Evaluate arccsc sqrt 2.

Answer:

1. The marked answer is correct.

2. The only equivalent equation is the 2nd one: x^2 -12x +36 = 28

Step-by-step explanation:

The square of a binomial is ...

(x -a)^2 = x^2 -2ax +a^2

This tells you the constant term in the perfect square trinomial is the square of half the x-coefficient.

1. The x-coefficient is -8, so half that is -4. The square of -4 is 16. To complete the square, the added constant term must be 16, the marked answer.

___

2. The x-coefficient is -12, so the square of half that is (-6)^2 = 36. Adding 36 to the equation gives ...

x^2 -12x +36 = 28 . . . . . . matches the 2nd choice

_____

The rule that makes algebra work is this: whatever you do on one side of the equal sign must also be done on the other side.

If you add 36 on one side of the equation, you must add 36 on the other side. Of course addition of signed numbers is done in the usual way: 36 + (-8) = 28.

Answer:

C

Step-by-step explanation:

A function in the form  [tex]y=a*b^x[/tex] is an exponential function. If

The given function can be written as  [tex]y=1*0.8^x[/tex], so a > 0 and 0 < b < 1, hence this is exponential decay function.

For end behavior, we take limits from -∞ and from ∞. If we do that we can see that C is the correct answer. Also, looking at the graph explains it. Attached is the graph.

From the graph, as we move towards negative infinity, the graph goes towards positive infinity and as we move towards positive infinity, the graph goes towards 0.

Answer:

plane velocity (with wind) = 500 mph

plane velocity (against wind) = 420 mph

velocity difference divided by 2 = 40

plane velocity = 500 - 40 = 460 mph

Step-by-step explanation:

Answer:

72 members

Step-by-step explanation:

Total surveyed members = 40

members voting yes = 12

probability of the members voting yes = 12/40 = 3/10

It is observed that, out of every 'n' members, n*(3/10) members are expected to vote yes:

Therefore,

number of members expecting to voye yes out of 240 are = 240 * 3/10

=> 24 * 3 = 72 members

Answer:

A

Step-by-step explanation:

Nature of roots is determined by using the Discriminant, D, which is:

[tex]D=b^2-4ac[/tex]

If

D > 0, there are 2 real unique solutions

D = 0, there are 2 real equal solutions

D < 0, there are no real solutions

Note: a is the coefficient of x^2, b is the coefficient of x, and c is the independent term (the constant)

Now, for our quadratic expression, a = 3, b = 12, & c = -3. Plugging it in the discriminant formula, we get:

[tex]D=b^2-4ac\\D=(12)^2-4(3)(-3)\\D=180[/tex]

Thus, D > 0 , which means there are 2 distinct real solutions. Answer choice A is right.

To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic. For each congruence, we substitute the given values of a and b and simplify the congruences to solve for c. The possible values of c are then determined using the Chinese Remainder Theorem when appropriate.

To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic:

a) To find c such that a.c ≡ 13a (mod 19), we divide both sides of the congruence by a. This gives us c ≡ 13 (mod 19).

b) To find c such that b.c ≡ 8b (mod 19), we divide both sides of the congruence by b. This gives us c ≡ 8 (mod 19).

c) To find c such that c.c ≡ a - b (mod 19), we square both sides of the congruence. This gives us c^2 ≡ (a - b)^2 (mod 19). Since we know a ≡ 11 (mod 19) and b ≡ 3 (mod 19), we substitute these values and simplify the congruence to c^2 ≡ 8 (mod 19). To solve this quadratic congruence, we can use the Chinese Remainder Theorem to find the two square roots of 8 modulo 19, which are 7 and 12. Therefore, c ≡ 7 (mod 19) or c ≡ 12 (mod 19).

d) To find c such that c.c ≡ 7a + 3b (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 7(11) + 3(3) ≡ 4 (mod 19). Similar to part (c), we use the Chinese Remainder Theorem to find the square roots of 4 modulo 19, which are 2 and 17. Therefore, c ≡ 2 (mod 19) or c ≡ 17 (mod 19).

e) To find c such that c.c ≡ 2a^2 + 3b^2 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 2(11^2) + 3(3^2) ≡ 2(121) + 3(9) ≡ 149 ≡ 2 (mod 19). Therefore, c ≡ ±4 (mod 19).

f) To find c such that c ≡ a^3 + 4b^3 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c ≡ 11^3 + 4(3^3) ≡ 11^3 + 4(27) ≡ 11^3 + 4(8) ≡ 11 + 32 ≡ 17 (mod 19). Therefore, c ≡ 17 (mod 19).

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Answer:

Step-by-step explanation:

Answer:

75 "I think"

Step-by-step explanation:

Is there answer choices?

Answer:

P(A') = 0.75

Step-by-step explanation:

We are given that the probability P(A) = 0.25 and we are to determine the probability of the complement of A.

According to the Complement Rule of any probability, the sum of the probabilities of an event and its complement must be equal to 1.

So for for the event A,

P(A) + P(A') = 1

0.25 + P(A') = 1

P(A') = 1 - 0.25

P(A') = 0.75

The probability of an event and its complement add up to 1. Therefore, if P(A) = 0.25, the probability of the complement of A is 0.75.

In the field of probability theory, the probability of an event and its complement always add up to 1. Therefore, if P(A) = 0.25, then the probability of the complement of A is 1 - 0.25 = 0.75.

This is because the complement of A, denoted by A', includes all outcomes that are not in A. So, all probabilities in the sample space (which has a total probability of 1) must either be in A or in A'. Therefore, P(A) + P(A') = 1.

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Answer:

18.15

Step-by-step explanation:

Percent means per hundred, so we can convert 4.6% and 3.65% to equivalent decimals.

4.6%= 4.6 divided by 100 = 0.046

3.65%= 3.65 divided by 100 = 0.0365

Since both sales tax rates apply to $220, we can add the two rates.

0.046 + 0.0365= 0.0825

0.0825 x 220 = 18.15

And so, Yuki pays$18.15 in sales tax for her handbag purchase.

Here is your answer

[tex]\bold{107.62} inches [/tex]

Since the door will be in shape of a rectangle where,

length= 80 inches

breadth= 72 inches

So,

widht of largest mattress that can fit diagonally is diagonal of the door.

i.e.

[tex]d= \sqrt{{l}^{2}+{b}^{2}}[/tex]

[tex]d= \sqrt{{80}^{2}+{72}^{2}}[/tex]

[tex]d= \sqrt{6400+5184}[/tex]

[tex]d= \sqrt{11584}[/tex]

[tex]d= 107.62[/tex]

HOPE IT IS USEFUL

The largest mattress to fit diagonally through the french doors measuring 72 inches by 80 inches is approximately 107.6 inches, using the Pythagorean theorem to calculate it.

To find the largest mattress that can fit diagonally through french doors with dimensions of 72 inches by 80 inches, we can use the Pythagorean theorem because the door creates a right-angle triangle. The diagonal can be calculated using the formula: diagonal = \/(width² + height²).

We plug in the dimensions: diagonal = \/(72² + 80²). First, square each dimension: 72² = 5184 and 80² = 6400. Then add these together: 5184 + 6400 = 11584. Now take the square root of 11584 to find the diagonal: diagonal = \/11584 which is approximately 107.6 inches.

Therefore, the largest mattress that can fit diagonally through the french doors rounded to the nearest tenth is 107.6 inches.

Answer:

The area of the triangle is 43.5 cm².

Step-by-step explanation:

Since,  the area of a triangle is,

[tex]A=\frac{1}{2}\times s_1\times s_2\times sin \theta[/tex]

Where, [tex]s_1[/tex] and [tex]s_2[/tex] are adjacent sides and [tex]\theta[/tex] is the included angle of these sides,

Given,

[tex]s_1=12\text{ cm}[/tex]

[tex]s_2=8\text{ cm}[/tex]

[tex]\theta = 65^{\circ}[/tex]

Hence, the area of the given triangle is,

[tex]A=\frac{1}{2}\times 12\times 8\times sin 65^{\circ}[/tex]

[tex]=\frac{96\times 0.90630778703}{2}[/tex]

[tex]=\frac{87.0055475555}2}=43.5027737778\approx 43.5\text{ square cm}[/tex]

Answer:

0.6826

Step-by-step explanation:

To solve this, we find the z scores for both sample means.  We then us a z table to find the area under the curve to the left of (probability less than) each z score, and subtract them to find the area between them.

The formula we use, since we are using sample means, is

[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]

Our x-bar will be 116 in the first z-score and 120 in the second; our mean, μ, is 118; our standard deviation, σ, is 6.3; and our sample size, n, is 10:

[tex]z=\frac{116-118}{6.3\div \sqrt{10}}=\frac{-2}{1.9922}\approx -1.0039\\\\z=\frac{120-118}{6.3\div \sqrt{10}}=\frac{2}{1.9922}\approx 1.0039[/tex]

Using a z table, we see that the area under the curve to the left of -1.00 is 0.1587.  The area under the curve to the left of 1.00 is 0.8413.  This makes the area between them

0.8413-0.1587 = 0.6826.

To solve this statistics problem, calculate the z-scores for the lengths 116 cm and 120 cm, using the given mean, standard deviation, and sample size. Then, use a z-table to find the probabilities associated with these z-scores. The difference between these probabilities will give the likelihood of the machine producing shells between these lengths.

This problem is essentially a question about probability in statistics, specifically relating to the normal distribution. Given that the machine is operating properly, and assuming that the lengths of the shells it produces are normally distributed with a mean of 118 cm and a standard deviation of 6.3 cm, we want to find the probability that the average length of 10 randomly selected shells is between 116 and 120 cm.

First, we need to find the z-scores corresponding to the lengths of 116 cm and 120 cm. The formula for the z-score is (X - μ)/σ, where X is the measurement (in this case, the average length of the shells), μ is the mean, and σ is the standard deviation. However, in this scenario, due to the application of the Central Limit Theorem, we must use σ/sqrt(N) as the standard deviation for the distribution of sample means, where N=10. Therefore, for 116 cm we get Z1 = (116 -118) / (6.3/ sqrt(10))  and for 120 cm we get Z2 = (120 - 118) / (6.3/sqrt(10)).

Once the Z-scores are calculated, we can use Z-tables (commonly found in statistics textbooks or online) to find the probabilities associated with these z-scores. Subtract the probability of Z1 from the probability of Z2 to get the desired range probability.

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➷ Find the multiplier:

1 + (3.4/100) = 1.034

Use this formula:

Final = original x multiplier^n

n is the number of years

Substitute the values in:

final = 6000 x 1.034^3

Solve:

final = 6633.0438

This can be rounded to the final answer of £6633.04

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

THX THIS HELPED ME A LOT

Step-by-step explanation:

Answer:

slope = - 5

Step-by-step explanation:

given the equation of a line in the form

y = mx ← m is the slope

y = - 5x is in this form with slope m = - 5

Answer:

a) 20.16; b) 20.49 and 21.51

Step-by-step explanation:

We use z scores for each of these.  The formula for a z score is

[tex]z=\frac{X-\mu}{\sigma}[/tex].

For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.

Using this, 21 as the mean and 1 as the standard deviation,

-0.84 = (X-21)/1

-0.84 = X-21

Add 21 to each side:

-0.84+21 = X-21+21

20.16 = X

For part b, we want the middle 39%.  This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want

50-19.5 = 30.5% = 0.305 and

50+19.5 = 69.5% = 0.695.

Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:

-0.51 = (X-21)/1

-0.51 = X-21

Add 21 to each side:

-0.51+21 = X-21+21

20.49 = X

0.51 = (X-21)/1

0.51 = X-21

Add 21 to each side:

0.51+21 = X-21+21

21.51 = X

The 20th percentile for incubation times is approximately 20.16 days. The incubation times that make up the middle 39% of fertilized eggs fall between roughly 20.5 days and 21.5 days.

This question focuses on statistics and their application in a biological context, specifically about the incubation time of fertilized eggs. In statistics, the normal distribution is a common continuous probability distribution that is symmetric about the mean.

(a) The 20th percentile of the normal distribution can be found using the z-table or a calculator that has the capability. Using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value in the data set, μ is the mean, and σ is the standard deviation, a Z-score associated with the 20th percentile is approximately -0.84. So the incubation time in days for the 20th percentile is (0.84 * 1) + 21 = 20.16 days.

(b) Similarly, to find the incubation times that make up the middle 39% of the fertilized eggs, note that since this is symmetric, this implies the incubation times falls between the 30.5 percentile and the 69.5 percentile. Using the formula Z = (X - μ) / σ and the Z-table, the Z-scores associated with these percentiles are approximately -0.5 and 0.5 respectively. Hence the incubation time falls between (0.5 * 1) + 21 = 20.5 days and (0.5 * 1) + 21 = 21.5 days

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Answer:

It would be $13.05

Step-by-step explanation:

Since you're dividing negative $65.25 with a negative number of 5 stores. The five stores are negative because he bought from those stores. So, when dividing the 2 negatives you get a positive $13.05.

If Tom has bought only one t-shirt  the change to Tom's account balance

would have been - $13.05.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Tom bought 5 t-shirts from a store.

After he bought the t-shirts, his account balance showed a change of

- $65.25.

Assuming all 5 t-shirts cost the same so the cost of 1 t-shirt would be

= - (65.25/5).

= - 13.05 dollars.

learn more about the unitary method here :

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3x+3=6x-57

60=3x

3x=60

60÷3=20

x=20

Answer:

The height of the building is approximately [tex]34\ ft[/tex]

Step-by-step explanation:

Let

h------> height of the building from the student's eye level

H----> height of the building from the ground (H=h+5 ft)

we know that

[tex]tan(30\°)=\frac{h}{50}[/tex]

[tex]h=tan(30\°)(50)=28.87\ ft[/tex]

Find the height of the building H

[tex]H=h+5=28.87+5=33.87\ ft[/tex]

The height of the building is approximately [tex]34\ ft[/tex]

QUESTION 1

We want to find the slope through the points (12,-18), (11,12).

We use the slope formula,

[tex]m = \frac{y_2-y_1} {x _2-x_1} [/tex]

We substitute the points to get,

[tex]m = \frac{12 - - 18}{11 - 12} [/tex]

[tex]m = \frac{30}{ - 1} = - 30[/tex]

The slope is -30.

QUESTION 2.

We want to find the slope through the points (-18, -20), (-18, -15).

We use the slope formula again to obtain,

[tex]m = \frac{ - 15 - - 20}{ - 18 - - 18} [/tex]

We simplify to get;

[tex]m = \frac{5}{0} [/tex]

Division by zero means the slope is not defined.

QUESTION 3

The given equation is 4x + y = 5.

At x-intercept, y=0.

We put y=0 into the equation to get,

[tex]4x + 0 = 5[/tex]

[tex]4x = 5[/tex]

[tex]x = \frac{5}{4} [/tex]

The x-intercept is

[tex]( \frac{5}{4} , 0)[/tex]

To find the y-intercept,we substitute x=0 into the equation to get,

[tex]4(0) + y = 5[/tex]

[tex]y = 5[/tex]

The y-intercept is (0,5)

QUESTION 4.

The given equation is

[tex]y = 5x - 4[/tex]

To find the y-intercept put x=0 into the equation.

[tex]y = 5(0) - 4[/tex]

[tex]y = - 4[/tex]

(0,-4)

To find the x-intercept, put y=0,

[tex]0 = 5x - 4[/tex]

[tex]4 = 5x[/tex]

[tex] \frac{4}{5} = x[/tex]

[tex]( \frac{4}{5} ,0)[/tex]

QUESTION 5

To find the equation of a line given the slope m, and a point

[tex](x_1,y_1) [/tex]

we use the formula,

[tex]y-y_1=m(x-x_1)[/tex]

The given line has slope zero and passes through

(3,4)

The equation is

[tex]y - 4 = 0(x - 3)[/tex]

[tex]y - 4 = 0[/tex]

[tex]y = 4[/tex]

Question 6

The given equation is

[tex]x = 1[/tex]

This is the equation of a line that is parallel to the y-axis.

The slope of all lines parallel to the x-axis is undefined.

The slope of x=1 is not defined.

Answer:

Two parallel lines never intersect.

Step-by-step explanation:

The definition of a parallel line is: 2 lines that are exactly the same, but will not touch each other.

Answer with explanation:

~p means other line is Similar to p.

If there are two parallel lines , it means Perpendicular distance between the two lines is always constant, if measured by taking a point anywhere on the line.

⇒Two Parallel lines never intersect.

Option B

Answer:

Step-by-step explanation:

You know there is only one solution because the ratio of x- and y-coefficients is different in the two equations. That means the lines will have different slopes, so must intersect in exactly one point.

__

The y-coefficients are opposites, so you can eliminate the y-variable by adding the equations:

  (2x -y) + (3x +y) = (2) + (-6)

  5x = -4

  x = -4/5 = -0.8

Substituting this into the second equation, we have ...

  3(-0.8) +y = -6

  y = -3.6 . . . . . . . add 2.4 to both sides

The solution is (x, y) = (-0.8, -3.6).

__

You can also find the solution by graphing (or using a graphing calculator).

The system of linear equations has one and only one solution, which is (x, y) = (-4/5, -18/5).

This is a question about solving a system of linear equations. To determine whether a system has one, many, or no solutions, we add or subtract the equations to eliminate one of the variables, usually y or x.

Given the system of equations:

2x - y = 2

3x + y = -6

When we add the two equations together, we get 5x = -4, so x = -4/5.

Substitute x = -4/5 into the first equation to find y:

2(-4/5) - y = 2 => -8/5 - y = 2 => -y = 2 + 8/5 => y = -18/5.

Therefore, the system of equations has one and only one solution, which is (x, y) = (-4/5, -18/5).

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Answer:

[tex]\large\boxed{x\approx0.52}[/tex]

Step-by-step explanation:

[tex]2^{5x}=6\Rightarrow\log_22^{5x}=\log_26\qquad\text{use}\ \log_ab^n=n\log_ab\\\\5x\log_22=\log_26\qquad\text{use}\ \log_aa=1\\\\5x=\log_26\qquad\text{divide both sides by 5}\\\\x=\dfrac{\log_26}{5}\\\\\log_26\approx2.585\\\\x\approx\dfrac{2.585}{5}\to\boxed{x\approx0.52}[/tex]

Answer:

a:  It is binomial because it is either on time, or it's not. There are only 2 choices

b:  0.0668

c:  0.0319

d:  0.9681

e:  0.097

Step-by-step explanation:

The formula (nCr)(p^r)(q^(n-r)) will tell us the probability of binomial events occuring.  n is the population, r is the desired number of chosen outcomes, p is the probability of success, and q is the probability of failure. nCr tells us how many different ways we can choose r items from a total of n outcomes

Here, n = 17, p = 0.85, q = 0.15 and r depends on the question.

b.  r = 12, plug in the values into the formula...

(17C12)(0.85^12)(0.15^5) = 0.0668

c.  Use the compliment: the probability of fewer than 12 means 1 - P(12 or more), so 1 - (the sum of the probabilities or 12, 13, 14, 15, 16, or 17 flights being on time).  This will save some time when calculating...we have

1 - [ (17C12)(0.85^12)(0.15^5) + (17C13)(0.85^13)(0.15^4) + (17C14)(0.85^14)(0.15^3) + (17C15)(0.85^15)(0.15^2) + (17C16)(0.85^16)(0.15^1) + (17C17)(0.85^17)(0.15^0) ]

= 1 - 0.9681 =  0.0319

d:  this is what we just calculated before subtracting from 1 in the last problem, 0.9681

e.  This is the probability of 10, 11, or 12 flights being on time

(17C10)(0.85^10)(0.15^7) + (17C11)(0.85^11)(0.15^6) + (17C12)(0.85^12)(0.15^5)

= 0.97

This question deals with the concept of binomial distribution. The situation of selecting 17 flights and recording if they are on time is a binomial experiment as it meets the required conditions. The probabilities for the various scenarios can be calculated using the binomial probability formula.

This question pertains to the topic of binomial distribution in probability statistics. A binomial experiment is defined as a statistical experiment that meets specific parameters, such as a fixed number of trials with two potential outcomes (often defined as success and failure), and each trial is independent while repeated under identical conditions.

(a) The situation described - selecting 17 flights and recording whether they are on time or not - represents a binomial experiment because it satisfies these conditions. There are a fixed number of trials (17 flights), there are two outcomes (the flight is on time, or it's not), and each flight is an independent occasion.

(b) The probability of exactly 12 flights being on time can be calculated using the binomial probability formula: P(X=k) = C(n, k) *[tex](p^k) * ((1-p)^(n-k)).[/tex]Here, n=17, k=12, p=0.85 (the probability of a flight being on time).

(c), (d), (e) The probabilities that fewer than 12 flights are on time, at least 12 flights are on time, and between 10 and 12 flights (inclusive) are on time can also be calculated using the binomial formula, varying the value of k as required.

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Answer:

100

Step-by-step explanation:

The total length of ten pens laid end-to-end is

10 pens × 130 mm/1 pen = 1300 mm

The number of tiles needed to stretch the same length is

1300 mm × 1 tile/13 mm = 100 tiles

Helen uses 100 tiles.

Answer:

D

Step-by-step explanation:

Exponential equation takes the form  [tex]y=a*b^x[/tex]  where

The equation given in the problem can be written as  [tex]y=-4.8*4^x[/tex], so it is an exponential equation,  where a = -4.8 and b = 4.

Thus we can say that the initial value = -4.8 and the base is 4

The correct answer is  D

Answer:

d

Step-by-step explanation:

Answer: third option.

Step-by-step explanation:

By definition we know tht the geometric sequences has a common ratio, which is represented with r.

This ratio can be calculated by dividing a term by the previous term.

Therefore, keeping the information above on mind, you have that the ratio r  of the geometric sequence given in the problem, is the shown below:

[tex]r=\frac{-\frac{1}{2}}{\frac{1}{10}}\\\\r=-5[/tex]

Answer:

The ratio of the sequence is -5

Step-by-step explanation:

The given geometric series is ;

[tex]\frac{1}{10},-\frac{1}{2},\frac{5}{2},...[/tex]

The ratio of the geometric sequence is given by;

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

[tex]r=\frac{\frac{5}{2}}{-\frac{1}{2}}[/tex]

We simplify to get;

[tex]r=-5[/tex]

If you multiply the numerator and the denominator by the same number, it will be equal to 1/3.

For example:

1/3 * 3/3 = 3/9

1/3 * 8/8 = 8/24

Answer:

2/6, 3/9, and 4/12

Step-by-step explanation:

Any fraction where you can divide both the numerator and the denominator by the same number to get 1/3 also equals 1/3.

For example: 2/6

When you divide both numbers by 2, you get 1/3. Which means they are equivalent fractions (or equal).