Which formula represents Charles's law? ?

Answer:

\(A = 43.0^o\)

\(B = 55.0^o\)

\(BC = 20.0\)

Step-by-step explanation:

I will solve this question with the attached triangle

From the attachment, we have:

\(\angle C =82^o\)

\(AB = 29\)

\(AC = 24\)

Required

Solve the triangle

First, we calculate \(\angle B\) using sine law:

\(\frac{AC}{\sin(B)} = \frac{AB}{\sin(C)}\)

This gives:

\(\frac{24}{\sin(B)} = \frac{29}{\sin(82^o)}\)

\(\frac{24}{\sin(B)} = \frac{29}{0.9903}\)

Cross multiply

\(\sin(B) * 29 = 24 * 0.9903\)

\(\sin(B) * 29 = 23.7672\)

Divide both sides by 29

\(\sin(B) = 0.8196\)

Take arcsin of both sides

\(B = \sin^{-1}(0.8196)\)

\(B = 55.0^o\)

Next, calculate \(\angle A\) using:

\(A + B + C = 180^o\) --- angles in a triangle

\(A + 55^o + 82^o = 180^o\)

Collect like terms

\(A = 180^o-55.0^o - 82^o\)

\(A = 43.0^o\)

Next, calculate BC using sine laws

\(\frac{BC}{\sin(A)} = \frac{AB}{\sin(C)}\)

This gives:

\(\frac{BC}{\sin(43.0)} = \frac{29}{\sin(82)}\)

\(\frac{BC}{0.6820} = \frac{29}{0.9903}\)

Make BC the subject

\(BC = \frac{29*0.6820}{0.9903}\)

\(BC = 20.0\)

Step-by-step explanation:

Number of children= 12481-3575=3575

Fraction of girls present= 1-⅗=⅖

Number of girls present= 3575×⅖=1430

Answer:

what?

Step-by-step explanation:

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The required answer is  sec θ = -√2.

Explanation:-

Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).

To determine three possible angles θ,  the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore  conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.

Therefore, sec θ = 1/cos θ.To find cos 11π/4,  the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.

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The top of the ladder sliding down the vertical wall with  -0.75 feet/s  when the bottom of the ladder is 6 feet from the vertical wall using pythagoras theorem and then differentiate the equation.

Given that the ladder is 10 feet long.

To calculate

velocity with which top of the ladder sliding.

given

x= -6 feet

y = 8 feet

By pythagoras  theorem  

   \(x^{2} +y^{2}\) = \(10^{2}\)

differentiate the given equation with respect to t

   2 x \(\frac{dx}{dt} +\) 2 y \(\frac{dy}{dt}\)  = 0

    x * \(\frac{dx}{dt}\)  = - y * \(\frac{dy}{dt}\)

   \(\frac{dy}{dt}\)=   \(\frac {\frac{-x dx}{dt}}{y}\)

   \(\frac{dx}{dt}\) = \(V_{x}\)    ,  \(\frac{dy}{dt}\) =\(V_{y}\)

\(V_{y}\) =-((-6)/8) *(1 feet)

\(V_{y}\) = -0.75 feet/s

so, the velocity at which the top of the ladder sliding down the vertical wall when the bottom of the ladder is 6 feet is -0.75 feet/s .

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Answer:

Your answer would be 30% discount

Step-by-step explanation:

137.40 / 458 = .3

Answer:

-68

Step-by-step explanation:

X/17=-4

X=-68

So the answer is -68

The cat population in Catonsville in 2007 was 200. The answer is option B.

Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.

We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.

From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:

\(p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200\)

Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.

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Answer:

1035

Step-by-step explanation:

(2.3 × 10^4)(4.5 × 10^6)

First we do the exponents:

10^-4 = 0.0001

10^6 = 1,000,000(1 mil)

Now we plug them into the equation:

(2.3 × 0.0001)(4.5 × 1,000,000)

Now we multiply the numbers in the paranthesis:

(0.00023)(4,500,000) = 0.00023 × 4,500,000

Now we multiply both of them:

0.00023 × 4,500,000 = 1035

Answer:

Angle 1 and angle 2

x=9

Step-by-step explanation:

The angle pair is complementary since it makes a right angle, so you could technically name it anything like angle 1 and angle 2. You make the equation 4x+8+5x+1=90. Then, you combine like terms and get 9x+9=90. Then, subtract the 9 from 90, 81. 9x=81. Then, divide the 9 from 81. X=9.

F(11) means to replace x in the equation with 11

12(11) + 5

12 x 11 = 132

Now you have 132 + 5 = 137

F(11) = 137

Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.

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Complete question:

A combination of values that, when arranged correctly, result in a final value. true/false

If x =1 and y =3

= 2(1) × 3(3)

= 2×9

= 18

Answer:

(3,1)

Step-by-step explanation:

work is in picture

Answer:

I think its some sort of learning platform. Search it up.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A product means we are multiplying. we are multiplying 0.34 and 0.02 which is 0.68

Answer:

To work out the charges for the job, we first need to calculate how many hours Pierre worked on the job.

She started at 9:30 am and finished at 1:00 pm, which means she worked for:

1:00 pm - 9:30 am = 3.5 hours

Now, we can use the formula C=20+30t, where t is the number of hours worked (in this case, 3.5) to calculate the charges for the job:

C = 20 + 30(3.5)

C = 20 + 105

C = 125

Therefore, Pierre should charge $125 for the job.

Answer:

The slope of this line equals 2.

Hope this helps :)

Step-by-step explanation:

a) When Lily's age is 20, and Raphael's age is divided by 3 then the expression of Lily's age in terms of h is h < 10.

b) Ethan's age is half of Raphael's age therefore, Ethan's age is half Raphael's age.

a) If Raphael is twice as old as his sister Lily, we can represent their ages as 2h and h, respectively, where h is Lily's age. The sum of their ages is less than 30, so we can write the equation:

2h + h < 30

Combining like terms, we get:

3h < 30

Dividing both sides by 3, we get:

h < 10

This is an expression of Lily's age in terms of h.

b) If Ethan's age is 16, and Raphael's age is twice Ethan's age, we can represent Raphael's age as 2 × 16 = 32.

Ethan's age is 16, which is half of Raphael's age of 32. Therefore, Ethan's age is half of Raphael's age.

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The question is -

Raphael is twice as old as his sister. The sum of their ages is less than 30.

a) Lily's age is 20, and Raphael's age is divided by 3. Write an expression in terms of h for Lily's age.

b) An expression for Ethan's age 16. Write a sentence to describe how Ethan's age compares with Raphael's age.

The equivalent ratios are: (1, 2), (2, 4), and (3, 6)

The graph can be plotted on a coordinate grid as shown in the diagram attached below.

Recall:

Let x = number of books

y = cost (dollars)

Using any of the ordered pairs from the table, say, (7, 14), find k:

k = y/x = 14/7 = 2

Write the equation by plugging in the value of k into y = kx

y = 2x

Using the equation, y = 2x, find the equivalent ratios when x = 1, x = 2, and x = 3:

When x = 1:

y = 2(1) = 2 --> (1, 2)

When x = 2:

y = 2(2) = 4 ---> (2, 4)

When x = 3:

y = 2(3) = 6 ---> (3, 6)

The graph for the three equivalent ratios, (1, 2), (2, 4), and (3, 6) can be plotted on a coordinate grid as shown in the diagram attached below.

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Answer:

Step-by-step explanation:

If x=10 and y=20 solve:

"x/y"

A.1/2

B.1

C.2

D.4

x/y =

10/20

1/2  is your answer

If the three numbers of a square in the complex plane are \(-19+32i,-5+12i and -22+15i\) , then the fourth complex number \(-2+19i\).

Given \(-19+32i,-5+12i and -22+15i\) are three numbers.

Complex numbers are those numbers which extends the real numbers with an imaginary i. In this \(i^{2}=-1\). Major complex numbers are in the form a+ bi where a and b are real numbers.

let the fourth complex numbers be \(x+yi\). Then according to question;

=\((-22+15i)-(-5+12i)\)

=(cos π/2+i sin π/2) \((x+yi)-(-5+12i)\)

\(-17+3i=-y+12\)\(+(x+5)i\)

Now solving for x and y by equating both sides.

x=-2 and y=29

Put the value of x and y in \(x+yi\)

Z=-2+29i

Hence if the three numbers which forms vertices of a square are \(-19+32i,-5+12i,-22+25i\) then the fourth complex numbers be \(-2+29i\).

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Answer:

83 m

Step-by-step explanation:

23.6 x 3.5 = 82.6 ≈ 83 m

If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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Answer:

\(a=3, b=2\)

Step-by-step explanation:

Using the remainder theorem,

\(b^2-ab+3=1 \implies b^2-ab+2=0 \\ \\ 2a-b=4 \implies b=2a-4 \\ \\ \therefore (2a-4)^2-a(2a-4)+2=0 \\ \\ 4a^2+16-16a-2a^2+4a+2=0 \\ \\ 2a^2 - 12a+18=0 \\ \\ a^2-6a+9=0 \\ \\ (a-3)^2=0 \\ \\ a=3 \\ \\ \therefore 2(3)-b=4 \implies b=2\)

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Choco Lovers will face a loss of 5.625 per gift box.

Choco Lovers will face a loss of 18 per gift box.

Gift boxes = (Fixed Cost + Profit) / Profit per unit

11 = (30,000 + Profit) / 8

Profit = 8 × Gift boxes – 30,000

Profit = 8G – 30,000

Here, Profit per unit = 8

Fixed Cost = 30,000

By substituting the values in the formula, we get:

8G – 30,000 = Profit

G = (30,000 + Profit) / 8 At 11 per gift box, Choco Lovers should produce 4375 boxes of chocolate.

per gift box Profit per unit = Selling price per unit – Variable cost per unit

Selling price per unit = 11

Variable cost per unit = 8

Profit per unit = 11 – 8 = 3

Profit/Loss per box = 3 × 4375 – 30,000

Profit/Loss per box = -5625

Suppose that Choco Lovers raises the price to 13 per gift box.

Now,

Gift boxes = (Fixed Cost + Profit) / Profit per unit

13 = (30,000 + Profit) / 10

Profit = 10 × Gift boxes – 30,000

Profit = 10G – 30,000

Here, Profit per unit = 10

Fixed Cost = 30,000

By substituting the values in the formula, we get:

10G – 30,000 = Profit

G = (30,000 + Profit) / 10

At 13 per gift box, Choco Lovers should produce 4000 boxes of chocolate.

Profit per unit = Selling price per unit – Variable cost per unit

Selling price per unit = 13

Variable cost per unit = 10

Profit per unit = 13 – 10 = 3

Profit/Loss per box = 3 × 4000 – 30,000

Profit/Loss per box = -18000

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