Two trees are next to each other in a clearing. The first tree is 13 feet tall and casts an 8-foot shadow. The second tree casts a 33-foot shadow. How tall is the second tree to the nearest tenth of afoot?

Answer:

1:2

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

Answer:

[tex]\textsf{a)} \quad \textsf{Recursive Rule}: \quad a_n=5n-2[/tex]

     [tex]\textsf{Explicit Rule}: \quad \begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]

b)  4998

c)  explicit rule (see below for explanation)

d)  see below

Step-by-step explanation:

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

Explicit Formula

[tex]a_n=a+(n-1)d[/tex]

where:

Given sequence:  3, 8, 13, 18, 23, ...

To find the common difference, subtract one term from the next term.

Therefore:

Substituting the found values of a and d into the formula to create a explicit rule for the given sequence:

[tex]\implies a_n=3+(n-1)5[/tex]

[tex]\implies a_n=3+5n-5[/tex]

[tex]\implies a_n=5n-2[/tex]

Recursive Formula

[tex]a_n=a_{n-1}+d \quad \textsf{for }n\geq 2[/tex]

where:

We already know the common difference our previous calculations.

Therefore:

[tex]\implies a_n=a_{n-1}+5[/tex]

When giving a recursive rule we also have to define the first term of the sequence, as it is not part of the formula.  Therefore, the full recursive rule for the given sequence is:

  [tex]\begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]

To find the 1000th term of the sequence, use the explicit rule and substitute n = 1000:

[tex]\implies a_{1000}=5(1000)-2[/tex]

[tex]\implies a_{1000}=5000-2[/tex]

[tex]\implies a_{1000}=4998[/tex]

Therefore, the 1000th term of the sequence is 4998.

We used the explicit rule to find the 1000th term as this rule allows us to find the nth term of the sequence without having to know any previous terms.

The disadvantage of a recursive rule when compared to an explicit rule is that we need to know the previous term to find the nth term, whereas the explicit rule doesn't need this information.

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A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.

To gauge the strength of the linear link between two variables, correlation coefficients are used.

For a value of correlation coefficient less than zero denotes a negative association, while a value greater than zero denotes a positive relationship.

Zero correlation coefficient means there is no correlation between the two variables under comparison.

A crucial idea in building diversified portfolios that may better resist portfolio volatility is the concept of a negative correlation, often known as an inverse correlation.

Since calculating the correlation coefficient takes time, it is frequently done by entering data into a calculator, computer, or statistics application.

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Answer:

The decimal number 8,500,000 has been converted to its corresponding scientific notation, which is [tex]$8.5 \times 10^{6}$[/tex].

Step-by-step explanation:

Step 1 of 1

Remember that the decimal lies at the end of 8,500,000. Move the decimal next to 8 such that the result is greater than 1 and less than 10 . So the decimal point will move 6 places to the left.

As 8,500,000 is greater than 1 so the power of 10 will have an exponent of 6 .

So,

[tex]$$8,500,000=8.5 \times 10^{6}$$[/tex]

Verifying the result we can see that

[tex]$$10^{6}=1,000,000$$[/tex]

when multiplied by 8.5 will result in 8,500,000.

Answer:

57 yd²

Step-by-step explanation:

See image

If the graph is translated 3 up, reflected across the x-axis, and is narrower than the graph y = x², we have; y = -(x² + 3)

We are given the original equation of the function as;

y = x²

Now, when we translate the graph 3 units upwards, it means we add 3 units to the function to get;

y = x² + 3

Now, when we reflect across the x-axis, it means we just change the sign of the function to get;

y = -(x² + 3)

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Answer:

y = (x - 2)² - 5

Step-by-step explanation:

y = x² - 4x - 1

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 - 1

y = (x - 2)² - 5 ← in vertex form

Answer:12

Step-by-step explanation:(1307.50-812.50)/41.25 = 12

The lacrosse team can bring 12 players to the tournament.

Let's assume the number of players on the lacrosse team is "n."

The total amount raised by the team is $1307.50, and they rented a bus for $812.50. The remaining amount after renting the bus is available for meals.

Amount available for meals = Total amount raised - Bus rental cost

Amount available for meals = $1307.50 - $812.50

Amount available for meals = $495

Now, the budgeted amount per player for meals is $41.25. To find the number of players the team can bring to the tournament, we need to divide the total amount available for meals by the budgeted amount per player:

Number of players = Amount available for meals / Budgeted amount per player

Number of players = $495 / $41.25

Number of players = 12

So, the lacrosse team can bring 12 players to the tournament.

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The degree the tree was leaning is 70 degrees.

Using cosine law,

c² = a² + b² - 2ab cos C

Therefore,

6² = 2² + 5² - 2 × 2 × 5 cos C

36  = 4 + 25  - 20 cos C

36  = 29 - 20 cos C

36  - 29 = - 20 cos C

7 = - 20 cos C

cos C = 7 / - 20

cos C = -0.35

C = cos⁻¹ 0.35

C = 69.5126848853

C = 70 degrees.

Therefore, the degree the tree was leaning is 70 degrees.

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Answer:

Step-by-step explanation:

A woman buys 3 dezen eggs. Later she discovers that x of them are broken. How many mang eggs are not broken

3 = 3

Dozen = 12

x = broken eggs

3 * 12 - x =

36 - x

Part A

If the number is n, then the expression is 7n+6.

Part B

Three times the sum of a number and 8.

The solution of the inequality is x ≥ -3 and the graph is shown below

From the question, we are to determine the graph that represents the given inequality

The given inequality is

−3x + 1 ≤ 10

First, we will solve the inequality

−3x + 1 ≤ 10

Subtract 1 from both sides

−3x +1 -1 ≤ 10 - 1

−3x ≤ 9

Divide both sides by -3 and flip the sign

x ≥ -3

The graph of the inequality is shown below

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The absolute value expression for the given statement is  |10|

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign

Marcus was going up stairs in his office. Therefore, he was ascending .

This means the 10 staircase will be added since there is an increase.

Hence, the absolute value expression for the given statement is as follows:

absolute value = |10|

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The profit percent of supplier is 17.972 %

The given parameters are:

Start by calculating the selling price without VAT

Selling price = Rs 47460 * (1 - 13%)

Evaluate

Selling price = Rs 41290.2

The percentage profit is then calculated as:

Percentage profit = (Selling price - Cost price)/Cost price * 100%

This gives

Percentage profit = (41290.2 - 35000)/35000 * 100%

Evaluate

Percentage profit = 17.972 %

Hence, the profit percent of supplier is 17.972 %

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The likelihood that it contains a letter just after an odd number is 1/2 . D's likelihood of being in the code but not at the first position is 1/4.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

A three-digit code is needed to unlock the lock on a locker. One letter and two numbers are required for the code, and neither a letter nor a number may be repeated.

Four letters, A, B, C, and D, as well as two numerals, 5 and 6, are available for selection.

The sample space has a size of (8, 16, 20, and 24)

If a random code is chosen,

The likelihood that it contains a letter after an odd number (1/8, 1/6, 1/3, 2/5, or 2/3)

= 1/2

If a random code is chosen,

Probability (1/8, 1/6, 1/3, 2/5, 2/3) that D is in the code but not at the first position.

= 1/4

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Answer:

$1265

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here length = 40 and  A = 2800 , then

2800 = 40 × width ( divide both sides by 40 )

70 = width

the perimeter (P) is calculated as

P = 2(length + width) = 2(40 + 70) = 2 × 110 = 220 ft

cost = 220 × $5.75 = $1265

Answer:

$1265

Step-by-step explanation:

area = length × width

area = 2800

length = 40

2800 / 40 = 70

So, the width of the lot is 70ft , and the length is 40

when building a fence, it would surround the entire property's perimeter (which is the length of the outside edges/sides of the shape added together)

so, it would need to cover 70 + 40 + 70 + 40

(the perimeter = 70 + 40 + 70 + 40)

= 220

so, if each foot costs 5.75, we can multiply 220 × 5.75 to find the cost:

220 × 5.75 = 1265

So, this will cost him $1265

hope this helps! have a lovely day :)

The point (6, 4) is the same distance from the y-axis as point G(-6, 4) but on the opposite side of the y-axis

An equation is an expression that shows the relationship between two or more numbers and variables.

Point G on the coordinate plane is at G(-6, 4).

The point (6, 4) is the same distance from the y-axis as point G(-6, 4) but on the opposite side of the y-axis

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The mean of the number of free throws made is 79.9

The standard deviation of throws is 3.46

Karissa is a college basketball player who makes 85% of her free throws. If Karissa takes 94 free throws then,

For binomial distribution B(94,0.85)

n  = no. of throws

P = probability of the success

mean = np

         = 94*0.85

         = 79.9

standard normal = (npq)^0.5

                            = (94*0.85*0.15)^0.5

                            = 3.46

the mean of the number of free throws made is 79.9

and standard devation of trows is 3.46

mean = np

standard deviation = (npq)^0.5

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Answer:

(0, 5)

(1, 6)

(4, 7)

(9, 8)

Step-by-step explanation:

y = √x + 5

y = √0 + 5

= 5

y = √1 + 5

= 6

y = √4 + 5

= 2 + 5

= 7

y = √9 + 5

= 3 + 5

= 8

Step-by-step explanation:

The equation of a parabola that relates it focus is

[tex] {x}^{2} = 4py[/tex]

So here, we isolate x^2.

[tex]y = \frac{1}{32} {x}^{2} [/tex]

[tex]32y = {x}^{2} [/tex]

Next, we factor out 4.

[tex] {x}^{2} = 4(8)(y)[/tex]

Our p=8 so this tells us the distance of the vertex to the focus.

Answer:

[tex](x + 5) ^{2} + {(y - \frac{1}{2}) }^{2} = 1[/tex]

Step-by-step explanation:

the formula of a circle is

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

knowing the values of h, k, and r we can substitute them into the formula

knowing the

Answer:

62.9643082106 degrees

Step-by-step explanation:

First, notice that triangle ABC is a right triangle. This allows us to use SIN, COS, and TAN to find the measure of angle A. Recall SOH CAH TOA, so SIN = OPPOSITE / HYPOTENUSE, COS = ADJACENT / HYPOTENUSE, and TAN = OPPOSITE / ADJACENT.

Looking at angle A, sides c and b correspond to hypotenuse and adjacent respectively. Therefore, we can use COS to set up an equation.

cos(A) = b/c

cos(A) = 5/11

A = arccos(5/11)

A = 62.9643082106 deg

The internet service provider charges 40 cents for each extra hour used.

Also, he provides 40 hours of free service for every account.

Solved using linear equations.

Let the number of free hours provided by the internet service provider be x, and the charge for each extra hour be p cents.

Let the time consumed by Wells, Ted, and Vino be t1, t2, and t3 respectively.

Chargeable time used by Wells = t1 - x.

Cost for Wells = p(t1 - x).

Chargeable time used by Ted = t2 - x.

Cost for Ted = p(t2 - x).

Chargeable time used by Vino = t3 - x.

Cost for Vino = p(t3 - x).

Now, we are given that Wells and Ted, in total used 105 hours, that is, t1 + t2 = 105.

The cost for them together is $10 or 1000 cents.

This can be shown as the linear equation:

p(t1 - x) + p(t2 - x) = 1000.

or, p{(t1 - x) + (t2 - x)} = 1000,

or, p{(t1 + t2) - 2x} = 1000,

or, p(105 - 2x) = 1000,

or, p = 1000/(105 - 2x) ... (i).

Time consumed by Vino is given as 105 hours, thus, t3 = 105.

The total cost to Vino is given as $26 or 2600 cents.

This now can be shown as the linear equation:

p(t3 - x) = 2600,

or, {1000/(105 - 2x)}(105 - x) = 2600 {Substituting t3 = 105, and p = 1000/(105 - 2x)}.

This is the required linear equation in one variable.

It can be solved as follows:

{1000/(105 - 2x)}(105 - x) = 2600,

or, 105000 - 1000x = 273000 - 5200x,

or, 5200x - 1000x = 273000 - 105000,

or, 4200x = 168000,

or, x = 168000/4200 = 40.

Substituting x = 40 in (i), we get:

p = 1000/(105 - 2x),

or, p = 1000/(105 - 2(40)),

or, p = 1000/(105 - 80),

or, p = 1000/25,

or, p = 40.

Thus, the internet service provider charges 40 cents for each extra hour, and he provides 40 hours of free internet on every account.

The provided question is incomplete. The complete question is:

"An Internet service provider allows a certain number of free hours each month and then charges for each additional hour used. Wells, Ted, and Vino each have separate accounts. This month the total hours used by Wells and Ted was 105, and each used all of their free hours. Their total cost was $10. Vino used 105 hours by himself and had to pay $26. What is the number of cents charged for each extra hour?"

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Answer:

30 degrees

Step-by-step explanation:

180-56-90=34

34 rounded off to nearest tenth is 30

Answer:

if x=0 then they have same value

1st and 2nd options are out

for x=-1

g(-1)=1

h(-1)=-1

3rd is true

4th

false

for all values except zero, g(x)>h(x)

correct ones are

ANSWER: g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).

Hence, the missing values are 3 and 2 respectively.

Given the expression: 2x² - x - 6

First, we factor -1 out of -x

2x² - x - 6

2x² -1(x) - 6

Not that, -1 can also be written as 3-4

2x² + (3-4)x - 6

2x² + 3x - 4x - 6

Next, we group the first two terms and the last two terms and factor out the GCF

(2x² + 3x) - 4x - 6

x(2x + 3) - 2( 2x + 3)

Factor out the GFC which is ( 2x+3 )

We have; ( 2x + 3 )( x - 2 )

The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).

Hence, the missing values are 3 and 2 respectively.

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Answer:

y + 6 = [tex]\frac{3}{5}[/tex] (x - 4)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = [tex]\frac{3}{5}[/tex] and (a, b ) = (4, - 6 ) , then

y - (- 6) = [tex]\frac{3}{5}[/tex] (x - 4) , that is

y + 6 = [tex]\frac{3}{5}[/tex] (x - 4)

The statement is " It was said that the circumstance was represented by the fact that the supper meal has 1500 calories."

Generally, the equation for Calories consumed  is  mathematically given as

x = 2/3 of daily calorie

The calories consumed during breakfast and lunch

Cbl=1 - 2/3

Cbl = 1/3

Hence, calories consumed per day

1/3 * cc = 750

cc/3 = 750

cc = 750 * 2

cc= 2250 calories

Calories consumed at dinner

cd= (2250 - (750))

cd= 1500 calories

In conclusion, It was said that the circumstance was represented by the fact that the supper meal has 1500 calories.

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