A carpenter cuts a board 3 3/8 feet off the end of a board that is 6 1/2 feet long. How long is the remaining piece of board?

Answers

Answer 1

Answer:

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

The remainingpiece of the board when $3(3)/(8)$ feet is cut off from the end of the board of $6(1)/(2)$ feet is

$3(1)/(8)$ feet

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example:

1/2, 1/3 is a fraction.

1/2 of 4 is 2.

1/4 of 20 is 5.

We have,

Length of the board = $6(1)/(2)$ feet.

The lengthcutoff from the board = $3(3)/(8)$ feet.

The remaininglength of the board:

= $6(1)/(2)$ - $3(3)/(8)$

= 13/2 - 27/8

Find the Lcm of 2 and 8.

The Lcm of 2 and 8 is 8.

= (13x4 - 27) / 8

= (52 - 27) / 8

= 25/8

Write it in a mixedfraction.

= $3(1)/(8)$ feet

Thus,

The remainingpiece of the board when $3(3)/(8)$ feet is cut off from the end of the board of $6(1)/(2)$ feet is $3(1)/(8)$ feet.

Learn more about fractions here:

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Answer 2

Answer:

Answer:

$6 * (1)/(2) - 3 * (3)/(8) = 1 * (7)/(8)$

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A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

What is the answer 6•4+2/2-7

Answers

Answer:

18 is the answer

Step-by-step explanation: Solve by multiplication/division first and then addition and/subtraction

A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =

Answers

Answer:

a) $(dB)/(dt) = (5\pi)/(4.2) \cdot \cos \left(2\pi\cdot (t)/(4.2) \right)$ , b) $(dB)/(dt)\approx 5.595$

Step-by-step explanation:

a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:

$(dB)/(dt) = \left((2\pi)/(4.2) \right)\cdot 0.25\cdot \cos (2\pi\cdot (t)/(4.2))$

$(dB)/(dt) = (5\pi)/(4.2) \cdot \cos \left(2\pi\cdot (t)/(4.2) \right)$

b) The rate of increase after one day is:

$(dB)/(dt) = (5\pi)/(4.2) \cdot \left(2\pi \cdot (1)/(4.2) \right)$

$(dB)/(dt)\approx 5.595$

In a study of factors affecting whether soldiers decide to reenlist, 320 subjects were measured for an index of satisfaction. The sample mean is 28.8 and the sample standard deviation is 7.3. Use the given sample data to construct the 98 percent confidence interval for the population mean.

Answers

Answer:

The 98 percent confidence interval for the population mean is between 27.85 and 29.75 subjects.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1-0.98)/(2) = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.01 = 0.99$ , so $z = 2.325$

Now, find M as such

$M = z*(\sigma)/(√(n))$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.325(7.3)/(√(320)) = 0.9488$

The lower end of the interval is the mean subtracted by M. So it is 28.8 - 0.9488 = 27.85 subjects.

The upper end of the interval is the mean added to M. So it is 28.8 + 0.9488 = 29.75 subjects.

The 98 percent confidence interval for the population mean is between 27.85 and 29.75 subjects.

T he equation for a parabola with directrix y = –p and focus (0, p) is:1.What is the parabola’s line of symmetry?

y-axis
x-axis
x = p
x = -p

Answers

The equation for a parabola with directrix y = –p and focus (0, p)

The distance between vertex and directrix is P

Also the distance between vertex and focus is also P

Focus (0,p) so focus lies on y axis

Directrix line is paralled to focus point

So Directex crosses the x axis .

Hence line of symmetry lies is the y-axis.

The graph is attached below.

The American Community Survey is an ongoing survey that provides data every year to give communities the current information they need to plan investments and services. The 2010 American Community Survey estimates that 14.6% of Americans live below the poverty line, 20.7% speak a language other than English (foreign language) at home, and 4.2% fall into both categories. a. Draw a Venn diagram summarizing the variables and their associated probabilities
b. What percent of Americans live below the poverty line and only speak English at home?
c. What percent of Americans live below the poverty line or speak a foreign language at home?

Answers

Answer:

b. 10.4

c. 26.9

Step-by-step explanation:

Let the universal set U = 100% which is the total no of people in the American community

Let A = 14.6% which is the total no of people living below poverty line

Let B = 20.7% which is the total no of people speaking foreign Language

C = 4.2% no of people who both speak foreign language and live below poverty line

X = no of people who neither live below poverty line nor speak foreign language

P (A) = 14.6%

P (B) = 20.7%

P (C) = P (A ∩ B) = 4.2%

P (A – C) = P (A ∩ U) = 14.6 – 4.2 = 10.4%

P (B – C) = P (B ∩ U) = 20.7 – 4.2 = 16.5%

P (X) = P (A ᴜ B) c =100 – (10.4 + 4.2 + 16.5) = 68.9%

a. The venn diagram is as shown above

b. Percent of Americans who live below poverty line and Speak English at home(minus foreign lang speakers living below poverty line) that is A only

= A – C

= 14.6 – 4.2

= 10.4%

c. Percentage of Americans Living below poverty line or Speaking foreign language

= A only + B only

A only = A – C ( People living below poverty line only)

= 14.6 -4.2

= 10.4%

B only = B – C ( people speaking foreign languages only)

= 20.7 – 4.2

= 16.5%

Hence

A only + B only = 10.4 + 16.5 = 26.9%

Can someone please help me with this question

Answers

Answer:

Step-by-step explanation:

The four sides of the quadrilateral touches the circle. This means that the opposite angles of the quadrilateral are supplementary.

It means that the sum of the angles is 180 degrees From the given diagram,

Angle B + angle R = 180

Angle B = 180 - 85

Angle B = 95 degrees

Angle D + angle I = 180

Angle D = 180 - 117

Angle D = 63 degrees

Answer

<B is 95, and <D is 63

Step-by-step explanation:

Opposite angles have sum 180, so angle of the B is 180-85=95, and angle of the D is 180-117=63

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