What is the exact value of sin(cos^-1 (√2/2)) + tan^-1 (sin(π/2))

What Is The Exact Value Of Sin(cos^-1 (2/2)) + Tan^-1 (sin(/2))

Answers

Answer 1

[tex]\qquad \qquad \textit{Inverse Trigonometric Identities} \\\\ \begin{array}{cccl} Function&Domain&Range\\[-0.5em] \hrulefill&\hrulefill&\hrulefill\\ y=cos^{-1}(\theta)&-1 ~\le~ \theta ~\le~ 1& 0 ~\le~ y ~\le~ \pi \\\\ y=tan^{-1}(\theta)&-\infty ~\le~ \theta ~\le~ +\infty &-\frac{\pi}{2} ~\le~ y ~\le~ \frac{\pi}{2} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \theta \hspace{5em}\stackrel{\textit{so we can say}}{cos(\theta )=-\cfrac{\sqrt{2}}{2}} \\\\\\ \theta =cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \stackrel{ \textit{on the II Quadrant} }{\theta =\cfrac{3\pi }{4}} \\\\[-0.35em] ~\dotfill\\\\ sin\left[ cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right) \right]\implies sin\left( \cfrac{3\pi }{4} \right)\implies \boxed{\cfrac{\sqrt{2}}{2}}[/tex]

now let's find the angle for the inverse tangent

[tex]sin\left( \cfrac{\pi }{2} \right)\implies 1\hspace{5em}\stackrel{\textit{so we can say}}{tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]}\implies tan^{-1}(1) \stackrel{ \textit{on the I Quadrant} }{\implies\boxed{\cfrac{\pi }{4}}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left[ cos^{-1}\left( -\frac{\sqrt{2}}{2} \right) \right]~~ + ~~tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]\implies \cfrac{\sqrt{2}}{2}~~ + ~~\cfrac{\pi }{4} \implies \boxed{\cfrac{2\sqrt{2}+\pi }{4}}[/tex]

for the sine function we end up in the II Quadrant because the inverse cosine function range is constrained to the I and II Quadrants only, so our angle comes from that range.

Likewise, our angle from the inverse tangent comes from the I Quadrant, because inverse tangent range is only I and IV Quadrants.


Related Questions

Right triangle STD has a longer leg measuring exactly 3√5 cm. The altitude from right angle T to hypotenuse
SD cuts the hypotenuse into two segments where the shorter part is 1 less than the longer part. Find the exact
length of each part of the hypotenuse, SU and UD, the exact length of altitude TU and the exact length of ST.

Answers

Answer:

Let's call the length of the hypotenuse SD as x.

Since the altitude from T to SD divides SD into two parts, let the length of the shorter part be y. Then the length of the longer part is x-y.

Using similar triangles, we have:

TU/TS = ST/TD

Substituting the values we have:

TU/(3√5) = √5/UD

TU = (3/5)UD

Using the Pythagorean theorem in triangle TUS, we have:

TU² + (3√5)² = TS²

(3/5 UD)² + 45 = ST²

9/25 UD² + 45 = ST²

Using the Pythagorean theorem in triangle TUD, we have:

TU² + UD² = TD²

(3/5 UD)² + UD² = x²

9/25 UD² + UD² = x²

34/25 UD² = x²

UD² = (25/34)x²

Substituting the value of UD² in the equation ST² = 9/25 UD² + 45, we get:

ST² = 9/25 (25/34)x² + 45

ST² = 45/34 x² + 45

Since y = x-y-1, we have y = (x-1)/2.

Using the Pythagorean theorem in triangle TUD, we have:

(1/4) (x-1)² + UD² = x²

(1/4) (x² - 2x + 1) + (25/34)x² = x²

(1/4)(x²) + (25/34)x² - (1/2)x + (1/4) = 0

(59/68)x² - (1/2)x + (1/4) = 0

Using the quadratic formula, we get:

x = [1/2 ± √(1/4 - 4(59/68)(1/4))]/(2(59/68))

x = [1/2 ± (3√34)/17]/(59/34)

x = 17/59 ± 6√34/59

Since x is the hypotenuse SD, we have:

UD² = (25/34) x²

UD² = (25/34) [(17/59 ± 6√34/59)²]

UD² = 136/59 ± 204√34/295

Therefore, the exact lengths of the two parts of the hypotenuse are:

SD = x = 17/59 ± 6√34/59

SU = x-y = (x-1)/2 = 8/59 ± 3√34/59

UD = y = (x-1)/2 = 8/59 ± 3√34/59

TU = (3/5) UD = (3/5) [8/59 ± 3√34/59] = 24/295 ± 9√34/295

ST² = 45/34 x² + 45 = 45/34 [(17/59 ± 6√34/59)²] + 45

ST = √[45/34 [(17/59 ± 6√34/59)²] + 45]

if 80% of all marketing personnel are extroverted, then what is the probability that 10 or more are extroverts at a party of 15 marketing personnel

Answers

The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.

Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:

P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]

P(X>=10) = 0.719

Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.

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- The Graduates Choice designs and sells two types of class rings, the GPA and the MVP. They
can produce up to 24 rings per day using at most 60 total hours of labor. It takes 3 hours to
make one GPA ring and 2 hours to make one MVP ring. How many of each ring type should be
made daily in order to maximize the company's profit if the profit on the GPA ring is $40 and
the profit on the MVP ring is $35?

Answers

The 12 of each type of the ring would give max profit for the company.

How many of each type should be made daily to maximize the company's profit?

Let x = number of VIP rings: let y = number of SST rings

:

The total production inequality;

x + y =< 24

y = 24 - x; arranged to plot graph (purple)

:

The labor inequality;

3x + 2y =< 60

2y = 60 - 3x

y = 60/2 - (3/2)x

y = 30 - 1.5x; arranged to plot the graph (red).

From the graph, the 3 corners of the area of feasibility (at or below the lines whichever is lower):

: x/y;.....profit on each type;... total profit

0,24; 40(0) + 35(24) = 0 + 840 = $840

12,12; 40(12) + 35(12) = 480 + 420 = $900

20,0; 40(20) + 35(0) = 800 + 35(0) = $800.

Therefore, the 12 of each type of the ring would give max profit for the company.

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a professor at a local university noted that the exam grades of her students were normally distributed with a mean of 68 and a standard deviation of 17. according to the professor's grading scheme only the top 12.3 percent of her students receive grades of a. what is the minimum score needed to receive a grade of a? write your answer to two decimal points.

Answers

A minimum score of 88.95 is required to receive an "A" grade on the exam.

To determine the minimum score required to receive an "A" grade on an exam, we must first understand the meaning of standard deviation and mean. The mean is the average of a set of values, whereas the standard deviation is a measure of how far apart the values are from the mean. The minimum score required to receive an "A" grade is determined by calculating the z-score that corresponds to the top 12.3 percent of exam scores.

The formula for calculating the z-score is given as: z = (x - μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. Solving for z, we have: z = invNorm(1 - 0.123) = invNorm(0.877) ≈ 1.15. The inverse normal distribution function is used to determine the value of z that corresponds to the area to the right of the z-score. We can then use the formula for the z-score to solve for the raw score (x):
x = zσ + μ
Substituting the values we have, we get:
x = 1.15(17) + 68 ≈ 88.95
Therefore, a minimum score of 88.95 is required to receive an "A" grade in the exam.

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Solve for x.

2x^2-28x+98=0

X=

11 POINT’S

Answers

First take out the highest common factor 2 form the quadratic equation and divide each and every term of that equation by that common factor.

⇒Factorise the equation and equate the factors of the equation to 0 and solve for the unknown variable x.

⇒Below are the steps on solving for the unknown variable.

[tex]2(x^{2} -14x+49)=0 \\\frac{2(x^{2} -14x+49)}{2} =\frac{0}{2} \\x^{2} -14x+49=0\\(x-7)(x-7)=0\\x-7=0\\x=7[/tex]

a 86-ft tree casts a shadow that is 110 ft long. what is the angle of elevation of the sun? round the answer to two decimal places

Answers

The angle of elevation of the sun is 38.24 degrees (rounded to two decimal places).

The ratio of the height of the tree and the length of the shadow can be found by using the formula for tan which is given by:

tan(x) = (opposite/hypotenuse)

In the given problem statement, the height of the tree is opposite to the angle we are trying to find and the length of the shadow is the hypotenuse of the right-angled triangle. Therefore, we can say that:

tan(x) = opposite/hypotenuse = 86/110

We can use the inverse tangent function to find the value of x. This is because tan is the ratio of the opposite side (height of the tree) to the adjacent side (length of the shadow), and the inverse tangent function gives the angle that has that ratio.

So, tan x = 86/110 => x = tan⁻¹ (86/110) = 38.24 degrees (rounded to two decimal places). Therefore, the angle of elevation of the sun is 38.24 degrees.

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Answer options
2 units
4 units
6 units
10 units

Answers

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

what is triangle ?

Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.

given

The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.

To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.

As a result, we have:

sin 30° = (6/2x)

Adding two times to both sides:

2x * sin 30° = 6

Using sin 30°, which has a value of 0.5:

x = (6/(2 * 0.5)) = 6/1 = 6

Consequently, the side YZ is 6 units long.

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

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Gerald had some green and yellow beads. The number of green beads was 1/3 the number of yellow beads. He gave each of his friends 2 green beads and 3 yellow beads. He then had 42 green beads and 270 yellow beads left.
a. How many friends did he give the beads to?
b. What was the total number of beads he had at first?

Answers

Answer:

Step-by-step explanation:

Let's use algebra to solve this problem.

Let's start by assigning variables to the unknown quantities. Let G be the initial number of green beads and Y be the initial number of yellow beads.

We know that the number of green beads is 1/3 the number of yellow beads:

G = (1/3)Y

After giving away some beads, he had 42 green beads and 270 yellow beads left. So we can set up two equations using this information:

G - 2f = 42

Y - 3f = 270

where f is the number of friends he gave the beads to.

Now we can substitute G = (1/3)Y into the first equation:

(1/3)Y - 2f = 42

Multiplying both sides by 3, we get:

Y - 6f = 126

Now we have two equations that we can solve simultaneously:

Y - 3f = 270

Y - 6f = 126

Subtracting the first equation from the second, we get:

3f = 144

So f = 48. He gave the beads to 48 friends.

To find the total number of beads he had at first, we can use the equation G = (1/3)Y:

G + Y = (4/3)Y = (4/3)(270) = 360

So he had a total of 360 beads at first.

if the five teachers have an average salary of $49,000, should we be concerned that the sample does not accurately reflect the population?

Answers

As a result, we should not be concerned that the sample does not accurately reflect the population.

We can learn more about average, population, and sample.

What is the population?

The entire group of people, items, or objects that we want to draw a conclusion about is known as the population. For example, if we want to learn about the average age of people in the United States, then the entire population is every individual in the United States.

What is a sample?

A smaller group of individuals, objects, or items that are selected from the population is known as a sample. A random sample is a sample in which every individual in the population has an equal chance of being selected for the sample.

What is an average?

A statistic that summarizes the central tendency of a group of numbers is known as an average.

The mean is the most commonly used average in statistics. The mean is calculated by adding up all the numbers in a group and then dividing by the number of numbers in the group. If we want to learn about the average salary of all teachers in the United States, we'd have to sample every teacher. That's not a feasible option. Instead, we take a smaller sample, which should be representative of the population, and then use the information gathered from that sample to make predictions about the population as a whole.

If we assume that the five teachers in the example are a random sample of all teachers in the United States, then we can conclude that the average salary of all teachers in the United States is around $49,000. As a result, we should not be concerned that the sample does not accurately reflect the population.

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What is the value of x given the following image?

Answers

The value of x given the following image is 13.

What is congruent angle?

When two angles have the same magnitude, they are considered congruent. In other words, they have the same angle degree. For example, if one angle measures 45 degrees, any other angle that also measures 45 degrees is congruent to it.

Congruent angles are denoted by the symbol ≅. So, if angle A and angle B have the same measure, we can write it as:

Angle A ≅ Angle B

Congruent angles have the same properties and characteristics, including being able to fit into the same spaces and be formed by the same geometric shapes. In practical terms, congruent angles are identical when placed side by side.

Finding the value of x :

Angle ABC and Angle EBD are congruent.

Value of Angle ABC is (-3x+14) degrees.

Value of Angle EBD is (-x-12) degrees.

Equating the two angles we get ,

[tex]-3x+14=-x-12[/tex]

[tex]-2x=-26[/tex]

[tex]2x=26[/tex]

[tex]x=13[/tex]

Therefore, the value of x given the following image is 13.

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8x + 4 + 8x - 1 simplify the variable expression

I do not understand this
Pls help!

Answers

Answer:

16x + 3

Step-by-step explanation:

Simplify by combining like terms.  Add the terms with x, then add the integers.

8x + 8x + 4 - 1 = 16x + 3

A math class is set up to have assignments worth 45%, quizzes worth 40% and the final exam is worth the rest of the grade. If Serena has 78% on assignments and 65% on quizzes and 96% on the final, what is her overall grade to 2 decimal places?

Answers

Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade.

To calculate Serena's overall grade, we need to first determine the weight of the final exam. We know that the assignments are worth 45% and the quizzes are worth 40%, which leaves 100% - 45% - 40% = 15% for the final exam.

Next, we can calculate Serena's grade for each component of the course. Her grade for assignments is 78% and her grade for quizzes is 65%. We can calculate her grade for the final exam by multiplying her score of 96% by the weight of the final, which is 15%:

Final grade = (0.45 * 78%) + (0.4 * 65%) + (0.15 * 96%)

Final grade = 35.1% + 26% + 14.4%

Final grade = 75.5%

Therefore, Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade. In this case, Serena's strong performance on the final exam helped to boost her overall grade, even though her scores on the assignments and quizzes were not as high. It's also worth noting that this calculation assumes that all assignments, quizzes, and the final exam were weighted equally within their respective categories (i.e., each assignment was worth the same percentage of the assignment grade).

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PLSSSS HELP IF YOU TURLY KNOW THISS

Answers

Given:-

[tex] \tt \: x - 5 = 2[/tex]

[tex] \: [/tex]

Solution:-

[tex] \tt \: x - 5 = 2[/tex]

[tex] \: [/tex]

[tex] \tt \: x = 2 + 5[/tex]

[tex] \: [/tex]

[tex] \boxed{ \tt{ \blue{ \: \: x = 7 \: \: }}}[/tex]

[tex] \: [/tex]

The value of x is 7 !

__________________

hope it helps ⸙

what happens to the sector area of a circle if you double its radius? what happens to the arc length of a circle if you double its radius? why do you think that happens?

Answers

The sector area of a circle is quadrupled when the radius is doubled. When the radius is doubled, the arc length of a circle is also doubled. This happens because the sector area and arc length are both dependent on the radius of a circle. Therefore, any change in the radius of a circle affects both its sector area and arc length.

Let us understand both these concepts in detail:

Sector area of a circle: A sector is a region of a circle, and the area enclosed by two radii and an arc is known as a sector area. The formula for the sector area of a circle is given by:

Sector Area = (θ/360)πr²

where θ is the central angle in degrees,

r is the radius of the circle,

and is a constant value.

If we double the radius of a circle, the sector area increases by a factor of 4. This is because the sector area is directly proportional to the square of the radius.

Hence, doubling the radius of a circle results in an increase in the sector area by a factor of 22 (four).

Arc length of a circle: The length of an arc is the distance between two points on a circle. The formula for the arc length of a circle is given:

Arc Length = (θ/360)2πr

where θ is the central angle in degrees,

r is the radius of the circle,

and 2pie is a constant value.

If we double the radius of a circle, the arc length also doubles.

This is because the arc length is directly proportional to the radius.

Hence, doubling the radius of a circle results in an increase in the arc length by a factor of 2.

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help please!! i have no clue how to do this without the answer to DC

Answers

Looks like your question already has an answer! https://brainly.com/question/22200751

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Subtract the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.

Subtract 2x2 - 6x - 4

from 4x2 - 4x + 3.

Answers

The answer to subtracting the two polynomials is 2x2 - 10x - 7.  The process of subtracting polynomials is like that of subtracting any other type of numerical expression.

What are polynomials?

Polynomials are mathematical expressions consisting of variables, coefficients, and exponents. They are used to represent a variety of functions, such as polynomial equations, rational equations, and trigonometric functions.

In this case, our like terms are 2x2 and 4x2, and -6x and -4x, and -4 and +3. We begin by subtracting the coefficients of the like terms. We subtract the coefficient of the term with the highest power first. In this case, that is 2x2 and 4x2, we subtract 2 from 4 to get 2. Next, we subtract the coefficients of the terms with the second highest power. This is -6x and -4x, so we subtract -6 from -4 to get -2. Thus, our answer now reads 2x2 -2x.

Finally, we subtract the coefficients of the terms with the lowest power. This is -4 and +3, so we subtract -4 from 3 to get -7. Thus, our answer now reads 2x2 -2x -7.

This answer can then be placed in the proper position on the grid.

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Julie works Sunday,
, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612

Answers

Julie hourly rate of pay from the given different rates of the day with total earning of $612 is equal to $12per hour.

Total number of hours Julie works in a week is equal to,

On Sunday = 10 hours

On Monday = 10 hours

On Tuesday = 7 hours

On Wednesday = 10 hours

On Thursday = 7 hours

On Friday = 7 hours

On Saturday = 0 hours

Total hours worked in whole week is

= 10 + 10 + 7 + 10 + 7 + 7 + 0

= 51 hours

Total money earned by Julie in whole week = $612

Hourly rate of pay = Weekly earnings / Total hours worked

Substitute the value we have,

⇒ Hourly rate of pay = $612 / 51 hours

⇒ Hourly rate of pay = $12 per hour

Therefore, Julie's hourly rate of pay is $12 per hour.

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The above question is incomplete , the complete question is:

Julie works Sunday, Monday, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612. What is Julie's hourly rate of pay, in dollars?

Exercise 3-23A (Algo) Using ratio analysis to assess financial risk LO 3-5

The following information was drawn from the balance sheets of two companies. Company Assets = Liabilities + Equity
East 206,000 91,000 115,000
West 603,000 169,000 434,000

Required
a. Compute the debt-to-assets ratio to measure the level of financial risk of both companies. B. Compare the two ratios computed in requirement a to identify which company has the higher level of financial risk

Answers

The answer based on debt to assets ratio for east and west company are,

East company debt to assets ratio is equal to 0.44.

West company debt to assets ratio is equal to 0.28.

After comparing both the company debt to assets ratio East company is at higher level of financial risk.

Assets = Liabilities + Equity

For East company,

206,000 =  91,000 + 115,000

Assets = 206,000

liabilities = 91,000

Equity = 115,000

For West company,

603,000 =  169,000 + 434,000

Assets = 603,000

liabilities = 169,000

Equity = 434,000

Debt-to-assets ratio = Total liabilities divided by the total assets.

Debt-to-assets ratio for East

= 91,000 / 206,000

= 0.44

Debt-to-assets ratio for West

= 169,000 / 603,000

= 0.28

Comparing the two ratios,

0.44 > 0.28

This implies,

Company East has a higher debt-to-assets ratio is greater than the compared to Company West.

This represents that Company East has a higher level of financial risk.

As larger proportion of their assets are financed through debt.

This shows it is difficult to repay if the company experiences financial difficulties.

Company West has a lower level of financial risk as smaller proportion of their assets are financed through debt.

Therefore, the answer of the following questions are,

Debt to asset ratio of east company = 0.44

Debt to asset ratio of west company = 0.28

Company east has a higher financial risk level .

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Mattew is going on a trip to Hawaii and takes a limo to the airport. The driver says it will cost $20 plus 20 cents a mile. Mattew lives 50 miles from the airport

Answers

Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.

We know that the cost per mile is $0.20, so we can set up an equation:

Cost = $20 + $0.20 x Distance

We can substitute $50 for Cost and solve for Distance:

$50 = $20 + $0.20 x Distance

$30 = $0.20 x Distance

Distance = $30 / $0.20

Distance = 150 miles

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Tell whether the given value is a solution of the inequality.
q/5 < q-20; q=15

Answers

Answer:

No, q=15 is not a solution to the inequality.

Step-by-step explanation:

As given, q=15. So, substituting is the best way to solve this problem.

Step 1: Substitute

[tex]\frac{15}{5}=3[/tex]

[tex]15-20=-5[/tex]

Step 2: Substitute values into inequality

[tex]3 < -5[/tex]

Equation is false since 3 is a bigger value than -5.

Hope this helps ya!

E
ON YOUR OWN
Surface Area 2
3.04 On Your Own: Surface Area 2
Now It's Time to Practice on Your Own

Two cubes are placed together to form a solid so that one of side of the first cube completely matches up with one side of the second cube. Each cube has a side length of 5 m.
What is the total surface area of the solid?
Enter your answer in the box.

Answers

250 is the total surface area of the solid.

How do you determine surface area?

The whole surface of a three-dimensional form is referred to as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face.

                         Instead, you may write out the cuboid's length, width, and height and apply the formula surface area (SA)=2lw+2lh+2hw.

Each side of a cube with side length = 5  has an area of 25; the overall area is 6 x 25 = 150

A cube with sides of length 5 has an area of 25 on each side, making its overall area 6 x 25 or 150.

Both have a combined area of 150 + 150 = 300

300 - 25 - 25 = 250 is the result from each of the two cubes.

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use the properties of geometric series to find the sum of the series. for what values of the variable does the series converge to this sum?
7−14z+28z2−56z3+⋯
sum =
domain =
(Give your domain as an interval or comma separated list of intervals; for example, to enter the region x<−1 and 2

Answers

a) The sum of the given series is 7 / (1 + 2z)

b) The domain of convergence is (-∞, -1/2) U (1/2, ∞).

The given series can be expressed as

7 – 14z + 28z^2 - 56z^3 + ...

This is a geometric series with first term (a) = 7 and common ratio (r) = -2z. The formula for the sum of an infinite geometric series is

sum = a / (1 - r)

Substituting the values of a and r, we get

sum = 7 / (1 + 2z)

So, the sum of the given series is 7 / (1 + 2z).

For the series to converge, the absolute value of the common ratio must be less than 1. That is,

|r| = |−2z| < 1

Simplifying this inequality, we get

1/2 < |z|

So, the domain of convergence of the given series is (-∞, -1/2) U (1/2, ∞).

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Show by completing the survey slip on the answer sheet , how Samantha, a 14 year old girl who feels a lot of pressure to achieve at school, would complete the survey form

Answers

Samantha would fill in the following information on the survey sheet based on the data provided:

Sex: Female

Age: 13-14

How much pressure do you feel to achieve at school? c. A lot

Samantha, a 14-year-old girl, would complete the survey slip by selecting "Female" under "Sex," "13-14" under "Age," and "A lot" under "How much pressure do you feel to achieve at school?"

This indicates that Samantha is feeling a significant amount of pressure to succeed academically. It's common for high school students to feel pressure to perform well in school, and this can be due to various factors such as parental expectations, college aspirations, or personal goals.

As a school counselor, it's essential to understand the level of pressure students are experiencing to provide appropriate support and guidance. Identifying and addressing the sources of pressure can help students like Samantha better manage stress and achieve academic success.

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The question is -

A school counselor conducted a survey among a group of high school students using the following survey slip:

Survey (please tick the correct boxes)

Sex:  Male  Female

Age:  13-14  15 -16  17–18

How much pressure do you feel to achieve at school?

a. None b. A little c. A lot  And d. the unbearable amount

Show, by completing the survey slip on the answer sheet, how Samantha – a 14-year-old girl who feels a lot of pressure to achieve at school – would complete the survey

solve the pair of simultaneous equations:(step by step, using factorization method)
y²+2y+11=x
x=5-3y​

Answers

Answer: (-3,-2)

Step-by-step explanation:

y²+2y+11 = 5-3y

y^2+2y+11-5+3y =0

y^2+5y+6=0

y^2+3y+2y+6=0

y(y+3)+2(y+3)=0

(y+3)(y+2)=0

y= -3, -2

All you do is plug in the x value to the equation

Hope it helps:)

Answer this for points

Answers

I think the answer is 6h + 35 = 80. 80= 6h + 35.

Can you solve this with workings out please

Answers

Answer:

Eighty biscuits.

Step-by-step explanation:

We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits

[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]

We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.

[tex]Biscuits=4*20=80[/tex]

Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.

[tex]Flour:\\1000-4(180) = 280g[/tex]

After making 4 servings we still have 280g of flour left.

Perform the indicated operation.
f(x) = −3x² + 3x; _g(x) = 2x+5
(ƒ + g)(3)

Answers

The composite function (f + g)(3) when evaluated from f(x) = −3x² + 3x and g(x) = 2x+5 is -7

Calculating the composite function

Given that

f(x) = −3x² + 3x and

g(x) = 2x+5

To perform the operation (ƒ + g)(3), we need to add the functions ƒ(x) and g(x) first, and then evaluate the sum at x = 3.

ƒ(x) = −3x² + 3x

g(x) = 2x + 5

To add the functions, we simply add their corresponding terms:

(ƒ + g)(x) = ƒ(x) + g(x) = (−3x² + 3x) + (2x + 5)

When the like terms are evaluated, we have

(ƒ + g)(3) = −3x² + 5x + 5

Now, we can evaluate the sum at x = 3:

(ƒ + g)(3) = −3(3)² + 5(3) + 5

So, we have

(ƒ + g)(3) = −27 + 15 + 5

Lastly, we have

(ƒ + g)(3) = -7

Therefore, (ƒ + g)(3) = -7.

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Solve for Z =

Please answer

Answers

Answer:

z = 32°

vertical angles are equal to each other. 32° ≅ z°

Error Analysis-Terrence constructed the circumscribed circle for triangle xyz. Explain Terrence's error.

Answers

Answer:

Step-by-step explanation:

eric from exercise 3.30 continues driving. after three years, he still has no traffic accidents. now, what is the conditional probability that he is a high-risk driver?

Answers

The conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. Generally, insurance companies use the number of traffic violations and/or the number of claims a driver has had within a certain time period as indicators of their riskiness.

As Eric has had no accidents or traffic violations, the probability that he is a high-risk driver is very low. However, this does not mean that the probability is zero. There are many other factors which can contribute to a driver's risk, such as age, gender, experience, and location.

If Eric is an experienced driver, who has been driving for many years with no traffic accidents, then the probability of him being a high-risk driver will be lower than the average driver. On the other hand, if Eric is a new driver, or is located in an area with a high rate of traffic accidents, then the probability of him being a high-risk driver may be higher than the average driver.

Overall, the conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. However, this probability can change depending on other factors, such as his age, experience, and location.

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