The rectangular room shown 20 feet long, 48 feet wide, and 10 feet tall. Use the Pythagorean Theorem to find the distance from B to C and the distance from A to B . Round to the nearest tenth, if necessary.

Edwin deposited $159.72 into the savings account.

Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is usually expressed as an annual percentage rate, interest expense or revenue is frequently expressed as a dollar amount.(APR).

We can use the formula for simple interest to solve this problem:

simple interest = principal x rate x time

Where:

We know the rate is 2.4% per year, which is equivalent to 0.024 as a decimal. We also know the time is 6 years, and the interest earned is $23. We can plug these values into the formula and solve for the principal:

23 = principal x 0.024 x 6

Simplifying:

23 = 0.144 x principal

Dividing both sides by 0.144:

principal = 23 ÷ 0.144

principal = $159.72 (rounded to the nearest cent)

Therefore, Edwin deposited $159.72 into the savings account.

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Answer:

To prove that ∆ABC=8 ∆EFG, we need to use the concept of similarity of triangles and the ratio of their corresponding sides.

Given that ∆ABC and ∆EFG are similar triangles, we can write:

AB/EF = BC/FG = AC/EG = k (a constant)

Let's assume that AB = x, BC = y, and AC = z. Similarly, let EF = p, FG = q, and EG = r.

From the given information, we can write:

EF = AB/2 (since E is the midpoint of AB)

FG = BC/2 (since F is the midpoint of BC)

EG = AC/2 (since G is the midpoint of AC)

Substituting these values in the above equation, we get:

x/p = y/q = z/r = k

Now, let's consider the area of the triangles.

Area of ∆ABC = (1/2) * AB * BC * sin(∠BAC)

Area of ∆EFG = (1/2) * EF * FG * sin(∠EFG)

Using the values we have assumed earlier, we get:

Area of ∆ABC = (1/2) * x * y * sin(∠BAC)

Area of ∆EFG = (1/2) * (x/2) * (y/2) * sin(∠EFG)

Simplifying these expressions, we get:

Area of ∆ABC = (xy/2) * sin(∠BAC)

Area of ∆EFG = (xy/8) * sin(∠EFG)

Now, since the triangles are similar, their corresponding angles are equal. Therefore,

sin(∠BAC) / sin(∠EFG) = z/r

Substituting the value of k from earlier, we get:

sin(∠BAC) / sin(∠EFG) = 2k

Solving for sin(∠EFG), we get:

sin(∠EFG) = sin(∠BAC) / (2k)

Substituting this value in the expression for the area of ∆EFG, we get:

Area of ∆EFG = (xy/8) * (sin(∠BAC) / (2k))

Area of ∆EFG = (xy/16) * sin(∠BAC)

Now, substituting the value of the area of ∆ABC in this expression, we get:

Area of ∆EFG = (1/2) * Area of ∆ABC * (1/8)

Area of ∆EFG = (1/16) * Area of ∆ABC

Therefore, we have proved that ∆ABC=8 ∆EFG.

Step-by-step explanation:

Hey ! APPROVED ANSWER ITO.

The measure of the angle ABC, when A, B and C lie on circumference is 40 degrees,

Given that,

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it

the center of the circle is point 'B'.

three points 'A', 'C', and 'D' lies on the circumference of the

circle.

And angle ADC = 20°.

So, the angle ABC = 40°.

Because the angle made from the center of the circle is twice

the angle made by the three points on the circumference

from the same base.

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According to the given information the missing measurement is the longer length or base of the parallelogram, which measures 10 meters.

A parallelogram is a four-sided geometric shape with two pairs of parallel sides. The opposite sides of a parallelogram have equal lengths and are parallel to each other. The opposite angles of a parallelogram are also equal.

Based on the clues provided, we can determine that the missing measurement is the longer length of the shape. Here's how we can calculate it:

Clue #1 tells us that the shape has four sides, with one set being parallel. This means that the shape is a parallelogram.

Clue #2 tells us that the area of the parallelogram is 40 square meters.

Clue #3 tells us that the height of the parallelogram is 4 meters.

Clue #4 tells us that one of the lengths of the parallelogram is 6 meters.

To find the missing measurement, we can use the formula for the area of a parallelogram:

Area = base x height

Since we know the area and height, we can plug those values in:

40 = base x 4

Solving for the base, we get:

base = 40 / 4 = 10

So the missing measurement is the longer length or base of the parallelogram, which measures 10 meters.

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Answer:

To round 5425.92 to the nearest whole number, we need to look at the digit in the ones place, which is 5. Since 5 is greater than or equal to 5, we need to round up the nearest whole number. Therefore, 5425.92 rounded to the nearest whole number is 5426.

Part A:

the cost of the fabric is 29.07

Part B:

Rounding to the nearest cent, the cost of the fabric is $29.07.

we need to calculate the area of the front of the bulletin board and then multiply it by the cost per square foot in order to find the cost of the fabric.

The area of a circle with radius 2.5 feet is:

A = πr^2

A = 3.14 x 2.5^2

A = 19.625 square feet

So, the cost of the fabric is:

Cost = area x cost per square foot

Cost = 19.625 x 1.48

Cost = 29.07

Rounding to the nearest cent, the cost of the fabric is $29.07.

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An exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:

y = 2(2)^(x + 1) + 2.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

A vertical stretch by a factor of k means that the definition of the function is multiplied by k.

The parent function in the context of this problem is given as follows:

y = 2^x.

Hence the exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:

y = 2(2)^(x + 1) + 2.

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The perimeter of the rectangle is 8x + 14.

To find the perimeter of a rectangle with an area of 3x^2 + 17x + 10, we need to use the formula for the area of a rectangle, which is A = lw, where A is the area, l is the length, and w is the width. In this case, we have:

A = lw = 3x^2 + 17x + 10

We can factor this quadratic expression to get:

A = (3x + 2)(x + 5)

Since the length and width of the rectangle are both positive numbers, we know that the factors (3x + 2) and (x + 5) must both be positive. This means that x > -5/3 and x > -5.

To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Since the opposite sides of a rectangle are equal in length, we can use the factored form of the area to find the length and width of the rectangle:

l = 3x + 2

w = x + 5

The perimeter is then given by:

P = 2l + 2w = 2(3x + 2) + 2(x + 5) = 8x + 14

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Answer:81/20 or 4 1/20

Step-by-step explanation:

To solve this problem, we need to use the rules of multiplication and fractions.

First, we need to convert the mixed numbers to improper fractions:

3 and 3/5 = (5 * 3 + 3) / 5 = 18/5

2 and 1/4 = (4 * 2 + 1) / 4 = 9/4

Now we can multiply the two fractions:

(18/5) * (9/4)

To simplify this expression, we can cancel out any common factors between the numerators and denominators:

(18/5) * (9/4) = (2 * 9)/(5 * 2) * (9/4) = 9/5 * 9/4

Then, we can multiply the numerators and denominators separately:

9/5 * 9/4 = (9 * 9) / (5 * 4) = 81/20

Therefore, 3 and 3/5 times 2 and 1/4 is equal to 81/20 or 4 1/20 as a mixed number.

Answer:

Step-by-step explanation:

[tex]\\8 \frac{1}{10}[/tex]

To find the sum of the given series, we need at least 31 terms to obtain an accuracy of 0.1.

To find out how many terms are necessary to find the sum of the series with the desired accuracy, we need to use the alternating series estimation theorem, which states that the error in approximating an alternating series is less than or equal to the absolute value of the first neglected term.

Let Sn denote the sum of the first n terms of the given series. Then the first neglected term is

|(-1)^(n+1) * (n+1)^2 / (3(n+1)^2 + 2)|

To get an error less than or equal to 0.1, we need to find the smallest value of n such that the absolute value of the first neglected term is less than or equal to 0.1.

So we need to solve the inequality:

|(-1)^(n+1) * (n+1)^2 / (3(n+1)^2 + 2)| ≤ 0.1

Simplifying, we get:

(n+1)^2 / (3(n+1)^2 + 2) ≤ 0.1

Solving for n, we get:

n ≥ 31

Therefore, we need at least 31 terms to find the sum of the given series accurate to 0.1.

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0.98

When you see this kind of problem, try to see how cos 2x and sin x relate--don't go straight to finding x because it is unnecessary. In this case, there is a formula that shows the relationship between cos 2x and sin x as shown:

cos 2x = 1 - 2(sin x)^2

All we have to do is plug in the value of sin x to find the value of cos 2x.

cos 2x = 1 - 2(-0.1)^2 = 1 - 2(0.01) = 1 - 0.02 = 0.98

Answer:

approximately 48 agate marbles in the tin.

Step-by-step explanation:

Out of the 10 marbles Naomi picked, 3 are agate. We can use this ratio to estimate the number of agate marbles in the tin.

If we assume that the distribution of marbles in the tin is similar to the distribution in the sample of 10 marbles, we can set up a proportion to estimate the number of agate marbles:

3/10 = x/160

Where x is the estimated number of agate marbles in the tin.

Solving for x, we can cross-multiply and get:

3 * 160 = 10 * x

x = 48

we estimate that there are approximately 48 agate marbles in the tin.

the probability that it rains in Spain when hurricanes happen in Hartford is approximately 0.2192.

what is bayes theorem ?

Let’s use Bayes’ theorem to solve this problem. Let A be the event that it rains in Spain and B be the event that hurricanes happen in Hartford. We want to find P(A|B). We know that P(B|A) = 0.08 and P(B|A’) = 0.03 where A’ is the complement of A (i.e., it does not rain in Spain). We also know that P(A) = 1/13 and P(A’) = 12/13.

Bayes’ theorem states that:

P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|A’) * P(A’)]

Substituting the values we have:

P(A|B) = (0.08 * 1/13) / [(0.08 * 1/13) + (0.03 * 12/13)] = 0.2192 (rounded to four decimal places)

Therefore, the probability that it rains in Spain when hurricanes happen in Hartford is approximately 0.2192.

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So, the probability of picking a 4 and then picking an even number is 15/28.

To find probability, you need to follow these steps:

Identify the total number of possible outcomes of an event. Let's call this number "n."

Identify the number of favorable outcomes, which are the outcomes that you're interested in. Let's call this number "f."

Calculate the probability of the event as the ratio of the number of favorable outcomes to the total number of outcomes:

Probability = f / n

For example, if you're flipping a fair coin, there are two possible outcomes: heads or tails. The total number of outcomes is 2, and the number of favorable outcomes is 1 (either heads or tails). Therefore, the probability of getting heads is:

Probability of heads = 1 / 2 = 0.5.

There are four possible outcomes for the first card: 4, 5, 6, or 7. If we pick a 4 on the first draw, then there are three even numbers left to choose from: 6, 4, and 6. If we pick a non-4 number on the first draw, then there are four even numbers left to choose from: 4, 6, 4, and 6.

Therefore, the probability of picking a 4 and then picking an even number is:

[tex](1/4) * (3/7) + (3/4) * (4/7)[/tex]

[tex]= (3/28) + (3/7)[/tex]

[tex]= (3/28) + (12/28)[/tex]

[tex]= 15/28[/tex]

So, the probability of picking a 4 and then picking an even number is 15/28.

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The valuable insights into complex phenomena like obesity and type 2 diabetes.

The measurement being employed in this scenario is quantitative measurement. Specifically, the researcher is measuring the weight of individuals, which is a numerical value that can be quantified and analyzed statistically.
Quantitative measurement involves collecting numerical data and using statistical methods to analyze and interpret the results. This type of measurement allows researchers to quantify variables and identify patterns, trends, and relationships between different variables.
In the context of this study on obesity and type 2 diabetes, measuring weight is a crucial component of understanding the relationship between these two variables. By collecting weight data from individuals with these conditions, the researcher can analyze the data to determine if there is a correlation between weight and the likelihood of developing type 2 diabetes.
Overall, quantitative measurement is an important tool for researchers in many different fields. It allows them to collect objective data and use statistical methods to analyze and interpret the results, providing valuable insights into complex phenomena like obesity and type 2 diabetes.

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When we substitute the figures for x and y, we will arrive at a final figure of -150.

The equivalent expressions for the properties of the expression are as follows:

5 (-6x) + 5 (2y)

5.-6x + 5.2y

-30x + 10y

The question tells us to substitute x for 4 and y for -3 in the equation. To do this, we will have the following:

5 (-6 *4 + 2 * -3)

= 5 (-24 + -6)

= 5 (-24 - 6)

= 5 ( -30)

= -150

So after substituting the letter, we will have -150 as the result.

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The inequality that is true for all values of x is:

√(4x²) ≤ 4x²

Let's try to find which inequality is true for all real values of x.

For example, let's look at option C, here we have the inequality:

4(x² - 3) ≤ 3(x² - 4)

Let's expand both sides to get:

4x² - 12 ≤ 3x² - 12

4x² ≤ 3x²

4 ≤3

We removed the x-variable, but 4 is not smaller or equal to 3, so this is false.

Now option D, we have:

√(4x²) ≤ 4x²

Notice that bout outcomes are always positive, but in the left side we have a square root.

We can simplify this to get:

2x ≤ 4x²

x ≤ 2x²

This is trivially true, the only region where we can have problems is the region between 0 and 1, but the factor corrects that.

So this one is the correct option.

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Answer:

D

Step-by-step explanation:

Common factor is 8 so 8(x+8) = 8x+64

The minimum sample size needed to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence is 385.

To calculate the minimum sample size, we need to use the formula:

[tex]n= \frac{z^2 * p * (1-p)}{E^2}[/tex]

Where:

n is the sample size

z is the z-score corresponding to the desired level of confidence (95% confidence level corresponds to a z-score of 1.96)

p is the estimated population proportion (since we have no reasonable estimate, we use 0.5, which gives the largest possible sample size)

E is the desired margin of error (0.05)

Plugging in the values, we get:

[tex]n = \frac {(1.96^2 * 0.5 * (1-0.5))} { 0.05^2 }= 384.16[/tex]

Since we cannot have a fractional sample size, we round up to the nearest whole number to get a minimum sample size of 385.

Therefore, we need to sample at least 385 voters in order to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence.

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Answer:

z= 63 degrees

x≈16

Step-by-step explanation:

90+27=117

180-117=63 (bc all angles in a triangle have to add up to 180)

so the angle opposite from the 27 is 63 degrees.

Because of opposite interior angles, z=63.

sin 63= [tex]\frac{14}{x}[/tex]

xsin63=14

x=[tex]\frac{14}{sin63}[/tex]

x≈16

Answer:

[tex] \frac{6}{14} = \frac{x + 6}{4x + 4} [/tex]

[tex]6(4x + 4) = 14(x + 6)[/tex]

[tex]24x + 24 = 14x + 84[/tex]

[tex]10x = 60[/tex]

[tex]x = 6[/tex]

The distance between the points (4, 5) and (2, 2) is approximately 3.61 units.

What is the distance?

To find the distance between two points, we can use the distance formula:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using the given points (4, 5) and (2, 2), we have:

distance = √[(2 - 4)² + (2 - 5)²]

= √[(-2)² + (-3)²]

= √[4 + 9]

= √13

So the distance between the points (4, 5) and (2, 2) is approximately 3.61 units.

To graph these points, we would plot them on a coordinate plane. The point (4, 5) would be two units to the right of the y-axis and five units up from the x-axis.

The point (2, 2) would be two units to the right of the y-axis and two units up from the x-axis. We could then use a ruler to measure the distance between the two points on the graph to verify that it is approximately 3.61 units.

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The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.

Let us consider the the distance of the person from the bottom of the lamppost is = xft

therefore the length of shadow is = yft

then the formula is

x + y/15 = y/6

or, 6(x + y) = 15y

=> 6x + 6y = 15y

=> 9y = 6x

therefore, y = 2x/3

Differentiation of both sides w.r.t t

dy/dt = 2/3 × dx/dt

we know that,

dx/dt = 6 ft/sec

then,

dy/dt = 2/3 × 6 => 4 ft/sec

The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.

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( To find the lowest common multiple of any number you should find the prime factorization of 418)

(Attached)

418 = 2 × 11 × 19

Answer:

x ≤ 9

Step-by-step explanation:

See the picture below. The circle above the 9 is closed indicating that 9 is included.  If 9 was not included you would have an open circle and the answer would have a < rather than a [tex]\leq[/tex] symbol

Helping in the name of Jesus.

The weight of a puppy modeled by the equation 2x - y = 2 is represented by graph H.

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. whereas there is a net change in the x coordinate, the y coordinate changes just little.

Given the modeled equation for puppy's growth is 2x - y = -2.

The standard equation of line is y = mx + c.

Converting the given model in standard form we have:

2x - y = -2

-y = - 2x - 2

y = 2x + 2

From the equation we see that the y-intercept is 2 and slope is 2.

The graph that has the y-intercept at 2 and slope of 2 is graph H.

Hence, the weight of a puppy modeled by the equation 2x - y = 2 is represented by graph H.

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If Joe borrowed $8000 at a rate of 14%, he will owe $11,992.18  after 3 years

We can use the formula for compound interest to calculate how much Joe will owe after 3 years:

A = P(1 + r/n)ⁿt

where:

A = the amount Joe will owe after 3 years

P = the initial principal (the amount Joe borrowed), which is $8000 in this case

r = the annual interest rate as a decimal, which is 0.14

n = the number of times the interest is compounded per year, which is 2 (since it's compounded semiannually)

t = the number of years, which is 3

Plugging in the values, we get:

A = 8000(1 + 0.14/2)²ˣ³

= 8000(1 + 0.07)⁶

= 8000(1.07)⁶

= 8000(1.499022)

= 11992.18

Therefore, Joe will owe approximately $11,992.18 after 3 years

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All possible values of v are integers greater than or equal to 28.

In a connected planar graph with 26 faces, the number of edges can be found using Euler's formula, which states that v - e + f = 2 for any connected planar graph. Since the graph is connected and planar, we know that e = 3v/2 - 3 (using the handshaking lemma and Euler's formula), and substituting this into Euler's formula gives:

v - (3v/2 - 3) + 26 = 2

Simplifying this equation yields v = 52 - 2f.

Since all vertices have the same degree, each face must have degree at least 3, and the sum of the degrees of the faces is equal to 2 times the number of edges. Therefore, we have:

3f ≤ 2e = 3v - 6

f ≤ (3v - 6)/3 = v - 2

Combining this with the fact that there are 26 faces, we get:

26 ≤ v - 2

v ≥ 28

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Step-by-step explanation:

30 is 5   below the mean of 25

      this is  ONE standard deviation BELOW the mean    ( the standard deviation is given as 5)

  this represents  a     Z -score of -1    

From Z-score table this represents .1587 of the sample or 15.87 %

The percentage of all scores that occur at 30 or below in a distribution with a mean of 25 and a standard deviation of 5 is 84.13%.

To find the percentage of all scores that occur at 30 or below, we need to calculate the z-score first. The z-score formula is (x - μ) / σ, where x is the score of interest, μ is the mean, and σ is the standard deviation.

So, for x = 30, μ = 25, and σ = 5, the z-score is calculated as (30 - 25) / 5 = 1.

We can then use a standard normal distribution table or a calculator to find the proportion of the area under the curve to the left of z = 1. This gives us the percentage of all scores that occur at 30 or below.

Using a standard normal distribution table, we find that the proportion of the area under the curve to the left of z = 1 is 0.8413.

Therefore, the percentage of all scores that occur at 30 or below in this distribution is 84.13%.

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