A red-throated loon is a type of diving bird that dives for its food. One particular loon dives for 8 seconds to a depth of 12 feet under the surface of the water. A. Assume the loon dives at a constant rate. Write an equation that can be used to represent the elevation, y, of the loon after x seconds into the dive. B. If the loon is at a depth of 22 feet under the surface of the water, how long was it diving for? Show your work. ​

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.

The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:

t = (P - μ) / (s / √n)

Plugging in the given values:

t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2

Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.

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Answer:

50%

Step-by-step explanation:

(38 / 76) x 100 = 50%.

If you buy an item at $76 with $38 discounts, you will pay $38 and get 50% discount cashback rewards.

The slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

According to the question,

We have the following information:

A line is passing through two points (2,7) and (-4,19).

We know that the slope of the line is denoted by m and the following formula is used to find the slope of the line passing through two points:

m = (y2-y1)/(x2-x1)

(More to know: we can also easily find the equation of the line using the slope given and the points from which the line is passing.)

In this case, we have x1 = 2, y1 = 7, x2 = -4 and y2 = 19.

m = (19-7)/(-4-2)

m = 12/(-6)

m = -2

Hence, the slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.

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The velocity of the object at time t = 2 sec is 46 m/s.

Given, Acceleration function is a(t) = r"(t) = 6t^2+6t+4.

Velocity function is given as v(t) = r'(t) = 2t^3 + 3t^2 + 4t + 10.

We have to find the velocity of the object at time t = 2 sec.

Therefore, substituting t = 2 sec in v(t),

we get:v(2) = 2(2^3) + 3(2^2) + 4(2) + 10= 16 + 12 + 8 + 10= 46

Therefore, the velocity of the object at time t = 2 sec is 46 m/s.

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Answer:

Net change means the differnce between the before result and the after result. You would subtract the numbers, but if you have a gain(the before result smaller than after result) you would do its absolute value. If it's a loss(the before result bigger than after result) you would put a negative behind its absolute value.

e.g. if 2019 had $1 net worth and 2020 had $2 net worth, since 2>1 it would be |2-1| = 1. If 2019 had $2 net worth and 2020 had $1 net worth, since 1<2 there would be a - |2-1| = -1 net change.

However, if there is no change it would be just 0.

Answer:

3 months

Step-by-step explanation:

Without the 5% interest it would take 2 months to pay it off but with the 5% interest added that's going to 5% of whatever the balance is.

After her 1rst payment of 60$ she will have 66$ left to pay: 120(1/20)+6-60

After her 2nd payment of 60$ she will have 9.3$ left to pay: 66(1/20)+ 3.3-60

so basically 2 payments of $60 and one payment of $0.47

Answer:a/b x c/d= a x c/b x d

Show that ac and bd are integers

Step-by-step explanation:

The required result can be proved by showing the numerators and denominators of the product as integers. The correct option is (A).

The given number can be checked for a rational number by first writing it in the form of p/q and then p and q should not have any common factors and q ≠ 0.

The given problem can be solved as follows,

A rational number can be written in the form of a/b where a and b are integers and b ≠ 0.

Now, in order to show the product of two rational numbers a/b and c/d as a rational number the suitable steps can be as follows,

First find the product of numbers as (a × b)/(c × d) = ab/cd.

Then, prove that ab and cd are integers having no common factors.

Hence, the best method to prove the given case is to show that ab and cd are integers.

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Answer:

See below

Step-by-step explanation:

\(d ) (-3x^3) (4xy)(-2x^2y^2),\\3x^3\cdot \:4xy\cdot \:2x^2y^2,\\24x^3x^2xy^2y,\\24yx^6y^2,\\24x^6y^{1+2},\\\\Solution = 24x^6y^3\)

First I removed the ( ) off the " main expression. " Afterwards I multiplied the terms, and through the exponential rule, I added exponents of like terms, simplifying the expression to the solution 24x^6y^3. The rest of these questions are performed in a like manner, so I don't think I need to explain them.

\(e ) (-28a^6 / -7a^5),\\\frac{28a^6}{7a^5},\\\frac{4a^6}{a^5},\\\\4a^{6-5},\\4a,\\\\Solution = 4a\)

____________________________________________

For part f ) can you be a bit more clear on the exponent part. One could say that this expression is ( 8z^3 )( 7z^1 * 1 ) or  ( 8z^3 )( 7z^11 ). You never know, an exponent and a multiplied number can be confused considering that a number next to another is taken to be multiplied. After you confirm the expression I will be happy to change my response!

Here's the solution,

volume :

=》

\( \dfrac{1}{2} \times 12 \times 5 \times 3\)

=》

\(90 \: \: m {}^{3} \)

surface area :

=》

\((13 \times 3) + (5 \times 3) + (12 \times 3) + (2 \times \dfrac{1}{2} \times 12 \times 5)\)

=》

\(39 + 15 + 36 + 60\)

=》

\(150 \: \: {m}^{2} \)

Answer: 50%

Step-by-step explanation:

I'm converting 7kg to grams to make it easier. So £10 = 7000g

£1 = 7000÷10 = 700g

700g÷2 = 350g and if you follow the ratios on top, she payed 50p per 350g

She sells a bag of 350g for 75p.

Percentage profit=\(\frac{Change in cost}{original cost}\) × 100

75p - 50p = 25p = change in cost

Percentage profit= \(\frac{25}{50}\) × 100

= 50%

the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane

the bottom of the ball as its reference point, the y-axis along a vertical line, and the positive direction as pointing upward can be calculated as follows:The y-coordinate of the ball = (y-coordinate of the center of the ball) - (the radius of the ball)As per the given problem, the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane.Hence, the y-coordinate of the ball = 0 - 2= -2Therefore, the y-coordinate of the ball is -2.

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Answer:

Step-by-step explanation:

p-1=5p+3p-8

7=7p

p=1

Answer:

p = 1

Step-by-step explanation:

\(p-1 = 5p + 3p - 8\)

combine like terms on the right side

\(p - 1 = 8p - 8\)

subtract 8p from both sides

\(-7p - 1 = -8\)

add 1 to both sides

\(-7p = -7\)

divide both sides by -7

\(p = 1\)

TRUE. The pressure to increase profitability and improve operational efficiencies is a common driver for organizations to implement new approaches and technology.

The pressure to increase profitability and improve operational efficiencies often drives organizations to implement new approaches and technology. By adopting innovative methods and leveraging technology, companies can streamline processes, reduce costs, and enhance their overall performance, contributing to higher profits and a competitive advantage in the market. The pressure to increase profitability and improve operational efficiencies is a common driver for organizations to implement new approaches and technology. By adopting innovative methods and leveraging technology, companies can streamline processes.

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If Katerina completes a 15-mile run in 2 1/2 hours. She will complete a mile in an average of five minutes. Option B is correct.

It is described as a single number that indicates either the closed value for each entry in the set of data or the mean value for the entire set of data.

It is given that, In 2 1/2 hours, Katerina completes a 15-mile run.

We have to find the average number of minutes it takes her to run 1 mile.

15 miles = 2 1/2 hours

15 miles=5/2 hours

The unitary approach allows us to calculate the value of a single unit and then use that value to calculate the value of the required number of units.

1 miles= 5 /30 hours

1 miles = 1/6 hours

As we know that 1 hour consists of 60 minutes.

1 hours = 60 minute

1 mile = 60 / 6 minutes

1 miles = 10 minute

Thus, the average number of minutes it takes her to run 1 mile will be 10 minutes. Option B is correct.

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Answer:

False

Step-by-step explanation:

Every linear equation in two variables can be written as y=mx+c. 

Here, for each value of x there is a unique value of y. 

Also, x & y are in direct variation.

Hence, xy  will always remain constant.

Consequently, the graph will maintain a definite slope making it a straight line. 

∴ The given statement is false. 

Answer:

False

Step-by-step explanation:

=> y = 2x + 5

=> y - 2x = 5

=> - 2x + y = 5

=> (-2x + y) = 5

=> (-2/5)x + y/5 = 1

=> x/(-5/2) + y/5 = 1, it is in form of x/a + y/b = 1, a is intercept of x.

So, here, x intercept is -5/2.

Method 2;

=> y = 2x + 5

=> y = 2(x + 5/2)

=> y = 2{x - (-5/2)}, says, x intercept is - 5/2 & not - 2/5

A string is wrapped around the edge of a uniform cylinder with a radius of 42 cm and a mass of 5 kg. The cylinder is initially at rest on a frictionless table.

In this scenario, the string wrapped around the cylinder can be used to apply a force and set the cylinder into motion. The tension in the string creates a torque that causes the cylinder to rotate. The key parameters of the cylinder are its radius (r = 42 cm) and mass (m = 5 kg).

To analyze the motion of the cylinder, we can consider the principles of rotational dynamics. The torque exerted on the cylinder is equal to the product of the tension in the string and the radius of the cylinder (τ = T * r). According to Newton's second law for rotation, the torque is also equal to the moment of inertia (I) multiplied by the angular acceleration (α) of the cylinder (τ = I * α).

Since the cylinder is initially at rest, the angular acceleration is zero. Therefore, the torque applied by the tension in the string is also zero. This implies that the tension in the string is zero, and there is no force acting on the cylinder to set it into motion.

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Answer:

25/24

Step-by-step explanation:

multiply first then add

Answer:

See below

Step-by-step explanation:

IN a right triangle , remember  S-O-H-C-A-H-T-O-A   <===memorize this!

sin z = O/H = opposite side/hypotenuse = 16/20

cos z = A/H = adjacent / hy[potenuse = 12/20

tan z  = O/A = 16/12

Answer:

AC = AB + BC = 14 + 6 = 20

    BD = CD + BC = 14 + 6 = 20

Step-by-step explanation:

AB = CD because it was given as true,

BC = BC because of the reflexive postulate,

AB+BC = CD + BC because of the addition postulate.

MANY get very technical and say AB+BC=AC and CD+BC=BD from the partition postulate, and then you can use the substitution postulate to get your final statement AC=BD.

The events are dependent.

Once the teacher selects one song for the recital, there is one less song to choose from, therefore when Bridget chooses a second song, the sample space is modified and the probability to select one particular song is different from the probability of the first event.

Since one event modifies the conditios for the other event, they are dependent.

Answer:

I think Teresa needs 6 tablespoons of butter..

Step-by-step explanation:

Hope this right...but if it's not,im so sorry

The number of nonzero letters that will see Ash and Bea's engraving prices being the same, is  25 letters

The formula for the cost to engrave with Ash, given that the number of letters engraved is x, would be :

= Flat fee + Cost per letter x Number of letters after 21 letters

= 1. 50 + 0. 08 x

The formula for the cost to engrave with Bea, given that the number of letters engraved is x, would be :

= Flat fee + Cost per letter x Number of letters after 15 letters

= 1. 60 + 0. 07 x

Equating these equations together will show the number of letters :

1. 50 + 0. 08 x = 1. 60 + 0. 07 x

0. 08 x - 0. 07 x =  1. 60 - 1. 50

0. 01 x = 1. 10

x = 0. 10 / 0. 01

x = 10 letters

Number of non zero number of letters would be 25 letters :
= 15 + 10

= 25 letters

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Answer:

its 2 it is a medium of exchange

Answer:

B

Step-by-step explanation:

It a medium of exchange

Ignoring mental and emotional health caused people to suffer from psychological problems without understanding their amount of cause or having access to the appropriate treatment. This prevented people from achieving their full potential and overall wellbeing.

For many years, the focus of health was mainly on physical health, and mental and emotional health were largely overlooked. This was a problem because it meant that people who were struggling with psychological issues, such as depression, anxiety, and stress, were not provided with the support and understanding they needed. Without understanding the cause of their distress or having access to appropriate treatment, people were unable to properly cope with their issues and this resulted in them suffering in silence. This had a detrimental effect on people's overall wellbeing, as they were unable to reach their full potential due to the lack of available treatment. Mental and emotional health is now recognised as being an important part of overall health, and there are now many more resources available to people who are struggling.

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Answer:

48 :> I think

Explanation

Answer:

arabella so B

Step-by-step explanation:

plz mark brainlyest

The probability of one who is more likely to brush both time morning and evening is Braxton, he has a 0.61 probability of brushing both times.

Probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

The probability of Braxton brushing both times = (0.72×0.85) = 0.612

The Probability of Arabella brushing both times = (0.82×0.79) = 0.6478

Hence, the probability of one who is more likely to brush both time morning and evening is Braxton, he has a 0.61 probability of brushing both times.

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