Please help with this! Thanks!

B: measure of BCD=45; acute
C: measure of BCD=90; right
D: measure of BCD=42; acute
E: measure of BCD=17; acute

Area of triangle = 1/2 base x height

15.588 = 1/2 * base x 5.196

15.588 = base x 2.598

base = 15.588 / 2.598 = 6

 equi center of triangle = 1/3*5.196 = 1.732

radius of circle = Sqrt(1.732^2 + 3^2) =

 sqrt (2.999824 +9) =

sqrt(11.999824) = 3.464

rounded to nearest tenth = 3.5 inches

The radius of the circle required to inscribe an equilateral triangle with the given dimensions is; radius = 3.5 inches

Usually, when we inscribe an equilateral triangle in a circle, the distance from the centroid of that triangle to one of the vertices is;

Centroid distance to vertex = ²/₃h

Where h is the altitude of the triangle.

We are given altitude = 5.196 in

Thus;

Centroid distance to vertex = ²/₃(5.196)

⇒ 3.464 inches

Approximating to the nearest tenth gives;

Centroid distance to vertex = 3.5 inches

Now, the distance from centroid to vertex of the inscribed equilateral triangle is also the radius of the circle.

Thus; radius = 3.5 inches

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Humans can hear up to 20,000 Hz, written as 2.0 x 10⁴ Hz in scientific notation, while dolphins can hear up to 150,000 Hz, written as 1.5 x 10⁵ Hz.

Humans can hear sounds with frequencies up to 20,000 Hz, while dolphins can hear sounds as high as 150,000 Hz. These numbers can be written in scientific notation as follows:

20,000 Hz = 2.0 x 10⁴ Hz

150,000 Hz = 1.5 x 10⁵ Hz

Writing these frequencies in scientific notation helps simplify and understand large numbers easily.

If the length of a rectangle is 6 ft greater than the width and the perimeter is 40 ft , then the dimensions of the rectangle will be 6ft x 7ft.

What is the Area of Rectangle?

The area of the rectangle is length times of width.

Let the Length and Width of the rectangle be 'L' and 'B' , then the dimensions of the rectangle will be L x B

Given data , we have L = 6 + B

The perimeter of the rectangle = 40 ft

= 2 x ( L + B ) = 40 ft

= 2 x ( 6 + B + B ) = 40 ft  

= ( 6 + 2B ) =  20 ft

Substract both sides by 6

2B = 14 ft

Divide both sides by 2

B = 7 ft

Now , Length of the rectangle will be L = 6 + 7 = 13 ft

Hence, the dimensions of the rectangle is Length x Width = 13 ft x 7 ft

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Answer:

3x + 8

Step-by-step explanation:

We have to find the sum of (x+5)and(2x+3).

Write it in sum form

x+5+2x+3

Group the like terms first.

(x+2x)+(5+3)

Combine the like terms

(1+2)x+8

= 3x +8

Therefore, the sum is 3x + 8

The sum of (x+5) and (2x+3) is calculated by adding the coefficients of like terms, which results in 3x + 8.

To find the sum of (x+5) and (2x+3), you simply need to add the like terms. The first step is to add the terms that contain the variable x, and then add the constant terms.

Step 1: Add the x terms together: x + 2x = 3x.

Step 2: Add the constant terms together: 5 + 3 = 8.

Step 3: Combine the results from step 1 and step 2 to get the final sum: 3x + 8.

Therefore, the sum of (x+5) and (2x+3) is 3x + 8.

A) In standard form, the length of time the light is on is [tex]2.67 \times 10^{-2} \text{ seconds}[/tex]

B) As a decimal, the length of time the light is on is [tex]0.0267 \text{ seconds}[/tex]

Step 1: Understanding the conversion

Step 2: Converting microseconds to seconds

First, let's calculate the time in seconds as a decimal:
[tex]26700 \times 10^{-6} = 0.0267[/tex]

Step 3: Converting seconds to standard form

Standard form (also known as scientific notation) expresses numbers as a product of a number between 1 and 10 and a power of 10.

Here, [tex]0.0267[/tex] can be written as:
[tex]2.67 \times 10^{-2}[/tex]

since gecko is 1/ the length of an iguana,

 that would mean iguanas are twice as long as geckos

 so 4*2 = 8 inches for iguanas 

Lorraine earned $2970 in simple interest over the 9 years.

We can use the formula for simple interest, which is:

[tex]\[ I = P \times r \times t \][/tex]

where:

[tex]\( I \)[/tex] is the interest earned,

[tex]\( P \)[/tex] is the principal amount (the initial amount of money),

[tex]\( r \)[/tex] is the annual interest rate (in decimal form), and

[tex]\( t \)[/tex] is the time the money is invested for, in years.

Given:

[tex]\( P = \$5500 \)[/tex] (the principal amount),

[tex]\( r = 6\% \)[/tex] per year (which we convert to a decimal by dividing by 100.

[tex]\( r = 0.06 \)[/tex]

[tex]\( t = 9 \)[/tex] years (the time period).

Now, we can calculate the simple interest:

[tex]\[ I = \$5500 \times 0.06 \times 9 \][/tex]

[tex]\[ I = \$5500 \times 0.54 \][/tex]

[tex]\[ I = \$2970 \][/tex]

Answer: After 24 minutes Chris begins riding so, he catch up to Samir.

Step-by-step explanation:

Since we have given that

Speed of Samir riding his bike = 6mph

Speed of Chris riding his bike = 9 mph

Time taken by Chris be x

Time taken by Samir be x+12

AS we have given that at any given time ,t, the distance traveled can be using the formula " d=rt "

where d means distance and r represents rate.

So, our equation becomes,

[tex]9x=6(x+12)\\\\9x=6x+72\\\\9x-6x=72\\\\3x=72\\\\x=\frac{72}{3}=24\ minutes[/tex]

As there is no need to change mph into miles per minutes as applying both will nullify the effect.

Hence, after 24 minutes Chris begins riding so, he catch up to Samir.

Two or more expressions with an Equal sign is called as Equation. The number is 16 in sentence one-half of the number is 2 less than two-thirds of the number

Two or more expressions with an Equal sign is called as Equation.

We x be the unknown number which we have to find.

Given,

one-half of the number is 2 less than two-thirds of the number

Which is one-half of the number is x/2

2 less than two-thirds of the number is 2/3 x-2

So let us form a equation

x/2 = 2x/3-2

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

Apply cross multiplication

3x=2(2x-6)

Use distributive law on RHS

3x=4x-16

16=4x-3x

16=x

Hence the number is 16 in sentence one-half of the number is 2 less than two-thirds of the number

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The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

We have been given a equation as

1/r = 1/r1 + 1/r2

Let r1 = x and r2 = y for an instance, then solve for equivalent r.

Therefore,

1/r = 1/x + 1/y

Solving further;

1/r = (y + x)/xy

Or

r = xy/(x +y)

Now substitute the real values of x and y, we get;

r = xy/(x +y)

r = r1 r2/(r1 + r2)

Hence, The solution of an equation 1/r =1/r1+1/r2 for R is r = r1 r2/(r1 + r2).

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The surface area to volume ratio for a cube with sides of 5 cm can be calculated using the formulas for surface area and volume of a cube. After calculating, the ratio is found to be 1.2 cm^-1.

The concept you're asking about relates to both geometry and biology, particularly cell biology. The surface area to volume ratio is important in determining how substances move in and out of cells.

To calculate the surface area and volume of a cube with sides measuring 5 cm, we use these two formulas:

Substituting 5 cm into these formulas, we get:

Finally, to get the surface area to volume ratio, divide the surface area by the volume:

So, the surface area to volume ratio for a cube with sides of 5 cm is 1.2 cm^-1.

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Answer:

420

Step-by-step explanation:

400 - 20 = 380 + 40 = 420 ÷ 2 = 210 + 210 = 420.

Hey there!

400 - 20 + 40 ÷ 2 + 210

400 - 20 = 380

380 + 40 ÷ 2 + 210

40 ÷ 2 = 20

380 + 20 + 210

380 + 20 = 400

400 + 210 = 610

Answer: 610 ✅

Good luck on your assignment and enjoy your day!

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The angle is 14 times its complement, resulting in one angle being 84 degrees and its complement being 6 degrees, following the principle that complementary angles sum up to 90 degrees.

The question mentions that the measure of an angle is 1414 times the measure of its complement. However, this seems to be a typo, and the correct interpretation might be that the angle is 14 times the measure of its complement. First, let's clarify that complementary angles sum up to 90 degrees. If we call the angle A and its complement C, then A = 14C. Knowing that A + C = 90, we can substitute the first equation into this to find C.

To find the measure of the angles, let's denote the measure of one angle as x and the measure of its complement as 90 - x (complementary angles add up to 90 degrees).

Given that x = 14 times the measure of its complement, we can set up the equation x = 14(90 - x) to solve for x. By solving this equation, we find that x = 70 degrees and 90 - x = 20 degrees. Therefore, the measure of the angle is 70 degrees and the measure of its complement is 20 degrees.

Therefore, A + C = 90 becomes 14C + C = 90, simplifying to 15C = 90. Solving for C gives C = 90 / 15, which equals 6 degrees. Subsequently, A, being 14 times C, is 14 * 6 = 84 degrees. Thus, the two angles are 84 degrees and 6 degrees.

Size is a continuous variable that can take on any value within a finite or infinite interval. Screen type is a qualitative variable that describes a characteristic of the data. Number of channels available is a discrete variable because it can only take on countable, distinct values.

In statistics, variables can be classified into different types. Size would be a continuous variable because it can take on any value within a finite or infinite interval. For example, the size of a TV screen can be 32.1 inches, 32.2 inches, 32.25 inches, and so on. On the other hand, screen type would be a qualitative variable because it describes a quality or characteristic of the data, such as LED, LCD, or Plasma. Finally, number of channels available is a discrete variable because it can only take on countable, distinct values. For instance, you could have 200, 300, or 400 channels, but not 300.5 channels.

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An array can be utilized to represent the multiplication of two numbers in Mathematics. In this representation, the number 12 can be depicted by a 3x4 or 2x6 arrays. There can be various arrays to represent a number such as 12.

In mathematics, specifically in multiplication, arrays are often used to represent and visualize the multiplication of two numbers. The number 12 can be represented by an array in multiple ways, here we will use two ways:

Remember, for any number, there can be multiple arrays that represent it. For the number 12, for instance, other arrays such as 1 row by 12 columns (1x12) or 12 rows by 1 column (12x1) are possible as well.

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31 people came last year, I know this because I removed 15 from 46 which equals to 31. This can be done in many ways either by subtraction or by finding the value of x. So, we all know that 31+x = 46 to find the value of x we have to add 15. So, 31+15 = 46 therefore the answer is 31 people came last year.

Hope this helps!

The y - intercept of the line is 0.

We have f(x) = 3x

We have to find the y - intercept of this function f(x).

The general equation of a straight line is as follows -

y = mx + c

where -

m - slope of line

c - intercept of line on y - axis.

According to question, we have -

f(x) = 3x

or

f(x) = 3x + 0

Comparing it with the general equation of a straight line, we get -

y = f(x)

m = 3

c = 0

Here, c is the y - intercept of the line f(x) = 3x.

Hence, the y - intercept of the line is 0.

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Using normal approximation: mean = 50,000, standard deviation = 500. Calculate Z-scores, find probabilities, and subtract. Result ≈ 0.3108.

To find the probability of getting between 49,800 and 50,200 heads when a fair coin is tossed 100,000 times, we can use the normal approximation to the binomial distribution since the number of trials is large.

The mean (μ) of a binomial distribution is given by n*p, where n is the number of trials and p is the probability of success (getting heads for a fair coin). In this case, n = 100,000 and p = 0.5, so μ = 100,000 * 0.5 = 50,000.

The standard deviation (σ) of a binomial distribution is given by sqrt(n*p*(1-p)). For this problem, σ = sqrt(100,000 * 0.5 * 0.5) = sqrt(25,000) = 500.

Now, we can use the normal distribution to approximate the probability of getting between 49,800 and 50,200 heads:

Z1 = (49,800 - μ) / σ = (49,800 - 50,000) / 500 = -0.4

Z2 = (50,200 - μ) / σ = (50,200 - 50,000) / 500 = 0.4

Now, we look up the corresponding probabilities for Z1 and Z2 in the standard normal distribution table (or use a calculator):

P(Z < -0.4) ≈ 0.3446

P(Z < 0.4) ≈ 0.6554

So, the probability of getting between 49,800 and 50,200 heads is approximately P(49,800 ≤ X ≤ 50,200) = P(-0.4 ≤ Z ≤ 0.4) = P(Z < 0.4) - P(Z < -0.4) ≈ 0.6554 - 0.3446 ≈ 0.3108.

Therefore, the probability is approximately 0.3108.