Using elimination method (linear combination), what would the resulting equation be after adding both equations together?

[tex] \sqrt{ \frac{1 - cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{ \frac{ - \sqrt{ 3}}{2} }{2} } = \sqrt{ \frac{2}{4} + \frac{ \sqrt{3} }{4} } = \sqrt{ \frac{2 + \sqrt{3} }{4} } [/tex]

[tex]= \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]

BTW:

[tex]sin(75) = \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]

[tex] = > sin(75) = \sqrt{ \frac{1 - cos(150)}{2} } [/tex]

Ans: True

Ok done. Thank to me >:33

The graph of the quadratic function  [tex]y=-2x^2-4x+4[/tex] opens downward.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is [tex]y=-2x^2-4x+4[/tex]

The general form of the quadratic function is y=[tex]ax^2+bx+c[/tex]

Then, a= -2

Which is negative value.

Then the graph is open downward.

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The procedure for creating a pie chart based on a given set of data involves a number of steps such as.

The Steps to draw a pie chart for weather conditions in Kaduna:

1. Draw a circle to represent 24-hour period.

2. Divide circle into sections for sunshine, cloudiness, and darkness.

Lastly, Use the weather duration to find section size.

Thus, Label pie chart sections attached as "Sunshine", "Cloudiness", and "Darkness".

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See text below



b Discuss the performance with your teach During a 24-hour period in Kaduna, the sun shone for 10 hours, it was cloudy for 3 hours and it was dark for the remainder of the time. Draw a pie chart to show the periods of sunshi cloudiness and darkness during the day.

The test statistic based on the information is given by 2.19.

This evidence-based test has an available degree of freedom of 11 - being acquired by subtracting 1 from the overall 12. With 11 degrees of freedom in combination with a 0.05 margin of significance, an applicable t-distribution table states that the essential critical value is 1.796.

Seeing as our experimental statistic of 2.19 surpasses the critical value of 1.796, we must discount the null hypothesis. Consequently, sufficient proof signifies that the average math score population attains a higher mean than its writing counterpart when contemplating a 0.05 level of significance.

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The solution is, the percent increase in salary is: 90.9%

Here, we have,

given that,

Suppose a worker makes $22,000 in wages per year.

and, he/she trains to be a teacher and can expect to earn a salary of $42,000.

now, we have to find the percent increase in salary the worker can expect.

so, we have,

previous salary = $22,000

expected salary = $42,000.

so, increase = $ 20000

so, the percent increase in salary is:

20000/22000 * 100

=90.90

so, the percent increase in salary is: 90.9%

Hence, The solution is, the percent increase in salary is: 90.9%.

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The correct interpretation of the P-value in this context is: Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone. So, the correct answer is C).

In other words, the P-value is the probability of obtaining a sample proportion of 0.15 or less (which corresponds to 10 black cars out of 70 total) if the true proportion of black cars that receive moving violations is actually 0.19.

Since the P-value is relatively high (larger than the significance level of 0.05), we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that black cars are less likely to receive tickets for moving violations.

So, the correct answer is C).

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Answer:

Its line plot and box plot

Step-by-step explanation:

The value of total of the debit side of the unadjusted trial balance is,

⇒ $24,350

We have to given that;

Consider the following information from a company's unadjusted trial balance at December 31, 2020.

Hence, We get;

The computation of the total of debit side is shown below;

= Accounts Receivable + Cash +  Equipment + Insurance Expense + Land + Notes Receivable + Prepaid Insurance + Rent Expense + Salaries and Wages Expense

= 5100 + 680 + 1760 + 6280 + 4600 + 5500 + 430

= $24350

Thus, The value of total of the debit side of the unadjusted trial balance is,

⇒ $24,350

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The cost per kilogram of cheese is found by dividing the cost per pound by the conversion factor 0.45359237 kilograms per pound. The result is $9.68 per kilogram.

Start with the given cost of cheese per pound: $4.40.

To convert from pounds to kilograms, we need to divide by the conversion factor 2.2 (since 1 kilogram is approximately equal to 2.2 pounds). So, we have

1 pound / 2.2 = 0.45359237 kilograms / 1 pound

Note that we can write this as a conversion factor with the pound unit cancelling out, leaving us with kilograms as the desired unit.

Now, we can multiply the cost per pound by the conversion factor to get the cost per kilogram

Cost per kilogram = Cost per pound * (1 pound / 0.45359237 kilograms)

            = $4.40 * (1 / 0.45359237)            

Evaluating this expression using a calculator gives us

Cost per kilogram = $9.68

So the cost of cheese per kilogram is approximately $9.68.

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The account's effective annual yield if you invest $1800 and it pays 6.3% interest compounded daily, is calculated as: 6.53%.

In order to find the effective annual yield of an account, the formula to apply is expressed as:

Effective annual yield = (1 + r/n)^n - 1

where:

r represents the annual interest rate (as a decimal)

n represents the number of times the interest is compounded per year

In this case, we are given the following:

Annual interest rate = 6.3% = 0.063

The interest is compounded daily, so n = 365 (days in a year)

Plugging in the variables we have:

Effective annual yield = (1 + 0.063/365)^365 - 1

Effective annual yield = 0.0653 or 6.53%

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1.) m<A = 51°

AB = 17.5

BC = 13.6

To calculate the missing part of the triangle, m <A ;

The sum of the interior triangle = 180°

That is , 180° = 90°+ 39° + m

make m the subject of formula;

m = 180 - 129

m <A = 51°

Using the formula from SOHCAHTOA;

Sin 39° = 11/AB

make AB the subject of formula;

AB = 11/0.629320391

= 17.5

Using the Pythagorean formula;

C² = a² + b²

C² = 17.5

a² = 11

b² = BC = ?

17.5² = 11² + b²

make b² the subject of formula;

b² = 17.5²-11²

b² = 306.25 - 121

b² = 185.25

b = √185.25

b = 13.60

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The most common amount of sleep: is 8 hours (6 individuals).

Outlier: Frankie (slept for 6 hours), as there is a significant difference between his sleep time and the rest of the individuals in the dataset (range of 4 hours).

The predominant resting time among the subjects is 8 hours.

Nonetheless, it's worth noting that an outlier exists within the dataset; Frankie spent a mere 6 hours sleeping - which amounts to two hours less than the sleep duration recorded by the second least rested individual (8 hours).

This information can be extracted from analyzing the figures and noticing the conspicuous discrepancy between Frankie's slumbering span and that of the other participants in the pool of data and this is the outlier.

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Answer:

Formula for finding the surface area of a cone is shown below

[tex]\pi \: r {}^{2} + \pi \: rl \\ or \\ \pi(r + l)r[/tex]

The formula for finding the surface area of a cone is:

Surface area = πr² + πrl

Where:

The number line where we plotting -2 1/6 and 11/6 is attached

From the question, we have the following parameters that can be used in our computation:

-2 1/6 and 11/6

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-13/6 and 11/6

This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6

Using the above as a guide, we have the following:

The number line is attached

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The exponential growth functions are,

[tex]y=\frac{9}{11}(4)^t[/tex]

[tex]V=0.8(9)^t[/tex]

[tex]P=0.9(8.3)^t[/tex]

[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]

The exponential decay functions are,

[tex]A= (0.97)^t[/tex]

[tex]y= 3.7 (0.2)^t[/tex]

The function which is neither exponential growth nor exponential decay is,

g(x)=2.1(x).

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

If the base is larger than 1, it will be an exponential growth.

For example, [tex]3^2=9[/tex]

If the base is smaller than 1, it will be an exponential decay.

For example, [tex]0.5^2=0.25[/tex]

If the function does not have an exponent, that means there will be no exponential growth or decay.

Therefore the exponential growth functions are,

[tex]y=\frac{9}{11}(4)^t[/tex]

[tex]V=0.8(9)^t[/tex]

[tex]P=0.9(8.3)^t[/tex]

[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]

The exponential decay functions are,

[tex]A= (0.97)^t[/tex]

[tex]y= 3.7 (0.2)^t[/tex]

The function which is neither exponential growth nor exponential decay is,

g(x)=2.1(x).

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The domain and range of the function are C. Domain: x≥0, Range: y≥0

The domain of the function is the set of all possible input values (x) for which the function is defined.

In this case, the function y = 3√x is defined for non-negative real numbers, because the root of a negative number is not a real number.

Therefore, the domain of the function is:

Domain: {x | x ≥ 0}

The range of the function is the set of all possible output values (y) that the function can take.

Since the root of any positive number is also positive, the function y = 3√x will always return a positive number for any positive input value.

Therefore, the range of the function is:

Range: {y | y ≥ 0} or [0, ∞) in interval notation.

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The equation of line perpendicular to the tangent is found to be -

y = -2x + 7.

The equation for a line should be written in the slope-intercept form so that the y-intercept (where its line crosses a vertical y-axis) and slope (steepness) are immediately visible. The y = mx + b form is a common name for this form.

Given condition of digression line:

Comparing with the standard form: y = 1/2 x + 7 y = mx + c

m is the slant and c is the y block:

m = 1/2

Let the incline of the line opposite to the digression be M.

Then, at that point, connection between the inclines of opposite lines:

m. M = -1 equation of line perpendicular to the tangent.

y - 3 = M(x - 2)

y - 3 = -2(x - 2)

y = -2x + 4 + 3

y = -2x + 7

Thus, the equation of line perpendicular to the tangent is found to be -

y = -2x + 7.

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The circle has the centre at (2,3). The equation of the tangent of the line on the circle : y = 1/2 x + 7. What is equation of line perpendicular to the tangent.

Answer:

---------------------

WX and YX are tangents drawn from point X to circle Z.

Tangent segments drawn to the same circle from the same point  are equal:

Substitute values for side lengths and solve for x:

Substitute 9 for x and find the length of tangent WX:

Answer:

Below.

Step-by-step explanation:

Exponential growth equation is

Nt = No e^kt                 where No  is initial quantity , Nt is quantity after                       time t and k is some constant.

Here we have:

1838 = 1600 e^4k

e^4k = 1838/1600 = 1.14875

4k = ln 1.14875 = 0.138674

k = 0.034669

Answer:

All of the answers appear to be correct based on the given formulas and values.

Answer:

8). YZ

9). 30°

10). XY

11). 90°

12). XY=10 and XZ=5√3

13). XY=12 and XZ=6√3

14). YZ=4 and XZ=4√3

15). YZ=3 and XZ=3√3

The length of the two unknown sides of the triangle are: 12√2

There are different methods of finding the missing sides of triangles such as:

Pythagoras Theorem

Law of sines or sine rule

Law of cosines or cosine rule

Now, we are given an Isosceles triangle with a base length and two equal base angles.

Thus, the two unknown sides will have equal side lengths.

∠D = 90°

Thus, using sine rule:

12/sin 90 = QR/sin 45

QR = 12 * 1/√2

Rationalizing the denominator gives:

QR = 12√2

Since the two unknown sides of the triangle are equal, then we say that:

PQ = 12√2

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Answer:

Step-by-step explanation:

a. The number of red roses left t hours before the store opens can be represented by the formula:

N(t) = 400 * (1/2)^(t/2)

Here, we're dividing the number of available roses by 2 every 2 hours, so the exponent t/2 represents the number of 2-hour intervals that have passed since the store opened.

b. The number of box chocolates left t hours after the store opens can be represented by the formula:

M(t) = 200 * (0.85)^t

Here, we're multiplying the number of available boxes by 0.85 every hour, so the exponent t represents the number of hours that have passed since the store opened.

c. We need to find the time t when the number of roses is equal to the number of boxes of chocolates:

400 * (1/2)^(t/2) = 200 * (0.85)^t

Dividing both sides by 200:

2 * (1/2)^(t/2) = 0.85^t

Taking the logarithm of both sides:

log(2) - (t/2) * log(2) = t * log(0.85)

Simplifying:

t * (log(0.85) + (log(2)/2)) = log(2)

t = log(2) / (log(0.85) + (log(2)/2))

Using a calculator, we get:

t ≈ 11.9 hours

Therefore, the number of roses will be equal to the number of boxes of chocolates approximately 11.9 hours before the store opens, or around 9 p.m. on the day before Valentine's Day.

d. To find the number of boxes of chocolate left at 12:30 p.m. (3.5 hours after the store opens), we can use the formula:

M(3.5) = 200 * (0.85)^3.5

M(3.5) ≈ 97.4

Therefore, there are approximately 97 boxes of chocolate left at 12:30 p.m.

e. To buy 36 red roses, we need to find the latest time we can arrive before the store runs out of roses. We can set N(t) equal to 36 and solve for t:

400 * (1/2)^(t/2) = 36

Dividing both sides by 400:

(1/2)^(t/2) = 0.09

Taking the logarithm of both sides:

t/2 * log(1/2) = log(0.09)

Simplifying:

t ≈ 5.2 hours

Therefore, the latest time we can arrive to successfully buy 36 red roses is approximately 5.2 hours before the store opens, or around 3:50 a.m. on the day before Valentine's Day.

The missing sides of the triangle have been identified here.

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.

1) Sin x = 5/14

x = Sin-1 (5/14)

x = 21°

2) Tan x = 8/5

x = Tan-1 (8/5)

x = 58°

3) Cos x = 9/13

x = Cos-1 (9/13)

x = 46°

4) Cos x = 3/5.8

x = Cos-(3/5.8)

x = 59°

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The missing sides of the triangle have been identified here.

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.

1) Sin x = 5/14

x = Sin-1 (5/14)

x = 21°

2) Tan x = 8/5

x = Tan-1 (8/5)

x = 58°

3) Cos x = 9/13

x = Cos-1 (9/13)

x = 46°

4) Cos x = 3/5.8

x = Cos-(3/5.8)

x = 59°

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Answer:

6 and -6

Step-by-step explanation:

M^2-6m+6m-36

m^2-36

(m-6)(m+6)

Answer:

The probability of both children being boys in a family with 2 children is  

3

1

​

.

There are 3 possible outcomes for the gender of each child: boy, girl, or unknown. There are 2 children, so there are 3

2

=9 possible combinations of genders for the 2 children.

Of these 9 combinations, 3 of them have both children being boys: BB, BG, and GB. So the probability of both children being boys is  

9

3

​

=

3

1

​

.

However, this is only the probability if we don't know the gender of the first child. If we know that the first child is a boy, then the probability of both children being boys is  

2

1

​

. This is because there are only 2 possible outcomes for the gender of the second child: boy or girl. If the first child is a boy, then the second child must be a boy in order for both children to be boys. So the probability is  

2

1

​

.

Step-by-step explanation:

Let's use the following notation for the children:

B: Boy G: Girl

There are 4 possible combinations for a family with 2 children:

1. BB (Both children are boys)

2. BG (First child is a boy, second child is a girl)

3. GB (First child is a girl, second child is a boy)

4. GG (Both children are girls)

Since we know that at least one child is a boy, we can eliminate the 4th combination (GG) as it doesn't meet the condition. Now we have 3 possible combinations left:

1. BB

2. BG

3. GB

Now, to find the probability that both children are boys (BB) from the remaining combinations, we can calculate it as follows:

Probability = (Number of favorable outcomes) / (Total possible outcomes)

Probability = 1 (BB) / 3 (BB, BG, GB)

Probability = 1/3

So, the probability that both children are boys is 1/3.

Answer: [tex]b=\sqrt{45}[/tex] or b=6.71 in.

Step-by-step explanation:

Use Pythagorean Theorem

[tex]a^2+b^2=c^2[/tex]

In this case, a=2in and c=7in, and we're solving for b.

[tex](2)^2+b^2= (7)^2\\4+b^2= 49\\b^2=45\\b=\sqrt{45}[/tex]

Therefore, b=6.71 in.

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

We have,

Assuming a standard atmospheric pressure of 101.3 kPa.

Maximum pressure differential in a stairwell:

Since each stairwell is no more than 20 stories high and each story is approximately 3 m high, the maximum height difference between two floors in a stairwell is:

= 20 x 3

= 60 m

Using the formula for hydrostatic pressure, the maximum pressure differential in a stairwell is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(60 m)

= 58,860 Pa

The atmospheric pressure difference between the top of the building and street level:

The atmospheric pressure decreases with increasing altitude.

Using the formula for hydrostatic pressure, the pressure difference between the top of the building and the street level is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(300 m)

= 2,943,000 Pa

The difference in static water pressure between consecutive floors:

Assuming a standard density of water of 1000 kg/m³, the difference in static water pressure between consecutive floors is:

ΔP = ρgh = (1000 kg/m³)(9.81 m/s²)(3 m) = 29,430 Pa

Therefore,

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

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Step-by-step explanation:

Arrange this equation into   y = mx + b form.....m is the slope

9x+3y =11

3y = -9x + 11

y = -9/3 x + 11/3

y = -3 x + 11/3        m = slope = - 3