a lighthouse is 150 feet tall and cast a shadow of 30 feet.Kyle is standing next to a lighthouse and is 6 feet tall. how long is his shadow?

Answer:

C. 16√3π in.

Step-by-step explanation:

Circumference of a circle = 2πr where

r is the radius of the circle.

Given the area of one of the smaller circle to be 48π in², we can get the radius of one of the smaller circle.

If A = πr²

48π = πr²

r² = 48

r = √48 in

The radius of one of the smaller circle is √48.

To get the circumference of the larger circle, we need the radius of the larger circle. The radius R of the larger circle will be equivalent to the diameter (2r) of one of the smaller circle.

R = 2r

R = 2√48 inches

Since C = 2πR

C = 2π(2√48)

C = 4√48π in

C = 4(√16×3)π in

C = 4(4√3)π in

C = 16√3π in

Thw circumference of the larger circle is 16√3π in.

Step-by-step explanation:

Given two circa inscribed side by side inside a big circle, it is notice that the internal two circle are identical and diameter of the one the internal circles is equal to the radius of the big circle

So, we are given the area of one of the small circle, so from their we can find the radius of the small circle.

Area of small circle

A = 48π in²

Area of a circle is given as πr²

A = πr²

48π = πr²

Divide both side by π

48 = r²

Take Square root of both sides

r = √48 = √(16 × 3)

r = 4√3 in

Then, the diameter of the small circle is

d = 2r = 2 × 4√3

d = 8√3

So, the radius of the big circle is

R = d = 8√3

So, we want to find the perimeter of the big circle

The perimeter of a circle is calculated using

Perimeter = 2πr

P = 2πR

P = 2π × 8√3

P = 16π√3 in

So the correct option is C

P = 16√3 π in.

Answer:

$52.50

Step-by-step explanation:

Start with       $50

Add 2% Tip:  $1         (50 x 0.02)

Add 3% Tax: $1.5      (50 x 0.03)

Total:            $52.50

Answer:

52.50

Step-by-step explanation:

Because 3+2=5% and 5% of 50 dollars is 2.50 so 50+2.50 =52.50 dollars he is paying in total

Answer:

39.5

Step-by-step explanation:

If the number to the right of the number your rounding to is equal to or greater than 5 round up

Answer:

39.5

Step-by-step explanation:

Step 1:  Round to the nearest tenth

39.473

Since the hundredths place is greater or equal to 5, we round up the tenth's place.

39.473

39.5

Answer:  39.5

Answer:

B

Step-by-step explanation:

So if she sews along the edge, that means 144 is the perimeter,

The shape is a rectangle, therefore 2 of the sides are 37,

You should add 37 to 37 and that will give you 74

Subtract 74 from 144 to get 70

but we're not done!

The question asked for the length of the quilt, but we only subtracted the length from the total perimeter!

Now you must divide by 2 and you should get 35 inches

Thank me later :)

Answer:

  a, d, g

Step-by-step explanation:

Translation is one of the "rigid motions," along with reflection and rotation. Figures subject to rigid motions are congruent. No angles or segment lengths are changed. Translation is accomplished by adding the same vertical and horizontal offsets to every point of the original figure, effectively sliding the figure to a new location. Every image line segment is parallel to its corresponding pre-image line segment.

__

The statements shown in bold are true of any translation.

Answer:

1,4,7

Step-by-step explanation:

1.) The sides of the image and pre-image are congruent.

4.) The image is a slide of the pre-image.

7.) Each point has moved the same number of units.

got 100

Answer:

58.50

Step-by-step explanation:

First find out how many were vanilla and chocolate

vanilla: 5/6 * 36 = 30

Chocolate = total - vanilla = 36-30 =6

Cost for vanilla = 1.50*30 =45

Cost for chocolate 2.25*6 =13.5

Add the cost together

45+13.50

58.50

Answer:

B. All sides have that same length, would be the correct answer.

Step-by-step explanation:

Answers A,C, and D are all properties for all parallelograms.

Option B, which states that all sides have the same length, is not a property for all parallelograms. It is only true for rhombuses, which are a special type of parallelogram.

Among the options given, the one that is not a property for all parallelograms is:

This statement is not true for all parallelograms; it is a specific property of a subset of parallelograms known as rhombi (singular: rhombus), where all four sides are congruent. However, a general parallelogram only requires opposite sides to be of equal length, not all four sides. To clarify further:

The key distinction here is understanding that while rhombi share all the properties of parallelograms, not all parallelograms are rhombi.

Answer:

The data set shows exponential GROWTH

raynas curve IS NOT a good fit for the data set

Step-by-step explanation:

Believe

Final answer:

With a correlation coefficient of r = 0.274, Rayna's exponential model is not a strong fit, and without the sign of the rate parameter, we cannot determine whether it represents growth or decay.

Explanation:

When Rayna found the curve of best fit for a set of data representing an exponential relationship with a correlation coefficient of r = 0.274, two aspects can be deduced. First, whether the relationship reflects growth or decay, and second whether the model fits well or not. The value of r indicates the strength and direction of the linear relationship between two variables.

In the context of exponential relationships, if the parameter representing the rate of change (often denoted by 'b') is positive, it indicates exponential growth; if the parameter is negative, it signifies exponential decay. Since we do not have the explicit sign of the parameter, we cannot directly conclude whether Rayna's data is demonstrating growth or decay.

The value of the correlation coefficient r = 0.274 is relatively low and thus, Rayna's exponential model is not a strong fit for the data. This is because the value of r is far from 1, and a higher correlation coefficient would suggest a stronger linear relationship between variables.

Answer:

1.89£÷0.7kg=2.7£

To find the price of a whole kg you need to divide the price she paid by the quantity she bought.

Answer:

x = 2.7

Step-by-step explanation:

To find x

1) 1.89 ÷ 0.7 = 2.7

Thankyou

Answer:

95°

Step-by-step explanation:

Answer:

 x = -1/12(y -2)² +5

Step-by-step explanation:

You want the equation of the parabola with focus (2, 2) and directrix x = 8.

The directrix is a vertical line to the right of the focus. This means the parabola opens to the left. The vertex is halfway between the focus and the directrix, so its coordinates are ...

  vertex = ((2 +8)/2, 2) = (5, 2)

The leading coefficient will be negative for a parabola that opens to the left. Its magnitude is 1/(4p), where p is the distance from the focus to the vertex. Here, that distance is 5 -2 = 3, so the leading coefficient is ...

  -1/(4p) = -1/(4·3) = -1/12

In vertex form, the equation of the parabola is ...

  x = a(y -k)² +h . . . . . . . . . . . vertex (h, k); leading coefficient 'a'

  x = -1/12(y -2)² +5

The equation of the parabola is [tex]\( (x-5)^2 = 12y \), with focus (2, 2) and directrix \(x = 8\).[/tex]

The standard equation for a parabola with a vertical axis of symmetry is:

[tex]\[ (x-h)^2 = 4p(y-k) \][/tex]

where (h, k) is the vertex of the parabola and p is the distance between the vertex and the focus (or the vertex and the directrix).

Given that the focus is at (2, 2) and the directrix is at x = 8, we can find the distance between the focus and the vertex, which is p. Since the directrix is a vertical line, the vertex's x-coordinate is the midpoint between the x-coordinate of the focus and the x-coordinate of the directrix:

[tex]\[ h = \frac{{x_f + x_d}}{2} = \frac{{2 + 8}}{2} = 5 \][/tex]

So, the vertex is at (5, k). Since the focus is above the vertex, k > 2.

Now, we find the distance between the focus and the vertex, which is equal to p. The distance formula is:

[tex]\[ p = \sqrt{(x_f - h)^2 + (y_f - k)^2} \]\[ p = \sqrt{(2 - 5)^2 + (2 - k)^2} \]\[ p = \sqrt{9 + (2 - k)^2} \][/tex]

Given that p is the distance from the focus to the vertex, we know that [tex]\(p = 3\).[/tex]

So, the equation of the parabola is:

[tex]\[ (x-5)^2 = 12(y-k) \][/tex]

Now, we need to find the value of k. Since the vertex lies on the parabola, we can substitute the coordinates of the vertex into the equation:

[tex]\[ (5-5)^2 = 12(0-k) \]\[ 0 = -12k \]\[ k = 0 \][/tex]

So, the equation of the parabola is:

[tex]\[ (x-5)^2 = 12y \][/tex]

Answer:

Hey i like your profile pic

Step-by-step explanation:

Answer:

The number of hours it will take before both cars meet is 5 hours

Step-by-step explanation:

Here we have, speed of first car, A = 30 mph

Speed of second car, B = (30 + 20) mph = 50 mph

Therefore, we have

Let the point where both cars meet be X and the time before they meet be Y

Then for car A, 30 × Y = X....................(1)

For car B, 50 × Y = 400 - X..................(2)

From plugging the value of X from equation (1) into equation (2) we have;

50·Y = 400 - 30·Y

80·Y = 400

Y = 5 hours

Therefore the number of hours it will take before both cars meet = 5 hours.

Answer

t = 5 hrs

Step-by-step explanation:

let

speed of the first car = 30 mph

speed of the second car = 20 mph + 30 mph = 50 mph

When the cars meet we know both cars will have traveled a total distance of  400 miles.

Therefore,

let's make a distance equation

speed = distance/time

distance = speed × time

first car + second car = 400 miles

30t + 50t = 400

80t = 400

divide both sides b 80

t = 400/80

t = 5 hrs

Answer:

- 7/2

Step-by-step explanation:

- sqrt(49/4)

We know that sqrt(a/b) = sqrt(a)/ sqrt(b)

- sqrt(49)/sqrt(4)

- 7/2

Answer:

37.68 or 37.7

Step-by-step explanation:

Circumference of a circle: 2πr

2 x 3.14 = 6.28

6.28 x 6 = 37.68 or 3.7

Answer:

no, both lines increase at different angles

Answer:

No

Step-by-step explanation:

Because both of these functions have a constant, different growth, as one grows the other will grow at a slightly different rate, which will constantly change the ratio between their values. Since a proportional growth is one where the ratio between the values stays constant and this is not the case here, this is not a proportional relationship. Hope this helps!

Answer:

a is 0, b is 2

Step-by-step explanation:

Ik its late, but it was pretty ez. Just plug in dem numbers.

a. In the case when r is an odd integer so it should be zero.

b. In the case when r is an even integer so it should be two.

a.. In the case when r is an odd integer

So,

[tex]= (-1)^r + 1[/tex]

= -1 + 1

= 0

b. In the case when r is an even integer

So,

= 1 + 1

= 2

Learn more about an integer here: https://brainly.com/question/18274355

Answer:

x² + 10x + 25

Step-by-step explanation:

Given

(x + 5)(x + 5)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x + 5) + 5(x + 5) ← distribute both parenthesis

= x² + 5x + 5x + 25 ← collect like terms

= x² + 10x + 25 ← in standard form

Answer:

x = 60°

Step-by-step explanation:

[tex] \cos \: (2x + 60) = - 1 \\ \cos \: (2x + 60) = \cos \: 180 \degree \\ 2x + 60 = 180 \degree \\ 2x = 180 \degree - 60 \degree \\ 2x = 120 \\ x = \frac{120}{2} \\ \huge \red{ \boxed{ x = 60 \degree}}[/tex]

Answer:

0.32 meters = 0.32 × 100

32 centimetres

0.32 meters is equivalent to 32 centimetres

Answer:

0.32 meters is a unit of measurement. It is equal to 32 centimeters, 3.2 decimeters, and 0.00032 kilometers. A meter is a unit used to measure length and one meter is around a yard. The width of most doorways is around the length of one meter. Therefore, 0.32 meters is a very small amount.

Answer:

Hawaii is 80 degrees warmer than Dakota.

Step-by-step explanation:

first you have to make the negative a positive by adding 58 degrees to it making it zero then you add the 12 degrees in Hawaii getting 80 degrees.

Answer:

200

Step-by-step explanation:

Given Arithmetic sequence is: 26, 28, 30,...

First term a = 26

Common Difference d = 2

n = 88

[tex] \because t_n=a +(n-1) d \\ \therefore \: t_{88}=26 +(88-1) \times 2 \\ \therefore \: t_{88}=26 +87 \times 2 \\ \therefore \: t_{88}=26 +174 \\ \huge \red{ \boxed{ \therefore \: t_{88}=200}} \\ [/tex]

The 88th term of the arithmetic sequence 26, 28, 30,... is 200.

The given sequence is an arithmetic sequence, where each term is obtained by adding 2 to the previous term. The first term of the sequence is 26, and the common difference is 2.

To find the 88th term of the sequence, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Plugging in the given values: an = 26 + (88 - 1)2 = 26 + 87*2 = 26 + 174 = 200.

https://brainly.com/question/32830972

#SPJ3

We have been given that Jackson purchases a new car for $48,000. The car's value can be modeled by the  following exponential function: [tex]y = 48000(0.76)^t[/tex] where y represents the car's  value and t represents time in years. We are asked to find the decay rate as a percentage.

We know that an exponential decay function is in form [tex]y=a\cdot (1-r)^x[/tex], where,

y = Final value,

a = Initial value,

r = Decay rate in decimal form,

x = time.

Upon comparing our given function [tex]y = 48000(0.76)^t[/tex] with standard decay function  [tex]y=a\cdot (1-r)^x[/tex], we can see that [tex]1-r=0.76[/tex].

Let us solve for r.

[tex]1-1-r=0.76-1[/tex]

[tex]-r=-0.24[/tex]

[tex]r=0.24[/tex]

Let us convert 0.24 into percentage.

[tex]0.24\times 100\%=24\%[/tex]

Therefore, the decay rate is 24%.

Answer:

He has 7 cookies left

Step-by-step explanation:

13-6=7 7+6=13

Answer:

Step-by-step explanation:

The first way you can explain is the simple standard way of subtraction using 13-6=7 or you can count up from 6 to 13 and see how many numbers are found in between.

Answer:

Remove D

Step-by-step explanation:

The sum of the values would go from 0 to 3. Because there are 3 values when you remove one, the avg. of that would be 3/3 = +1

Answer:

$1.54

Step-by-step explanation:

18% of $15.85 is 2.853, so your total is $18.703

20% of $14.30 is 2.86, so their total is $17.16

So the difference is $1.543, rounded (since your dealing with money) would be $1.54

Answer:

The value of given expression is 244.

Step-by-step explanation:

The given expression is [tex]\dfrac{1}{2}\times (734 - 246)[/tex].

We need to simply the above expression.

First of all, we will subtract 246 from 734. By doing so, we get 488.

Now, we can divide 488 by 2.

As a result we get 244.

So, the value of given expression is 244.

The required statement is "[tex]\dfrac{1}{2}[/tex] the difference between 734 and 246".

Important information:

(734-246) is the difference between 734 and 246.

[tex]\dfrac{1}{2}\times (734-246)[/tex] is [tex]\dfrac{1}{2}[/tex] the difference between 734 and 246.

Therefore, the required statement is "[tex]\dfrac{1}{2}[/tex] the difference between 734 and 246".

Find out more about 'Phrase for Expression' here:

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Answer:

Distance between A to C is 16.62km

Step-by-step explanation:

See attached document to get a better illustration of the angle.

A = 83°

B = 53°

C = ?

180° = 83° + 53° + C (sum of angles in a triangle is equal to 180°)

180° = 142° + c

C = 180 - 142

C = 38°

To find the distance AC, we have to use sine rule.

a / sin(A) = b / sin(B) = c / sin(C)

a / sin(A) = c / sin(C)

a /sin83 = 10.31 / sin38

Cross multiply

10.31 * sin83 = a * sin38

10.23 = (0.61566)a

a = 10.23 / 0.61566

a = 16.616 km

a = 16.62km

The distance between A and C is 16.62km

Answer:

one solution

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Since this is a linear system, there can be 1, 0, or infinite solutions. In order to determine this, we need to solve this equation.

First, isolate the variables to one side:

0 = 97x -97

97x = 97

x = 1.

Thus there is one solution.

If we had gotten a statement such as 1 = 1, there would have been infinite.

If we had gotten a statement such as 1 = 0, there would have been no solution.