A penguin can dive 48 meters below the surface of the water to reach a fish. It dives 2% of the total depth every 1 second.

What is the total depth of the penguin after 4 seconds?

−3.84 meters
−0.96 meters
−1.92 meters
−2.88 meters

pls help

For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5.

(a) To sketch the solution curve for the given slope field, beginning at the point (0, 0) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of y(1) is 0.75 and y(-1) is 0.5.

(b) To sketch the For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5. curve for the given slope field, beginning at the point (0, 4) and following the arrows, draw a curved line that gradually moves from right to left, gradually decreasing in value and then slowly increasing. The estimated value of Y(0.5) is -0.5 and Y(-1) is 0.75.

(c) To sketch the solution curve for the given slope field, beginning at the point (0, -1) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of Y(1) is and y(-1) is -1.5.

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Answer:

See below

Step-by-step explanation:

2x = 10

Divide by 2.

x = 5

x has to equal 5 to make the first statement true.

Proof:

2x = 10

2(5) = 10

10 = 10

-3x = 21

Divide by -3.

x = -7

x has to equal -7 to make the second statement true.

Proof:

-3x = 21

-3(-7) = 21

21 = 21

1/3(x) = 6

Multiply by 3 to cancel the fraction.

x = 18

x has to equal 18 to make the third statement true.

Proof:

1/3(x) = 6

1/3(18) = 6

6 = 6

-1/2(x) = -7

Multiply by -2 to cancel the fraction.

x = 14

x has to equal 14 to make the fourth statement true.

Proof:

-1/2(x) = -7

-1/2(14) = -7

-7 = -7

Answer:

\(\textsf{a)}\quad P(t)=310000(1.0085)^t\)

where P is the population, and t is the number of years after 500 BC.

b)   42,013,000

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}\)

Define the variables:

The population in 500 BC is the initial value (when t = 0), therefore if the population was 310,000 in 500 BC:

If the population increases by 0.85% each year then the growth rate in decimal form is:

Therefore, the function that models the given scenario is:

\(\boxed{P(t)=310000(1.0085)^t}\)

where P is the population, and t is the number of years after 500 BC.

To use the function to calculate the population in 80 AD, first calculate the number of years (value of t):

⇒ 80 AD - 500 BC = 580 years

Therefore, to find the population in 80 AD, substitute t = 580 into the function:

\(\implies P(580)=310000(1.0085)^{580}\)

\(\implies P(580)=42013142.9844236...\)

Therefore, the population in 80 AD is 42,013,000 (to the nearest thousand).

Answer:

DE = 8

Step-by-step explanation:

Since the 3 angles are congruent then the triangle is equilateral with 3 congruent sides , then

5x - 12 = 3x - 4 ( subtract 3x from both sides )

2x - 12 = - 4 ( add 12 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Then

EF = 3x - 4 = 3(4) - 4 = 12 - 4 = 8 , so

DE = EF = 8

9514 1404 393

Answer:

  C(3, -2)

  D(1, 7)

Step-by-step explanation:

It looks like your tool will do the rotation for you and give you the coordinates. The image(s) should look like the attached.

Area of a Triangle = 1/2 X Base X Perpendicular Height

Base = 2x

Perpendicular Height = x+1

Therefore:

The biconditional for the conditional statement is : Two line intersect each other at right angles . The two lines are perpendicular.

A conditional statements are part of mathematical reasoning, a fundamental ability that enables students to evaluate a given hypothesis without reference to a particular context or meaning.

The truth value for the conditional statement is true as we know that when two lines intersect at 90° then they are said to be perpendicular.

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The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

Answer:

The answer will be D

Have a great day :)

Answer: it would be D two of the fourth graders own two pets

Step-by-step explanation: if you look at the graph it is showing how many people own how many pets then look for the one with for and however many stars are there which is two people who own four pets

Hope this helps :)

Answer:

$31.50

Step-by-step explanation:

To solve this problem, create the equation

y = 0.10x + 25

Where x is equal to the number of international minutes and y is equaled to the total price paid. Since we are give the number of international minutes (the x), plug this into the equation and solve for y.

y = 0.10(65) + 25

y = 6.5 + 25

y = 31.5 or $31.50

Answer: Find the missing values in the ratio table. Then write equivalent ratios. PLS help me

Step-by-step explanation:

I cant see the work

Step-by-step explanation:

Since DE is a midsegment, it divides the side AB into two congruent segments. Therefore, we can conclude that angle ADE is congruent to angle BDE. Using this fact and the given angle measures, we can set up an equation and solve for x:

ADE = BDE (since DE is a midsegment)

3x + 7 = 5x - 2 (substitute the given angle measures)

7 = 2x - 2 (subtract 3x from both sides)

9 = 2x (add 2 to both sides)

x = 4.5

Therefore, the solution is x = 4.5.

Answer:

\(6\sqrt{3}\)

Step-by-step explanation:

because of the 90-60-30 theorem

which \(6*\sqrt{3}=6\sqrt{3}\)

Check the picture below.

\(\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{10^2+4^2-7^2}{2(10)(4)}\right)=\measuredangle A \implies \cos^{-1}\left(\cfrac{ 67 }{ 80 }\right)=\measuredangle A \\\\\\ \cos^{-1}(0.8375) = \measuredangle A \implies 33.12^o \approx \measuredangle A\)

Make sure your calculator is in Degree mode.

Answer:

pppppppppppppppppppppppppppppppppppppppppp

Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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Answer:

250

Step-by-step explanation:

Answer:

Its D

Step-by-step explanation:

[-2 -2 5 1 ]

[-5 -5 7 4 ]

[9 -2 2 -1]

Answer:

  (a)  7(x +3.5x) = 56

Step-by-step explanation:

You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.

The morning run is given as x.

The evening run is 3.5 times as long, so is 3.5x

The total mileage each day is (x +3.5x).

In 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:

  7(x +3.5x) = 56

*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

According to the solution we have come to find that, The sum of the given vectors u and v is (1, 0).

In mathematics, a vector is a mathematical object that has both magnitude (or length) and direction. It is usually represented as a directed line segment, where the length of the segment corresponds to the magnitude of the vector, and the direction of the segment represents the direction of the vector.

A vector can be specified in terms of its components or coordinates, which are typically expressed as a sequence of numbers or symbols. For example, a two-dimensional vector can be written as (x, y), where x and y are the components of the vector along the x-axis and y-axis, respectively.

To find the sum of two vectors, we simply add their corresponding components.

So, for the given vectors u = (8, 1) and v = (-7, -1), their sum u + v can be computed as:

u + v = (8, 1) + (-7, -1) = (8 - 7, 1 - 1) = (1, 0)

Therefore, the sum of the given vectors u and v is (1, 0).

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The equation will be

P = 8h

here, P = total pay

h= working hours.

Answer:

Step-by-step explanation:

385

Answer:

\(x > 1\)

if you graph

\(f(x) = x + 1\)

you'll see that it's that part of graph from x=1 to right and x=1 on this graph is not ncluded so it's x>1

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

<95141404393>

Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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Answer:

8 weeks

Step-by-step explanation:

Divide 24 novels into 3 novels per week, 8 * 3 is 24 so it is 8 weeks.

It will take her approximately 8 weeks long to read 24 similar novels .

If a girl reads 3 novels per week, we can determine how long it will take her to read 24 similar novels by dividing 24 by the number of novels she reads in a week .

Number of weeks required = Total number of novels / Number of novels read per week .

Number of weeks required = 24 / 3 weeks .

Number of weeks required = 8 weeks .

Therefore, it will take her approximately 8 weeks to read 24 similar novels .

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