solve the system of equations, with a complete solution

Answer:

sin(35)

Step-by-step explanation:

Because of the co-function identity [tex]\cos(\theta)=\sin(90^\circ-\theta)[/tex], then [tex]\cos(55^\circ)=\sin(90^\circ-55^\circ)=\sin(35^\circ)[/tex].

Composition is sometimes referred to as has-a relationship.

A form of aggregation, a composition association relationship represents a whole-part relationship. The lifetime of the part classifier is a function of the lifetime of the whole classifier, according to a composition association relationship.

Data typically only flows in one direction (from the whole classifier to the part classifier) in a composition association relationship. For instance, if a student is removed from a class that has a composition association relationship with a schedule class, the schedule is also removed.

Any association may be named to describe the type of connection between the two classifiers; however, names are not required if association end names are used.

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On solving the provided question, we can say that equation, k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.

a. f(x) = 2x+4 represents the function where you multiply the input by 2, then add 4 to the result.

b. g(x) = 2(x+4) represents the function where you add 4 to the input, then multiply the result by 2.

c. h(x) = 4x+2 represents the function where you multiply the input by 4, then add 2 to the result.

d. k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

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As the angle increases from 0 to π/2, the value of sine increases, and the value of cosine decreases.

Trigonometry is a branch of mathematics that deals with the relationships between angles and sides of triangles.

Let us first understand the concept of sine and cosine. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle and the length of the hypotenuse. Similarly, the cosine of an angle is defined as the ratio of the length of the adjacent side and the length of the hypotenuse.

As the angle θ increases from 0 to π/2, the length of the opposite side (the numerator in sine) of the triangle increases, and the length of the hypotenuse (the denominator in sine) remains the same. Therefore, the value of sine increases as θ increases.

On the other hand, as the angle θ increases from 0 to π/2, the length of the adjacent side (the numerator in cosine) decreases and the length of the hypotenuse (the denominator in cosine) remains the same. Therefore, the value of cosine decreases as θ increases.

This behavior is consistent with the fact that sine is an increasing function, while cosine is a decreasing function within this range of angles.

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Complete Question:

If 0< θ <π/2, as Theta increases, the value of

cos(θ) [Decreases/Increases/Remains The Same]

and the value of sin(θ) [Decreases/Increases Remains The Same]​

Answer:

1.66

Step-by-step explanation:

hope this helps

Answer:

3/5 or 0.8

Step-by-step explanation:

3 Cartons, divided by 5 people =

3/5 or 0.8

5050 flips expect to make before running out of coins .

Let's approach this problem using the concept of geometric distribution.

The probability of getting heads on any given coin flip is 1/2, assuming a fair coin.

So the probability of getting tails on a given flip is also 1/2.

The number of flips it takes to get the first head is a geometric distribution with a probability of success p = 1/2.

The expected number of flips until the first head appears is 1/p = 2 flips.

After the first head appears, there will be 99 coins left to flip.

The expected number of flips until the next head appears is still 2, since the probability of getting heads on any given flip is still 1/2.

So the expected number of flips until the second head appears (and the number of coins remaining drops to 98) is 2+1 = 3 flips.

Similarly, the expected number of flips until the third head appears (and the number of coins remaining drops to 97) is 2+1+1 = 4 flips.

We can generalize this pattern: after k heads have been obtained, the expected number of additional flips until the next head appears (and the number of coins remaining drops to 100-k) is k+1 flips.

Using this formula, we can calculate the expected number of flips to obtain all 100 heads:

E(number of flips) = (2 + 3 + 4 + ... + 101)

= (1 + 2 + 3 + ... + 100) + 100

= (100 x 101 / 2) + 100

= 5050

Therefore, we expect to make 5050 flips before running out of coins to flip and obtaining all 100 heads.

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The number of panels that Plant B produced is; 11000 panels

We are told that Plant A produced 4000 fewer panels than Plant B did.

Thus;

A = B - 4000    -----(1)

Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. Thus;

0.04A + 0.02B = 500   ------(2)

Put eq 1 in eq 2 to get;

0.04(B - 4000) + 0.02B = 500

0.04B - 160 + 0.02B = 500

0.06B = 660

B = 660/0.06

B = 11000 panels

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The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is option C, MN/LK||MN.

The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.

In this case, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.

However, we need to establish that MN/LK||MN, which means that MN is parallel to LK and forms a transversal with LN.

This information is necessary to establish that the included angles between the corresponding sides are congruent, which is required for the triangles to be similar.

Therefore, option C is the correct additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.

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The percentage of white marbles on the jar is obtained dividing the number of white marbles by the total number of marbles.

A percentage is calculated applying a proportion, dividing the number of total outcomes by the number of desired outcomes, and then multiplying by 100%.

The outcomes for this problem are given as follows:

The problem is incomplete, hence the standard procedure to obtain the percentage of white marbles was presented.

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In the given word problem, Ling collected 4/5 bags.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Belle and Ling are collecting clothes for a clothing drive. Ling collected 1/5 as many clothes as Belle did and Belle collected 4 bags of clothes, we need to find how many bags of clothes did Ling collect.

Since, Belle collected 4 bags, and Ling is collected 1/5 of the Belle collection,

So, Ling collected = 4 x 1/5 = 4/5

Hence, Ling collected 4/5 bags.

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A minimum score of 182 is required to stay out of the bottom 1.5% of students and avoid going to summer school.

To find the minimum score required to avoid going to summer school, we need to determine the score that separates the bottom 1.5% of students from the rest of the distribution. This score is also known as the cutoff or the critical value.

We know that the test scores have a normal distribution with a mean of 400 and a standard deviation of 100. To find the critical value, we can use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can standardize the test scores using the z-score formula:

z = (x - mu) / sigma

where x is the test score, mu is the mean, and sigma is the standard deviation.

Substituting the given values, we get:

z = (x - 400) / 100

To find the z-score corresponding to the bottom 1.5% of the distribution, we can use a standard normal table or a calculator. The area to the left of this z-score is 0.015, which corresponds to a z-score of approximately -2.17.

Now we can solve for x, the minimum score required to stay out of the bottom 1.5%:

-2.17 = (x - 400) / 100

x = -2.17 * 100 + 400

x ≈ 182

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Answer:

e would equal a half because it's in the middle

The weight of Franklin’s mountain bike in kilograms which  weighs 17,000 grams is equal to option A. 17 kilograms.

Weight of Franklin’s mountain bike  in grams is equal to 17,000 grams

Convert the grams into kilograms.

One kilograms is equal to one thousand grams

1 kilograms = 1000 grams

⇒ 1 grams = ( 1 / 1000 ) kilograms

⇒ 17,000 grams = ( 17,000 / 1000 ) kilograms

⇒ 17,000 grams = 17 kilograms

Therefore, after converting grams into kilograms the weight of Franklin’s mountain bike whose weight in grams is 17,000 grams  is equal to option A. 17 kilograms.

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The  original two-digit number is 11 * 10 + 3 = 113.

Let us correspond to the original two-digit number as "10x + y," with x and y showing the tens and units digits, respectively.

We know from the first piece of information:

x + y = 14

According to the second piece of information:

2(10x + y) + 10y + x = 222

When we simplify this equation, we get:

20x + 22y = 202

We get 10x + 11y = 101 by dividing both sides by 2.

We now have two equations with two variables that can be solved by substitution or elimination. For example, in the first equation, we can solve for x and then substitute into the second equation:

x = 14 - y\s10(14 - y) + 11y = 101

When we simplify this equation, we get: y = 3

Putting y = 3 back into the first equation yields: x = 11.

The  original two-digit number is 11 * 10 + 3 = 113.

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The area of the side panel of the stairway is 360 square inches.

The side panel of the stairway is essentially a right triangle with the three steps forming the three horizontal segments (treads) and the three risers forming the three vertical segments (risers).

The height of the side panel would be the total height of the three risers, which is -

3 risers x 8 inches/riser = 24 inches

The length of the side panel would be the total length of the three treads, which is -

3 treads x 10 inches/tread = 30 inches

Now, we can calculate the area of the side panel using the formula for the area of a right triangle:

Area = (base x height)/2

we have the base as the length of the side panel (30 inches) and the height is the total height of the three risers (24 inches).

Substituting these values into the formula we get,

Area = (30 inches x 24 inches)/2

Area = 360 square inches

Therefore, the area of the side panel of the stairway is 360 square inches.

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The next two days when Alicia would be allowed to eat junk foods are Thursday and Tuesday.

The first day after Saturday when Alicia would have junk food can be determined by counting the fifth day after Saturday.

Sunday - first day

Monday - second day

Tuesday - third day

Wednesday - fourth day

Thursday - fifth day

The next day after Thursday when Alicia would have junk food is the fifth day after Thursday.

Friday - first day

Saturday - second day

Sunday - third day

Monday - fourth day

Tuesday - fifth day

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The percentage increase in her taxes from 2010 to 2011 is 44.30%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Sophia paid $3,360,00 in taxes in 2010 and her taxes rose to $4,848,60 in 2011.

So, The amount of tax increase is $(484860 - 336000) = $148860.

Therefore, The percentage increase is,

= (148860/336000)×100%.

= 44.30%.

The net amount change will now be divided by the starting total, and the result will be multiplied by 100% to determine the percentage change.

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Answer:

144 egg sandwiches

Step-by-step explanation:

[tex]25\% + 45\% = 70\%[/tex], and [tex]100\% - 70\% = 30\%.[/tex] Thus, [tex]30\%[/tex] of the [tex]480[/tex] sandwiches are egg sandwiches. Since "of" means multiply, we have [tex]30\% \cdot 480.[/tex] We know [tex]30\% = \frac{30}{100} = \frac{3}{10},[/tex] so we can rewrite it as [tex]\frac{3}{10} \cdot 480.[/tex] We cancel [tex]480[/tex] with [tex]10[/tex] which is [tex]480 \div 10 = 48.[/tex] We multiply [tex]48[/tex] by the numerator, [tex]3,[/tex] to get [tex]48 \cdot 3 = 144.[/tex] Thus, Lillian makes [tex]\boxed{144 \text{ egg sandwiches.}}[/tex]

Answer:

396cm^3

Step-by-step explanation:

use formula V=Area of base * Height that is V=1/2b*h *Height

Answer:

solution: Mr. Schwartz will need to order more wheels after building 12 cars.

explanation:

Mr. Schwartz begins with total number of wheels = 85

he has to order more wheels once he left with less than 40 wheels

so min. no. of wheels he can use before ordering more wheels = 85-40 = 45

Mr. Schwartz uses 4 wheels to build 1 car

Mr. Schwartz uses 45 wheels to build 45÷4 = 11.25 cars

then, if he builds 12 cars then he needs 12×4 = 48 wheels

total supply of wheels he begins with = 85

wheels he used to build 12 cars = 48

so total number of wheels remaining are = 85-48 = 37

since 37 is less than 40 so after building 12 cars Mr. Schwartz need to order more wheels.

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After '2' hours, both Car A and Car B will be '20' miles from McDonald Middle School

What is a graph?

A diagram or pictorial representation that organises the depiction of data or values is known as a graph.

The relationships between two or more items are frequently represented by the points on a graph.

Given that, both the cars are traveling at a constant speed and given a graph showing the distance from The school in Y-axis and Time in X-axis

To find the point where the cars meet, We should look at the point of intersection of both the lines of Car A and Car B

We can see the point of intersection to be (2 hours, 20 miles)

i.e., After 2 hours, Both the cars are 20 miles from the school

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Hi there, here's your answer:

Given 2 angles:

(6d + 8)° and (8d + 4)°

Observe the figure carefully. You will notice that the two angles form a linear pair.

We know that in a linear pair, sum of the two angles = 180°.

Hence,

(8d + 4 + 6d + 8)° = 180°

(14d + 12)° = 180°

(14d)° = (180 - 12)°

= 14d = 168°

Or

d = 12

Thus, we find the value of d to be d = 12.

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Answer: All she needs to sell is 53 tickets

Step-by-step explanation: You divide 160 by 3 which gives you 53.3333 so you take the decimal place and get rid of it and it gives you 53. So she needs to sell at least 53 tickets to reach her goal

The altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.

What is the altitude?

The height of an object or point in relation to sea level or ground level.

Part A:

To create a table for the given equation, we substitute the given values of x in the equation and calculate the corresponding values of y:

x y = -128x + 3,840

0 3,840

5 3,200

8 2,624

10 2,304

30 0

Part B:

To find the altitude after 5 minutes, we substitute x = 5 in the given equation:

y = -128(5) + 3,840

y = 3,200

So the altitude of the airplane after 5 minutes of descending is 3,200 feet.

To find the altitude after 30 minutes, we substitute x = 30 in the given equation:

y = -128(30) + 3,840

y = 0

The altitude of the airplane is decreasing as time (x) increases, as given by the negative slope (-128) of the equation.

At 5 minutes, the airplane has descended to an altitude of 3,200 feet, which is still relatively high.

At 30 minutes, the altitude has decreased to 0, which means the airplane has landed on the ground.

Hence, the altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.

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Answer:

b) 2/3

Step-by-step explanation:

For a 6-sided die

total number of numbers: 6

numbers less than 2: 1

prime numbers: 2, 3, 5

total number of desired outcomes: 1 + 3 = 4

p(less than 2 or prime) = 4/6 = 2/3

When the smaller data point is included, the mean will drop when compared to the other values, but the median may increase or decrease depending on whether the collection of numbers is even or odd.

1. Calculate the original set of numbers' mean and median.

2. Include the lesser data point in the collection.

3. Determine the updated median and mean.

4. Evaluate the original mean and median in comparison to the new mean and median. Depending on whether the collection of numbers is even or odd, the median will decline while the mean will increase.

We must first determine the mean and median of the initial set of data in order to evaluate how the addition of a smaller data point will impact those values. Adding together all the values and dividing by the total number of values yields the mean. We place the middle value in the set of integers after sorting them from least to largest to determine the median. We include the new, smaller data point in the set after finding the mean and median. We next perform the same calculations as previously to determine the new mean and median. Finally, we contrast the updated mean and median with the baseline values. The median may stay the same or drop depending on whether the set of numbers is even or odd, while the mean often decreases as it is compared to other values. The mean and median of a set of numbers can therefore be significantly affected by the addition of a tiny data point.

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The complete question is

how do you know how adding a smaller data point will affect the mean or median if its smaller than them other value.

The correct statements are Two data sets could have different means but the same standard deviation, and could have the same mean but different standard deviations. If two data sets have different means they must have different standard deviations. Correct options are A, C , D.

The mean and standard deviation are both measures of the central tendency of a data set, but they capture different aspects of the distribution. The mean represents the average value of the data, while the standard deviation measures how spread out the data is around the mean.

It is possible for two data sets to have different means but the same standard deviation if one data set is more spread out than the other, but the values are symmetrically distributed around the mean. For example, the data sets {1, 2, 3, 7, 8, 9} and {0, 4, 5, 5, 5, 9} have different means (5 and 4.67, respectively) but the same standard deviation (3.16).

Similarly, two data sets could have the same mean but different standard deviations if one data set is more spread out than the other. For example, the data sets {1, 2, 3, 4, 5} and {1, 3, 3, 3, 5} have the same mean (3) but different standard deviations (1.41 and 1.26, respectively).

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Complete question is:

Which of the following statements is true?

multiple select question.

A. two data sets could have different means but the same standard deviation.

B. if two data sets have the same mean they must have the same standard deviation.

C.  two data sets could have the same mean but different standard deviations.

D. if two data sets have different means they must have different standard deviations.

£40 is shared as £5, £15 and £20. 88p is shared as 16p, 32p and 40p. 180° is shared as 40°, 40° and 100°

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

a) Share £40 in the ratio 1:3:4

For the first ratio = (1/8) * £40 = £5

For the second ratio = (3/8) * £40 = £15

For the third ratio = (4/8) * £40 = £20

b) Share 88p in the ratio 2:4:5

For the first ratio = (2/11) * 88p = 16p

For the second ratio = (4/11) * 88p = £32

For the third ratio = (5/11) * 88p = 40p

c) Share 180° in the ratio 2:2:5

For the first ratio = (2/9) * 180° = 40°

For the second ratio = (2/9) * 180° = 40°

For the third ratio = (5/9) * 180° = 100°

The ratios are shown above

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