Samra's guardians invested money for her into a 529 college savings plan, which compounds annually. The growth of the savings plan per year, x, can be represented by the exponential function f(x) = 400(1. 02)x. What is the meaning of the y-intercept in the context of the problem?.

Triangle ABC to be isosceles we need to prove that opposite pair of sides of triangle ABC are congruent to each other.

Explanation :

Let us consider a triangle ABC,

To prove : Triangle ABC is an isosceles triangle.

In triangle ADC and triangle ADB,

m ∠CAD ≅ m ∠BAD ( AD bisect angle A )

AD = DA ( common side )

m ∠ADC ≅ m ∠ADB ( each 90° )

By Angle side angle (ASA ) theorem ,

ΔADC ≅ΔADB

By congruence parts congruent triangles :

AC ≅ AB

Therefore, by congruence parts congruent triangles side AC ≅ AB implies ABC is an isosceles triangle.

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Answer:

a.) c(t)=44t+48

b.) the total initial cost of setting up a website and maintaining it for 6 months is $312

Step-by-step explanation:

h

As calculated with the help of Pythagorean theorem, The ladder will reach 19.36 feet high on the building.

What is Pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle. The square whose side is the hypotenuse, or the side across from the right angle, has an area equal to the sum of the areas of the squares on its other two sides. The Pythagorean equation, which connects the lengths of the sides B, P, and the hypotenuse H, can be used to express this theorem.

H² = B² + P²

As given in the question,

the length of the ladder is 20 ft. which will work as a hypotenuse of a right angled triangle,

The base is 5 ft.

we need to find the perpendicular line to the base.

Applying Pythagorean theorem.

H² = B² + P²

20² = 5² + P²

400 = 25 + P²

400 - 25 = P²

P = 19.36 ft.

Therefore, the ladder will go 19.36 ft. high on the building.

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The possible values of k are -0.56, -3.56, -2, and -1.

We have the equation of the parabola, y=0.5(x-3)(x+k)

When we Substitute x=0, we get that y=0.5*(-3) * k  for instance y = -1.5k

So, the y-intercept is (0,-1.5k).

We will now substitute y=0, 0=0.5(x-3)(x+k) for instance  0=0.5(x-3)(x+k) x=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

We can see that 'k' cannot be 0 or -3 since height = 0 if k=0, which is not conceivable. If k = -3, the base is also 0, which is not feasible.

We know that area of a triangle is 1/2*base*height

when we substitute we will get

1.5=1/2*(3+k) *(1.5k)

3=4.5k+1.5k^2

k=-0.56 and k=-3.56

or

1.5=1/2*(-3-k) *(1.5k)

3=-4.5k-1.5k^2

k=-2 and k=-1

hence the possible values of k will be -0.56, -3.56, -2, and -1.

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Your question is incomplete, most probably the full question was:

The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all possible values of k.

The equation of a line passes through (6,1) is 3x - 2y = 16.

Here we have to find the equation of a line.

Data given:

Point = (6,1)

The equation of another line is 2x + 3y = 18

From the given equation we can find the slope;

So we have

3y = -2x + 18

y = -2/3x + 18/3

So the slope is -2/3

As the line is perpendicular, so the slope of the line perpendicular to it will be 3/2

The general formula of the line is:

(y - y1) = m(x-x1)

(x1, y1) is the point

The point is (6,1 ) and the slope is 3/2

Now put that in the equation we get:

(y - 1) = 3/2(x - 6)

2y - 2 = 3x - 18

3x - 2y = 16

Therefore the equation is 3x - 2y = 16.

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Answer:

Step-by-step explanation:

(x+4)(x+5) = 0

x = -4

x = -5

The value of f(g(2)) is output of the function g(2) is in the input of f(x) which

is equal to 1.

When the output of one function is given to the input of another function they are called composite functions.

In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

From the graphs f(x) = -x + 5 and g(x) = x².

Now, f(g(2)) is the output of g(2) is the input of f(x).

g(2) = (2)².

g(2) = 4.

Now, f(g(2)) = -(4) + 5.

f(g(2)) = 1.

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In order to break even,

Total charge for x glasses =  Per day cost

1.25x = 0.6x  + 15

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the number of  glasses of lemonade Jennifer needs to sell each day

Total charge for x glasses = 1.25x

It costs her $0.60 to make each glass of lemonade:

=> For x glasses, cost = 0.6x

Per day cost = 0.6x  + 15

In order to break even,

Total charge for x glasses =  Per day cost

1.25x = 0.6x  + 15

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After solving the given fraction, the resultant fraction is (A) 1 15/21.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

A fraction appears in the numerator or denominator of a complex fraction.

The numerator of a proper fraction is less than the denominator.

So, we have:

2 4/7 * 2/3

Now, solve the fraction as follows:

2 4/7 * 2/3

14+4/7 * 2/3

18/7 * 2/3

36/21

1 15/21

Therefore, after solving the given fraction, the resultant fraction is (A) 1 15/21.

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The answer to this Question based on ages is 20 years and 30 years

What is age?

The age is measure of how old the person is. It also gives us idea about how many years before he was born This data is used at various places in application forms medical form etc

Let age of Tom be x and age of George be y

given 1st condition george is 3 times as old as Tom

hence we can write y = 3x

After 15 years age of tom = x + 15 and age of George be y + 15

according to 2nd condition

x + 15 = 2/3(y + 15)

3x + 45 = 2y + 30

2y - 3x = 15

put y = 3x here

2(3x) - 3x = 15

3x = 15

x = 5

and y = 3(5)

y = 15

present age of tom = 5 years and after 15 years he will be 20 years old

present age of george = 15 tears and after 15 years he will be 30 years old

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The solution to this problem is , we reject null hypothesis  R H0 at  p value =0.005 .

The likelihood of rejecting the null hypothesis when it is true is the significance level, often known as alpha or. A significance level of 0.05, for instance, represents a 5% likelihood of drawing the incorrect conclusion that a difference exists when there isn't one.

Given that Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly.

Persons surveyed = 750

Of those survived no of persons who took multiple vitamin = 296

Sample proportion = p =0.395

q =1-p = 0.605

[tex]H_{0}\\[/tex] : p= 0.35

[tex]H_{A}[/tex] : p ≠ 0.35

(Two tailed test)

Assuming H0 is true standard error = [tex]\sqrt{(0.35 * 0.65)/750}[/tex]

=>0.0174

p difference = 0.045

Test statistic = 0.045/0.0174

=>2.58

p value = 0.005 for right tailed

Reject H0:

Therefore , we reject  R H0 at  p value =0.005 .

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Answer:

Hope this helps you out

Step-by-step explanation:

After 9 weeks, the sunflower would be 39 inches tall.

After w weeks, the sunflower would be 15 + (2 * w) inches tall.

Answer:

A. The y-intercept of the graph of f is at (0, 100).

D. The value of f when x = 5 is less than 1.

E. The value of f is never 0.

The first two statements are not true because the function f is defined by the equation f(x) = 100 • e^-x, where e^-x is the base of the natural logarithm (commonly known as "e") raised to the power of -x. Since e is always greater than 1, the value of e^-x will always be between 0 and 1, so the function f will always decrease as x increases. This means that statements B and C are not true.

Step-by-step explanation:

A confidence interval estimate of the population mean rating for Miami is:

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

Now, According to the question:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

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The complete question is this:

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Required:

Develop a confidence interval estimate of the population mean rating for Miami.

Answer:

79°

Step-by-step explanation:

All three of the angles form a straight line = 180°

28 + x + 73 = 180

x = 79°

Answer:x=79

Step-by-step explanation:

By evaluating the exponential equation for the population:

P(x) = 200*(1.2)^x

We will get:

a) 240 badgers

b) 288 badgers

We know that the number of badgers increases by 20% each year, that increase after x years is given by the exponential equation:

P(x) = A*(1 + 20%/100%)^x

P(x) = A*(1.2)^x

Where A is the initial amount.

Here we know that the initial population of badgers is 200, then we have:

P(x) = 200*(1.2)^x

a) To find the population after one year, we need to evaluate the exponential equation in x = 1, we will get:

P(1) = 200*1.2^1 =240

b) The population after 2 years is:

P(2) = 200*1.2^2 = 288

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The point is on the line that passes through point h and is perpendicular to line fg is  (-6, 10).

You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points.

The slope of the perpendicular lines is negative reciprocals.

So if FG is 3/4, it would be -4/3.

The slope is calculated as m = (y2-y1)/(x2-x1).

So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3

m= (10-(-6)/(-6-6) (-6-6)

m = 16/-12

m= -4/3

As a result, the ultimate answer to this question is A) (-6, 10)

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Answer:

The point is on the line that passes through point h and is perpendicular to line fg is  (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is

Step-by-step explanation:

The point is on the line that passes through point h and is perpendicular to line fg is  (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is

The length of each side of the sign will be 14.81-inch approx.

It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.

           [tex]s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1[/tex]

Also, it is a square. So, the measurement of length from side to side

            [tex]2x+s=36....................Eq.2[/tex]

solving Eq.1 we get,

[tex]s=\sqrt{2} x[/tex]...putting this value in Eq.2,

            [tex]s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }[/tex]

Putting this value of x in Eq.1,

          s = 14.8

Hence, The length of each side of the sign will be 14.81-inch approx.

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Using percentages, we know that 83 students more are needed to vote for the vending machine.

Additionally, "pct," "pct," and occasionally "pc" are used. A % is a number without dimensions and without a standard measurement.

For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

So, 65% of the school population is:

650/100 * 65

422.5

Rounding off: 423

Students voted for vending machines is 340.

A number of more votes/asks for the vending machine  will be:

423 - 340

83

Therefore, using percentages, we know that 83 students more are needed to vote for the vending machine.

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Weight represents the top 10% of the zucchinis is 5.9

The formula for calculating a z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

We're looking for:

Weight is 10% of zucchinis at the top.

Top 10% = 90% of the population

90th percentile Z score is 1.282.

Hence

1.282 = x - 5 / 0.7

1.282 × 0.7 = x - 5

0.8974 = x - 5

x = 5 + 0.8974

x = 5.8974

5.9 ounces, roughly.

The top 10% of the zucchinis have a weight of 5.9 ounces.

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The recursive equation for f( n ) is  f( n-1 ) + 3.75

Any term of a sequence in terms of its preceding terms is a recursive equation. The equation can be defined as a mathematical statement made up of expressions. For example, b (n )  = 2b ( n-1 ) + 4 is a recursive equation.

As per the question,

As we know,

⇒   f ( n )   =   total cost

                =   g × n + c

    f ( n )   =   3.75 ( n ) + 2.55

Replace n with n - 1,

⇒   f ( n - 1 )   =   3.75 ( n - 1 )  +  2.55

⇒   f ( n - 1 )   =   3.75 n  -  3.75  +  2.55

⇒   f ( n - 1 )   =   3.75 n  +  2.55  -  3.75

⇒   f ( n - 1 )   =   f ( n )  -  3.75

⇒   f ( n )   =   f ( n - 1 )  +  3.75

Therefore, f( n-1 ) + 3.75 is the recursive equation for f ( n ).

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The prove the SAS congruence rule,  two sides and one angles between the includes sides of the triangle and the two sides and one angles between the includes sides of the another triangle should be equal

The SAS congruence rule is used to prove the congruence of the one triangle angle and another triangle.

SAS congruence rule stands for the side-angle-side congruence rule of triangles.

Side-angle-side rule of congruence states that if two sides and one angles between the includes sides of the triangle is equal to the two sides and one angles between the includes sides of the another triangle, then the both the triangles are congruent

Therefore, to prove the SAS congruence rule two sides and one angle of both triangle should be equal

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The equation of the parallel to y = 7/8x + 9 will be y = 7/8x+11, 7x - 8y = 3, and (y-6) = 7/8(x-1).

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of the line is y = 7/8x+9. For the equation to be parallel the slope of the line must be the same.

The equations having the same slope of the line as that of y = 7/8x + 9 are,

y = 7/8x+11,

7x - 8y = 3,

(y-6) = 7/8(x-1)

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The cost per month is 39.96, the setup fee is 24.94, and the equations are x  = 39.96  and 6x + y = 264.70.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given data:

A company offers premium cable for 39.96 per month plus a one-time set fee,

The total cost for setup and 6 months I'd 264.70

Write the equation as shown below,

The number of months × price per month + one-time setup fee = total cost

Calculate the equations,

x = number of months, y = setup fees

1 × x + y = 39.96 ⇒ x  = 39.96  (y = 0 for one month)

6 × x + y = 264.70 ⇒ 6x + y = 264.70

Solve the above equation by the elimination method

x = 39.96  and y = 24.94

Therefore, the cost per month is 39.96, the setup fee is 24.94, and the equations are x  = 39.96  and 6x + y = 264.70.

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Answer:

1. 20 minutes (segment A)

2. 40 minutes (segment B)

3. 10 minutes (segment C)

4. 10 minutes (Segment D  minus Segment B)

5. Segments C & E (approaching x axis)

6. Segment A (greatest slope)

7. 115 minutes

The  balloon's vertical distance above the ground is 300.19 feet.

What is angle of depression?

If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.

Given that a balloon make 22° angle with a fixed point. The horizontal distance of the balloon along the ground is 743 feet.

Here need to find the vertical distance.

To find the vertical distance, use tangent of 22°. The tangent of angle is the ratio of vertical distance to horizontal distance.

Therefore,

tan 22° = vertical distance/ horizontal distance

tan 22° = vertical distance/ 743

Multiply both sides by 743:

vertical distance = 743 × tan 22°

vertical distance = 300.191

vertical distance = 300.19 ( rounding to the nearest hundredth)

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Answer:

216.025 I think

Answer: S=237.5 in

Step-by-step explanation:

S=2(5)(6,5)+2(6.5)(7.5)+2(5)(7.5)

S=6,5(10)+97.5+7.5(10)

S=65+97.5+75

S=237,5 in

By reading the graph we can see that k(x) = 80 for x ∈ (5, 6]

Look at the graph and try to identify the line where y = 80, now move to the right until you hit the graph of k(x) (red graph).

Now, move downwards until you intercept the x-axis, that value in the x-axis is the input that gives k(x) = 80.

In this case, there is a set of values.

The open circle means taht the value does not belong to the set.

The closed circle means taht the value does belong to the set.

Then k(x) = 80 for all the values of x in the set:

(5, 6]

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