

                                                         = 78

Fraction of student who prefer Historical movies = 18/78

                                                                                = 3/13.

Answer:

Explanation:

We are given the equation for the height:

If we differentiate this equation, we get the equation of the velocity:

The problem tells us that the object hits the ground at a velocity of -25m/s. We can write this:

Where t0 is the time when the object hits the ground, and the velocity is -25m/s

Now, we can solve for v0:

And if we use this in the height h(t) equation, we can find the value of t0. At t0, the height is 0. Thus:

And solve:

Next, we can use the quadratic formula to solve this:

Let's see which of the two solutions is the time we are looking for.

Let's go back to our solution for v0:

If we use t0 = 0.43751 s:

This means that the initial velocity is negative, thus the object goes downwards. But, the problem tells us that initially the object is thrown upwards.

The correct value of t0 = 4.66 seconds

Now we can find v0:

Thus, v0 = 20.7 m/s

Notice that:

cannot be expressed as a product of factors, meaning that

is not a factor of the given polynomial.

Answer: Not a factor.

Answer:

Of course it is

Step-by-step explanation:

In the expression: 9 + 3y + 6 + y

Combining like terms, the expression becomes: 3y + y + 9 + 6

Final answer: 4y + 15 which is option B

So you're correct

if we take the black boxes as representation of negative numbers, and the white boxes as a representation of positive numbers, then we get:

after combining the similar terms we get:

therefore, the final expression is x + 1

Answer:

Step-by-step explanation:

The area of the floor is 4×3=12 sqare meters

=12×100×100= 120000 square centimetres.

Area of each tile is 20×20=400 square centimetres.

Therefore number of tiles required will be

120000÷400 =300.

300 tiles will be required to cover the floor.

The value of the function at x = 0 will be 1.

What is a function?

A statement, principle, or rule that creates a relationship between two variables is known as a function. Functions are abundant in mathematics and are required for the creation of complex relationships.

When the required parameters and natural laws are given values, the expression yields the calculation result that the mathematical model represents.

The table represents a function.

x     f(x)

-3     1

-1     8

0      1

3     0

6     13

9     -3

In the above table, we can see that at the value of x = 0 in the function the value of the whole function is 1.

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Number of cartons of cloth face masks purchased will be 19  and number of cartons of  hand-sanitizer purchased will be 5.

We had given that Maleri Designs sells cartons of cloth face masks ($10) and cartons of hand-sanitizer ($4) on eBay.

Also given that Mod World, purchased 24 cartons.

Let number of cartons of cloth face masks be x and let number of cartons of  hand-sanitizer be y.

As total carton purchased is 24.

∴ x + y = 24 --(1)

also Mod World, purchased 24 cartons for $210.

∴ Also price of cartons of cloth face masks is $10 and cartons of hand-sanitizer is $4 which is buyed at $210.

∴ 10x + 4y = 210  --(2)

Now multiplying equation (1) by 10

∴ 10x + 10y = 240 --(3)

Now subtracting (2) from (3) by simplification

∴ y = 5

∴ x = 19

Number of cartons of cloth face masks purchased will be 19  and number of cartons of  hand-sanitizer purchased will be 5.

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Answer:

-12≤x<1

Step-by-step explanation:minus both side by 4

• x-intercept can be found by letting y equal to 0.

• y-intercept can be found by letting x equal to 0.

X intercept is the x-axis cutting point of the graph.

Y intercept is the y-axis cutting point of the graph.

The equation given is:

First, finding x intercept (let y = 0):

Second, find y intercept (let x = 0):

Hence,

Evaluate the given expression at x=6. This is, replace every x in the equation for 6 and solve:

The balance after 6 months is 1197.04.

Given,

{x : x is a letter in the word "nonintervention"}

A={x : x is a letter in the word "nonintervention"}

The roster form of the set is,

A={e, i, n, o, v, t, r}

The number of elements in the set A is,

n(A)=7

Hence, the number of elements in the set A is 7.

Given the matrices A and B:

We know that:

Then, using the matrices A and B:

And the element C₄₁ (fourth row and first column) is:

Now, for the matrix (A + B) - A = B:

Answer

P (0.3 < Z < 1.4) = 0.3013

Explanation

P (0.3 < Z < 1.4) = P (0 < Z < 1.4) - P (0 < Z < 0.3)

P (0.3 < Z < 1.4) = 0.4192 - 0.1179

P (0.3 < Z < 1.4) = 0.3013

After 7 weeks she would have the total of 119$

A. $381

B. 17 weeks

500-211=289/17=17

The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25° so option (A) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

Let's suppose the two congruent interior angles are x degrees.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠x+  m∠x +  95.5° = 180°

2m∠x = 180° - 95.5°

m∠x = 84.5/2 = 42.25°

Hence "The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25°".

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Answer:

$ 0.75 for one pen

$1.05 per notebook

Step-by-step explanation:

John and Ariana bought school supplies. John spent $10.30 on 5 notebooks and 7 pens. Ariana spent $7.20 on 4 notebooks and 4 pens. What is the cost of 1 notebook and what is the cost of 1 pen?

John: 5n + 7p = 10.5

let's solve for n:

5n + 7p = 10.5

subtract 7p from both sides:

5n + 7p -7p = 10.5 - 7p

5n = 10.5 - 7p

divide both sides by 5:

5n/5 = (10.5 - 7p)/5

n = 2.1 - 7/5 p

Ariana: 4n + 4p = 7.20

Let's substitute in: n = 2.1 - 7/5 p

4n + 4p = 7.20

4(2.1 - 7/5p) + 4p = 7.20

multiply left side:

8.4 - 5.6p + 4p = 7.2

subtract 8.4 from both sides:

8.4 - 5.6p + 4p - 8.4 = 7.2 - 8.4

- 5.6p + 4p = -1.2

combine p terms on left side:

-1.6p = -1.2

divide both sides by -1.6:

-1.6p/(-1.6) = -1.2/(-1.6)

p = 0.75 cents for one pen

Now solve to find the price of a notebook:

4n + 4p = 7.20 when p = 0.75

4n + 4(0.75) = 7.20

4n + 3 = 7.20

subtract 3 from both sides:

4n + 3 - 3 = 7.20 - 3

4n = 4.2

divide both sides by 4:

4n/4 = 4.2/4

n = 1.05 per notebook

CHECK: when n = 1,05 and p = 0.75

John: 5n + 7p = 10.5

5(1.05) + 7(0.75) = 10.5

10.5 = 10.5

Ariana: 4n + 4p = 7.20

4n + 4p = 7.20

4(1.05) + 4(0.75) = 7.20

7.2 = 7.2

Answer assumes no additional sales tax.