In ΔCDE, the measure of ∠E=90°, the measure of ∠D=23°, and EC = 1.3 feet. Find the length of DE to the nearest tenth of a foot.

To determine whether the boxplot represents the information given in the histogram, we need to examine the characteristics of both the boxplot and the histogram.

The boxplot provides a visual representation of the distribution of a dataset, showing the minimum, first quartile, median, third quartile, and maximum values. It also displays any outliers that may be present. On the other hand, a histogram provides a graphical representation of the frequency or count of data values within specified intervals or bins.

Without specific information or visuals of the boxplot and histogram in question, it is not possible to directly compare them and determine their compatibility. Therefore, it is not possible to answer the question based on the information provided.

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Answer:

$27.35

Step-by-step explanation:

To solve this, we just set up an equation based on the situation given:

2 candles for 5.95 each would be (2 x 5.95)

3 cans of candy for 2.50 each would be (3 x 2.50)

1 ornament for 7.95 would just be 7.95

(2 x 5.95) + (3 x 2.50) + 7.95 = total cost

   11.90     +     7.50     + 7.95 = total cost

                $27.35 = total cost

The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

20 ft/sec must she let out the string when the kite is 500 ft away from her.

What is rate?

A rate is a unique ratio where the two words are expressed in several units.

For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.

Let x = distance of girl from the point on the ground directly below the     kite at time t

y = length of string at time t

At time t, we have a right triangle with horizontal leg of length x, vertical leg of length 300, and hypotenuse of length y.

Given:  dx/dt = 25

Find:  dy/dt when y = 500

By the Pythagorean Theorem, \(x^2 +300^2 = y^2\)

Differentiating both sides, with respect to t,

\((2x)\frac{dx}{dt} = 2y\frac{dy}{dt}\)           ...(1)

Since, \(x^2 +300^2 = y^2\),  y = 500,

So, x = 400

Plug these values in equation (1).

\(2(400)(25) = 2(500)\frac{dy}{dt}\)

After solving,

\(\frac{dy}{dt} = 20 ft/sec\)

Therefore, 20 ft/sec must she let out the string when the kite is 500 ft away from her.

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The probability that a randomly selected grapefruit weighs more than 1.25 pounds is approximately 0.019.

To find the probability that a randomly selected grapefruit weighs more than 1.25 pounds, we need to calculate the area under the normal distribution curve to the right of 1.25 pounds.

First, we calculate the z-score using the formula:

z = (x - μ) / σ,

where

x is the value we're interested in,

μ is the mean, and

σ is the standard deviation.

In this case, x = 1.25, μ = 1, and σ = 0.12.

z = (1.25 - 1) / 0.12 = 2.08

Next, we look up the corresponding area under the standard normal distribution curve for a z-score of 2.08. Using a standard normal distribution table or calculator, we find that the area to the right of 2.08 is approximately 0.019.

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When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Answer:i think its 115 degres

Step-by-step explanation:

Answer:A

Step-by-step explanation:

i made an 100 on my test.

Answer:

14.75

Step-by-step explanation:

So eighty five hundreths is basically the same thing as .85 in standard form and thirteen and nine tenths is the same as 13.9. So just add them up!

                  13.90

                     .85.   +

              __________

                    14.75

17.75 is the sum of one and eighty-five hundredths added to thirteen and nine tenths

A number system is defined as a system of writing to express numbers.

We need to find sum one and eighty-five hundredths added to thirteen and nine tenths

one and eighty-five hundredths can be written as Zero point eight five

0.85

thirteen and nine tenths is the same as 13.9.

Thirteen point nine.

We just need to add 0.85 and 13.9 to find the sum

13.9+0.85=17.75

Hence, 17.75 is the sum of one and eighty-five hundredths added to thirteen and nine tenths

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Answer:

18213

Step-by-step explanation:

Given equation,

→ 467 × 39

Let's solve the problem,

→ 467 × 39

→ 18213

Thus, the answer is 18213.

SOLUTION

The shape is a parallelogram

The consecutive angle of a parallelogram is supplementary that is added up to 180 degree

Hence we have

Therefore the right option is D

Answer:

The answer is 1.35 answer (1). You can graph both equations to give you the answer.

Step-by-step explanation:

Graph the equations and see where they intersect.

The positive x coordinate is given as √13/2 - 1.

The equation for a circle having the centre located at a point (a, b) and the radius r can be written as (x - a)² + (y - b)² = r².

Given that,

The equation for the line is y = x + 2

And, the equation of the circle is x² + y² = 13.

In order to find the point of intersection substitute the equation of line into that of circle as below,

x² + y² = 13

=> x² + (x + 2)² = 13

=> x² + x² + 4x + 4 = 13

=> 2x² + 4x - 9 = 0

Use quadratic formula to solve the above equation as,

x = (-4 ± √(4² - 4 × 1 × -9))/(2 × 2)

  = -1 ± √13/2

Thus, the positive x coordinate is given as √13/2 - 1.

Hence, the positive x-coordinate of the point of intersection of the circle and line is given as √13/2 - 1.

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Answer:

0.707

Step-by-step explanation:

Answer: 27 cubic units

Step-by-step explanation:

3 * 3 * 3 = 27 cubic units

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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To find the value of s3 in the given sigma summation series and calculate the truncation error, let's first analyze the series and determine its pattern.

The series can be written as:

s = (0.2 * 1) / 0.8 + (0.2 * 2) / 0.8 + (0.2 * 3) / 0.8 + ...

We notice that each term in the series has the form (0.2 * n) / 0.8. We can simplify this expression by dividing both the numerator and denominator by 0.2:

s = n / 4

Now, let's calculate s3 by substituting n = 3:

s3 = 3 / 4

s3 = 0.75

So, the value of s3 in the series is 0.75.

Now, let's calculate the truncation error. The truncation error is the difference between the actual sum of the series and the sum obtained by truncating or stopping at a certain term.

Given that the series sum is 0.3125 and we have s3 = 0.75, we can calculate the truncation error:

Truncation error = |Actual sum - Sum truncated at s3|

Truncation error = |0.3125 - 0.75|

Truncation error = |-0.4375|

Truncation error = 0.4375

The truncation error in this case is 0.4375.

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A single song may be downloaded for $0.35. Adjusting the solution c = 0.35s yields the answer because c/s = 0.35.

An equation is an mathematical statement that uses an equal sign to express the relationship across two or more objects, such as variables or integers. Equations can be used to represent relationships between physical, chemical, and other sorts of events as well as to solve mathematical problems. An equation in mathematics is a claim made regarding the equivalence of two expressions. A assertion claiming two expressions equal equal is what an equation is, in other words.

This indicates that each music download costs $0.35. Consequently, it costs $0.35 to buy a single song.

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In the expression 2*4 + 3y, the coefficient of y is 3. The coefficient is the number next to the variable.

Answer:

Work shown below!

Step-by-step explanation:

f(n) = 16 - 2(n - 1)

f(1) = 16 - 2(1 - 1)

f(1) = 16 - 2(0)

f(1) = 16

Common difference is -2

Answer:

x³-13x+12

Step-by-step explanation:

Answer: \(\frac{8}{5}\)

Step-by-step explanation:

343 is equal to 7 to the power of 3.

49 is equal to 7 to the power of 2.

You can then make the equation:

\((7^{3})^x = (7^2)^{4-x}\)

The powers law means if something is to the power of something, it is multiplied.

So, we can remove the 7 and make the equation:

3x = 2(4-x)

3x = 8 - 2x

5x = 8

x = \(\frac{8}{5}\)

You can verify this by plugging it in,

\(343^{8/5} = 11388.6066\)

\(49^{4-(8/5)} = 11388.6066\)

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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Answer:

I think it's line "A"

Step-by-step explanation:

The formula used to calculate the likely size of the chance error is SE = s/√n where SE is the standard error, s is the standard deviation, and n is the sample size. In this problem, there are eight students, so n = 8.

The standard deviation can be calculated using the formula σ = √(Σ(x - µ)² / n), where σ is the standard deviation, x is each data point, µ is the mean, and n is the sample size. Using the given data, the mean can be calculated as follows:

Mean = (9.93 + 9.96 + 10.10 + 10.02 + 10.02 + 9.90 + 9.93 + 9.92) / 8 = 9.985Next, calculate the sum of the squared deviations from the mean:Σ(x - µ)² = (9.93 - 9.985)² + (9.96 - 9.985)² + (10.10 - 9.985)² + (10.02 - 9.985)² + (10.02 - 9.985)² + (9.90 - 9.985)² + (9.93 - 9.985)² + (9.92 - 9.985)²Σ(x - µ)² = 0.0211.

Then, calculate the variance by dividing the sum of squared deviations by the sample size:

Variance = Σ(x - µ)² / n

Variance = 0.0211 / 8Variance = 0.00264Finally, calculate the standard deviation by taking the square root of the variance:

Standard deviation = √(Σ(x - µ)² / n)Standard deviation = √(0.00264)Standard deviation = 0.05134The standard error can now be calculated by dividing the standard deviation by the square root of the sample size:

Standard error = s/√nStandard error = 0.05134/√8Standard error = 0.01813

Given the measurements of eight students to determine the correct length of a ruler in a laboratory, we can calculate the size of the chance error using the formula SE = s/√n. This formula calculates the standard error, where s is the standard deviation and n is the sample size. To find the standard deviation, we use the formula σ = √(Σ(x - µ)² / n), where x is each data point, µ is the mean, and n is the sample size. Using the given measurements, the mean of the data is calculated to be 9.985. Using this mean, we can calculate the sum of the squared deviations from the mean, which is equal to 0.0211. Then, we can calculate the variance by dividing the sum of squared deviations by the sample size, which is equal to 0.00264. Finally, the standard deviation can be calculated by taking the square root of the variance, which is equal to 0.05134. By dividing the standard deviation by the square root of the sample size, we can find the standard error, which is equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.

Given the measurements of eight students, we used the formulas SE = s/√n and σ = √(Σ(x - µ)² / n) to calculate the size of the chance error. The mean of the data was found to be 9.985, and the sum of the squared deviations from the mean was equal to 0.0211. We used these values to calculate the variance, which was equal to 0.00264, and the standard deviation, which was equal to 0.05134. Finally, we found the standard error to be equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.

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The amount of money Justin saves in the first month would be 5 times the value of x, where x represents the number of months of gym membership, based on the discounted price provided.

A linear equation is an equation in mathematics that represents a relationship between two variables that is a straight line when graphed on a coordinate plane. It is an equation of the form:

y = mx + b

To calculate the amount of money Justin saves in the first month by joining the gym at the discounted price rather than the regular price, we need to know the discounted price.

The equation given is y = 15x + 20, where y represents the regular price in dollars and x represents the number of months of gym membership. However, we need to know the discounted price, which is not provided in the given information.

Once we have the discounted price, we can substitute it into the equation and calculate the savings. For example, if the discounted price is y = 10x + 20, then we can calculate the savings by subtracting the discounted price from the regular price:

Savings = Regular price - Discounted price

= (15x + 20) - (10x + 20)

= 15x - 10x

= 5x

Hence, the amount of money Justin saves in the first month would be 5 times the value of x, where x represents the number of months of gym membership, based on the discounted price provided.

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Answer:

0.762

Step-by-step explanation:

2/3 / 7/8 = 2*8 / 7*3 = 16/21 = 0.762

Hey there! :)

Answer:

4 - 40i

Step-by-step explanation:

Subtracting the two expressions:

(7 - 10i) - (3 + 30i)

Distribute the negative sign:

7 - 10i - 3 - 30i

Combine like terms:

4 - 40i

Answer:

4 - 40i.

Step-by-step explanation:

(7 - 10i) – (3 + 30i)

= 7 - 10i - 3 - 30i

= 7 - 3 - 10i - 30i

= 4 - 40i

Hope this helps!

Answer: Using trigonometry, we can find the length of side AC. Since we know the length of side BC and one angle, we can use the tangent function:

tan(70) = AC/6

Multiplying both sides by 6, we get:

AC = 6 * tan(70)

Using a calculator, we get:

AC ≈ 19.22

Rounding to the nearest hundredth, we get:

AC ≈ 19.22 units.

Answer:2.33

Step-by-step explanation:

Answer:

well the equation would be c = 7(3a + 4b) which would equal to 27 + 28 which leaves the answer of c = 55

Answer:

top lines of explanation

Step-by-step explanation:

at the secretary job she made 12.75 an hour

second job she made 13.50 an hour

180 minutes is 3 hours divide 40.50 by 3 and get 13.50

102.00 divided by 8 is 12.75

Step-by-step explanation:

8 hours = 102.00

1 hour = 102 ÷ 8 = 12.75

180 min = 3hr

3hr = 40.50

1hr = 40.50 ÷ 3 = 13.5

2nd job