The height of an arrow shot
into the air can be represented
by the equation
h = -16t² + vt + h0
Where t is time in seconds and h = height in feet
The arrow is shot into the air with an initial
velocity of 112 feet per second by someone
that is holding the bow 5 feet off the ground.
What is the maximum height of the arrow?

The function rule that represents the deer population t years after 2011, assuming a 15% annual growth rate, is d(t) = 100 × 1.15^t

Assuming the deer population started at a baseline value of P0 in 2011, we can use the following formula to calculate the population after t years

d(t) = P0 × (1 + r)^t

Where r is the annual growth rate, expressed as a decimal, and t is the number of years since 2011.

Given that the deer population increases by 15% each year, we can express r as

r = 0.15

And since the baseline population in 2011 is not given, we can use P0 as an arbitrary constant value, such as 100

P0 = 100

Therefore, the function rule that represents the deer population t years after 2011 would be

d(t) = 100 × (1 + 0.15)^t

Simplifying the expression

d(t) = 100 × 1.15^t

This function rule gives us the deer population at any time t years after 2011, assuming the population continues to increase by 15% annually.

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The given question is incomplete, the complete question is:

If the deer population continues to increase by 15% each year, write a function rule d that represents the deer population t years after 2011.

Yes, all rational and irrational numbers have decimal expansions. Rational numbers can be expressed as terminating or repeating decimals, while irrational numbers have non-repeating, non-terminating decimal expansions.

In decimal form, rational numbers have a finite or repeating pattern of digits after the decimal point, while irrational numbers have an infinite, non-repeating pattern of digits after the decimal point. For example, the rational number 1/4 is expressed as 0.25, while the irrational number pi is expressed as 3.14159265358979323846... where the decimal goes on infinitely without repeating. In conclusion, every real number can be represented in decimal form, either as a terminating or repeating decimal, or as a non-repeating, non-terminating decimal.

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Answer:

x=15

Step-by-step explanation:

(2x+60)=6x

2x+60=6x

subtract 2x from both sides

60=4x

divide by 4

15=x

The probability of Thuy rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

We know that:

Thuy rolls a number cube 7 times,

so the total outcomes are: 6.

Also, it is asked to find the probability of rolling a 4 exactly 2 times.

So it could be done by the method that:

1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6,

where 1/6 denotes the probability of rolling a 4 and 5/6 denotes the probability of rolling a number other than 4

therefore we know that, the probability of rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

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Answer:

X = 34, Y=56

Step-by-step explanation:

BOA is an isosceles triangle.

Angle CBO = 90°

Angle DBO = 90 - 56 = 34

Angle ODB = 34° and ODB is x

Angle EBD is also 90°

Y = 180 - (90+34) = 56

The value of x is 34 degree and y is 56 degree.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.

We have, BOA is an isosceles triangle.

< CBO = 90°

So, < DBO = 90 - 56

<DBO = 34

and, <ODB = 34°

Now, let the angle ODB be x

As, from the figure < EBD is also 90°

So, <y = 180 - (90+34)  (Angle sum property)

<y = 56

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Answer: $10,00; $15,00 and $20,00

First, let’s mark the streaming platforms as letters x, y, z:

x - Disney +

y - Netflix

z - Hulu

Each platform costs $540,00 per year, so that would be $540,00/12=$45,00 per month

Since we know that Disney + and Hulu per year cost $300,00 and all three platforms cost $540,00 per year, we can find how much does Netflix cost per year:

$540,00-$300,00 = $240,00

Per month: $240,00/12 = $20,00

Now we can write equations according to the given information:

y = 2x

x+y+z = 540,00

x+z = 300,00

We can find how much does Disney + cost per year from the first equation, since we already know the price of Netflix per year:

2x = 240,00 / : 2

x = 120,00 (per year)

Per month: $120,00/12 = $10,00

And finally, since we know that all three platforms cost $45,00 per month, we can find the price of Hulu per month:

$45,00 - $20,00 - $10,00 = $15,00

So, Netflix costs $20,00 per month, Disney + - $10,00 per month and Hulu - $15,00 per month

Ans :-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ∼

Answer:

15 yards and 2 feet

Step-by-step explanation:

There are 3 feet in a yard

47/3= 15 and R 2

15 yard and 2 feet

The total energy required per week for hot water is 7844.81 BTUs (British thermal units).

Given data:

Kimono takes a 6-minute shower every day.Shower uses about 1.9 gal per minute of water.

Kimono uses 23 gallons of hot water per day for clothes and dishwashers.

Hot water heats the water from 64 to 107 F.

Conversion:1 gallon = 3.785 L1 F = 1.8 K or 5/9 C1 BTU = 1055.06 J (joules)

Firstly, we need to calculate the hot water usage per week:

Hot water usage per day = 23 gallons

Therefore, hot water usage per week = 23 × 7 = 161 gallons

Now, we need to calculate the amount of energy required to heat 1 gallon of water from 64 to 107 F:

Energy required to heat 1 gallon of water = mass of water × specific heat × temperature riseQ = m × Cp × ΔT

Temperature rise (ΔT) = 107 - 64 = 43 F

Specific heat of water = 1 Btu/lb F

So, mass of water = 1 gallon = 3.785 LSo,

mass of water = 3.785 × 8.33 lb = 31.46 lb

Energy required to heat 1 gallon of water from 64 to 107 F is:

Q = m × Cp × ΔTQ = 31.46 × 1 × 43Q = 1350.58 BTUs

Now, we need to calculate the total energy required per week for hot water.

Total hot water energy usage per week = (1350.58 × 161) BTUs

Total hot water energy usage per week = 217782.38 BTUs ≈ 7844.81 BTUs

Hence, the total energy required per week for hot water is 7844.81 BTUs (British thermal units).

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The area of the stained glass is given as 20ft².

Let's start by finding the length of one side of the square stained glass. Since the area of a square is given by the formula A = s^2, where s is the length of one side of the square, we have:

s^2 = A

s^2 = 20ft²

s = sqrt(20)ft

s = 2sqrt(5)ft

Now, we can use the given equation p^2 = 5A to find the perimeter p of the square, by substituting the value of A:

p^2 = 5A

p^2 = 5(20ft²)

p^2 = 100ft²

p = sqrt(100ft²)

p = 10ft

Therefore, the perimeter of the square stained glass is 10 feet.

Answer: Falso. Las razones trigonométricas dependen tanto del tamaño del triángulo como de la medida del ángulo. Esto se debe a que las razones trigonométricas de un triángulo se calculan relacionando los lados del triángulo con el ángulo. Por lo tanto, si cambia el tamaño del triángulo, los lados cambiarán y, por consiguiente, las razones trigonométricas también cambiarán.

Step-by-step explanation:

Answer: -125

Step-by-step explanation:

-5*-5=25

But, because its squared you have to multiply 25 * -5

A negative times a positive is a negative so,

25 * -5 = -125

Hope this helped!

The seventh exam result, based on the provided statement, is 88.

The aggregate of all values split by the total amount of values determines the mean (also known as the arithmetic mean, which differs from the geometric imply) of a dataset. The term "average" is frequently used to describe this gauge of central trend.

To find the 7th test score, we can use the formula for the mean of a set of numbers:

Mean = (sum all the numbers) / (number)

We know that the mean of the 7 test scores is 85, so we can plug in the given values and solve for the missing number:

85 = (75 + 82 + 82 + 83 + 90 + 95 + x) / 7

Multiplying both sides by 7, we get:

595 = 507 + x

Subtracting 507 from both sides, we get:

x = 88

Therefore, the 7th test score is 88.

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By SAS congruency rule both triangles are similar.

What are congruent triangles?

When two triangles can be superimposed, have identical side lengths, and equal angles, they are said to be congruent.

The figures must be the same size and shape or one could mirror the other for them to be congruent, but since they mirror one another and are the same size and shape, they are.

In the given figure according to question:

Therefore, by SAS congruency rule both triangles are similar.

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The distance DE is 338.25m

Similar triangles are triangles that have the same shape, but their sizes may vary. . The ratio of corresponding sides of Similar triangles are equal.

Therefore AB /DE = CB/CE

CE = 80+250

= 330

represent DE by x

82/x = 80/330

330× 82 = 80x

80x = 27060

x = 338.25

Therefore the distance DE is 338.25m

Using cosine rule to find the angle of D

c² = a²+b² +2abcos C

330² = 300²+ 338.25²+2× 300× 338.25cos D

108900 = 90000 + 114413.1 + 202950cosD

202950cos D = 108900-204413.1

202950cos D = -955131

cos D = -955131/202950

cosD = -0.471

D = cos^-1( 0.471)

D = 62° ( nearest degree)

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The flag pole is 6.8 meters tall.

Trigonometric functions are mathematical formulas that connect the angles and side lengths of a right triangle. The six trigonometric functions are sin, cos, tangent, cosec, sec, and cotangent.

Height,p of the flagpole should be calculated.

Given;

base,b=2.9m

Angle subtended=67

Using trigonomteric identity

tan67=Height/base

Tan67=h/b

Tan67=h/2.9

h=2.9tan67

h=6.8m

Height pf the flag pole is 6.8m.

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The complete question is attached below:

By using the complement probability that none of the 6 people prefer brand A paint, the probability that at least 1 person in a sample of 6 prefers brand A paint is 0.9939 or approximately 99.39%.

To find the probability that at least 1 person in the sample of 6 prefers brand A paint, we need to find the probability of the complement event that none of the 6 people prefer brand A paint, and subtract it from 1.

The probability that one person prefers brand A paint is 0.53, and the probability that one person does not prefer brand A paint is 0.47. Since we are dealing with a binomial distribution, we can use the formula for the probability of k successes in n trials:

P(k successes) = n! / (k! * (n - k)!) * p^k * (1 - p)^(n - k)

Using this formula, we can calculate the probability of 0 people preferring brand A paint:

P(0 people prefer brand A) = 6! / (0! * 6!) * 0.53^0 * 0.47^6 = 0.0061

Therefore, the probability of at least 1 person preferring brand A paint is:

P(at least 1 person prefers brand A) = 1 - P(0 people prefer brand A) = 1 - 0.0061 = 0.9939

So, the probability that at least 1 person prefers brand A paint is 0.9939 or approximately 99.39%.

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The expression has basic mathematical operators. is The measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given to us

∠J = (7x + 13)°,

∠K = (83 - 2x)°,

the sum of the two angles is 141°.

As it is given that the sum of the two angles is 141°, therefore, the expression for the sum of the two angles can be written as,

∠J + ∠K = 141°

(7x + 13)° + (83 - 2x)° = 141°

7x + 13 +83 - 2x = 141

5x = 141 - 83 - 13

5x = 45

x = 9

Now, we got the value of x, substitute the value of x in given measurements, therefore,

∠J = (7x + 13)°

∠J = 7(9) + 13

∠J = 63 + 13

∠J = 76°

∠K = (83 - 2x)°

∠K = (83 - 2(9))°

∠K = (83 - 18)°

∠K = 65°

Hence, the measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

Answer:

To determine the cost of the shirt, we can set up an equation using algebra. Let x be the cost of the shirt in dollars. We know that Marissa spent a total of 45 on the hat and the shirt, and the hat cost 10. Therefore, we can write the equation:

x + 10 = 45

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 10 from both sides:

x = 35

Thus, the cost of the shirt is $35.

Step-by-step explanation:

c = y axis intercept  =  6   ( from the graph)

slope = rise/run = 6/3 = 2  ( using points  (-3,0) and  (0,6)  )

then

y =  2x + 6

Answer:

3a⁴bc-3a²4b²c²-3a²bc³

Step-by-step explanation:

remove brackets by multiplying by the numbers out the brackets.As they are no like terms that is where we end our answers

The points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16) and The slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(a) To find where the tangent line is horizontal, we need to find values of t where the derivative of y with respect to x (dy/dx) is equal to 0.

We have:

dy/dx = (dy/dt)/(dx/dt) = (5t^4 - 5)/(12t^2 - 3)

Setting dy/dx = 0, we get:

5t^4 - 5 = 0

t^4 = 1

t = ±1 or t = ±i

Substituting t = 1 into the parametric equations gives us the point (1,-4). Substituting t = -1 gives us the point (-1,4). Substituting t = i or t = -i gives us points on the imaginary axis, which are not part of the real plane.

Therefore, the points where the tangent line is horizontal are (1,-4) and (-1,4).

To find where the tangent line is vertical, we need to find values of t where dx/dt is equal to 0.

We have:

dx/dt = 12t^2 - 3

Setting dx/dt = 0, we get:

t^2 = 1/4

t = ±1/2

Substituting t = 1/2 into the parametric equations gives us the point (13/16, -5/16). Substituting t = -1/2 gives us the point (-13/16, 5/16).

Therefore, the points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16).

(b) To determine the intervals where the slope of the tangent line is positive or negative, we need to examine the sign of the derivative dy/dx.

From part (a), we know that dy/dx is equal to:

dy/dx = (5t^4 - 5)/(12t^2 - 3)

The denominator is always positive, so the sign of dy/dx is determined by the numerator.

For t < -1, we have 5t^4 - 5 > 0, so dy/dx > 0.

For -1 < t < 1, we have 5t^4 - 5 < 0, so dy/dx < 0.

For t > 1, we have 5t^4 - 5 > 0, so dy/dx > 0.

Therefore, the slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(c) To determine the intervals where the curve is concave upward or downward, we need to examine the sign of the second derivative d^2y/dx^2.

We have:

d^2y/dx^2 = ((d^2y/dt^2)(dx/dt) - (dy/dt)(d^2x/dt^2)) / (dx/dt)^3

Calculating the second derivatives, we get:

d^2y/dt^2 = 20t^3

d^2x/dt^2 = 24t

Substituting these into the expression for d^2y/dx^2, we get:

d^2y/dx^2 = (20t^3)(12t^2 - 3) - (5t^4 - 5)(24t) / (12t^2 - 3)^3

Simplifying this expression, we get:

d^2

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Answer:

-0.5x^2 - 5x - 0.8

Step-by-step explanation:

The 2 zeroes of the function are at x = -8 and x = -2 so we can write the quadratic as

y = a(x + 2)(x + 8)   where a is a value to be found.

When x = -6, y = 4 so:

4 = a(-6+2)(-6 + 8)

4 = -8a

a = -0.5

The function is:

-0.5(x + 2)(x + 8)

= -0.5(x^2 + 10x + 16)

= -0.5x^2 - 5x - 0.8

Answer:

( 4x + 3 ) ( x + 3 )

Step-by-step explanation:

9 × 4 = 36

Factors of 36 = { 1, 2, 3, 4, 6, 9, 12, 18, 36 }

3 and 12 add up to 15

4x² + 15x + 9

4x² + 3x + 12x + 9

( 4x² + 3x ) + ( 12x + 9 )

x (4x + 3) + 3 ( 4x + 3 )

( 4x + 3 ) ( x + 3 )

there are 200 green balloons,  there are 120 red balloons ,  there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits.  To solve this problem, we need to use the given ratio and the total number of balloons to find the number of green balloons.

Let's assume the number of green balloons is x. Then, the number of red balloons is 3/5 of x, or (3/5)x.

The total number of balloons is 320, so we can write an equation based on the given information:

x + (3/5)x = 320

To solve for x, we can simplify the equation:

(8/5)x = 320

x = 200

Therefore, there are 200 green balloons.

To check our answer, we can use the ratio given in the problem:

(3/5)x = (3/5) * 200 = 120

So there are 120 red balloons.

Let's assume the number of bananas is x. According to the given ratio, the number of apples is twice that of bananas, or 2x.

The total number of fruits in the bowl is 15, so we can write an equation based on the given information:

x + 2x = 15

To solve for x, we can simplify the equation:

3x = 15

x = 5

Therefore, there are 5 bananas in the bowl.

To find the number of apples, we can use the ratio given in the problem:

2x = 2 * 5 = 10

So there are 10 apples in the bowl.

To check our answer, we can verify that the ratio of apples to bananas is 2:1:

10/5 = 2

Therefore, there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits.

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The surface area of right triangular prism of height 3 in, base 8 in, slop 5 in and  width 4 in is 76  in².

Surface area is a measure of the total area occupied by the surfaces of a three-dimensional object. 

It is the sum of the areas of all the faces, including the base(s), of the object.

The units for measuring surface area are squared units, such as square meters or square inches.

To find the surface area of a right triangular prism, we need to add the areas of all of its faces.The prism has two congruent triangular faces and three rectangular faces.

The area of ​​every single triangle face is (1/2)bh, where b is the base of the triangle and h is its height.

In this case, the base is 8 in and the height is 5 in, so the area of each triangular face is (1/2)(8)(5) = 20  inches². Since there are two triangular faces, their combined area is 2(20) = 40 inches².

The area of ​​each rectangular face is lw.

In this case, the width is 4 in and the height is 3 in, so the area of each rectangular face is (4)(3) = 12 inches². Since there are three rectangular faces, their combined area is 3(12) = 36 inches²

Therefore, the total surface area of the right triangular prism is the sum of the areas of all its faces:

Surface area = 2(triangular face area) + 3(rectangular face area)

Surface area = 2(20) + 3(12)

Surface area = 40 + 36

Surface area = 76 inches²

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Therefore, the sum of the numbers between 1 and 5,000 that have exactly 8 factors is 4,007,146.

In mathematics, a factor of a given integer is a positive integer that divides the integer evenly without leaving a remainder. In general, an integer n can have many factors, and they can be found by dividing n by all positive integers less than or equal to the square root of n, and checking if each of these divisors divides n evenly. The concept of factors is important in many areas of mathematics, including number theory, algebra, and geometry, and is used in various contexts, such as prime factorization, greatest common divisors, and divisibility tests.

Here,

To find the sum of the numbers between 1 and 5,000 that have exactly 8 factors, we need to identify all the integers in that range that have exactly 8 factors. Then we can add them up to find the final answer.

Now let's focus on finding the integers between 1 and 5,000 that have exactly 8 factors. Since 8 can be expressed as 2 x 2 x 2, we know that the prime factorization of such integers must take the form p² x q², where p and q are distinct primes. Moreover, since p and q are distinct, we can assume without loss of generality that p < q. Therefore, we can iterate over all pairs of distinct primes (p, q) such that p² x q² is less than or equal to 5,000, and add up all such integers.

The get_primes function implements the Sieve of Eratosthenes algorithm to generate a list of all primes less than or equal to the square root of 5,000 (rounded up to the nearest integer). The main loop then iterates over all pairs of distinct primes in this list, calculates their product squared, and adds it to the sum s if it is less than or equal to 5,000.

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To have a margin of error within 4% at a 99% confidence level, a sample size of at least 469 graduates is needed for the administrator's analysis of the proportion of graduates who have not found employment in their major field one year after graduation.

To determine the sample size needed for the administrator's analysis, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

where:

n = sample size needed

Z = the Z-score corresponding to the desired confidence level (99% corresponds to a Z-score of approximately 2.576)

p = the expected proportion of graduates who have not found employment in their major field (13%, or 0.13)

E = the desired margin of error (4%, or 0.04)

Substituting the given values into the formula, we get:

n = (2.576^2 * 0.13 * (1 - 0.13)) / 0.04^2

Simplifying and solving for n, we get:

n ≈ 468.42

Rounding up to the nearest whole number, we get:

n = 469

Therefore, a sample size of at least 469 graduates is needed for the administrator's analysis to have a margin of error within 4% at a 99% confidence level.

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