Directions - Find the slope ( rise over
run)

Note that the feature of the function graphed  is that it has a Horizontal Asymptote which is y = -1

A horizontal asymptote is a straight line that a function approaches but never touches as the input values get very large or very small.

It represents the long-term behavior of the function. A horizontal asymptote can have three different types of behavior:

1) the function approaches the line without ever crossing it,

2) the function approaches the line and oscillates around it, or

3) the function approaches the line and crosses it infinitely many times.

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Answer:

90 degree counter-clockwise

Step-by-step explanation:

The 95% confidence interval for the true mean cholesterol content of all eggs is (216.77, 233.23) milligrams.

To construct a confidence interval for the true mean cholesterol content of all eggs, we can use the formula:

Confidence Interval = mean ± (critical value) * (standard deviation / sqrt(sample size))

Given that the sample mean is 225 milligrams (mean), the standard deviation is 15.7 milligrams (s), and the sample size is 12 eggs, we need to determine the critical value for a 95% confidence level.

Since the sample size is small (n < 30) and the population standard deviation is unknown, we use a t-distribution. With a 95% confidence level and 12 degrees of freedom (sample size minus 1), the critical value can be found using statistical tables or software, which is approximately 2.201.

Plugging in the values into the confidence interval formula:

Confidence Interval = 225 ± (2.201) * (15.7 /  √(12))

                  = 225 ± (2.201) * (15.7 / 3.464)

                  ≈ 225 ± (2.201) * 4.529

                  ≈ 225 ± 9.972

                  ≈ (215.03, 234.97)

Therefore, we can be 95% confident that the true mean cholesterol content of all eggs lies within the interval of (216.77, 233.23) milligrams.

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Answer:

6

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

4x = 2x + 12

4x - 2x = 2x - 2x + 12

2x = 12

2x ÷ 2 = 12 ÷ 2

X = 6

Plug into HI

9 × 6 + 13 = 67

1) Option B, which states that the confidence interval size shrank from 0.99 to 0.90, is the right answer.

2) Option D is the best decision. Confidence interval: 0.88

1) A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such as 90% or 99%, are occasionally used.

Therefore, the correct choice is option B which states that From 0.99 to 0.90 the confidence interval size became smaller

2) In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

It can be calculated as:

df=n-1=19

t critical value 0.12 (two tail) = 1.62797

M = 51.5

sM = √(6.842 / 20) = 1.53

μ = M ± Z (sM)

μ = 51.5 ± 1.62797 * 1.53

μ = 51.5 ± 2.49

therefore, CI { 49.01 and 53.99 }

The correct choice is option D. 0.88 confidence interval

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Answer:

85° = ∠x {corresponding angles}

∠x = ∠1 {vertically opp. angles}

And, ∠2 + 103° = 180° ( co-interior angles)

∠2 = 180° - 103°

∠2 = 77°

Now, m∠1 + m∠2 = 85° + 77°

= 162°

Hemce, option A. is the right answer.

Taking into the rules of precedence, the parenthesized expressions that is equivalent to ¬p ^ r → q ^ s is (¬p ^ r) → (q ^ s). So, the correct answer is option 1. (¬p ^ r) → (q ^ s)

According to the rules of precedence, logical negation (¬) has the highest precedence, followed by conjunction (^), and then implication (→). Parentheses can be used to change the order of evaluation.

In the given expression, ¬p is evaluated first, followed by the conjunction ^ of ¬p and r. The implication → is evaluated last with q and s.

Option 1 has the same order of evaluation with the given expression as the parentheses group ¬p and r first, and then q and s are grouped next with the implication →.

Option 2 is not equivalent because the parentheses group r and q with the conjunction ^ before evaluating the implication →, which changes the order of evaluation.

Option 3 is not equivalent because it uses logical negation ¬ on the entire expression of (p ^ r) → (q ^ s), which changes the meaning of the expression.

Option 4 is not equivalent because it uses conjunction ^ to connect ¬p and (r → q), which changes the meaning of the expression.

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Given :

Joseph tweets 13 times a day.

To Find :

An algebraic expression to describe the number of posts after any given number of days.

Solution :

Let, number of tweets after x days are y.

Let, the relationship is , y = mx + c.

For, x = 1

13 = m +c     ...... 1)

x = 2

26 = 2m + c   .......2)

So, m = 13 and c = 0.

Therefore, algebraic expression to describe the number of posts after any given number of days is y = 13x.

Hence, this is the required solution.

The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Answer:

it will be always negative

Step-by-step explanation:

brainliest please

(a) The amount of salt added in the tank will be equal to the amount of salt drained from the tank.
(b) The concentration of salt in the solution in the tank is a decreasing function of time, and it has a vertical asymptote at t = 40.

(a) Given that a tank contains 40 liters of a saltwater solution. The solution contains 4 kg of salt. A second saltwater solution containing 0.5 kg of salt per liter is added to the tank at 6 liters per minute. The solution in the tank is kept thoroughly mixed and drains from the tank at 7 liters per minute.
Let's determine the amount of salt added in the tank per minute
= 0.5 kg/liter × 6 liters/minute
= 3 kg/minute
Let's determine the amount of salt drained from the tank per minute
= 4 kg/40 liters × 7 liters/minute
= 0.7 kg/minute
The amount of salt added in the tank per minute is more than the amount of salt drained from the tank per minute
i.e 3 kg/minute - 0.7 kg/minute = 2.3 kg/minute.
Therefore, the amount of salt in the tank after t minutes is given by,
`S(t) = S(0) + 2.3t`
where S(0) is the initial amount of salt present in the tank,
S(t) is the amount of salt present after t minutes.
Since there are 4 kg of salt in the solution initially,
`S(0) = 4 kg`
The domain of the function `S(t) = 4 + 2.3t` is 0 ≤ t ≤ 17.39
This is because after 17.39 minutes, the amount of salt added in the tank will be equal to the amount of salt drained from the tank. And after that time, the amount of salt in the tank will decrease.
(b) Let C(t) be the concentration of salt in the tank after t minutes.
Then we have,
`C(t) = S(t)/V(t)`
where V(t) is the volume of the solution in the tank after t minutes.
Since the solution is draining from the tank at 7 liters per minute, we have,
V(t) = 40 + (6 - 7)t= 40 - t liters
Therefore, the concentration of the solution in the tank after t minutes is given by,
`C(t) = S(t)/(40 - t)`
Substituting the value of S(t) from part (a), we get,
`C(t) = (4 + 2.3t)/(40 - t)`
The domain of the function `C(t) = (4 + 2.3t)/(40 - t)` is 0 ≤ t < 40.
This is because as t approaches 40, the volume of the solution in the tank approaches 0, and the concentration of salt in the solution becomes undefined.
The concentration of salt in the solution in the tank is given by the function
`C(t) = (4 + 2.3t)/(40 - t)`.
The domain of this function is 0 ≤ t < 40, and the range is the set of all positive real numbers. As t increases, the concentration of salt in the solution in the tank increases, but as t approaches 40, the concentration becomes undefined. This is because as t approaches 40, the volume of the solution in the tank approaches 0, and the concentration of salt in the solution becomes undefined.
Therefore, we can conclude that the concentration of salt in the solution in the tank is a decreasing function of time, and it has a vertical asymptote at t = 40.

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Answer:

Hope it helps dear.Please let me know

The soda left in the bottle is 0.4 liters in a 2-liter bottle.

Let’s understand this with the concept of Ratio.

How does ratio work?

When two objects are related using numbers or amounts, the relationship is known as a ratio.

Initially, we are given that the bottle is 2 liters. From that, Sergio poured ⅘ of the soda.

So, the soda left is the initial quantity- the final quantity

= 2(initial quantity) - ⅘*2(final quantity)

=2 - 1.6= 0.4 liter

So finally, the soda left in the 2-liter bottle is 0.4 liter.

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The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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Answer:

d

Step-by-step explanation:

ive had this exac problem before

Answer:

B. 1

Step-by-step explanation:

Since the sides are equal to each other, the equations will be equal.

4x + 7 = x + 10

      -7          -7

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

4x= x + 3

-x    -x

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

3x = 3

----   ---

3      3

x = 1

The answer is 1.

Answer:

1. slope, rise, run

2. standard form

3. y-intercept, x-intercept

4. slope formula

5. rate of change

Answer: $17.82

Step-by-step explanation: Add each item up to get $19.80. Then you take 10% of that by multiplying it 0.9 to get 17.82. You multiply it by 0.9 because that is 90% of 19.80 which is a 10% decrease.

Answer:

224

Step-by-step explanation:

200*0.12=24

200+24=224

The amount to be paid for the loan is $248.

'Simple interest is the interest amount for a particular principal amount of money at some rate of interest.

According to the given problem,

Principal amount (P) = $200

Rate of interest (r) = 12%

Time period (t) = 2 years

We know,

Final amount to be paid with interest (A) = P( 1 + rt )  

                                                                   = 200{ 1 + ( 0.12 × 2 )

                                                                   = 200( 1 + 0.24 )

                                                                   = 200 × 1.24

                                                                   = $248

Hence, we can conclude, we have to pay $248 for the loan.

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Answer:

\(x=1\frac{2}{9} +1\frac{1}{9}y\)

Step-by-step explanation:

x - 3y + 8x - 7y = 5 + 6

9x - 10y = 11

9x - 10y + 10y = 11 + 10y

9x = 11 + 10y

9x ÷ 9 = 11 + 10y ÷ 9

\(x=1\frac{2}{9} +1\frac{1}{9}y\)

Answer:

x = -1

y = -2

Step-by-step explanation:

x - 3y = 5     ----------------(I)

8x - 7y = 6 ----------(II)

Multiply equation (I) by (-8) and then add the two equations

(I)*(-8)     -8x + 24y = -40

(II)           8x   - 7y   = 6    {Now add and x will be eliminated}

                       17y = -34     {Divide both sides by 17}

                           y = -34/17

y = -2

Plugin  y  =-2 in equation (I)

x - 3*(-2) = 5

x  + 6 = 5         {Subtract 6 from both sides}

     x = 5 - 6

x = - 1

The answer to the formula are-

Part 1:  7√6 - 4√6

As both the digits have the same value √6. It means they can simply be added with sign to solve.

=  7√6 - 4√6

Take √6 common from both;

= √6(7 - 4)

= 3√6

Thus, the simplification of the expression is 3√6.

Part 2: -0.7√7 + 2.3√7

Here, also the common term is √7.

= √7( -0.7 + 2.3)

Simply add the number with sign.

= 1.6√7.

Thus, the simplification of the number is 1.6√7.

Part 3: √45 + √20

In thus, first write the number in its prime factors;

= √3×3×5 + √2×2×5

Take the root of 3 and 2 from the first and second digits of expression.

= 3√5 + 2√5

Now, both have the same term √5.

= √5(3 + 2)

Do the addition;

= 2√5

Thus, the simplification of given expression is 2√5.

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The shortest distance from the point x Distance = 5 to the line r = t 0 1 is 5 units.

To find the shortest distance from a point to a line, we can use the formula for the distance between a point and a line in three-dimensional space. The given line equation r = t 0 1 represents a line passing through the origin (0, 0, 0) with a direction vector of (0, 1, 0). Let's denote the given point as P(x, y, z), where x is the distance from the origin.

The shortest distance between the point P and the line can be found by taking the projection of the vector connecting the point P and a point on the line onto the direction vector of the line. In this case, since the direction vector of the line is (0, 1, 0), the projection of the vector OP (where O is the origin) onto this direction vector will be 0, as the x-component of the vector OP is 0.

Therefore, the shortest distance between the point P and the line is simply the distance between the point P and the origin, which is equal to the magnitude of vector OP. Since the given point P has a distance of 5 units from the origin, the shortest distance from the point P to the line r = t 0 1 is 5 units.

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(a)  a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .

(B) the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.

In this problem, we are dealing with a population of novelty coins, where 80% of the coins are fair (with a 50% chance of landing heads) and the remaining 20% of the coins have a 75% chance of landing heads. We need to determine the prior distribution for the parameter 0, which represents the probability of heads for a randomly selected coin. The prior distribution can be expressed as a weighted combination of   a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .

Given the sequence of tosses HHHTH from a randomly selected coin, we can use this data to calculate the posterior distribution of 0. The posterior distribution represents the updated probabilities for the parameter 0 after taking into account the observed data. In this case, the posterior distribution will be a combination of the prior distribution and the likelihood of observing the given sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for 0 based on the data and the prior distribution.

To summarize, the prior distribution for the parameter 0 is a weighted combination of the probabilities of heads for fair coins and biased coins in the population. The posterior distribution is obtained by updating the prior distribution with the observed data, reflecting the updated probabilities for 0 based on the sequence of tosses HHHTH.

Now, let's explain the process of determining the posterior distribution of 0. We start with the prior distribution, which is a combination of 0.8 for fair coins and 0.75 for biased coins. After observing the sequence HHHTH, we calculate the likelihood of obtaining this sequence for each possible value of 0, considering the probabilities associated with fair and biased coins. For example, for a fair coin (0.5), the likelihood of observing HHHTH is (0.5)^4 * (1-0.5) = 0.03125, while for a biased coin (0.75), the likelihood is (0.75)^4 * (1-0.75) = 0.0703125.

To obtain the posterior distribution, we multiply the prior distribution by the corresponding likelihoods for each value of 0 and normalize the result to ensure it sums to 1. The normalized values represent the updated probabilities for 0, given the observed data. In this case, the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.

In conclusion, the process of determining the posterior distribution involves updating the prior distribution with the observed data, considering the likelihood of obtaining the sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for the parameter 0, reflecting our updated beliefs about the probability of heads for the randomly selected coin.

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There is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

Given that,

Over 62% of a newsletter publisher's subscribers, in their estimation, own a Rolls-Royce. A potential advertiser wants to verify this claim for marketing purposes. The advertiser decides to reject the null hypothesis following a test with a significance threshold of 0.02 after executing the analysis.

We have to find what is the verdict in relation to the publisher's assertion.

We know that,

First we have to write the null hypothesis and alternative hypothesis for the hypothesis test.

H₀:P=0.62

H₁:P>0.62

At 0.02 level of significance, rejecting H₀ then accepting H₁.

That is sufficient evidence that percentage over 62%.

Therefore, there is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

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Answer:

F(x)>0 over the interval \((-\infty,-4)\)

Step-by-step explanation:

If you pay close attention to the intervals given in the options, you can see that they are talking about the region to the left of either x=-3 or x=-4. The only statements that makes sense is that:

F(x)>0 over the interval \((-\infty,-4)\)

When they say F(x)>0, they mean that the graph is above the x-axis and that will only happen when the x-values that are to the left of x=-4, therefore the answer would be:

F(x)>0 over the interval \((-\infty,-4)\)

The division of 4x³ + 14x² + 13x + 11 by x + 2 will have a quotient of 4x² + 14x + 1 and a remainder of 8 using synthetic division and can be expressed as (4x² + 14x + 1) + 9/(x + 2).

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall divide 4x³ + 14x² + 13x + 11 by x + 2 as follows;

4x³ divided by x equals 4x²

x + 2 multiplied by 4x² equals 4x³ + 8x²

subtract 4x³ + 8x² from 4x³ + 14x² + 13x + 11 will give us 6x² + 13x + 11

6x² divided by x equals 6x

x + 2 multiplied by 6x equals 6x² + 12x

subtract 6x² + 12x from 6x² + 13x + 11 will give us x + 11

x divided by x equals 1

x + 2 multiplied by 1 equals x + 2

subtract x + 2 from x + 11 will give result to a remainder of 9.

Therefore by synthetic division, 4x³ + 14x² + 13x + 11 by x + 2 will result to a quotient of 4x² + 14x + 1 and a remainder of 9.

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