A rectangle has a length of 5.50 m and a width of 12.0 m. What are the perimeter and area of this rectangle?

The exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II is (-√(45) - 1)/8, found by using the Pythagorean identity and the angle sum identity.

To find the exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II, we can use trigonometric identities and properties of angles. First, we use the Pythagorean identity to find cos θ. Since θ is in the second quadrant, cos θ is negative and solving for cos θ gives cos θ = -√(1 - sin² θ) = -√(1 - (1/4)²) = -√(15)/4.

Next, we apply the angle sum identity for cosine, which is cos(α + β) = cos α cos β - sin α sin β. Using this identity, we find:

cos(θ + π/6) = cos θ cos(π/6) - sin θ sin(π/6) = (-√(15)/4)(√(3)/2) - (1/4)(1/2) = -√(45)/8 - 1/8 = (-√(45) - 1) / 8.

Answer:

9yb

Step-by-step explanation:

Answer: Second option is correct.

Step-by-step explanation:

The two interior angles that are not adjacent to an exterior angle are called "Remote interior angles"

As remote interior angles are those interior angles that are inside the are inside the triangle but opposite to the exterior angles.

Hence, Second option is correct.

Final answer:

The sample from the refuse deposit near the Strait of Magellan, with 60% carbon-14 remaining compared to a contemporary living sample, is estimated to be approximately 7777 years old, based on the known half-life of carbon-14 being 5730 years.

Explanation:

The age of a sample can be estimated using radiocarbon dating, which measures the decay of carbon-14 (14 C). Since the half-life of 14 C is known to be approximately 5730 years, we can use this information to estimate the age of the sample. Radiocarbon dating works on the principle that living organisms continually replenish carbon while alive, maintaining a constant level of 14 C relative to 12 C. When an organism dies, it no longer absorbs carbon, and the 14 C begins to decay at a known rate.

In the case of the refuse deposit near the Strait of Magellan, the sample had 60% of the carbon-14 of a contemporary living sample. To determine the age, we use the half-life formula, which is Time = Half-life / log2 (Starting amount / Remaining amount). Here, starting amount is 100% (contemporary living sample), the remaining amount is 60%, and the half-life is 5730 years.

So the calculation will be: Age of sample = 5730 / log2 (100/60). Calculating this, we get:

Age of sample = 5730 / log2 (1.6667)

Age of sample = 5730 / 0.737

Age of sample ≈ 7777 years

Thus, the sample from the refuse deposit near the Strait of Magellan is estimated to be approximately 7777 years old.

Answer:

10.5 days

Step-by-step explanation:

Point slope form

y-5=10(x-1)

Substitute for y

100-5=10(x-1)

Distribute the 10

100-5=10x-10

Combine like terms

95=10x-10

Add ten to both sides

105=10x

Divide by 10

X = 10.5

Answer:

B.

The leading coefficient is positive so the left end goes down.

done

C.

f(x) is odd so both ends go in opposite directions.

Step-by-step explanation:

APEX

The correct statement is (a), 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' Correlation values range from -1 to +1, and units or nominal variables can't be used.

The correct statement among the given options is (a) 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' In a correlation, the value ranges from -1 to +1 where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. The other statements, (b), (c), (d) and (e), are blunders because the correlation value (r) in (d) exceeds +1 which is impossible, the units in (b) and (c) are incorrectly applied as correlation doesn't have physical units, and in (e), gender is a nominal variable for which correlation cannot be calculated.

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Answer:

D. 200 muffins

Step-by-step explanation:

Break even is a condition where the total production cost is same as the profit produced. In this question, the carrot muffin cost is $1.4 and sold at $2. Then the profit for every muffin should be: $2- $1.4= $0.6/muffin

The electricity cost is $120/day. Then to cover this cost, the muffin need to sold would be:

cost= muffin profit * muffin sold

$120= $0.6/muffin * muffin sold

muffin sold= $120 / ($0.6 / muffin)= 200 muffin

Answer:

5/8

Step-by-step explanation:

The account value after 18 years with an initial deposit of $6,000 and a change in interest rate and compounding periods is approximately $15,526 when rounded to the nearest dollar.

To calculate the value of the account after 18 years with a change in the interest rate and compounding periods, we need to use the compound interest formula separately for the two different periods and rates.

First, we compound the original $6,000 at 5.25% semiannually for 10 years:

A = P(1 + r/n)(nt)

A = $6,000(1 + 0.0525/2)(2*10) = $6,000(1.02625)20 = $9,984.21 (rounded)

Now, we take the amount after 10 years and compound it at 5.4% quarterly for the remaining 8 years:

A = P(1 + r/n)(nt)

A = $9,984.21(1 + 0.054/4)(4*8) = $9,984.21(1.0135)32 = $15,526.14 (rounded)

So, after 18 years, the value of the account would be $15,526 (rounded to the nearest dollar).

Answer:  The given statement is FALSE.

Step-by-step explanation:  We are given to check whether he following statement is true or false :

"The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. "

Let us consider the right-angled triangle ABC as shown in the attached figure below.

With respect to acute angle C, we can see that

perpendicular, p = AB

base, b = BC

and

hypotenuse, h = AC.

We know that

sine of an angle in a right-angled triangle is equal to the ratio of the perpendicular to the base.

So, we must have

[tex]\sin \angle C=\dfrac{p}{h}\\\\\\\Rightarrow \sin \angle C=\dfrac{AB}{AC}.[/tex]

Since AB is the opposite side to angle C, not adjacent, therefore

sine of any angle in a right-angled triangle is the ratio of the length of the OPPOSITE SIDE to length of the hypotenuse.

Thus, the given statement is FALSE.

Final answer:

The statement is false; sine is the ratio of the opposite side to the hypotenuse, not the adjacent side to the hypotenuse.

Explanation:

The statement is false. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse, not the adjacent side to the hypotenuse. Therefore, the sine of angle A would be expressed as sin(A) = opposite/hypotenuse. The ratio of the adjacent side to the hypotenuse, on the other hand, defines the cosine of the angle, which is cos(A) = adjacent/hypotenuse.

Answer:

Step-by-step explanation:

It said free points

Final answer:

To simplify (x - 4)(x^2 + 3x - 1), use the FOIL method to distribute each term and combine like terms, resulting in x^3 - x^2 - 12x + 4 (option B).

Explanation:

To simplify the expression (x − 4)(x2 + 3x − 1), we need to use the distributive property, also known as the FOIL method, which stands for First, Outside, Inside, Last. We will multiply each term in the first binomial by each term in the second binomial.

Combine like terms:

x3 + 3x2 - 4x2 - 12x + 4

Simplify the expression by combining 3x2 and -4x2:

x3 - x2 - 12x + 4

Therefore, the simplified form of the expression is x3 - x2 - 12x + 4, which corresponds to option B.

Move all terms not containing  y  to the right side of the equation. You should get y=6.21

7 WEEKS is how long you can last.

First off, you need at least $100 in your account to avoid the fee and you currently have $247. With that being said, you're taking out $20 every week.

The first thing you can do would be to start at $147 (since that's $100 less than what you can use) and divide that by 20 (since that's what you're taking out every week) 147 / 20 = 7.35. That's 7 weeks because you have to round down to the nearest whole number.

Second What you can do to find how many weeks you can take this out by starting at $100 and adding $20 for every week. So 120, 140, 160, 180, 200, 220, 240. This also gives you 7.

You can take $20 out of your account for 7 WEEKS until you have to pay the low-balance fee.

May I have brainliest please? :)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division

The possible number of weeks to withdraw avoiding the low balance fee is 7 weeks.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total amount in account = $247

Amount withdrawals per week = $20

Amount needed in account to avoid low balance fee = $100

The possible number of weeks to withdraw avoiding the low balance fee:

= (247 - 100) ÷ 20

= 147÷ 20

= 7.35

This means 7 weeks.

Thus,

The possible number of weeks to withdraw avoiding the low balance fee is 7 weeks.

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Answer: [tex]13\sqrt{7}[/tex]

Step-by-step explanation:

In the simple radical form there are no square root is remain to find.

Since, the given expression,

[tex]5\sqrt{28} + \sqrt{63}[/tex]

[tex]5\sqrt{4\times 7} + \sqrt{9\times 7}[/tex]

[tex]5\sqrt{4} \times \sqrt{7} + \sqrt{9}\times \sqrt{7}[/tex]

[tex]5\times 2 \times \sqrt{7} + 3\times \sqrt{7}[/tex]

[tex]10 \sqrt{7} + 3\sqrt{7}[/tex]

[tex](10 + 3)\sqrt{7}[/tex]

[tex]13\sqrt{7}[/tex]

Since, we do not need to find further square root of 7.

Thus, the required radical form of [tex]5\sqrt{28} + \sqrt{63}[/tex] is [tex]13\sqrt{7}[/tex].

Answer:

[tex]13\sqrt{7}[/tex]

Step-by-step explanation:

[tex]5\sqrt{28} +\sqrt{63}[/tex]

To simplify the given expression we simplify each radical

[tex]5\sqrt{28} = 5\sqrt{4*7} = 5*2\sqrt{7} =10\sqrt{7}[/tex]

[tex]\sqrt{63} = \sqrt{9*7} =3\sqrt{7}[/tex]

[tex]5\sqrt{28} +\sqrt{63}[/tex]

[tex]10\sqrt{7}+3\sqrt{7}[/tex]

[tex]13\sqrt{7}[/tex]

Martha earns $6.50 per hour, so for 1.5 hours, she will earn $9.75; for 2.5 hours, she will earn $16.25; and for 3.5 hours, she will earn $22.75. We simply multiply her hourly wage by the number of hours to find the total earnings for each duration.

If Martha earns $6.50 per hour for babysitting, we can find out how much she will earn for different numbers of hours by multiplying her hourly rate by the number of hours worked.

As a result:

Proportion is a mathematical concept that describes the relationship between two or more quantities. It is often represented using ratios and can be used to solve for unknown values, scale measurements, and interpret data.

Proportion is a mathematical concept that describes the relationship between two or more numbers or quantities. It is a way of expressing that one quantity is equal to another quantity, or that one quantity is a fraction or multiple of another quantity. Proportions can be represented using ratios, which compare the relative sizes of different quantities.

For example, if we have two ratios, such as 1:2 and 3:6, we can determine if they are proportional by cross-multiplying and checking if the products are equal. In this case, 1 × 6 = 2 × 3, so the ratios are proportional.

Proportions are used in many different areas of mathematics, such as solving for unknown values, scaling up or down, and interpreting data. They are also used in real-world applications, such as finding the missing side length of a similar triangle or calculating the unit price of a product.

The graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0)

The given function is f(x) = 4x² + 20x + 25

The table of values for the function from -1 to -4 is

x          -1     -2   -3    -4

f(x)       9      1   1      9

The graph of the function is attached below

From the graph, we can observe that the graph touches the x-axis at the point (-2.5, 0)

Hence, the graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0).

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Answer:

false

Step-by-step explanation:

<3

The correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.

Let's analyze each statement and determine which one is true:

A. "2/5 of the total tuba and trumpet players are tuba players."

To find out if this statement is true, we need to determine what portion of the total number of players are tuba players. Since the ratio of trumpet players to tuba players is 5:2, for every 5 + 2 = 7 players, 2 are tuba players. So, the proportion of tuba players is 2/7, not 2/5. Therefore, Statement A is false.

B. "The number of trumpet players is 2.5 times the number of tuba players."

According to the given ratio, for every 5 trumpet players, there are 2 tuba players. Thus, the number of trumpet players is indeed 2.5 times the number of tuba players. Therefore, Statement B is true.

C. "There are 2 trumpet players for every 5 tuba players."

This statement matches the given ratio, so it is true. However, it doesn't provide any additional information beyond what's already given in the initial problem.

D. "If there are a total of 100 trumpet and tuba players, 52 of them are tuba players."

To verify this statement, we can calculate the number of tuba players using the given ratio. Since the total ratio parts is 5 (trumpet) + 2 (tuba) = 7, and the total number of players is 100, we can find the number of tuba players as (2/7) * 100 = 28. Thus, Statement D is false.

Therefore, the correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.