An animal shelter has 8 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the animal shelter?

The answers to all the parts are given below.

We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.

[A] -

For [x] = 1000ft, we can write -

1000 = -16t² + 1800

16t² = 800

t² = (800/16)

t² = 50

t = 7.07 seconds

[B] -

For [x] = 950ft, we can write -

950 = -16t² + 1800

16t² = 850

t² = 53.125

t² = √(53.125)

t = 7.29 seconds

[C] -

The domain of the function will be -

0 ≤ x ≤ 10

[D] -

The range of the function will be -

0 ≤ h ≤ 1800

Therefore, the answers to all the parts are given above.

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The equation of the line that is normal to the curve y² + ln(x) = 19 at the point (e³, -4) is given as follows:

y + 4 = -8e³(x - e³).

The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:

y - y' = m(x - x').

The derivative of the function is found applying implicit differentiation, as follows:

2y dy/dx + 1/x = 0

dy/dx = -1/(2xy).

At x = e³, y = -4, the numeric value of the derivative is given as follows:

dy/dx = e^(-3)/8.

The normal line is perpendicular to the tangent line, hence it's slope is calculated as follows:

m x e^(-3)/8 = -1.

m = -8e³.

Then the equation of the line normal to the curve at the point is given as follows:

y + 4 = -8e³(x - e³).

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G(1) has a value of 3,The collection of all possible inputs and outputs constitutes a function's domain and range, respectively.

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Answer:

gg

Step-by-step explanation:

Step-by-step explanation:

chances of winning $20=7/20

chances of winning $30=3/20

chances of winning $15=1/2

The quadratic equation will be written as F(x) = -2x² - 4x + 1.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The point from which the quadratic equation passes are,

(0,1), (-1,3), and (-2,1).

The quadratic equation will be written as,

y =ax²+ bx +c

For point (0,1)

1 = 0 + 0 + c

c = 1

For points (-1,3),

3 = a - b + c

3 = a - b + 1

a - b = 2

For point (-2,1),

1 = 4a - 2b + c

1 = 4a - 2b + 1

4a = 2b

b = 2a

calculate the values of a and b,

a - b = 2

a  - 2a = 2

-a = 2

a = -2

b = 2a = 2 x -2 = -4

The quadratic equation will be written as,

F(x) = -2x² - 4x + 1

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Area of composite figure is 48 square feet.

What do you mean by composite figure?

A compound shape or figure is a two-dimensional figure made up of basic two-dimensional shapes such as triangles, rectangles, circles, and semicircles.

To find the perimeter of a compound 2D shape, add the lengths of the sides. Find individual regions for each part of the compound shape. The area of ​​a composite shape is the sum of its individual areas.

Let the given composite figure be divided into four rectangles A,B,C and D having dimension 3 and 4

Area of rectangle A = 3 × 4 = 12

Area of rectangle A = area of rectangle B = area of rectangle C = area of rectangle D = 12 square feet.

Total area = Area of rectangle A + area of rectangle B + area of rectangle C + area of rectangle D = 12 + 12 + 12 + 12 =48 square feet

Therefore, area of composite figure is 48 square feet.

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The amount A in an account to the nearest cent, the amount A in the account after 10 years is $30,441.65.

Generally, To find the amount A in the account after 10 years, we can use the formula for continuous compound interest:

A(t) = A(0) * e^(rt)

where A(t) is the amount in the account after t years, A(0) is the initial amount in the account, r is the interest rate, and t is the number of years.

In this case, we know that A(0) = $15,000, A(8) = $22,377.37, and t = 10 years. We can rearrange the formula to solve for r:

r = (1/t) * ln(A(t)/A(0))

Substituting the known values, we get:

r = (1/10) * ln(22377.37/15000)

Solving this equation, we get r = 0.0658082.

Now that we have the value of r, we can use the formula for continuous compound interest to find the amount A in the account after 10 years:

A(10) = 15000 * e^(0.0658082 * 10)

Solving this equation, we get A(10) = $30,441.65.

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The cost of each apple and each orange will be $2.5 and $1.75, respectively. The cost of 1 apple and 1 orange will be $4.25.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

9 apples and 6 oranges cost $33 and 18 apples and 20 oranges cost $80.

Let 'x' be the cost of each apple and 'y' be the cost of each orange. Then the equations are given as,

9x + 6y = 33               ...1

18x + 20y = 80          ...2

Multiply equation 1 by negative 2, then we have

-18x - 12y = - 66          ...3

Add equations 2 and 3, then we have

20y - 12y = 80 - 66

8y = 14

y = $1.75

Then the cost of each apple is calculated as,

9x + 6(1.75) = 33

9x = 33 - 7.5

9x = 22.5

x = $2.5

The cost of each apple and each orange will be $2.5 and $1.75, respectively.

The cost of 1 apple and 1 orange will be given as,

⇒ $2.5 + $1.75

⇒ $4.25

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Answer:

y=3x^2 - 2x + 5

Step-by-step explanation:

The easiest way to find the answer to this question would be to just plug the different x values into the equations. If you take the equations and plug in x and it gives out the correct f(x) value, then the answer would be correct.

For example, plugging -3 into y=3x^2 - 2x + 5 gives you 10. Plugging in 0 gives 5. Plugging in 2 gives 13.

Answer:

n = 45

m = 135

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

180 - 55 - 80 = 45

m = the sum of 55 + 80

n= 45°;

m= 135.

The sum of all interior angles of a triangle must equa 360°. Hence, the value of n is given by the following expression:

[tex]n+55+80=180\\ \\n=180-55-80\\\\ n=45[/tex]

Since "m" and "n" are opposites angles and, since there's a straight line adjacent to them, the sum of m and n should equal 180 (check the attached image). Find m with the following expression:

[tex]45+m=180\\ \\m=180-45\\ \\m=135.[/tex]

Answer:

[tex]\huge\boxed{\sf Option \ 2}[/tex]

Step-by-step explanation:

Given that,

8 + (n - 4)

According to Associative Property:

Using Associative property for the given expression.

We get:

[tex]\rule[225]{225}{2}[/tex]

The answer to this question is = 12 + n is the expression not equivalent to 8 + (n - 4)

Let us consider any random value of n for example let us take the value of n = 5

As per the original equation given in question 8 + (n - 4) if we substitute the value of n = 5

= 8+ (5 - 4)

= 8+1

= 9

Now we will be substituting the value of n in all the answer options-

Option 1- (8 - 4) + n

= (8 - 4) + 5

= 4 + 5

= 9

Therefore, this answer matches the original equation so this is not the correct option

Option 2- (8 + 4) - n

= (8 + 4) - 5

= 13 - 5

= 9

Therefore, this answer matches the original equation so this is not the correct option

Option 3- n+4

= 5 + 4

= 9

Therefore, this answer matches the original equation so this is not the correct option

Option 4- 12 + n

= 12 + 5

= 17

Therefore, this answer does not match the original equation so the correct option is = 12 + n

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Let (r,q) represent P's polar coordinates, with r being positive and 0 equaling q being pi/2. If so, r = 3m. And A = 0.20136

All points in a plane that are at a specific distance from a specific point, the center, form a circle.
Formula for the first circle: x²+ y² = 9

Formula for the second circle:

center is (0, 7.5) and the radius is 15/2, so

x² + (y - 7.5)² = (7.5)²

Combining these yields:

9 - y² + (y - 7.5)² = (7.5)²

9 - y² + y² - 15y + (7.5)² = 7.5²

9 - 15y = 0

y = 9/15 = 3/5

∴ y = 0.6

x² + y² = 9 = x² + (3/5)²

x² = 9 - (9/25)

x² = [(225 - 9)/25] = 216/25

∴ x = 2.9394

r = √(x² + y²) =

r = √[( 216/25) + (9/25)]

r = √(225/25) = 15/5
∴ r = 3

The x and y values appear to be accurate because this must be the same as the radius of the circle cantered at the origin.

sin(A) = y/r

sin(A) = (3/5)/3 = 1/5

Sin(A) = 0.2

∴ A = 0.20136

COMPLETE QUESTION:

A circle C has center at the origin and radius 4. Another circle K has a diameter with one end at the origin and the other end at the point (0,14). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,q) be the polar coordinates of P, chosen so that r is positive and 0 = q =pi/2. Find r and q.

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[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=4500\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1 \cdot 10}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=4500\left[ \cfrac{(1.04)^{10}-1}{0.04} \right](1.04) \implies A \approx 56188.58[/tex]

so every year you were putting in 4500 bucks, so for 10 years that'd be a total deposits for 4500*10 = 45000, so let's squeeze out the 45000 from the the total, that gives us 56188.58 - 45000 ≈ 11188.58.

so, if we take 56188.58 to be the 100%, what's 11188.58 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 56188.58 & 100\\ 11188.58& x \end{array} \implies \cfrac{56188.58}{11188.58}~~=~~\cfrac{100}{x} \implies 56188.58x=1118858 \\\\\\ x=\cfrac{1118858}{56188.58}\implies x\approx \stackrel{\%}{19.91}[/tex]

Answer:-1.34

Step-by-step explanation:

Answer: You would have to know the number of yards separate from his neighbors yard to get the answer.

Step-by-step explanation:

For example if his yard was 50 yards from his neighbors than you would add that to the width. Length plus width to get your answer.

Answer: Slants upwards.

Step-by-step explanation:

     This is a positive slope, so the line with this given slope will slant upwards. For every increase of one in y, there is a positive change of 2 in x. See attached for a visual example, if the graph was y = ½x.

The amount borrowed is $66,000, the annual interest rate is 4 %, the number of payments per year is 12, the loan term is 20 years, and the payment amount is $10668.39.

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

The total amount paid is,

A = 4800[1 + 0.04/12]^(12 x 20)

A = $10668.39

Hence "The amount borrowed is $66,000, the annual interest rate is 4 %, the number of payments per year is 12, the loan term is 20 years, and the payment amount is $10668.39".

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Answer: 120

Step-by-step explanation:

We can put it in an equation like this:

6 = 5%x

Then, we solve:

6 = 1/20 x

x = 20/1 *6

x=120

Therefore, 5% of 120 is 6.

Answer:

120

Step-by-step explanation:

5/100=6/x

Cross multiply

5x=100(6)

5x=600

/5. /5

x=120

Hopes this helps please mark brainliest

The total years taken to double the money according to Compounding will be 12.5  years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $900

Total amount = $1800

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/1200)^12t

T = A[tex](1+r/1200)^{12t[/tex]

1800 = 900 (1+6/1200)^12t

2 = (1+1/200)^12t

2 = 1.005^12t

taking log on both sides

log 2 = 12t *log 1.005

0.3/0.002 = 12t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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The measure of the side QR is 58.72 if the sides KL=11, NM=17 and OP=38

Having four edges (sides) and four corners, a quadrilateral is a four-sided polygon in geometry (vertices). The term is derived from the Latin terms quadri, a four-letter version, and latus, which means "side." In comparison to other polygons, it is also known as a tetragon. Tetragon is a Greek word that means "four" and "gon" is a word that means "corner" or "angle" (e.g. pentagon). A quadrangle, or 4-angle, is the equivalent term as "gon" denotes "angle." There are four closed sides to a quadrilateral. These shapes below are quadrilaterals: with Raphael, a creation. a four-sided form. One set of parallel sides make up the shape, and there are no right angles.

From the both figures,

KL/NM=OP/QR

11/17=38/QR

QR=(17×38)/11

QR=58.72

Therefore, the measure of the side QR is 58.72 if the sides KL=11, NM=17 and OP=38.

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After 25 years, Sample left will be 100g if nearest hundred...ig...

The equation of the line is y = x - 2.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Key Concept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

We have,

y-intercept(c) = −2 and

the line is equally inclined to the axis i.e., the same angle to the x-axis and y-axis(say)=θ

but the angle between the axes is 90°

2θ = 90° ⇒ θ = 45°

As slope and y-intercept are given.

The equation of a line is y = mx + c

c = -2 and

m = tan45°

as the line is equally inclined to the axes.

c = -2 and m = 1

Hence, the equation of the line is y = x - 2.

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The roots of a quadratic function are the values of x that make the function is 0. These roots can be found by solving the equation f(x) is 0.

A quadratic function is a type of mathematical function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0. This type of function is called a quadratic function because the highest power of x in the function is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve. The shape of the parabola is determined by the value of the constant a. If a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards.

The roots of a quadratic function are the values of x that make the function equal to 0. These roots can be found by solving the equation f(x) = 0. To solve this equation, we can use the quadratic formula, which is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

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What is a NPV  net present value ?

The difference between the current value of cash inflows and withdrawals over a period of time is known as net present value (NPV). To evaluate the profitability of a proposed investment or project, NPV is used in capital budgeting and investment planning.

Using the appropriate discount rate, computations are performed to determine the current value of a stream of future payments, or NPV. Projects that have a positive NPV are generally worthwhile pursuing, whereas those that have a negative NPV are not.

1.

NPV of project A = [tex]-50+\frac{8}{/(1.10)^1} +\frac{8}{(1.10)^2} \frac{8}{(1.10)^3} +\frac{8}{(1.10)^4} +\frac{8}{(1.10)^5} +\frac{8}{(1.10)^6} +\frac{8}{(1.10)^7} +\frac{8}{(1.10)^8} +\frac{8}{(1.10)^9} +\frac{8}{(1.10)^1^0} +\frac{8}{(1.10)^1^1} +\frac{8}{(1.10)^1^2} +\frac{8}{(1.10)^1^3} +\frac{8}{(1.10)^1^4} +\frac{8}{(1.10)^1^5} +\frac{8}{(1.10)^1^6} +\frac{8}{(1.10)^1^7} +\frac{8}{(1.10)^1^8} +\frac{8}{(1.10)^1^9} +\frac{8}{(1.10)^2^0}[/tex]

=$18.11

2.

NPV of project B  = [tex]-15+\frac{3.4}{/(1.10)^1} +\frac{3.4}{(1.10)^2} \frac{3.4}{(1.10)^3} +\frac{3.4}{(1.10)^4} +\frac{3.4}{(1.10)^5} +\frac{3.4}{(1.10)^6} +\frac{3.4}{(1.10)^7} +\frac{3.4}{(1.10)^8} +\frac{3.4}{(1.10)^9} +\frac{3.4}{(1.10)^1^0} +\frac{3.4}{(1.10)^1^1} +\frac{3.4}{(1.10)^1^2} +\frac{3.4}{(1.10)^1^3} +\frac{3.4}{(1.10)^1^4} +\frac{3.4}{(1.10)^1^5} +\frac{3.4}{(1.10)^1^6} +\frac{3.4}{(1.10)^1^7} +\frac{3.4}{(1.10)^1^8} +\frac{3.4}{(1.10)^1^9} +\frac{3.4}{(1.10)^2^0}[/tex]

= $13.95

Use function IRR in excel as = IRR(-50,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8)

= 15.03% is the IRR for A.

Use function IRR in excel as = IRR(-15,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4)

= 22.26% is the IRR for B.

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Present Value of Annuity = $4,000 × 26.1948  = $104779.2

What is a present value?

The worth of an anticipated revenue stream assessed as of the valuation date is known as the present value in the fields of economics and finance.

Here, we have

Where , Annuity Amount = $4,000            

n = No. of periods = 8 years × 4 quarters per year = 32 periods but since the first payment is at beginning of the quarter,

Then, n = 31 when considered for PVAF

r  = 5.4% / 4 quarters = 1.35%,

Present value of Annuity  = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n, r)

PVAF(n₀,r) when the first payment is at beginning of n i.e.

n₀ = 1 + { [1-(1+r)^ -n ]/r }

= 1 + { [1-(1+0.0135)^ {-31}]/0.0135 }

= 1 + [ (1 - 0.65987 ) ] / 0.0135]

= 1 + 25.1948

= 26.1948

PVAF(32,35%) = 26.1948

Hence, Present Value of Annuity = $4,000 × 26.1948  = $104779.2

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The concurrent parts in ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance. They are in alignment with one another when moved. The symbol ≅ used for concurrence.

Here we have,

ABDE is an isosceles trapezoid.  

If we draw two diagonals in a given trapezoid as given picture

Then the diagonal  will divide the trapezoid into 4 triangles

Here ΔAOB, ΔBOD, ΔEOD, and AOE

Here ΔAOB and ΔEOD will be two concurrent triangles

And ΔBOD and AOE will be two concurrent triangles

From ΔAOB and ΔEOD

Side AB ≅ Side ED  

From ΔBOD and AOE

Side AE ≅ Side BD    

Therefore,

The concurrent parts in ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD      

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